News <2009>

December 2009

December 31, 2009

Contributions page is available. 7871 contributions since September, 2006 were classified by the date and the label.

Factorizations of 822...221 and Factorizations of 822...223 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Factorizations of 688...889 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

December 29, 2009

I'm organizing about 8,000 contributions now. New contributions will stay on the CGI server for several days.

Lazarusuk and yoyo@home found the largest known ECM-factor from the near-repdigit number (64·10³⁴¹-1)/9. Congratulations!

Dec 28, 2009

To provide equal opportunity for making reservations, I limit the maximum number of reservations per person to ten.

Factorizations of 811...117 and Factorizations of 811...119 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Factorizations of 688...887 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Dec 27, 2009 (3rd)

By Dmitry Domanov / ECMNET, GMP-ECM, GGNFS/msieve / Dec 27, 2009

2·10²³⁸+9 = 2(0)₂₃₇9_<239> = 11 · 41 · 449 · 5945281 · 205709886542393_<15> · C212

C212 = P33 · C179

P33 = 934803133267021438680222877011857_<33>

C179 = [86389190127266350770385031495384179967873028613332220537337837050627344935518971489006603171048516781100773290444922675961442798454864564423577019533963800409624412975235359485611_<179>]

Factor=934803133267021438680222877011857  Method=ECM  B1=11000000  Sigma=3043688549

2·10²³⁶+9 = 2(0)₂₃₅9_<237> = 11 · 19 · 138107 · 4159291 · 8773419562122098610424962990443_<31> · C192

C192 = P34 · C159

P34 = 1621538670024234287528298561381857_<34>

C159 = [117098815752117581980530614048280187555582803440778045542092028045520633300570987039138508825936717768032379425461484880728406097864186809255527187439657366723_<159>]

Factor=1621538670024234287528298561381857  Method=ECM  B1=11000000  Sigma=632518576

2·10²³⁰+9 = 2(0)₂₂₉9_<231> = 11 · 6067 · 75913 · 6084433096051_<13> · C208

C208 = P34 · C174

P34 = 7073788323327073327258989897992617_<34>

C174 = [917223094434762491286013571173061287620094347946329312148732779955057197042337509159978376511017279572890823924278440190462392904036852604802751256146369522413326232732297267_<174>]

Factor=7073788323327073327258989897992617  Method=ECM  B1=11000000  Sigma=3376074941

(73·10¹⁴⁷+17)/9 = 8(1)₁₄₆3_<148> = 7 · 19 · 271 · 3607 · 1058306453509113059_<19> · C122

C122 = P41 · P82

P41 = 20886560597602026806323136874983100754199_<41>

P82 = 2822506181531805700235175141346358488148133171290045158430063248803979898962951993_<82>

N=58952446397670366423086907740884604848531269883950816758660393478899455749858136033331454447681313330213403804277730168607
  ( 122 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=20886560597602026806323136874983100754199 (pp41)
 r2=2822506181531805700235175141346358488148133171290045158430063248803979898962951993 (pp82)
Version: Msieve-1.40
Total time: 11.58 hours.
Scaled time: 21.05 units (timescale=1.818).
Factorization parameters were as follows:
n: 58952446397670366423086907740884604848531269883950816758660393478899455749858136033331454447681313330213403804277730168607
m: 100000000000000000000000000000
deg: 5
c5: 7300
c0: 17
skew: 0.30
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 3150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 340178 x 340406
Total sieving time: 11.35 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,148.000,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 11.58 hours.
 --------- CPU info (if available) ----------

(73·10¹⁴⁵+17)/9 = 8(1)₁₄₄3_<146> = 34487617 · 6700001606333501_<16> · C123

C123 = P33 · P91

P33 = 324397557949150882736842313530027_<33>

P91 = 1082093232200827485232398232958400591728533542755009125044382690865675948375507134070094007_<91>

N=351028401999251916134821853431037226688119725436192589359670396617620377086980693969736688732001770672798265995087907248189
  ( 123 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=324397557949150882736842313530027 (pp33)
 r2=1082093232200827485232398232958400591728533542755009125044382690865675948375507134070094007 (pp91)
Version: Msieve-1.40
Total time: 8.47 hours.
Scaled time: 15.43 units (timescale=1.823).
Factorization parameters were as follows:
n: 351028401999251916134821853431037226688119725436192589359670396617620377086980693969736688732001770672798265995087907248189
m: 100000000000000000000000000000
deg: 5
c5: 73
c0: 17
skew: 0.75
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2480001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 264058 x 264283
Total sieving time: 8.32 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 8.47 hours.
 --------- CPU info (if available) ----------

(62·10¹⁵³-53)/9 = 6(8)₁₅₂3_<154> = 83 · 4562669 · 3487114261_<10> · C136

C136 = P53 · P84

P53 = 47815697752352098457986363218128078130226492291799893_<53>

P84 = 109097663147591498526380294134197245187003896362469052701235847091686578792333022573_<84>

N=5216580886553157179266336194939601662516617965583607797830691218065927043923999858324138677299551882803062017504735600577449123167984689
  ( 136 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=47815697752352098457986363218128078130226492291799893 (pp53)
 r2=109097663147591498526380294134197245187003896362469052701235847091686578792333022573 (pp84)
Version: Msieve-1.40
Total time: 20.98 hours.
Scaled time: 38.93 units (timescale=1.855).
Factorization parameters were as follows:
n: 5216580886553157179266336194939601662516617965583607797830691218065927043923999858324138677299551882803062017504735600577449123167984689
m: 1000000000000000000000000000000
deg: 5
c5: 62000
c0: -53
skew: 0.24
type: snfs
lss: 1
rlim: 2700000
alim: 2700000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2700000/2700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1350000, 2650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 543748 x 543975
Total sieving time: 20.36 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,154.000,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,50,50,2.4,2.4,100000
total time: 20.98 hours.
 --------- CPU info (if available) ----------

(62·10¹⁵⁶-53)/9 = 6(8)₁₅₅3_<157> = 20149 · 2889493 · C147

C147 = P45 · P50 · P53

P45 = 296092480355417714661032125185595033281118861_<45>

P50 = 20758746508962225695125662243311466530433706035881_<50>

P53 = 19250655970989913827479711758654941345071207658101759_<53>

N=118324325232403481461848194651933546395362047639327777783779588329505585659637347051183152187156073511947777164282926783552707472321495695098960619
  ( 147 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=296092480355417714661032125185595033281118861 (pp45)
 r2=20758746508962225695125662243311466530433706035881 (pp50)
 r3=19250655970989913827479711758654941345071207658101759 (pp53)
Version: Msieve-1.40
Total time: 19.06 hours.
Scaled time: 35.45 units (timescale=1.860).
Factorization parameters were as follows:
n: 118324325232403481461848194651933546395362047639327777783779588329505585659637347051183152187156073511947777164282926783552707472321495695098960619
m: 10000000000000000000000000000000
deg: 5
c5: 620
c0: -53
skew: 0.61
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 543425 x 543651
Total sieving time: 18.43 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,157.000,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 19.06 hours.
 --------- CPU info (if available) ----------

(62·10¹⁶⁰-53)/9 = 6(8)₁₅₉3_<161> = 3 · 313 · 391516847 · C150

C150 = P37 · P113

P37 = 2929674531395509720008490951855848061_<37>

P113 = 63960780933066026225889687195304074812081561846826503281813538817936673009349384729463814205722125431075503229891_<113>

N=187384270907771063333728440077318565961035336376917852099045312850421888141782541628479746273647356028707209272617957631716937170730104800242449591351
  ( 150 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=2929674531395509720008490951855848061 (pp37)
 r2=63960780933066026225889687195304074812081561846826503281813538817936673009349384729463814205722125431075503229891 (pp113)
Version: Msieve-1.40
Total time: 41.96 hours.
Scaled time: 39.10 units (timescale=0.932).
Factorization parameters were as follows:
n: 187384270907771063333728440077318565961035336376917852099045312850421888141782541628479746273647356028707209272617957631716937170730104800242449591351
m: 100000000000000000000000000000000
deg: 5
c5: 62
c0: -53
skew: 0.97
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 768947 x 769180
Total sieving time: 40.53 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.19 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 41.96 hours.
 --------- CPU info (if available) ----------

(62·10¹⁶⁹-53)/9 = 6(8)₁₆₈3_<170> = 3 · 7 · 71 · 173 · 1072793 · C159

C159 = P29 · P37 · P94

P29 = 33706548729056745629121167503_<29>

P37 = 1526568046346414834239657673989825139_<37>

P94 = 4838146872015767768001030987421981831864644663863774917922618347544565075277396770748172624401_<94>

N=248948493442257142683928751621912829309459505384922441830057514377894366183213675105899542351187849850875664732974936041147563855368202345946081094604866632717
  ( 159 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=33706548729056745629121167503 (pp29)
 r2=1526568046346414834239657673989825139 (pp37)
 r3=4838146872015767768001030987421981831864644663863774917922618347544565075277396770748172624401 (pp94)
Version: Msieve-1.40
Total time: 69.31 hours.
Scaled time: 129.34 units (timescale=1.866).
Factorization parameters were as follows:
n: 248948493442257142683928751621912829309459505384922441830057514377894366183213675105899542351187849850875664732974936041147563855368202345946081094604866632717
m: 2000000000000000000000000000000000
deg: 5
c5: 19375
c0: -53
skew: 0.31
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 6250001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1070817 x 1071042
Total sieving time: 67.45 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.45 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 69.31 hours.
 --------- CPU info (if available) ----------

Dec 27, 2009 (2nd)

By Sinkiti Sibata / Msieve / Dec 27, 2009

(62·10¹⁶¹-53)/9 = 6(8)₁₆₀3_<162> = 13 · 149 · 77641013 · 127707233 · 102322578465517031591779_<24> · C120

C120 = P56 · P65

P56 = 11960866514737977396638783337798921138905588800243622081_<56>

P65 = 29307498526691833945064051908979105022980074012255518963162561629_<65>

Number: 68883_161
N=350543077758640963295488151903925902635545192222483092013586934585860075590002114231556808952263151226072780805347729949
  ( 120 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=11960866514737977396638783337798921138905588800243622081 (pp56)
 r2=29307498526691833945064051908979105022980074012255518963162561629 (pp65)
Version: Msieve v. 1.42
Total time: 1.58 hours.
Scaled time: 1.25 units (timescale=0.795).
Factorization parameters were as follows:
name: 68883_161
n: 350543077758640963295488151903925902635545192222483092013586934585860075590002114231556808952263151226072780805347729949
m: 100000000000000000000000000000000
deg: 5
c5: 620
c0: -53
skew: 0.61
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1800000, 3300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 690612 x 690837
Total sieving time: 0.00 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.38 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,162.000,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000
total time: 1.58 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.30 BogoMIPS (lpj=1860651)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860572)
Total of 2 processors activated (7442.44 BogoMIPS).

Total time: 24 hours 46 min.

Dec 27, 2009

By Robert Backstrom / GGNFS / Dec 27, 2009

(62·10¹⁵⁴-53)/9 = 6(8)₁₅₃3_<155> = 3² · 13903 · 274848383 · 27177024634853961229302371_<26> · C116

C116 = P57 · P60

P57 = 720951878610382542862347981801121436850590767518884611777_<57>

P60 = 102234334845267243275213765013617623444440744591194671442489_<60>

Number: n
N=73706035765178311721843203682271976549090303768877381733915205101899361643335375393433365408866574563129973347592953
  ( 116 digits)
Divisors found:
 r1=720951878610382542862347981801121436850590767518884611777 (pp57)
 r2=102234334845267243275213765013617623444440744591194671442489 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.02 hours.
Scaled time: 45.76 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_6_8_153_3
n: 73706035765178311721843203682271976549090303768877381733915205101899361643335375393433365408866574563129973347592953
Y0: -36882076435815646343086
Y1:  1177126619933
c0:  722179055622719498049770419635
c1:  12974758915145902336777681
c2:  3315676937663850719
c3: -388879982959281
c4:  193270566
c5:  1080
skew: 300296.60
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [2250000, 3200001)
Primes: RFBsize:315948, AFBsize:316070, largePrimes:9281020 encountered
Relations: rels:9124074, finalFF:821552
Max relations in full relation-set: 48
Initial matrix: 632099 x 821552 with sparse part having weight 81612006.
Pruned matrix : 469228 x 472452 with weight 39927825.
Total sieving time: 21.93 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 2.46 hours.
Total square root time: 0.21 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,56,56,2.4,2.4,60000
total time: 25.02 hours.
 --------- CPU info (if available) ----------

Dec 26, 2009 (4th)

By juno1369 / GGNFS+Msieve v1.43, GGNFS, Msieve / Dec 26, 2009

(71·10¹³⁷-53)/9 = 7(8)₁₃₆3_<138> = 3⁴ · 73 · 761 · 2819 · 213289 · 1785968911_<10> · C114

C114 = P45 · P69

P45 = 497338274574517430075176129186594377221125453_<45>

P69 = 328272113722656687403829731159683520949633917603574352244659948723827_<69>

Number: 78883_137
N=163262286629755842749264899133973489972910643771041742794018259519611687324709943115531731693939442113292017268631
  ( 114 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=497338274574517430075176129186594377221125453 (pp45)
 r2=328272113722656687403829731159683520949633917603574352244659948723827 (pp69)
Version: Msieve v. 1.43
Total time: 10.80 hours.
Scaled time: 23.30 units (timescale=2.158).
Factorization parameters were as follows:
n: 163262286629755842749264899133973489972910643771041742794018259519611687324709943115531731693939442113292017268631 
m: 1000000000000000000000000000
deg: 5
c5: 7100
c0: -53
skew: 0.38 
type: snfs 
lss: 1 
rlim: 1440000 
alim: 1440000 
lpbr: 26 
lpba: 26 
mfbr: 48 
mfba: 48 
rlambda: 2.3 
alambda: 2.3 
qintsize: 100000Factor base limits: 1440000/1440000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [720000, 1220001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 221440 x 221665
Total sieving time: 10.59 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs ,138.000,5,0,0,0,0,0,0,0,0,1440000,1440000,26,26,48,48,2.3,2.3,
total time: 10.80 hours.
 --------- CPU info (if available) ----------

(71·10¹³⁸-53)/9 = 7(8)₁₃₇3_<139> = 27248575999_<11> · 395925893367391_<15> · C114

C114 = P42 · P73

P42 = 419162038746174165070948225788357647335121_<42>

P73 = 1744520907848239545736800443327766019464664837271375568832178853070200547_<73>

Number: 78883_138
N=731236940368994714565704238447233851060682074228769030364565102172640486050475266877178494695869713470771586511187
  ( 114 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=419162038746174165070948225788357647335121 (pp42)
 r2=1744520907848239545736800443327766019464664837271375568832178853070200547 (pp73)
Version: Msieve v. 1.43
Total time: 12.73 hours.
Scaled time: 27.29 units (timescale=2.144).
Factorization parameters were as follows:
n: 731236940368994714565704238447233851060682074228769030364565102172640486050475266877178494695869713470771586511187
m: 1000000000000000000000000000
deg: 5
c5: 71000
c0: -53
skew: 0.24 
type: snfs 
lss: 1 
rlim: 1500000 
alim: 1500000 
lpbr: 26 
lpba: 26 
mfbr: 48 
mfba: 48 
rlambda: 2.3 
alambda: 2.3 
qintsize: 100000Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [750000, 1350001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 210289 x 210514
Total sieving time: 12.46 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs ,139.000,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,48,48,2.3,2.3,
total time: 12.73 hours.
 --------- CPU info (if available) ----------

Dec 26, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Dec 26, 2009

2·10²⁰⁰-1 = 1(9)₂₀₀_<201> = 47 · 199 · 8832847 · 26986789362889673_<17> · 22887618087703883422612434497873_<32> · C142

C142 = P63 · P79

P63 = 446230848885739862951514158743047799808097303689909318714879633_<63>

P79 = 8783486649009658366262878191277303628728254895476682026895585605704238396823777_<79>

Number: 19999_200
N=3919462703564142473698047873878421629698357069094950750629640809045036371942703314337013367544634521328393484746001349161465007919976067433841
  ( 142 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=446230848885739862951514158743047799808097303689909318714879633
 r2=8783486649009658366262878191277303628728254895476682026895585605704238396823777
Version: 
Total time: 292.58 hours.
Scaled time: 698.68 units (timescale=2.388).
Factorization parameters were as follows:
n: 3919462703564142473698047873878421629698357069094950750629640809045036371942703314337013367544634521328393484746001349161465007919976067433841
m: 10000000000000000000000000000000000000000
deg: 5
c5: 2
c0: -1
skew: 0.87
type: snfs
lss: 1
rlim: 15000000
alim: 15000000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 15000000/15000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7500000, 13900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 37340287
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2846374 x 2846621
Total sieving time: 255.33 hours.
Total relation processing time: 12.54 hours.
Matrix solve time: 23.55 hours.
Time per square root: 1.16 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15000000,15000000,29,29,56,56,2.6,2.6,100000
total time: 292.58 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673795)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672307)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

(5·10¹⁸³+1)/3 = 1(6)₁₈₂7_<184> = 5234609 · C177

C177 = P41 · P136

P41 = 54006465837377625552336265338881733819761_<41>

P136 = 5895474211042055406296762574818982802357058721360340818720086118739001638924818762801489852596577981672047174850728107083024670512804683_<136>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 318393726573783575175656226982123529506533662144902640611107088737032062311944725320776903617188345235846013841084724124890066606057236876081225296228747298349631589802918740763 (177 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=7499907357
Step 1 took 17155ms
Step 2 took 7042ms
********** Factor found in step 2: 54006465837377625552336265338881733819761
Found probable prime factor of 41 digits: 54006465837377625552336265338881733819761
Probable prime cofactor 5895474211042055406296762574818982802357058721360340818720086118739001638924818762801489852596577981672047174850728107083024670512804683 has 136 digits

Dec 26, 2009 (2nd)

By Sinkiti Sibata / Msieve / Dec 26, 2009

(73·10¹³¹+17)/9 = 8(1)₁₃₀3_<132> = 3 · C132

C132 = P54 · P78

P54 = 901115896568616616303029954905224423463773024413969713_<54>

P78 = 300039508125337654128915079093446004442270863338652763310722672562208472089267_<78>

Number: 81113_131
N=270370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370371
  ( 132 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=901115896568616616303029954905224423463773024413969713 (pp54)
 r2=300039508125337654128915079093446004442270863338652763310722672562208472089267 (pp78)
Version: Msieve-1.40
Total time: 3.78 hours.
Scaled time: 7.93 units (timescale=2.099).
Factorization parameters were as follows:
name: 81113_131
n: 270370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370371
m: 100000000000000000000000000
deg: 5
c5: 730
c0: 17
skew: 0.47
type: snfs
lss: 1
rlim: 1150000
alim: 1150000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1150000/1150000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [575000, 1075001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 166370 x 166606
Total sieving time: 3.61 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,132.000,5,0,0,0,0,0,0,0,0,1150000,1150000,26,26,47,47,2.3,2.3,50000
total time: 3.78 hours.
 --------- CPU info (if available) ----------

2·10²³⁴+9 = 2(0)₂₃₃9_<235> = 11 · 131 · 271489 · 823651 · 319703161 · 1078869731_<10> · 140239420405201921_<18> · 31537930735794751543553_<23> · 87211834129437057201132899_<26> · 11429780024455220807441469459289_<32> · C106

C106 = P52 · P54

P52 = 4421646001155731662524341299889414727107084802590443_<52>

P54 = 923111247852638260463789169912288203586464742324595249_<54>

Number: 20009_234
N=4081671157689495451002320427478185479062625058013970660200302602803251158698157130376845326821666690605307
  ( 106 digits)
Divisors found:
 r1=4421646001155731662524341299889414727107084802590443 (pp52)
 r2=923111247852638260463789169912288203586464742324595249 (pp54)
Version: Msieve-1.40
Total time: 9.09 hours.
Scaled time: 30.30 units (timescale=3.333).
Factorization parameters were as follows:
name: 20009_234
n: 4081671157689495451002320427478185479062625058013970660200302602803251158698157130376845326821666690605307
skew: 5227.48
# norm 2.82e+14
c5: 447180
c4: 4762122818
c3: -12903767621588
c2: -188566052319945831
c1: 258817026744121798005
c0: 489303287558624884234365
# alpha -5.68
Y1: 228435784339
Y0: -98190388035999720407
# Murphy_E 1.67e-09
# M 912139391631407218912303459389075224416911338056911672306885508693816487338766124197096291587759584551275
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 275751 x 275999
Polynomial selection time: 0.97 hours.
Total sieving time: 7.91 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 9.09 hours.
 --------- CPU info (if available) ----------

(73·10¹⁴⁹+17)/9 = 8(1)₁₄₈3_<150> = 3 · 59009 · 145691963372458235831977_<24> · 124135506707574799618920655151513_<33> · C90

C90 = P45 · P46

P45 = 152895783386268092363880036050242160838011941_<45>

P46 = 1656966451277186284241276583314458613058031559_<46>

Sat Dec 26 08:14:37 2009  Msieve v. 1.42
Sat Dec 26 08:14:37 2009  random seeds: d11307ec a5c8cf28
Sat Dec 26 08:14:37 2009  factoring 253343183612790017211717265292660824382436949602662535789530283629893510565256412396846019 (90 digits)
Sat Dec 26 08:14:38 2009  searching for 15-digit factors
Sat Dec 26 08:14:38 2009  commencing quadratic sieve (90-digit input)
Sat Dec 26 08:14:38 2009  using multiplier of 3
Sat Dec 26 08:14:38 2009  using 32kb Intel Core sieve core
Sat Dec 26 08:14:38 2009  sieve interval: 35 blocks of size 32768
Sat Dec 26 08:14:38 2009  processing polynomials in batches of 6
Sat Dec 26 08:14:38 2009  using a sieve bound of 1573699 (59667 primes)
Sat Dec 26 08:14:38 2009  using large prime bound of 125895920 (26 bits)
Sat Dec 26 08:14:38 2009  using double large prime bound of 380207692734720 (42-49 bits)
Sat Dec 26 08:14:38 2009  using trial factoring cutoff of 49 bits
Sat Dec 26 08:14:38 2009  polynomial 'A' values have 11 factors
Sat Dec 26 09:37:36 2009  59859 relations (15315 full + 44544 combined from 640664 partial), need 59763
Sat Dec 26 09:37:37 2009  begin with 655979 relations
Sat Dec 26 09:37:37 2009  reduce to 147934 relations in 10 passes
Sat Dec 26 09:37:37 2009  attempting to read 147934 relations
Sat Dec 26 09:37:39 2009  recovered 147934 relations
Sat Dec 26 09:37:39 2009  recovered 129529 polynomials
Sat Dec 26 09:37:40 2009  attempting to build 59859 cycles
Sat Dec 26 09:37:40 2009  found 59859 cycles in 6 passes
Sat Dec 26 09:37:40 2009  distribution of cycle lengths:
Sat Dec 26 09:37:40 2009     length 1 : 15315
Sat Dec 26 09:37:40 2009     length 2 : 11329
Sat Dec 26 09:37:40 2009     length 3 : 10572
Sat Dec 26 09:37:40 2009     length 4 : 8147
Sat Dec 26 09:37:40 2009     length 5 : 5744
Sat Dec 26 09:37:40 2009     length 6 : 3734
Sat Dec 26 09:37:40 2009     length 7 : 2259
Sat Dec 26 09:37:40 2009     length 9+: 2759
Sat Dec 26 09:37:40 2009  largest cycle: 18 relations
Sat Dec 26 09:37:40 2009  matrix is 59667 x 59859 (15.1 MB) with weight 3707861 (61.94/col)
Sat Dec 26 09:37:40 2009  sparse part has weight 3707861 (61.94/col)
Sat Dec 26 09:37:41 2009  filtering completed in 3 passes
Sat Dec 26 09:37:41 2009  matrix is 56143 x 56207 (14.2 MB) with weight 3508721 (62.42/col)
Sat Dec 26 09:37:41 2009  sparse part has weight 3508721 (62.42/col)
Sat Dec 26 09:37:41 2009  saving the first 48 matrix rows for later
Sat Dec 26 09:37:41 2009  matrix is 56095 x 56207 (10.8 MB) with weight 2963212 (52.72/col)
Sat Dec 26 09:37:41 2009  sparse part has weight 2486996 (44.25/col)
Sat Dec 26 09:37:41 2009  matrix includes 64 packed rows
Sat Dec 26 09:37:41 2009  using block size 22482 for processor cache size 1024 kB
Sat Dec 26 09:37:42 2009  commencing Lanczos iteration
Sat Dec 26 09:37:42 2009  memory use: 10.0 MB
Sat Dec 26 09:38:04 2009  lanczos halted after 889 iterations (dim = 56091)
Sat Dec 26 09:38:04 2009  recovered 15 nontrivial dependencies
Sat Dec 26 09:38:04 2009  prp45 factor: 152895783386268092363880036050242160838011941
Sat Dec 26 09:38:04 2009  prp46 factor: 1656966451277186284241276583314458613058031559
Sat Dec 26 09:38:04 2009  elapsed time 01:23:27

Dec 26, 2009

By Markus Tervooren / Msieve / Dec 26, 2009

(7·10¹⁸²-61)/9 = (7)₁₈₁1_<182> = 89 · 997 · 30467369 · 17618593319_<11> · 196795518289527012783177637059304087_<36> · C124

C124 = P46 · P79

P46 = 1822983903915540903242968668361589445511954993_<46>

P79 = 4551621541782307730013990392915456127532722433651555998138128258792296417129087_<79>

N=8297532807384384619591502124535182691958946812580208156234462702919765706096384805864725674578023949954423362371961815181391
  ( 124 digits)
Divisors found:
 r1=1822983903915540903242968668361589445511954993 (pp46)
 r2=4551621541782307730013990392915456127532722433651555998138128258792296417129087 (pp79)
Version: Msieve-1.39
Total time: 42.29 hours.
Scaled time: 0.00 units (timescale=0.000).
Factorization parameters were as follows:
# Murphy_E = 1.855e-10, selected by Markus Tervooren
n: 8297532807384384619591502124535182691958946812580208156234462702919765706096384805864725674578023949954423362371961815181391
Y0: -1225653561529813741731415
Y1: 22064329640861
c0: -26207728649600251358721533684
c1: -77212770881249363965820
c2: 41665440464405440487
c3: 476421430964662
c4: -4195615430
c5: 3000
skew: 102794.61
type: gnfs
# selected mechanically
rlim: 6700000
alim: 6700000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsite: 500000
Factor base limits: 6700000/6700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [3350000, 1910001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 737257 x 737496
Total sieving time: 40.76 hours.
Total relation processing time: 0.73 hours.
Matrix solve time: 0.73 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6700000,6700000,28,28,56,56,2.6,2.6,180000
total time: 42.29 hours.
 --------- CPU info (if available) ----------
[    0.144009] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.236014] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.332940] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.432541] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197988k/10485760k available (2226k kernel code, 189848k reserved, 1082k data, 392k init)
[    0.083990] Calibrating delay using timer specific routine.. 5337.16 BogoMIPS (lpj=10674326)
[    0.156009] Calibrating delay using timer specific routine.. 5333.34 BogoMIPS (lpj=10666681)
[    0.256016] Calibrating delay using timer specific routine.. 5333.37 BogoMIPS (lpj=10666743)
[    0.352020] Calibrating delay using timer specific routine.. 5333.36 BogoMIPS (lpj=10666726)
[    0.440025] Total of 4 processors activated (21337.23 BogoMIPS).

Dec 25, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Dec 25, 2009

(5·10¹⁹¹+13)/9 = (5)₁₉₀7_<191> = 3 · 1087 · C188

C188 = P67 · P121

P67 = 8263197315557210185325930076431111786216503129518233759467018348421_<67>

P121 = 2061714725211655682692980576776961371384554185324182600243072178639205766966196819025797458956364109859801326886670622197_<121>

Number: n
N=17036355582813724488057514736447579133871682169750247027155950799005076833963678489897441139391461378581893761286585573614092473338103512896521176189989437459538655490817404340863402500937
  ( 188 digits)
SNFS difficulty: 191 digits.
Divisors found:

Fri Dec 25 05:20:04 2009  prp67 factor: 8263197315557210185325930076431111786216503129518233759467018348421
Fri Dec 25 05:20:04 2009  prp121 factor: 2061714725211655682692980576776961371384554185324182600243072178639205766966196819025797458956364109859801326886670622197
Fri Dec 25 05:20:04 2009  elapsed time 09:13:45 (Msieve 1.42 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: ~ 24.00 hours.
Scaled time: 0.00 units (timescale=0.842).
Factorization parameters were as follows:
name: KA_5_190_7
n: 17036355582813724488057514736447579133871682169750247027155950799005076833963678489897441139391461378581893761286585573614092473338103512896521176189989437459538655490817404340863402500937
m: 100000000000000000000000000000000000000
deg: 5
c5: 50
c0: 13
skew: 0.76
type: snfs
lss: 1
rlim: 11000000
alim: 11000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 100000)
Primes: RFBsize:726517, AFBsize:726768, 
Relations: 
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2552794 hash collisions in 24691333 relations
Msieve: matrix is 1871363 x 1871588 (506.0 MB)

Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,56,56,2.5,2.5,100000
total time: 0.00 hours.
 --------- CPU info (if available) ----------

(73·10¹¹⁰+17)/9 = 8(1)₁₀₉3_<111> = 3 · 237151 · C106

C106 = P35 · P71

P35 = 17288961375083169232608048029605549_<35>

P71 = 65942473216422422125262858007207153303242664770758593943399626307735729_<71>

Number: n
N=1140076872416183656701301577351014207700454016092575491439506349837742073068932327379477085782351203960221
  ( 106 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=17288961375083169232608048029605549 (pp35)
 r2=65942473216422422125262858007207153303242664770758593943399626307735729 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.58 hours.
Scaled time: 1.06 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_8_1_109_3
n: 1140076872416183656701301577351014207700454016092575491439506349837742073068932327379477085782351203960221
m: 10000000000000000000000
deg: 5
c5: 73
c0: 17
skew: 0.75
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
qintsize: 20000
Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [255000, 375001)
Primes: RFBsize:42291, AFBsize:42236, largePrimes:1115199 encountered
Relations: rels:1060215, finalFF:113391
Max relations in full relation-set: 48
Initial matrix: 84592 x 113391 with sparse part having weight 4903067.
Pruned matrix : 70920 x 71406 with weight 2269024.
Total sieving time: 0.55 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.58 hours.
 --------- CPU info (if available) ----------

(73·10¹⁴⁴+17)/9 = 8(1)₁₄₃3_<145> = 23 · 29 · 34883 · 7724676628270769389_<19> · 11144636683362884724877_<23> · C97

C97 = P43 · P55

P43 = 1643004455893277707598416968329253428023223_<43>

P55 = 2464652666595249043946775012950632313839966108011752407_<55>

Number: n
N=4049435313445243145081571668959828155766049931757007601017678699980977351454635253218358122147761
  ( 97 digits)
Divisors found:

Sat Dec 26 00:13:50 2009  prp43 factor: 1643004455893277707598416968329253428023223
Sat Dec 26 00:13:50 2009  prp55 factor: 2464652666595249043946775012950632313839966108011752407
Sat Dec 26 00:13:50 2009  elapsed time 00:07:56 (Msieve 1.43 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.18 hours.
Scaled time: 3.99 units (timescale=1.834).
Factorization parameters were as follows:
name: KA_8_1_143_3
n: 4049435313445243145081571668959828155766049931757007601017678699980977351454635253218358122147761
Y0: -230281139953553709142197
Y1:  10717884922201
c0:  1605908082544278887090075744
c1: -6967643114888019667902
c2: -6574508700636113
c3: -107188944
c4:  1440
skew: 1751097.82
type: gnfs
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 20000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 50/50
Sieved  special-q in [600000, 918469)
Primes: RFBsize:92938, AFBsize:93099, largePrimes:2465023 encountered
Relations: rels:2425587, finalFF:203641
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 276018 hash collisions in 2772746 relations
Msieve: matrix is 164646 x 164877 (45.3 MB)

Total sieving time: 2.13 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,96,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,50,50,2.4,2.4,60000
total time: 2.18 hours.
 --------- CPU info (if available) ----------

Dec 25, 2009 (4th)

By Sinkiti Sibata / Msieve / Dec 25, 2009

(61·10¹⁶⁴+11)/9 = 6(7)₁₆₃9_<165> = 7 · 17² · 44711 · 167411401 · 149334670797750991643_<21> · C129

C129 = P60 · P70

P60 = 120914647031434162711029575123136458526463272062610139034489_<60>

P70 = 2478862669511374046524623309725596551727978452206500258616198344907609_<70>

Number: 67779_164
N=299730804723366427812204067615768836287014813862082169550356765685497896283053155240966553527690369103612485282297406365169526801
  ( 129 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=120914647031434162711029575123136458526463272062610139034489 (pp60)
 r2=2478862669511374046524623309725596551727978452206500258616198344907609 (pp70)
Version: Msieve-1.40
Total time: 48.01 hours.
Scaled time: 161.12 units (timescale=3.356).
Factorization parameters were as follows:
name: 67779_164
n: 299730804723366427812204067615768836287014813862082169550356765685497896283053155240966553527690369103612485282297406365169526801
m: 100000000000000000000000000000000
deg: 5
c5: 610000
c0: 11
skew: 0.11
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 801796 x 802044
Total sieving time: 46.61 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.22 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,165.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 48.01 hours.
 --------- CPU info (if available) ----------

(73·10¹¹²+17)/9 = 8(1)₁₁₁3_<113> = 271 · 953 · 1061 · 427877789 · 7623957549581_<13> · C83

C83 = P33 · P51

P33 = 571785873333381219056107281470633_<33>

P51 = 158697155111456401907712179353505517156780184656403_<51>

Fri Dec 25 16:39:59 2009  Msieve v. 1.39
Fri Dec 25 16:39:59 2009  random seeds: 28e46ee7 78aecebb
Fri Dec 25 16:39:59 2009  factoring 90740791430927162098033555988150928454479341098957224962459877227052620215639913099 (83 digits)
Fri Dec 25 16:40:00 2009  searching for 15-digit factors
Fri Dec 25 16:40:02 2009  commencing quadratic sieve (83-digit input)
Fri Dec 25 16:40:02 2009  using multiplier of 11
Fri Dec 25 16:40:02 2009  using 64kb Pentium 4 sieve core
Fri Dec 25 16:40:02 2009  sieve interval: 6 blocks of size 65536
Fri Dec 25 16:40:02 2009  processing polynomials in batches of 17
Fri Dec 25 16:40:02 2009  using a sieve bound of 1380721 (52941 primes)
Fri Dec 25 16:40:02 2009  using large prime bound of 121503448 (26 bits)
Fri Dec 25 16:40:02 2009  using trial factoring cutoff of 27 bits
Fri Dec 25 16:40:02 2009  polynomial 'A' values have 11 factors
Fri Dec 25 17:18:18 2009  53124 relations (27397 full + 25727 combined from 277486 partial), need 53037
Fri Dec 25 17:18:19 2009  begin with 304883 relations
Fri Dec 25 17:18:20 2009  reduce to 75578 relations in 2 passes
Fri Dec 25 17:18:20 2009  attempting to read 75578 relations
Fri Dec 25 17:18:22 2009  recovered 75578 relations
Fri Dec 25 17:18:22 2009  recovered 68355 polynomials
Fri Dec 25 17:18:22 2009  attempting to build 53124 cycles
Fri Dec 25 17:18:22 2009  found 53124 cycles in 1 passes
Fri Dec 25 17:18:22 2009  distribution of cycle lengths:
Fri Dec 25 17:18:22 2009     length 1 : 27397
Fri Dec 25 17:18:22 2009     length 2 : 25727
Fri Dec 25 17:18:22 2009  largest cycle: 2 relations
Fri Dec 25 17:18:22 2009  matrix is 52941 x 53124 (7.3 MB) with weight 1706774 (32.13/col)
Fri Dec 25 17:18:22 2009  sparse part has weight 1706774 (32.13/col)
Fri Dec 25 17:18:23 2009  filtering completed in 4 passes
Fri Dec 25 17:18:23 2009  matrix is 38259 x 38323 (5.8 MB) with weight 1368218 (35.70/col)
Fri Dec 25 17:18:23 2009  sparse part has weight 1368218 (35.70/col)
Fri Dec 25 17:18:23 2009  saving the first 48 matrix rows for later
Fri Dec 25 17:18:23 2009  matrix is 38211 x 38323 (3.7 MB) with weight 1020504 (26.63/col)
Fri Dec 25 17:18:23 2009  sparse part has weight 728962 (19.02/col)
Fri Dec 25 17:18:23 2009  matrix includes 64 packed rows
Fri Dec 25 17:18:23 2009  using block size 15329 for processor cache size 512 kB
Fri Dec 25 17:18:23 2009  commencing Lanczos iteration
Fri Dec 25 17:18:23 2009  memory use: 4.2 MB
Fri Dec 25 17:18:35 2009  lanczos halted after 606 iterations (dim = 38205)
Fri Dec 25 17:18:35 2009  recovered 14 nontrivial dependencies
Fri Dec 25 17:18:35 2009  prp33 factor: 571785873333381219056107281470633
Fri Dec 25 17:18:35 2009  prp51 factor: 158697155111456401907712179353505517156780184656403
Fri Dec 25 17:18:35 2009  elapsed time 00:38:36

(73·10¹¹⁵+17)/9 = 8(1)₁₁₄3_<116> = 274403 · 1673293444661515580711_<22> · C90

C90 = P35 · P55

P35 = 28808302077391310472306578254891243_<35>

P55 = 6131994033354338944152150549622399890480568691762354927_<55>

Fri Dec 25 17:44:14 2009  Msieve v. 1.39
Fri Dec 25 17:44:14 2009  random seeds: 8d3e7221 e242d567
Fri Dec 25 17:44:14 2009  factoring 176652336449632923363153391827937121757134931223406692705517673513355035983000313950204261 (90 digits)
Fri Dec 25 17:44:16 2009  searching for 15-digit factors
Fri Dec 25 17:44:18 2009  commencing quadratic sieve (90-digit input)
Fri Dec 25 17:44:18 2009  using multiplier of 5
Fri Dec 25 17:44:18 2009  using 64kb Pentium 4 sieve core
Fri Dec 25 17:44:18 2009  sieve interval: 18 blocks of size 65536
Fri Dec 25 17:44:18 2009  processing polynomials in batches of 6
Fri Dec 25 17:44:18 2009  using a sieve bound of 1575269 (59635 primes)
Fri Dec 25 17:44:18 2009  using large prime bound of 126021520 (26 bits)
Fri Dec 25 17:44:18 2009  using double large prime bound of 380890718607520 (42-49 bits)
Fri Dec 25 17:44:18 2009  using trial factoring cutoff of 49 bits
Fri Dec 25 17:44:18 2009  polynomial 'A' values have 11 factors
Fri Dec 25 19:47:24 2009  59756 relations (16412 full + 43344 combined from 629864 partial), need 59731
Fri Dec 25 19:47:27 2009  begin with 646276 relations
Fri Dec 25 19:47:27 2009  reduce to 144537 relations in 11 passes
Fri Dec 25 19:47:27 2009  attempting to read 144537 relations
Fri Dec 25 19:47:31 2009  recovered 144537 relations
Fri Dec 25 19:47:31 2009  recovered 121227 polynomials
Fri Dec 25 19:47:32 2009  attempting to build 59756 cycles
Fri Dec 25 19:47:32 2009  found 59756 cycles in 6 passes
Fri Dec 25 19:47:32 2009  distribution of cycle lengths:
Fri Dec 25 19:47:32 2009     length 1 : 16412
Fri Dec 25 19:47:32 2009     length 2 : 11517
Fri Dec 25 19:47:32 2009     length 3 : 10312
Fri Dec 25 19:47:32 2009     length 4 : 7860
Fri Dec 25 19:47:32 2009     length 5 : 5568
Fri Dec 25 19:47:32 2009     length 6 : 3577
Fri Dec 25 19:47:32 2009     length 7 : 2093
Fri Dec 25 19:47:32 2009     length 9+: 2417
Fri Dec 25 19:47:32 2009  largest cycle: 18 relations
Fri Dec 25 19:47:32 2009  matrix is 59635 x 59756 (14.7 MB) with weight 3624148 (60.65/col)
Fri Dec 25 19:47:32 2009  sparse part has weight 3624148 (60.65/col)
Fri Dec 25 19:47:33 2009  filtering completed in 3 passes
Fri Dec 25 19:47:33 2009  matrix is 55478 x 55542 (13.8 MB) with weight 3407636 (61.35/col)
Fri Dec 25 19:47:33 2009  sparse part has weight 3407636 (61.35/col)
Fri Dec 25 19:47:34 2009  saving the first 48 matrix rows for later
Fri Dec 25 19:47:34 2009  matrix is 55430 x 55542 (10.5 MB) with weight 2861767 (51.52/col)
Fri Dec 25 19:47:34 2009  sparse part has weight 2417834 (43.53/col)
Fri Dec 25 19:47:34 2009  matrix includes 64 packed rows
Fri Dec 25 19:47:34 2009  using block size 21845 for processor cache size 512 kB
Fri Dec 25 19:47:35 2009  commencing Lanczos iteration
Fri Dec 25 19:47:35 2009  memory use: 9.3 MB
Fri Dec 25 19:48:08 2009  lanczos halted after 877 iterations (dim = 55430)
Fri Dec 25 19:48:08 2009  recovered 18 nontrivial dependencies
Fri Dec 25 19:48:09 2009  prp35 factor: 28808302077391310472306578254891243
Fri Dec 25 19:48:09 2009  prp55 factor: 6131994033354338944152150549622399890480568691762354927
Fri Dec 25 19:48:09 2009  elapsed time 02:03:55

(73·10¹²³+17)/9 = 8(1)₁₂₂3_<124> = 7 · 61 · 479 · 1213 · 4957 · 16427 · 3549179 · C102

C102 = P31 · P71

P31 = 3193529529869076315969156217591_<31>

P71 = 35422576410829697301610949465338800906401213092713734855093957967741107_<71>

Number: 81113_123
N=113123043792028395932085995982383600135916831346114549233543698978046601074915653928514213454447213237
  ( 102 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=3193529529869076315969156217591 (pp31)
 r2=35422576410829697301610949465338800906401213092713734855093957967741107 (pp71)
Version: Msieve-1.40
Total time: 1.87 hours.
Scaled time: 6.30 units (timescale=3.367).
Factorization parameters were as follows:
name: 81113_123
n: 113123043792028395932085995982383600135916831346114549233543698978046601074915653928514213454447213237
m: 1000000000000000000000000
deg: 5
c5: 73000
c0: 17
skew: 0.19
type: snfs
lss: 1
rlim: 840000
alim: 840000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 840000/840000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [420000, 820001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 98706 x 98954
Total sieving time: 1.83 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,124.000,5,0,0,0,0,0,0,0,0,840000,840000,25,25,46,46,2.2,2.2,50000
total time: 1.87 hours.
 --------- CPU info (if available) ----------

(61·10¹⁵⁵+11)/9 = 6(7)₁₅₄9_<156> = 23 · 163 · 659 · C150

C150 = P63 · P87

P63 = 287586298285800146257914734984871284131275628557401661706046609_<63>

P87 = 953933893847574957429258954829395060019674797190928406852259555726105076178805065202941_<87>

Number: 67779_155
N=274338317340983504666607211706744571553032362611932844318536648833326834663356977248673607965777329302089167238841952301201525375012609443561389877069
  ( 150 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=287586298285800146257914734984871284131275628557401661706046609 (pp63)
 r2=953933893847574957429258954829395060019674797190928406852259555726105076178805065202941 (pp87)
Version: Msieve-1.40
Total time: 21.05 hours.
Scaled time: 43.74 units (timescale=2.078).
Factorization parameters were as follows:
name: 67779_155
n: 274338317340983504666607211706744571553032362611932844318536648833326834663356977248673607965777329302089167238841952301201525375012609443561389877069
m: 10000000000000000000000000000000
deg: 5
c5: 61
c0: 11
skew: 0.71
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1450000, 2250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 505234 x 505482
Total sieving time: 19.89 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.90 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000
total time: 21.05 hours.
 --------- CPU info (if available) ----------

(73·10¹²⁰+17)/9 = 8(1)₁₁₉3_<121> = 10589 · 36209 · 18764467 · 1567176671341_<13> · 4390730828021_<13> · C81

C81 = P39 · P42

P39 = 360048390588018911510814299879560340171_<39>

P42 = 455047772435609644108134553747154826524269_<42>

Fri Dec 25 19:56:23 2009  Msieve v. 1.39
Fri Dec 25 19:56:23 2009  random seeds: 1569a2e8 b5b575d0
Fri Dec 25 19:56:23 2009  factoring 163839218106104326862614741818043845416922147853654362408606857663521535227109999 (81 digits)
Fri Dec 25 19:56:24 2009  searching for 15-digit factors
Fri Dec 25 19:56:26 2009  commencing quadratic sieve (81-digit input)
Fri Dec 25 19:56:26 2009  using multiplier of 71
Fri Dec 25 19:56:26 2009  using 64kb Pentium 4 sieve core
Fri Dec 25 19:56:26 2009  sieve interval: 6 blocks of size 65536
Fri Dec 25 19:56:26 2009  processing polynomials in batches of 17
Fri Dec 25 19:56:26 2009  using a sieve bound of 1309421 (50080 primes)
Fri Dec 25 19:56:26 2009  using large prime bound of 129632679 (26 bits)
Fri Dec 25 19:56:26 2009  using trial factoring cutoff of 27 bits
Fri Dec 25 19:56:26 2009  polynomial 'A' values have 10 factors
Fri Dec 25 20:21:09 2009  50248 relations (25817 full + 24431 combined from 269212 partial), need 50176
Fri Dec 25 20:21:10 2009  begin with 295029 relations
Fri Dec 25 20:21:10 2009  reduce to 71658 relations in 2 passes
Fri Dec 25 20:21:10 2009  attempting to read 71658 relations
Fri Dec 25 20:21:12 2009  recovered 71658 relations
Fri Dec 25 20:21:12 2009  recovered 61972 polynomials
Fri Dec 25 20:21:12 2009  attempting to build 50248 cycles
Fri Dec 25 20:21:12 2009  found 50248 cycles in 1 passes
Fri Dec 25 20:21:12 2009  distribution of cycle lengths:
Fri Dec 25 20:21:12 2009     length 1 : 25817
Fri Dec 25 20:21:12 2009     length 2 : 24431
Fri Dec 25 20:21:12 2009  largest cycle: 2 relations
Fri Dec 25 20:21:12 2009  matrix is 50080 x 50248 (6.7 MB) with weight 1555105 (30.95/col)
Fri Dec 25 20:21:12 2009  sparse part has weight 1555105 (30.95/col)
Fri Dec 25 20:21:13 2009  filtering completed in 3 passes
Fri Dec 25 20:21:13 2009  matrix is 35746 x 35810 (5.3 MB) with weight 1246641 (34.81/col)
Fri Dec 25 20:21:13 2009  sparse part has weight 1246641 (34.81/col)
Fri Dec 25 20:21:13 2009  saving the first 48 matrix rows for later
Fri Dec 25 20:21:13 2009  matrix is 35698 x 35810 (4.0 MB) with weight 1001957 (27.98/col)
Fri Dec 25 20:21:13 2009  sparse part has weight 841452 (23.50/col)
Fri Dec 25 20:21:13 2009  matrix includes 64 packed rows
Fri Dec 25 20:21:13 2009  using block size 14324 for processor cache size 512 kB
Fri Dec 25 20:21:13 2009  commencing Lanczos iteration
Fri Dec 25 20:21:13 2009  memory use: 4.2 MB
Fri Dec 25 20:21:25 2009  lanczos halted after 566 iterations (dim = 35692)
Fri Dec 25 20:21:25 2009  recovered 15 nontrivial dependencies
Fri Dec 25 20:21:26 2009  prp39 factor: 360048390588018911510814299879560340171
Fri Dec 25 20:21:26 2009  prp42 factor: 455047772435609644108134553747154826524269
Fri Dec 25 20:21:26 2009  elapsed time 00:25:03

(73·10¹²⁵+17)/9 = 8(1)₁₂₄3_<126> = 3² · 181 · 22403867450161_<14> · C110

C110 = P34 · P76

P34 = 4516668276671408372535932075721397_<34>

P76 = 4920600161360611078855281402744796833170083005776431740107754894291722737241_<76>

Number: 81113_125
N=22224718651001685202078956554482624604027299135041508119387553597492430813525656454710046261023614812552445677
  ( 110 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=4516668276671408372535932075721397 (pp34)
 r2=4920600161360611078855281402744796833170083005776431740107754894291722737241 (pp76)
Version: Msieve-1.40
Total time: 1.64 hours.
Scaled time: 5.46 units (timescale=3.333).
Factorization parameters were as follows:
name: 81113_125
n: 22224718651001685202078956554482624604027299135041508119387553597492430813525656454710046261023614812552445677
m: 10000000000000000000000000
deg: 5
c5: 73
c0: 17
skew: 0.75
type: snfs
lss: 1
rlim: 910000
alim: 910000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 910000/910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [455000, 755001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 113154 x 113400
Total sieving time: 1.59 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000
total time: 1.64 hours.
 --------- CPU info (if available) ----------

(73·10¹³⁰+17)/9 = 8(1)₁₂₉3_<131> = 389 · 1092391 · 43074381051448309_<17> · 66226550654595469_<17> · C89

C89 = P40 · P49

P40 = 8807863511118081438403447564327236999049_<40>

P49 = 7596803243687871089056339899052422078693151715803_<49>

Fri Dec 25 21:03:55 2009  Msieve v. 1.39
Fri Dec 25 21:03:55 2009  random seeds: cbfa3e39 c71df5d4
Fri Dec 25 21:03:55 2009  factoring 66911606091221882292853807626770775644445001777494391969489392127703598145079039029271347 (89 digits)
Fri Dec 25 21:03:56 2009  searching for 15-digit factors
Fri Dec 25 21:03:58 2009  commencing quadratic sieve (89-digit input)
Fri Dec 25 21:03:58 2009  using multiplier of 3
Fri Dec 25 21:03:58 2009  using 64kb Pentium 4 sieve core
Fri Dec 25 21:03:58 2009  sieve interval: 17 blocks of size 65536
Fri Dec 25 21:03:58 2009  processing polynomials in batches of 6
Fri Dec 25 21:03:58 2009  using a sieve bound of 1564393 (59333 primes)
Fri Dec 25 21:03:58 2009  using large prime bound of 125151440 (26 bits)
Fri Dec 25 21:03:58 2009  using double large prime bound of 376170311388240 (42-49 bits)
Fri Dec 25 21:03:58 2009  using trial factoring cutoff of 49 bits
Fri Dec 25 21:03:58 2009  polynomial 'A' values have 11 factors
Fri Dec 25 22:51:44 2009  59844 relations (16470 full + 43374 combined from 627408 partial), need 59429
Fri Dec 25 22:51:46 2009  begin with 643878 relations
Fri Dec 25 22:51:47 2009  reduce to 143646 relations in 12 passes
Fri Dec 25 22:51:47 2009  attempting to read 143646 relations
Fri Dec 25 22:51:51 2009  recovered 143646 relations
Fri Dec 25 22:51:51 2009  recovered 117928 polynomials
Fri Dec 25 22:51:51 2009  attempting to build 59844 cycles
Fri Dec 25 22:51:51 2009  found 59844 cycles in 5 passes
Fri Dec 25 22:51:51 2009  distribution of cycle lengths:
Fri Dec 25 22:51:51 2009     length 1 : 16470
Fri Dec 25 22:51:51 2009     length 2 : 11794
Fri Dec 25 22:51:51 2009     length 3 : 10691
Fri Dec 25 22:51:51 2009     length 4 : 7819
Fri Dec 25 22:51:51 2009     length 5 : 5432
Fri Dec 25 22:51:51 2009     length 6 : 3362
Fri Dec 25 22:51:51 2009     length 7 : 1970
Fri Dec 25 22:51:51 2009     length 9+: 2306
Fri Dec 25 22:51:51 2009  largest cycle: 16 relations
Fri Dec 25 22:51:52 2009  matrix is 59333 x 59844 (14.5 MB) with weight 3561626 (59.52/col)
Fri Dec 25 22:51:52 2009  sparse part has weight 3561626 (59.52/col)
Fri Dec 25 22:51:53 2009  filtering completed in 3 passes
Fri Dec 25 22:51:53 2009  matrix is 54879 x 54943 (13.3 MB) with weight 3277217 (59.65/col)
Fri Dec 25 22:51:53 2009  sparse part has weight 3277217 (59.65/col)
Fri Dec 25 22:51:53 2009  saving the first 48 matrix rows for later
Fri Dec 25 22:51:53 2009  matrix is 54831 x 54943 (9.8 MB) with weight 2710493 (49.33/col)
Fri Dec 25 22:51:53 2009  sparse part has weight 2233703 (40.65/col)
Fri Dec 25 22:51:53 2009  matrix includes 64 packed rows
Fri Dec 25 22:51:53 2009  using block size 21845 for processor cache size 512 kB
Fri Dec 25 22:51:54 2009  commencing Lanczos iteration
Fri Dec 25 22:51:54 2009  memory use: 8.9 MB
Fri Dec 25 22:52:25 2009  lanczos halted after 869 iterations (dim = 54824)
Fri Dec 25 22:52:26 2009  recovered 13 nontrivial dependencies
Fri Dec 25 22:52:26 2009  prp40 factor: 8807863511118081438403447564327236999049
Fri Dec 25 22:52:26 2009  prp49 factor: 7596803243687871089056339899052422078693151715803
Fri Dec 25 22:52:26 2009  elapsed time 01:48:31

Dec 25, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve / Dec 25, 2009

(55·10¹⁷⁷+53)/9 = 6(1)₁₇₆7_<178> = 3⁴ · 997 · C173

C173 = P48 · P126

P48 = 121267649127676182373047910614477486882780677773_<48>

P126 = 624015021606932925999715651797548114366055875459187905620591759468551484260290666283449260213316132801468484092282493219437597_<126>

N=75672834690628813738884692486237863109217914374123742971025559531819051117687768380587578923326908021733238123148595305807683682047514284967385008248338981278540697538431481
  ( 173 digits)
SNFS difficulty: 178 digits.
Divisors found:
 r1=121267649127676182373047910614477486882780677773 (pp48)
 r2=624015021606932925999715651797548114366055875459187905620591759468551484260290666283449260213316132801468484092282493219437597 (pp126)
Version: Msieve-1.40
Total time: 147.29 hours.
Scaled time: 137.28 units (timescale=0.932).
Factorization parameters were as follows:
n: 75672834690628813738884692486237863109217914374123742971025559531819051117687768380587578923326908021733238123148595305807683682047514284967385008248338981278540697538431481
m: 100000000000000000000000000000000000
deg: 5
c5: 5500
c0: 53
skew: 0.40
type: snfs
lss: 1
rlim: 6700000
alim: 6700000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 6700000/6700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3350000, 8450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1468416 x 1468643
Total sieving time: 142.34 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 4.36 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
snfs,178.000,5,0,0,0,0,0,0,0,0,6700000,6700000,28,28,53,53,2.5,2.5,100000
total time: 147.29 hours.
 --------- CPU info (if available) ----------

(52·10¹⁷⁷-43)/9 = 5(7)₁₇₆3_<178> = 1413829 · C172

C172 = P81 · P92

P81 = 271121766413527308744259064278710042949573284426474347177776678588863597246745619_<81>

P92 = 15072995285706770627247105190000837027452280994595682721723013910859090500939619886537534323_<92>

N=4086617107003589385829387979577288185330600643909396240830947574125143689779865724764294534754753069697804881479852073891381332380208481915265408884509921481153504262380937
  ( 172 digits)
SNFS difficulty: 178 digits.
Divisors found:
 r1=271121766413527308744259064278710042949573284426474347177776678588863597246745619 (pp81)
 r2=15072995285706770627247105190000837027452280994595682721723013910859090500939619886537534323 (pp92)
Version: Msieve-1.40
Total time: 105.99 hours.
Scaled time: 193.23 units (timescale=1.823).
Factorization parameters were as follows:
n: 4086617107003589385829387979577288185330600643909396240830947574125143689779865724764294534754753069697804881479852073891381332380208481915265408884509921481153504262380937
m: 100000000000000000000000000000000000
deg: 5
c5: 5200
c0: -43
skew: 0.38
type: snfs
lss: 1
rlim: 6700000
alim: 6700000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 6700000/6700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3350000, 8650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1459175 x 1459403
Total sieving time: 102.82 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 2.80 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,178.000,5,0,0,0,0,0,0,0,0,6700000,6700000,28,28,53,53,2.5,2.5,100000
total time: 105.99 hours.
 --------- CPU info (if available) ----------

2·10²¹⁷+9 = 2(0)₂₁₆9_<218> = 17324807 · 7919188963783_<13> · 107411105875493866921_<21> · 5173938809178624041155896767_<28> · 102699093136418169307668176696792069_<36> · C115

C115 = P57 · P58

P57 = 467066681050485435798497334956180095244989456946079206083_<57>

P58 = 5468458395983536988518042915683384244729834087373257219201_<58>

N=2554134713474691857135037986459326191117445872689622770299892736169738699608043094133510769381527789483430383599683
  ( 115 digits)
Divisors found:
 r1=467066681050485435798497334956180095244989456946079206083 (pp57)
 r2=5468458395983536988518042915683384244729834087373257219201 (pp58)
Version: Msieve-1.40
Total time: 22.32 hours.
Scaled time: 43.68 units (timescale=1.957).
Factorization parameters were as follows:
name: g115
n: 2554134713474691857135037986459326191117445872689622770299892736169738699608043094133510769381527789483430383599683
skew: 60651.13
# norm 2.66e+015
c5: 6900
c4: -682319433
c3: -117961116338270
c2: 2224219007371410074
c1: 119713655432085105195716
c0: -887417118007395530941272320
# alpha -5.12
Y1: 1998997353529
Y0: -12992127184589368498929
# Murphy_E 5.54e-010
# M 67608055054870856438233574117739099823167547769002258983372983365697756513358289959208203033225734867962755866536
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 455680 x 455911
Total sieving time: 21.73 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 22.32 hours.
 --------- CPU info (if available) ----------

(73·10¹³⁴+17)/9 = 8(1)₁₃₃3_<135> = 3⁴ · 1789 · 9296754845646857307863_<22> · C108

C108 = P51 · P57

P51 = 702123156757712519031453798485544502938488592323083_<51>

P57 = 857512216009165830019053825024336782383782476909346058033_<57>

N=602079184062656978792886796353667221061735953627208317903017723089717045559245411279120372197442712003475739
  ( 108 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=702123156757712519031453798485544502938488592323083 (pp51)
 r2=857512216009165830019053825024336782383782476909346058033 (pp57)
Version: Msieve-1.40
Total time: 4.77 hours.
Scaled time: 8.73 units (timescale=1.829).
Factorization parameters were as follows:
n: 602079184062656978792886796353667221061735953627208317903017723089717045559245411279120372197442712003475739
m: 100000000000000000000000000
deg: 5
c5: 730000
c0: 17
skew: 0.12
type: snfs
lss: 1
rlim: 1290000
alim: 1290000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1290000/1290000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [645000, 1620001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 207813 x 208040
Total sieving time: 4.55 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,135.000,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,47,47,2.3,2.3,75000
total time: 4.77 hours.
 --------- CPU info (if available) ----------

(73·10¹⁴⁶+17)/9 = 8(1)₁₄₅3_<147> = 3 · 92119 · 42752273 · 574403817618745025267_<21> · C114

C114 = P42 · P72

P42 = 537815482522942323727899388886316826443949_<42>

P72 = 222228652714126808627854028677300737955480939500280191440675614780670851_<72>

N=119518010089871485840556901782793184277006355051084040481066496229121998790947123624282808570238561315302969630599
  ( 114 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=537815482522942323727899388886316826443949 (pp42)
 r2=222228652714126808627854028677300737955480939500280191440675614780670851 (pp72)
Version: Msieve-1.40
Total time: 9.01 hours.
Scaled time: 17.26 units (timescale=1.916).
Factorization parameters were as follows:
n: 119518010089871485840556901782793184277006355051084040481066496229121998790947123624282808570238561315302969630599
m: 100000000000000000000000000000
deg: 5
c5: 730
c0: 17
skew: 0.47
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 319844 x 320071
Total sieving time: 8.75 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,147.000,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000
total time: 9.01 hours.
 --------- CPU info (if available) ----------

Dec 25, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 25, 2009

2·10²¹⁵+9 = 2(0)₂₁₄9_<216> = 218794321 · C207

C207 = P32 · C176

P32 = 10826531273093526781328991763529_<32>

C176 = [84431521515330295235327680873213130349430459871381881520420584924480627631102287648956120680337807274004266843502840550795215945616015601670178617482078519562517437776926226801_<176>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3239976602
Step 1 took 82088ms
Step 2 took 23591ms
********** Factor found in step 2: 10826531273093526781328991763529
Found probable prime factor of 32 digits: 10826531273093526781328991763529
Composite cofactor 84431521515330295235327680873213130349430459871381881520420584924480627631102287648956120680337807274004266843502840550795215945616015601670178617482078519562517437776926226801 has 176 digits

Dec 25, 2009

Factorizations of 811...113 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Factorizations of 688...883 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Dec 24, 2009 (5th)

By Sinkiti Sibata / Msieve / Dec 24, 2009

(61·10¹⁶²+11)/9 = 6(7)₁₆₁9_<163> = 3566273 · 462804838788405557_<18> · C139

C139 = P39 · P101

P39 = 113990293046369827455829809216336468347_<39>

P101 = 36025247970230741843823484703167564104166807793409098338045741430171486725099060883837298016220812837_<101>

Number: 67779_162
N=4106528573194742072817881820216336322356298983908951601481939266256212139543924891157991054137712590592643943196774682498617901874261770439
  ( 139 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=113990293046369827455829809216336468347 (pp39)
 r2=36025247970230741843823484703167564104166807793409098338045741430171486725099060883837298016220812837 (pp101)
Version: Msieve-1.40
Total time: 51.17 hours.
Scaled time: 105.97 units (timescale=2.071).
Factorization parameters were as follows:
name: 67779_162
n: 4106528573194742072817881820216336322356298983908951601481939266256212139543924891157991054137712590592643943196774682498617901874261770439
m: 100000000000000000000000000000000
deg: 5
c5: 6100
c0: 11
skew: 0.28
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 3900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 751394 x 751640
Total sieving time: 48.65 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.11 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,163.000,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 51.17 hours.
 --------- CPU info (if available) ----------

Dec 24, 2009 (4th)

By Lionel Debroux / ggnfs + msieve / Dec 24, 2009

(26·10¹⁶⁷-11)/3 = 8(6)₁₆₆3_<168> = 7 · 17 · 691 · 229656809 · 1622000506706154937986411401046767_<34> · C122

C122 = P55 · P67

P55 = 6538852158315471876807191983737005179049140997548308893_<55>

P67 = 4327083287726406607500646865729506028074771488004120304654473098593_<67>

Number: 86663_167
N=28294157895160621844921147954393461978100031316274893426210418177756993778953017327769043546792385145405456209408807687549
  ( 122 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=6538852158315471876807191983737005179049140997548308893 (pp55)
 r2=4327083287726406607500646865729506028074771488004120304654473098593 (pp67)
Version: Msieve v. 1.44
Total time: 143.51 hours.
Scaled time: 214.83 units (timescale=1.497).
Factorization parameters were as follows:
n: 28294157895160621844921147954393461978100031316274893426210418177756993778953017327769043546792385145405456209408807687549
m: 1000000000000000000000000000000000
deg: 5
c5: 2600
c0: -11
skew: 0.34
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 4450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 851629 x 851854
Total sieving time: 140.47 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.88 hours.
Time per square root: 1.02 hours.
Prototype def-par.txt line would be:
snfs,168.000,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000
total time: 143.51 hours.
 --------- CPU info (if available) ----------

Dec 24, 2009 (3rd)

By matsui / Msieve / Dec 24, 2009

4·10¹⁷⁹+3 = 4(0)₁₇₈3_<180> = 9679838127597185553923930374350132743_<37> · C143

C143 = P51 · P93

P51 = 191036532994880646588869280641375529254981954340701_<51>

P93 = 216309437884752288522244329757285002058432970681423732981110681293149999573768732312881302121_<93>

N=41323005067574566304410175051619336014247547874804676702862982021554231126531999977945569827460087540832516415965598056089191661607896947926821
  ( 143 digits)
SNFS difficulty: 179 digits.
Divisors found:
 r1=191036532994880646588869280641375529254981954340701 (pp51)
 r2=216309437884752288522244329757285002058432970681423732981110681293149999573768732312881302121 (pp93)
Version: Msieve v. 1.43
Total time: 10.99 hours.
Scaled time: 20.72 units (timescale=1.886).
Factorization parameters were as follows:
n: 41323005067574566304410175051619336014247547874804676702862982021554231126531999977945569827460087540832516415965598056089191661607896947926821
m: 200000000000000000000000000000000000
deg: 5
c5: 1250
c0: 3
skew: 0.30
type: snfs
lss: 1
rlim: 6900000
alim: 6900000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

Factor base limits: 6900000/6900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3450000, 9050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1522746 x 1522973
Total sieving time:
Total relation processing time:
Matrix solve time:
Time per square root:
Prototype def-par.txt line would be:
snfs,179.000,5,0,0,0,0,0,0,0,0,6900000,6900000,28,28,53,53,2.5,2.5,100000
total time:

Dec 24, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 24, 2009

2·10²¹⁷+9 = 2(0)₂₁₆9_<218> = 17324807 · 7919188963783_<13> · 107411105875493866921_<21> · 5173938809178624041155896767_<28> · C150

C150 = P36 · C115

P36 = 102699093136418169307668176696792069_<36>

C115 = [2554134713474691857135037986459326191117445872689622770299892736169738699608043094133510769381527789483430383599683_<115>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=34838519
Step 1 took 15671ms
Step 2 took 6740ms
********** Factor found in step 2: 102699093136418169307668176696792069
Found probable prime factor of 36 digits: 102699093136418169307668176696792069
Composite cofactor 2554134713474691857135037986459326191117445872689622770299892736169738699608043094133510769381527789483430383599683 has 115 digits

Dec 24, 2009

By Dmitry Domanov / ECMNET, GMP-ECM / Dec 24, 2009

2·10²⁴⁸+9 = 2(0)₂₄₇9_<249> = 11² · 41 · 11107489204958914007580419_<26> · C220

C220 = P38 · C182

P38 = 63380532867978197628346597706813686961_<38>

C182 = [57264962758655073499640385596911912843405767555810142578271507896184241753434450997205171439568565855573766028794311486964572257868682891212249064270760929321618096156966261093582291_<182>]

Factor=63380532867978197628346597706813686961  Method=ECM  B1=11000000  Sigma=2228662224

Dec 23, 2009 (5th)

By Dmitry Domanov / GGNFS/msieve / Dec 23, 2009

(67·10¹⁶⁸-13)/9 = 7(4)₁₆₇3_<169> = 3 · 165813763 · 3342031677563_<13> · C148

C148 = P48 · P101

P48 = 134458719408023859753384075009085595975442745241_<48>

P101 = 33303580730790575224290199066707126131966069352843461148291487710116357017637216068492699986663689089_<101>

N=4477956816763840155316795837966177700076915229952603768994579222454907835059410228107125848550858785511065070923028621198385715228005928586658375449
  ( 148 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=134458719408023859753384075009085595975442745241 (pp48)
 r2=33303580730790575224290199066707126131966069352843461148291487710116357017637216068492699986663689089 (pp101)
Version: Msieve-1.40
Total time: 74.13 hours.
Scaled time: 69.09 units (timescale=0.932).
Factorization parameters were as follows:
n: 4477956816763840155316795837966177700076915229952603768994579222454907835059410228107125848550858785511065070923028621198385715228005928586658375449
m: 1000000000000000000000000000000000
deg: 5
c5: 67000
c0: -13
skew: 0.18
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 5350001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 977381 x 977607
Total sieving time: 72.12 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.63 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,169.000,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000
total time: 74.13 hours.
 --------- CPU info (if available) ----------

Dec 23, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Dec 23, 2009

(61·10¹⁹⁰+11)/9 = 6(7)₁₈₉9_<191> = 3 · 139 · 1699 · C185

C185 = P70 · P116

P70 = 1246377540553231270517304854428178026702512130082057989845012070878697_<70>

P116 = 76755282987069738064818275995174521908382367033378985164674128789540497512724588327483330081841463307730148032229929_<116>

Number: n
N=95666060833891254663524428642293149980702116744901116579759539435353816221105909073016258368623915856524119531135930964861228537280044514515913265071678188153812833586377905719371922513
  ( 185 digits)
SNFS difficulty: 191 digits.
Divisors found:

Wed Dec 23 21:52:20 2009  prp70 factor: 1246377540553231270517304854428178026702512130082057989845012070878697
Wed Dec 23 21:52:20 2009  prp116 factor: 76755282987069738064818275995174521908382367033378985164674128789540497512724588327483330081841463307730148032229929
Wed Dec 23 21:52:20 2009  elapsed time 05:36:34 (Msieve 1.42 - dependency 2)

Version: GGNFS-0.77.1-20050930-k8
Total time: ~ 24.00 hours.
Scaled time: 0.00 units (timescale=0.841).
Factorization parameters were as follows:
name: KA_6_7_189_9
n: 95666060833891254663524428642293149980702116744901116579759539435353816221105909073016258368623915856524119531135930964861228537280044514515913265071678188153812833586377905719371922513
m: 100000000000000000000000000000000000000
deg: 5
c5: 61
c0: 11
skew: 0.71
type: snfs
lss: 1
rlim: 11000000
alim: 11000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 100000)
Primes: RFBsize:726517, AFBsize:725315, 
Relations: 
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2883289 hash collisions in 27132787 relations
Msieve: matrix is 1475928 x 1476154 (394.4 MB)

Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,56,56,2.5,2.5,100000
total time: 0.00 hours.
 --------- CPU info (if available) ----------

Dec 23, 2009 (3rd)

By Serge Batalov / GMP-ECM / Dec 23, 2009

2·10²⁴³+9 = 2(0)₂₄₂9_<244> = 7 · 41 · 227 · 421 · C236

C236 = P30 · C207

P30 = 275090641212239281388428941781_<30>

C207 = [265072290148445136560818600872536028741814594689355689084826099010496505157655840038152578998319195828775892660393313465582532270823126127399141068370073694442972122406251271400377317474155401123483513864341_<207>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=1128384573
Step 1 took 12352ms
Step 2 took 5633ms
********** Factor found in step 2: 275090641212239281388428941781
Found probable prime factor of 30 digits: 275090641212239281388428941781
Composite cofactor has 207 digits

2·10²⁴¹+9 = 2(0)₂₄₀9_<242> = 23 · 11827 · 229376321 · 2727862121_<10> · 1386106253052049787_<19> · C200

C200 = P36 · C165

P36 = 105073858185151552219454459705794081_<36>

C165 = [806799021435633334778607190153883588562873305480699334566341552479925686226196132085236650925436195560862698365853607109043802721553143632271788112834805134902749927_<165>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=3024908771
Step 1 took 12365ms
Step 2 took 6264ms
********** Factor found in step 2: 105073858185151552219454459705794081
Found probable prime factor of 36 digits: 105073858185151552219454459705794081
Composite cofactor has 165 digits

2·10²¹⁴+9 = 2(0)₂₁₃9_<215> = 11 · 792769 · C208

C208 = P30 · C179

P30 = 108073286126852074103935205123_<30>

C179 = [21221315106860899445933896803600324185433315879614766539100261924328043844792993941275529908813313478966866705232058311046676551390445994002560932483470016746642554197765912727337_<179>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=1593094740
Step 1 took 9704ms
********** Factor found in step 1: 108073286126852074103935205123
Found probable prime factor of 30 digits: 108073286126852074103935205123
Composite cofactor has 179 digits

2·10²⁴⁵+9 = 2(0)₂₄₄9_<246> = 54073807 · 17143423889_<11> · 52441815947_<11> · 37907299299807143021_<20> · C198

C198 = P29 · C169

P29 = 48780799114142980351071675283_<29>

C169 = [2224825781921510311089625162072229302525980695051171437726573831123721374767914069312979236788707893034386059250449392062243210924920047371675945471981646433600136489923_<169>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=2117120045
Step 1 took 12313ms
Step 2 took 6164ms
********** Factor found in step 2: 48780799114142980351071675283
Found probable prime factor of 29 digits: 48780799114142980351071675283
Composite cofactor has 169 digits

2·10²⁰²+9 = 2(0)₂₀₁9_<203> = 11 · 8179 · 114752140758891510899_<21> · C178

C178 = P29 · P150

P29 = 10154618909493427970970822721_<29>

P150 = 190771140703131610829744107752674358172987961363517807716872722844099059240912537213495175536293431424182489626904601379938938663722516836938490051459_<150>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=1119420523
Step 1 took 8429ms
Step 2 took 4324ms
********** Factor found in step 2: 10154618909493427970970822721
Found probable prime factor of 29 digits: 10154618909493427970970822721
Probable prime (finally!..) cofactor has 150 digits

2·10²¹⁶+9 = 2(0)₂₁₅9_<217> = 11 · 107 · 37489 · C209

C209 = P29 · C181

P29 = 17914893243474064093353886339_<29>

C181 = [2530086983479833387914671916161109783095426465559142662484628525176449853888833345433073938167065639727700285403571069487621676918739169062674186666507709307416989039849336443021227_<181>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=3828974228
Step 1 took 12349ms
Step 2 took 6312ms
********** Factor found in step 2: 17914893243474064093353886339
Found probable prime factor of 29 digits: 17914893243474064093353886339
Composite cofactor has 181 digits

2·10²¹²+9 = 2(0)₂₁₁9_<213> = 11 · 17 · 20353 · 1381923056737330482439098571_<28> · C179

C179 = P31 · C149

P31 = 2240943540763641964491268576729_<31>

C149 = [16968567436598174394441700560052214494982970741460114303653787912012932829033703060581255810085925490346029906192195604150265745128887761473827164841_<149>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=1282349060
Step 1 took 8312ms
Step 2 took 4321ms
********** Factor found in step 2: 2240943540763641964491268576729
Found probable prime factor of 31 digits: 2240943540763641964491268576729
Composite cofactor has 149 digits

Dec 23, 2009 (2nd)

By Sinkiti Sibata / Msieve / Dec 23, 2009

(65·10¹⁶⁶+61)/9 = 7(2)₁₆₅9_<167> = 17 · 89 · 137 · 224359 · 342267997426477_<15> · 3264304339047261683_<19> · C124

C124 = P56 · P68

P56 = 21177806111690930656883533457082414880466382692793184597_<56>

P68 = 65634163160831350012251236459552088191190938657828797749306617552113_<68>

Number: 72229_166
N=1389987581723173895596548377609939173843736140303008202201819784338719027287887136391659956712211103906587187700701876403461
  ( 124 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=21177806111690930656883533457082414880466382692793184597 (pp56)
 r2=65634163160831350012251236459552088191190938657828797749306617552113 (pp68)
Version: Msieve-1.40
Total time: 52.43 hours.
Scaled time: 174.18 units (timescale=3.322).
Factorization parameters were as follows:
name:72229_166
n: 1389987581723173895596548377609939173843736140303008202201819784338719027287887136391659956712211103906587187700701876403461
m: 1000000000000000000000000000000000
deg: 5
c5: 650
c0: 61
skew: 0.62
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 5000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 858499 x 858747
Total sieving time: 50.86 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.40 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,167.000,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 52.43 hours.
 --------- CPU info (if available) ----------

Dec 23, 2009

Factorizations of 200...009 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Dec 22, 2009 (7th)

By Robert Backstrom / GGNFS, Msieve / Dec 22, 2009

(31·10¹⁹⁰-13)/9 = 3(4)₁₈₉3_<191> = 3 · 19 · 59 · 359 · C185

C185 = P61 · P124

P61 = 3258043336272548779008002886122874571288404601111566773541731_<61>

P124 = 8756710898999513727194865930909654610791856616776070564855670702424349065435730402674191725009366629927668168079773573912709_<124>

Number: n
N=28529743592150565629776143667689964147315447760981121316476488316195700420390373401885705613724021482712862027491076862534400198493390256613999839681247298302305396548250744787362759279
  ( 185 digits)
SNFS difficulty: 191 digits.
Divisors found:

Tue Dec 22 19:08:25 2009  prp61 factor: 3258043336272548779008002886122874571288404601111566773541731
Tue Dec 22 19:08:25 2009  prp124 factor: 8756710898999513727194865930909654610791856616776070564855670702424349065435730402674191725009366629927668168079773573912709
Tue Dec 22 19:08:25 2009  elapsed time 07:20:56 (Msieve 1.42 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: ~ 24.00 hours.
Scaled time: 0.00 units (timescale=0.841).
Factorization parameters were as follows:
name: KA_3_4_189_3
n: 28529743592150565629776143667689964147315447760981121316476488316195700420390373401885705613724021482712862027491076862534400198493390256613999839681247298302305396548250744787362759279
m: 100000000000000000000000000000000000000
deg: 5
c5: 31
c0: -13
skew: 0.84
type: snfs
lss: 1
rlim: 10900000
alim: 10900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10900000/10900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 100000)
Primes: RFBsize:720341, AFBsize:720005, 
Relations: 
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2227733 hash collisions in 23635251 relations
Msieve: matrix is 1696684 x 1696911 (458.6 MB)

Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,10900000,10900000,28,28,56,56,2.5,2.5,100000
total time: 0.00 hours.
 --------- CPU info (if available) ----------

Dec 22, 2009 (6th)

By Jo Yeong Uk / GMP-ECM / Dec 22, 2009

5·10¹⁹⁹-1 = 4(9)₁₉₉_<200> = 7 · 233 · 29033 · 110474303778793_<15> · C178

C178 = P49 · C130

P49 = 4139828065935440294061146400286899184110194422807_<49>

C130 = [2308769366424866095094566070967993074645236095443441497801367460951396604272172809333678904945474562731467084910099433652462194263_<130>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 9557908220897645269387286854345517770093707575325287236420262235191730767688983930835321863692114212272671692252102550740452830644042128960613717269023912901214844723199991756241 (178 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=6195808489
Step 1 took 17127ms
Step 2 took 6986ms
********** Factor found in step 2: 4139828065935440294061146400286899184110194422807
Found probable prime factor of 49 digits: 4139828065935440294061146400286899184110194422807
Composite cofactor 2308769366424866095094566070967993074645236095443441497801367460951396604272172809333678904945474562731467084910099433652462194263 has 130 digits

Dec 22, 2009 (5th)

By Sinkiti Sibata / Msieve / Dec 22, 2009

(61·10¹⁵⁶+11)/9 = 6(7)₁₅₅9_<157> = 1031 · 856255798213763_<15> · C139

C139 = P54 · P86

P54 = 661542050937201180007812167768624715936624530911929887_<54>

P86 = 11605602178758045128535674160139984140449568658770410887945323629142397528821410828089_<86>

Number: 67779_156
N=7677593867696847684957279122264293269278228013253544279472612563182051822662480904492016418127582884422641770308593475797958842809778195943
  ( 139 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=661542050937201180007812167768624715936624530911929887 (pp54)
 r2=11605602178758045128535674160139984140449568658770410887945323629142397528821410828089 (pp86)
Version: Msieve v. 1.42
Total time: 1.57 hours.
Scaled time: 1.25 units (timescale=0.796).
Factorization parameters were as follows:
name: 67779_156
n: 7677593867696847684957279122264293269278228013253544279472612563182051822662480904492016418127582884422641770308593475797958842809778195943
m: 10000000000000000000000000000000
deg: 5
c5: 610
c0: 11
skew: 0.45
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 621877 x 622123
Total sieving time: 0.00 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.26 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,157.000,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 1.57 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.30 BogoMIPS (lpj=1860651)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860572)
Total of 2 processors activated (7442.44 BogoMIPS).

Total time: 21 hours 36 min.

(61·10¹⁶⁰+11)/9 = 6(7)₁₅₉9_<161> = 3 · 37096537 · 318602231 · 306165298424039_<15> · C130

C130 = P36 · P95

P36 = 329941288039669879685932268781811517_<36>

P95 = 18923055277115022873260438445332513123376717790659675808990381692014965745788428750512725960013_<95>

Number: 67779_160
N=6243497231777202897086408485077339585620666600947801130141434691549613209529400593909446684764902280951362671525963210087044869721
  ( 130 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=329941288039669879685932268781811517 (pp36)
 r2=18923055277115022873260438445332513123376717790659675808990381692014965745788428750512725960013 (pp95)
Version: Msieve-1.40
Total time: 32.20 hours.
Scaled time: 67.15 units (timescale=2.085).
Factorization parameters were as follows:
name: 67779_160
n: 6243497231777202897086408485077339585620666600947801130141434691549613209529400593909446684764902280951362671525963210087044869721
m: 100000000000000000000000000000000
deg: 5
c5: 61
c0: 11
skew: 0.71
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 2950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 613100 x 613348
Total sieving time: 30.38 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.37 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 32.20 hours.
 --------- CPU info (if available) ----------

Dec 22, 2009 (4th)

By Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve (Lionel Debroux + Jeff Gilchrist) / Dec 22, 2009

(47·10²⁰⁵+61)/9 = 5(2)₂₀₄9_<206> = 17 · 8761 · C201

C201 = P41 · P43 · P118

P41 = 20194671096761091832186829435988704365487_<41>

P43 = 9471896794686022886422445694883334722867319_<43>

P118 = 1833069811112554214479030625907879474746219426511471381872548281127265355644588248308625697591882480899120783940961589_<118>

Sun Dec 20 15:19:03 2009  Msieve v. 1.43
Sun Dec 20 15:19:03 2009  random seeds: 5540a3c0 8848d85a
Sun Dec 20 15:19:03 2009  factoring
350632967108389602464278333941345818851072750372454274103964912830406294085567872471059724730739992226392516448043281536637787938673548025153066210694603907841719802481735379537806067143975118487831917
(201 digits)
Sun Dec 20 15:19:05 2009  no P-1/P+1/ECM available, skipping
Sun Dec 20 15:19:05 2009  commencing number field sieve (201-digit input)
Sun Dec 20 15:19:05 2009  R0: -100000000000000000000000000000000000000000
Sun Dec 20 15:19:05 2009  R1:  1
Sun Dec 20 15:19:05 2009  A0:  61
Sun Dec 20 15:19:05 2009  A1:  0
Sun Dec 20 15:19:05 2009  A2:  0
Sun Dec 20 15:19:05 2009  A3:  0
Sun Dec 20 15:19:05 2009  A4:  0
Sun Dec 20 15:19:05 2009  A5:  47
Sun Dec 20 15:19:05 2009  skew 1.05, size 2.211741e-14, alpha
0.903629, combined = 7.847376e-12
Sun Dec 20 15:19:05 2009
Sun Dec 20 15:19:05 2009  commencing linear algebra
Sun Dec 20 15:19:06 2009  read 2801241 cycles
Sun Dec 20 15:19:13 2009  cycles contain 7840037 unique relations
Sun Dec 20 15:20:33 2009  read 7840037 relations
Sun Dec 20 15:20:48 2009  using 20 quadratic characters above 536866608
Sun Dec 20 15:21:44 2009  building initial matrix
Sun Dec 20 15:24:22 2009  memory use: 1037.1 MB
Sun Dec 20 15:24:27 2009  read 2801241 cycles
Sun Dec 20 15:24:30 2009  matrix is 2800834 x 2801241 (826.2 MB) with
weight 244934261 (87.44/col)
Sun Dec 20 15:24:30 2009  sparse part has weight 185757819 (66.31/col)
Sun Dec 20 15:25:51 2009  filtering completed in 3 passes
Sun Dec 20 15:25:52 2009  matrix is 2794922 x 2795122 (825.1 MB) with
weight 244600938 (87.51/col)
Sun Dec 20 15:25:52 2009  sparse part has weight 185554338 (66.39/col)
Sun Dec 20 15:26:18 2009  read 2795122 cycles
Sun Dec 20 15:26:21 2009  matrix is 2794922 x 2795122 (825.1 MB) with
weight 244600938 (87.51/col)
Sun Dec 20 15:26:21 2009  sparse part has weight 185554338 (66.39/col)
Sun Dec 20 15:26:22 2009  saving the first 48 matrix rows for later
Sun Dec 20 15:26:24 2009  matrix is 2794874 x 2795122 (786.2 MB) with
weight 193230385 (69.13/col)
Sun Dec 20 15:26:24 2009  sparse part has weight 178134501 (63.73/col)
Sun Dec 20 15:26:24 2009  matrix includes 64 packed rows
Sun Dec 20 15:26:24 2009  using block size 65536 for processor cache
size 6144 kB
Sun Dec 20 15:26:40 2009  commencing Lanczos iteration (5 threads)
Sun Dec 20 15:26:40 2009  memory use: 868.2 MB
Sun Dec 20 15:26:55 2009  linear algebra at 0.0%, ETA 14h22m
Mon Dec 21 04:57:45 2009  lanczos halted after 44202 iterations (dim = 2794871)
Mon Dec 21 04:57:53 2009  recovered 35 nontrivial dependencies
Mon Dec 21 04:57:54 2009  BLanczosTime: 49129
Mon Dec 21 04:57:54 2009  elapsed time 13:38:51
Mon Dec 21 05:37:36 2009
Mon Dec 21 05:37:36 2009
Mon Dec 21 05:37:36 2009  Msieve v. 1.43
Mon Dec 21 05:37:36 2009  random seeds: 0aeca43c 249cbc15
Mon Dec 21 05:37:36 2009  factoring
350632967108389602464278333941345818851072750372454274103964912830406294085567872471059724730739992226392516448043281536637787938673548025153066210694603907841719802481735379537806067143975118487831917
(201 digits)
Mon Dec 21 05:37:38 2009  no P-1/P+1/ECM available, skipping
Mon Dec 21 05:37:38 2009  commencing number field sieve (201-digit input)
Mon Dec 21 05:37:38 2009  R0: -100000000000000000000000000000000000000000
Mon Dec 21 05:37:38 2009  R1:  1
Mon Dec 21 05:37:38 2009  A0:  61
Mon Dec 21 05:37:38 2009  A1:  0
Mon Dec 21 05:37:38 2009  A2:  0
Mon Dec 21 05:37:38 2009  A3:  0
Mon Dec 21 05:37:39 2009  A4:  0
Mon Dec 21 05:37:39 2009  A5:  47
Mon Dec 21 05:37:39 2009  skew 1.05, size 2.211741e-14, alpha
0.903629, combined = 7.847376e-12
Mon Dec 21 05:37:39 2009
Mon Dec 21 05:37:39 2009  commencing square root phase
Mon Dec 21 05:37:39 2009  reading relations for dependency 1
Mon Dec 21 05:37:39 2009  read 1398917 cycles
Mon Dec 21 05:37:43 2009  cycles contain 3920050 unique relations
Mon Dec 21 05:38:29 2009  read 3920050 relations
Mon Dec 21 05:38:59 2009  multiplying 3920050 relations
Mon Dec 21 05:42:51 2009  multiply complete, coefficients have about
115.67 million bits
Mon Dec 21 05:42:52 2009  initial square root is modulo 200748451
Mon Dec 21 05:50:46 2009  reading relations for dependency 2
Mon Dec 21 05:50:46 2009  read 1397154 cycles
Mon Dec 21 05:50:50 2009  cycles contain 3917288 unique relations
Mon Dec 21 05:51:37 2009  read 3917288 relations
Mon Dec 21 05:52:06 2009  multiplying 3917288 relations
Mon Dec 21 05:55:55 2009  multiply complete, coefficients have about
115.60 million bits
Mon Dec 21 05:55:56 2009  initial square root is modulo 198217301
Mon Dec 21 06:03:50 2009  sqrtTime: 1571
Mon Dec 21 06:03:50 2009  prp41 factor:
20194671096761091832186829435988704365487
Mon Dec 21 06:03:50 2009  prp43 factor:
9471896794686022886422445694883334722867319
Mon Dec 21 06:03:50 2009  prp118 factor:
1833069811112554214479030625907879474746219426511471381872548281127265355644588248308625697591882480899120783940961589
Mon Dec 21 06:03:50 2009  elapsed time 00:26:14

(52·10²⁰⁴-61)/9 = 5(7)₂₀₃1_<205> = 7523 · C201

C201 = P91 · P111

P91 = 3211532119533007796194142514339179383220263052671540257631331121185606037989314798053426139_<91>

P111 = 239142906066221075904871087733166044872867257339926740249703577575802462447115323671565908100642055353656660443_<111>

Mon Dec 21 06:29:10 2009  Msieve v. 1.43
Mon Dec 21 06:29:10 2009  random seeds: 7dbbed41 b0edb4a0
Mon Dec 21 06:29:10 2009  factoring
768015123990133959561049817596408052343184604250668320853087568493656490466273797391702482756583514259973119470660345311415363256384125718167988538851226608770141935102722022833680417091290413103519577
(201 digits)
Mon Dec 21 06:29:13 2009  no P-1/P+1/ECM available, skipping
Mon Dec 21 06:29:13 2009  commencing number field sieve (201-digit input)
Mon Dec 21 06:29:13 2009  R0: -100000000000000000000000000000000000000000
Mon Dec 21 06:29:13 2009  R1:  1
Mon Dec 21 06:29:13 2009  A0: -305
Mon Dec 21 06:29:13 2009  A1:  0
Mon Dec 21 06:29:13 2009  A2:  0
Mon Dec 21 06:29:13 2009  A3:  0
Mon Dec 21 06:29:13 2009  A4:  0
Mon Dec 21 06:29:13 2009  A5:  26
Mon Dec 21 06:29:13 2009  skew 1.64, size 2.306128e-14, alpha
0.489715, combined = 8.078711e-12
Mon Dec 21 06:29:13 2009
Mon Dec 21 06:29:13 2009  commencing linear algebra
Mon Dec 21 06:29:13 2009  read 2813450 cycles
Mon Dec 21 06:29:20 2009  cycles contain 7921881 unique relations
Mon Dec 21 06:30:39 2009  read 7921881 relations
Mon Dec 21 06:30:55 2009  using 20 quadratic characters above 536868812
Mon Dec 21 06:31:51 2009  building initial matrix
Mon Dec 21 06:34:32 2009  memory use: 1056.5 MB
Mon Dec 21 06:34:35 2009  read 2813450 cycles
Mon Dec 21 06:34:39 2009  matrix is 2812972 x 2813450 (831.2 MB) with
weight 247146150 (87.84/col)
Mon Dec 21 06:34:39 2009  sparse part has weight 186954905 (66.45/col)
Mon Dec 21 06:35:59 2009  filtering completed in 3 passes
Mon Dec 21 06:36:01 2009  matrix is 2806020 x 2806220 (829.9 MB) with
weight 246729422 (87.92/col)
Mon Dec 21 06:36:01 2009  sparse part has weight 186695144 (66.53/col)
Mon Dec 21 06:36:26 2009  read 2806220 cycles
Mon Dec 21 06:36:30 2009  matrix is 2806020 x 2806220 (829.9 MB) with
weight 246729422 (87.92/col)
Mon Dec 21 06:36:30 2009  sparse part has weight 186695144 (66.53/col)
Mon Dec 21 06:36:30 2009  saving the first 48 matrix rows for later
Mon Dec 21 06:36:32 2009  matrix is 2805972 x 2806220 (790.2 MB) with
weight 195218319 (69.57/col)
Mon Dec 21 06:36:32 2009  sparse part has weight 179071456 (63.81/col)
Mon Dec 21 06:36:32 2009  matrix includes 64 packed rows
Mon Dec 21 06:36:33 2009  using block size 65536 for processor cache
size 6144 kB
Mon Dec 21 06:36:49 2009  commencing Lanczos iteration (5 threads)
Mon Dec 21 06:36:49 2009  memory use: 870.2 MB
Mon Dec 21 06:37:03 2009  linear algebra at 0.0%, ETA 13h22m
Mon Dec 21 20:02:14 2009  lanczos halted after 44375 iterations (dim = 2805971)
Mon Dec 21 20:02:21 2009  recovered 36 nontrivial dependencies
Mon Dec 21 20:02:21 2009  BLanczosTime: 48788
Mon Dec 21 20:02:21 2009  elapsed time 13:33:11
Mon Dec 21 20:03:02 2009
Mon Dec 21 20:03:02 2009
Mon Dec 21 20:03:02 2009  Msieve v. 1.43
Mon Dec 21 20:03:02 2009  random seeds: 4c5d3413 72c52ec2
Mon Dec 21 20:03:02 2009  factoring
768015123990133959561049817596408052343184604250668320853087568493656490466273797391702482756583514259973119470660345311415363256384125718167988538851226608770141935102722022833680417091290413103519577
(201 digits)
Mon Dec 21 20:03:04 2009  no P-1/P+1/ECM available, skipping
Mon Dec 21 20:03:04 2009  commencing number field sieve (201-digit input)
Mon Dec 21 20:03:04 2009  R0: -100000000000000000000000000000000000000000
Mon Dec 21 20:03:04 2009  R1:  1
Mon Dec 21 20:03:04 2009  A0: -305
Mon Dec 21 20:03:04 2009  A1:  0
Mon Dec 21 20:03:04 2009  A2:  0
Mon Dec 21 20:03:04 2009  A3:  0
Mon Dec 21 20:03:04 2009  A4:  0
Mon Dec 21 20:03:04 2009  A5:  26
Mon Dec 21 20:03:04 2009  skew 1.64, size 2.306128e-14, alpha
0.489715, combined = 8.078711e-12
Mon Dec 21 20:03:04 2009
Mon Dec 21 20:03:04 2009  commencing square root phase
Mon Dec 21 20:03:04 2009  reading relations for dependency 1
Mon Dec 21 20:03:05 2009  read 1402676 cycles
Mon Dec 21 20:03:08 2009  cycles contain 3955496 unique relations
Mon Dec 21 20:03:55 2009  read 3955496 relations
Mon Dec 21 20:04:25 2009  multiplying 3955496 relations
Mon Dec 21 20:08:13 2009  multiply complete, coefficients have about
114.53 million bits
Mon Dec 21 20:08:14 2009  initial square root is modulo 166254931
Mon Dec 21 20:15:59 2009  reading relations for dependency 2
Mon Dec 21 20:15:59 2009  read 1402788 cycles
Mon Dec 21 20:16:03 2009  cycles contain 3959826 unique relations
Mon Dec 21 20:16:49 2009  read 3959826 relations
Mon Dec 21 20:17:19 2009  multiplying 3959826 relations
Mon Dec 21 20:21:07 2009  multiply complete, coefficients have about
114.66 million bits
Mon Dec 21 20:21:08 2009  initial square root is modulo 169698701
Mon Dec 21 20:28:54 2009  reading relations for dependency 3
Mon Dec 21 20:28:55 2009  read 1403085 cycles
Mon Dec 21 20:28:58 2009  cycles contain 3957196 unique relations
Mon Dec 21 20:29:45 2009  read 3957196 relations
Mon Dec 21 20:30:14 2009  multiplying 3957196 relations
Mon Dec 21 20:34:02 2009  multiply complete, coefficients have about
114.58 million bits
Mon Dec 21 20:34:04 2009  initial square root is modulo 167615221
Mon Dec 21 20:41:49 2009  sqrtTime: 2325
Mon Dec 21 20:41:49 2009  prp91 factor:
3211532119533007796194142514339179383220263052671540257631331121185606037989314798053426139
Mon Dec 21 20:41:49 2009  prp111 factor:
239142906066221075904871087733166044872867257339926740249703577575802462447115323671565908100642055353656660443
Mon Dec 21 20:41:49 2009  elapsed time 00:38:47

Dec 22, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 22, 2009

(61·10¹⁶⁹+11)/9 = 6(7)₁₆₈9_<170> = 3 · 44939 · 665221 · 1479879893_<10> · 15992251210919_<14> · 17093209147337_<14> · C124

C124 = P34 · P91

P34 = 1241527496479518969376421541593971_<34>

P91 = 1504737326775329431837876707667921530091717850110212903089127410272542747798721969528414183_<91>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1130343346
Step 1 took 11375ms
Step 2 took 5675ms
********** Factor found in step 2: 1241527496479518969376421541593971
Found probable prime factor of 34 digits: 1241527496479518969376421541593971
Probable prime cofactor 1504737326775329431837876707667921530091717850110212903089127410272542747798721969528414183 has 91 digits

Dec 22, 2009 (2nd)

By Erik Branger / GMP-ECM / Dec 22, 2009

(7·10¹⁹⁸-61)/9 = (7)₁₉₇1_<198> = 3 · 55217759 · 16455860360011147359007_<23> · C168

C168 = P39 · P129

P39 = 434084681211224686141852439499199000759_<39>

P129 = 657295177045586107322565512403951199388892719101664080289634387135256356887900786390289588541880076660837466117973684510067141071_<129>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 285321767389508735329154872093616199691336844403413182896276528395142827577131174381103348822433774083626337309145249185346327131003838382411204837961455467643089072889 (168 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2338097098
Step 1 took 60922ms
Step 2 took 25844ms
********** Factor found in step 2: 434084681211224686141852439499199000759
Found probable prime factor of 39 digits: 434084681211224686141852439499199000759
Probable prime cofactor 657295177045586107322565512403951199388892719101664080289634387135256356887900786390289588541880076660837466117973684510067141071 has 129 digits

Dec 22, 2009

By Dmitry Domanov / GGNFS/msieve / Dec 22, 2009

(16·10¹⁹⁴-7)/9 = 1(7)₁₉₄_<195> = 3² · 47 · 658871 · 141500762332327_<15> · C172

C172 = P65 · P107

P65 = 50759659653424490277812732539608015788481050765357913219568146221_<65>

P107 = 88809460563826870360116122356762381837736186016835833547259653844156804262828325126109903907817049613269507_<107>

N=4507937992224076175282785699191828465701998428817043371078391278475687732184850987495627021938332564937967244359115982438252106208394489099068936319590238462061614856583047
  ( 172 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=50759659653424490277812732539608015788481050765357913219568146221 (pp65)
 r2=88809460563826870360116122356762381837736186016835833547259653844156804262828325126109903907817049613269507 (pp107)
Version: Msieve-1.40
Total time: 653.14 hours.
Scaled time: 609.38 units (timescale=0.933).
Factorization parameters were as follows:
n: 4507937992224076175282785699191828465701998428817043371078391278475687732184850987495627021938332564937967244359115982438252106208394489099068936319590238462061614856583047
m: 200000000000000000000000000000000000000
deg: 5
c5: 5000
c0: -7
skew: 0.27
type: snfs
lss: 1
rlim: 12500000
alim: 12500000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 240000Factor base limits: 12500000/12500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6250000, 13450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2046136 x 2046361
Total sieving time: 643.51 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 8.29 hours.
Time per square root: 0.93 hours.
Prototype def-par.txt line would be:
snfs,195.000,5,0,0,0,0,0,0,0,0,12500000,12500000,28,28,55,55,2.5,2.5,100000
total time: 653.14 hours.
 --------- CPU info (if available) ----------

Dec 21, 2009 (8th)

By Erik Branger / GMP-ECM / Dec 21, 2009

(7·10¹⁸¹-61)/9 = (7)₁₈₀1_<181> = 1543 · 401279 · 418897712018139077_<18> · C155

C155 = P36 · P120

P36 = 268433173310371919110756037126438297_<36>

P120 = 111711786778438585359052002351568932688057440788273618433487598683804565986777722541166941624891570654575541803729075647_<120>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 29987149421107919103277239628662886957675353245492249296599091718376560326703805877339985194027146015977494170980827460525338426184127596850743513190853159 (155 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3585440498
Step 1 took 86331ms
Step 2 took 16988ms
********** Factor found in step 2: 268433173310371919110756037126438297
Found probable prime factor of 36 digits: 268433173310371919110756037126438297
Probable prime cofactor 111711786778438585359052002351568932688057440788273618433487598683804565986777722541166941624891570654575541803729075647 has 120 digits

(7·10¹⁸²-61)/9 = (7)₁₈₁1_<182> = 89 · 997 · 30467369 · 17618593319_<11> · C160

C160 = P36 · C124

P36 = 196795518289527012783177637059304087_<36>

C124 = [8297532807384384619591502124535182691958946812580208156234462702919765706096384805864725674578023949954423362371961815181391_<124>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 1632917269353564083516157160874442162362313033488821728473083869495445441341139923036407878727107841361742487465761237276409809989350912818623879601262132645017 (160 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=866390266
Step 1 took 54928ms
Step 2 took 17971ms
********** Factor found in step 2: 196795518289527012783177637059304087
Found probable prime factor of 36 digits: 196795518289527012783177637059304087
Composite cofactor 8297532807384384619591502124535182691958946812580208156234462702919765706096384805864725674578023949954423362371961815181391 has 124 digits

(7·10¹⁸⁹-61)/9 = (7)₁₈₈1_<189> = 3 · 1291 · 355909522613_<12> · 6586408395714765506229052421915313517957_<40> · C134

C134 = P36 · P99

P36 = 382640466874904910800421145827775571_<36>

P99 = 223886997322957868294489493212024580830634045157977060128729169814295853294679370899387519951925857_<99>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 85668225182877184644786666541917164742621853107779269580528230063969136871950475692301384534838463105695144272049997293525583827839347 (134 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3346361410
Step 1 took 39203ms
Step 2 took 14056ms
********** Factor found in step 2: 382640466874904910800421145827775571
Found probable prime factor of 36 digits: 382640466874904910800421145827775571
Probable prime cofactor 223886997322957868294489493212024580830634045157977060128729169814295853294679370899387519951925857 has 99 digits

Dec 21, 2009 (7th)

By Wataru Sakai / Msieve / Dec 21, 2009

(29·10¹⁸²+43)/9 = 3(2)₁₈₁7_<183> = 3 · 742607 · C177

C177 = P62 · P115

P62 = 92642261978496379962548769773717521411016408848388445396158257_<62>

P115 = 1561226968708799973532631702023503117190130380194927134171352062656951184851221466845822869614201993417026721388591_<115>

Number: 32227_182
N=144635597843014417326267335760917157268120832967380333618464958460406927765840353521320708540866713359027597918424425580970025070336540602778330136138505841457739298723830245887
  ( 177 digits)
SNFS difficulty: 183 digits.
Divisors found:
 r1=92642261978496379962548769773717521411016408848388445396158257
 r2=1561226968708799973532631702023503117190130380194927134171352062656951184851221466845822869614201993417026721388591
Version: 
Total time: 343.63 hours.
Scaled time: 691.04 units (timescale=2.011).
Factorization parameters were as follows:
n: 144635597843014417326267335760917157268120832967380333618464958460406927765840353521320708540866713359027597918424425580970025070336540602778330136138505841457739298723830245887
m: 1000000000000000000000000000000000000
deg: 5
c5: 2900
c0: 43
skew: 0.43
type: snfs
lss: 1
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [4000000, 7300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1547536 x 1547784
Total sieving time: 343.63 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,183,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,53,53,2.5,2.5,100000
total time: 343.63 hours.
 --------- CPU info (if available) ----------

(19·10¹⁷⁸+53)/9 = 2(1)₁₇₇7_<179> = 3 · 383489 · C173

C173 = P33 · P50 · P91

P33 = 730783028829272890571582357107873_<33>

P50 = 15813081752003936184143208732888457782336476081569_<50>

P91 = 1587932203573024046038962979456799562125934051816159402995982719650736127433087927236287023_<91>

Number: 21117_178
N=18350036212347777998944003705548365238734454018334390391998302525071219870809950316794059378592442122295651340813001251762207095997634970069642250591378206511887008589651951
  ( 173 digits)
SNFS difficulty: 179 digits.
Divisors found:
 r1=730783028829272890571582357107873
 r2=15813081752003936184143208732888457782336476081569
 r3=1587932203573024046038962979456799562125934051816159402995982719650736127433087927236287023
Version: 
Total time: 199.73 hours.
Scaled time: 402.06 units (timescale=2.013).
Factorization parameters were as follows:
n: 18350036212347777998944003705548365238734454018334390391998302525071219870809950316794059378592442122295651340813001251762207095997634970069642250591378206511887008589651951
m: 100000000000000000000000000000000000
deg: 5
c5: 19000
c0: 53
skew: 0.31
type: snfs
lss: 1
rlim: 6800000
alim: 6800000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 6800000/6800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3400000, 9900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1341541 x 1341789
Total sieving time: 199.73 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,179,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000
total time: 199.73 hours.
 --------- CPU info (if available) ----------

Dec 21, 2009 (6th)

By Dmitry Domanov / Msieve, ECMNET, GMP-ECM, GGNFS/msieve / Dec 21, 2009

(71·10¹²⁷+1)/9 = 7(8)₁₂₆9_<128> = 877 · C125

C125 = P42 · P84

P42 = 724119670299098648278589761262529662613773_<42>

P84 = 124224111994143947053481632133918283439721570965704847381544868928732662785337506609_<84>

Number: pss5
N=89953123020397820853921195996452552894970226783225642974787786646395540352210819713670340808311161788926897250728493601925757
  ( 125 digits)
SNFS difficulty: 128 digits.
Divisors found:
r1=93855586060542351442594594185778692558497789498069 (pp50)
r2=124224111994143947053481632133918283439721570965704847381544868928732662785337506609 (pp84)
Version: Msieve-1.40
Total time: 2.78 hours.
Scaled time: 5.27 units (timescale=1.894).
Factorization parameters were as follows:
n: 89953123020397820853921195996452552894970226783225642974787786646395540352210819713670340808311161788926897250728493601925757
m: 10000000000000000000000000
deg: 5
c5: 7100
c0: 1
skew: 0.17
type: snfs
lss: 1
rlim: 980000
alim: 980000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 980000/980000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [490000, 840001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 130951 x 131178
Total sieving time: 2.54 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,128.000,5,0,0,0,0,0,0,0,0,980000,980000,26,26,47,47,2.3,2.3,50000
total time: 2.78 hours.
 --------- CPU info (if available) ----------

(61·10¹⁸⁶+11)/9 = 6(7)₁₈₅9_<187> = 11064356141_<11> · C177

C177 = P34 · P143

P34 = 6593937000538782954599208778732781_<34>

P143 = 92900143664152041610733982563617930749541509401481860046283875992578438137971694644621795839901683792618731990044520768286581883999169058387899_<143>

Factor=6593937000538782954599208778732781  Method=ECM  B1=11000000  Sigma=2002082671

(71·10¹³³+1)/9 = 7(8)₁₃₂9_<134> = 113 · 10338933259_<11> · 732116512273_<12> · C110

C110 = P33 · P36 · P42

P33 = 721463809668823308576757999477337_<33>

P36 = 186615596727761291998883929740028807_<36>

P42 = 685044798746716350174109578435853792446181_<42>

N=92231965102753226805070876269963837258857967842991246775531878200725154058404849711786393278310308556651813579
  ( 110 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=721463809668823308576757999477337 (pp33)
 r2=186615596727761291998883929740028807 (pp36)
 r3=685044798746716350174109578435853792446181 (pp42)
Version: Msieve-1.40
Total time: 3.80 hours.
Scaled time: 7.04 units (timescale=1.855).
Factorization parameters were as follows:
n: 92231965102753226805070876269963837258857967842991246775531878200725154058404849711786393278310308556651813579
m: 100000000000000000000000000
deg: 5
c5: 71000
c0: 1
skew: 0.11
type: snfs
lss: 1
rlim: 1240000
alim: 1240000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1240000/1240000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [620000, 1370001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 169732 x 169958
Total sieving time: 3.60 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,134.000,5,0,0,0,0,0,0,0,0,1240000,1240000,26,26,47,47,2.3,2.3,75000
total time: 3.80 hours.
 --------- CPU info (if available) ----------

(71·10¹³⁷+1)/9 = 7(8)₁₃₆9_<138> = 3 · 81203 · 91125075823_<11> · 331490003387_<12> · C111

C111 = P31 · P80

P31 = 1124786677524254377539152840831_<31>

P80 = 95311215416391831577161704682854083086498483281881740792036442945373555652793891_<80>

N=107204785319001861480239990708059678466162206746209771789971212092030666843417489070498898114318212014772163421
  ( 111 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=1124786677524254377539152840831 (pp31)
 r2=95311215416391831577161704682854083086498483281881740792036442945373555652793891 (pp80)
Version: Msieve-1.40
Total time: 4.38 hours.
Scaled time: 8.31 units (timescale=1.899).
Factorization parameters were as follows:
n: 107204785319001861480239990708059678466162206746209771789971212092030666843417489070498898114318212014772163421
m: 1000000000000000000000000000
deg: 5
c5: 7100
c0: 1
skew: 0.17
type: snfs
lss: 1
rlim: 1440000
alim: 1440000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1440000/1440000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [720000, 1545001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 188590 x 188815
Total sieving time: 4.24 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138.000,5,0,0,0,0,0,0,0,0,1440000,1440000,26,26,48,48,2.3,2.3,75000
total time: 4.38 hours.
 --------- CPU info (if available) ----------

(71·10¹⁴⁶+1)/9 = 7(8)₁₄₅9_<147> = 3 · 143873 · 484733 · 100371170821_<12> · C125

C125 = P54 · P72

P54 = 275763158471737845393339532576042411061713280853158923_<54>

P72 = 136228339594136412294146908581272692925053002012783776467237808792805929_<72>

N=37566757199839558738674053617549413778397450213184321917251642377603230103467738504126931658773651479533067016587356533654467
  ( 125 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=275763158471737845393339532576042411061713280853158923 (pp54)
 r2=136228339594136412294146908581272692925053002012783776467237808792805929 (pp72)
Version: Msieve-1.40
Total time: 9.29 hours.
Scaled time: 17.65 units (timescale=1.899).
Factorization parameters were as follows:
n: 37566757199839558738674053617549413778397450213184321917251642377603230103467738504126931658773651479533067016587356533654467
m: 100000000000000000000000000000
deg: 5
c5: 710
c0: 1
skew: 0.27
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 341056 x 341281
Total sieving time: 9.04 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,147.000,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000
total time: 9.29 hours.
 --------- CPU info (if available) ----------

(61·10¹⁸⁵+11)/9 = 6(7)₁₈₄9_<186> = 449 · 4241 · C180

C180 = P38 · P42 · P101

P38 = 93294348110671834780090636675095012293_<38>

P42 = 211932646641119217655915149848691440234801_<42>

P101 = 18001948543574024260951655439691780805894373278122437636957145375740930619748197779058194059900366167_<101>

Factor=93294348110671834780090636675095012293  Method=ECM  B1=11000000  Sigma=96355152
Factor=211932646641119217655915149848691440234801  Method=ECM  B1=11000000  Sigma=583579203

(61·10¹⁵⁸+11)/9 = 6(7)₁₅₇9_<159> = 7 · 47947 · C154

C154 = P36 · P118

P36 = 370424065561157043005740122638615381_<36>

P118 = 5451658618654229583422200616066216555531534316702994687574391619950836910293242281617785667350933415824446950885802371_<118>

N=2019425549573421181655273464980015963393442693503176953653521530552418824886341102162738552919377579940284593339007588074265864325722085331654230646868351
  ( 154 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=370424065561157043005740122638615381 (pp36)
 r2=5451658618654229583422200616066216555531534316702994687574391619950836910293242281617785667350933415824446950885802371 (pp118)
Version: Msieve-1.40
Total time: 26.64 hours.
Scaled time: 50.45 units (timescale=1.894).
Factorization parameters were as follows:
n: 2019425549573421181655273464980015963393442693503176953653521530552418824886341102162738552919377579940284593339007588074265864325722085331654230646868351
m: 10000000000000000000000000000000
deg: 5
c5: 61000
c0: 11
skew: 0.18
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1600000, 3200001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 571466 x 571692
Total sieving time: 26.07 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,159.000,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000
total time: 26.64 hours.
 --------- CPU info (if available) ----------

(61·10¹⁶⁵+11)/9 = 6(7)₁₆₄9_<166> = 59 · 318756319633_<12> · C153

C153 = P58 · P96

P58 = 2752738908947720923391736911537353829351043020914446781171_<58>

P96 = 130921655593937280434022421470604766061837566769549361700021420587916908256274349687404863625667_<96>

N=360393135377284193093901844159276001250820053284430212998748937525336740416091877204027563021808549174725531214464896270870837855123940777121408807916057
  ( 153 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=2752738908947720923391736911537353829351043020914446781171 (pp58)
 r2=130921655593937280434022421470604766061837566769549361700021420587916908256274349687404863625667 (pp96)
Version: Msieve-1.40
Total time: 31.56 hours.
Scaled time: 57.73 units (timescale=1.829).
Factorization parameters were as follows:
n: 360393135377284193093901844159276001250820053284430212998748937525336740416091877204027563021808549174725531214464896270870837855123940777121408807916057
m: 1000000000000000000000000000000000
deg: 5
c5: 61
c0: 11
skew: 0.71
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 3800001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 789471 x 789696
Total sieving time: 30.57 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.77 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 31.56 hours.
 --------- CPU info (if available) ----------

Dec 21, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Dec 21, 2009

(61·10¹⁶⁷+11)/9 = 6(7)₁₆₆9_<168> = 6151 · 57763746961_<11> · 1494794490361357_<16> · 15944572173789759241324007_<26> · C113

C113 = P51 · P63

P51 = 113794270147369588653878589256850130478318915747067_<51>

P63 = 703349993642721287585740997082676211944799701617899993459389933_<63>

Number: n
N=80037199184730508977115416119352537885292239945463872142115955448280340669721848637051339150323473728208754076511
  ( 113 digits)
Divisors found:

Mon Dec 21 17:45:03 2009  prp51 factor: 113794270147369588653878589256850130478318915747067
Mon Dec 21 17:45:03 2009  prp63 factor: 703349993642721287585740997082676211944799701617899993459389933
Mon Dec 21 17:45:03 2009  elapsed time 00:45:19 (Msieve 1.43 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.16 hours.
Scaled time: 18.57 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_6_7_166_9
n: 80037199184730508977115416119352537885292239945463872142115955448280340669721848637051339150323473728208754076511
Y0: -8028180428284353607319
Y1:  771316934069
c0: -34736039266361789859349168152
c1:  1204731244369413931166325
c2:  24032766499366145074
c3: -147570282929998
c4: -286500260
c5:  2400
skew: 152736.69
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1750000, 2264753)
Primes: RFBsize:250150, AFBsize:250087, largePrimes:8195560 encountered
Relations: rels:4505389, finalFF:42038
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1357077 hash collisions in 16229987 relations
Msieve: matrix is 491541 x 491767 (136.2 MB)

Total sieving time: 10.08 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,28,28,56,56,2.6,2.6,100000
total time: 10.16 hours.
 --------- CPU info (if available) ----------

(38·10¹⁹⁰+43)/9 = 4(2)₁₈₉7_<191> = 286019 · C186

C186 = P84 · P102

P84 = 188842861071824615765500506301613040939280352144625291368044466035794298278708578687_<84>

P102 = 781709935162927917642790206127488798633371159901073266383347626263833358205329671027987439772257663759_<102>

Number: n
N=147620340684437824837588489653562253634276821547597265294341362714442824505442723113577147749702719827082194617218514232348977593174657006080792612456592821533612180387394621414039704433
  ( 186 digits)
SNFS difficulty: 191 digits.
Divisors found:

Mon Dec 21 19:00:33 2009  prp84 factor: 188842861071824615765500506301613040939280352144625291368044466035794298278708578687
Mon Dec 21 19:00:33 2009  prp102 factor: 781709935162927917642790206127488798633371159901073266383347626263833358205329671027987439772257663759
Mon Dec 21 19:00:33 2009  elapsed time 07:33:48 (Msieve 1.42 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: ~ 24.00 hours.
Scaled time: 0.00 units (timescale=0.842).
Factorization parameters were as follows:
name: KA_4_2_189_7
n: 147620340684437824837588489653562253634276821547597265294341362714442824505442723113577147749702719827082194617218514232348977593174657006080792612456592821533612180387394621414039704433
m: 100000000000000000000000000000000000000
deg: 5
c5: 38
c0: 43
skew: 1.03
type: snfs
lss: 1
rlim: 10900000
alim: 10900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10900000/10900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 100000)
Primes: RFBsize:720341, AFBsize:719599, 
Relations: 
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 3456972 hash collisions in 28295349 relations
Msieve: matrix is 1717412 x 1717637 (458.7 MB)

Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,10900000,10900000,28,28,56,56,2.5,2.5,100000
total time: 0.00 hours.
 --------- CPU info (if available) ----------

Dec 21, 2009 (4th)

By Sinkiti Sibata / GGNFS, Msieve / Dec 21, 2009

(71·10¹⁴³+1)/9 = 7(8)₁₄₂9_<144> = 3³ · 54004287143754025206083_<23> · 320887221940942009472382611_<27> · C94

C94 = P45 · P49

P45 = 295063233854536538035258174435435024654526569_<45>

P49 = 5714211568086633684135476067653822678501841181531_<49>

Number: 78889_143
N=1686053744208644329921490279259958118702718188924695072185385038825047520812339510474391597139
  ( 94 digits)
Divisors found:
 r1=295063233854536538035258174435435024654526569 (pp45)
 r2=5714211568086633684135476067653822678501841181531 (pp49)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 9.18 hours.
Scaled time: 4.30 units (timescale=0.468).
Factorization parameters were as follows:
name: 78889_143
n:  1686053744208644329921490279259958118702718188924695072185385038825047520812339510474391597139
m:  3784972111785690146622
deg: 4
c4: 8215248
c3: -4984644872
c2: -163098087209936902
c1: 25562022657187109
c0: 152167515497780200289077
skew: 1635.250
type: gnfs
# adj. I(F,S) = 53.638
# E(F1,F2) = 5.547655e-05
# GGNFS version 0.77.1-20050930-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1261313568.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1320001)
Primes: RFBsize:92938, AFBsize:92860, largePrimes:1892544 encountered
Relations: rels:1980884, finalFF:243238
Max relations in full relation-set: 28
Initial matrix: 185873 x 243238 with sparse part having weight 18964805.
Pruned matrix : 160862 x 161855 with weight 10326242.
Polynomial selection time: 0.17 hours.
Total sieving time: 8.38 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 9.18 hours.
 --------- CPU info (if available) ----------

(71·10¹⁴⁷+1)/9 = 7(8)₁₄₆9_<148> = 7 · 2174741 · 31792409060705638610778619_<26> · C116

C116 = P50 · P66

P50 = 35517930811933628614278811967488815401384738320451_<50>

P66 = 458922300996904483924595822228849043087866682853051242773033813363_<66>

Number: 78889_147
N=16299970534861432777150839936346263087416463359327069772929385905070511275097374886630381406471729284710112419986713
  ( 116 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=35517930811933628614278811967488815401384738320451 (pp50)
 r2=458922300996904483924595822228849043087866682853051242773033813363 (pp66)
Version: Msieve v. 1.42
Total time: 0.60 hours.
Scaled time: 0.48 units (timescale=0.796).
Factorization parameters were as follows:
name: 78889_147
n: 16299970534861432777150839936346263087416463359327069772929385905070511275097374886630381406471729284710112419986713
m: 100000000000000000000000000000
deg: 5
c5: 7100
c0: 1
skew: 0.17
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 369540 x 369788
Total sieving time: 0.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,148.000,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 0.60 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.30 BogoMIPS (lpj=1860651)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860572)
Total of 2 processors activated (7442.44 BogoMIPS).

Total time: 9 hours 13 min.

(71·10¹²⁸+1)/9 = 7(8)₁₂₇9_<129> = 3 · C129

C129 = P31 · P37 · P61

P31 = 7704415077626433601853291814961_<31>

P37 = 7241043645876529869856793659292249699_<37>

P61 = 4713611088784942439934240499030695683756265201980233925675617_<61>

Number: 78889_128
N=262962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962963
  ( 129 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=7704415077626433601853291814961 (pp31)
 r2=7241043645876529869856793659292249699 (pp37)
 r3=4713611088784942439934240499030695683756265201980233925675617 (pp61)
Version: Msieve-1.40
Total time: 3.31 hours.
Scaled time: 6.95 units (timescale=2.099).
Factorization parameters were as follows:
name: 78889_128
n: 262962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962963
m: 10000000000000000000000000
deg: 5
c5: 71000
c0: 1
skew: 0.11
type: snfs
lss: 1
rlim: 1020000
alim: 1020000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1020000/1020000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [510000, 960001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 152161 x 152394
Total sieving time: 3.10 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,129.000,5,0,0,0,0,0,0,0,0,1020000,1020000,26,26,47,47,2.3,2.3,50000
total time: 3.31 hours.
 --------- CPU info (if available) ----------

Dec 21, 2009 (3rd)

By juno1369 / Msieve v1.43 / Dec 21, 2009

(23·10¹³⁵+7)/3 = 7(6)₁₃₄9_<136> = 1805893807_<10> · 28528225268830327527152392361_<29> · C99

C99 = P37 · P62

P37 = 3458833797702092192028014218740192151_<37>

P62 = 43023914661672714363772351729455871813057323558894140821120397_<62>

Msieve v. 1.43
Sat Dec 19 22:27:52 2009
random seeds: 75b3f540 5533574a
factoring 1488125701412441595485831783466556452645334142990187120517913439002770
74936886619081486558885403947 (99 digits)
searching for 15-digit factors
searching for 20-digit factors
searching for 25-digit factors
200 of 214 curves
completed 214 ECM curves
searching for 30-digit factors
425 of 430 curves
completed 430 ECM curves
commencing quadratic sieve (99-digit input)
using multiplier of 47
using 64kb Opteron sieve core
sieve interval: 18 blocks of size 65536
processing polynomials in batches of 6
using a sieve bound of 2567269 (94118 primes)
using large prime bound of 385090350 (28 bits)
using double large prime bound of 2844544577802900 (43-52 bits)
using trial factoring cutoff of 52 bits
polynomial 'A' values have 13 factors

sieving in progress (press Ctrl-C to pause)
94500 relations (22703 full + 71797 combined from 1416345 partial), need 94214
94500 relations (22703 full + 71797 combined from 1416345 partial), need 94214
sieving complete, commencing postprocessing
begin with 1439048 relations
reduce to 247787 relations in 11 passes
attempting to read 247787 relations
recovered 247787 relations
recovered 237649 polynomials
attempting to build 94500 cycles
found 94500 cycles in 5 passes
distribution of cycle lengths:
   length 1 : 22703
   length 2 : 16212
   length 3 : 16087
   length 4 : 12823
   length 5 : 9707
   length 6 : 6522
   length 7 : 4339
   length 9+: 6107
largest cycle: 19 relations
matrix is 94118 x 94500 (25.6 MB) with weight 6327221 (66.95/col)
sparse part has weight 6327221 (66.95/col)
filtering completed in 3 passes
matrix is 90199 x 90263 (24.5 MB) with weight 6059463 (67.13/col)
sparse part has weight 6059463 (67.13/col)
saving the first 48 matrix rows for later
matrix is 90151 x 90263 (14.4 MB) with weight 4716111 (52.25/col)
sparse part has weight 3236903 (35.86/col)
matrix includes 64 packed rows
using block size 21845 for processor cache size 512 kB
commencing Lanczos iteration
memory use: 15.1 MB
linear algebra at 26.7%, ETA 0h 0m90263 dimensions (26.7%, ETA 0h 0m)
linear algebra completed 88361 of 90263 dimensions (97.9%, ETA 0h 0m)
lanczos halted after 1427 iterations (dim = 90149)
recovered 16 nontrivial dependencies
prp37 factor: 3458833797702092192028014218740192151
prp62 factor: 43023914661672714363772351729455871813057323558894140821120397
elapsed time 17:36:29

Dec 21, 2009 (2nd)

By Jo Yeong Uk / GMP-ECM v6.2.3, YAFU v1.10, Msieve / Dec 21, 2009

(61·10¹⁵⁹+11)/9 = 6(7)₁₅₈9_<160> = 167 · 5153 · 127787011978227509711432050637_<30> · C125

C125 = P32 · P37 · P57

P32 = 27682035015166481474010757311683_<32>

P37 = 5486643505504392984455778494096868727_<37>

P57 = 405806725364661937722524130979655905519377159864333334037_<57>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 61634516966514961863963271009532422308818742105568058503065608758517820356226982703368854909438046148816322722175542245883017 (125 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3551862618
Step 1 took 4258ms
Step 2 took 734ms
********** Factor found in step 2: 27682035015166481474010757311683
Found probable prime factor of 32 digits: 27682035015166481474010757311683
Composite cofactor 2226516834212027242444909816545471671278027082282232388885126145417248627018316263049829960899 has 94 digits

12/20/09 23:12:45 v1.10 @ 조영욱-PC, starting SIQS on c94: 2226516834212027242444909816545471671278027082282232388885126145417248627018316263049829960899
12/20/09 23:12:45 v1.10 @ 조영욱-PC, random seeds: 3976414213, 2696250688
12/20/09 23:12:45 v1.10 @ 조영욱-PC, ==== sieve params ====
12/20/09 23:12:45 v1.10 @ 조영욱-PC, n = 94 digits, 311 bits
12/20/09 23:12:45 v1.10 @ 조영욱-PC, factor base: 79491 primes (max prime = 2148583)
12/20/09 23:12:45 v1.10 @ 조영욱-PC, single large prime cutoff: 279315790 (130 * pmax)
12/20/09 23:12:45 v1.10 @ 조영욱-PC, double large prime range from 44 to 51 bits
12/20/09 23:12:45 v1.10 @ 조영욱-PC, double large prime cutoff: 1595775810273505
12/20/09 23:12:45 v1.10 @ 조영욱-PC, using 16 large prime slices of factor base
12/20/09 23:12:45 v1.10 @ 조영욱-PC, buckets hold 1024 elements
12/20/09 23:12:45 v1.10 @ 조영욱-PC, sieve interval: 13 blocks of size 65536
12/20/09 23:12:45 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors
12/20/09 23:12:45 v1.10 @ 조영욱-PC, using multiplier of 1
12/20/09 23:12:45 v1.10 @ 조영욱-PC, using small prime variation correction of 20 bits
12/20/09 23:12:45 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
12/20/09 23:12:45 v1.10 @ 조영욱-PC, trial factoring cutoff at 98 bits
12/20/09 23:12:45 v1.10 @ 조영욱-PC, ==== sieving started ====
12/21/09 00:58:14 v1.10 @ 조영욱-PC, sieve time = 3007.8790, relation time = 1158.4010, poly_time = 2159.9650
12/21/09 00:58:14 v1.10 @ 조영욱-PC, 79567 relations found: 20778 full + 58789 from 1066144 partial, using 770025 polys (376 A polys)
12/21/09 00:58:14 v1.10 @ 조영욱-PC, on average, sieving found 1.41 rels/poly and 171.71 rels/sec
12/21/09 00:58:14 v1.10 @ 조영욱-PC, trial division touched 54208468 sieve locations out of 1312073318400
12/21/09 00:58:14 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
12/21/09 00:58:15 v1.10 @ 조영욱-PC, begin with 1086922 relations
12/21/09 00:58:15 v1.10 @ 조영욱-PC, reduce to 198647 relations in 10 passes
12/21/09 00:58:17 v1.10 @ 조영욱-PC, recovered 198647 relations
12/21/09 00:58:17 v1.10 @ 조영욱-PC, recovered 175214 polynomials
12/21/09 00:58:18 v1.10 @ 조영욱-PC, attempting to build 79567 cycles
12/21/09 00:58:18 v1.10 @ 조영욱-PC, found 79566 cycles in 5 passes
12/21/09 00:58:18 v1.10 @ 조영욱-PC, distribution of cycle lengths:
12/21/09 00:58:18 v1.10 @ 조영욱-PC,    length 1 : 20778
12/21/09 00:58:18 v1.10 @ 조영욱-PC,    length 2 : 15063
12/21/09 00:58:18 v1.10 @ 조영욱-PC,    length 3 : 13884
12/21/09 00:58:18 v1.10 @ 조영욱-PC,    length 4 : 10553
12/21/09 00:58:18 v1.10 @ 조영욱-PC,    length 5 : 7602
12/21/09 00:58:18 v1.10 @ 조영욱-PC,    length 6 : 4939
12/21/09 00:58:18 v1.10 @ 조영욱-PC,    length 7 : 2983
12/21/09 00:58:18 v1.10 @ 조영욱-PC,    length 9+: 3764
12/21/09 00:58:18 v1.10 @ 조영욱-PC, largest cycle: 18 relations
12/21/09 00:58:18 v1.10 @ 조영욱-PC, matrix is 79491 x 79566 (21.7 MB) with weight 5045160 (63.41/col)
12/21/09 00:58:18 v1.10 @ 조영욱-PC, sparse part has weight 5045160 (63.41/col)
12/21/09 00:58:18 v1.10 @ 조영욱-PC, filtering completed in 3 passes
12/21/09 00:58:18 v1.10 @ 조영욱-PC, matrix is 75051 x 75113 (20.7 MB) with weight 4812529 (64.07/col)
12/21/09 00:58:18 v1.10 @ 조영욱-PC, sparse part has weight 4812529 (64.07/col)
12/21/09 00:58:19 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
12/21/09 00:58:19 v1.10 @ 조영욱-PC, matrix is 75003 x 75113 (14.7 MB) with weight 3938249 (52.43/col)
12/21/09 00:58:19 v1.10 @ 조영욱-PC, sparse part has weight 3094533 (41.20/col)
12/21/09 00:58:19 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
12/21/09 00:58:19 v1.10 @ 조영욱-PC, using block size 30045 for processor cache size 4096 kB
12/21/09 00:58:19 v1.10 @ 조영욱-PC, commencing Lanczos iteration
12/21/09 00:58:19 v1.10 @ 조영욱-PC, memory use: 12.5 MB
12/21/09 00:58:46 v1.10 @ 조영욱-PC, lanczos halted after 1187 iterations (dim = 75003)
12/21/09 00:58:47 v1.10 @ 조영욱-PC, recovered 18 nontrivial dependencies
12/21/09 00:58:48 v1.10 @ 조영욱-PC, prp57 = 405806725364661937722524130979655905519377159864333334037
12/21/09 00:58:52 v1.10 @ 조영욱-PC, prp37 = 5486643505504392984455778494096868727
12/21/09 00:58:52 v1.10 @ 조영욱-PC, Lanczos elapsed time = 32.2300 seconds.
12/21/09 00:58:52 v1.10 @ 조영욱-PC, Sqrt elapsed time = 5.0380 seconds.
12/21/09 00:58:52 v1.10 @ 조영욱-PC, SIQS elapsed time = 6367.1110 seconds.
12/21/09 00:58:52 v1.10 @ 조영욱-PC, 
12/21/09 00:58:52 v1.10 @ 조영욱-PC,

Dec 21, 2009

R269 was factored!

10,269- factors

Dec 20, 2009 (7th)

By Dmitry Domanov / GGNFS/msieve / Dec 20, 2009

(67·10¹⁶⁶-13)/9 = 7(4)₁₆₅3_<167> = 137 · 11527 · 58211147497_<11> · C150

C150 = P62 · P89

P62 = 17788336493283764799874776176211295255153824486286341342116449_<62>

P89 = 45525417396388831878214850618002065197423668437999160251956317248051096197439673036095869_<89>

N=809821443644159015473592889696952371909415095654781991402504051499052333199909815633411495946416476907278319907167916022551376537940892055496525849181
  ( 150 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=17788336493283764799874776176211295255153824486286341342116449 (pp62)
 r2=45525417396388831878214850618002065197423668437999160251956317248051096197439673036095869 (pp89)
Version: Msieve-1.40
Total time: 49.67 hours.
Scaled time: 97.21 units (timescale=1.957).
Factorization parameters were as follows:
n: 809821443644159015473592889696952371909415095654781991402504051499052333199909815633411495946416476907278319907167916022551376537940892055496525849181
m: 1000000000000000000000000000000000
deg: 5
c5: 670
c0: -13
skew: 0.45
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 5000001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 780936 x 781162
Total sieving time: 48.68 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.74 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,167.000,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 49.67 hours.
 --------- CPU info (if available) ----------

(71·10¹¹²+1)/9 = 7(8)₁₁₁9_<113> = 5051 · C110

C110 = P41 · P69

P41 = 98236346472193703857978997992081697635961_<41>

P69 = 158988703783081621446358550237337124641120027141738051862791804638899_<69>

N=15618469389999780021557887327041949888910886733100156184693899997800215578873270419498889108867331001561846939
  ( 110 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=98236346472193703857978997992081697635961 (pp41)
 r2=158988703783081621446358550237337124641120027141738051862791804638899 (pp69)
Version: Msieve-1.40
Total time: 0.63 hours.
Scaled time: 1.15 units (timescale=1.839).
Factorization parameters were as follows:
n: 15618469389999780021557887327041949888910886733100156184693899997800215578873270419498889108867331001561846939
m: 10000000000000000000000
deg: 5
c5: 7100
c0: 1
skew: 0.17
type: snfs
lss: 1
rlim: 550000
alim: 550000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 550000/550000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [275000, 425001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 58007 x 58232
Total sieving time: 0.60 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113.000,5,0,0,0,0,0,0,0,0,550000,550000,25,25,45,45,2.2,2.2,50000
total time: 0.63 hours.
 --------- CPU info (if available) ----------

(71·10¹¹⁶+1)/9 = 7(8)₁₁₅9_<117> = 3³ · 229 · C114

C114 = P38 · P76

P38 = 69062373742930933617093979060672902017_<38>

P76 = 1847460201071538131005754622201707103824735757708006940124048686203421459999_<76>

N=127589986881592898089744280913616187754955343504591442485668589501680234334285765629773392995130015993674411917983
  ( 114 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=69062373742930933617093979060672902017 (pp38)
 r2=1847460201071538131005754622201707103824735757708006940124048686203421459999 (pp76)
Version: Msieve-1.40
Total time: 1.01 hours.
Scaled time: 1.74 units (timescale=1.716).
Factorization parameters were as follows:
n: 127589986881592898089744280913616187754955343504591442485668589501680234334285765629773392995130015993674411917983
m: 100000000000000000000000
deg: 5
c5: 710
c0: 1
skew: 0.27
type: snfs
lss: 1
rlim: 640000
alim: 640000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 640000/640000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [320000, 570001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 68355 x 68580
Total sieving time: 0.99 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,117.000,5,0,0,0,0,0,0,0,0,640000,640000,25,25,45,45,2.2,2.2,50000
total time: 1.01 hours.
 --------- CPU info (if available) ----------

(71·10¹¹⁹+1)/9 = 7(8)₁₁₈9_<120> = 3 · 97 · 151 · 32503 · 55903 · C106

C106 = P33 · P74

P33 = 260989837407163028509237560550469_<33>

P74 = 37858529723818689954388142150403461018862646893677049576191518747847970649_<74>

N=9880691517093688526006305501973337174111399990396107651046656181201523968850157329106890129857500995184381
  ( 106 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=260989837407163028509237560550469 (pp33)
 r2=37858529723818689954388142150403461018862646893677049576191518747847970649 (pp74)
Version: Msieve-1.40
Total time: 0.87 hours.
Scaled time: 1.63 units (timescale=1.877).
Factorization parameters were as follows:
n: 9880691517093688526006305501973337174111399990396107651046656181201523968850157329106890129857500995184381
m: 100000000000000000000000
deg: 5
c5: 710000
c0: 1
skew: 0.07
type: snfs
lss: 1
rlim: 720000
alim: 720000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 720000/720000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [360000, 560001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 83243 x 83476
Total sieving time: 0.83 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120.000,5,0,0,0,0,0,0,0,0,720000,720000,25,25,46,46,2.2,2.2,50000
total time: 0.87 hours.
 --------- CPU info (if available) ----------

(71·10¹²⁵+1)/9 = 7(8)₁₂₄9_<126> = 3² · 17² · 8017 · C119

C119 = P50 · P69

P50 = 93855586060542351442594594185778692558497789498069_<50>

P69 = 403091349005361519278707604706130227063580410609001894218505818152893_<69>

N=37832374796832820648705549577241062132093143328063816374483772583456660214541642689067013300738664329499778795170263617
  ( 119 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=93855586060542351442594594185778692558497789498069 (pp50)
 r2=403091349005361519278707604706130227063580410609001894218505818152893 (pp69)
Version: Msieve-1.40
Total time: 1.16 hours.
Scaled time: 2.17 units (timescale=1.877).
Factorization parameters were as follows:
n: 37832374796832820648705549577241062132093143328063816374483772583456660214541642689067013300738664329499778795170263617
m: 10000000000000000000000000
deg: 5
c5: 71
c0: 1
skew: 0.43
type: snfs
lss: 1
rlim: 910000
alim: 910000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 910000/910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [455000, 805001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 105126 x 105351
Total sieving time: 1.06 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000
total time: 1.16 hours.
 --------- CPU info (if available) ----------

Dec 20, 2009 (6th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Dec 20, 2009

5·10¹⁷⁷-1 = 4(9)₁₇₇_<178> = 30973583 · 39989645019285243151_<20> · C151

C151 = P46 · P105

P46 = 4068269709359954401976297716690750943446114169_<46>

P105 = 992250373611379227883163588164400121551512275167316952271377534693843762018044616947203837967745867950487_<105>

Number: 49999_177
N=4036742139064271940352924607719840667525658401516025842099488707237906836850173332467826613777240396308955876191838587875549878107435969243156241150303
  ( 151 digits)
SNFS difficulty: 179 digits.
Divisors found:
 r1=4068269709359954401976297716690750943446114169
 r2=992250373611379227883163588164400121551512275167316952271377534693843762018044616947203837967745867950487
Version: 
Total time: 58.68 hours.
Scaled time: 140.12 units (timescale=2.388).
Factorization parameters were as follows:
n: 4036742139064271940352924607719840667525658401516025842099488707237906836850173332467826613777240396308955876191838587875549878107435969243156241150303
m: 500000000000000000000000000000000000
deg: 5
c5: 4
c0: -25
skew: 1.44
type: snfs
lss: 1
rlim: 8400000
alim: 8400000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [4200000, 7900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 18197177
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1358940 x 1359188
Total sieving time: 50.53 hours.
Total relation processing time: 3.44 hours.
Matrix solve time: 4.54 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,179,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,53,53,2.5,2.5,100000
total time: 58.68 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673795)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672307)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

Dec 20, 2009 (5th)

By Sinkiti Sibata / Msieve / Dec 20, 2009

(71·10¹³¹+1)/9 = 7(8)₁₃₀9_<132> = 3 · 79 · 2284487 · 45931576133_<11> · 39603835123065114431682400489_<29> · C84

C84 = P31 · P54

P31 = 1532456056702866758290212627089_<31>

P54 = 522687579393372373737375787659559334612594552826524567_<54>

un Dec 20 17:15:07 2009  Msieve v. 1.42
Sun Dec 20 17:15:07 2009  random seeds: 7d08a9d0 f29a90b1
Sun Dec 20 17:15:07 2009  factoring 800995746804734024923714661924756289455931590264912350707560684056840671070668195463 (84 digits)
Sun Dec 20 17:15:07 2009  searching for 15-digit factors
Sun Dec 20 17:15:08 2009  commencing quadratic sieve (84-digit input)
Sun Dec 20 17:15:08 2009  using multiplier of 3
Sun Dec 20 17:15:08 2009  using 32kb Intel Core sieve core
Sun Dec 20 17:15:08 2009  sieve interval: 12 blocks of size 32768
Sun Dec 20 17:15:08 2009  processing polynomials in batches of 17
Sun Dec 20 17:15:08 2009  using a sieve bound of 1409171 (53780 primes)
Sun Dec 20 17:15:08 2009  using large prime bound of 119779535 (26 bits)
Sun Dec 20 17:15:08 2009  using trial factoring cutoff of 27 bits
Sun Dec 20 17:15:08 2009  polynomial 'A' values have 11 factors
Sun Dec 20 17:49:19 2009  53880 relations (27179 full + 26701 combined from 282088 partial), need 53876
Sun Dec 20 17:49:19 2009  begin with 309267 relations
Sun Dec 20 17:49:19 2009  reduce to 77244 relations in 2 passes
Sun Dec 20 17:49:19 2009  attempting to read 77244 relations
Sun Dec 20 17:49:20 2009  recovered 77244 relations
Sun Dec 20 17:49:20 2009  recovered 72260 polynomials
Sun Dec 20 17:49:21 2009  attempting to build 53880 cycles
Sun Dec 20 17:49:21 2009  found 53880 cycles in 1 passes
Sun Dec 20 17:49:21 2009  distribution of cycle lengths:
Sun Dec 20 17:49:21 2009     length 1 : 27179
Sun Dec 20 17:49:21 2009     length 2 : 26701
Sun Dec 20 17:49:21 2009  largest cycle: 2 relations
Sun Dec 20 17:49:21 2009  matrix is 53780 x 53880 (7.4 MB) with weight 1725223 (32.02/col)
Sun Dec 20 17:49:21 2009  sparse part has weight 1725223 (32.02/col)
Sun Dec 20 17:49:21 2009  filtering completed in 3 passes
Sun Dec 20 17:49:21 2009  matrix is 39816 x 39880 (6.0 MB) with weight 1405910 (35.25/col)
Sun Dec 20 17:49:21 2009  sparse part has weight 1405910 (35.25/col)
Sun Dec 20 17:49:21 2009  saving the first 48 matrix rows for later
Sun Dec 20 17:49:21 2009  matrix is 39768 x 39880 (3.4 MB) with weight 1012656 (25.39/col)
Sun Dec 20 17:49:21 2009  sparse part has weight 661658 (16.59/col)
Sun Dec 20 17:49:21 2009  matrix includes 64 packed rows
Sun Dec 20 17:49:21 2009  using block size 15952 for processor cache size 1024 kB
Sun Dec 20 17:49:21 2009  commencing Lanczos iteration
Sun Dec 20 17:49:21 2009  memory use: 4.5 MB
Sun Dec 20 17:49:28 2009  lanczos halted after 631 iterations (dim = 39768)
Sun Dec 20 17:49:28 2009  recovered 18 nontrivial dependencies
Sun Dec 20 17:49:28 2009  prp31 factor: 1532456056702866758290212627089
Sun Dec 20 17:49:28 2009  prp54 factor: 522687579393372373737375787659559334612594552826524567
Sun Dec 20 17:49:28 2009  elapsed time 00:34:21

(71·10¹⁴⁰+1)/9 = 7(8)₁₃₉9_<141> = 3 · 61487 · 493397 · 4051652638609_<13> · 2427466305004739511993872503_<28> · C90

C90 = P31 · P60

P31 = 6037781829603402624141784211479_<31>

P60 = 145966079967011519653813948740251707221351710207307695892649_<60>

Sun Dec 20 18:01:33 2009  Msieve v. 1.42
Sun Dec 20 18:01:33 2009  random seeds: 299a7a18 3d24d2a3
Sun Dec 20 18:01:33 2009  factoring 881311345363259388487258500198771493671200333042707513734834036896310666196643565497517871 (90 digits)
Sun Dec 20 18:01:34 2009  searching for 15-digit factors
Sun Dec 20 18:01:34 2009  commencing quadratic sieve (90-digit input)
Sun Dec 20 18:01:35 2009  using multiplier of 1
Sun Dec 20 18:01:35 2009  using 32kb Intel Core sieve core
Sun Dec 20 18:01:35 2009  sieve interval: 36 blocks of size 32768
Sun Dec 20 18:01:35 2009  processing polynomials in batches of 6
Sun Dec 20 18:01:35 2009  using a sieve bound of 1616473 (61176 primes)
Sun Dec 20 18:01:35 2009  using large prime bound of 135783732 (27 bits)
Sun Dec 20 18:01:35 2009  using double large prime bound of 435638070401436 (42-49 bits)
Sun Dec 20 18:01:35 2009  using trial factoring cutoff of 49 bits
Sun Dec 20 18:01:35 2009  polynomial 'A' values have 11 factors
Sun Dec 20 19:27:09 2009  61479 relations (15765 full + 45714 combined from 674996 partial), need 61272
Sun Dec 20 19:27:10 2009  begin with 690761 relations
Sun Dec 20 19:27:11 2009  reduce to 152744 relations in 10 passes
Sun Dec 20 19:27:11 2009  attempting to read 152744 relations
Sun Dec 20 19:27:13 2009  recovered 152744 relations
Sun Dec 20 19:27:13 2009  recovered 133119 polynomials
Sun Dec 20 19:27:13 2009  attempting to build 61479 cycles
Sun Dec 20 19:27:13 2009  found 61479 cycles in 6 passes
Sun Dec 20 19:27:13 2009  distribution of cycle lengths:
Sun Dec 20 19:27:13 2009     length 1 : 15765
Sun Dec 20 19:27:13 2009     length 2 : 11546
Sun Dec 20 19:27:13 2009     length 3 : 10666
Sun Dec 20 19:27:13 2009     length 4 : 8235
Sun Dec 20 19:27:13 2009     length 5 : 5948
Sun Dec 20 19:27:13 2009     length 6 : 3896
Sun Dec 20 19:27:13 2009     length 7 : 2419
Sun Dec 20 19:27:13 2009     length 9+: 3004
Sun Dec 20 19:27:13 2009  largest cycle: 18 relations
Sun Dec 20 19:27:13 2009  matrix is 61176 x 61479 (15.6 MB) with weight 3834534 (62.37/col)
Sun Dec 20 19:27:13 2009  sparse part has weight 3834534 (62.37/col)
Sun Dec 20 19:27:14 2009  filtering completed in 3 passes
Sun Dec 20 19:27:14 2009  matrix is 57752 x 57813 (14.7 MB) with weight 3626853 (62.73/col)
Sun Dec 20 19:27:14 2009  sparse part has weight 3626853 (62.73/col)
Sun Dec 20 19:27:14 2009  saving the first 48 matrix rows for later
Sun Dec 20 19:27:14 2009  matrix is 57704 x 57813 (11.1 MB) with weight 3058489 (52.90/col)
Sun Dec 20 19:27:14 2009  sparse part has weight 2559872 (44.28/col)
Sun Dec 20 19:27:14 2009  matrix includes 64 packed rows
Sun Dec 20 19:27:14 2009  using block size 23125 for processor cache size 1024 kB
Sun Dec 20 19:27:15 2009  commencing Lanczos iteration
Sun Dec 20 19:27:15 2009  memory use: 10.3 MB
Sun Dec 20 19:27:38 2009  lanczos halted after 914 iterations (dim = 57704)
Sun Dec 20 19:27:38 2009  recovered 18 nontrivial dependencies
Sun Dec 20 19:27:39 2009  prp31 factor: 6037781829603402624141784211479
Sun Dec 20 19:27:39 2009  prp60 factor: 145966079967011519653813948740251707221351710207307695892649
Sun Dec 20 19:27:39 2009  elapsed time 01:26:06

(71·10¹¹⁴+1)/9 = 7(8)₁₁₃9_<115> = 293 · 95071 · 8107423 · C101

C101 = P32 · P69

P32 = 42398963895894229799188757473783_<32>

P69 = 823876433612668009486141208252372609064801449929114534675087671870307_<69>

Number: 78889_114
N=34931507163421610206610224383858619167543865784783833609556884978012331018677064688324578980128661381
  ( 101 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=42398963895894229799188757473783 (pp32)
 r2=823876433612668009486141208252372609064801449929114534675087671870307 (pp69)
Version: Msieve-1.40
Total time: 0.69 hours.
Scaled time: 2.33 units (timescale=3.357).
Factorization parameters were as follows:
name: 78889_114
n: 34931507163421610206610224383858619167543865784783833609556884978012331018677064688324578980128661381
m: 10000000000000000000000
deg: 5
c5: 710000
c0: 1
skew: 0.07
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [300000, 450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 64107 x 64355
Total sieving time: 0.67 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115.000,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000
total time: 0.69 hours.
 --------- CPU info (if available) ----------

(71·10¹¹⁸+1)/9 = 7(8)₁₁₇9_<119> = 79 · 181068263 · 9695661421_<10> · C99

C99 = P37 · P63

P37 = 4629826203506991550366336552853175767_<37>

P63 = 122858238080954372067688156624451271378033096834390976714196851_<63>

Number: 78889_118
N=568812289983903075646333463174718043205943712690409987847046675098502761266067007380611790140909717
  ( 99 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=4629826203506991550366336552853175767 (pp37)
 r2=122858238080954372067688156624451271378033096834390976714196851 (pp63)
Version: Msieve-1.40
Total time: 1.34 hours.
Scaled time: 4.50 units (timescale=3.357).
Factorization parameters were as follows:
name: 78889_118
n: 568812289983903075646333463174718043205943712690409987847046675098502761266067007380611790140909717
m: 100000000000000000000000
deg: 5
c5: 71000
c0: 1
skew: 0.11
type: snfs
lss: 1
rlim: 700000
alim: 700000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [350000, 650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 80643 x 80889
Total sieving time: 1.31 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,119.000,5,0,0,0,0,0,0,0,0,700000,700000,25,25,45,45,2.2,2.2,50000
total time: 1.34 hours.
 --------- CPU info (if available) ----------

(71·10¹²¹+1)/9 = 7(8)₁₂₀9_<122> = 59 · 661 · 5507 · 249726804891671_<15> · C100

C100 = P30 · P70

P30 = 837424794414531343286736123919_<30>

P70 = 1756452120257436723413400175349062946231050201120212949001708369397677_<70>

Number: 78889_121
N=1470896555705551631901652642187255901230418889313472168255707759560509498224919426240522739662736163
  ( 100 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=837424794414531343286736123919 (pp30)
 r2=1756452120257436723413400175349062946231050201120212949001708369397677 (pp70)
Version: Msieve v. 1.42
Total time: 0.05 hours.
Scaled time: 0.04 units (timescale=0.796).
Factorization parameters were as follows:
name: 78889_121
n: 1470896555705551631901652642187255901230418889313472168255707759560509498224919426240522739662736163
m: 1000000000000000000000000
deg: 5
c5: 710
c0: 1
skew: 0.27
type: snfs
lss: 1
rlim: 780000
alim: 780000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 780000/780000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [390000, 690001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 97717 x 97954
Total sieving time: 0.00 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,122.000,5,0,0,0,0,0,0,0,0,780000,780000,25,25,46,46,2.2,2.2,50000
total time: 0.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.30 BogoMIPS (lpj=1860651)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860572)
Total of 2 processors activated (7442.44 BogoMIPS).

Total time: 1 hour 19 min

(71·10¹²⁶+1)/9 = 7(8)₁₂₅9_<127> = C127

C127 = P52 · P76

P52 = 7587196654306648843559104301528059865200491996390383_<52>

P76 = 1039763333985945036629986381863723907672179016478373540234641288978651293783_<76>

Number: 78889_126
N=7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
  ( 127 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=7587196654306648843559104301528059865200491996390383 (pp52)
 r2=1039763333985945036629986381863723907672179016478373540234641288978651293783 (pp76)
Version: Msieve v. 1.42
Total time: 0.12 hours.
Scaled time: 0.09 units (timescale=0.796).
Factorization parameters were as follows:
name: 78889_126
n: 7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
m: 10000000000000000000000000
deg: 5
c5: 710
c0: 1
skew: 0.27
type: snfs
lss: 1
rlim: 950000
alim: 950000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 950000/950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [475000, 825001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 142132 x 142357
Total sieving time: 0.00 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,127.000,5,0,0,0,0,0,0,0,0,950000,950000,26,26,46,46,2.3,2.3,50000
total time: 0.12 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.30 BogoMIPS (lpj=1860651)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860572)
Total of 2 processors activated (7442.44 BogoMIPS).

Total time: 1 hour 54 min.

(71·10¹⁰⁸+1)/9 = 7(8)₁₀₇9_<109> = 191 · 254002043 · C99

C99 = P47 · P52

P47 = 91795782432987139797997126963526524873114196143_<47>

P52 = 1771424040471773033547607068923205730064620491353771_<52>

Number: 78889_108
N=162609255815709883194299336104259587695147701740090484869532846062341352279399593674717448496705253
  ( 99 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=91795782432987139797997126963526524873114196143 (pp47)
 r2=1771424040471773033547607068923205730064620491353771 (pp52)
Version: Msieve-1.40
Total time: 0.64 hours.
Scaled time: 2.14 units (timescale=3.357).
Factorization parameters were as follows:
name: 78889_108
n: 162609255815709883194299336104259587695147701740090484869532846062341352279399593674717448496705253
m: 1000000000000000000000
deg: 5
c5: 71000
c0: 1
skew: 0.11
type: snfs
lss: 1
rlim: 470000
alim: 470000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 470000/470000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [235000, 385001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 49881 x 50111
Total sieving time: 0.62 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,109.000,5,0,0,0,0,0,0,0,0,470000,470000,25,25,44,44,2.2,2.2,50000
total time: 0.64 hours.
 --------- CPU info (if available) ----------

(61·10¹⁶³+11)/9 = 6(7)₁₆₂9_<164> = 3 · 68531 · 1194517 · 53428043521649_<14> · 229355260976131_<15> · 10688166830659133_<17> · 1484592475394454432301_<22> · C88

C88 = P43 · P45

P43 = 1871588248380026241365627576216769897016787_<43>

P45 = 758381797619450576082406619267293711227799391_<45>

Sun Dec 20 19:38:10 2009  Msieve v. 1.42
Sun Dec 20 19:38:10 2009  random seeds: 3250e898 fa2901fd
Sun Dec 20 19:38:10 2009  factoring 1419378460209883058482089957602475403206110804677664224171468339314844093054113795376717 (88 digits)
Sun Dec 20 19:38:11 2009  searching for 15-digit factors
Sun Dec 20 19:38:12 2009  commencing quadratic sieve (88-digit input)
Sun Dec 20 19:38:12 2009  using multiplier of 7
Sun Dec 20 19:38:12 2009  using 32kb Intel Core sieve core
Sun Dec 20 19:38:12 2009  sieve interval: 24 blocks of size 32768
Sun Dec 20 19:38:12 2009  processing polynomials in batches of 9
Sun Dec 20 19:38:12 2009  using a sieve bound of 1508383 (57277 primes)
Sun Dec 20 19:38:12 2009  using large prime bound of 120670640 (26 bits)
Sun Dec 20 19:38:12 2009  using double large prime bound of 352275850752880 (42-49 bits)
Sun Dec 20 19:38:12 2009  using trial factoring cutoff of 49 bits
Sun Dec 20 19:38:12 2009  polynomial 'A' values have 11 factors
Sun Dec 20 20:31:41 2009  57399 relations (15538 full + 41861 combined from 608371 partial), need 57373
Sun Dec 20 20:31:41 2009  begin with 623909 relations
Sun Dec 20 20:31:42 2009  reduce to 138787 relations in 10 passes
Sun Dec 20 20:31:42 2009  attempting to read 138787 relations
Sun Dec 20 20:31:44 2009  recovered 138787 relations
Sun Dec 20 20:31:44 2009  recovered 119426 polynomials
Sun Dec 20 20:31:44 2009  attempting to build 57399 cycles
Sun Dec 20 20:31:44 2009  found 57399 cycles in 5 passes
Sun Dec 20 20:31:44 2009  distribution of cycle lengths:
Sun Dec 20 20:31:44 2009     length 1 : 15538
Sun Dec 20 20:31:44 2009     length 2 : 11111
Sun Dec 20 20:31:44 2009     length 3 : 10290
Sun Dec 20 20:31:44 2009     length 4 : 7582
Sun Dec 20 20:31:44 2009     length 5 : 5361
Sun Dec 20 20:31:44 2009     length 6 : 3370
Sun Dec 20 20:31:44 2009     length 7 : 1860
Sun Dec 20 20:31:44 2009     length 9+: 2287
Sun Dec 20 20:31:44 2009  largest cycle: 22 relations
Sun Dec 20 20:31:44 2009  matrix is 57277 x 57399 (13.8 MB) with weight 3395606 (59.16/col)
Sun Dec 20 20:31:44 2009  sparse part has weight 3395606 (59.16/col)
Sun Dec 20 20:31:45 2009  filtering completed in 3 passes
Sun Dec 20 20:31:45 2009  matrix is 53367 x 53430 (13.0 MB) with weight 3193737 (59.77/col)
Sun Dec 20 20:31:45 2009  sparse part has weight 3193737 (59.77/col)
Sun Dec 20 20:31:45 2009  saving the first 48 matrix rows for later
Sun Dec 20 20:31:45 2009  matrix is 53319 x 53430 (9.0 MB) with weight 2572383 (48.14/col)
Sun Dec 20 20:31:45 2009  sparse part has weight 2027747 (37.95/col)
Sun Dec 20 20:31:45 2009  matrix includes 64 packed rows
Sun Dec 20 20:31:45 2009  using block size 21372 for processor cache size 1024 kB
Sun Dec 20 20:31:46 2009  commencing Lanczos iteration
Sun Dec 20 20:31:46 2009  memory use: 8.8 MB
Sun Dec 20 20:32:03 2009  lanczos halted after 845 iterations (dim = 53317)
Sun Dec 20 20:32:03 2009  recovered 18 nontrivial dependencies
Sun Dec 20 20:32:04 2009  prp43 factor: 1871588248380026241365627576216769897016787
Sun Dec 20 20:32:04 2009  prp45 factor: 758381797619450576082406619267293711227799391
Sun Dec 20 20:32:04 2009  elapsed time 00:53:54

(71·10¹⁰⁹+1)/9 = 7(8)₁₀₈9_<110> = 17 · 1171 · C106

C106 = P48 · P58

P48 = 640071740902143598334229762236177766260184004567_<48>

P58 = 6191293170857901796165747872454979438270371959359205290981_<58>

Number: 78889_109
N=3962871798306569994920826286677494795242321238202084135675334751036765403571049826135976736268091067910227
  ( 106 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=640071740902143598334229762236177766260184004567 (pp48)
 r2=6191293170857901796165747872454979438270371959359205290981 (pp58)
Version: Msieve-1.40
Total time: 0.46 hours.
Scaled time: 1.52 units (timescale=3.287).
Factorization parameters were as follows:
name: 78889_109
n: 3962871798306569994920826286677494795242321238202084135675334751036765403571049826135976736268091067910227
m: 1000000000000000000000
deg: 5
c5: 710000
c0: 1
skew: 0.07
type: snfs
lss: 1
rlim: 490000
alim: 490000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 490000/490000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [245000, 345001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 50567 x 50809
Total sieving time: 0.45 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,110.000,5,0,0,0,0,0,0,0,0,490000,490000,25,25,44,44,2.2,2.2,50000
total time: 0.46 hours.
 --------- CPU info (if available) ----------

Dec 20, 2009 (4th)

By Erik Branger / GMP-ECM / Dec 20, 2009

(7·10¹⁷⁸-61)/9 = (7)₁₇₇1_<178> = 631 · 1024697 · 6580916367326053_<16> · C154

C154 = P30 · P124

P30 = 186853769745984246704156867807_<30>

P124 = 9782333637560272544478678024910065237123917040258780920153923456086893930036713667499114063668907467528111774118161057376943_<124>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 1827865917091083679227195736806847949179150862459087072361259147703090009125078037186612403122755531495802543275504447567473492126110741317289394220774001 (154 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=790654530
Step 1 took 48033ms
Step 2 took 16552ms
********** Factor found in step 2: 186853769745984246704156867807
Found probable prime factor of 30 digits: 186853769745984246704156867807
Probable prime cofactor 9782333637560272544478678024910065237123917040258780920153923456086893930036713667499114063668907467528111774118161057376943 has 124 digits

Dec 20, 2009 (3rd)

By juno1369 / GMP-ECM 5.1 beta / Dec 20, 2009

(23·10¹⁴⁷+7)/3 = 7(6)₁₄₆9_<148> = 277 · 268507 · 404735883876508589_<18> · 11428779322469336699_<20> · C104

C104 = P37 · P68

P37 = 1576927594338858417099868817129842397_<37>

P68 = 14131487848710943543825233712682918947740417532191773099546602894313_<68>

Using B1=3000000, B2=4016636514, polynomial Dickson(12), sigma=3492825937
Step 1 took 33200ms
Step 2 took 30915ms
********** Factor found in step 2: 1576927594338858417099868817129842397
Found probable prime factor of 37 digits: 1576927594338858417099868817129842397
Probable prime cofactor 14131487848710943543825233712682918947740417532191773099
546602894313 has 68 digits

Dec 20, 2009 (2nd)

By Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve (Lionel Debroux + Jeff Gilchrist) / Dec 20, 2009

(34·10²⁰⁵-61)/9 = 3(7)₂₀₄1_<206> = 29 · 10631 · C201

C201 = P76 · P125

P76 = 6653243940397392494635175065150674777204673885975283838243914877021705541471_<76>

P125 = 18417507036875378011545196305661182023918816674371806336236801413263317602935876713906011448012567514226718926734700609166399_<125>

Fri Dec 18 20:08:07 2009  Msieve v. 1.43
Fri Dec 18 20:08:07 2009  random seeds: 000c36bf be452018
Fri Dec 18 20:08:07 2009  factoring
122536167090317444356867125024011682742330587441989035896249348125611104083301527989963567114320117086911659712739184291151699414457321554003671039405829333788879554516160538236509939304953236234232929
(201 digits)
Fri Dec 18 20:08:09 2009  no P-1/P+1/ECM available, skipping
Fri Dec 18 20:08:09 2009  commencing number field sieve (201-digit input)
Fri Dec 18 20:08:09 2009  R0: -100000000000000000000000000000000000000000
Fri Dec 18 20:08:09 2009  R1:  1
Fri Dec 18 20:08:09 2009  A0: -61
Fri Dec 18 20:08:09 2009  A1:  0
Fri Dec 18 20:08:09 2009  A2:  0
Fri Dec 18 20:08:09 2009  A3:  0
Fri Dec 18 20:08:09 2009  A4:  0
Fri Dec 18 20:08:09 2009  A5:  34
Fri Dec 18 20:08:09 2009  skew 1.12, size 2.293652e-14, alpha
0.988805, combined = 8.014853e-12
Fri Dec 18 20:08:09 2009
Fri Dec 18 20:08:09 2009  commencing linear algebra
Fri Dec 18 20:08:10 2009  read 2849179 cycles
Fri Dec 18 20:08:17 2009  cycles contain 8158912 unique relations
Fri Dec 18 20:09:38 2009  read 8158912 relations
Fri Dec 18 20:09:55 2009  using 20 quadratic characters above 536869560
Fri Dec 18 20:10:52 2009  building initial matrix
Fri Dec 18 20:13:37 2009  memory use: 1077.2 MB
Fri Dec 18 20:13:40 2009  read 2849179 cycles
Fri Dec 18 20:13:43 2009  matrix is 2848753 x 2849179 (844.7 MB) with
weight 251220916 (88.17/col)
Fri Dec 18 20:13:43 2009  sparse part has weight 190104494 (66.72/col)
Fri Dec 18 20:15:06 2009  filtering completed in 3 passes
Fri Dec 18 20:15:07 2009  matrix is 2841034 x 2841234 (843.4 MB) with
weight 250791225 (88.27/col)
Fri Dec 18 20:15:07 2009  sparse part has weight 189847200 (66.82/col)
Fri Dec 18 20:15:32 2009  read 2841234 cycles
Fri Dec 18 20:15:35 2009  matrix is 2841034 x 2841234 (843.4 MB) with
weight 250791225 (88.27/col)
Fri Dec 18 20:15:35 2009  sparse part has weight 189847200 (66.82/col)
Fri Dec 18 20:15:36 2009  saving the first 48 matrix rows for later
Fri Dec 18 20:15:38 2009  matrix is 2840986 x 2841234 (803.6 MB) with
weight 198459543 (69.85/col)
Fri Dec 18 20:15:38 2009  sparse part has weight 182257595 (64.15/col)
Fri Dec 18 20:15:38 2009  matrix includes 64 packed rows
Fri Dec 18 20:15:38 2009  using block size 65536 for processor cache
size 6144 kB
Fri Dec 18 20:15:55 2009  commencing Lanczos iteration (5 threads)
Fri Dec 18 20:15:55 2009  memory use: 886.4 MB
Fri Dec 18 20:16:10 2009  linear algebra at 0.0%, ETA 14h39m
Sat Dec 19 10:10:47 2009  lanczos halted after 44931 iterations (dim = 2840986)
Sat Dec 19 10:10:54 2009  recovered 37 nontrivial dependencies
Sat Dec 19 10:10:54 2009  BLanczosTime: 50565
Sat Dec 19 10:10:54 2009  elapsed time 14:02:47
Sat Dec 19 12:35:30 2009
Sat Dec 19 12:35:30 2009
Sat Dec 19 12:35:30 2009  Msieve v. 1.43
Sat Dec 19 12:35:30 2009  random seeds: 28422809 e2d017fb
Sat Dec 19 12:35:30 2009  factoring
122536167090317444356867125024011682742330587441989035896249348125611104083301527989963567114320117086911659712739184291151699414457321554003671039405829333788879554516160538236509939304953236234232929
(201 digits)
Sat Dec 19 12:35:33 2009  no P-1/P+1/ECM available, skipping
Sat Dec 19 12:35:33 2009  commencing number field sieve (201-digit input)
Sat Dec 19 12:35:33 2009  R0: -100000000000000000000000000000000000000000
Sat Dec 19 12:35:33 2009  R1:  1
Sat Dec 19 12:35:33 2009  A0: -61
Sat Dec 19 12:35:33 2009  A1:  0
Sat Dec 19 12:35:33 2009  A2:  0
Sat Dec 19 12:35:33 2009  A3:  0
Sat Dec 19 12:35:33 2009  A4:  0
Sat Dec 19 12:35:33 2009  A5:  34
Sat Dec 19 12:35:33 2009  skew 1.12, size 2.293652e-14, alpha
0.988805, combined = 8.014853e-12
Sat Dec 19 12:35:33 2009
Sat Dec 19 12:35:33 2009  commencing square root phase
Sat Dec 19 12:35:33 2009  reading relations for dependency 1
Sat Dec 19 12:35:33 2009  read 1420842 cycles
Sat Dec 19 12:35:37 2009  cycles contain 4076728 unique relations
Sat Dec 19 12:36:24 2009  read 4076728 relations
Sat Dec 19 12:36:55 2009  multiplying 4076728 relations
Sat Dec 19 12:40:50 2009  multiply complete, coefficients have about
118.51 million bits
Sat Dec 19 12:40:51 2009  initial square root is modulo 320981651
Sat Dec 19 12:48:53 2009  sqrtTime: 800
Sat Dec 19 12:48:54 2009  prp76 factor:
6653243940397392494635175065150674777204673885975283838243914877021705541471
Sat Dec 19 12:48:54 2009  prp125 factor:
18417507036875378011545196305661182023918816674371806336236801413263317602935876713906011448012567514226718926734700609166399
Sat Dec 19 12:48:54 2009  elapsed time 00:13:24

Dec 20, 2009

Factorizations of 788...889 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Factorizations of 677...779 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Dec 19, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / Dec 19, 2009

(22·10¹⁹⁰-1)/3 = 7(3)₁₉₀_<191> = 13 · 29² · C187

C187 = P79 · P109

P79 = 1589086954460310120342930905879429521528809366833603609513909755118328264030697_<79>

P109 = 4220990897919505612367717770836984034814470888118032848168472213249861735519420554262095622041612365536173433_<109>

Number: n
N=6707521570779596938931064971493033324186713009542973871154608372206469709442361047592914418122503734869965547730113722979359126802646422147016677337723711088752705875179121314674227872801
  ( 187 digits)
SNFS difficulty: 191 digits.
Divisors found:

Sun Dec 20 01:10:59 2009  prp79 factor: 1589086954460310120342930905879429521528809366833603609513909755118328264030697
Sun Dec 20 01:10:59 2009  prp109 factor: 4220990897919505612367717770836984034814470888118032848168472213249861735519420554262095622041612365536173433
Sun Dec 20 01:10:59 2009  elapsed time 05:31:12 (Msieve 1.42 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: ~ 24.00 hours.
Scaled time: 0.00 units (timescale=0.841).
Factorization parameters were as follows:
name: KA_7_3_190
n: 6707521570779596938931064971493033324186713009542973871154608372206469709442361047592914418122503734869965547730113722979359126802646422147016677337723711088752705875179121314674227872801
m: 100000000000000000000000000000000000000
deg: 5
c5: 22
c0: -1
skew: 0.54
type: snfs
lss: 1
rlim: 10800000
alim: 10800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10800000/10800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 100000)
Primes: RFBsize:714154, AFBsize:715059, 
Relations: 
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2607696 hash collisions in 25900935 relations
Msieve: matrix is 1487381 x 1487606 (399.5 MB)

Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,10800000,10800000,28,28,56,56,2.5,2.5,100000
total time: 0.00 hours.
 --------- CPU info (if available) ----------

Dec 19, 2009 (5th)

By Lionel Debroux / GMP-ECM 6.2.3 / Dec 19, 2009

4·10¹⁸⁴+9 = 4(0)₁₈₃9_<185> = 86629 · 17315047017625261_<17> · C164

C164 = P45 · P119

P45 = 288744426922067304879725083649398238432589757_<45>

P119 = 92354785582575909641556220757639434258139568193136633677444230328449938740199812268290197677719701254300588804590341373_<119>

GMP-ECM 6.2.3 [powered by GMP 4.2.2] [ECM]
Input number is 26666929636551284865749676559985064929619556026911197840995261892026232694863092865560797017860538142122468810446558611395066656624799409134739874379357033093116361 (164 digits)
Run 35 out of 100:
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1323134362
Step 1 took 318837ms
********** Factor found in step 1: 288744426922067304879725083649398238432589757
Found probable prime factor of 45 digits: 288744426922067304879725083649398238432589757
Probable prime cofactor 92354785582575909641556220757639434258139568193136633677444230328449938740199812268290197677719701254300588804590341373 has 119 digits

Dec 19, 2009 (4th)

By Erik Branger / GMP-ECM / Dec 19, 2009

4·10²³²+9 = 4(0)₂₃₁9_<233> = 6781 · 86869 · C224

C224 = P42 · C183

P42 = 101923364225918527839065891102757815508373_<42>

C183 = [666235353567257533671029519064380742774418132917318448895197569176610167844598276515950058676003746683731464996043877358855070285429649231163084825310162994068656389331159825129096997_<183>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 67904948601819198358348975988027569864095494226722118685189278313149540860095860499224382037763303411691122682004950443910691554199279454139415979313395714972638320593552945621688300060030181474837730472727141115135982655881 (224 digits)
Run 236 out of 500:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1485941456
Step 1 took 127406ms
Step 2 took 29578ms
********** Factor found in step 2: 101923364225918527839065891102757815508373
Found probable prime factor of 42 digits: 101923364225918527839065891102757815508373
Composite cofactor 666235353567257533671029519064380742774418132917318448895197569176610167844598276515950058676003746683731464996043877358855070285429649231163084825310162994068656389331159825129096997 has 183 digits

Dec 19, 2009 (3rd)

By Sinkiti Sibata / Msieve / Dec 19, 2009

(23·10¹⁴¹+7)/3 = 7(6)₁₄₀9_<142> = 9138981342729282882631_<22> · C120

C120 = P49 · P72

P49 = 2083853324801408599389966838086141184874984236681_<49>

P72 = 402570218528526070940163750097373007378101682310498374715713110986762579_<72>

Number: 76669_141
N=838897288346698676736378991019063509193383444639059360334579951375235148072501160068008255407397685675289825881689960299
  ( 120 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=2083853324801408599389966838086141184874984236681 (pp49)
 r2=402570218528526070940163750097373007378101682310498374715713110986762579 (pp72)
Version: Msieve v. 1.42
Total time: 0.30 hours.
Scaled time: 0.21 units (timescale=0.682).
Factorization parameters were as follows:
name: 76669_141
n: 838897288346698676736378991019063509193383444639059360334579951375235148072501160068008255407397685675289825881689960299
m: 10000000000000000000000000000
deg: 5
c5: 230
c0: 7
skew: 0.50
type: snfs
lss: 1
rlim: 1650000
alim: 1650000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1650000/1650000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [825000, 1625001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 264587 x 264812
Total sieving time: 0.00 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,142.000,5,0,0,0,0,0,0,0,0,1650000,1650000,26,26,48,48,2.3,2.3,100000
total time: 0.30 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.30 BogoMIPS (lpj=1860651)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860572)
Total of 2 processors activated (7442.44 BogoMIPS).

Total time: 4 hours 44 min.

(71·10¹⁴¹-53)/9 = 7(8)₁₄₀3_<142> = 233754297133941847_<18> · C125

C125 = P49 · P77

P49 = 1028967226993553793418908374844708409590884949523_<49>

P77 = 32798553711507640264348032595324966676169736366141269700962862828462355796743_<77>

Number: 78883_141
N=33748636861929148339334334363836166800737368700426691036330973643596267989705810764371598304678331614234259024551154002803589
  ( 125 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=1028967226993553793418908374844708409590884949523 (pp49)
 r2=32798553711507640264348032595324966676169736366141269700962862828462355796743 (pp77)
Version: Msieve-1.40
Total time: 8.15 hours.
Scaled time: 27.07 units (timescale=3.322).
Factorization parameters were as follows:
name: 78883_141
n: 33748636861929148339334334363836166800737368700426691036330973643596267989705810764371598304678331614234259024551154002803589
m: 10000000000000000000000000000
deg: 5
c5: 710
c0: -53
skew: 0.60
type: snfs
lss: 1
rlim: 1680000
alim: 1680000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1680000/1680000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [840000, 2240001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 293687 x 293935
Total sieving time: 7.94 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142.000,5,0,0,0,0,0,0,0,0,1680000,1680000,26,26,48,48,2.3,2.3,100000
total time: 8.15 hours.
 --------- CPU info (if available) ----------

(71·10¹⁴²-53)/9 = 7(8)₁₄₁3_<143> = 7 · 29 · 9883 · 439015815397321_<15> · C122

C122 = P42 · P81

P42 = 386490477254802054771629653876754876141479_<42>

P81 = 231745890891283210023353126279632762290504685320045999233520726993901299486391013_<81>

Number: 78883_142
N=89567579972411332167997785100721330165586386507326808361935784453289559482928541490572916963000743105308267240364502128227
  ( 122 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=386490477254802054771629653876754876141479 (pp42)
 r2=231745890891283210023353126279632762290504685320045999233520726993901299486391013 (pp81)
Version: Msieve-1.40
Total time: 8.84 hours.
Scaled time: 29.36 units (timescale=3.322).
Factorization parameters were as follows:
name: 78883_142
n: 89567579972411332167997785100721330165586386507326808361935784453289559482928541490572916963000743105308267240364502128227
m: 10000000000000000000000000000
deg: 5
c5: 7100
c0: -53
skew: 0.38
type: snfs
lss: 1
rlim: 1750000
alim: 1750000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1750000/1750000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [875000, 2375001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 326827 x 327075
Total sieving time: 8.56 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,143.000,5,0,0,0,0,0,0,0,0,1750000,1750000,26,26,48,48,2.3,2.3,100000
total time: 8.84 hours.
 --------- CPU info (if available) ----------

(23·10¹⁴²+7)/3 = 7(6)₁₄₁9_<143> = 67 · 89 · 465529 · 37894385693_<11> · C123

C123 = P32 · P92

P32 = 71949625685388118004628906184513_<32>

P92 = 10129584265009358087759358380931186887271440274828731755903178974061895680101063464082645483_<92>

Number: 76669_142
N=728819796216020631469069013156918914136300178569459943687460673644864973048609517087817464282035309952331459120412764004779
  ( 123 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=71949625685388118004628906184513 (pp32)
 r2=10129584265009358087759358380931186887271440274828731755903178974061895680101063464082645483 (pp92)
Version: Msieve v. 1.42
Total time: 0.36 hours.
Scaled time: 0.24 units (timescale=0.682).
Factorization parameters were as follows:
name: 76669_142
n: 728819796216020631469069013156918914136300178569459943687460673644864973048609517087817464282035309952331459120412764004779
m: 10000000000000000000000000000
deg: 5
c5: 2300
c0: 7
skew: 0.31
type: snfs
lss: 1
rlim: 1720000
alim: 1720000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1720000/1720000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [860000, 2160001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 304107 x 304332
Total sieving time: 0.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,143.000,5,0,0,0,0,0,0,0,0,1720000,1720000,26,26,48,48,2.3,2.3,100000
total time: 0.36 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.30 BogoMIPS (lpj=1860651)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860572)
Total of 2 processors activated (7442.44 BogoMIPS).

Total time: 7 hours 28 min.

Dec 19, 2009 (2nd)

By Dmitry Domanov / ECMNET, GMP-ECM / Dec 19, 2009

(10²²¹+53)/9 = (1)₂₂₀7_<221> = 373669 · C215

C215 = P41 · P174

P41 = 47430347717597954312536069175541845627383_<41>

P174 = 626922868782558004553335157712002344289399823572657343183104607051391681936448830280881347095951536584729574529903284010942437487887893901180186138277399954934031929504291071_<174>

Factor=47430347717597954312536069175541845627383  Method=ECM  B1=11000000  Sigma=2749378352

Dec 19, 2009

By Erik Branger / PFGW / Dec 19, 2009

(7·10³⁷⁹⁶³-61)/9 = (7)₃₇₉₆₂1_<37963> is PRP.

(7·10⁹¹⁸⁵⁶-61)/9 = (7)₉₁₈₅₅1_<91856> is PRP.

PRP91856 is the second largest unprovable near-repdigit PRP in our tables so far. Congratulations!

Note: (7·10³⁷⁹⁶³-61)/9-1 = 70·(10³⁷⁹⁶²-1)/9 = 70·Π_d|37962,d>1Φ_d(10) = 2·5·7·Π_{d=2,3,6,9,18,19,27,37,38,54,57,74,111,114,171,222,333,342,513,666,703,999,1026,1406,1998,2109,4218,6327,12654,18981,37962}Φ_d(10)

Dec 18, 2009 (6th)

By Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve (Lionel Debroux + Jeff Gilchrist) / Dec 18, 2009

(10²¹⁰+17)/9 = (1)₂₀₉3_<210> = 991 · 17033 · C202

C202 = P53 · P150

P53 = 54717842005390052986694843098297751937806958850145813_<53>

P150 = 120299474039985466509894312228083847477033404838138052450639905530474929720985885145271068672098287759467609956582980764206909588207568280635808876067_<150>

Thu Dec 17 06:26:40 2009  Msieve v. 1.43
Thu Dec 17 06:26:40 2009  random seeds: 55bc7df8 28c1ed01
Thu Dec 17 06:26:40 2009  factoring
6582527613851446978131730819618752244107085954717989475947006360900491620682609825013574653008474800244477708589488281346603735332968305847034815192608016332462195046388618988800401944934168042595957471
(202 digits)
Thu Dec 17 06:26:42 2009  no P-1/P+1/ECM available, skipping
Thu Dec 17 06:26:42 2009  commencing number field sieve (202-digit input)
Thu Dec 17 06:26:42 2009  R0: -1000000000000000000000000000000000000000000
Thu Dec 17 06:26:42 2009  R1:  1
Thu Dec 17 06:26:42 2009  A0:  17
Thu Dec 17 06:26:42 2009  A1:  0
Thu Dec 17 06:26:42 2009  A2:  0
Thu Dec 17 06:26:42 2009  A3:  0
Thu Dec 17 06:26:42 2009  A4:  0
Thu Dec 17 06:26:42 2009  A5:  1
Thu Dec 17 06:26:42 2009  skew 1.76, size 2.505786e-14, alpha
1.047729, combined = 7.967069e-12
Thu Dec 17 06:26:42 2009
Thu Dec 17 06:26:42 2009  commencing linear algebra
Thu Dec 17 06:26:43 2009  read 2888485 cycles
Thu Dec 17 06:26:50 2009  cycles contain 8004660 unique relations
Thu Dec 17 06:28:10 2009  read 8004660 relations
Thu Dec 17 06:28:26 2009  using 20 quadratic characters above 536868864
Thu Dec 17 06:29:23 2009  building initial matrix
Thu Dec 17 06:32:05 2009  memory use: 1052.8 MB
Thu Dec 17 06:32:08 2009  read 2888485 cycles
Thu Dec 17 06:32:11 2009  matrix is 2888023 x 2888485 (844.9 MB) with
weight 248051754 (85.88/col)
Thu Dec 17 06:32:11 2009  sparse part has weight 189723693 (65.68/col)
Thu Dec 17 06:33:34 2009  filtering completed in 3 passes
Thu Dec 17 06:33:35 2009  matrix is 2881653 x 2881853 (843.8 MB) with
weight 247679676 (85.94/col)
Thu Dec 17 06:33:35 2009  sparse part has weight 189487001 (65.75/col)
Thu Dec 17 06:34:00 2009  read 2881853 cycles
Thu Dec 17 06:34:04 2009  matrix is 2881653 x 2881853 (843.8 MB) with
weight 247679676 (85.94/col)
Thu Dec 17 06:34:04 2009  sparse part has weight 189487001 (65.75/col)
Thu Dec 17 06:34:04 2009  saving the first 48 matrix rows for later
Thu Dec 17 06:34:06 2009  matrix is 2881605 x 2881853 (799.4 MB) with
weight 195469859 (67.83/col)
Thu Dec 17 06:34:07 2009  sparse part has weight 180734590 (62.71/col)
Thu Dec 17 06:34:07 2009  matrix includes 64 packed rows
Thu Dec 17 06:34:07 2009  using block size 65536 for processor cache
size 6144 kB
Thu Dec 17 06:34:23 2009  commencing Lanczos iteration (5 threads)
Thu Dec 17 06:34:23 2009  memory use: 885.9 MB
Thu Dec 17 06:34:38 2009  linear algebra at 0.0%, ETA 14h51m
Thu Dec 17 20:55:45 2009  lanczos halted after 45570 iterations (dim = 2881603)
Thu Dec 17 20:55:53 2009  recovered 34 nontrivial dependencies
Thu Dec 17 20:55:54 2009  BLanczosTime: 52152
Thu Dec 17 20:55:54 2009  elapsed time 14:29:14
Thu Dec 17 21:23:08 2009
Thu Dec 17 21:23:08 2009
Thu Dec 17 21:23:08 2009  Msieve v. 1.43
Thu Dec 17 21:23:08 2009  random seeds: f9fbe826 ee5d58a0
Thu Dec 17 21:23:08 2009  factoring
6582527613851446978131730819618752244107085954717989475947006360900491620682609825013574653008474800244477708589488281346603735332968305847034815192608016332462195046388618988800401944934168042595957471
(202 digits)
Thu Dec 17 21:23:10 2009  no P-1/P+1/ECM available, skipping
Thu Dec 17 21:23:10 2009  commencing number field sieve (202-digit input)
Thu Dec 17 21:23:10 2009  R0: -1000000000000000000000000000000000000000000
Thu Dec 17 21:23:10 2009  R1:  1
Thu Dec 17 21:23:10 2009  A0:  17
Thu Dec 17 21:23:10 2009  A1:  0
Thu Dec 17 21:23:10 2009  A2:  0
Thu Dec 17 21:23:10 2009  A3:  0
Thu Dec 17 21:23:10 2009  A4:  0
Thu Dec 17 21:23:10 2009  A5:  1
Thu Dec 17 21:23:10 2009  skew 1.76, size 2.505786e-14, alpha
1.047729, combined = 7.967069e-12
Thu Dec 17 21:23:11 2009
Thu Dec 17 21:23:11 2009  commencing square root phase
Thu Dec 17 21:23:11 2009  reading relations for dependency 1
Thu Dec 17 21:23:11 2009  read 1439936 cycles
Thu Dec 17 21:23:15 2009  cycles contain 3996572 unique relations
Thu Dec 17 21:24:02 2009  read 3996572 relations
Thu Dec 17 21:24:33 2009  multiplying 3996572 relations
Thu Dec 17 21:27:39 2009  multiply complete, coefficients have about
97.23 million bits
Thu Dec 17 21:27:41 2009  initial square root is modulo 9532921
Thu Dec 17 21:33:58 2009  sqrtTime: 647
Thu Dec 17 21:33:59 2009  prp53 factor:
54717842005390052986694843098297751937806958850145813
Thu Dec 17 21:33:59 2009  prp150 factor:
120299474039985466509894312228083847477033404838138052450639905530474929720985885145271068672098287759467609956582980764206909588207568280635808876067
Thu Dec 17 21:33:59 2009  elapsed time 00:10:51

Dec 18, 2009 (6th)

By Sinkiti Sibata / Msieve / Dec 18, 2009

(64·10¹⁶⁶+71)/9 = 7(1)₁₆₅9_<167> = 503 · 20117 · 395429341 · C152

C152 = P48 · P104

P48 = 210228399327928377239219774246468321235282735719_<48>

P104 = 84536835945892939231027778594787388720995315395727328509256533229038199119074887652958622708169064322511_<104>

Number: 71119_166
N=17772043705152750668618075206786427141878408477059419522437704603544996626585922137963280383978633254754888183355446140445126615312662697395867395470409
  ( 152 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=210228399327928377239219774246468321235282735719 (pp48)
 r2=84536835945892939231027778594787388720995315395727328509256533229038199119074887652958622708169064322511 (pp104)
Version: Msieve-1.40
Total time: 45.88 hours.
Scaled time: 153.20 units (timescale=3.339).
Factorization parameters were as follows:
name: 71119_166
n: 17772043705152750668618075206786427141878408477059419522437704603544996626585922137963280383978633254754888183355446140445126615312662697395867395470409
m: 2000000000000000000000000000000000
deg: 5
c5: 20
c0: 71
skew: 1.29
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 4600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 798327 x 798575
Total sieving time: 44.54 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,167.000,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 45.88 hours.
 --------- CPU info (if available) ----------

(71·10¹³⁹-53)/9 = 7(8)₁₃₈3_<140> = 801174683 · C131

C131 = P32 · P38 · P62

P32 = 14659793272247047053381486853609_<32>

P38 = 68028420190133278374253607086763647043_<38>

P62 = 98734831756079313401932916138550660196735650678372000189629323_<62>

Number: 78883_139
N=98466527416329865342099044945593829865051900159567185036585696616288221989272330624667141271722996879681592346183621092890785827401
  ( 131 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=14659793272247047053381486853609 (pp32)
 r2=68028420190133278374253607086763647043 (pp38)
 r3=98734831756079313401932916138550660196735650678372000189629323 (pp62)
Version: Msieve v. 1.42
Total time: 0.62 hours.
Scaled time: 0.50 units (timescale=0.796).
Factorization parameters were as follows:
name: 78883_139
n: 98466527416329865342099044945593829865051900159567185036585696616288221989272330624667141271722996879681592346183621092890785827401
m: 1000000000000000000000000000
deg: 5
c5: 710000
c0: -53
skew: 0.15
type: snfs
lss: 1
rlim: 1560000
alim: 1560000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1560000/1560000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [780000, 2180001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 306659 x 306907
Total sieving time: 0.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,140.000,5,0,0,0,0,0,0,0,0,1560000,1560000,26,26,48,48,2.3,2.3,100000
total time: 0.62 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.30 BogoMIPS (lpj=1860651)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860572)
Total of 2 processors activated (7442.44 BogoMIPS).

Total time: 8 hours 14 min.

Dec 18, 2009 (5th)

By Dmitry Domanov / YAFU v1.14, Msieve, GGNFS/msieve, ECMNET, GMP-ECM / Dec 18, 2009

(23·10¹⁴⁵+7)/3 = 7(6)₁₄₄9_<146> = 109 · 359 · 4339 · 1679273 · 490556707 · 74145169250683_<14> · 176715146310626906597009_<24> · C86

C86 = P33 · P54

P33 = 308224982757838303873874799904859_<33>

P54 = 135725355871998971820929399371563345018944591056562047_<54>

12/17/09 19:19:44 v1.14 @ REPGMAIL, starting SIQS on c86: 41833945473448350880238225571747760250081278595496669485943405224873781172003230286373
12/17/09 19:19:44 v1.14 @ REPGMAIL, random seeds: 0, 3887612160
12/17/09 19:19:44 v1.14 @ REPGMAIL, ==== sieve params ====
12/17/09 19:19:44 v1.14 @ REPGMAIL, n = 86 digits, 286 bits
12/17/09 19:19:44 v1.14 @ REPGMAIL, factor base: 57516 primes (max prime = 1506473)
12/17/09 19:19:44 v1.14 @ REPGMAIL, single large prime cutoff: 165712030 (110 * pmax)
12/17/09 19:19:44 v1.14 @ REPGMAIL, double large prime range from 43 to 50 bits
12/17/09 19:19:44 v1.14 @ REPGMAIL, double large prime cutoff: 623501162502699
12/17/09 19:19:44 v1.14 @ REPGMAIL, allocating 12 large prime slices of factor base
12/17/09 19:19:44 v1.14 @ REPGMAIL, buckets hold 1024 elements
12/17/09 19:19:44 v1.14 @ REPGMAIL, sieve interval: 18 blocks of size 32768
12/17/09 19:19:44 v1.14 @ REPGMAIL, polynomial A has ~ 11 factors
12/17/09 19:19:44 v1.14 @ REPGMAIL, using multiplier of 2
12/17/09 19:19:44 v1.14 @ REPGMAIL, using small prime variation correction of 21 bits
12/17/09 19:19:44 v1.14 @ REPGMAIL, using SSE2 for trial division and x128 sieve scanning
12/17/09 19:19:44 v1.14 @ REPGMAIL, trial factoring cutoff at 93 bits
12/17/09 19:19:44 v1.14 @ REPGMAIL, ==== sieving started ( 8 threads) ====
12/17/09 19:27:13 v1.14 @ REPGMAIL, trial division touched 12867503 sieve locations out of 5630374969344
12/17/09 19:27:13 v1.14 @ REPGMAIL, 57789 relations found: 19383 full + 38406 from 538217 partial, using 4772928 polys (383 A polys)
12/17/09 19:27:13 v1.14 @ REPGMAIL, on average, sieving found 0.12 rels/poly and 1243.53 rels/sec
12/17/09 19:27:13 v1.14 @ REPGMAIL, trial division touched 12867503 sieve locations out of 5630374969344
12/17/09 19:27:13 v1.14 @ REPGMAIL, ==== post processing stage (msieve-1.38) ====
12/17/09 19:27:13 v1.14 @ REPGMAIL, begin with 557600 relations
12/17/09 19:27:13 v1.14 @ REPGMAIL, reduce to 118522 relations in 9 passes
12/17/09 19:27:17 v1.14 @ REPGMAIL, recovered 118522 relations
12/17/09 19:27:17 v1.14 @ REPGMAIL, recovered 88934 polynomials
12/17/09 19:27:17 v1.14 @ REPGMAIL, attempting to build 57789 cycles
12/17/09 19:27:17 v1.14 @ REPGMAIL, found 57789 cycles in 5 passes
12/17/09 19:27:17 v1.14 @ REPGMAIL, distribution of cycle lengths:
12/17/09 19:27:17 v1.14 @ REPGMAIL,    length 1 : 19383
12/17/09 19:27:17 v1.14 @ REPGMAIL,    length 2 : 15799
12/17/09 19:27:17 v1.14 @ REPGMAIL,    length 3 : 10625
12/17/09 19:27:17 v1.14 @ REPGMAIL,    length 4 : 6108
12/17/09 19:27:17 v1.14 @ REPGMAIL,    length 5 : 3174
12/17/09 19:27:17 v1.14 @ REPGMAIL,    length 6 : 1511
12/17/09 19:27:17 v1.14 @ REPGMAIL,    length 7 : 662
12/17/09 19:27:17 v1.14 @ REPGMAIL,    length 9+: 527
12/17/09 19:27:17 v1.14 @ REPGMAIL, largest cycle: 18 relations
12/17/09 19:27:18 v1.14 @ REPGMAIL, matrix is 57516 x 57789 (11.5 MB) with weight 2782363 (48.15/col)
12/17/09 19:27:18 v1.14 @ REPGMAIL, sparse part has weight 2782363 (48.15/col)
12/17/09 19:27:19 v1.14 @ REPGMAIL, filtering completed in 3 passes
12/17/09 19:27:19 v1.14 @ REPGMAIL, matrix is 50686 x 50748 (10.3 MB) with weight 2498924 (49.24/col)
12/17/09 19:27:19 v1.14 @ REPGMAIL, sparse part has weight 2498924 (49.24/col)
12/17/09 19:27:19 v1.14 @ REPGMAIL, saving the first 48 matrix rows for later
12/17/09 19:27:19 v1.14 @ REPGMAIL, matrix is 50638 x 50748 (8.4 MB) with weight 2108203 (41.54/col)
12/17/09 19:27:19 v1.14 @ REPGMAIL, sparse part has weight 1895287 (37.35/col)
12/17/09 19:27:19 v1.14 @ REPGMAIL, matrix includes 64 packed rows
12/17/09 19:27:19 v1.14 @ REPGMAIL, using block size 20299 for processor cache size 6144 kB
12/17/09 19:27:20 v1.14 @ REPGMAIL, commencing Lanczos iteration
12/17/09 19:27:20 v1.14 @ REPGMAIL, memory use: 7.7 MB
12/17/09 19:27:34 v1.14 @ REPGMAIL, lanczos halted after 802 iterations (dim = 50632)
12/17/09 19:27:35 v1.14 @ REPGMAIL, recovered 14 nontrivial dependencies
12/17/09 19:27:35 v1.14 @ REPGMAIL, prp54 = 135725355871998971820929399371563345018944591056562047
12/17/09 19:27:39 v1.14 @ REPGMAIL, prp33 = 308224982757838303873874799904859
12/17/09 19:27:39 v1.14 @ REPGMAIL, Lanczos elapsed time = 21.9690 seconds.
12/17/09 19:27:39 v1.14 @ REPGMAIL, Sqrt elapsed time = 4.4530 seconds.
12/17/09 19:27:39 v1.14 @ REPGMAIL, SIQS elapsed time = 474.8220 seconds.

(22·10¹⁷³+23)/9 = 2(4)₁₇₂7_<174> = 7 · 26557 · C169

C169 = P51 · P118

P51 = 624738918926696617026480583427783554414155170496779_<51>

P118 = 2104769569075983439269108367771371408243333338166694269946412434388897100049518126394608775065678536993872431454145207_<118>

N=1314931465174338992917898667795116942234463038770754250665385206184242219939023041783142698155689080868882804342381854902094386975962455120492549419009486035128991788253
  ( 169 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=624738918926696617026480583427783554414155170496779 (pp51)
 r2=2104769569075983439269108367771371408243333338166694269946412434388897100049518126394608775065678536993872431454145207 (pp118)
Version: Msieve-1.40
Total time: 94.38 hours.
Scaled time: 174.60 units (timescale=1.850).
Factorization parameters were as follows:
n: 1314931465174338992917898667795116942234463038770754250665385206184242219939023041783142698155689080868882804342381854902094386975962455120492549419009486035128991788253
m: 10000000000000000000000000000000000
deg: 5
c5: 22000
c0: 23
skew: 0.25
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 240000Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 8080001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 970616 x 970843
Total sieving time: 92.89 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.14 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 94.38 hours.
 --------- CPU info (if available) ----------

(23·10¹⁰²+7)/3 = 7(6)₁₀₁9_<103> = C103

C103 = P38 · P66

P38 = 16366251904462813283148459651532808177_<38>

P66 = 468443643139581039544972884127926202489907608934281528490340905597_<66>

N=7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 103 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=16366251904462813283148459651532808177 (pp38)
 r2=468443643139581039544972884127926202489907608934281528490340905597 (pp66)
Version: Msieve-1.40
Total time: 0.29 hours.
Scaled time: 0.55 units (timescale=1.899).
Factorization parameters were as follows:
n: 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 10000000000000000000000000
deg: 4
c4: 2300
c0: 7
skew: 0.23
type: snfs
lss: 1
rlim: 370000
alim: 370000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2Factor base limits: 370000/370000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [185000, 245001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 29258 x 29485
Total sieving time: 0.28 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103.000,4,0,0,0,0,0,0,0,0,370000,370000,25,25,43,43,2.2,2.2,10000
total time: 0.29 hours.
 --------- CPU info (if available) ----------

(71·10¹⁰²-53)/9 = 7(8)₁₀₁3_<103> = C103

C103 = P32 · P72

P32 = 70844568918754187799073067693869_<32>

P72 = 111354885904323972056732251864761215138728152912876090552311636191082207_<72>

N=7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
  ( 103 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=70844568918754187799073067693869 (pp32)
 r2=111354885904323972056732251864761215138728152912876090552311636191082207 (pp72)
Version: Msieve-1.40
Total time: 0.34 hours.
Scaled time: 0.65 units (timescale=1.888).
Factorization parameters were as follows:
n: 7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
m: 10000000000000000000000000
deg: 4
c4: 7100
c0: -53
skew: 0.29
type: snfs
lss: 1
rlim: 380000
alim: 380000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2Factor base limits: 380000/380000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [190000, 250001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 30812 x 31042
Total sieving time: 0.33 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103.000,4,0,0,0,0,0,0,0,0,380000,380000,25,25,43,43,2.2,2.2,10000
total time: 0.34 hours.
 --------- CPU info (if available) ----------

(23·10¹⁰¹+7)/3 = 7(6)₁₀₀9_<102> = 127 · 499 · C98

C98 = P35 · P63

P35 = 15503305797418981345720755638978753_<35>

P63 = 780329456446274801345339576045023254771125029723964628297791201_<63>

N=12097686186020334632519632440734487347398208490471757162619201657908993840699772247907889269352353
  ( 98 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=15503305797418981345720755638978753 (pp35)
 r2=780329456446274801345339576045023254771125029723964628297791201 (pp63)
Version: Msieve-1.40
Total time: 0.24 hours.
Scaled time: 0.46 units (timescale=1.899).
Factorization parameters were as follows:
n: 12097686186020334632519632440734487347398208490471757162619201657908993840699772247907889269352353
m: 10000000000000000000000000
deg: 4
c4: 230
c0: 7
skew: 0.42
type: snfs
lss: 1
rlim: 360000
alim: 360000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [180000, 230001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 28464 x 28690
Total sieving time: 0.23 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,102.000,4,0,0,0,0,0,0,0,0,360000,360000,25,25,43,43,2.2,2.2,10000
total time: 0.24 hours.
 --------- CPU info (if available) ----------

(71·10¹¹²-53)/9 = 7(8)₁₁₁3_<113> = 7² · 96853717 · C104

C104 = P32 · P72

P32 = 47211579907345209783386536065091_<32>

P72 = 352091007064452232705688454932089110461872691511398725150686552297151261_<72>

N=16622772714681033343850236198164510360461350285372364831785947387382841694980130661290056398395768729751
  ( 104 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=47211579907345209783386536065091 (pp32)
 r2=352091007064452232705688454932089110461872691511398725150686552297151261 (pp72)
Version: Msieve-1.40
Total time: 1.16 hours.
Scaled time: 2.19 units (timescale=1.894).
Factorization parameters were as follows:
n: 16622772714681033343850236198164510360461350285372364831785947387382841694980130661290056398395768729751
m: 10000000000000000000000
deg: 5
c5: 7100
c0: -53
skew: 0.38
type: snfs
lss: 1
rlim: 550000
alim: 550000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 550000/550000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [275000, 575001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 61515 x 61746
Total sieving time: 1.13 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,113.000,5,0,0,0,0,0,0,0,0,550000,550000,25,25,45,45,2.2,2.2,50000
total time: 1.16 hours.
 --------- CPU info (if available) ----------

(23·10¹¹⁷+7)/3 = 7(6)₁₁₆9_<118> = C118

C118 = P56 · P63

P56 = 14569581354226241661746116562056802057508343476522953837_<56>

P63 = 526210498453531331924932909008559187519482724594784737411043137_<63>

N=7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 118 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=14569581354226241661746116562056802057508343476522953837 (pp56)
 r2=526210498453531331924932909008559187519482724594784737411043137 (pp63)
Version: Msieve-1.40
Total time: 1.40 hours.
Scaled time: 2.63 units (timescale=1.883).
Factorization parameters were as follows:
n: 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 100000000000000000000000
deg: 5
c5: 2300
c0: 7
skew: 0.31
type: snfs
lss: 1
rlim: 660000
alim: 660000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 660000/660000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [330000, 680001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 73555 x 73781
Total sieving time: 1.36 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,118.000,5,0,0,0,0,0,0,0,0,660000,660000,25,25,45,45,2.2,2.2,50000
total time: 1.40 hours.
 --------- CPU info (if available) ----------

(8·10²¹⁴+1)/9 = (8)₂₁₃9_<214> = 3 · 1699 · 2459 · C207

C207 = P30 · C178

P30 = 335641198293710957912166662603_<30>

C178 = [2112997836126207443444981630168333103292685356156473714928084867103157017340713491392612217986513249301447225320298675488334218036013653216145526375104840470441559720260810151081_<178>]

Factor=335641198293710957912166662603  Method=ECM  B1=11000000  Sigma=265716689

(71·10¹¹⁴-53)/9 = 7(8)₁₁₃3_<115> = 29 · 103 · C112

C112 = P53 · P59

P53 = 56519698895229316188490043104959016857411842457689633_<53>

P59 = 46728385615779825473711854488768379726422437915981202391673_<59>

N=2641074284864040471673548339099058884797083658817840270803109771974853996949745192128854666517873749209537626009
  ( 112 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=56519698895229316188490043104959016857411842457689633 (pp53)
 r2=46728385615779825473711854488768379726422437915981202391673 (pp59)
Version: Msieve-1.40
Total time: 1.53 hours.
Scaled time: 2.87 units (timescale=1.877).
Factorization parameters were as follows:
n: 2641074284864040471673548339099058884797083658817840270803109771974853996949745192128854666517873749209537626009
m: 10000000000000000000000
deg: 5
c5: 710000
c0: -53
skew: 0.15
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [300000, 700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 68831 x 69064
Total sieving time: 1.49 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115.000,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000
total time: 1.53 hours.
 --------- CPU info (if available) ----------

(71·10¹²⁰-53)/9 = 7(8)₁₁₉3_<121> = 59 · C120

C120 = P46 · P74

P46 = 2214181774753291992262900298930816059454662351_<46>

P74 = 60387987423709368360648898963089341431741881661843328297994020494593986887_<74>

N=133709981167608286252354048964218455743879472693032015065913370998116760828625235404896421845574387947269303201506591337
  ( 120 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=2214181774753291992262900298930816059454662351 (pp46)
 r2=60387987423709368360648898963089341431741881661843328297994020494593986887 (pp74)
Version: Msieve-1.40
Total time: 1.30 hours.
Scaled time: 2.52 units (timescale=1.934).
Factorization parameters were as follows:
n: 133709981167608286252354048964218455743879472693032015065913370998116760828625235404896421845574387947269303201506591337
m: 1000000000000000000000000
deg: 5
c5: 71
c0: -53
skew: 0.94
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 675001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 73350 x 73577
Total sieving time: 1.27 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 1.30 hours.
 --------- CPU info (if available) ----------

(23·10¹²⁷+7)/3 = 7(6)₁₂₆9_<128> = 977 · 2884173194897_<13> · C113

C113 = P36 · P77

P36 = 903364418940510837202718011796346043_<36>

P77 = 30118108980930079273273885810813189661278080103264113178198009378613739190807_<77>

N=27207628019144882054012175877546708769211265306368105830557938863759367147355611190125656060628084554910176426701
  ( 113 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=903364418940510837202718011796346043 (pp36)
 r2=30118108980930079273273885810813189661278080103264113178198009378613739190807 (pp77)
Version: Msieve-1.40
Total time: 2.10 hours.
Scaled time: 3.95 units (timescale=1.877).
Factorization parameters were as follows:
n: 27207628019144882054012175877546708769211265306368105830557938863759367147355611190125656060628084554910176426701
m: 10000000000000000000000000
deg: 5
c5: 2300
c0: 7
skew: 0.31
type: snfs
lss: 1
rlim: 960000
alim: 960000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 960000/960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [480000, 930001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 147422 x 147647
Total sieving time: 2.02 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,128.000,5,0,0,0,0,0,0,0,0,960000,960000,26,26,47,47,2.3,2.3,50000
total time: 2.10 hours.
 --------- CPU info (if available) ----------

(71·10¹¹⁷-53)/9 = 7(8)₁₁₆3_<118> = 2341 · 54773 · 60533682573218171561_<20> · C91

C91 = P43 · P48

P43 = 4704278905960870672702840636154862664420573_<43>

P48 = 216051725822903176121266690809152805746919124127_<48>

12/17/09 22:34:05 v1.14 @ REPGMAIL, starting SIQS on c91: 1016367576385124944414837275702956041270890279227086998560930210620703853098252911119464771
12/17/09 22:34:05 v1.14 @ REPGMAIL, random seeds: 0, 3887612160
12/17/09 22:34:06 v1.14 @ REPGMAIL, ==== sieve params ====
12/17/09 22:34:06 v1.14 @ REPGMAIL, n = 91 digits, 302 bits
12/17/09 22:34:06 v1.14 @ REPGMAIL, factor base: 66328 primes (max prime = 1763191)
12/17/09 22:34:06 v1.14 @ REPGMAIL, single large prime cutoff: 211582920 (120 * pmax)
12/17/09 22:34:06 v1.14 @ REPGMAIL, double large prime range from 43 to 50 bits
12/17/09 22:34:06 v1.14 @ REPGMAIL, double large prime cutoff: 967977118911139
12/17/09 22:34:06 v1.14 @ REPGMAIL, allocating 13 large prime slices of factor base
12/17/09 22:34:06 v1.14 @ REPGMAIL, buckets hold 1024 elements
12/17/09 22:34:06 v1.14 @ REPGMAIL, sieve interval: 22 blocks of size 32768
12/17/09 22:34:06 v1.14 @ REPGMAIL, polynomial A has ~ 12 factors
12/17/09 22:34:06 v1.14 @ REPGMAIL, using multiplier of 5
12/17/09 22:34:06 v1.14 @ REPGMAIL, using small prime variation correction of 21 bits
12/17/09 22:34:06 v1.14 @ REPGMAIL, using SSE2 for trial division and x128 sieve scanning
12/17/09 22:34:06 v1.14 @ REPGMAIL, trial factoring cutoff at 96 bits
12/17/09 22:34:06 v1.14 @ REPGMAIL, ==== sieving started ( 8 threads) ====
12/17/09 22:56:17 v1.14 @ REPGMAIL, trial division touched 29986440 sieve locations out of 34609201938432
12/17/09 22:56:17 v1.14 @ REPGMAIL, 66603 relations found: 18480 full + 48123 from 829499 partial, using 24004296 polys (847 A polys)
12/17/09 22:56:17 v1.14 @ REPGMAIL, on average, sieving found 0.04 rels/poly and 636.88 rels/sec
12/17/09 22:56:17 v1.14 @ REPGMAIL, trial division touched 29986440 sieve locations out of 34609201938432
12/17/09 22:56:17 v1.14 @ REPGMAIL, ==== post processing stage (msieve-1.38) ====
12/17/09 22:56:17 v1.14 @ REPGMAIL, begin with 847979 relations
12/17/09 22:56:18 v1.14 @ REPGMAIL, reduce to 160269 relations in 11 passes
12/17/09 22:56:22 v1.14 @ REPGMAIL, failed to read relation 72710
12/17/09 22:56:28 v1.14 @ REPGMAIL, recovered 160268 relations
12/17/09 22:56:28 v1.14 @ REPGMAIL, recovered 134681 polynomials
12/17/09 22:56:28 v1.14 @ REPGMAIL, attempting to build 66602 cycles
12/17/09 22:56:28 v1.14 @ REPGMAIL, found 66602 cycles in 6 passes
12/17/09 22:56:28 v1.14 @ REPGMAIL, distribution of cycle lengths:
12/17/09 22:56:28 v1.14 @ REPGMAIL,    length 1 : 18480
12/17/09 22:56:28 v1.14 @ REPGMAIL,    length 2 : 13601
12/17/09 22:56:28 v1.14 @ REPGMAIL,    length 3 : 11904
12/17/09 22:56:28 v1.14 @ REPGMAIL,    length 4 : 8618
12/17/09 22:56:28 v1.14 @ REPGMAIL,    length 5 : 5823
12/17/09 22:56:28 v1.14 @ REPGMAIL,    length 6 : 3680
12/17/09 22:56:28 v1.14 @ REPGMAIL,    length 7 : 2109
12/17/09 22:56:28 v1.14 @ REPGMAIL,    length 9+: 2387
12/17/09 22:56:28 v1.14 @ REPGMAIL, largest cycle: 18 relations
12/17/09 22:56:31 v1.14 @ REPGMAIL, matrix is 66328 x 66602 (16.2 MB) with weight 3980066 (59.76/col)
12/17/09 22:56:31 v1.14 @ REPGMAIL, sparse part has weight 3980066 (59.76/col)
12/17/09 22:56:32 v1.14 @ REPGMAIL, filtering completed in 3 passes
12/17/09 22:56:32 v1.14 @ REPGMAIL, matrix is 61864 x 61928 (15.2 MB) with weight 3735380 (60.32/col)
12/17/09 22:56:32 v1.14 @ REPGMAIL, sparse part has weight 3735380 (60.32/col)
12/17/09 22:56:32 v1.14 @ REPGMAIL, saving the first 48 matrix rows for later
12/17/09 22:56:32 v1.14 @ REPGMAIL, matrix is 61816 x 61928 (12.9 MB) with weight 3247323 (52.44/col)
12/17/09 22:56:32 v1.14 @ REPGMAIL, sparse part has weight 3019707 (48.76/col)
12/17/09 22:56:32 v1.14 @ REPGMAIL, matrix includes 64 packed rows
12/17/09 22:56:32 v1.14 @ REPGMAIL, using block size 24771 for processor cache size 6144 kB
12/17/09 22:56:33 v1.14 @ REPGMAIL, commencing Lanczos iteration
12/17/09 22:56:33 v1.14 @ REPGMAIL, memory use: 11.0 MB
12/17/09 22:57:01 v1.14 @ REPGMAIL, lanczos halted after 979 iterations (dim = 61812)
12/17/09 22:57:02 v1.14 @ REPGMAIL, recovered 16 nontrivial dependencies
12/17/09 22:57:04 v1.14 @ REPGMAIL, prp43 = 4704278905960870672702840636154862664420573
12/17/09 22:57:06 v1.14 @ REPGMAIL, prp48 = 216051725822903176121266690809152805746919124127
12/17/09 22:57:06 v1.14 @ REPGMAIL, Lanczos elapsed time = 44.6400 seconds.
12/17/09 22:57:06 v1.14 @ REPGMAIL, Sqrt elapsed time = 4.2340 seconds.
12/17/09 22:57:06 v1.14 @ REPGMAIL, SIQS elapsed time = 1380.3237 seconds.

(71·10¹²⁸-53)/9 = 7(8)₁₂₇3_<129> = 3² · 2377 · 8831 · C121

C121 = P51 · P71

P51 = 165003680788079684382461700620601145550349398065163_<51>

P71 = 25306998018702680821578149424957973175262997834761086043278516609659927_<71>

N=4175747822782582172672610354365328861810822794603033200758691974801465054889408209589736969803438969113914787009215823101
  ( 121 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=165003680788079684382461700620601145550349398065163 (pp51)
 r2=25306998018702680821578149424957973175262997834761086043278516609659927 (pp71)
Version: Msieve-1.40
Total time: 2.54 hours.
Scaled time: 4.90 units (timescale=1.928).
Factorization parameters were as follows:
n: 4175747822782582172672610354365328861810822794603033200758691974801465054889408209589736969803438969113914787009215823101
m: 10000000000000000000000000
deg: 5
c5: 71000
c0: -53
skew: 0.24
type: snfs
lss: 1
rlim: 1020000
alim: 1020000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1020000/1020000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [510000, 1060001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 162277 x 162502
Total sieving time: 2.44 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,129.000,5,0,0,0,0,0,0,0,0,1020000,1020000,26,26,47,47,2.3,2.3,50000
total time: 2.54 hours.
 --------- CPU info (if available) ----------

9·10²¹⁷-1 = 8(9)₂₁₇_<218> = 4283 · 9437 · C211

C211 = P34 · C178

P34 = 1577290686429983687836459293964961_<34>

C178 = [1411720564399112483471084781044967565528016798392234290981345680970916119805289999619210137081639694786400613276406019352676005253348050274461896592584529492199240348443770814929_<178>]

Factor=1577290686429983687836459293964961  Method=ECM  B1=11000000  Sigma=421968920

(71·10¹³¹-53)/9 = 7(8)₁₃₀3_<132> = 3 · C132

C132 = P48 · P85

P48 = 196715840065308398795279369007364211116917928283_<48>

P85 = 1336765574524455904141319038788517795589445839396460183951749385129955666167430296067_<85>

N=262962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962961
  ( 132 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=196715840065308398795279369007364211116917928283 (pp48)
 r2=1336765574524455904141319038788517795589445839396460183951749385129955666167430296067 (pp85)
Version: Msieve-1.40
Total time: 3.13 hours.
Scaled time: 5.94 units (timescale=1.899).
Factorization parameters were as follows:
n: 262962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962961
m: 100000000000000000000000000
deg: 5
c5: 710
c0: -53
skew: 0.60
type: snfs
lss: 1
rlim: 1150000
alim: 1150000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1150000/1150000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [575000, 1225001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 185212 x 185437
Total sieving time: 3.00 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,132.000,5,0,0,0,0,0,0,0,0,1150000,1150000,26,26,47,47,2.3,2.3,50000
total time: 3.13 hours.
 --------- CPU info (if available) ----------

(71·10¹³²-53)/9 = 7(8)₁₃₁3_<133> = C133

C133 = P60 · P74

P60 = 517214393087147489390495048364390108944880537532928038319981_<60>

P74 = 15252647633801751029471431177710620169842615413914822823473476439081203743_<74>

N=7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
  ( 133 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=517214393087147489390495048364390108944880537532928038319981 (pp60)
 r2=15252647633801751029471431177710620169842615413914822823473476439081203743 (pp74)
Version: Msieve-1.40
Total time: 3.53 hours.
Scaled time: 6.41 units (timescale=1.818).
Factorization parameters were as follows:
n: 7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
m: 100000000000000000000000000
deg: 5
c5: 7100
c0: -53
skew: 0.38
type: snfs
lss: 1
rlim: 1190000
alim: 1190000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1190000/1190000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [595000, 1345001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 205361 x 205586
Total sieving time: 3.43 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,133.000,5,0,0,0,0,0,0,0,0,1190000,1190000,26,26,47,47,2.3,2.3,75000
total time: 3.53 hours.
 --------- CPU info (if available) ----------

(71·10¹²¹-53)/9 = 7(8)₁₂₀3_<122> = 73 · 83 · 635363 · C113

C113 = P52 · P61

P52 = 3100375569266222976004203131079653569034995145663653_<52>

P61 = 6609653005401652853305308565447112625996842016862736480888983_<61>

N=20492406699274351032060072910217225536645754047004998692822135641463339761256101427317966891992832342738951234899
  ( 113 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=3100375569266222976004203131079653569034995145663653 (pp52)
 r2=6609653005401652853305308565447112625996842016862736480888983 (pp61)
Version: Msieve-1.40
Total time: 1.87 hours.
Scaled time: 3.54 units (timescale=1.894).
Factorization parameters were as follows:
n: 20492406699274351032060072910217225536645754047004998692822135641463339761256101427317966891992832342738951234899
m: 1000000000000000000000000
deg: 5
c5: 710
c0: -53
skew: 0.60
type: snfs
lss: 1
rlim: 780000
alim: 780000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 780000/780000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [390000, 840001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 92638 x 92863
Total sieving time: 1.81 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,122.000,5,0,0,0,0,0,0,0,0,780000,780000,25,25,46,46,2.2,2.2,50000
total time: 1.87 hours.
 --------- CPU info (if available) ----------

(23·10¹¹⁵+7)/3 = 7(6)₁₁₄9_<116> = 101540519 · 3192714031843379_<16> · C93

C93 = P39 · P55

P39 = 145717171735411817146963718723119073599_<39>

P55 = 1622917518152125158739229174383634945061249878227930231_<55>

N=236486950704981546873301241060210324387354907053759004965902155459257877449591326407926071369
  ( 93 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=145717171735411817146963718723119073599 (pp39)
 r2=1622917518152125158739229174383634945061249878227930231 (pp55)
Version: Msieve-1.40
Total time: 1.03 hours.
Scaled time: 2.00 units (timescale=1.934).
Factorization parameters were as follows:
n: 236486950704981546873301241060210324387354907053759004965902155459257877449591326407926071369
m: 100000000000000000000000
deg: 5
c5: 23
c0: 7
skew: 0.79
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [305000, 555001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 62040 x 62274
Total sieving time: 1.01 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116.000,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000
total time: 1.03 hours.
 --------- CPU info (if available) ----------

(23·10¹¹⁸+7)/3 = 7(6)₁₁₇9_<119> = 79 · 97 · 241 · 439 · 3301 · 253823 · C102

C102 = P45 · P57

P45 = 616662315237088461756368984825451529618304609_<45>

P57 = 183021574262896725676823532935622444218431584201994836991_<57>

N=112862507723294616972009178085600140935549884805945509772132374654095565184658821451591703944738991519
  ( 102 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=616662315237088461756368984825451529618304609 (pp45)
 r2=183021574262896725676823532935622444218431584201994836991 (pp57)
Version: Msieve-1.40
Total time: 1.42 hours.
Scaled time: 2.65 units (timescale=1.866).
Factorization parameters were as follows:
n: 112862507723294616972009178085600140935549884805945509772132374654095565184658821451591703944738991519
m: 100000000000000000000000
deg: 5
c5: 23000
c0: 7
skew: 0.20
type: snfs
lss: 1
rlim: 680000
alim: 680000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 680000/680000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [340000, 690001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 70562 x 70793
Total sieving time: 1.39 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,119.000,5,0,0,0,0,0,0,0,0,680000,680000,25,25,45,45,2.2,2.2,50000
total time: 1.42 hours.
 --------- CPU info (if available) ----------

(23·10¹³²+7)/3 = 7(6)₁₃₁9_<133> = 515119773492893_<15> · C119

C119 = P43 · P77

P43 = 1325930876011785899835125289730218699242507_<43>

P77 = 11224770657653797020738499348061137631067325221162132058552569512965365014419_<77>

N=14883269991134289211077349683781442707264471531662519776756720046042023420857648997080679874326196989860850194432708433
  ( 119 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=1325930876011785899835125289730218699242507 (pp43)
 r2=11224770657653797020738499348061137631067325221162132058552569512965365014419 (pp77)
Version: Msieve-1.40
Total time: 3.14 hours.
Scaled time: 5.93 units (timescale=1.888).
Factorization parameters were as follows:
n: 14883269991134289211077349683781442707264471531662519776756720046042023420857648997080679874326196989860850194432708433
m: 100000000000000000000000000
deg: 5
c5: 2300
c0: 7
skew: 0.31
type: snfs
lss: 1
rlim: 1170000
alim: 1170000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1170000/1170000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [585000, 1235001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 187019 x 187244
Total sieving time: 3.01 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,133.000,5,0,0,0,0,0,0,0,0,1170000,1170000,26,26,47,47,2.3,2.3,50000
total time: 3.14 hours.
 --------- CPU info (if available) ----------

(71·10¹³⁴-53)/9 = 7(8)₁₃₃3_<135> = 3 · 1248424878698281_<16> · C120

C120 = P49 · P71

P49 = 3749028001261114267397282247344700583630333114637_<49>

P71 = 56184107410696183723363555425171112886122517296076068553504744503648013_<71>

N=210635791908562071728644557621682794294921668230253551186820616199446384520540884426027237215207303593232937643026266281
  ( 120 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=3749028001261114267397282247344700583630333114637 (pp49)
 r2=56184107410696183723363555425171112886122517296076068553504744503648013 (pp71)
Version: Msieve-1.40
Total time: 4.59 hours.
Scaled time: 8.74 units (timescale=1.905).
Factorization parameters were as follows:
n: 210635791908562071728644557621682794294921668230253551186820616199446384520540884426027237215207303593232937643026266281
m: 100000000000000000000000000
deg: 5
c5: 710000
c0: -53
skew: 0.15
type: snfs
lss: 1
rlim: 1290000
alim: 1290000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1290000/1290000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [645000, 1620001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 231832 x 232057
Total sieving time: 4.41 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,135.000,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,47,47,2.3,2.3,75000
total time: 4.59 hours.
 --------- CPU info (if available) ----------

(71·10¹⁵⁰-53)/9 = 7(8)₁₄₉3_<151> = 1307 · C148

C148 = P48 · P101

P48 = 128415372495535273586931730868534677776502526639_<48>

P101 = 47002746513966858009036774509430398095275660887836235273369621377326418835059116058961137334091595271_<101>

N=6035875201904276120037405423786449035110090963189662501062654084842302133809402363342684689279945592110856074130748958598996854543908866785683924169
  ( 148 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=128415372495535273586931730868534677776502526639 (pp48)
 r2=47002746513966858009036774509430398095275660887836235273369621377326418835059116058961137334091595271 (pp101)
Version: Msieve-1.40
Total time: 11.65 hours.
Scaled time: 22.67 units (timescale=1.946).
Factorization parameters were as follows:
n: 6035875201904276120037405423786449035110090963189662501062654084842302133809402363342684689279945592110856074130748958598996854543908866785683924169
m: 1000000000000000000000000000000
deg: 5
c5: 71
c0: -53
skew: 0.94
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1900001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 396211 x 396438
Total sieving time: 11.37 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 11.65 hours.
 --------- CPU info (if available) ----------

(71·10¹³⁵-53)/9 = 7(8)₁₃₄3_<136> = C136

C136 = P64 · P73

P64 = 6745880366212108691779530567928483529559329688486999836127929329_<64>

P73 = 1169438006698389308964930379145889791962225646934827427481335042336893027_<73>

N=7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
  ( 136 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=6745880366212108691779530567928483529559329688486999836127929329 (pp64)
 r2=1169438006698389308964930379145889791962225646934827427481335042336893027 (pp73)
Version: Msieve-1.40
Total time: 3.20 hours.
Scaled time: 6.27 units (timescale=1.958).
Factorization parameters were as follows:
n: 7888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
m: 1000000000000000000000000000
deg: 5
c5: 71
c0: -53
skew: 0.94
type: snfs
lss: 1
rlim: 1340000
alim: 1340000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1340000/1340000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [670000, 1270001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 185613 x 185840
Total sieving time: 2.99 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1340000,1340000,26,26,48,48,2.3,2.3,75000
total time: 3.20 hours.
 --------- CPU info (if available) ----------

(71·10¹³⁶-53)/9 = 7(8)₁₃₅3_<137> = 7 · 51980300653_<11> · C126

C126 = P39 · P87

P39 = 954769764248960953148801851587662128903_<39>

P87 = 227080768266703753928456788022703634642399994316630471933625214253812105368451884403791_<87>

Number: ass5
N=216809851583473676705627523909375219620660574439738030217619127587489482104551329168343620455085044000722121819194881943871273
  ( 126 digits)
SNFS difficulty: 137 digits.
Divisors found:
r1=954769764248960953148801851587662128903 (pp39)
r2=227080768266703753928456788022703634642399994316630471933625214253812105368451884403791 (pp87)
Version: Msieve-1.40
Total time: 13.24 hours.
Scaled time: 25.08 units (timescale=1.894).
Factorization parameters were as follows:
n: 216809851583473676705627523909375219620660574439738030217619127587489482104551329168343620455085044000722121819194881943871273
m: 1000000000000000000000000000
deg: 5
c5: 710
c0: -53
skew: 0.60
type: snfs
lss: 1
rlim: 1390000
alim: 1390000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1390000/1390000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [695000, 1595001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 244174 x 244400
Total sieving time: 12.77 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,137.000,5,0,0,0,0,0,0,0,0,1390000,1390000,26,26,48,48,2.3,2.3,75000
total time: 13.24 hours.
 --------- CPU info (if available) ----------

(71·10¹⁴⁸-53)/9 = 7(8)₁₄₇3_<149> = 7 · 103 · C147

C147 = P61 · P86

P61 = 4623071854794763055981863186790303195310782012328269473558183_<61>

P86 = 23667366222130787792273066730206177697377235694310735886378311300462181777177208904581_<86>

Fri Dec 18 14:56:52 2009  Msieve v. 1.42
Fri Dec 18 14:56:52 2009  random seeds: 802eda00 a82eb800
Fri Dec 18 14:56:52 2009  factoring 109415934658653105255047002619818153798736323008167668361843119124672522730775157959623979041454769610109415934658653105255047002619818153798736323 (147 digits)
Fri Dec 18 14:56:53 2009  searching for 15-digit factors
Fri Dec 18 14:56:54 2009  commencing number field sieve (147-digit input)
Fri Dec 18 14:56:54 2009  R0: -100000000000000000000000000000
Fri Dec 18 14:56:54 2009  R1:  1
Fri Dec 18 14:56:54 2009  A0: -53
Fri Dec 18 14:56:54 2009  A1:  0
Fri Dec 18 14:56:54 2009  A2:  0
Fri Dec 18 14:56:54 2009  A3:  0
Fri Dec 18 14:56:54 2009  A4:  0
Fri Dec 18 14:56:54 2009  A5:  71000
Fri Dec 18 14:56:54 2009  skew 0.24, size 6.808355e-011, alpha 0.102333, combined = 1.009260e-009
Fri Dec 18 14:56:54 2009  
Fri Dec 18 14:56:54 2009  commencing relation filtering
Fri Dec 18 14:56:54 2009  estimated available RAM is 4096.0 MB
Fri Dec 18 14:56:54 2009  commencing duplicate removal, pass 1
Fri Dec 18 14:57:39 2009  found 1113252 hash collisions in 5720106 relations
Fri Dec 18 14:57:49 2009  added 1576 free relations
Fri Dec 18 14:57:49 2009  commencing duplicate removal, pass 2
Fri Dec 18 14:57:58 2009  found 1143824 duplicates and 4577857 unique relations
Fri Dec 18 14:57:58 2009  memory use: 26.6 MB
Fri Dec 18 14:57:58 2009  reading ideals above 100000
Fri Dec 18 14:57:58 2009  commencing singleton removal, initial pass
Fri Dec 18 14:58:48 2009  memory use: 74.6 MB
Fri Dec 18 14:58:49 2009  reading all ideals from disk
Fri Dec 18 14:58:49 2009  memory use: 151.9 MB
Fri Dec 18 14:58:49 2009  keeping 5077417 ideals with weight <= 200, target excess is 24183
Fri Dec 18 14:58:50 2009  commencing in-memory singleton removal
Fri Dec 18 14:58:50 2009  begin with 4577857 relations and 5077417 unique ideals
Fri Dec 18 14:58:55 2009  reduce to 1888309 relations and 1753238 ideals in 15 passes
Fri Dec 18 14:58:55 2009  max relations containing the same ideal: 113
Fri Dec 18 14:58:56 2009  removing 326014 relations and 272505 ideals in 53509 cliques
Fri Dec 18 14:58:56 2009  commencing in-memory singleton removal
Fri Dec 18 14:58:56 2009  begin with 1562295 relations and 1753238 unique ideals
Fri Dec 18 14:58:58 2009  reduce to 1528026 relations and 1445324 ideals in 7 passes
Fri Dec 18 14:58:58 2009  max relations containing the same ideal: 95
Fri Dec 18 14:58:58 2009  removing 245675 relations and 192166 ideals in 53509 cliques
Fri Dec 18 14:58:59 2009  commencing in-memory singleton removal
Fri Dec 18 14:58:59 2009  begin with 1282351 relations and 1445324 unique ideals
Fri Dec 18 14:58:59 2009  reduce to 1257014 relations and 1226970 ideals in 7 passes
Fri Dec 18 14:58:59 2009  max relations containing the same ideal: 85
Fri Dec 18 14:59:00 2009  relations with 0 large ideals: 577
Fri Dec 18 14:59:00 2009  relations with 1 large ideals: 164
Fri Dec 18 14:59:00 2009  relations with 2 large ideals: 2220
Fri Dec 18 14:59:00 2009  relations with 3 large ideals: 18794
Fri Dec 18 14:59:00 2009  relations with 4 large ideals: 86118
Fri Dec 18 14:59:00 2009  relations with 5 large ideals: 224100
Fri Dec 18 14:59:00 2009  relations with 6 large ideals: 364557
Fri Dec 18 14:59:00 2009  relations with 7+ large ideals: 560484
Fri Dec 18 14:59:00 2009  commencing 2-way merge
Fri Dec 18 14:59:01 2009  reduce to 799629 relation sets and 769585 unique ideals
Fri Dec 18 14:59:01 2009  commencing full merge
Fri Dec 18 14:59:23 2009  memory use: 87.9 MB
Fri Dec 18 14:59:23 2009  found 402653 cycles, need 397785
Fri Dec 18 14:59:23 2009  weight of 397785 cycles is about 28219113 (70.94/cycle)
Fri Dec 18 14:59:23 2009  distribution of cycle lengths:
Fri Dec 18 14:59:23 2009  1 relations: 33585
Fri Dec 18 14:59:23 2009  2 relations: 41457
Fri Dec 18 14:59:23 2009  3 relations: 43885
Fri Dec 18 14:59:23 2009  4 relations: 41345
Fri Dec 18 14:59:23 2009  5 relations: 38853
Fri Dec 18 14:59:23 2009  6 relations: 34460
Fri Dec 18 14:59:23 2009  7 relations: 30544
Fri Dec 18 14:59:23 2009  8 relations: 26123
Fri Dec 18 14:59:23 2009  9 relations: 22197
Fri Dec 18 14:59:23 2009  10+ relations: 85336
Fri Dec 18 14:59:23 2009  heaviest cycle: 23 relations
Fri Dec 18 14:59:23 2009  commencing cycle optimization
Fri Dec 18 14:59:24 2009  start with 2542001 relations
Fri Dec 18 14:59:31 2009  pruned 75418 relations
Fri Dec 18 14:59:31 2009  memory use: 62.5 MB
Fri Dec 18 14:59:31 2009  distribution of cycle lengths:
Fri Dec 18 14:59:31 2009  1 relations: 33585
Fri Dec 18 14:59:31 2009  2 relations: 42324
Fri Dec 18 14:59:31 2009  3 relations: 45477
Fri Dec 18 14:59:31 2009  4 relations: 42542
Fri Dec 18 14:59:31 2009  5 relations: 40031
Fri Dec 18 14:59:31 2009  6 relations: 35283
Fri Dec 18 14:59:31 2009  7 relations: 31283
Fri Dec 18 14:59:31 2009  8 relations: 26361
Fri Dec 18 14:59:31 2009  9 relations: 22186
Fri Dec 18 14:59:31 2009  10+ relations: 78713
Fri Dec 18 14:59:31 2009  heaviest cycle: 23 relations
Fri Dec 18 14:59:32 2009  RelProcTime: 158
Fri Dec 18 14:59:32 2009  
Fri Dec 18 14:59:32 2009  commencing linear algebra
Fri Dec 18 14:59:32 2009  read 397785 cycles
Fri Dec 18 14:59:32 2009  cycles contain 1226470 unique relations
Fri Dec 18 15:00:02 2009  read 1226470 relations
Fri Dec 18 15:00:03 2009  using 20 quadratic characters above 67107968
Fri Dec 18 15:00:10 2009  building initial matrix
Fri Dec 18 15:00:24 2009  memory use: 134.1 MB
Fri Dec 18 15:00:24 2009  read 397785 cycles
Fri Dec 18 15:00:36 2009  matrix is 397608 x 397785 (113.2 MB) with weight 35897815 (90.24/col)
Fri Dec 18 15:00:36 2009  sparse part has weight 26902376 (67.63/col)
Fri Dec 18 15:00:39 2009  filtering completed in 2 passes
Fri Dec 18 15:00:40 2009  matrix is 397460 x 397637 (113.2 MB) with weight 35892088 (90.26/col)
Fri Dec 18 15:00:40 2009  sparse part has weight 26900033 (67.65/col)
Fri Dec 18 15:00:41 2009  read 397637 cycles
Fri Dec 18 15:01:23 2009  matrix is 397460 x 397637 (113.2 MB) with weight 35892088 (90.26/col)
Fri Dec 18 15:01:23 2009  sparse part has weight 26900033 (67.65/col)
Fri Dec 18 15:01:23 2009  saving the first 48 matrix rows for later
Fri Dec 18 15:01:24 2009  matrix is 397412 x 397637 (106.4 MB) with weight 28341079 (71.27/col)
Fri Dec 18 15:01:24 2009  sparse part has weight 25515877 (64.17/col)
Fri Dec 18 15:01:24 2009  matrix includes 64 packed rows
Fri Dec 18 15:01:24 2009  using block size 65536 for processor cache size 6144 kB
Fri Dec 18 15:01:27 2009  commencing Lanczos iteration (6 threads)
Fri Dec 18 15:01:27 2009  memory use: 123.9 MB
Fri Dec 18 15:11:30 2009  lanczos halted after 6286 iterations (dim = 397412)
Fri Dec 18 15:11:31 2009  recovered 37 nontrivial dependencies
Fri Dec 18 15:11:31 2009  BLanczosTime: 719
Fri Dec 18 15:11:31 2009  
Fri Dec 18 15:11:31 2009  commencing square root phase
Fri Dec 18 15:11:31 2009  reading relations for dependency 1
Fri Dec 18 15:11:32 2009  read 198961 cycles
Fri Dec 18 15:11:32 2009  cycles contain 768805 unique relations
Fri Dec 18 15:11:51 2009  read 768805 relations
Fri Dec 18 15:11:55 2009  multiplying 613156 relations
Fri Dec 18 15:13:05 2009  multiply complete, coefficients have about 21.74 million bits
Fri Dec 18 15:13:05 2009  initial square root is modulo 1749431
Fri Dec 18 15:14:40 2009  sqrtTime: 189
Fri Dec 18 15:14:40 2009  prp61 factor: 4623071854794763055981863186790303195310782012328269473558183
Fri Dec 18 15:14:40 2009  prp86 factor: 23667366222130787792273066730206177697377235694310735886378311300462181777177208904581
Fri Dec 18 15:14:40 2009  elapsed time 00:17:48

Dec 18, 2009 (3rd)

By Erik Branger / YAFU, Msieve, GGNFS, Msieve / Dec 18, 2009

(23·10¹⁰⁴+7)/3 = 7(6)₁₀₃9_<105> = 31 · 59 · 1259081973381863_<16> · C87

C87 = P39 · P48

P39 = 485355677072414738525607759311522393567_<39>

P48 = 685928354668540614395845427196619202593904737841_<48>

12/17/09 17:20:06 v1.14 @ ERIK-DATOR, starting SIQS on c87: 332919221003316962952714214283774363080007369160491821897306409696378607336009959868847
12/17/09 17:20:06 v1.14 @ ERIK-DATOR, random seeds: 0, 4234451912
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, ==== sieve params ====
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, n = 88 digits, 292 bits
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, factor base: 59299 primes (max prime = 1555291)
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, single large prime cutoff: 171082010 (110 * pmax)
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, double large prime range from 43 to 50 bits
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, double large prime cutoff: 660340325177177
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, allocating 12 large prime slices of factor base
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, buckets hold 1024 elements
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, polynomial A has ~ 11 factors
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, using multiplier of 13
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, using small prime variation correction of 21 bits
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, trial factoring cutoff at 96 bits
12/17/09 17:20:07 v1.14 @ ERIK-DATOR, ==== sieving started ( 2 threads) ====
12/17/09 17:47:38 v1.14 @ ERIK-DATOR, trial division touched 13557846 sieve locations out of 45420989644800
12/17/09 17:47:38 v1.14 @ ERIK-DATOR, 59732 relations found: 19973 full + 39759 from 551163 partial, using 38503850 polys (547 A polys)
12/17/09 17:47:38 v1.14 @ ERIK-DATOR, on average, sieving found 0.01 rels/poly and 345.78 rels/sec
12/17/09 17:47:38 v1.14 @ ERIK-DATOR, trial division touched 13557846 sieve locations out of 45420989644800
12/17/09 17:47:38 v1.14 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ====
12/17/09 17:47:39 v1.14 @ ERIK-DATOR, begin with 571136 relations
12/17/09 17:47:40 v1.14 @ ERIK-DATOR, reduce to 122343 relations in 9 passes
12/17/09 17:47:53 v1.14 @ ERIK-DATOR, recovered 122343 relations
12/17/09 17:47:53 v1.14 @ ERIK-DATOR, recovered 98940 polynomials
12/17/09 17:47:53 v1.14 @ ERIK-DATOR, attempting to build 59732 cycles
12/17/09 17:47:53 v1.14 @ ERIK-DATOR, found 59732 cycles in 4 passes
12/17/09 17:47:53 v1.14 @ ERIK-DATOR, distribution of cycle lengths:
12/17/09 17:47:53 v1.14 @ ERIK-DATOR,    length 1 : 19973
12/17/09 17:47:53 v1.14 @ ERIK-DATOR,    length 2 : 16102
12/17/09 17:47:53 v1.14 @ ERIK-DATOR,    length 3 : 11108
12/17/09 17:47:53 v1.14 @ ERIK-DATOR,    length 4 : 6291
12/17/09 17:47:53 v1.14 @ ERIK-DATOR,    length 5 : 3390
12/17/09 17:47:53 v1.14 @ ERIK-DATOR,    length 6 : 1583
12/17/09 17:47:53 v1.14 @ ERIK-DATOR,    length 7 : 755
12/17/09 17:47:53 v1.14 @ ERIK-DATOR,    length 9+: 530
12/17/09 17:47:53 v1.14 @ ERIK-DATOR, largest cycle: 17 relations
12/17/09 17:47:53 v1.14 @ ERIK-DATOR, matrix is 59299 x 59732 (12.1 MB) with weight 2922762 (48.93/col)
12/17/09 17:47:53 v1.14 @ ERIK-DATOR, sparse part has weight 2922762 (48.93/col)
12/17/09 17:47:53 v1.14 @ ERIK-DATOR, filtering completed in 3 passes
12/17/09 17:47:53 v1.14 @ ERIK-DATOR, matrix is 52382 x 52443 (10.8 MB) with weight 2612003 (49.81/col)
12/17/09 17:47:53 v1.14 @ ERIK-DATOR, sparse part has weight 2612003 (49.81/col)
12/17/09 17:47:54 v1.14 @ ERIK-DATOR, saving the first 48 matrix rows for later
12/17/09 17:47:54 v1.14 @ ERIK-DATOR, matrix is 52334 x 52443 (9.0 MB) with weight 2228680 (42.50/col)
12/17/09 17:47:54 v1.14 @ ERIK-DATOR, sparse part has weight 2043916 (38.97/col)
12/17/09 17:47:54 v1.14 @ ERIK-DATOR, matrix includes 64 packed rows
12/17/09 17:47:54 v1.14 @ ERIK-DATOR, using block size 20977 for processor cache size 2048 kB
12/17/09 17:47:54 v1.14 @ ERIK-DATOR, commencing Lanczos iteration
12/17/09 17:47:54 v1.14 @ ERIK-DATOR, memory use: 8.1 MB
12/17/09 17:48:20 v1.14 @ ERIK-DATOR, lanczos halted after 829 iterations (dim = 52333)
12/17/09 17:48:21 v1.14 @ ERIK-DATOR, recovered 19 nontrivial dependencies
12/17/09 17:48:22 v1.14 @ ERIK-DATOR, prp39 = 485355677072414738525607759311522393567
12/17/09 17:48:23 v1.14 @ ERIK-DATOR, prp48 = 685928354668540614395845427196619202593904737841
12/17/09 17:48:23 v1.14 @ ERIK-DATOR, Lanczos elapsed time = 42.5920 seconds.
12/17/09 17:48:23 v1.14 @ ERIK-DATOR, Sqrt elapsed time = 2.5280 seconds.
12/17/09 17:48:23 v1.14 @ ERIK-DATOR, SIQS elapsed time = 1696.8740 seconds.

(23·10¹⁰⁸+7)/3 = 7(6)₁₀₇9_<109> = 17 · 2242460041_<10> · 62518635437_<11> · C88

C88 = P43 · P46

P43 = 2080914820955598617907251122725823898148173_<43>

P46 = 1545856417436797515310721619019024547744620877_<46>

2/17/09 18:11:31 v1.14 @ ERIK-DATOR, starting SIQS on c88: 3216795530113556618934915882743498388485970004369579124482771856979467751789282255207721
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, random seeds: 0, 4234451912
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, ==== sieve params ====
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, n = 88 digits, 291 bits
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, factor base: 61083 primes (max prime = 1611749)
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, single large prime cutoff: 177292390 (110 * pmax)
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, double large prime range from 43 to 50 bits
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, double large prime cutoff: 704112687915357
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, allocating 12 large prime slices of factor base
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, buckets hold 1024 elements
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, polynomial A has ~ 11 factors
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, using multiplier of 1
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, using small prime variation correction of 20 bits
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, trial factoring cutoff at 97 bits
12/17/09 18:11:31 v1.14 @ ERIK-DATOR, ==== sieving started ( 2 threads) ====
12/17/09 18:39:06 v1.14 @ ERIK-DATOR, trial division touched 12387346 sieve locations out of 36035391651840
12/17/09 18:39:06 v1.14 @ ERIK-DATOR, 61605 relations found: 20676 full + 40929 from 577615 partial, using 30547580 polys (487 A polys)
12/17/09 18:39:06 v1.14 @ ERIK-DATOR, on average, sieving found 0.02 rels/poly and 361.41 rels/sec
12/17/09 18:39:06 v1.14 @ ERIK-DATOR, trial division touched 12387346 sieve locations out of 36035391651840
12/17/09 18:39:06 v1.14 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ====
12/17/09 18:39:07 v1.14 @ ERIK-DATOR, begin with 598291 relations
12/17/09 18:39:08 v1.14 @ ERIK-DATOR, reduce to 126888 relations in 9 passes
12/17/09 18:39:20 v1.14 @ ERIK-DATOR, recovered 126888 relations
12/17/09 18:39:20 v1.14 @ ERIK-DATOR, recovered 99447 polynomials
12/17/09 18:39:20 v1.14 @ ERIK-DATOR, attempting to build 61605 cycles
12/17/09 18:39:20 v1.14 @ ERIK-DATOR, found 61605 cycles in 5 passes
12/17/09 18:39:20 v1.14 @ ERIK-DATOR, distribution of cycle lengths:
12/17/09 18:39:20 v1.14 @ ERIK-DATOR,    length 1 : 20676
12/17/09 18:39:20 v1.14 @ ERIK-DATOR,    length 2 : 16707
12/17/09 18:39:20 v1.14 @ ERIK-DATOR,    length 3 : 11348
12/17/09 18:39:20 v1.14 @ ERIK-DATOR,    length 4 : 6423
12/17/09 18:39:20 v1.14 @ ERIK-DATOR,    length 5 : 3462
12/17/09 18:39:20 v1.14 @ ERIK-DATOR,    length 6 : 1681
12/17/09 18:39:20 v1.14 @ ERIK-DATOR,    length 7 : 723
12/17/09 18:39:20 v1.14 @ ERIK-DATOR,    length 9+: 585
12/17/09 18:39:20 v1.14 @ ERIK-DATOR, largest cycle: 15 relations
12/17/09 18:39:21 v1.14 @ ERIK-DATOR, matrix is 61083 x 61605 (12.2 MB) with weight 2961410 (48.07/col)
12/17/09 18:39:21 v1.14 @ ERIK-DATOR, sparse part has weight 2961410 (48.07/col)
12/17/09 18:39:22 v1.14 @ ERIK-DATOR, filtering completed in 4 passes
12/17/09 18:39:22 v1.14 @ ERIK-DATOR, matrix is 53728 x 53792 (10.9 MB) with weight 2631067 (48.91/col)
12/17/09 18:39:22 v1.14 @ ERIK-DATOR, sparse part has weight 2631067 (48.91/col)
12/17/09 18:39:22 v1.14 @ ERIK-DATOR, saving the first 48 matrix rows for later
12/17/09 18:39:22 v1.14 @ ERIK-DATOR, matrix is 53680 x 53792 (9.2 MB) with weight 2274175 (42.28/col)
12/17/09 18:39:22 v1.14 @ ERIK-DATOR, sparse part has weight 2084036 (38.74/col)
12/17/09 18:39:22 v1.14 @ ERIK-DATOR, matrix includes 64 packed rows
12/17/09 18:39:22 v1.14 @ ERIK-DATOR, using block size 21516 for processor cache size 2048 kB
12/17/09 18:39:24 v1.14 @ ERIK-DATOR, commencing Lanczos iteration
12/17/09 18:39:24 v1.14 @ ERIK-DATOR, memory use: 8.3 MB
12/17/09 18:39:47 v1.14 @ ERIK-DATOR, lanczos halted after 851 iterations (dim = 53676)
12/17/09 18:39:48 v1.14 @ ERIK-DATOR, recovered 13 nontrivial dependencies
12/17/09 18:39:49 v1.14 @ ERIK-DATOR, prp43 = 2080914820955598617907251122725823898148173
12/17/09 18:39:53 v1.14 @ ERIK-DATOR, prp46 = 1545856417436797515310721619019024547744620877
12/17/09 18:39:53 v1.14 @ ERIK-DATOR, Lanczos elapsed time = 41.3880 seconds.
12/17/09 18:39:53 v1.14 @ ERIK-DATOR, Sqrt elapsed time = 5.2320 seconds.
12/17/09 18:39:53 v1.14 @ ERIK-DATOR, SIQS elapsed time = 1702.0760 seconds.

(71·10¹⁰⁶-53)/9 = 7(8)₁₀₅3_<107> = 7 · 395216035203671863_<18> · C89

C89 = P41 · P48

P41 = 53297442354068332478494079591206476081077_<41>

P48 = 535028447019444715581687239232391799724047883719_<48>

Thu Dec 17 17:30:46 2009  Msieve v. 1.43
Thu Dec 17 17:30:46 2009  random seeds: 71c02d80 12ee9b7a
Thu Dec 17 17:30:46 2009  factoring 28515647812805557665654578219032714046939482963930944496594790241418751535994394512285363 (89 digits)
Thu Dec 17 17:30:49 2009  searching for 15-digit factors
Thu Dec 17 17:30:50 2009  commencing quadratic sieve (89-digit input)
Thu Dec 17 17:30:50 2009  using multiplier of 1
Thu Dec 17 17:30:50 2009  using 64kb Pentium 4 sieve core
Thu Dec 17 17:30:50 2009  sieve interval: 15 blocks of size 65536
Thu Dec 17 17:30:50 2009  processing polynomials in batches of 7
Thu Dec 17 17:30:50 2009  using a sieve bound of 1546823 (58611 primes)
Thu Dec 17 17:30:50 2009  using large prime bound of 123745840 (26 bits)
Thu Dec 17 17:30:50 2009  using double large prime bound of 368599753674560 (42-49 bits)
Thu Dec 17 17:30:50 2009  using trial factoring cutoff of 49 bits
Thu Dec 17 17:30:50 2009  polynomial 'A' values have 11 factors
Thu Dec 17 19:21:41 2009  58786 relations (15786 full + 43000 combined from 626816 partial), need 58707
Thu Dec 17 19:21:43 2009  begin with 642602 relations
Thu Dec 17 19:21:44 2009  reduce to 143411 relations in 10 passes
Thu Dec 17 19:21:44 2009  attempting to read 143411 relations
Thu Dec 17 19:21:49 2009  recovered 143411 relations
Thu Dec 17 19:21:49 2009  recovered 123175 polynomials
Thu Dec 17 19:21:49 2009  attempting to build 58786 cycles
Thu Dec 17 19:21:49 2009  found 58786 cycles in 6 passes
Thu Dec 17 19:21:49 2009  distribution of cycle lengths:
Thu Dec 17 19:21:49 2009     length 1 : 15786
Thu Dec 17 19:21:49 2009     length 2 : 11230
Thu Dec 17 19:21:49 2009     length 3 : 10197
Thu Dec 17 19:21:49 2009     length 4 : 7832
Thu Dec 17 19:21:49 2009     length 5 : 5528
Thu Dec 17 19:21:49 2009     length 6 : 3586
Thu Dec 17 19:21:49 2009     length 7 : 2143
Thu Dec 17 19:21:49 2009     length 9+: 2484
Thu Dec 17 19:21:49 2009  largest cycle: 16 relations
Thu Dec 17 19:21:49 2009  matrix is 58611 x 58786 (14.3 MB) with weight 3525701 (59.98/col)
Thu Dec 17 19:21:49 2009  sparse part has weight 3525701 (59.98/col)
Thu Dec 17 19:21:51 2009  filtering completed in 3 passes
Thu Dec 17 19:21:51 2009  matrix is 54725 x 54789 (13.5 MB) with weight 3315509 (60.51/col)
Thu Dec 17 19:21:51 2009  sparse part has weight 3315509 (60.51/col)
Thu Dec 17 19:21:51 2009  saving the first 48 matrix rows for later
Thu Dec 17 19:21:51 2009  matrix is 54677 x 54789 (9.5 MB) with weight 2710808 (49.48/col)
Thu Dec 17 19:21:51 2009  sparse part has weight 2160529 (39.43/col)
Thu Dec 17 19:21:51 2009  matrix includes 64 packed rows
Thu Dec 17 19:21:51 2009  using block size 21845 for processor cache size 512 kB
Thu Dec 17 19:21:52 2009  commencing Lanczos iteration
Thu Dec 17 19:21:52 2009  memory use: 9.2 MB
Thu Dec 17 19:22:19 2009  lanczos halted after 866 iterations (dim = 54674)
Thu Dec 17 19:22:20 2009  recovered 15 nontrivial dependencies
Thu Dec 17 19:22:20 2009  prp41 factor: 53297442354068332478494079591206476081077
Thu Dec 17 19:22:20 2009  prp48 factor: 535028447019444715581687239232391799724047883719
Thu Dec 17 19:22:20 2009  elapsed time 01:51:34

(23·10¹³⁶+7)/3 = 7(6)₁₃₅9_<137> = 749773 · 4153301 · 14435189 · 32457907 · 188176079764936119047_<21> · C90

C90 = P36 · P55

P36 = 181640374412425783567041523872410101_<36>

P55 = 1537317554685431513606392745565325440665719944957889313_<55>

12/17/09 19:00:07 v1.14 @ ERIK-DATOR, starting SIQS on c90: 279238936223856629565358566671998470909289797293239621891946305210805050327370355301150613
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, random seeds: 0, 4234451912
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, ==== sieve params ====
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, n = 91 digits, 300 bits
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, factor base: 65244 primes (max prime = 1727969)
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, single large prime cutoff: 190076590 (110 * pmax)
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, double large prime range from 43 to 50 bits
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, double large prime cutoff: 798126145132792
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, allocating 13 large prime slices of factor base
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, buckets hold 1024 elements
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, polynomial A has ~ 12 factors
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, using multiplier of 5
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, using small prime variation correction of 19 bits
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, trial factoring cutoff at 97 bits
12/17/09 19:00:07 v1.14 @ ERIK-DATOR, ==== sieving started ( 2 threads) ====
12/17/09 20:01:35 v1.14 @ ERIK-DATOR, trial division touched 24313873 sieve locations out of 127655263862784
12/17/09 20:01:35 v1.14 @ ERIK-DATOR, 65511 relations found: 18382 full + 47129 from 776551 partial, using 108214708 polys (901 A polys)
12/17/09 20:01:35 v1.14 @ ERIK-DATOR, on average, sieving found 0.01 rels/poly and 215.54 rels/sec
12/17/09 20:01:35 v1.14 @ ERIK-DATOR, trial division touched 24313873 sieve locations out of 127655263862784
12/17/09 20:01:35 v1.14 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ====
12/17/09 20:01:37 v1.14 @ ERIK-DATOR, begin with 794933 relations
12/17/09 20:01:37 v1.14 @ ERIK-DATOR, reduce to 155460 relations in 10 passes
12/17/09 20:02:01 v1.14 @ ERIK-DATOR, recovered 155460 relations
12/17/09 20:02:01 v1.14 @ ERIK-DATOR, recovered 132922 polynomials
12/17/09 20:02:01 v1.14 @ ERIK-DATOR, attempting to build 65511 cycles
12/17/09 20:02:01 v1.14 @ ERIK-DATOR, found 65511 cycles in 5 passes
12/17/09 20:02:01 v1.14 @ ERIK-DATOR, distribution of cycle lengths:
12/17/09 20:02:01 v1.14 @ ERIK-DATOR,    length 1 : 18382
12/17/09 20:02:01 v1.14 @ ERIK-DATOR,    length 2 : 13580
12/17/09 20:02:01 v1.14 @ ERIK-DATOR,    length 3 : 11794
12/17/09 20:02:01 v1.14 @ ERIK-DATOR,    length 4 : 8587
12/17/09 20:02:01 v1.14 @ ERIK-DATOR,    length 5 : 5541
12/17/09 20:02:01 v1.14 @ ERIK-DATOR,    length 6 : 3548
12/17/09 20:02:01 v1.14 @ ERIK-DATOR,    length 7 : 1864
12/17/09 20:02:01 v1.14 @ ERIK-DATOR,    length 9+: 2215
12/17/09 20:02:01 v1.14 @ ERIK-DATOR, largest cycle: 17 relations
12/17/09 20:02:02 v1.14 @ ERIK-DATOR, matrix is 65244 x 65511 (15.5 MB) with weight 3798781 (57.99/col)
12/17/09 20:02:02 v1.14 @ ERIK-DATOR, sparse part has weight 3798781 (57.99/col)
12/17/09 20:02:02 v1.14 @ ERIK-DATOR, filtering completed in 3 passes
12/17/09 20:02:02 v1.14 @ ERIK-DATOR, matrix is 60588 x 60650 (14.5 MB) with weight 3552557 (58.57/col)
12/17/09 20:02:02 v1.14 @ ERIK-DATOR, sparse part has weight 3552557 (58.57/col)
12/17/09 20:02:03 v1.14 @ ERIK-DATOR, saving the first 48 matrix rows for later
12/17/09 20:02:04 v1.14 @ ERIK-DATOR, matrix is 60540 x 60650 (12.5 MB) with weight 3129931 (51.61/col)
12/17/09 20:02:04 v1.14 @ ERIK-DATOR, sparse part has weight 2911807 (48.01/col)
12/17/09 20:02:04 v1.14 @ ERIK-DATOR, matrix includes 64 packed rows
12/17/09 20:02:04 v1.14 @ ERIK-DATOR, using block size 24260 for processor cache size 2048 kB
12/17/09 20:02:05 v1.14 @ ERIK-DATOR, commencing Lanczos iteration
12/17/09 20:02:05 v1.14 @ ERIK-DATOR, memory use: 10.7 MB
12/17/09 20:02:54 v1.14 @ ERIK-DATOR, lanczos halted after 959 iterations (dim = 60538)
12/17/09 20:02:54 v1.14 @ ERIK-DATOR, recovered 17 nontrivial dependencies
12/17/09 20:02:57 v1.14 @ ERIK-DATOR, prp55 = 1537317554685431513606392745565325440665719944957889313
12/17/09 20:03:00 v1.14 @ ERIK-DATOR, prp36 = 181640374412425783567041523872410101
12/17/09 20:03:00 v1.14 @ ERIK-DATOR, Lanczos elapsed time = 79.7520 seconds.
12/17/09 20:03:00 v1.14 @ ERIK-DATOR, Sqrt elapsed time = 5.3220 seconds.
12/17/09 20:03:00 v1.14 @ ERIK-DATOR, SIQS elapsed time = 3773.2500 seconds.

(23·10¹³⁹+7)/3 = 7(6)₁₃₈9_<140> = 2131 · 16091 · 9230651 · 17938289 · 371558381039545550824559959_<27> · C92

C92 = P42 · P50

P42 = 775231789371928457084912814154799110990573_<42>

P50 = 46877896298271797921498266587994595101347397988693_<50>

Number: 76669_139
N=36341235429300947152532358431311731673430180271977943420379116126867369874894462531083591089
  ( 92 digits)
Divisors found:
 r1=775231789371928457084912814154799110990573 (pp42)
 r2=46877896298271797921498266587994595101347397988693 (pp50)
Version: Msieve v. 1.43
Total time: 2.11 hours.
Scaled time: 1.64 units (timescale=0.777).
Factorization parameters were as follows:
n: 36341235429300947152532358431311731673430180271977943420379116126867369874894462531083591089
# Murphy_E = 3.229128e-008
skew: 555236.39
Y0: -11092746106454675872026
Y1: 708120481289
c0: 29526976497269909000205785
c1: -682708658988982613014
c2: 439706832670957
c3: 2783592832
c4: 2400
type: gnfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [350000, 790001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 105343 x 105568
Total sieving time: 2.03 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
gnfs,91,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000
total time: 2.11 hours.
 --------- CPU info (if available) ----------

(71·10¹⁴³-53)/9 = 7(8)₁₄₂3_<144> = 3 · 17 · 6301 · 153929 · 419651 · 35797100488701217_<17> · 6937361701708324267103_<22> · C90

C90 = P33 · P57

P33 = 153780535368606699808334225196851_<33>

P57 = 995139386383652479833893377455100373087666602506469998827_<57>

Thu Dec 17 19:27:30 2009  Msieve v. 1.43
Thu Dec 17 19:27:30 2009  random seeds: 914d6de8 98ee6a6a
Thu Dec 17 19:27:30 2009  factoring 153033067604464838667101747728037243338673247578173298965964268593285084430575079814093777 (90 digits)
Thu Dec 17 19:27:31 2009  searching for 15-digit factors
Thu Dec 17 19:27:32 2009  commencing quadratic sieve (90-digit input)
Thu Dec 17 19:27:32 2009  using multiplier of 73
Thu Dec 17 19:27:32 2009  using 64kb Pentium 4 sieve core
Thu Dec 17 19:27:32 2009  sieve interval: 18 blocks of size 65536
Thu Dec 17 19:27:32 2009  processing polynomials in batches of 6
Thu Dec 17 19:27:32 2009  using a sieve bound of 1575281 (59405 primes)
Thu Dec 17 19:27:32 2009  using large prime bound of 126022480 (26 bits)
Thu Dec 17 19:27:32 2009  using double large prime bound of 380896014563600 (42-49 bits)
Thu Dec 17 19:27:32 2009  using trial factoring cutoff of 49 bits
Thu Dec 17 19:27:32 2009  polynomial 'A' values have 12 factors
Thu Dec 17 21:28:20 2009  60034 relations (16546 full + 43488 combined from 628080 partial), need 59501
Thu Dec 17 21:28:22 2009  begin with 644626 relations
Thu Dec 17 21:28:23 2009  reduce to 144631 relations in 10 passes
Thu Dec 17 21:28:23 2009  attempting to read 144631 relations
Thu Dec 17 21:28:28 2009  recovered 144631 relations
Thu Dec 17 21:28:28 2009  recovered 123342 polynomials
Thu Dec 17 21:28:28 2009  attempting to build 60034 cycles
Thu Dec 17 21:28:28 2009  found 60033 cycles in 5 passes
Thu Dec 17 21:28:28 2009  distribution of cycle lengths:
Thu Dec 17 21:28:28 2009     length 1 : 16546
Thu Dec 17 21:28:28 2009     length 2 : 11699
Thu Dec 17 21:28:28 2009     length 3 : 10471
Thu Dec 17 21:28:28 2009     length 4 : 7896
Thu Dec 17 21:28:28 2009     length 5 : 5549
Thu Dec 17 21:28:28 2009     length 6 : 3432
Thu Dec 17 21:28:28 2009     length 7 : 2116
Thu Dec 17 21:28:28 2009     length 9+: 2324
Thu Dec 17 21:28:28 2009  largest cycle: 18 relations
Thu Dec 17 21:28:29 2009  matrix is 59405 x 60033 (14.5 MB) with weight 3561514 (59.33/col)
Thu Dec 17 21:28:29 2009  sparse part has weight 3561514 (59.33/col)
Thu Dec 17 21:28:30 2009  filtering completed in 3 passes
Thu Dec 17 21:28:30 2009  matrix is 55134 x 55198 (13.3 MB) with weight 3276690 (59.36/col)
Thu Dec 17 21:28:30 2009  sparse part has weight 3276690 (59.36/col)
Thu Dec 17 21:28:30 2009  saving the first 48 matrix rows for later
Thu Dec 17 21:28:30 2009  matrix is 55086 x 55198 (8.4 MB) with weight 2562204 (46.42/col)
Thu Dec 17 21:28:30 2009  sparse part has weight 1871413 (33.90/col)
Thu Dec 17 21:28:30 2009  matrix includes 64 packed rows
Thu Dec 17 21:28:30 2009  using block size 21845 for processor cache size 512 kB
Thu Dec 17 21:28:31 2009  commencing Lanczos iteration
Thu Dec 17 21:28:31 2009  memory use: 8.6 MB
Thu Dec 17 21:28:57 2009  lanczos halted after 872 iterations (dim = 55084)
Thu Dec 17 21:28:57 2009  recovered 17 nontrivial dependencies
Thu Dec 17 21:28:58 2009  prp33 factor: 153780535368606699808334225196851
Thu Dec 17 21:28:58 2009  prp57 factor: 995139386383652479833893377455100373087666602506469998827
Thu Dec 17 21:28:58 2009  elapsed time 02:01:28

(71·10¹⁴⁶-53)/9 = 7(8)₁₄₅3_<147> = 3² · 155009 · 767549 · 548065700787859763_<18> · 28313464398271296426643_<23> · C95

C95 = P32 · P63

P32 = 90043846252206546356078001486191_<32>

P63 = 527267048811299110914254879692935600567639860720341154915317553_<63>

Number: 78883_146
N=47477153077019301591159437118623653232470390621832433349503030875070890539062923001884709410623
  ( 95 digits)
Divisors found:
 r1=90043846252206546356078001486191 (pp32)
 r2=527267048811299110914254879692935600567639860720341154915317553 (pp63)
Version: Msieve v. 1.43
Total time: 3.39 hours.
Scaled time: 3.11 units (timescale=0.917).
Factorization parameters were as follows:
n: 47477153077019301591159437118623653232470390621832433349503030875070890539062923001884709410623
# Murphy_E = 2.199459e-008
skew: 821603.19
Y0: -59297521755283477345156
Y1: 2701252515379
c0: -412061918369381128218326745
c1: 525673834041331095722
c2: -1165956053512201
c3: 1411579704
c4: 3840
type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 840001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 141600 x 141825
Total sieving time: 3.14 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 3.39 hours.
 --------- CPU info (if available) ----------

Dec 18, 2009 (2nd)

By Markus Tervooren / Msieve / Dec 18, 2009

(55·10²⁰¹+53)/9 = 6(1)₂₀₀7_<202> = 3 · 29 · 183770345533477853_<18> · 9930904669574722752815513_<25> · 3182926213879566929452257852809267_<34> · C125

C125 = P37 · P43 · P46

P37 = 1013944414775298531887586674648494811_<37>

P43 = 2482825775424863871031919439485952104015647_<43>

P46 = 4803410675320021647238892316395541852769020721_<46>

N=12092333369161073721453095497369483934473764519498218736238482790936465340160389049119166372609930051353777385455408331203957
  ( 125 digits)
Divisors found:
 r1=1013944414775298531887586674648494811 (pp37)
 r2=2482825775424863871031919439485952104015647 (pp43)
 r3=4803410675320021647238892316395541852769020721 (pp46)
Version: Msieve-1.39
Total time: 41.67 hours.
Scaled time: 0.00 units (timescale=0.000).
Factorization parameters were as follows:
n: 12092333369161073721453095497369483934473764519498218736238482790936465340160389049119166372609930051353777385455408331203957
Y0: -1274220013688769562210121
Y1: 23595695924081
c0: -4189165970554800237272722358592
c1: 28436094983909550967213948
c2: 554318636804277421328
c3: -207429849887747
c4: -6490537500
c5: 3600
skew: 301287.21
type: gnfs
# selected mechanically
rlim: 6800000
alim: 6800000
lpbr: 29
lpba: 29
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6

Factor base limits: 6800000/6800000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 55/55
Sieved algebraic special-q in [3400000, 6100001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 953591 x 953835
Total sieving time: 39.29 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 1.74 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
gnfs,124,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6800000,6800000,29,29,55,55,2.6,2.6,300000
total time: 41.67 hours.
 --------- CPU info (if available) ----------
[    0.144009] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.236014] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.332940] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.432541] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197988k/10485760k available (2226k kernel code, 189848k reserved, 1082k data, 392k init)
[    0.083990] Calibrating delay using timer specific routine.. 5337.16 BogoMIPS (lpj=10674326)
[    0.156009] Calibrating delay using timer specific routine.. 5333.34 BogoMIPS (lpj=10666681)
[    0.256016] Calibrating delay using timer specific routine.. 5333.37 BogoMIPS (lpj=10666743)
[    0.352020] Calibrating delay using timer specific routine.. 5333.36 BogoMIPS (lpj=10666726)
[    0.440025] Total of 4 processors activated (21337.23 BogoMIPS).

Dec 18, 2009

Factorizations of 766...669 and Factorizations of 788...883 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Dec 17, 2009 (6th)

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 17, 2009

(29·10²⁰²+43)/9 = 3(2)₂₀₁7_<203> = 13 · 37 · 67 · 281 · C196

C196 = P43 · P153

P43 = 3674105515071385923953475204266498683006339_<43>

P153 = 968451029165192787220172854208092971645574837169322265433382588380652505264113029568531164766001228858681871429432540061664423654443730298774148095125139_<153>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1735727886
Step 1 took 75389ms
Step 2 took 22706ms
********** Factor found in step 2: 3674105515071385923953475204266498683006339
Found probable prime factor of 43 digits: 3674105515071385923953475204266498683006339
Probable prime cofactor 968451029165192787220172854208092971645574837169322265433382588380652505264113029568531164766001228858681871429432540061664423654443730298774148095125139 has 153 digits

(58·10¹⁹⁷-31)/9 = 6(4)₁₉₆1_<198> = 7 · 701359 · C192

C192 = P34 · P158

P34 = 5096513647532794501083118207545671_<34>

P158 = 25755730864699073082591851139288692898367531568560403723880529183734319522625123361538086832200835064883598563324719178361854842928202684987796418138149494567_<158>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3484559451
Step 1 took 23184ms
Step 2 took 9180ms
********** Factor found in step 2: 5096513647532794501083118207545671
Found probable prime factor of 34 digits: 5096513647532794501083118207545671
Probable prime cofactor 25755730864699073082591851139288692898367531568560403723880529183734319522625123361538086832200835064883598563324719178361854842928202684987796418138149494567 has 158 digits

Dec 17, 2009 (5th)

By Robert Backstrom / GGNFS, GMP-ECM / Dec 17, 2009

(23·10¹⁴⁵-11)/3 = 7(6)₁₄₄3_<146> = 73 · 3038768926042968579379669855909439_<34> · C111

C111 = P48 · P63

P48 = 845283140698843865336212986554806013518603912649_<48>

P63 = 408868673677092400223227385697963975271696927286475015890283721_<63>

Number: n
N=345609796619143374458216318336570804191938122766182957592489445289969179338203424935277656426699958813310686929
  ( 111 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=845283140698843865336212986554806013518603912649 (pp48)
 r2=408868673677092400223227385697963975271696927286475015890283721 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.21 hours.
Scaled time: 14.97 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_7_6_144_3
n: 345609796619143374458216318336570804191938122766182957592489445289969179338203424935277656426699958813310686929
m: 100000000000000000000000000000
deg: 5
c5: 23
c0: -11
skew: 0.86
type: snfs
lss: 1
rlim: 1930000
alim: 1930000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
qintsize: 50000
Factor base limits: 1930000/1930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [965000, 2265001)
Primes: RFBsize:144125, AFBsize:143033, largePrimes:3989739 encountered
Relations: rels:3985007, finalFF:336507
Max relations in full relation-set: 48
Initial matrix: 287225 x 336507 with sparse part having weight 43143938.
Pruned matrix : 272402 x 273902 with weight 29441363.
Total sieving time: 7.15 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.86 hours.
Total square root time: 0.13 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000
total time: 8.21 hours.
 --------- CPU info (if available) ----------

(23·10¹⁴⁵-17)/3 = 7(6)₁₄₄1_<146> = 43 · 1398251 · 1256710869813684340075674424685443_<34> · C106

C106 = P36 · P70

P36 = 352755190695254784102272351641732783_<36>

P70 = 2876366371462316267559577405110123487885940029900306706265095862354433_<70>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 1014653167874607433393138777593797766888773887153826194843762435948768275207619865105895761692478221477039 (106 digits)
Using B1=6248000, B2=14271184210, polynomial Dickson(12), sigma=1751604143
Step 1 took 43078ms
Step 2 took 20937ms
********** Factor found in step 2: 352755190695254784102272351641732783
Found probable prime factor of 36 digits: 352755190695254784102272351641732783
Probable prime cofactor 2876366371462316267559577405110123487885940029900306706265095862354433 has 70 digits

Dec 17, 2009 (4th)

By Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve / Dec 17, 2009

(44·10²⁰³-17)/9 = 4(8)₂₀₂7_<204> = 7 · 163 · C201

C201 = P47 · P70 · P85

P47 = 25630033563617031385847435547249273144166992113_<47>

P70 = 4318542942595009757820233830306013464597471777655328897723327414407359_<70>

P85 = 3871133112888410851242347512433614554822820895229540799493946065464240230365835632021_<85>

Msieve v. 1.44
Wed Dec 16 08:27:43 2009
random seeds: b663c5c9 2a7cea5e
factoring 428474048105949946440743986756256694907001655467913136624793066510857921900866686142759762391664232155029701041970980621287369753627422339078780796572207615152400428474048105949946440743986756256694907 (201 digits)
searching for 15-digit factors
commencing number field sieve (201-digit input)
R0: -100000000000000000000000000000000000000000
R1:  1
A0: -425
A1:  0
A2:  0
A3:  0
A4:  0
A5:  11
skew 2.08, size 2.533068e-14, alpha 0.591541, combined = 8.538608e-12

commencing linear algebra
read 2577934 cycles
cycles contain 7049519 unique relations
read 7049519 relations
using 20 quadratic characters above 536869920
building initial matrix
memory use: 942.8 MB
read 2577934 cycles
matrix is 2577640 x 2577934 (760.6 MB) with weight 223821725 (86.82/col)
sparse part has weight 171040876 (66.35/col)
filtering completed in 3 passes
matrix is 2573115 x 2573315 (759.9 MB) with weight 223594494 (86.89/col)
sparse part has weight 170906338 (66.41/col)
read 2573315 cycles
matrix is 2573115 x 2573315 (759.9 MB) with weight 223594494 (86.89/col)
sparse part has weight 170906338 (66.41/col)
saving the first 48 matrix rows for later
matrix is 2573067 x 2573315 (719.2 MB) with weight 176770577 (68.69/col)
sparse part has weight 162792089 (63.26/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (2 threads)
memory use: 735.8 MB
linear algebra at 0.0%, ETA 22h41m73315 dimensions (0.0%, ETA 22h41m)
linear algebra completed 2573030 of 2573315 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 40690 iterations (dim = 2573066)
recovered 37 nontrivial dependencies
BLanczosTime: 80905

commencing square root phase
reading relations for dependency 1
read 1286702 cycles
cycles contain 3522180 unique relations
read 3522180 relations
multiplying 3522180 relations
multiply complete, coefficients have about 98.19 million bits
initial square root is modulo 11164921
reading relations for dependency 2
read 1286513 cycles
cycles contain 3523688 unique relations
read 3523688 relations
multiplying 3523688 relations
multiply complete, coefficients have about 98.23 million bits
initial square root is modulo 11235751
sqrtTime: 3833
prp47 factor: 25630033563617031385847435547249273144166992113
prp70 factor: 4318542942595009757820233830306013464597471777655328897723327414407359
prp85 factor: 3871133112888410851242347512433614554822820895229540799493946065464240230365835632021
elapsed time 23:32:21

(47·10²⁰³+43)/9 = 5(2)₂₀₂7_<204> = 5113 · C201

C201 = P51 · P74 · P77

P51 = 181487491329456893529699014005976048522291563291883_<51>

P74 = 30049111668022269060293639919135523844585639431557126784120834903582570631_<74>

P77 = 18728423468739666763833572416758539431513609604685681999119733206665398554423_<77>

Tue Dec 15 17:32:50 2009  Msieve v. 1.43
Tue Dec 15 17:32:50 2009  random seeds: c7eef5b7 40a71adb
Tue Dec 15 17:32:50 2009  factoring
102136167068692005128539452810917704326661885824803876828128735032705304561357759089032314144772584045026837907729752048156116217919464545711367538083751656996327444205402351304952517547862746376339179
(201 digits)
Tue Dec 15 17:32:52 2009  no P-1/P+1/ECM available, skipping
Tue Dec 15 17:32:52 2009  commencing number field sieve (201-digit input)
Tue Dec 15 17:32:52 2009  R0: -50000000000000000000000000000000000000000
Tue Dec 15 17:32:52 2009  R1:  1
Tue Dec 15 17:32:52 2009  A0:  1075
Tue Dec 15 17:32:52 2009  A1:  0
Tue Dec 15 17:32:52 2009  A2:  0
Tue Dec 15 17:32:52 2009  A3:  0
Tue Dec 15 17:32:52 2009  A4:  0
Tue Dec 15 17:32:52 2009  A5:  376
Tue Dec 15 17:32:52 2009  skew 1.23, size 1.228381e-14, alpha
0.965678, combined = 5.741146e-12
Tue Dec 15 17:32:52 2009
Tue Dec 15 17:32:52 2009  commencing linear algebra
Tue Dec 15 17:32:53 2009  read 3494552 cycles
Tue Dec 15 17:33:02 2009  cycles contain 10342707 unique relations
Tue Dec 15 17:34:42 2009  read 10342707 relations
Tue Dec 15 17:35:03 2009  using 20 quadratic characters above 536870684
Tue Dec 15 17:36:16 2009  building initial matrix
Tue Dec 15 17:39:41 2009  memory use: 1331.6 MB
Tue Dec 15 17:39:44 2009  read 3494552 cycles
Tue Dec 15 17:39:49 2009  matrix is 3494250 x 3494552 (1047.8 MB) with
weight 306605268 (87.74/col)
Tue Dec 15 17:39:49 2009  sparse part has weight 236229949 (67.60/col)
Tue Dec 15 17:41:36 2009  filtering completed in 3 passes
Tue Dec 15 17:41:38 2009  matrix is 3483497 x 3483697 (1046.3 MB) with
weight 306109139 (87.87/col)
Tue Dec 15 17:41:38 2009  sparse part has weight 235953625 (67.73/col)
Tue Dec 15 17:42:10 2009  read 3483697 cycles
Tue Dec 15 17:42:14 2009  matrix is 3483497 x 3483697 (1046.3 MB) with
weight 306109139 (87.87/col)
Tue Dec 15 17:42:14 2009  sparse part has weight 235953625 (67.73/col)
Tue Dec 15 17:42:14 2009  saving the first 48 matrix rows for later
Tue Dec 15 17:42:17 2009  matrix is 3483449 x 3483697 (993.8 MB) with
weight 243574570 (69.92/col)
Tue Dec 15 17:42:17 2009  sparse part has weight 225668811 (64.78/col)
Tue Dec 15 17:42:17 2009  matrix includes 64 packed rows
Tue Dec 15 17:42:17 2009  using block size 65536 for processor cache
size 6144 kB
Tue Dec 15 17:42:37 2009  commencing Lanczos iteration (5 threads)
Tue Dec 15 17:42:37 2009  memory use: 1100.4 MB
Tue Dec 15 17:42:57 2009  linear algebra at 0.0%, ETA 22h53m
Wed Dec 16 16:00:00 2009  lanczos halted after 55088 iterations (dim = 3483449)
Wed Dec 16 16:00:09 2009  recovered 39 nontrivial dependencies
Wed Dec 16 16:00:09 2009  BLanczosTime: 80837
Wed Dec 16 16:00:09 2009  elapsed time 22:27:19
Wed Dec 16 16:52:37 2009
Wed Dec 16 16:52:37 2009
Wed Dec 16 16:52:37 2009  Msieve v. 1.43
Wed Dec 16 16:52:37 2009  random seeds: 0a15e1d6 f5d23238
Wed Dec 16 16:52:37 2009  factoring
102136167068692005128539452810917704326661885824803876828128735032705304561357759089032314144772584045026837907729752048156116217919464545711367538083751656996327444205402351304952517547862746376339179
(201 digits)
Wed Dec 16 16:52:40 2009  no P-1/P+1/ECM available, skipping
Wed Dec 16 16:52:40 2009  commencing number field sieve (201-digit input)
Wed Dec 16 16:52:40 2009  R0: -50000000000000000000000000000000000000000
Wed Dec 16 16:52:40 2009  R1:  1
Wed Dec 16 16:52:40 2009  A0:  1075
Wed Dec 16 16:52:40 2009  A1:  0
Wed Dec 16 16:52:40 2009  A2:  0
Wed Dec 16 16:52:40 2009  A3:  0
Wed Dec 16 16:52:40 2009  A4:  0
Wed Dec 16 16:52:40 2009  A5:  376
Wed Dec 16 16:52:40 2009  skew 1.23, size 1.228381e-14, alpha
0.965678, combined = 5.741146e-12
Wed Dec 16 16:52:40 2009
Wed Dec 16 16:52:40 2009  commencing square root phase
Wed Dec 16 16:52:40 2009  reading relations for dependency 1
Wed Dec 16 16:52:41 2009  read 1742548 cycles
Wed Dec 16 16:52:45 2009  cycles contain 5168802 unique relations
Wed Dec 16 16:53:42 2009  read 5168802 relations
Wed Dec 16 16:54:22 2009  multiplying 5168802 relations
Wed Dec 16 17:00:50 2009  multiply complete, coefficients have about
169.25 million bits
Wed Dec 16 17:00:51 2009  initial square root is modulo 1186001
Wed Dec 16 17:15:18 2009  reading relations for dependency 2
Wed Dec 16 17:15:19 2009  read 1741131 cycles
Wed Dec 16 17:15:24 2009  cycles contain 5164836 unique relations
Wed Dec 16 17:16:20 2009  read 5164836 relations
Wed Dec 16 17:17:01 2009  multiplying 5164836 relations
Wed Dec 16 17:23:31 2009  multiply complete, coefficients have about
169.12 million bits
Wed Dec 16 17:23:33 2009  initial square root is modulo 1173121
Wed Dec 16 17:38:01 2009  reading relations for dependency 3
Wed Dec 16 17:38:01 2009  read 1741280 cycles
Wed Dec 16 17:38:06 2009  cycles contain 5166270 unique relations
Wed Dec 16 17:39:02 2009  read 5166270 relations
Wed Dec 16 17:39:43 2009  multiplying 5166270 relations
Wed Dec 16 17:46:10 2009  multiply complete, coefficients have about
169.17 million bits
Wed Dec 16 17:46:12 2009  initial square root is modulo 1177921
Wed Dec 16 18:00:39 2009  sqrtTime: 4079
Wed Dec 16 18:00:40 2009  prp51 factor:
181487491329456893529699014005976048522291563291883
Wed Dec 16 18:00:40 2009  prp74 factor:
30049111668022269060293639919135523844585639431557126784120834903582570631
Wed Dec 16 18:00:40 2009  prp77 factor:
18728423468739666763833572416758539431513609604685681999119733206665398554423
Wed Dec 16 18:00:40 2009  elapsed time 01:08:03

Dec 17, 2009 (3rd)

By Sinkiti Sibata / Msieve / Dec 17, 2009

(23·10¹²⁸-17)/3 = 7(6)₁₂₇1_<129> = 439 · 33359 · C122

C122 = P30 · P92

P30 = 796330877846429536306828912489_<30>

P92 = 65740875249676750527318907470608197372316851127687878872318015560789092527574729697323746949_<92>

Number: 76661_128
N=52351488897967699267919055402510909424344621384131030040809351286980551171497718965963406354783354402531463074116301746061
  ( 122 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=796330877846429536306828912489 (pp30)
 r2=65740875249676750527318907470608197372316851127687878872318015560789092527574729697323746949 (pp92)
Version: Msieve v. 1.42
Total time: 0.19 hours.
Scaled time: 0.15 units (timescale=0.796).
Factorization parameters were as follows:
name: 76661_128
n: 52351488897967699267919055402510909424344621384131030040809351286980551171497718965963406354783354402531463074116301746061
m: 10000000000000000000000000
deg: 5
c5: 23000
c0: -17
skew: 0.24
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 169338 x 169580
Total sieving time: 0.00 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,129.000,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 0.19 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 2 hours 24 min.

(68·10¹⁴⁹-23)/9 = 7(5)₁₄₈3_<150> = 3 · 16553 · 50929 · C141

C141 = P59 · P83

P59 = 17113117275140880783030116386021552160919406381244764651037_<59>

P83 = 17457182741759537230668434734479558816443041150505523061434504635431445561687384479_<83>

Number: 75553_149
N=298746815553296382052316567908906005368897905967537402451862449042826513609541950162254094199336945246739671451464771736035835617887685054723
  ( 141 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=17113117275140880783030116386021552160919406381244764651037 (pp59)
 r2=17457182741759537230668434734479558816443041150505523061434504635431445561687384479 (pp83)
Version: Msieve-1.40
Total time: 22.23 hours.
Scaled time: 45.60 units (timescale=2.051).
Factorization parameters were as follows:
name: 75553_149
n: 298746815553296382052316567908906005368897905967537402451862449042826513609541950162254094199336945246739671451464771736035835617887685054723
m: 200000000000000000000000000000
deg: 5
c5: 21250
c0: -23
skew: 0.26
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 2050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 463542 x 463790
Total sieving time: 20.70 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.75 hours.
Time per square root: 0.66 hours.
Prototype def-par.txt line would be:
snfs,150.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 22.23 hours.
 --------- CPU info (if available) ----------

(68·10¹⁵⁰-23)/9 = 7(5)₁₄₉3_<151> = 563 · C149

C149 = P32 · P41 · P77

P32 = 14954759575038077017989758004101_<32>

P41 = 61061284304473599603372195208904250303373_<41>

P77 = 14696456667525975952009223329233872114376566246538367924642568716200666134747_<77>

Number: 75553_150
N=13420169725675942372212354450365107558713242549832247878429050720347345569370436155516084468127096901519636865995658180382869548056048944148411288731
  ( 149 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=14954759575038077017989758004101 (pp32)
 r2=61061284304473599603372195208904250303373 (pp41)
 r3=14696456667525975952009223329233872114376566246538367924642568716200666134747 (pp77)
Version: Msieve v. 1.42
Total time: 0.63 hours.
Scaled time: 0.50 units (timescale=0.796).
Factorization parameters were as follows:
name: 75553_150
n: 13420169725675942372212354450365107558713242549832247878429050720347345569370436155516084468127096901519636865995658180382869548056048944148411288731
m: 1000000000000000000000000000000
deg: 5
c5: 68
c0: -23
skew: 0.81
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 2000001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 398069 x 398296
Total sieving time: 0.00 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.45 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 0.63 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 14 hours.

Dec 17, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve / Dec 17, 2009

(23·10¹⁵⁰-11)/3 = 7(6)₁₄₉3_<151> = 5237 · 32719 · C143

C143 = P68 · P76

P68 = 20730300332205578545577304811001844751211485934910034956055592189129_<68>

P76 = 2158332705171856636744098266679217747556662312757756507611949426597067237949_<76>

N=44742885195034304652153743813549596473742407300168222159879171955251379934289392690015188828330301604066088673017825843645727010012790454056421
  ( 143 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=20730300332205578545577304811001844751211485934910034956055592189129 (pp68)
 r2=2158332705171856636744098266679217747556662312757756507611949426597067237949 (pp76)
Version: Msieve-1.40
Total time: 11.42 hours.
Scaled time: 22.03 units (timescale=1.928).
Factorization parameters were as follows:
n: 44742885195034304652153743813549596473742407300168222159879171955251379934289392690015188828330301604066088673017825843645727010012790454056421
m: 1000000000000000000000000000000
deg: 5
c5: 23
c0: -11
skew: 0.86
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 458174 x 458422
Total sieving time: 11.07 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 11.42 hours.
 --------- CPU info (if available) ----------

(23·10¹⁴⁰-17)/3 = 7(6)₁₃₉1_<141> = 31 · 6983 · C136

C136 = P35 · P102

P35 = 12092697592643045806310843800295173_<35>

P102 = 292873213870386294147063822532631373146765490196977576713937119242887016739140553003906553448857860809_<102>

N=3541627208320052231302133137465950334067836019580578948259906162277358685224793238263740358689844306988246417182127409268900355548574957
  ( 136 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=12092697592643045806310843800295173 (pp35)
 r2=292873213870386294147063822532631373146765490196977576713937119242887016739140553003906553448857860809 (pp102)
Version: Msieve-1.40
Total time: 4.50 hours.
Scaled time: 8.89 units (timescale=1.976).
Factorization parameters were as follows:
n: 3541627208320052231302133137465950334067836019580578948259906162277358685224793238263740358689844306988246417182127409268900355548574957
m: 10000000000000000000000000000
deg: 5
c5: 23
c0: -17
skew: 0.94
type: snfs
lss: 1
rlim: 1590000
alim: 1590000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1590000/1590000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [795000, 1595001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 195465 x 195690
Total sieving time: 4.35 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1590000,1590000,26,26,48,48,2.3,2.3,100000
total time: 4.50 hours.
 --------- CPU info (if available) ----------

(23·10¹³⁵-17)/3 = 7(6)₁₃₄1_<136> = 824172551 · 194129529985105327_<18> · C110

C110 = P55 · P56

P55 = 1905320850171848469909562071495906961196008761575322601_<55>

P56 = 25149462747812728594322660597906703351892283482122779893_<56>

N=47917795744027780378413304806221669354275218945932946509109283412132135919751097227147273714466857302391261693
  ( 110 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=1905320850171848469909562071495906961196008761575322601 (pp55)
 r2=25149462747812728594322660597906703351892283482122779893 (pp56)
Version: Msieve-1.40
Total time: 3.71 hours.
Scaled time: 6.97 units (timescale=1.877).
Factorization parameters were as follows:
n: 47917795744027780378413304806221669354275218945932946509109283412132135919751097227147273714466857302391261693
m: 1000000000000000000000000000
deg: 5
c5: 23
c0: -17
skew: 0.94
type: snfs
lss: 1
rlim: 1310000
alim: 1310000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1310000/1310000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [655000, 1330001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 155675 x 155900
Total sieving time: 3.59 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1310000,1310000,26,26,48,48,2.3,2.3,75000
total time: 3.71 hours.
 --------- CPU info (if available) ----------

(23·10¹³¹-17)/3 = 7(6)₁₃₀1_<132> = 7 · 191 · 2996638793_<10> · 3890997715465607_<16> · C104

C104 = P48 · P56

P48 = 512631118506491300694853903522261777639574203531_<48>

P56 = 95934504107332076044084320068184723105024374504364475513_<56>

N=49179012143907225906578389671542644025191118244977237920486566849786794594596600064062738910557527636403
  ( 104 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=512631118506491300694853903522261777639574203531 (pp48)
 r2=95934504107332076044084320068184723105024374504364475513 (pp56)
Version: Msieve-1.40
Total time: 2.36 hours.
Scaled time: 4.28 units (timescale=1.813).
Factorization parameters were as follows:
n: 49179012143907225906578389671542644025191118244977237920486566849786794594596600064062738910557527636403
m: 100000000000000000000000000
deg: 5
c5: 230
c0: -17
skew: 0.59
type: snfs
lss: 1
rlim: 1120000
alim: 1120000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1120000/1120000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [560000, 1010001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 143159 x 143390
Total sieving time: 2.27 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,132.000,5,0,0,0,0,0,0,0,0,1120000,1120000,26,26,47,47,2.3,2.3,50000
total time: 2.36 hours.
 --------- CPU info (if available) ----------

(23·10¹³⁰-17)/3 = 7(6)₁₂₉1_<131> = 13 · 61 · 10399 · C124

C124 = P47 · P78

P47 = 30318235100717866400373492092541671420427759317_<47>

P78 = 306646420444444276169168758599822702752172077221617339445341659227794033863719_<78>

N=9296978267828239215778055420580947152701372448227048054585065552387441787273738328300636467090051056983564680553199310519923
  ( 124 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=30318235100717866400373492092541671420427759317 (pp47)
 r2=306646420444444276169168758599822702752172077221617339445341659227794033863719 (pp78)
Version: Msieve-1.40
Total time: 2.14 hours.
Scaled time: 4.18 units (timescale=1.957).
Factorization parameters were as follows:
n: 9296978267828239215778055420580947152701372448227048054585065552387441787273738328300636467090051056983564680553199310519923
m: 100000000000000000000000000
deg: 5
c5: 23
c0: -17
skew: 0.94
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 940001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 118274 x 118500
Total sieving time: 2.07 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 2.14 hours.
 --------- CPU info (if available) ----------

(23·10¹⁴⁸-11)/3 = 7(6)₁₄₇3_<149> = 51005438018230242249981203_<26> · C124

C124 = P39 · P86

P39 = 127187830640740361371221967602054087623_<39>

P86 = 11818015082134451599966379985993827454800138229230558833671370815526360219428259516027_<86>

N=1503107700776231921657131924014173176654439989939501657160233819006711595971027654175356316074967623086933826733503030833821
  ( 124 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=127187830640740361371221967602054087623 (pp39)
 r2=11818015082134451599966379985993827454800138229230558833671370815526360219428259516027 (pp86)
Version: Msieve-1.40
Total time: 12.94 hours.
Scaled time: 25.18 units (timescale=1.946).
Factorization parameters were as follows:
n: 1503107700776231921657131924014173176654439989939501657160233819006711595971027654175356316074967623086933826733503030833821
m: 100000000000000000000000000000
deg: 5
c5: 23000
c0: -11
skew: 0.22
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 3500001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 440688 x 440913
Total sieving time: 12.55 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,149.000,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000
total time: 12.94 hours.
 --------- CPU info (if available) ----------

Dec 17, 2009

By Agnew yoyo / GMP-ECM / Dec 17, 2009

(64·10³⁴⁷-1)/9 = 7(1)₃₄₇_<348> = 3 · 443 · 5987 · 2586730480696668987564422124671_<31> · C311

C311 = P47 · P265

P47 = 14659087572470179449229116683122603300318536157_<47>

P265 = 2356921431952052588934037590177099728109555193853091850719231714273453062213133365460581304663024067212955079325297428858553446842378615826672539689330219694793449179709509610909732438351804460200561335905172483023901987009557897904983940745732286127093215612360831_<265>

GMP-ECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [ECM]
Input number is 34550317672416953827084892267499412045197057142161000818419076015596720334161716626133851628318223460475062662606699081504178180162856355490806191872531832714709422759302739849459589670365940831870050834695459866677147871642828326730993136466595287731450202444255399833480033929257170613279218153276120804066467 (311 digits)
[Thu Dec 17 03:28:23 2009]
Using MODMULN
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1594316881
dF=65536, k=5, d=690690, d2=17, i0=46
Expected number of curves to find a factor of n digits:
20	25	30	35	40	45	50	55	60	65
2	5	14	55	246	1277	7553	49797	358989	2841353
Step 1 took 848438ms
Using 36 small primes for NTT
Estimated memory usage: 402M
Initializing tables of differences for F took 234ms
Computing roots of F took 14437ms
Building F from its roots took 16016ms
Computing 1/F took 7422ms
Initializing table of differences for G took 313ms
Computing roots of G took 11594ms
Building G from its roots took 15109ms
Computing roots of G took 11594ms
Building G from its roots took 15109ms
Computing G * H took 4079ms
Reducing  G * H mod F took 4062ms
Computing roots of G took 11594ms
Building G from its roots took 15062ms
Computing G * H took 4031ms
Reducing  G * H mod F took 4063ms
Computing roots of G took 10969ms
Building G from its roots took 15078ms
Computing G * H took 3828ms
Reducing  G * H mod F took 3922ms
Computing roots of G took 11328ms
Building G from its roots took 14860ms
Computing G * H took 3968ms
Reducing  G * H mod F took 4000ms
Computing polyeval(F,G) took 27656ms
Computing product of all F(g_i) took 188ms
Step 2 took 231031ms
********** Factor found in step 2: 14659087572470179449229116683122603300318536157
Found probable prime factor of 47 digits: 14659087572470179449229116683122603300318536157
Probable prime cofactor 2356921431952052588934037590177099728109555193853091850719231714273453062213133365460581304663024067212955079325297428858553446842378615826672539689330219694793449179709509610909732438351804460200561335905172483023901987009557897904983940745732286127093215612360831 has 265 digits

Dec 16, 2009 (8th)

By Sinkiti Sibata / Msieve, GGNFS / Dec 16, 2009

(68·10¹⁴⁷-23)/9 = 7(5)₁₄₆3_<148> = 7 · 13 · 191 · 114145524058937334950410751_<27> · C118

C118 = P40 · P78

P40 = 7444412125212146417878210412001724747661_<40>

P78 = 511566797573705714139540064583403760560721746535899396273870560730050344203583_<78>

Number: 75553_147
N=3808314070713642463132865247438710710836951689144171374141341852389397914903274595705945055940917351089773374687069363
  ( 118 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=7444412125212146417878210412001724747661 (pp40)
 r2=511566797573705714139540064583403760560721746535899396273870560730050344203583 (pp78)
Version: Msieve v. 1.42
Total time: 0.58 hours.
Scaled time: 0.46 units (timescale=0.796).
Factorization parameters were as follows:
name: 75553_147
n: 3808314070713642463132865247438710710836951689144171374141341852389397914903274595705945055940917351089773374687069363
m: 100000000000000000000000000000
deg: 5
c5: 6800
c0: -23
skew: 0.32
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 362627 x 362851
Total sieving time: 0.00 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,148.000,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 0.58 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 9 hours.

(68·10¹⁴⁸+31)/9 = 7(5)₁₄₇9_<149> = 11 · 367 · 28001 · C141

C141 = P38 · P43 · P61

P38 = 92800742277266402244455752296406105709_<38>

P43 = 5095578428923988067283965606586821860079463_<43>

P61 = 1413478385719658305746935999570713543673849123265009091961921_<61>

Number: 75559_148
N=668396415648338433890954543438052444688739402620290681217271324456091212669680527046851157307702894290060746844549914253438855080660983466907
  ( 141 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=92800742277266402244455752296406105709 (pp38)
 r2=5095578428923988067283965606586821860079463 (pp43)
 r3=1413478385719658305746935999570713543673849123265009091961921 (pp61)
Version: Msieve-1.40
Total time: 15.20 hours.
Scaled time: 30.49 units (timescale=2.006).
Factorization parameters were as follows:
name: 75559_148
n: 668396415648338433890954543438052444688739402620290681217271324456091212669680527046851157307702894290060746844549914253438855080660983466907
m: 200000000000000000000000000000
deg: 5
c5: 2125
c0: 31
skew: 0.43
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 2800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 361343 x 361575
Total sieving time: 14.29 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.46 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,149.000,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000
total time: 15.20 hours.
 --------- CPU info (if available) ----------

(68·10¹⁴⁸-23)/9 = 7(5)₁₄₇3_<149> = 31 · 61089959452919_<14> · C134

C134 = P44 · P91

P44 = 33379177452900859040901458273531293497645001_<44>

P91 = 1195251348071351262939369843658738348823063310087712346521340434884593591391504262928936177_<91>

Number: 75553_148
N=39896506848092604746137269695445224030913290669912862255101837235764336396056343724509946701322150758800725954828675926061567732101177
  ( 134 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=33379177452900859040901458273531293497645001 (pp44)
 r2=1195251348071351262939369843658738348823063310087712346521340434884593591391504262928936177 (pp91)
Version: Msieve-1.40
Total time: 11.69 hours.
Scaled time: 38.84 units (timescale=3.322).
Factorization parameters were as follows:
name: 75553_148
n: 39896506848092604746137269695445224030913290669912862255101837235764336396056343724509946701322150758800725954828675926061567732101177
m: 200000000000000000000000000000
deg: 5
c5: 2125
c0: -23
skew: 0.40
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 2900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 388346 x 388594
Total sieving time: 11.35 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,149.000,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000
total time: 11.69 hours.
 --------- CPU info (if available) ----------

(23·10¹¹³-11)/3 = 7(6)₁₁₂3_<114> = 73 · 4001 · 184073 · 271519425493_<12> · C92

C92 = P38 · P55

P38 = 11411606196574225655815607303001588809_<38>

P55 = 4602326201348474538346286072127148267220249089588845731_<55>

Number: 76663_113
N=52519934197964169378187398269922763301280269896278975894836658825836486587279754057397024379
  ( 92 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=11411606196574225655815607303001588809 (pp38)
 r2=4602326201348474538346286072127148267220249089588845731 (pp55)
Version: Msieve-1.40
Total time: 1.57 hours.
Scaled time: 3.23 units (timescale=2.051).
Factorization parameters were as follows:
name: 76663_113
n: 52519934197964169378187398269922763301280269896278975894836658825836486587279754057397024379
m: 10000000000000000000000
deg: 5
c5: 23000
c0: -11
skew: 0.22
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [280000, 530001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 68760 x 68985
Total sieving time: 1.49 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,114.000,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000
total time: 1.57 hours.
 --------- CPU info (if available) ----------

(23·10¹²⁰-11)/3 = 7(6)₁₁₉3_<121> = 17 · 79 · 499 · 569 · C113

C113 = P56 · P57

P56 = 25522691488157552788809468757639086299259225092491527019_<56>

P57 = 787755212873123836676281249152475749953193949007977372369_<57>

Number: 76663_120
N=20105633266348618800994983033463626316231562973668231677796065657826655924279261934685768126702001408007987538011
  ( 113 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=25522691488157552788809468757639086299259225092491527019 (pp56)
 r2=787755212873123836676281249152475749953193949007977372369 (pp57)
Version: Msieve-1.40
Total time: 1.16 hours.
Scaled time: 3.88 units (timescale=3.357).
Factorization parameters were as follows:
name: 76663_120
n: 20105633266348618800994983033463626316231562973668231677796065657826655924279261934685768126702001408007987538011
m: 1000000000000000000000000
deg: 5
c5: 23
c0: -11
skew: 0.86
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 620001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 82925 x 83157
Total sieving time: 1.13 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 1.16 hours.
 --------- CPU info (if available) ----------

(23·10¹¹⁴-11)/3 = 7(6)₁₁₃3_<115> = 107 · 22651 · 8445108594849167_<16> · C93

C93 = P37 · P57

P37 = 3059870380737586822512005449734369637_<37>

P57 = 122412891178728360371674809568046004111359888829192602221_<57>

Number: 76663_114
N=374567579938244331406279693518468187924635006153465102723180322997238243405496028525121163777
  ( 93 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=3059870380737586822512005449734369637 (pp37)
 r2=122412891178728360371674809568046004111359888829192602221 (pp57)
Version: Msieve-1.40
Total time: 1.06 hours.
Scaled time: 2.17 units (timescale=2.045).
Factorization parameters were as follows:
name: 76663_114
n: 374567579938244331406279693518468187924635006153465102723180322997238243405496028525121163777
m: 10000000000000000000000
deg: 5
c5: 230000
c0: -11
skew: 0.14
type: snfs
lss: 1
rlim: 590000
alim: 590000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 590000/590000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [295000, 445001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 58900 x 59126
Total sieving time: 1.00 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,115.000,5,0,0,0,0,0,0,0,0,590000,590000,25,25,45,45,2.2,2.2,50000
total time: 1.06 hours.
 --------- CPU info (if available) ----------

(23·10¹²⁶-11)/3 = 7(6)₁₂₅3_<127> = 47 · 61 · 1057464970577446092973_<22> · C103

C103 = P32 · P72

P32 = 13413698726583970462081322925539_<32>

P72 = 188523003684124076180996738433766325149793904672787761086552059533456187_<72>

Number: 76663_126
N=2528790774449520292669339776762899096930856296816157041815109917097158021385913870850834746574719859793
  ( 103 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=13413698726583970462081322925539 (pp32)
 r2=188523003684124076180996738433766325149793904672787761086552059533456187 (pp72)
Version: Msieve-1.40
Total time: 1.66 hours.
Scaled time: 5.53 units (timescale=3.339).
Factorization parameters were as follows:
name: 76663_126
n: 2528790774449520292669339776762899096930856296816157041815109917097158021385913870850834746574719859793
m: 10000000000000000000000000
deg: 5
c5: 230
c0: -11
skew: 0.54
type: snfs
lss: 1
rlim: 930000
alim: 930000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 930000/930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [465000, 765001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 120459 x 120690
Total sieving time: 1.59 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,127.000,5,0,0,0,0,0,0,0,0,930000,930000,26,26,46,46,2.3,2.3,50000
total time: 1.66 hours.
 --------- CPU info (if available) ----------

(23·10¹²⁰-17)/3 = 7(6)₁₁₉1_<121> = 251 · 941 · 641701847 · 137279406996157_<15> · C93

C93 = P44 · P49

P44 = 40385545056978807490330733028374505691311499_<44>

P49 = 9123859816461408438093111424239616025271490303651_<49>

Number: 76661_120
N=368472051711260603290907951809574825594060081448813710281059755320847323776252661535937982849
  ( 93 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=40385545056978807490330733028374505691311499 (pp44)
 r2=9123859816461408438093111424239616025271490303651 (pp49)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.37 hours.
Scaled time: 1.11 units (timescale=0.468).
Factorization parameters were as follows:
name: 76661_120
n: 368472051711260603290907951809574825594060081448813710281059755320847323776252661535937982849
m: 1000000000000000000000000
deg: 5
c5: 23
c0: -17
skew: 0.94
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 570001)
Primes: RFBsize:59531, AFBsize:59778, largePrimes:1289988 encountered
Relations: rels:1259145, finalFF:145398
Max relations in full relation-set: 28
Initial matrix: 119374 x 145398 with sparse part having weight 6389763.
Pruned matrix : 104465 x 105125 with weight 3571061.
Total sieving time: 2.21 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 2.37 hours.
 --------- CPU info (if available) ----------

(23·10¹¹⁸-17)/3 = 7(6)₁₁₇1_<119> = 13 · 19 · C117

C117 = P37 · P80

P37 = 9220814096092378075081918296352874047_<37>

P80 = 33662034586998177818149074936349876698328006634392197039896356491332469987852029_<80>

Number: 76661_118
N=310391363022941970310391363022941970310391363022941970310391363022941970310391363022941970310391363022941970310391363
  ( 117 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=9220814096092378075081918296352874047 (pp37)
 r2=33662034586998177818149074936349876698328006634392197039896356491332469987852029 (pp80)
Version: Msieve v. 1.42
Total time: 0.04 hours.
Scaled time: 0.03 units (timescale=0.795).
Factorization parameters were as follows:
name: 76661_118
n: 310391363022941970310391363022941970310391363022941970310391363022941970310391363022941970310391363022941970310391363
m: 100000000000000000000000
deg: 5
c5: 23000
c0: -17
skew: 0.24
type: snfs
lss: 1
rlim: 680000
alim: 680000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 680000/680000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [340000, 640001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 79185 x 79410
Total sieving time: 0.00 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,119.000,5,0,0,0,0,0,0,0,0,680000,680000,25,25,45,45,2.2,2.2,50000
total time: 0.04 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 83 min.

(23·10¹²⁵-17)/3 = 7(6)₁₂₄1_<126> = 7² · 31 · 521 · 14370729157_<11> · C110

C110 = P46 · P65

P46 = 2558995386883296022720615957313118525870831481_<46>

P65 = 26342851081520675035689188882287686037742543187479440491093033967_<65>

Number: 76661_125
N=67411234394965052867362708500102595217340895755614475022353081977374166777198257577218719672431852753265915127
  ( 110 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=2558995386883296022720615957313118525870831481 (pp46)
 r2=26342851081520675035689188882287686037742543187479440491093033967 (pp65)
Version: Msieve v. 1.42
Total time: 0.09 hours.
Scaled time: 0.07 units (timescale=0.795).
Factorization parameters were as follows:
name: 76661_125
n: 67411234394965052867362708500102595217340895755614475022353081977374166777198257577218719672431852753265915127
m: 10000000000000000000000000
deg: 5
c5: 23
c0: -17
skew: 0.94
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 645001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 130853 x 131095
Total sieving time: 0.00 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 0.09 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 71 min.

(23·10¹³⁹-17)/3 = 7(6)₁₃₈1_<140> = 7333 · 870461 · 21472703873_<11> · 4636213698349_<13> · 12226441866109_<14> · C94

C94 = P42 · P53

P42 = 371170686541166156016178439269165816819121_<42>

P53 = 26585916743770808161710550311179305870423365914583949_<53>

Wed Dec 16 18:14:05 2009  Msieve v. 1.42
Wed Dec 16 18:14:05 2009  random seeds: a37cea14 4740c28b
Wed Dec 16 18:14:05 2009  factoring 9867912970111695460549107729778455971521528100356802580128959817623419385028243844407302888829 (94 digits)
Wed Dec 16 18:14:06 2009  searching for 15-digit factors
Wed Dec 16 18:14:07 2009  commencing quadratic sieve (94-digit input)
Wed Dec 16 18:14:07 2009  using multiplier of 5
Wed Dec 16 18:14:07 2009  using 32kb Intel Core sieve core
Wed Dec 16 18:14:07 2009  sieve interval: 36 blocks of size 32768
Wed Dec 16 18:14:07 2009  processing polynomials in batches of 6
Wed Dec 16 18:14:07 2009  using a sieve bound of 2092049 (77647 primes)
Wed Dec 16 18:14:07 2009  using large prime bound of 297070958 (28 bits)
Wed Dec 16 18:14:07 2009  using double large prime bound of 1782987509181578 (42-51 bits)
Wed Dec 16 18:14:07 2009  using trial factoring cutoff of 51 bits
Wed Dec 16 18:14:07 2009  polynomial 'A' values have 12 factors
Wed Dec 16 21:09:09 2009  77957 relations (19573 full + 58384 combined from 1128063 partial), need 77743
Wed Dec 16 21:09:10 2009  begin with 1147636 relations
Wed Dec 16 21:09:12 2009  reduce to 200886 relations in 11 passes
Wed Dec 16 21:09:12 2009  attempting to read 200886 relations
Wed Dec 16 21:09:15 2009  recovered 200886 relations
Wed Dec 16 21:09:15 2009  recovered 182269 polynomials
Wed Dec 16 21:09:15 2009  attempting to build 77957 cycles
Wed Dec 16 21:09:15 2009  found 77957 cycles in 6 passes
Wed Dec 16 21:09:15 2009  distribution of cycle lengths:
Wed Dec 16 21:09:15 2009     length 1 : 19573
Wed Dec 16 21:09:15 2009     length 2 : 13851
Wed Dec 16 21:09:15 2009     length 3 : 13195
Wed Dec 16 21:09:15 2009     length 4 : 10679
Wed Dec 16 21:09:15 2009     length 5 : 7717
Wed Dec 16 21:09:15 2009     length 6 : 5129
Wed Dec 16 21:09:15 2009     length 7 : 3326
Wed Dec 16 21:09:15 2009     length 9+: 4487
Wed Dec 16 21:09:15 2009  largest cycle: 21 relations
Wed Dec 16 21:09:16 2009  matrix is 77647 x 77957 (20.5 MB) with weight 5073118 (65.08/col)
Wed Dec 16 21:09:16 2009  sparse part has weight 5073118 (65.08/col)
Wed Dec 16 21:09:17 2009  filtering completed in 3 passes
Wed Dec 16 21:09:17 2009  matrix is 73626 x 73690 (19.5 MB) with weight 4814531 (65.33/col)
Wed Dec 16 21:09:17 2009  sparse part has weight 4814531 (65.33/col)
Wed Dec 16 21:09:17 2009  saving the first 48 matrix rows for later
Wed Dec 16 21:09:17 2009  matrix is 73578 x 73690 (12.6 MB) with weight 3834182 (52.03/col)
Wed Dec 16 21:09:17 2009  sparse part has weight 2868194 (38.92/col)
Wed Dec 16 21:09:17 2009  matrix includes 64 packed rows
Wed Dec 16 21:09:17 2009  using block size 29476 for processor cache size 1024 kB
Wed Dec 16 21:09:18 2009  commencing Lanczos iteration
Wed Dec 16 21:09:18 2009  memory use: 12.5 MB
Wed Dec 16 21:09:56 2009  lanczos halted after 1165 iterations (dim = 73576)
Wed Dec 16 21:09:56 2009  recovered 17 nontrivial dependencies
Wed Dec 16 21:09:57 2009  prp42 factor: 371170686541166156016178439269165816819121
Wed Dec 16 21:09:57 2009  prp53 factor: 26585916743770808161710550311179305870423365914583949
Wed Dec 16 21:09:57 2009  elapsed time 02:55:52

(23·10¹⁰²-11)/3 = 7(6)₁₀₁3_<103> = 24365927 · C96

C96 = P36 · P61

P36 = 245245101836602285803147368918044021_<36>

P61 = 1282990085704394596547225527931058487571930541873060963231389_<61>

Number: 76663_102
N=314647034223925347337151041561713070332463306923092508102263733559846365240553608597229510975169
  ( 96 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=245245101836602285803147368918044021 (pp36)
 r2=1282990085704394596547225527931058487571930541873060963231389 (pp61)
Version: Msieve v. 1.42
Total time: 0.02 hours.
Scaled time: 0.01 units (timescale=0.796).
Factorization parameters were as follows:
name: 76663_102
n: 314647034223925347337151041561713070332463306923092508102263733559846365240553608597229510975169
m: 10000000000000000000000000
deg: 4
c4: 2300
c0: -11
skew: 0.26
type: snfs
lss: 1
rlim: 370000
alim: 370000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2
Factor base limits: 370000/370000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [185000, 235001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 29754 x 29979
Total sieving time: 0.00 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103.000,4,0,0,0,0,0,0,0,0,370000,370000,25,25,43,43,2.2,2.2,10000
total time: 0.02 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 17 min.

(23·10¹⁰⁴-11)/3 = 7(6)₁₀₃3_<105> = 7 · 17 · 317 · C101

C101 = P50 · P52

P50 = 10594311962989340631950058167917525981867419492781_<50>

P52 = 1918348913925488028058767174886260061337183152503001_<52>

Number: 76663_104
N=20323586847988406719154538787123682280483171186455654817131900078643444759607312956728432698000335781
  ( 101 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=10594311962989340631950058167917525981867419492781 (pp50)
 r2=1918348913925488028058767174886260061337183152503001 (pp52)
Version: Msieve v. 1.42
Total time: 0.02 hours.
Scaled time: 0.01 units (timescale=0.793).
Factorization parameters were as follows:
name: 76663_104
n: 20323586847988406719154538787123682280483171186455654817131900078643444759607312956728432698000335781
m: 100000000000000000000000000
deg: 4
c4: 23
c0: -11
skew: 0.83
type: snfs
lss: 1
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [200000, 240001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 39072 x 39301
Total sieving time: 0.00 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,105.000,4,0,0,0,0,0,0,0,0,400000,400000,25,25,44,44,2.2,2.2,20000
total time: 0.02 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 13 min.

(23·10¹²⁷-17)/3 = 7(6)₁₂₆1_<128> = 179 · 1291 · C123

C123 = P44 · P80

P44 = 17325323742942685585564136440668567011871023_<44>

P80 = 19148993397947114116728493211346650542616183424561745135636491481312527026611163_<80>

Number: 76661_127
N=331762509970905870321247080850523679909760597287913603272620794008657559064545117537687499909847144029645143934443728029749
  ( 123 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=17325323742942685585564136440668567011871023 (pp44)
 r2=19148993397947114116728493211346650542616183424561745135636491481312527026611163 (pp80)
Version: Msieve-1.40
Total time: 2.33 hours.
Scaled time: 7.77 units (timescale=3.339).
Factorization parameters were as follows:
name: 76661_127
n: 331762509970905870321247080850523679909760597287913603272620794008657559064545117537687499909847144029645143934443728029749
m: 10000000000000000000000000
deg: 5
c5: 2300
c0: -17
skew: 0.37
type: snfs
lss: 1
rlim: 960000
alim: 960000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 960000/960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [480000, 930001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 143966 x 144214
Total sieving time: 2.26 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,128.000,5,0,0,0,0,0,0,0,0,960000,960000,26,26,47,47,2.3,2.3,50000
total time: 2.33 hours.
 --------- CPU info (if available) ----------

Dec 16, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Dec 16, 2009

(2·10¹⁹⁸+1)/3 = (6)₁₉₇7_<198> = 457 · 23735503197283_<14> · C182

C182 = P81 · P102

P81 = 129389304721127158993072298490322182653518774585778107201775886232669989219843001_<81>

P102 = 475002306456793448468446173700751795865776779342906923374169016985392423513854627200194137571758416857_<102>

Number: 66667_198
N=61460218173376274139436257924925696309875419738351789195735595207504741324042282642242875514121009483559905778993186545329492535174833115309207892574829946390934849157827781851867857
  ( 182 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=129389304721127158993072298490322182653518774585778107201775886232669989219843001
 r2=475002306456793448468446173700751795865776779342906923374169016985392423513854627200194137571758416857
Version: 
Total time: 278.57 hours.
Scaled time: 663.27 units (timescale=2.381).
Factorization parameters were as follows:
n: 61460218173376274139436257924925696309875419738351789195735595207504741324042282642242875514121009483559905778993186545329492535174833115309207892574829946390934849157827781851867857
m: 10000000000000000000000000000000000000000
deg: 5
c5: 1
c0: 50
skew: 2.19
type: snfs
lss: 1
rlim: 15000000
alim: 15000000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 15000000/15000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7500000, 13600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 37116511
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2764086 x 2764334
Total sieving time: 244.16 hours.
Total relation processing time: 12.36 hours.
Matrix solve time: 20.63 hours.
Time per square root: 1.42 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15000000,15000000,29,29,56,56,2.6,2.6,100000
total time: 278.57 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673795)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672307)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

Dec 16, 2009 (6th)

By Robert Backstrom / GMP-ECM, Msieve / Dec 16, 2009

(23·10¹¹⁷-17)/3 = 7(6)₁₁₆1_<118> = 83 · 1172292529_<10> · 2618649367751318479_<19> · C89

C89 = P34 · P56

P34 = 1118338087153059584933843463282641_<34>

P56 = 26905559319248589651357853745624920225257541945854546857_<56>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 30089511742871643769964632131175135743122042073471668918174706140412512932354920769209337 (89 digits)
Using B1=922000, B2=871204962, polynomial Dickson(3), sigma=3498851850
Step 1 took 5719ms
Step 2 took 2687ms
********** Factor found in step 2: 1118338087153059584933843463282641
Found probable prime factor of 34 digits: 1118338087153059584933843463282641
Probable prime cofactor 26905559319248589651357853745624920225257541945854546857 has 56 digits

(23·10¹¹¹-11)/3 = 7(6)₁₁₀3_<112> = 29 · 102328133850591764833_<21> · C91

C91 = P42 · P50

P42 = 114020995310251665818999261240617858936247_<42>

P50 = 22658371947974329014450969228515292119437447560997_<50>

Wed Dec 16 18:42:30 2009  
Wed Dec 16 18:42:30 2009  
Wed Dec 16 18:42:30 2009  Msieve v. 1.43
Wed Dec 16 18:42:30 2009  random seeds: b9219cc0 d0de1132
Wed Dec 16 18:42:30 2009  factoring 2583530121617918870290587730447033099093456835689377352764840295500870921278374451066758259 (91 digits)
Wed Dec 16 18:42:30 2009  searching for 15-digit factors
Wed Dec 16 18:42:31 2009  commencing quadratic sieve (91-digit input)
Wed Dec 16 18:42:31 2009  using multiplier of 59
Wed Dec 16 18:42:31 2009  using 64kb Opteron sieve core
Wed Dec 16 18:42:31 2009  sieve interval: 18 blocks of size 65536
Wed Dec 16 18:42:31 2009  processing polynomials in batches of 6
Wed Dec 16 18:42:31 2009  using a sieve bound of 1678553 (63529 primes)
Wed Dec 16 18:42:31 2009  using large prime bound of 154426876 (27 bits)
Wed Dec 16 18:42:31 2009  using double large prime bound of 549162818684260 (42-49 bits)
Wed Dec 16 18:42:31 2009  using trial factoring cutoff of 49 bits
Wed Dec 16 18:42:31 2009  polynomial 'A' values have 12 factors
Wed Dec 16 19:47:58 2009  64234 relations (17173 full + 47061 combined from 718510 partial), need 63625
Wed Dec 16 19:47:59 2009  begin with 735683 relations
Wed Dec 16 19:47:59 2009  reduce to 156774 relations in 9 passes
Wed Dec 16 19:47:59 2009  attempting to read 156774 relations
Wed Dec 16 19:48:00 2009  recovered 156774 relations
Wed Dec 16 19:48:00 2009  recovered 135082 polynomials
Wed Dec 16 19:48:00 2009  attempting to build 64234 cycles
Wed Dec 16 19:48:00 2009  found 64234 cycles in 5 passes
Wed Dec 16 19:48:01 2009  distribution of cycle lengths:
Wed Dec 16 19:48:01 2009     length 1 : 17173
Wed Dec 16 19:48:01 2009     length 2 : 12267
Wed Dec 16 19:48:01 2009     length 3 : 11466
Wed Dec 16 19:48:01 2009     length 4 : 8568
Wed Dec 16 19:48:01 2009     length 5 : 5959
Wed Dec 16 19:48:01 2009     length 6 : 3853
Wed Dec 16 19:48:01 2009     length 7 : 2264
Wed Dec 16 19:48:01 2009     length 9+: 2684
Wed Dec 16 19:48:01 2009  largest cycle: 18 relations
Wed Dec 16 19:48:01 2009  matrix is 63529 x 64234 (15.4 MB) with weight 3780171 (58.85/col)
Wed Dec 16 19:48:01 2009  sparse part has weight 3780171 (58.85/col)
Wed Dec 16 19:48:02 2009  filtering completed in 3 passes
Wed Dec 16 19:48:02 2009  matrix is 59295 x 59359 (14.2 MB) with weight 3484662 (58.70/col)
Wed Dec 16 19:48:02 2009  sparse part has weight 3484662 (58.70/col)
Wed Dec 16 19:48:02 2009  saving the first 48 matrix rows for later
Wed Dec 16 19:48:02 2009  matrix is 59247 x 59359 (8.2 MB) with weight 2616342 (44.08/col)
Wed Dec 16 19:48:02 2009  sparse part has weight 1796079 (30.26/col)
Wed Dec 16 19:48:02 2009  matrix includes 64 packed rows
Wed Dec 16 19:48:02 2009  using block size 23743 for processor cache size 1024 kB
Wed Dec 16 19:48:02 2009  commencing Lanczos iteration
Wed Dec 16 19:48:02 2009  memory use: 8.9 MB
Wed Dec 16 19:48:20 2009  lanczos halted after 939 iterations (dim = 59244)
Wed Dec 16 19:48:20 2009  recovered 16 nontrivial dependencies
Wed Dec 16 19:48:21 2009  prp42 factor: 114020995310251665818999261240617858936247
Wed Dec 16 19:48:21 2009  prp50 factor: 22658371947974329014450969228515292119437447560997
Wed Dec 16 19:48:21 2009  elapsed time 01:05:51

Dec 16, 2009 (5th)

By Serge Batalov / Msieve, GMP-ECM / Dec 16, 2009

(68·10¹³⁵-23)/9 = 7(5)₁₃₄3_<136> = 7 · 13 · 29 · 673 · 1231 · 39201067 · 19451678419_<11> · 3508444016179_<13> · C97

C97 = P44 · P53

P44 = 49354536817403980992556188494349510678134521_<44>

P53 = 26173228415604033307918617128471408780767311182184547_<53>

Divisors found:
 r1=49354536817403980992556188494349510678134521 (pp44)
 r2=26173228415604033307918617128471408780767311182184547 (pp53)
Version: Msieve v. 1.44 SVN157
Total time: 1.38 hours.
Scaled time: 3.31 units (timescale=2.400).
Factorization parameters were as follows:
name: test
type: gnfs
n:  1291767565468253325983099240866543604203429986670042714470360827476299445498122120010631513446987
skew:  1028695.48
Y0:  -173066555608276491936265
Y1:   6118599925867
c0:  -178362389484675470839201668
c1:  -1431652149419258675948
c2:  -1867644117274291
c3:  -2880742358
c4:   1440
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [937500, 1217501)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 151064 x 151296
Total sieving time: 1.28 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
gnfs,96,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,25,25,46,46,2.5,2.5,70000
total time: 1.38 hours.

(23·10¹³²-17)/3 = 7(6)₁₃₁1_<133> = 97 · 109 · 5616540927610014119_<19> · C111

C111 = P28 · P83

P28 = 6765672016507302473411933737_<28>

P83 = 19082201642817897816379464000476263038247593631835682844121143546670724325874838919_<83>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=4049908066
Step 1 took 4545ms
Step 2 took 2884ms
********** Factor found in step 2: 6765672016507302473411933737
Found probable prime factor of 28 digits: 6765672016507302473411933737
Probable prime cofactor has 83 digits

(23·10¹⁴⁵-17)/3 = 7(6)₁₄₄1_<146> = 43 · 1398251 · C139

C139 = P34 · C106

P34 = 1256710869813684340075674424685443_<34>

C106 = [1014653167874607433393138777593797766888773887153826194843762435948768275207619865105895761692478221477039_<106>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=31174486
Step 1 took 6084ms
Step 2 took 3536ms
********** Factor found in step 2: 1256710869813684340075674424685443
Found probable prime factor of 34 digits: 1256710869813684340075674424685443
Composite cofactor has 106 digits

(23·10¹⁰⁹-11)/3 = 7(6)₁₀₈3_<110> = 31 · 2160293 · C103

C103 = P39 · P64

P39 = 395005637395866571582641984926624812093_<39>

P64 = 2898203891676581815541170847707467709328545235576051915248772777_<64>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=3105122533
Step 1 took 4672ms
Step 2 took 2761ms
********** Factor found in step 2: 395005637395866571582641984926624812093
Found probable prime factor of 39 digits: 395005637395866571582641984926624812093
Probable prime cofactor has 64 digits

(23·10¹⁰⁸-11)/3 = 7(6)₁₀₇3_<109> = 4129 · 48239 · C101

C101 = P31 · P71

P31 = 3490683832872464247555442771201_<31>

P71 = 11026886073725625310081747759869262788979540725428702635385850485874473_<71>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=1966405737
Step 1 took 4600ms
Step 2 took 2760ms
********** Factor found in step 2: 3490683832872464247555442771201
Found probable prime factor of 31 digits: 3490683832872464247555442771201
Probable prime cofactor has 71 digits

(23·10¹²²-17)/3 = 7(6)₁₂₁1_<123> = 783504322140893_<15> · C108

C108 = P30 · P79

P30 = 741688256826905058083748714823_<30>

P79 = 1319300666580334226218159946688540099971933859484532199655146475100465378632399_<79>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=3326129902
Step 1 took 4316ms
Step 2 took 2776ms
********** Factor found in step 2: 741688256826905058083748714823
Found probable prime factor of 30 digits: 741688256826905058083748714823
Probable prime cofactor has 79 digits

(23·10¹⁴⁹-17)/3 = 7(6)₁₄₈1_<150> = 7 · 2170830172909759_<16> · 2025999339574266401_<19> · C116

C116 = P30 · P35 · P52

P30 = 282319935301119438794660871407_<30>

P35 = 38746341941048510460017005102921493_<35>

P52 = 2276518268891766986132754409859082639389235326181847_<52>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=2296079492
Step 1 took 5028ms
Step 2 took 2753ms
********** Factor found in step 2: 38746341941048510460017005102921493
Found probable prime factor of 35 digits: 38746341941048510460017005102921493

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=1494950385
Step 1 took 4837ms
Step 2 took 2800ms
********** Factor found in step 2: 282319935301119438794660871407
Found probable prime factor of 30 digits: 282319935301119438794660871407

(23·10¹⁰⁹-17)/3 = 7(6)₁₀₈1_<110> = 4423 · C107

C107 = P41 · P67

P41 = 15657590962371840382069424283498865142543_<41>

P67 = 1107043531122213731069211459476835017897299236455125765923081029149_<67>

SNFS difficulty: 110 digits.
Divisors found:
 r1=15657590962371840382069424283498865142543 (pp41)
 r2=1107043531122213731069211459476835017897299236455125765923081029149 (pp67)
Version: Msieve v. 1.44 SVN157
Total time: 0.63 hours.
Scaled time: 1.52 units (timescale=2.400).
Factorization parameters were as follows:
n: 17333634787851382922601552490767955384731328660788303564699675936393096691536664405757781294747155022985907
m: 1000000000000000000000
deg: 5
c5: 230000
c0: -17
skew: 0.15
type: snfs
lss: 1
rlim: 480000
alim: 480000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 480000/480000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [300000, 550001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 53200 x 53427
Total sieving time: 0.61 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,110.000,5,0,0,0,0,0,0,0,0,480000,480000,25,25,44,44,2.2,2.2,50000
total time: 0.63 hours.

(23·10¹⁰¹-11)/3 = 7(6)₁₀₀3_<102> = 1187 · 144616811 · C91

C91 = P39 · P53

P39 = 117490606566065595674608813209924208099_<39>

P53 = 38013156698927423089936634558266123507013784775835341_<53>

SNFS difficulty: 102 digits.
Divisors found:
 r1=117490606566065595674608813209924208099 (pp39)
 r2=38013156698927423089936634558266123507013784775835341 (pp53)
Version: Msieve v. 1.44 SVN157
Total time: 0.25 hours.
Scaled time: 0.59 units (timescale=2.400).
Factorization parameters were as follows:
n: 4466188838047882679105645836099257794848851734404077705552959099165042916804289190642626759
m: 10000000000000000000000000
deg: 4
c4: 230
c0: -11
skew: 0.47
type: snfs
lss: 1
rlim: 360000
alim: 360000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [225000, 305001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 31084 x 31313
Total sieving time: 0.23 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,102.000,4,0,0,0,0,0,0,0,0,360000,360000,25,25,43,43,2.2,2.2,10000
total time: 0.25 hours.

Dec 16, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve / Dec 16, 2009

(68·10¹³⁹-41)/9 = 7(5)₁₃₈1_<140> = 599 · 821 · 10853 · C131

C131 = P50 · P81

P50 = 26314862340375890781828977363194955018961042928123_<50>

P81 = 537954467230265270119267925540183493428275358501670203932591652282443058644303651_<81>

N=14156197750554683790147026237153098492357917675483143856926387225621787416644308258645266789658964485380813320181708505491379477073
  ( 131 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=26314862340375890781828977363194955018961042928123 (pp50)
 r2=537954467230265270119267925540183493428275358501670203932591652282443058644303651 (pp81)
Version: Msieve-1.40
Total time: 6.06 hours.
Scaled time: 11.27 units (timescale=1.860).
Factorization parameters were as follows:
n: 14156197750554683790147026237153098492357917675483143856926387225621787416644308258645266789658964485380813320181708505491379477073
m: 2000000000000000000000000000
deg: 5
c5: 21250
c0: -41
skew: 0.29
type: snfs
lss: 1
rlim: 1560000
alim: 1560000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1560000/1560000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [780000, 1980001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 255672 x 255897
Total sieving time: 5.92 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,140.000,5,0,0,0,0,0,0,0,0,1560000,1560000,26,26,48,48,2.3,2.3,100000
total time: 6.06 hours.
 --------- CPU info (if available) ----------

(68·10¹³⁵-41)/9 = 7(5)₁₃₄1_<136> = 3 · 367859203 · C127

C127 = P49 · P79

P49 = 1708072995693845187847890294158793372992730136343_<49>

P79 = 4008271182346875021369471912260587784241104960646929039911381637642429568831473_<79>

N=6846419765984537618101995720679356004907449654096375885744847108034751324458555189438929215856857381704593424344798894479523239
  ( 127 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=1708072995693845187847890294158793372992730136343 (pp49)
 r2=4008271182346875021369471912260587784241104960646929039911381637642429568831473 (pp79)
Version: Msieve-1.40
Total time: 4.22 hours.
Scaled time: 8.04 units (timescale=1.905).
Factorization parameters were as follows:
n: 6846419765984537618101995720679356004907449654096375885744847108034751324458555189438929215856857381704593424344798894479523239
m: 1000000000000000000000000000
deg: 5
c5: 68
c0: -41
skew: 0.90
type: snfs
lss: 1
rlim: 1340000
alim: 1340000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1340000/1340000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [670000, 1495001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 168089 x 168314
Total sieving time: 4.10 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1340000,1340000,26,26,48,48,2.3,2.3,75000
total time: 4.22 hours.
 --------- CPU info (if available) ----------

(68·10¹³⁸-41)/9 = 7(5)₁₃₇1_<139> = 3² · 103969 · 4437413462063_<13> · C121

C121 = P41 · P81

P41 = 11410900863836166592220488321239541570811_<41>

P81 = 159466770155403882014625840449690972139449148893901469976263858019351462850409067_<81>

N=1819659505319461587167496116262275636870772186566922955290666967512874577913658754479211365347032761992684206423096943337
  ( 121 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=11410900863836166592220488321239541570811 (pp41)
 r2=159466770155403882014625840449690972139449148893901469976263858019351462850409067 (pp81)
Version: Msieve-1.40
Total time: 5.40 hours.
Scaled time: 10.19 units (timescale=1.888).
Factorization parameters were as follows:
n: 1819659505319461587167496116262275636870772186566922955290666967512874577913658754479211365347032761992684206423096943337
m: 2000000000000000000000000000
deg: 5
c5: 2125
c0: -41
skew: 0.45
type: snfs
lss: 1
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [750000, 1800001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 214144 x 214369
Total sieving time: 5.26 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,139.000,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,48,48,2.3,2.3,75000
total time: 5.40 hours.
 --------- CPU info (if available) ----------

Dec 16, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 16, 2009

(53·10¹⁹⁹-17)/9 = 5(8)₁₉₈7_<200> = 3 · 19 · 29 · 2087 · C194

C194 = P32 · P36 · P37 · P90

P32 = 17033129343042131723119795399783_<32>

P36 = 179440627551006617308087186383630077_<36>

P37 = 6418601372244116209995402203201277923_<37>

P90 = 870126567592585573632839389930035462775978166234114786224389433355392972174658899238979469_<90>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3769953513
Step 1 took 25038ms
Step 2 took 9558ms
********** Factor found in step 2: 17033129343042131723119795399783
Found probable prime factor of 32 digits: 17033129343042131723119795399783
Composite cofactor 1002175111884014052862920762883581298496554004464709613050251304739359685726211840475054410063345510265115970720689986952986565831641247191170176592569731656952299 has 163 digits
---------------------------
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4056795063
Step 1 took 17322ms
Step 2 took 7340ms
********** Factor found in step 2: 6418601372244116209995402203201277923
Found probable prime factor of 37 digits: 6418601372244116209995402203201277923
Composite cofactor 156136057337616932522918625137023487892475982796937651766950011790633232673692347250804848273683749803164350079769169093889113 has 126 digits
---------------------------
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4016537737
Step 1 took 11682ms
Step 2 took 5633ms
********** Factor found in step 2: 179440627551006617308087186383630077
Found probable prime factor of 36 digits: 179440627551006617308087186383630077
Probable prime cofactor 870126567592585573632839389930035462775978166234114786224389433355392972174658899238979469 has 90 digits

Dec 16, 2009 (2nd)

By juno1369 / GMP-ECM + Msieve v1.43 / Dec 16, 2009

(68·10¹⁴¹+31)/9 = 7(5)₁₄₀9_<142> = 624851 · 1592881 · 73898372251340891_<17> · C114

C114 = P38 · P76

P38 = 12691592973270826647859080507280059533_<38>

P76 = 8093858248747963723614320594420759566733031650636803553239263136703583574963_<76>

Number: 75559_141
N=102723954476459774940437404231851091242454241248712021855259577828447262557110513731009155996686407321671608272279
  ( 114 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=12691592973270826647859080507280059533 (pp38)
 r2=8093858248747963723614320594420759566733031650636803553239263136703583574963 (pp76)
Version: Msieve v. 1.43
Total time: 24.33 hours.
Scaled time: 39.86 units (timescale=1.638).
Factorization parameters were as follows:
n: 102723954476459774940437404231851091242454241248712021855259577828447262557110513731009155996686407321671608272279
m: 10000000000000000000000000000
deg: 5
c5: 680
c0: 31
skew: 0.54
type: snfs
lss: 1
rlim: 1680000
alim: 1680000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
qintsize: 5
Factor base limits: 1680000/1680000
Large primes per side: 2
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [840000, 1640001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 253831 x 254056
Total sieving time: 23.80 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,142.000,5,0,0,0,0,0,0,0,0,1680000,1680000,26,26,48,48,2.3,2.3,100000
total time: 24.33 hours.
 --------- CPU info (if available) ----------

Dec 16, 2009

Factorizations of 766...661 and Factorizations of 766...663 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Dec 15, 2009 (5th)

By Dmitry Domanov / GGNFS/msieve, YAFU v1.14 / Dec 15, 2009

(68·10¹⁰²-23)/9 = 7(5)₁₀₁3_<103> = 251 · C101

C101 = P42 · P59

P42 = 475408704971357587178647157962547319178567_<42>

P59 = 63317761428424632567026630310285880151845690096680698073109_<59>

N=30101814962372731297034085878707392651615759185480301018149623727312970340858787073926516157591854803
  ( 101 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=475408704971357587178647157962547319178567 (pp42)
 r2=63317761428424632567026630310285880151845690096680698073109 (pp59)
Version: Msieve-1.40
Total time: 0.42 hours.
Scaled time: 0.79 units (timescale=1.911).
Factorization parameters were as follows:
n: 30101814962372731297034085878707392651615759185480301018149623727312970340858787073926516157591854803
m: 20000000000000000000000000
deg: 4
c4: 425
c0: -23
skew: 0.48
type: snfs
lss: 1
rlim: 380000
alim: 380000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2Factor base limits: 380000/380000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [190000, 280001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 34910 x 35140
Total sieving time: 0.40 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103.000,4,0,0,0,0,0,0,0,0,380000,380000,25,25,43,43,2.2,2.2,10000
total time: 0.42 hours.
 --------- CPU info (if available) ----------

(68·10¹⁰⁶+31)/9 = 7(5)₁₀₅9_<107> = 11 · 191 · C104

C104 = P28 · P77

P28 = 1246448664957339799134281813_<28>

P77 = 28851337696777360109702926354001502481219789662031045816855532298591111394943_<77>

N=35961711354381511449574276799407689460045480987889364852715638055952192077846528108308213020254905071659
  ( 104 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=1246448664957339799134281813 (pp28)
 r2=28851337696777360109702926354001502481219789662031045816855532298591111394943 (pp77)
Version: Msieve-1.40
Total time: 0.40 hours.
Scaled time: 0.74 units (timescale=1.834).
Factorization parameters were as follows:
n: 35961711354381511449574276799407689460045480987889364852715638055952192077846528108308213020254905071659
m: 1000000000000000000000
deg: 5
c5: 680
c0: 31
skew: 0.54
type: snfs
lss: 1
rlim: 440000
alim: 440000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2Factor base limits: 440000/440000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [220000, 320001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 38652 x 38877
Total sieving time: 0.39 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107.000,5,0,0,0,0,0,0,0,0,440000,440000,25,25,44,44,2.2,2.2,50000
total time: 0.40 hours.
 --------- CPU info (if available) ----------

(68·10¹⁰⁸+31)/9 = 7(5)₁₀₇9_<109> = 11 · 29 · 5297 · C103

C103 = P48 · P56

P48 = 150578119693288207836470725802931710300783336777_<48>

P56 = 29695037467385152935692049177562015039149743749687411169_<56>

N=4471422906060599484984139928708422260400283093674929001366216966459133463228168754393748372122598262313
  ( 103 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=150578119693288207836470725802931710300783336777 (pp48)
 r2=29695037467385152935692049177562015039149743749687411169 (pp56)
Version: Msieve-1.40
Total time: 0.64 hours.
Scaled time: 1.26 units (timescale=1.963).
Factorization parameters were as follows:
n: 4471422906060599484984139928708422260400283093674929001366216966459133463228168754393748372122598262313
m: 2000000000000000000000
deg: 5
c5: 2125
c0: 31
skew: 0.43
type: snfs
lss: 1
rlim: 470000
alim: 470000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2Factor base limits: 470000/470000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [235000, 385001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 44728 x 44959
Total sieving time: 0.62 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,109.000,5,0,0,0,0,0,0,0,0,470000,470000,25,25,44,44,2.2,2.2,50000
total time: 0.64 hours.
 --------- CPU info (if available) ----------

(68·10¹¹⁸-23)/9 = 7(5)₁₁₇3_<119> = 19 · 31 · 19207 · C112

C112 = P30 · P83

P30 = 127468924906638624877222907711_<30>

P83 = 52394686868873641010380131832209559693086903605068551738708211241825910072617577101_<83>

N=6678694405995298965223714114871599104453867100090361753152174336867276083780960548883392519824943169466949925811
  ( 112 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=127468924906638624877222907711 (pp30)
 r2=52394686868873641010380131832209559693086903605068551738708211241825910072617577101 (pp83)
Version: Msieve-1.40
Total time: 1.10 hours.
Scaled time: 2.17 units (timescale=1.969).
Factorization parameters were as follows:
n: 6678694405995298965223714114871599104453867100090361753152174336867276083780960548883392519824943169466949925811
m: 200000000000000000000000
deg: 5
c5: 2125
c0: -23
skew: 0.40
type: snfs
lss: 1
rlim: 700000
alim: 700000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [350000, 600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 78114 x 78339
Total sieving time: 1.06 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,119.000,5,0,0,0,0,0,0,0,0,700000,700000,25,25,45,45,2.2,2.2,50000
total time: 1.10 hours.
 --------- CPU info (if available) ----------

(68·10¹²⁷-23)/9 = 7(5)₁₂₆3_<128> = 11047 · 442948658389_<12> · C113

C113 = P46 · P67

P46 = 2930179327475689888309979195558841620446520287_<46>

P67 = 5269561271030268835690782346468544997247579366619279931709924249093_<67>

N=15440759501239414746052470786880310377793924823079230995536396814451703822625126232937210152415871427113265849691
  ( 113 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=2930179327475689888309979195558841620446520287 (pp46)
 r2=5269561271030268835690782346468544997247579366619279931709924249093 (pp67)
Version: Msieve-1.40
Total time: 2.86 hours.
Scaled time: 2.67 units (timescale=0.932).
Factorization parameters were as follows:
n: 15440759501239414746052470786880310377793924823079230995536396814451703822625126232937210152415871427113265849691
m: 10000000000000000000000000
deg: 5
c5: 6800
c0: -23
skew: 0.32
type: snfs
lss: 1
rlim: 980000
alim: 980000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 980000/980000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [490000, 890001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 139843 x 140068
Total sieving time: 2.70 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,128.000,5,0,0,0,0,0,0,0,0,980000,980000,26,26,47,47,2.3,2.3,50000
total time: 2.86 hours.
 --------- CPU info (if available) ----------

(68·10¹³⁴-23)/9 = 7(5)₁₃₃3_<135> = 3² · 39906263 · 116212627 · 12319813631_<11> · 121288423449913428549107_<24> · C86

C86 = P35 · P51

P35 = 15879193363065865107998274559766137_<35>

P51 = 762917520428606904550569900796832771668642509188273_<51>

12/14/09 21:48:57 v1.14 @ REPGMAIL, starting SIQS on c86: 12114514826956601318952190098073537821701752211837444802265577948466686443108582911401
12/14/09 21:48:57 v1.14 @ REPGMAIL, random seeds: 0, 3887612160
12/14/09 21:48:57 v1.14 @ REPGMAIL, ==== sieve params ====
12/14/09 21:48:57 v1.14 @ REPGMAIL, n = 86 digits, 283 bits
12/14/09 21:48:57 v1.14 @ REPGMAIL, factor base: 56327 primes (max prime = 1476803)
12/14/09 21:48:57 v1.14 @ REPGMAIL, single large prime cutoff: 162448330 (110 * pmax)
12/14/09 21:48:57 v1.14 @ REPGMAIL, double large prime range from 42 to 50 bits
12/14/09 21:48:57 v1.14 @ REPGMAIL, double large prime cutoff: 601571775592514
12/14/09 21:48:57 v1.14 @ REPGMAIL, allocating 12 large prime slices of factor base
12/14/09 21:48:57 v1.14 @ REPGMAIL, buckets hold 1024 elements
12/14/09 21:48:57 v1.14 @ REPGMAIL, sieve interval: 18 blocks of size 32768
12/14/09 21:48:57 v1.14 @ REPGMAIL, polynomial A has ~ 11 factors
12/14/09 21:48:57 v1.14 @ REPGMAIL, using multiplier of 1
12/14/09 21:48:57 v1.14 @ REPGMAIL, using small prime variation correction of 19 bits
12/14/09 21:48:57 v1.14 @ REPGMAIL, using SSE2 for trial division and x128 sieve scanning
12/14/09 21:48:57 v1.14 @ REPGMAIL, trial factoring cutoff at 94 bits
12/14/09 21:48:57 v1.14 @ REPGMAIL, ==== sieving started ( 8 threads) ====
12/14/09 21:55:25 v1.14 @ REPGMAIL, trial division touched 10682534 sieve locations out of 4744629190656
12/14/09 21:55:25 v1.14 @ REPGMAIL, 56750 relations found: 19827 full + 36923 from 490861 partial, using 4022072 polys (367 A polys)
12/14/09 21:55:25 v1.14 @ REPGMAIL, on average, sieving found 0.13 rels/poly and 1315.91 rels/sec
12/14/09 21:55:25 v1.14 @ REPGMAIL, trial division touched 10682534 sieve locations out of 4744629190656
12/14/09 21:55:25 v1.14 @ REPGMAIL, ==== post processing stage (msieve-1.38) ====
12/14/09 21:55:26 v1.14 @ REPGMAIL, begin with 510688 relations
12/14/09 21:55:26 v1.14 @ REPGMAIL, reduce to 112219 relations in 9 passes
12/14/09 21:55:33 v1.14 @ REPGMAIL, recovered 112219 relations
12/14/09 21:55:33 v1.14 @ REPGMAIL, recovered 82618 polynomials
12/14/09 21:55:36 v1.14 @ REPGMAIL, attempting to build 56750 cycles
12/14/09 21:55:36 v1.14 @ REPGMAIL, found 56750 cycles in 4 passes
12/14/09 21:55:36 v1.14 @ REPGMAIL, distribution of cycle lengths:
12/14/09 21:55:36 v1.14 @ REPGMAIL,    length 1 : 19827
12/14/09 21:55:36 v1.14 @ REPGMAIL,    length 2 : 16452
12/14/09 21:55:36 v1.14 @ REPGMAIL,    length 3 : 10389
12/14/09 21:55:36 v1.14 @ REPGMAIL,    length 4 : 5444
12/14/09 21:55:36 v1.14 @ REPGMAIL,    length 5 : 2627
12/14/09 21:55:36 v1.14 @ REPGMAIL,    length 6 : 1196
12/14/09 21:55:36 v1.14 @ REPGMAIL,    length 7 : 484
12/14/09 21:55:36 v1.14 @ REPGMAIL,    length 9+: 331
12/14/09 21:55:36 v1.14 @ REPGMAIL, largest cycle: 13 relations
12/14/09 21:55:36 v1.14 @ REPGMAIL, matrix is 56327 x 56750 (10.6 MB) with weight 2564365 (45.19/col)
12/14/09 21:55:36 v1.14 @ REPGMAIL, sparse part has weight 2564365 (45.19/col)
12/14/09 21:55:36 v1.14 @ REPGMAIL, filtering completed in 3 passes
12/14/09 21:55:36 v1.14 @ REPGMAIL, matrix is 48272 x 48334 (9.3 MB) with weight 2235142 (46.24/col)
12/14/09 21:55:36 v1.14 @ REPGMAIL, sparse part has weight 2235142 (46.24/col)
12/14/09 21:55:36 v1.14 @ REPGMAIL, saving the first 48 matrix rows for later
12/14/09 21:55:46 v1.14 @ REPGMAIL, matrix is 48224 x 48334 (7.6 MB) with weight 1897902 (39.27/col)
12/14/09 21:55:46 v1.14 @ REPGMAIL, sparse part has weight 1696057 (35.09/col)
12/14/09 21:55:46 v1.14 @ REPGMAIL, matrix includes 64 packed rows
12/14/09 21:55:46 v1.14 @ REPGMAIL, using block size 19333 for processor cache size 6144 kB
12/14/09 21:55:47 v1.14 @ REPGMAIL, commencing Lanczos iteration
12/14/09 21:55:47 v1.14 @ REPGMAIL, memory use: 7.0 MB
12/14/09 21:55:59 v1.14 @ REPGMAIL, lanczos halted after 764 iterations (dim = 48220)
12/14/09 21:55:59 v1.14 @ REPGMAIL, recovered 15 nontrivial dependencies
12/14/09 21:56:00 v1.14 @ REPGMAIL, prp35 = 15879193363065865107998274559766137
12/14/09 21:56:02 v1.14 @ REPGMAIL, prp51 = 762917520428606904550569900796832771668642509188273
12/14/09 21:56:02 v1.14 @ REPGMAIL, Lanczos elapsed time = 33.8740 seconds.
12/14/09 21:56:02 v1.14 @ REPGMAIL, Sqrt elapsed time = 3.1880 seconds.
12/14/09 21:56:02 v1.14 @ REPGMAIL, SIQS elapsed time = 425.1639 seconds.

(68·10¹³⁰+31)/9 = 7(5)₁₂₉9_<131> = 11 · 56131 · 8228147 · 1229854799_<10> · 1169247389592624844202971_<25> · C86

C86 = P34 · P52

P34 = 6328328267930458654843816832915939_<34>

P52 = 1634254345465820314671612324574857719012196626173507_<52>

12/14/09 21:58:42 v1.14 @ REPGMAIL, starting SIQS on c86: 10342097971399540079633988595037935069400821487904349185261500024432707324650559828073
12/14/09 21:58:42 v1.14 @ REPGMAIL, random seeds: 0, 3887612160
12/14/09 21:58:43 v1.14 @ REPGMAIL, ==== sieve params ====
12/14/09 21:58:43 v1.14 @ REPGMAIL, n = 86 digits, 284 bits
12/14/09 21:58:43 v1.14 @ REPGMAIL, factor base: 56327 primes (max prime = 1475729)
12/14/09 21:58:43 v1.14 @ REPGMAIL, single large prime cutoff: 162330190 (110 * pmax)
12/14/09 21:58:43 v1.14 @ REPGMAIL, double large prime range from 42 to 50 bits
12/14/09 21:58:43 v1.14 @ REPGMAIL, double large prime cutoff: 600784520801526
12/14/09 21:58:43 v1.14 @ REPGMAIL, allocating 12 large prime slices of factor base
12/14/09 21:58:43 v1.14 @ REPGMAIL, buckets hold 1024 elements
12/14/09 21:58:43 v1.14 @ REPGMAIL, sieve interval: 18 blocks of size 32768
12/14/09 21:58:43 v1.14 @ REPGMAIL, polynomial A has ~ 11 factors
12/14/09 21:58:43 v1.14 @ REPGMAIL, using multiplier of 2
12/14/09 21:58:43 v1.14 @ REPGMAIL, using small prime variation correction of 21 bits
12/14/09 21:58:43 v1.14 @ REPGMAIL, using SSE2 for trial division and x128 sieve scanning
12/14/09 21:58:43 v1.14 @ REPGMAIL, trial factoring cutoff at 92 bits
12/14/09 21:58:43 v1.14 @ REPGMAIL, ==== sieving started ( 8 threads) ====
12/14/09 22:05:23 v1.14 @ REPGMAIL, trial division touched 13815966 sieve locations out of 3668761903104
12/14/09 22:05:23 v1.14 @ REPGMAIL, 58137 relations found: 19063 full + 39074 from 549464 partial, using 3110048 polys (311 A polys)
12/14/09 22:05:23 v1.14 @ REPGMAIL, on average, sieving found 0.18 rels/poly and 1418.23 rels/sec
12/14/09 22:05:23 v1.14 @ REPGMAIL, trial division touched 13815966 sieve locations out of 3668761903104
12/14/09 22:05:23 v1.14 @ REPGMAIL, ==== post processing stage (msieve-1.38) ====
12/14/09 22:05:24 v1.14 @ REPGMAIL, begin with 568527 relations
12/14/09 22:05:24 v1.14 @ REPGMAIL, reduce to 121540 relations in 9 passes
12/14/09 22:05:27 v1.14 @ REPGMAIL, recovered 121540 relations
12/14/09 22:05:27 v1.14 @ REPGMAIL, recovered 84249 polynomials
12/14/09 22:05:28 v1.14 @ REPGMAIL, attempting to build 58137 cycles
12/14/09 22:05:28 v1.14 @ REPGMAIL, found 58137 cycles in 4 passes
12/14/09 22:05:28 v1.14 @ REPGMAIL, distribution of cycle lengths:
12/14/09 22:05:28 v1.14 @ REPGMAIL,    length 1 : 19063
12/14/09 22:05:28 v1.14 @ REPGMAIL,    length 2 : 15070
12/14/09 22:05:28 v1.14 @ REPGMAIL,    length 3 : 10885
12/14/09 22:05:28 v1.14 @ REPGMAIL,    length 4 : 6333
12/14/09 22:05:28 v1.14 @ REPGMAIL,    length 5 : 3437
12/14/09 22:05:28 v1.14 @ REPGMAIL,    length 6 : 1799
12/14/09 22:05:28 v1.14 @ REPGMAIL,    length 7 : 862
12/14/09 22:05:28 v1.14 @ REPGMAIL,    length 9+: 688
12/14/09 22:05:28 v1.14 @ REPGMAIL, largest cycle: 16 relations
12/14/09 22:05:28 v1.14 @ REPGMAIL, matrix is 56327 x 58137 (11.8 MB) with weight 2860361 (49.20/col)
12/14/09 22:05:28 v1.14 @ REPGMAIL, sparse part has weight 2860361 (49.20/col)
12/14/09 22:05:28 v1.14 @ REPGMAIL, filtering completed in 4 passes
12/14/09 22:05:28 v1.14 @ REPGMAIL, matrix is 48817 x 48881 (9.8 MB) with weight 2374448 (48.58/col)
12/14/09 22:05:28 v1.14 @ REPGMAIL, sparse part has weight 2374448 (48.58/col)
12/14/09 22:05:28 v1.14 @ REPGMAIL, saving the first 48 matrix rows for later
12/14/09 22:05:28 v1.14 @ REPGMAIL, matrix is 48769 x 48881 (7.9 MB) with weight 1988288 (40.68/col)
12/14/09 22:05:28 v1.14 @ REPGMAIL, sparse part has weight 1773744 (36.29/col)
12/14/09 22:05:28 v1.14 @ REPGMAIL, matrix includes 64 packed rows
12/14/09 22:05:28 v1.14 @ REPGMAIL, using block size 19552 for processor cache size 6144 kB
12/14/09 22:05:29 v1.14 @ REPGMAIL, commencing Lanczos iteration
12/14/09 22:05:29 v1.14 @ REPGMAIL, memory use: 7.2 MB
12/14/09 22:05:42 v1.14 @ REPGMAIL, lanczos halted after 773 iterations (dim = 48763)
12/14/09 22:05:42 v1.14 @ REPGMAIL, recovered 14 nontrivial dependencies
12/14/09 22:05:43 v1.14 @ REPGMAIL, prp52 = 1634254345465820314671612324574857719012196626173507
12/14/09 22:05:44 v1.14 @ REPGMAIL, prp34 = 6328328267930458654843816832915939
12/14/09 22:05:44 v1.14 @ REPGMAIL, Lanczos elapsed time = 18.6090 seconds.
12/14/09 22:05:44 v1.14 @ REPGMAIL, Sqrt elapsed time = 2.5000 seconds.
12/14/09 22:05:44 v1.14 @ REPGMAIL, SIQS elapsed time = 421.9790 seconds.

(68·10¹¹⁹-23)/9 = 7(5)₁₁₈3_<120> = 3 · 5381 · 19433 · 4054741 · 111624977 · 3066829543_<10> · C88

C88 = P35 · P54

P35 = 17163877973414236572565193518549799_<35>

P54 = 101091059547567240552656506384975203422975075543975963_<54>

12/14/09 22:17:32 v1.14 @ REPGMAIL, starting SIQS on c88: 1735114610277596319882101492881858349358905458206119477631290544003282647794410274481437
12/14/09 22:17:32 v1.14 @ REPGMAIL, random seeds: 0, 3887612160
12/14/09 22:17:33 v1.14 @ REPGMAIL, ==== sieve params ====
12/14/09 22:17:33 v1.14 @ REPGMAIL, n = 89 digits, 294 bits
12/14/09 22:17:33 v1.14 @ REPGMAIL, factor base: 60488 primes (max prime = 1597793)
12/14/09 22:17:33 v1.14 @ REPGMAIL, single large prime cutoff: 175757230 (110 * pmax)
12/14/09 22:17:33 v1.14 @ REPGMAIL, double large prime range from 43 to 50 bits
12/14/09 22:17:33 v1.14 @ REPGMAIL, double large prime cutoff: 693176384915362
12/14/09 22:17:33 v1.14 @ REPGMAIL, allocating 12 large prime slices of factor base
12/14/09 22:17:33 v1.14 @ REPGMAIL, buckets hold 1024 elements
12/14/09 22:17:33 v1.14 @ REPGMAIL, sieve interval: 18 blocks of size 32768
12/14/09 22:17:33 v1.14 @ REPGMAIL, polynomial A has ~ 11 factors
12/14/09 22:17:33 v1.14 @ REPGMAIL, using multiplier of 13
12/14/09 22:17:33 v1.14 @ REPGMAIL, using small prime variation correction of 20 bits
12/14/09 22:17:33 v1.14 @ REPGMAIL, using SSE2 for trial division and x128 sieve scanning
12/14/09 22:17:33 v1.14 @ REPGMAIL, trial factoring cutoff at 98 bits
12/14/09 22:17:33 v1.14 @ REPGMAIL, ==== sieving started ( 8 threads) ====
12/14/09 22:31:20 v1.14 @ REPGMAIL, trial division touched 13149469 sieve locations out of 20630231580672
12/14/09 22:31:20 v1.14 @ REPGMAIL, 61829 relations found: 19559 full + 42270 from 580301 partial, using 17488464 polys (735 A polys)
12/14/09 22:31:20 v1.14 @ REPGMAIL, on average, sieving found 0.03 rels/poly and 724.59 rels/sec
12/14/09 22:31:20 v1.14 @ REPGMAIL, trial division touched 13149469 sieve locations out of 20630231580672
12/14/09 22:31:20 v1.14 @ REPGMAIL, ==== post processing stage (msieve-1.38) ====
12/14/09 22:31:20 v1.14 @ REPGMAIL, begin with 599860 relations
12/14/09 22:31:20 v1.14 @ REPGMAIL, reduce to 130589 relations in 9 passes
12/14/09 22:31:28 v1.14 @ REPGMAIL, recovered 130589 relations
12/14/09 22:31:28 v1.14 @ REPGMAIL, recovered 110394 polynomials
12/14/09 22:31:28 v1.14 @ REPGMAIL, attempting to build 61829 cycles
12/14/09 22:31:28 v1.14 @ REPGMAIL, found 61829 cycles in 5 passes
12/14/09 22:31:28 v1.14 @ REPGMAIL, distribution of cycle lengths:
12/14/09 22:31:28 v1.14 @ REPGMAIL,    length 1 : 19559
12/14/09 22:31:28 v1.14 @ REPGMAIL,    length 2 : 16198
12/14/09 22:31:28 v1.14 @ REPGMAIL,    length 3 : 11684
12/14/09 22:31:28 v1.14 @ REPGMAIL,    length 4 : 6913
12/14/09 22:31:28 v1.14 @ REPGMAIL,    length 5 : 3770
12/14/09 22:31:28 v1.14 @ REPGMAIL,    length 6 : 1976
12/14/09 22:31:28 v1.14 @ REPGMAIL,    length 7 : 948
12/14/09 22:31:28 v1.14 @ REPGMAIL,    length 9+: 781
12/14/09 22:31:28 v1.14 @ REPGMAIL, largest cycle: 18 relations
12/14/09 22:31:32 v1.14 @ REPGMAIL, matrix is 60488 x 61829 (12.7 MB) with weight 3090998 (49.99/col)
12/14/09 22:31:32 v1.14 @ REPGMAIL, sparse part has weight 3090998 (49.99/col)
12/14/09 22:31:33 v1.14 @ REPGMAIL, filtering completed in 4 passes
12/14/09 22:31:33 v1.14 @ REPGMAIL, matrix is 54334 x 54398 (11.2 MB) with weight 2705367 (49.73/col)
12/14/09 22:31:33 v1.14 @ REPGMAIL, sparse part has weight 2705367 (49.73/col)
12/14/09 22:31:33 v1.14 @ REPGMAIL, saving the first 48 matrix rows for later
12/14/09 22:31:33 v1.14 @ REPGMAIL, matrix is 54286 x 54398 (9.5 MB) with weight 2342063 (43.05/col)
12/14/09 22:31:33 v1.14 @ REPGMAIL, sparse part has weight 2168736 (39.87/col)
12/14/09 22:31:33 v1.14 @ REPGMAIL, matrix includes 64 packed rows
12/14/09 22:31:33 v1.14 @ REPGMAIL, using block size 21759 for processor cache size 6144 kB
12/14/09 22:31:33 v1.14 @ REPGMAIL, commencing Lanczos iteration
12/14/09 22:31:33 v1.14 @ REPGMAIL, memory use: 8.5 MB
12/14/09 22:31:51 v1.14 @ REPGMAIL, lanczos halted after 860 iterations (dim = 54286)
12/14/09 22:31:51 v1.14 @ REPGMAIL, recovered 18 nontrivial dependencies
12/14/09 22:31:51 v1.14 @ REPGMAIL, prp35 = 17163877973414236572565193518549799
12/14/09 22:31:52 v1.14 @ REPGMAIL, prp54 = 101091059547567240552656506384975203422975075543975963
12/14/09 22:31:52 v1.14 @ REPGMAIL, Lanczos elapsed time = 31.2030 seconds.
12/14/09 22:31:52 v1.14 @ REPGMAIL, Sqrt elapsed time = 1.5160 seconds.
12/14/09 22:31:52 v1.14 @ REPGMAIL, SIQS elapsed time = 860.5803 seconds.

(68·10¹¹⁹+31)/9 = 7(5)₁₁₈9_<120> = 3 · 7² · 43686701 · C111

C111 = P40 · P71

P40 = 6634669135672764257553453456120632517947_<40>

P71 = 17732931987917711009328662473632708127743210594667847722218063513552451_<71>

N=117652136545221912976539918304840573257486417659088317570207254929124209859585794047601347460666857922983338097
  ( 111 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=6634669135672764257553453456120632517947 (pp40)
 r2=17732931987917711009328662473632708127743210594667847722218063513552451 (pp71)
Version: Msieve-1.40
Total time: 1.52 hours.
Scaled time: 2.93 units (timescale=1.922).
Factorization parameters were as follows:
n: 117652136545221912976539918304840573257486417659088317570207254929124209859585794047601347460666857922983338097
m: 200000000000000000000000
deg: 5
c5: 21250
c0: 31
skew: 0.27
type: snfs
lss: 1
rlim: 720000
alim: 720000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 720000/720000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [360000, 710001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 76233 x 76462
Total sieving time: 1.48 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120.000,5,0,0,0,0,0,0,0,0,720000,720000,25,25,46,46,2.2,2.2,50000
total time: 1.52 hours.
 --------- CPU info (if available) ----------

(68·10¹²³+31)/9 = 7(5)₁₂₂9_<124> = 643 · 509084894483527_<15> · C107

C107 = P35 · P73

P35 = 15805941502604126681615117882084741_<35>

P73 = 1460309293729239363139970762663567667195019351405645904493488161939164559_<73>

N=23081563272393504608498474761706374197973657306420442943852972944554259658162200187498273275712430781894219
  ( 107 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=15805941502604126681615117882084741 (pp35)
 r2=1460309293729239363139970762663567667195019351405645904493488161939164559 (pp73)
Version: Msieve-1.40
Total time: 1.58 hours.
Scaled time: 3.11 units (timescale=1.963).
Factorization parameters were as follows:
n: 23081563272393504608498474761706374197973657306420442943852972944554259658162200187498273275712430781894219
m: 2000000000000000000000000
deg: 5
c5: 2125
c0: 31
skew: 0.43
type: snfs
lss: 1
rlim: 840000
alim: 840000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 840000/840000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [420000, 770001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 99439 x 99664
Total sieving time: 1.53 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,124.000,5,0,0,0,0,0,0,0,0,840000,840000,25,25,46,46,2.2,2.2,50000
total time: 1.58 hours.
 --------- CPU info (if available) ----------

(68·10¹³²-23)/9 = 7(5)₁₃₁3_<133> = 1451 · 15013853 · C123

C123 = P37 · P86

P37 = 3546780733597351884342375925933239181_<37>

P86 = 97785056439323570071160433088360953550212624698377101232129668524217662486037165530171_<86>

N=346822154212722509605722778538195475035879413238053901483291920294207306311553273500401847353147649829138159828113214829951
  ( 123 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=3546780733597351884342375925933239181 (pp37)
 r2=97785056439323570071160433088360953550212624698377101232129668524217662486037165530171 (pp86)
Version: Msieve-1.40
Total time: 5.41 hours.
Scaled time: 5.04 units (timescale=0.933).
Factorization parameters were as follows:
n: 346822154212722509605722778538195475035879413238053901483291920294207306311553273500401847353147649829138159828113214829951
m: 100000000000000000000000000
deg: 5
c5: 6800
c0: -23
skew: 0.32
type: snfs
lss: 1
rlim: 1190000
alim: 1190000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1190000/1190000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [595000, 1345001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 151774 x 151999
Total sieving time: 5.26 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,133.000,5,0,0,0,0,0,0,0,0,1190000,1190000,26,26,47,47,2.3,2.3,75000
total time: 5.41 hours.
 --------- CPU info (if available) ----------

(68·10¹³³+31)/9 = 7(5)₁₃₂9_<134> = 1622420191243_<13> · C122

C122 = P58 · P65

P58 = 3775676221594506443793913356406245596727082658528011309483_<58>

P65 = 12334124159941821239867158087321352017654694921147016591540360511_<65>

N=46569659304886651490438767131553120040397812939779228259856637279984635433151663202704620061831030849474071331459013025813
  ( 122 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=3775676221594506443793913356406245596727082658528011309483 (pp58)
 r2=12334124159941821239867158087321352017654694921147016591540360511 (pp65)
Version: Msieve-1.40
Total time: 4.95 hours.
Scaled time: 4.61 units (timescale=0.932).
Factorization parameters were as follows:
n: 46569659304886651490438767131553120040397812939779228259856637279984635433151663202704620061831030849474071331459013025813
m: 200000000000000000000000000
deg: 5
c5: 2125
c0: 31
skew: 0.43
type: snfs
lss: 1
rlim: 1240000
alim: 1240000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1240000/1240000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [620000, 1295001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 160015 x 160240
Total sieving time: 4.77 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,134.000,5,0,0,0,0,0,0,0,0,1240000,1240000,26,26,47,47,2.3,2.3,75000
total time: 4.95 hours.
 --------- CPU info (if available) ----------

(68·10¹³³-23)/9 = 7(5)₁₃₂3_<134> = 31 · 1481 · 2157345597104996955689_<22> · C108

C108 = P50 · P59

P50 = 47411469848704408241807854830975592670012824018181_<50>

P59 = 16089646730547195710003465003961823026277166216107972643747_<59>

N=762833800841643829710558482948388661851497005201100350789886529905966617825111340108110622150732462163964207
  ( 108 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=47411469848704408241807854830975592670012824018181 (pp50)
 r2=16089646730547195710003465003961823026277166216107972643747 (pp59)
Version: Msieve-1.40
Total time: 4.88 hours.
Scaled time: 4.55 units (timescale=0.932).
Factorization parameters were as follows:
n: 762833800841643829710558482948388661851497005201100350789886529905966617825111340108110622150732462163964207
m: 200000000000000000000000000
deg: 5
c5: 2125
c0: -23
skew: 0.40
type: snfs
lss: 1
rlim: 1240000
alim: 1240000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1240000/1240000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [620000, 1295001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 167310 x 167535
Total sieving time: 4.71 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,134.000,5,0,0,0,0,0,0,0,0,1240000,1240000,26,26,47,47,2.3,2.3,75000
total time: 4.88 hours.
 --------- CPU info (if available) ----------

(68·10¹²⁹+31)/9 = 7(5)₁₂₈9_<130> = 2671 · 99105211 · C119

C119 = P44 · P76

P44 = 15850593937734961158350585904613693897074287_<44>

P76 = 1800737813772841770073771228425346708559403534164709399543295848456867471397_<76>

N=28542763874437913205487855707701668432438723177861207312592884591693426607608310073610917901821200641516476277956668939
  ( 119 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=15850593937734961158350585904613693897074287 (pp44)
 r2=1800737813772841770073771228425346708559403534164709399543295848456867471397 (pp76)
Version: Msieve-1.40
Total time: 2.51 hours.
Scaled time: 4.56 units (timescale=1.813).
Factorization parameters were as follows:
n: 28542763874437913205487855707701668432438723177861207312592884591693426607608310073610917901821200641516476277956668939
m: 20000000000000000000000000
deg: 5
c5: 21250
c0: 31
skew: 0.27
type: snfs
lss: 1
rlim: 1060000
alim: 1060000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1060000/1060000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [530000, 1030001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 151239 x 151466
Total sieving time: 2.42 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,130.000,5,0,0,0,0,0,0,0,0,1060000,1060000,26,26,47,47,2.3,2.3,50000
total time: 2.51 hours.
 --------- CPU info (if available) ----------

(68·10¹³¹-23)/9 = 7(5)₁₃₀3_<132> = 3 · 43 · 1101629849_<10> · 103335380363_<12> · C110

C110 = P54 · P57

P54 = 107465839243862724082249298851749174717083735327064911_<54>

P57 = 478764037949569470056242460435709304889925309933652412501_<57>

N=51450779138031025275378865230083848138539241379756745451743759286339154927443801592785384612075213434574852411
  ( 110 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=107465839243862724082249298851749174717083735327064911 (pp54)
 r2=478764037949569470056242460435709304889925309933652412501 (pp57)
Version: Msieve-1.40
Total time: 2.62 hours.
Scaled time: 4.82 units (timescale=1.839).
Factorization parameters were as follows:
n: 51450779138031025275378865230083848138539241379756745451743759286339154927443801592785384612075213434574852411
m: 100000000000000000000000000
deg: 5
c5: 680
c0: -23
skew: 0.51
type: snfs
lss: 1
rlim: 1150000
alim: 1150000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1150000/1150000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [575000, 1075001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 158594 x 158824
Total sieving time: 2.52 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132.000,5,0,0,0,0,0,0,0,0,1150000,1150000,26,26,47,47,2.3,2.3,50000
total time: 2.62 hours.
 --------- CPU info (if available) ----------

(68·10¹³⁸-23)/9 = 7(5)₁₃₇3_<139> = 353 · 8747 · 3440792217051907_<16> · C117

C117 = P39 · P79

P39 = 105491386872953299968777534235333470421_<39>

P79 = 6741509055502669216548343696385596867253895536109530691752085630089326932209789_<79>

N=711171139881550079123670628242749562640990066684770750496910658551665628899866129078044125043581325269317051798151169
  ( 117 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=105491386872953299968777534235333470421 (pp39)
 r2=6741509055502669216548343696385596867253895536109530691752085630089326932209789 (pp79)
Version: Msieve-1.40
Total time: 6.88 hours.
Scaled time: 6.42 units (timescale=0.933).
Factorization parameters were as follows:
n: 711171139881550079123670628242749562640990066684770750496910658551665628899866129078044125043581325269317051798151169
m: 2000000000000000000000000000
deg: 5
c5: 2125
c0: -23
skew: 0.40
type: snfs
lss: 1
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [750000, 1650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 228654 x 228880
Total sieving time: 6.57 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,139.000,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,48,48,2.3,2.3,75000
total time: 6.88 hours.
 --------- CPU info (if available) ----------

(68·10¹³⁹-23)/9 = 7(5)₁₃₈3_<140> = C140

C140 = P36 · P105

P36 = 164718007347958713783029320020009041_<36>

P105 = 458696391317727327867207967595193328572030528906800158169735169192289759788564814046706350284250216889233_<105>

N=75555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
  ( 140 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=164718007347958713783029320020009041 (pp36)
 r2=458696391317727327867207967595193328572030528906800158169735169192289759788564814046706350284250216889233 (pp105)
Version: Msieve-1.40
Total time: 6.80 hours.
Scaled time: 13.07 units (timescale=1.922).
Factorization parameters were as follows:
n: 75555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
m: 2000000000000000000000000000
deg: 5
c5: 21250
c0: -23
skew: 0.26
type: snfs
lss: 1
rlim: 1560000
alim: 1560000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1560000/1560000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [780000, 2080001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 245317 x 245544
Total sieving time: 6.67 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140.000,5,0,0,0,0,0,0,0,0,1560000,1560000,26,26,48,48,2.3,2.3,100000
total time: 6.80 hours.
 --------- CPU info (if available) ----------

(68·10¹⁴⁰+31)/9 = 7(5)₁₃₉9_<141> = 3² · 11 · 61 · C138

C138 = P35 · P51 · P53

P35 = 64577825418450786827092826500152721_<35>

P51 = 121323237318025912960150232176754713404906484098187_<51>

P53 = 15968861963782638135182074151294697288027680707033603_<53>

N=125112693418704347666096299976081396846424168828540413239866791779360085371014332762966642748063513090835495207079906533458446026752037681
  ( 138 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=64577825418450786827092826500152721 (pp35)
 r2=121323237318025912960150232176754713404906484098187 (pp51)
 r3=15968861963782638135182074151294697288027680707033603 (pp53)
Version: Msieve-1.40
Total time: 5.62 hours.
Scaled time: 5.23 units (timescale=0.930).
Factorization parameters were as follows:
n: 125112693418704347666096299976081396846424168828540413239866791779360085371014332762966642748063513090835495207079906533458446026752037681
m: 10000000000000000000000000000
deg: 5
c5: 68
c0: 31
skew: 0.85
type: snfs
lss: 1
rlim: 1620000
alim: 1620000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1620000/1620000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [810000, 1510001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 202238 x 202469
Total sieving time: 5.44 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000
total time: 5.62 hours.
 --------- CPU info (if available) ----------

(68·10¹⁴⁴+31)/9 = 7(5)₁₄₃9_<145> = 11 · 79 · 64627 · C138

C138 = P55 · P83

P55 = 2799109163358252944851206027149459226073495227890800061_<55>

P83 = 48063212413234688284492794240032724922427393061352740109590143514766355380635138413_<83>

N=134534178286319345832622898895901146596617568992049775936590496402371088128677003335143827037621475929875855995224923013657314268043843193
  ( 138 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=2799109163358252944851206027149459226073495227890800061 (pp55)
 r2=48063212413234688284492794240032724922427393061352740109590143514766355380635138413 (pp83)
Version: Msieve-1.40
Total time: 8.14 hours.
Scaled time: 15.33 units (timescale=1.883).
Factorization parameters were as follows:
n: 134534178286319345832622898895901146596617568992049775936590496402371088128677003335143827037621475929875855995224923013657314268043843193
m: 20000000000000000000000000000
deg: 5
c5: 21250
c0: 31
skew: 0.27
type: snfs
lss: 1
rlim: 1890000
alim: 1890000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1890000/1890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [945000, 2445001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 296638 x 296867
Total sieving time: 7.81 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,145.000,5,0,0,0,0,0,0,0,0,1890000,1890000,26,26,49,49,2.3,2.3,100000
total time: 8.14 hours.
 --------- CPU info (if available) ----------

(68·10¹⁴⁷+31)/9 = 7(5)₁₄₆9_<148> = 113 · 1399231 · 494128459174997_<15> · 854839314133520650537403_<24> · C102

C102 = P37 · P65

P37 = 3307593458679400865926471611006730181_<37>

P65 = 34202831604401379070594480213491731602791057229970797659864243443_<65>

N=113129062083031078829244010170332132313320715044935113709770505518972384982973295951897659466799453183
  ( 102 digits)
Divisors found:
 r1=3307593458679400865926471611006730181 (pp37)
 r2=34202831604401379070594480213491731602791057229970797659864243443 (pp65)
Version: Msieve-1.40
Total time: 5.05 hours.
Scaled time: 9.94 units (timescale=1.969).
Factorization parameters were as follows:
name: g2
n: 113129062083031078829244010170332132313320715044935113709770505518972384982973295951897659466799453183
skew: 9373.09
# norm 1.77e+014
c5: 95040
c4: 993742740
c3: -20272824328200
c2: -64071914268138185
c1: 842627983672225941408
c0: -11947393337441418505264
# alpha -6.12
Y1: 113350393709
Y0: -16410706557440026473
# Murphy_E 2.82e-009
# M 92210185113258973315463136410439353282245099000867708977336273077550890938594157433529679528411226221
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 213563 x 213788
Polynomial selection time: 0.50 hours.
Total sieving time: 4.35 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 5.05 hours.
 --------- CPU info (if available) ----------

(68·10¹⁴²-23)/9 = 7(5)₁₄₁3_<143> = 67 · 1201 · 81317837369_<11> · 212049219970753086168503801_<27> · C101

C101 = P49 · P53

P49 = 2959672947226504162711354061714811058096170521161_<49>

P53 = 18398498042538049399399151846094729471619424141236051_<53>

N=54453536926099656419822835317968628649294196449567335387500606200426331378061740221365333895391575211
  ( 101 digits)
Divisors found:
 r1=2959672947226504162711354061714811058096170521161 (pp49)
 r2=18398498042538049399399151846094729471619424141236051 (pp53)
Version: Msieve-1.40
Total time: 3.76 hours.
Scaled time: 7.23 units (timescale=1.922).
Factorization parameters were as follows:
name: g1
n: 54453536926099656419822835317968628649294196449567335387500606200426331378061740221365333895391575211
skew: 2931.88
# norm 5.35e+013
c5: 409200
c4: 8901108
c3: -4950728848596
c2: 6043929165090551
c1: 23397151429743759722
c0: -69366011719193748738633
# alpha -6.24
Y1: 38386560253
Y0: -10588101280949284690
# Murphy_E 3.19e-009
# M 37728834848942648417473990291487294399973387734390897856397569738356643094034402185983653030400545834
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 237990 x 238238
Polynomial selection time: 0.43 hours.
Total sieving time: 3.07 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 3.76 hours.
 --------- CPU info (if available) ----------

(68·10¹³²+31)/9 = 7(5)₁₃₁9_<133> = 11 · 19 · 15264131 · 72747172267872895085143_<23> · C101

C101 = P47 · P54

P47 = 36954238232459266794746422219280310036992683933_<47>

P54 = 880983270993343639800108777244778655265600180659756359_<54>

N=32556065675099242514509548230892736110901273716548379934378236917526599026909990576685356401273879947
  ( 101 digits)
Divisors found:
 r1=36954238232459266794746422219280310036992683933 (pp47)
 r2=880983270993343639800108777244778655265600180659756359 (pp54)
Version: Msieve-1.40
Total time: 3.88 hours.
Scaled time: 7.39 units (timescale=1.905).
Factorization parameters were as follows:
name: g0
n: 32556065675099242514509548230892736110901273716548379934378236917526599026909990576685356401273879947
skew: 9331.96
# norm 1.42e+014
c5: 77700
c4: -857413225
c3: -17143839924827
c2: 70864659807859085
c1: 721204846229342710248
c0: -1087149978755970537439980
# alpha -6.52
Y1: 25776775063
Y0: -13318154067841040467
# Murphy_E 3.25e-009
# M 27532399991660424287791386334789384309991547594287584614629526678504506374241159243714975923135653028
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 195770 x 196001
Polynomial selection time: 0.43 hours.
Total sieving time: 3.28 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 3.88 hours.
 --------- CPU info (if available) ----------

Dec 15, 2009 (4th)

By Sinkiti Sibata / Msieve / Dec 15, 2009

(68·10¹⁴⁰-23)/9 = 7(5)₁₃₉3_<141> = 3 · 48157279 · 158546731887285436938346074863_<30> · C104

C104 = P44 · P60

P44 = 33766940649557270429843570725392477009158467_<44>

P60 = 976864212320039983752591722330942844497734391931800612763689_<60>

Number: 75553_140
N=32985715880087302264179078807117361590859919830808006197563651961591828459277939695772641530229024504763
  ( 104 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=33766940649557270429843570725392477009158467 (pp44)
 r2=976864212320039983752591722330942844497734391931800612763689 (pp60)
Version: Msieve v. 1.42
Total time: 0.36 hours.
Scaled time: 0.28 units (timescale=0.796).
Factorization parameters were as follows:
name: 75553_140
n: 32985715880087302264179078807117361590859919830808006197563651961591828459277939695772641530229024504763
m: 10000000000000000000000000000
deg: 5
c5: 68
c0: -23
skew: 0.81
type: snfs
lss: 1
rlim: 1620000
alim: 1620000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1620000/1620000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [810000, 1710001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 274332 x 274557
Total sieving time: 0.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000
total time: 0.36 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 5.5 hours.

(67·10¹⁶⁷+41)/9 = 7(4)₁₆₆9_<168> = 12007 · 2883731174759_<13> · C152

C152 = P46 · P47 · P59

P46 = 9099568540339976268577524952845344061739489817_<46>

P47 = 98953310001994328393191015800849486407545328609_<47>

P59 = 23877666584598768009724339692120824825964814162219197525241_<59>

Number: 74449_167
N=21500225265668832778209732491679555951323094270407199545497962211634757197950504508122504681536277486547015682731062252501472455955612542806915181492273
  ( 152 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=9099568540339976268577524952845344061739489817 (pp46)
 r2=98953310001994328393191015800849486407545328609 (pp47)
 r3=23877666584598768009724339692120824825964814162219197525241 (pp59)
Version: Msieve-1.40
Total time: 70.12 hours.
Scaled time: 230.47 units (timescale=3.287).
Factorization parameters were as follows:
name: 74449_167
n: 21500225265668832778209732491679555951323094270407199545497962211634757197950504508122504681536277486547015682731062252501472455955612542806915181492273
m: 1000000000000000000000000000000000
deg: 5
c5: 6700
c0: 41
skew: 0.36
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2300000, 6000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 984373 x 984621
Total sieving time: 67.85 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.86 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,168.000,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000
total time: 70.12 hours.
 --------- CPU info (if available) ----------

(68·10¹⁴³+31)/9 = 7(5)₁₄₂9_<144> = 3 · 7 · 256517971 · 722066453072714543_<18> · C117

C117 = P51 · P67

P51 = 151840443799935154578099961093885897305133766399969_<51>

P67 = 1279277258851732954711573830325981672571369287299325807035602299847_<67>

Number: 75559_143
N=194246026727211654968913305488461548367824105430564236553497494764492736602120625486924694056985227303799150069504743
  ( 117 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=151840443799935154578099961093885897305133766399969 (pp51)
 r2=1279277258851732954711573830325981672571369287299325807035602299847 (pp67)
Version: Msieve v. 1.42
Total time: 0.44 hours.
Scaled time: 0.35 units (timescale=0.796).
Factorization parameters were as follows:
name: 75559_143
n: 194246026727211654968913305488461548367824105430564236553497494764492736602120625486924694056985227303799150069504743
m: 20000000000000000000000000000
deg: 5
c5: 2125
c0: 31
skew: 0.43
type: snfs
lss: 1
rlim: 1820000
alim: 1820000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1820000/1820000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [910000, 2010001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 310126 x 310351
Total sieving time: 0.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,144.000,5,0,0,0,0,0,0,0,0,1820000,1820000,26,26,49,49,2.3,2.3,100000
total time: 0.44 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 6 hours 40 min.

Dec 15, 2009 (3rd)

By [XTBA>TSA] IvanleFou + Beyond + Grubix + jiri kovar + veebee / yoyo@home, GMP-ECM / Dec 15, 2009

(10²⁰¹+17)/9 = (1)₂₀₀3_<201> = 163 · 6610512331_<10> · 591785342633_<12> · C177

C177 = P33 · C144

P33 = 434937654132758116503430906897943_<33>

C144 = [400630080585560047283559589031720836640469685776195262402744444159188517127238066932342627397734279890091910596475172516678632844545173721295559_<144>]

GMP-ECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [ECM]
Input number is 174249107424901328154797173904681562657513437449116292897023905780144007058356290870928174957782571238810560254724268067008224047626355412568808491125189068775485687967752135137 (177 digits)
[Mon Dec 14 18:53:21 2009]
Using MODMULN
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3868083629
dF=16384, k=2, d=158340, d2=11, i0=8
Expected number of curves to find a factor of n digits:
20	25	30	35	40	45	50	55	60	65
3	11	54	322	2350	20265	199745	2246256	2.8e+007	4e+008
Step 1 took 15735ms
Using 22 small primes for NTT
Estimated memory usage: 60M
Initializing tables of differences for F took 15ms
Computing roots of F took 750ms
Building F from its roots took 1672ms
Computing 1/F took 890ms
Initializing table of differences for G took 16ms
Computing roots of G took 687ms
Building G from its roots took 1453ms
Computing roots of G took 688ms
Building G from its roots took 1453ms
Computing G * H took 532ms
Reducing  G * H mod F took 515ms
Computing polyeval(F,G) took 2812ms
Computing product of all F(g_i) took 16ms
Step 2 took 11671ms
********** Factor found in step 2: 434937654132758116503430906897943
Found probable prime factor of 33 digits: 434937654132758116503430906897943
Composite cofactor 400630080585560047283559589031720836640469685776195262402744444159188517127238066932342627397734279890091910596475172516678632844545173721295559 has 144 digits

(10²²⁴+17)/9 = (1)₂₂₃3_<224> = 13 · 2062057 · 13114217 · 83966699 · 96847363 · C193

C193 = P30 · C163

P30 = 435014947587352996741211293991_<30>

C163 = [8934536893073881695362159200583021969912162189671777515715892258132715300674118774530310082315129943003392553047646488635199933129656686153169261847420414263935387_<163>]

GMP-ECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [ECM]
Input number is 3886657098257806331434095545293329839817212614797090398280354923445762056113132379813681173655176220583770329799839670015856368240944943756244089374109897160110332176285865766830274002285359517 (193 digits)
[Mon Dec 14 20:03:58 2009]
Using MODMULN
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2823076904
dF=16384, k=2, d=158340, d2=11, i0=8
Expected number of curves to find a factor of n digits:
20	25	30	35	40	45	50	55	60	65
3	11	54	322	2350	20265	199745	2246256	2.8e+007	4e+008
Step 1 took 16578ms
Using 24 small primes for NTT
Estimated memory usage: 62M
Initializing tables of differences for F took 15ms
Computing roots of F took 469ms
Building F from its roots took 1781ms
Computing 1/F took 1047ms
Initializing table of differences for G took 16ms
Computing roots of G took 437ms
Building G from its roots took 1641ms
Computing roots of G took 437ms
Building G from its roots took 1625ms
Computing G * H took 578ms
Reducing  G * H mod F took 562ms
Computing polyeval(F,G) took 3141ms
Computing product of all F(g_i) took 16ms
Step 2 took 11922ms
********** Factor found in step 2: 435014947587352996741211293991
Found probable prime factor of 30 digits: 435014947587352996741211293991
Composite cofactor 8934536893073881695362159200583021969912162189671777515715892258132715300674118774530310082315129943003392553047646488635199933129656686153169261847420414263935387 has 163 digits

(10²³²+17)/9 = (1)₂₃₁3_<232> = 3² · 7 · 1031 · 242681851207_<12> · 60172454155949833693_<20> · C196

C196 = P29 · C168

P29 = 11034650601549874189730158399_<29>

C168 = [106160918079293499828871171668387354975740392989821399884697192605813176167742276299320496961036627957248078891805720005695913237091468581973936046925810427808436406829_<168>]

GMP-ECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [ECM]
Input number is 1171448638544762932351907908494663970476643690362893130411085823792270499423543789663011576627567935696315395295800785938152719188074903690312546061914970458942515265396550984538283442184575306771 (196 digits)
[Mon Dec 14 20:25:19 2009]
Using MODMULN
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2768889511
dF=16384, k=2, d=158340, d2=11, i0=8
Expected number of curves to find a factor of n digits:
20	25	30	35	40	45	50	55	60	65
3	11	54	322	2350	20265	199745	2246256	2.8e+007	4e+008
Step 1 took 11485ms
Using 24 small primes for NTT
Estimated memory usage: 66M
Initializing tables of differences for F took 16ms
Computing roots of F took 547ms
Building F from its roots took 1016ms
Computing 1/F took 687ms
Initializing table of differences for G took 16ms
Computing roots of G took 531ms
Building G from its roots took 1032ms
Computing roots of G took 515ms
Building G from its roots took 1031ms
Computing G * H took 375ms
Reducing  G * H mod F took 360ms
Computing polyeval(F,G) took 1781ms
Computing product of all F(g_i) took 16ms
Step 2 took 7984ms
********** Factor found in step 2: 11034650601549874189730158399
Found probable prime factor of 29 digits: 11034650601549874189730158399
Composite cofactor 106160918079293499828871171668387354975740392989821399884697192605813176167742276299320496961036627957248078891805720005695913237091468581973936046925810427808436406829 has 168 digits

(10²³⁷+17)/9 = (1)₂₃₆3_<237> = 6689 · 9661 · C229

C229 = P30 · P199

P30 = 245770041528399372761722440431_<30>

P199 = 6995927008257020513213147481935171254602692742046147638121409624025066318654782565640266876425207293906006549803982132091174899763423630705114910859456080952174977330381795175212974818157466438019187_<199>

GMP-ECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [ECM]
Input number is 1719389271348978713120039345953880983197197850781980217907177570052513982585072918121216259313173002381434952114088919670771135995384994134329291632029354871682571868524334037507490025036216312932327429399336120762515923242549597 (229 digits)
[Mon Dec 14 20:27:43 2009]
Using MODMULN
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3076026454
dF=16384, k=2, d=158340, d2=11, i0=8
Expected number of curves to find a factor of n digits:
20	25	30	35	40	45	50	55	60	65
3	11	54	322	2350	20265	199745	2246256	2.8e+007	4e+008
Step 1 took 26785ms
Using 27 small primes for NTT
Estimated memory usage: 72M
Initializing tables of differences for F took 16ms
Computing roots of F took 1076ms
Building F from its roots took 2277ms
Computing 1/F took 1389ms
Initializing table of differences for G took 15ms
Computing roots of G took 952ms
Building G from its roots took 2075ms
Computing roots of G took 952ms
Building G from its roots took 2028ms
Computing G * H took 748ms
Reducing  G * H mod F took 702ms
Computing polyeval(F,G) took 4150ms
Computing product of all F(g_i) took 31ms
Step 2 took 16520ms
********** Factor found in step 2: 245770041528399372761722440431
Found probable prime factor of 30 digits: 245770041528399372761722440431
Probable prime cofactor 6995927008257020513213147481935171254602692742046147638121409624025066318654782565640266876425207293906006549803982132091174899763423630705114910859456080952174977330381795175212974818157466438019187 has 199 digits

(10²⁴³+17)/9 = (1)₂₄₂3_<243> = 205998011 · 848344039447395897683339_<24> · C210

C210 = P34 · P177

P34 = 5698757463712416358165250190011999_<34>

P177 = 111568675330136835985158131132148286419662624343188790396091914312571328418864051146305057278675143858079578156757844170432496065307678374623319281825292812203036012184988862303_<177>

GMP-ECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [ECM]
Input number is 635802821254124632245644134156344521699797959589567830765446538580491656222953927253387514145875048283079324184181135147768813698398498051741476677385558200484481165819627480049581712885502706227662268928773697 (210 digits)
[Tue Dec 15 06:52:15 2009]
Using MODMULN
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=978631340
dF=16384, k=2, d=158340, d2=11, i0=8
Expected number of curves to find a factor of n digits:
20	25	30	35	40	45	50	55	60	65
3	11	54	322	2350	20265	199745	2246256	2.8e+007	4e+008
Step 1 took 26067ms
Using 25 small primes for NTT
Estimated memory usage: 66M
Initializing tables of differences for F took 15ms
Computing roots of F took 952ms
Building F from its roots took 1841ms
Computing 1/F took 1029ms
Initializing table of differences for G took 32ms
Computing roots of G took 826ms
Building G from its roots took 1592ms
Computing roots of G took 734ms
Building G from its roots took 1684ms
Computing G * H took 546ms
Reducing  G * H mod F took 546ms
Computing polyeval(F,G) took 3276ms
Computing product of all F(g_i) took 16ms
Step 2 took 13136ms
********** Factor found in step 2: 5698757463712416358165250190011999
Found probable prime factor of 34 digits: 5698757463712416358165250190011999
Probable prime cofactor 111568675330136835985158131132148286419662624343188790396091914312571328418864051146305057278675143858079578156757844170432496065307678374623319281825292812203036012184988862303 has 177 digits

Dec 15, 2009 (2nd)

By Markus Tervooren / Msieve, GMP-ECM / Dec 15, 2009

(68·10¹⁰⁴-23)/9 = 7(5)₁₀₃3_<105> = 3 · 659591 · 404904091 · C90

C90 = P40 · P51

P40 = 7708013546252113778869071536500067456077_<40>

P51 = 122342061281926836162513959260860360435732273533123_<51>

Used 4th degree poly for snfs,

n: 943014265637498297505998356358191789999906362475486416043098179590323289763284335407138471
m: 100000000000000000000000000
deg: 4
c4: 68
c0: -23
skew: 0.76
type: snfs
lss: 1
rlim: 100000
alim: 100000
lpbr: 23
lpba: 23
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4

total time: about 12 min.

Msieve v. 1.44
Mon Dec 14 18:03:45 2009
random seeds: f7271fc6 28bb6c01
factoring 943014265637498297505998356358191789999906362475486416043098179590323289763284335407138471 (90 digits)
searching for 15-digit factors
commencing number field sieve (90-digit input)
R0: -100000000000000000000000000
R1:  1
A0: -23
A1:  0
A2:  0
A3:  0
A4:  68
skew 0.76, size 5.461466e-11, alpha -0.039522, combined = 2.254282e-07

commencing square root phase
reading relations for dependency 1
read 18586 cycles
cycles contain 30766 unique relations
read 30766 relations
multiplying 30766 relations
multiply complete, coefficients have about 0.75 million bits
initial square root is modulo 9200017
sqrtTime: 1
prp40 factor: 7708013546252113778869071536500067456077
prp51 factor: 122342061281926836162513959260860360435732273533123
elapsed time 00:00:02

(68·10¹⁰⁷-23)/9 = 7(5)₁₀₆3_<108> = 3² · 29 · 367 · 294703 · 713281 · C92

C92 = P38 · P54

P38 = 55841787356899758089337509139209931113_<38>

P54 = 671978392635978033818610453543331621206951997598183941_<54>

~12 mins. sieve time

prp38 factor: 55841787356899758089337509139209931113
prp54 factor: 671978392635978033818610453543331621206951997598183941

(68·10¹¹⁴-23)/9 = 7(5)₁₁₃3_<115> = 109 · 59833 · 786691 · 273886423817_<12> · C91

C91 = P40 · P52

P40 = 3046332219582280736969449366056318755789_<40>

P52 = 1765010021743646241126701494557487844073819577055603_<52>

~41 mins total

prp40 factor: 3046332219582280736969449366056318755789
prp52 factor: 1765010021743646241126701494557487844073819577055603

(68·10¹⁰⁸-23)/9 = 7(5)₁₀₇3_<109> = 1221209464999528236083_<22> · C88

C88 = P30 · P59

P30 = 194946478745404642036108878353_<30>

P59 = 31736632767257197268708000583187127425753435733110756525547_<59>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=720988234
Step 1 took 8113ms
Step 2 took 3832ms
********** Factor found in step 2: 194946478745404642036108878353
Found probable prime factor of 30 digits: 194946478745404642036108878353
Probable prime cofactor 31736632767257197268708000583187127425753435733110756525547 has 59 digits

(68·10¹⁴⁶-23)/9 = 7(5)₁₄₅3_<147> = 3 · 1536852924590281489_<19> · 16213118378585185452280153_<26> · C104

C104 = P48 · P56

P48 = 222262927902466959012561494161438438028846547583_<48>

P56 = 45475685662992432516577150080876318212189203602993452141_<56>

prp48 factor: 222262927902466959012561494161438438028846547583
prp56 factor: 45475685662992432516577150080876318212189203602993452141

done by gnfs in about 12 CPU-hours (parameters were non-optimal).

poly:

Y0: -77566047231907110907
Y1: 31039371907
c0: -558398743597374860738736
c1: 137065067169670849580
c2: 59521037394430008
c3: -264552505753
c4: -300678770
c5: 3600

Dec 15, 2009

Factorizations of 755...553 and Factorizations of 755...559 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Dec 14, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve / Dec 14, 2009

(14·10¹⁸⁹+31)/9 = 1(5)₁₈₈9_<190> = 269 · C187

C187 = P65 · P123

P65 = 15476888878283271998699894906904401294117352114726080949942811469_<65>

P123 = 373636746554657431899738325086669472686287739421434557195295928619410609529013993014149729410980424907284192083404696637519_<123>

N=5782734407269723254853366377529946303180503923998347790169351507641470466749277158199091284593143329202808756712102437009500206526228831061544816191656340355225113589425857083849648905411
  ( 187 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=15476888878283271998699894906904401294117352114726080949942811469 (pp65)
 r2=373636746554657431899738325086669472686287739421434557195295928619410609529013993014149729410980424907284192083404696637519 (pp123)
Version: Msieve-1.40
Total time: 477.33 hours.
Scaled time: 443.92 units (timescale=0.930).
Factorization parameters were as follows:
n: 5782734407269723254853366377529946303180503923998347790169351507641470466749277158199091284593143329202808756712102437009500206526228831061544816191656340355225113589425857083849648905411
m: 20000000000000000000000000000000000000
deg: 5
c5: 4375
c0: 31
skew: 0.37
type: snfs
lss: 1
rlim: 10300000
alim: 10300000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 300000Factor base limits: 10300000/10300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5150000, 10850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2109440 x 2109664
Total sieving time: 466.75 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 8.57 hours.
Time per square root: 1.60 hours.
Prototype def-par.txt line would be:
snfs,190.000,5,0,0,0,0,0,0,0,0,10300000,10300000,28,28,54,54,2.5,2.5,100000
total time: 477.33 hours.
 --------- CPU info (if available) ----------

(28·10¹⁸⁸-1)/9 = 3(1)₁₈₈_<189> = 19 · 503 · C185

C185 = P43 · P143

P43 = 2416629624381304027373196419958393926957531_<43>

P143 = 13470503866653980725975346962207094079095769556923068819279584548159094120699797381682796572270886434971475080102868213043108034624212177560433_<143>

N=32553218699498912955018427447013823491797751502679827467940892655761338402334530826735493471917035796914419913268924464906467626986618301884598839710276353574459674700335995721576970923
  ( 185 digits)
SNFS difficulty: 189 digits.
Divisors found:
 r1=2416629624381304027373196419958393926957531 (pp43)
 r2=13470503866653980725975346962207094079095769556923068819279584548159094120699797381682796572270886434971475080102868213043108034624212177560433 (pp143)
Version: Msieve-1.40
Total time: 215.19 hours.
Scaled time: 419.84 units (timescale=1.951).
Factorization parameters were as follows:
n: 32553218699498912955018427447013823491797751502679827467940892655761338402334530826735493471917035796914419913268924464906467626986618301884598839710276353574459674700335995721576970923
m: 20000000000000000000000000000000000000
deg: 5
c5: 875
c0: -1
skew: 0.26
type: snfs
lss: 1
rlim: 10100000
alim: 10100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 300000Factor base limits: 10100000/10100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5050000, 8350001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1713525 x 1713749
Total sieving time: 210.31 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.72 hours.
Time per square root: 0.94 hours.
Prototype def-par.txt line would be:
snfs,189.000,5,0,0,0,0,0,0,0,0,10100000,10100000,28,28,54,54,2.5,2.5,100000
total time: 215.19 hours.
 --------- CPU info (if available) ----------

Dec 14, 2009 (3rd)

By Sinkiti Sibata / Msieve / Dec 14, 2009

(68·10¹⁴⁶-41)/9 = 7(5)₁₄₅1_<147> = 13099 · 51047 · 34085993869_<11> · 257027694399899_<15> · C114

C114 = P35 · P38 · P41

P35 = 91745407526091275078581201574964401_<35>

P38 = 31940625612168213799541729966676659153_<38>

P41 = 44012334266984213041400029357929142350469_<41>

Number: 75551_146
N=128973995797215448814484116169921270822336396257811193385527946367660864173463162736114202640935324439767195543557
  ( 114 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=91745407526091275078581201574964401 (pp35)
 r2=31940625612168213799541729966676659153 (pp38)
 r3=44012334266984213041400029357929142350469 (pp41)
Version: Msieve v. 1.42
Total time: 0.46 hours.
Scaled time: 0.37 units (timescale=0.796).
Factorization parameters were as follows:
name: 75551_146
n: 128973995797215448814484116169921270822336396257811193385527946367660864173463162736114202640935324439767195543557
m: 100000000000000000000000000000
deg: 5
c5: 680
c0: -41
skew: 0.57
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 334952 x 335178
Total sieving time: 0.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,147.000,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000
total time: 0.46 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 8 hours 43 min.

(68·10¹²⁵-41)/9 = 7(5)₁₂₄1_<126> = 19 · 23 · 36109 · 76006820388463240697_<20> · C99

C99 = P42 · P58

P42 = 104832014910643936866343141389359887599647_<42>

P58 = 6009287840164729715877654115282117404072734705183137859033_<58>

Sun Dec 13 21:19:36 2009  Msieve v. 1.42
Sun Dec 13 21:19:36 2009  random seeds: 4eb821a4 a5b6dbf8
Sun Dec 13 21:19:36 2009  factoring 629965752462500244411755920304594721110450811886953027877206783027562086509752461510463877026561351 (99 digits)
Sun Dec 13 21:19:37 2009  searching for 15-digit factors
Sun Dec 13 21:19:38 2009  commencing quadratic sieve (99-digit input)
Sun Dec 13 21:19:38 2009  using multiplier of 1
Sun Dec 13 21:19:38 2009  using 32kb Intel Core sieve core
Sun Dec 13 21:19:38 2009  sieve interval: 36 blocks of size 32768
Sun Dec 13 21:19:38 2009  processing polynomials in batches of 6
Sun Dec 13 21:19:38 2009  using a sieve bound of 2632339 (96471 primes)
Sun Dec 13 21:19:38 2009  using large prime bound of 394850850 (28 bits)
Sun Dec 13 21:19:38 2009  using double large prime bound of 2975633911281600 (43-52 bits)
Sun Dec 13 21:19:38 2009  using trial factoring cutoff of 52 bits
Sun Dec 13 21:19:38 2009  polynomial 'A' values have 13 factors
Mon Dec 14 07:13:00 2009  96785 relations (22492 full + 74293 combined from 1461184 partial), need 96567
Mon Dec 14 07:13:03 2009  begin with 1483676 relations
Mon Dec 14 07:13:04 2009  reduce to 257448 relations in 11 passes
Mon Dec 14 07:13:04 2009  attempting to read 257448 relations
Mon Dec 14 07:13:09 2009  recovered 257448 relations
Mon Dec 14 07:13:09 2009  recovered 248142 polynomials
Mon Dec 14 07:13:09 2009  attempting to build 96785 cycles
Mon Dec 14 07:13:09 2009  found 96785 cycles in 6 passes
Mon Dec 14 07:13:09 2009  distribution of cycle lengths:
Mon Dec 14 07:13:09 2009     length 1 : 22492
Mon Dec 14 07:13:09 2009     length 2 : 16333
Mon Dec 14 07:13:09 2009     length 3 : 16143
Mon Dec 14 07:13:09 2009     length 4 : 13204
Mon Dec 14 07:13:09 2009     length 5 : 10086
Mon Dec 14 07:13:09 2009     length 6 : 7088
Mon Dec 14 07:13:09 2009     length 7 : 4658
Mon Dec 14 07:13:09 2009     length 9+: 6781
Mon Dec 14 07:13:09 2009  largest cycle: 25 relations
Mon Dec 14 07:13:10 2009  matrix is 96471 x 96785 (26.6 MB) with weight 6591370 (68.10/col)
Mon Dec 14 07:13:10 2009  sparse part has weight 6591370 (68.10/col)
Mon Dec 14 07:13:11 2009  filtering completed in 3 passes
Mon Dec 14 07:13:11 2009  matrix is 92862 x 92926 (25.6 MB) with weight 6344118 (68.27/col)
Mon Dec 14 07:13:11 2009  sparse part has weight 6344118 (68.27/col)
Mon Dec 14 07:13:11 2009  saving the first 48 matrix rows for later
Mon Dec 14 07:13:11 2009  matrix is 92814 x 92926 (15.5 MB) with weight 4996132 (53.76/col)
Mon Dec 14 07:13:11 2009  sparse part has weight 3495382 (37.61/col)
Mon Dec 14 07:13:12 2009  matrix includes 64 packed rows
Mon Dec 14 07:13:12 2009  using block size 37170 for processor cache size 1024 kB
Mon Dec 14 07:13:12 2009  commencing Lanczos iteration
Mon Dec 14 07:13:12 2009  memory use: 16.0 MB
Mon Dec 14 07:14:15 2009  lanczos halted after 1469 iterations (dim = 92810)
Mon Dec 14 07:14:16 2009  recovered 14 nontrivial dependencies
Mon Dec 14 07:14:17 2009  prp42 factor: 104832014910643936866343141389359887599647
Mon Dec 14 07:14:17 2009  prp58 factor: 6009287840164729715877654115282117404072734705183137859033
Mon Dec 14 07:14:17 2009  elapsed time 09:54:41

(68·10¹²⁶-41)/9 = 7(5)₁₂₅1_<127> = 3 · 508284318280477357_<18> · C109

C109 = P49 · P61

P49 = 2168385789520885323592002973154798753361401333233_<49>

P61 = 2285082504146138317270373988148621575643144140324925007627257_<61>

Number: 75551_126
N=4954940429873285846004037959569307310974025261223476931270036000767248081276571677583695407987754373710731881
  ( 109 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=2168385789520885323592002973154798753361401333233 (pp49)
 r2=2285082504146138317270373988148621575643144140324925007627257 (pp61)
Version: Msieve-1.40
Total time: 2.30 hours.
Scaled time: 4.79 units (timescale=2.085).
Factorization parameters were as follows:
name: 75551_126
n: 4954940429873285846004037959569307310974025261223476931270036000767248081276571677583695407987754373710731881
m: 10000000000000000000000000
deg: 5
c5: 680
c0: -41
skew: 0.57
type: snfs
lss: 1
rlim: 950000
alim: 950000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 950000/950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [475000, 775001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 145579 x 145827
Total sieving time: 2.13 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,127.000,5,0,0,0,0,0,0,0,0,950000,950000,26,26,46,46,2.3,2.3,50000
total time: 2.30 hours.
 --------- CPU info (if available) ----------

(68·10¹⁴⁵-41)/9 = 7(5)₁₄₄1_<146> = 811 · 4057 · 12858849151_<11> · C130

C130 = P43 · P88

P43 = 1255612128577662110396954971095716478536029_<43>

P88 = 1422272908489788307449303177089974136622832027358183808413023957457841927697351017801047_<88>

Number: 75551_145
N=1785823114047205532864564142717380990154970562116196561108798970213154646674726763889941941960613721969295735669951892273343422363
  ( 130 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1255612128577662110396954971095716478536029 (pp43)
 r2=1422272908489788307449303177089974136622832027358183808413023957457841927697351017801047 (pp88)
Version: Msieve v. 1.42
Total time: 0.44 hours.
Scaled time: 0.30 units (timescale=0.682).
Factorization parameters were as follows:
name: 75551_145
n: 1785823114047205532864564142717380990154970562116196561108798970213154646674726763889941941960613721969295735669951892273343422363
m: 100000000000000000000000000000
deg: 5
c5: 68
c0: -41
skew: 0.90
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2280001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 329999 x 330224
Total sieving time: 0.00 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 0.44 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 8 hours.

(68·10¹³³-41)/9 = 7(5)₁₃₂1_<134> = 2734133 · 108774481 · 391631987 · 990996343417_<12> · C99

C99 = P47 · P52

P47 = 65828579710371249588047984796227037042501776203_<47>

P52 = 9943861199397675884477351880290014463455082068241051_<52>

Number: 75551_133
N=654590259593417765323944837115022385143444623850744621666113724888551685839988859703266523459509353
  ( 99 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=65828579710371249588047984796227037042501776203 (pp47)
 r2=9943861199397675884477351880290014463455082068241051 (pp52)
Version: Msieve-1.40
Total time: 4.55 hours.
Scaled time: 9.50 units (timescale=2.085).
Factorization parameters were as follows:
name: 75551_133
n: 654590259593417765323944837115022385143444623850744621666113724888551685839988859703266523459509353
m: 200000000000000000000000000
deg: 5
c5: 2125
c0: -41
skew: 0.45
type: snfs
lss: 1
rlim: 1240000
alim: 1240000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1240000/1240000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [620000, 1220001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 204050 x 204298
Total sieving time: 4.29 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,134.000,5,0,0,0,0,0,0,0,0,1240000,1240000,26,26,47,47,2.3,2.3,75000
total time: 4.55 hours.
 --------- CPU info (if available) ----------

(68·10¹³⁶-41)/9 = 7(5)₁₃₅1_<137> = 7 · 2716576406767969_<16> · 157123207681893377227_<21> · C101

C101 = P42 · P60

P42 = 181326086978689447388189009200639340728847_<42>

P60 = 139458764202539283672117846442259581514338059678176104912213_<60>

Number: 75551_136
N=25287512007730180440331763459094413686105338359406603987718124220534323648253614342533793796371708411
  ( 101 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=181326086978689447388189009200639340728847 (pp42)
 r2=139458764202539283672117846442259581514338059678176104912213 (pp60)
Version: Msieve v. 1.42
Total time: 0.16 hours.
Scaled time: 0.13 units (timescale=0.796).
Factorization parameters were as follows:
name: 75551_136
n: 25287512007730180440331763459094413686105338359406603987718124220534323648253614342533793796371708411
m: 1000000000000000000000000000
deg: 5
c5: 680
c0: -41
skew: 0.57
type: snfs
lss: 1
rlim: 1390000
alim: 1390000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1390000/1390000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [695000, 1370001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 196507 x 196734
Total sieving time: 0.00 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137.000,5,0,0,0,0,0,0,0,0,1390000,1390000,26,26,48,48,2.3,2.3,75000
total time: 0.16 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 4 hours.

Dec 14, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Dec 14, 2009

(68·10¹¹⁴-41)/9 = 7(5)₁₁₃1_<115> = 3 · 829 · 4703 · 15359 · C104

C104 = P48 · P57

P48 = 333997449831259753820683440609596186256762920339_<48>

P57 = 125924300771012935160478043723824767531313398139327105091_<57>

Number: n
N=42058395329302856748555982678684448285323587877262098896368420867466531192794508644386219233543914345849
  ( 104 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=333997449831259753820683440609596186256762920339 (pp48)
 r2=125924300771012935160478043723824767531313398139327105091 (pp57)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.12 hours.
Scaled time: 2.04 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_5_113_1
n: 42058395329302856748555982678684448285323587877262098896368420867466531192794508644386219233543914345849
m: 100000000000000000000000
deg: 5
c5: 34
c0: -205
skew: 1.43
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
qintsize: 50000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [300000, 550001)
Primes: RFBsize:49098, AFBsize:49197, largePrimes:1306149 encountered
Relations: rels:1298818, finalFF:162913
Max relations in full relation-set: 48
Initial matrix: 98361 x 162913 with sparse part having weight 8032972.
Pruned matrix : 78797 x 79352 with weight 2865906.
Total sieving time: 1.07 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000
total time: 1.12 hours.
 --------- CPU info (if available) ----------

(26·10¹⁹¹-71)/9 = 2(8)₁₉₀1_<192> = 977 · C189

C189 = P64 · P126

P64 = 2357695266025173133599952969468394108657649003264896879481391411_<64>

P126 = 125414746118265231875647176337445819091154835277185222972199907719810763192008226592232607294689716776008863337203936248400923_<126>

Number: n
N=295689753212782895485044922097122711247583304901626293642670305925167747071534174911861708176958944615034686682588422608893437962015239394973274195382690776754236324348913908791083816672353
  ( 189 digits)
SNFS difficulty: 192 digits.
Divisors found:

Mon Dec 14 17:52:20 2009  prp64 factor: 2357695266025173133599952969468394108657649003264896879481391411
Mon Dec 14 17:52:20 2009  prp126 factor: 125414746118265231875647176337445819091154835277185222972199907719810763192008226592232607294689716776008863337203936248400923
Mon Dec 14 17:52:20 2009  elapsed time 10:44:17 (Msieve 1.42 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: ~ 570.00 hours.
Scaled time: 0.00 units (timescale=0.841).
Factorization parameters were as follows:
name: KA_2_8_190_1
n: 295689753212782895485044922097122711247583304901626293642670305925167747071534174911861708176958944615034686682588422608893437962015239394973274195382690776754236324348913908791083816672353
m: 100000000000000000000000000000000000000
deg: 5
c5: 260
c0: -71
skew: 0.77
type: snfs
lss: 1
rlim: 11300000
alim: 11300000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 11300000/11300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 100000)
Primes: RFBsize:745001, AFBsize:744681, 
Relations: 
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2971555 hash collisions in 25633478 relations
Msieve: matrix is 1999084 x 1999311 (539.2 MB)

Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,192,5,0,0,0,0,0,0,0,0,11300000,11300000,28,28,56,56,2.5,2.5,100000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656)
Total of 2 processors activated (11993.08 BogoMIPS).

Dec 14, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Dec 14, 2009

(68·10¹⁴⁴-41)/9 = 7(5)₁₄₃1_<145> = 3 · 433 · 2182819 · 123348484942824364443388367321_<30> · C107

C107 = P47 · P60

P47 = 24892467603668557753000090400586736677794572369_<47>

P60 = 867836189664191492656674254659120524677089561991211694320479_<60>

Number: 75551_144
N=21602584236507048793078528427619328574849069639901071407067296022517802018044160637327267054645009844244751
  ( 107 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=24892467603668557753000090400586736677794572369
 r2=867836189664191492656674254659120524677089561991211694320479
Version: 
Total time: 6.29 hours.
Scaled time: 14.99 units (timescale=2.381).
Factorization parameters were as follows:
n: 21602584236507048793078528427619328574849069639901071407067296022517802018044160637327267054645009844244751
m: 100000000000000000000000000000
deg: 5
c5: 34
c0: -205
skew: 1.43
type: snfs
lss: 1
rlim: 2550000
alim: 2550000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2550000/2550000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1275000, 2625001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4846416
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 395311 x 395559
Total sieving time: 5.52 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2550000,2550000,26,26,49,49,2.3,2.3,75000
total time: 6.29 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673795)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672307)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

Dec 13, 2009 (5th)

By Serge Batalov / GMP-ECM, Msieve / Dec 13, 2009

(68·10¹⁰⁵-41)/9 = 7(5)₁₀₄1_<106> = 3 · 593 · 19891 · C99

C99 = P30 · P69

P30 = 894072190013208651293443978613_<30>

P69 = 238814807518177285306701902214891055326157967452167884477203413512843_<69>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4100245333
Step 1 took 7252ms
Step 2 took 4064ms
********** Factor found in step 2: 894072190013208651293443978613
Found probable prime factor of 30 digits: 894072190013208651293443978613
Probable prime cofactor has 69 digits

(68·10¹⁰⁴-41)/9 = 7(5)₁₀₃1_<105> = 29 · 251 · 3460469994043_<13> · C89

C89 = P40 · P50

P40 = 1219491298385716085076638074015566815389_<40>

P50 = 24596929157866137036858482091193628353907400534847_<50>

SNFS difficulty: 105 digits.
Divisors found:
 r1=1219491298385716085076638074015566815389 (pp40)
 r2=24596929157866137036858482091193628353907400534847 (pp50)
Version: Msieve v. 1.44 SVN157
Total time: 0.27 hours.
Scaled time: 0.65 units (timescale=2.400).
Factorization parameters were as follows:
c4: 68
c0: -41
m: 100000000000000000000000000
skew: 1
type: snfs
lss: 1
n: 29995741075027653585003958776986225169555673026120542765581718340570596425604843110360483
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [281250, 361251)
Pruned matrix : 36923 x 37154
Total sieving time: 0.24 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105.000,4,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.27 hours.

(68·10¹⁴⁹-41)/9 = 7(5)₁₄₈1_<150> = 97812977672561_<14> · C136

C136 = P32 · P105

P32 = 21519667365367654842470583146011_<32>

P105 = 358950340046869773901826232727800735939422222200866796152564338086970669249438689493918216794682673538781_<105>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2986990002
Step 1 took 9185ms
Step 2 took 4904ms
********** Factor found in step 2: 21519667365367654842470583146011
Found probable prime factor of 32 digits: 21519667365367654842470583146011
Probable prime cofactor has 105 digits

(68·10¹¹¹-41)/9 = 7(5)₁₁₀1_<112> = 3² · C111

C111 = P36 · P76

P36 = 490713461048873329138186470584317409_<36>

P76 = 1710786924501943345697249840772477005309394792793479896885711790729024795271_<76>

SNFS difficulty: 112 digits.
Divisors found:
 r1=490713461048873329138186470584317409 (pp36)
 r2=1710786924501943345697249840772477005309394792793479896885711790729024795271 (pp76)
Version: Msieve v. 1.44 SVN157
Total time: 0.55 hours.
Scaled time: 1.32 units (timescale=2.400).
Factorization parameters were as follows:
n: 839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839
m: 10000000000000000000000
deg: 5
c5: 680
c0: -41
skew: 0.57
type: snfs
lss: 1
rlim: 530000
alim: 530000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 530000/530000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [331250, 531251)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 53227 x 53452
Total sieving time: 0.52 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,112.000,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000
total time: 0.55 hours.

(68·10¹⁰⁸-41)/9 = 7(5)₁₀₇1_<109> = 3 · C109

C109 = P40 · P70

P40 = 1007951436257840014703722478246051500193_<40>

P70 = 2498650657088072640392035749835149369157792772913697850301258944896469_<70>

SNFS difficulty: 109 digits.
Divisors found:
 r1=1007951436257840014703722478246051500193 (pp40)
 r2=2498650657088072640392035749835149369157792772913697850301258944896469 (pp70)
Version: Msieve v. 1.44 SVN157
Total time: 0.52 hours.
Scaled time: 1.26 units (timescale=2.400).
Factorization parameters were as follows:
n: 2518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518517
m: 2000000000000000000000
deg: 5
c5: 2125
c0: -41
skew: 0.45
type: snfs
lss: 1
rlim: 470000
alim: 470000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 470000/470000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [293750, 493751)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 50272 x 50498
Total sieving time: 0.50 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,109.000,5,0,0,0,0,0,0,0,0,470000,470000,25,25,44,44,2.2,2.2,50000
total time: 0.52 hours.

(68·10¹³¹-41)/9 = 7(5)₁₃₀1_<132> = 1746581 · 23676437375413375371741998899_<29> · C98

C98 = P29 · P29 · P40

P29 = 34364227725649240817067390053_<29>

P29 = 53175703139543086944405198143_<29>

P40 = 9998652804651218056314025782798260070851_<40>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1271878404
Step 1 took 7553ms
Step 2 took 4068ms
********** Factor found in step 2: 53175703139543086944405198143
Found probable prime factor of 29 digits: 53175703139543086944405198143
Composite cofactor has 69 digits

Input number is 18270957934982272959259478432488575544300788306364705919210711590286972123621551472888331313643729 (98 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1343956971
Step 1 took 7161ms
Step 2 took 3960ms
********** Factor found in step 2: 34364227725649240817067390053
Found probable prime factor of 29 digits: 34364227725649240817067390053

Dec 13, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve, GMP-ECM / Dec 13, 2009

(64·10³²⁵-1)/9 = 7(1)₃₂₅_<326> = 2351 · 2693 · 559369 · 409481053 · 2055038511900243647232933024391865987_<37> · C269

C269 = P47 · P223

P47 = 12496473753502778180221449028316893490069009723_<47>

P223 = 1909452370878388370477013318447201720289355200397538489045339139889365737763581492405077795412274181233885926950655705548382204171049999441505150369579481408460023023185682075605079763890070556419189377761194302127528120161_<223>

Factor=12496473753502778180221449028316893490069009723  Method=ECM  B1=11000000  Sigma=889830216

7·10¹⁷³+3 = 7(0)₁₇₂3_<174> = 37 · 4830247 · 253488539 · 22348446469487_<14> · 4395944156853610582716741443564661893213_<40> · C105

C105 = P45 · P60

P45 = 290110443363764923642894085090214904885689697_<45>

P60 = 542132919827093529306769989453942968418390454867117966238849_<60>

Number: g105-1
N=157278421733130527374822423031190273787717697677845850752050907400924177459930910588027890386838400438753
  ( 105 digits)
Divisors found:
 r1=290110443363764923642894085090214904885689697 (pp45)
 r2=542132919827093529306769989453942968418390454867117966238849 (pp60)
Version: Msieve-1.40
Total time: 6.56 hours.
Scaled time: 12.53 units (timescale=1.911).
Factorization parameters were as follows:
name: g105-1
n: 157278421733130527374822423031190273787717697677845850752050907400924177459930910588027890386838400438753
skew: 13202.27
# norm 5.31e+014
c5: 69300
c4: 887486732
c3: 18054159829435
c2: -309959698006720573
c1: -3462703690957884986615
c0: 9494266772135327220966825
# alpha -7.07
Y1: 53466939577
Y0: -74333807980636864352
# Murphy_E 2.06e-009
# M 39261685110727373311766962481659204345999512574698899717038255884429614107360099199141019944888487217157
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2000001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 276557 x 276783
Polynomial selection time: 0.74 hours.
Total sieving time: 5.46 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 6.56 hours.
 --------- CPU info (if available) ----------

Dec 13, 2009 (3rd)

By Sinkiti Sibata / Msieve / Dec 13, 2009

(68·10¹²⁴-41)/9 = 7(5)₁₂₃1_<125> = 7 · 1783 · 4457 · C118

C118 = P54 · P65

P54 = 134509083086339760880041377384167466787761390470732873_<54>

P65 = 10097707207448267830934383611435301631763864956190969829855808911_<65>

Number: 75551_124
N=1358233337748190901605136788947794869526437745266105904453441981294278644002074637506547408746159417968092394414031303
  ( 118 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=134509083086339760880041377384167466787761390470732873 (pp54)
 r2=10097707207448267830934383611435301631763864956190969829855808911 (pp65)
Version: Msieve-1.40
Total time: 2.65 hours.
Scaled time: 5.30 units (timescale=2.000).
Factorization parameters were as follows:
name: 75551_124
n: 1358233337748190901605136788947794869526437745266105904453441981294278644002074637506547408746159417968092394414031303
m: 2000000000000000000000000
deg: 5
c5: 21250
c0: -41
skew: 0.29
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 790001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 144439 x 144679
Total sieving time: 2.45 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,125.000,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 2.65 hours.
 --------- CPU info (if available) ----------

Dec 13, 2009 (2nd)

By Jo Yeong Uk / GMP-ECM, YAFU v1.10, Msieve, GGNFS / Dec 13, 2009

(5·10¹⁹⁷+1)/3 = 1(6)₁₉₆7_<198> = 43 · 1108021631163049657_<19> · 3724929267509920843996372775497_<31> · C147

C147 = P40 · P108

P40 = 4165800965005235814760754107643841829553_<40>

P108 = 225431971171671469726015875312550232768705870586001468772728174911639271142852844564263297791187529959640337_<108>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 939104723049981509289811750930030691770734096377436694089298811115147192934297884941625038686793082121971137561628863866898691665347893823937479361 (147 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4906593635
Step 1 took 4696ms
Step 2 took 4555ms
********** Factor found in step 2: 4165800965005235814760754107643841829553
Found probable prime factor of 40 digits: 4165800965005235814760754107643841829553
Probable prime cofactor 225431971171671469726015875312550232768705870586001468772728174911639271142852844564263297791187529959640337 has 108 digits

(5·10¹⁸⁴+1)/3 = 1(6)₁₈₃7_<185> = 7 · 1181 · 53401647263_<11> · C170

C170 = P40 · C131

P40 = 2807399202518527814628463571806496953001_<40>

C131 = [13447513409050908682573458648523764418473862031020518471328356268352372416765725844067113777872896048108156781413061310462101954727_<131>]

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 37752538420426730353013726919101946495182605494565204069301466012242640645018256590170744393249454374498071184500225276512486394242670676202699669483096059890131548785727 (170 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=8330428008
Step 1 took 5523ms
Step 2 took 5085ms
********** Factor found in step 2: 2807399202518527814628463571806496953001
Found probable prime factor of 40 digits: 2807399202518527814628463571806496953001
Composite cofactor 13447513409050908682573458648523764418473862031020518471328356268352372416765725844067113777872896048108156781413061310462101954727 has 131 digits

(68·10¹⁴⁸-41)/9 = 7(5)₁₄₇1_<149> = 7 · 960499 · 25761403841_<11> · 180258765687439_<15> · 167420142728256349478014981_<27> · C92

C92 = P44 · P48

P44 = 76180334184904123317889342999934709966538801_<44>

P48 = 189738274266043670657541526420182749846309412553_<48>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 14454325141254200952289562052566937159494074260230698612511874552142164528479835960990968953 (92 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=7439269695
Step 1 took 2839ms
Step 2 took 3401ms
********** Factor found in step 2: 76180334184904123317889342999934709966538801
Found probable prime factor of 44 digits: 76180334184904123317889342999934709966538801
Probable prime cofactor 189738274266043670657541526420182749846309412553 has 48 digits

(68·10¹³²-41)/9 = 7(5)₁₃₁1_<133> = 3 · 29 · 21236947 · 6386548725541727_<16> · 782726109051719592811_<21> · C87

C87 = P31 · P57

P31 = 2737841057306658717210311098427_<31>

P57 = 298793251879729100538739305699668971422640914787280856661_<57>

12/13/09 16:02:35 v1.10 @ 조영욱-PC, starting SIQS on c87: 818048432642492312825176391448402735182696250821329401587176489745428307949924449572247
12/13/09 16:02:35 v1.10 @ 조영욱-PC, random seeds: 3158097181, 843817604
12/13/09 16:02:36 v1.10 @ 조영욱-PC, ==== sieve params ====
12/13/09 16:02:36 v1.10 @ 조영욱-PC, n = 87 digits, 290 bits
12/13/09 16:02:36 v1.10 @ 조영욱-PC, factor base: 59894 primes (max prime = 1570097)
12/13/09 16:02:36 v1.10 @ 조영욱-PC, single large prime cutoff: 172710670 (110 * pmax)
12/13/09 16:02:36 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
12/13/09 16:02:36 v1.10 @ 조영욱-PC, double large prime cutoff: 671698694327176
12/13/09 16:02:36 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base
12/13/09 16:02:36 v1.10 @ 조영욱-PC, buckets hold 1024 elements
12/13/09 16:02:36 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536
12/13/09 16:02:36 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors
12/13/09 16:02:36 v1.10 @ 조영욱-PC, using multiplier of 2
12/13/09 16:02:36 v1.10 @ 조영욱-PC, using small prime variation correction of 20 bits
12/13/09 16:02:36 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
12/13/09 16:02:36 v1.10 @ 조영욱-PC, trial factoring cutoff at 96 bits
12/13/09 16:02:36 v1.10 @ 조영욱-PC, ==== sieving started ====
12/13/09 16:28:36 v1.10 @ 조영욱-PC, sieve time = 715.4150, relation time = 331.7410, poly_time = 512.5390
12/13/09 16:28:36 v1.10 @ 조영욱-PC, 59960 relations found: 19502 full + 40458 from 551248 partial, using 275738 polys (269 A polys)
12/13/09 16:28:36 v1.10 @ 조영욱-PC, on average, sieving found 2.07 rels/poly and 365.77 rels/sec
12/13/09 16:28:36 v1.10 @ 조영욱-PC, trial division touched 13368403 sieve locations out of 325273780224
12/13/09 16:28:36 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
12/13/09 16:28:36 v1.10 @ 조영욱-PC, begin with 570750 relations
12/13/09 16:28:36 v1.10 @ 조영욱-PC, reduce to 124129 relations in 9 passes
12/13/09 16:28:37 v1.10 @ 조영욱-PC, recovered 124129 relations
12/13/09 16:28:37 v1.10 @ 조영욱-PC, recovered 99998 polynomials
12/13/09 16:28:37 v1.10 @ 조영욱-PC, attempting to build 59960 cycles
12/13/09 16:28:37 v1.10 @ 조영욱-PC, found 59960 cycles in 6 passes
12/13/09 16:28:37 v1.10 @ 조영욱-PC, distribution of cycle lengths:
12/13/09 16:28:37 v1.10 @ 조영욱-PC,    length 1 : 19502
12/13/09 16:28:37 v1.10 @ 조영욱-PC,    length 2 : 16271
12/13/09 16:28:37 v1.10 @ 조영욱-PC,    length 3 : 11173
12/13/09 16:28:37 v1.10 @ 조영욱-PC,    length 4 : 6439
12/13/09 16:28:37 v1.10 @ 조영욱-PC,    length 5 : 3497
12/13/09 16:28:37 v1.10 @ 조영욱-PC,    length 6 : 1688
12/13/09 16:28:37 v1.10 @ 조영욱-PC,    length 7 : 758
12/13/09 16:28:37 v1.10 @ 조영욱-PC,    length 9+: 632
12/13/09 16:28:37 v1.10 @ 조영욱-PC, largest cycle: 16 relations
12/13/09 16:28:37 v1.10 @ 조영욱-PC, matrix is 59894 x 59960 (13.1 MB) with weight 2945380 (49.12/col)
12/13/09 16:28:37 v1.10 @ 조영욱-PC, sparse part has weight 2945380 (49.12/col)
12/13/09 16:28:38 v1.10 @ 조영욱-PC, filtering completed in 4 passes
12/13/09 16:28:38 v1.10 @ 조영욱-PC, matrix is 53222 x 53286 (11.8 MB) with weight 2672822 (50.16/col)
12/13/09 16:28:38 v1.10 @ 조영욱-PC, sparse part has weight 2672822 (50.16/col)
12/13/09 16:28:38 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
12/13/09 16:28:38 v1.10 @ 조영욱-PC, matrix is 53174 x 53286 (8.4 MB) with weight 2131376 (40.00/col)
12/13/09 16:28:38 v1.10 @ 조영욱-PC, sparse part has weight 1674370 (31.42/col)
12/13/09 16:28:38 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
12/13/09 16:28:38 v1.10 @ 조영욱-PC, using block size 21314 for processor cache size 4096 kB
12/13/09 16:28:38 v1.10 @ 조영욱-PC, commencing Lanczos iteration
12/13/09 16:28:38 v1.10 @ 조영욱-PC, memory use: 7.5 MB
12/13/09 16:28:49 v1.10 @ 조영욱-PC, lanczos halted after 842 iterations (dim = 53171)
12/13/09 16:28:49 v1.10 @ 조영욱-PC, recovered 16 nontrivial dependencies
12/13/09 16:28:51 v1.10 @ 조영욱-PC, prp57 = 298793251879729100538739305699668971422640914787280856661
12/13/09 16:28:51 v1.10 @ 조영욱-PC, prp31 = 2737841057306658717210311098427
12/13/09 16:28:51 v1.10 @ 조영욱-PC, Lanczos elapsed time = 13.7280 seconds.
12/13/09 16:28:51 v1.10 @ 조영욱-PC, Sqrt elapsed time = 1.8880 seconds.
12/13/09 16:28:51 v1.10 @ 조영욱-PC, SIQS elapsed time = 1576.0030 seconds.
12/13/09 16:28:51 v1.10 @ 조영욱-PC, 
12/13/09 16:28:51 v1.10 @ 조영욱-PC,

(68·10¹¹⁸-41)/9 = 7(5)₁₁₇1_<119> = 7² · 491 · 21563 · 1108229 · 34549578298961779_<17> · C88

C88 = P41 · P48

P41 = 34532780382054814199867027222353498860857_<41>

P48 = 110147803244464195761021537297140065029831121169_<48>

12/13/09 16:32:06 v1.10 @ 조영욱-PC, starting SIQS on c88: 3803709899006866793179568153424366834859009484791078711335046454459323665574328638181833
12/13/09 16:32:06 v1.10 @ 조영욱-PC, random seeds: 1170905327, 2669193264
12/13/09 16:32:07 v1.10 @ 조영욱-PC, ==== sieve params ====
12/13/09 16:32:07 v1.10 @ 조영욱-PC, n = 88 digits, 291 bits
12/13/09 16:32:07 v1.10 @ 조영욱-PC, factor base: 61083 primes (max prime = 1616803)
12/13/09 16:32:07 v1.10 @ 조영욱-PC, single large prime cutoff: 177848330 (110 * pmax)
12/13/09 16:32:07 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
12/13/09 16:32:07 v1.10 @ 조영욱-PC, double large prime cutoff: 708091897184765
12/13/09 16:32:07 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base
12/13/09 16:32:07 v1.10 @ 조영욱-PC, buckets hold 1024 elements
12/13/09 16:32:07 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536
12/13/09 16:32:07 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors
12/13/09 16:32:07 v1.10 @ 조영욱-PC, using multiplier of 1
12/13/09 16:32:07 v1.10 @ 조영욱-PC, using small prime variation correction of 17 bits
12/13/09 16:32:07 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
12/13/09 16:32:07 v1.10 @ 조영욱-PC, trial factoring cutoff at 100 bits
12/13/09 16:32:07 v1.10 @ 조영욱-PC, ==== sieving started ====
12/13/09 17:08:26 v1.10 @ 조영욱-PC, sieve time = 1059.0880, relation time = 331.8220, poly_time = 788.1500
12/13/09 17:08:26 v1.10 @ 조영욱-PC, 61186 relations found: 20399 full + 40787 from 541207 partial, using 423346 polys (413 A polys)
12/13/09 17:08:26 v1.10 @ 조영욱-PC, on average, sieving found 1.33 rels/poly and 257.62 rels/sec
12/13/09 17:08:26 v1.10 @ 조영욱-PC, trial division touched 10182730 sieve locations out of 499399262208
12/13/09 17:08:26 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
12/13/09 17:08:26 v1.10 @ 조영욱-PC, begin with 561606 relations
12/13/09 17:08:27 v1.10 @ 조영욱-PC, reduce to 123607 relations in 9 passes
12/13/09 17:08:27 v1.10 @ 조영욱-PC, failed to read relation 54067
12/13/09 17:08:28 v1.10 @ 조영욱-PC, recovered 123606 relations
12/13/09 17:08:28 v1.10 @ 조영욱-PC, recovered 107337 polynomials
12/13/09 17:08:28 v1.10 @ 조영욱-PC, attempting to build 61185 cycles
12/13/09 17:08:28 v1.10 @ 조영욱-PC, found 61185 cycles in 4 passes
12/13/09 17:08:28 v1.10 @ 조영욱-PC, distribution of cycle lengths:
12/13/09 17:08:28 v1.10 @ 조영욱-PC,    length 1 : 20399
12/13/09 17:08:28 v1.10 @ 조영욱-PC,    length 2 : 17522
12/13/09 17:08:28 v1.10 @ 조영욱-PC,    length 3 : 11422
12/13/09 17:08:28 v1.10 @ 조영욱-PC,    length 4 : 6306
12/13/09 17:08:28 v1.10 @ 조영욱-PC,    length 5 : 3105
12/13/09 17:08:28 v1.10 @ 조영욱-PC,    length 6 : 1417
12/13/09 17:08:28 v1.10 @ 조영욱-PC,    length 7 : 612
12/13/09 17:08:28 v1.10 @ 조영욱-PC,    length 9+: 402
12/13/09 17:08:28 v1.10 @ 조영욱-PC, largest cycle: 14 relations
12/13/09 17:08:28 v1.10 @ 조영욱-PC, matrix is 61083 x 61185 (12.7 MB) with weight 2845786 (46.51/col)
12/13/09 17:08:28 v1.10 @ 조영욱-PC, sparse part has weight 2845786 (46.51/col)
12/13/09 17:08:28 v1.10 @ 조영욱-PC, filtering completed in 4 passes
12/13/09 17:08:28 v1.10 @ 조영욱-PC, matrix is 54561 x 54625 (11.6 MB) with weight 2598928 (47.58/col)
12/13/09 17:08:28 v1.10 @ 조영욱-PC, sparse part has weight 2598928 (47.58/col)
12/13/09 17:08:28 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
12/13/09 17:08:28 v1.10 @ 조영욱-PC, matrix is 54513 x 54625 (8.3 MB) with weight 2093151 (38.32/col)
12/13/09 17:08:28 v1.10 @ 조영욱-PC, sparse part has weight 1624518 (29.74/col)
12/13/09 17:08:28 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
12/13/09 17:08:28 v1.10 @ 조영욱-PC, using block size 21850 for processor cache size 4096 kB
12/13/09 17:08:29 v1.10 @ 조영욱-PC, commencing Lanczos iteration
12/13/09 17:08:29 v1.10 @ 조영욱-PC, memory use: 7.5 MB
12/13/09 17:08:40 v1.10 @ 조영욱-PC, lanczos halted after 863 iterations (dim = 54511)
12/13/09 17:08:40 v1.10 @ 조영욱-PC, recovered 15 nontrivial dependencies
12/13/09 17:08:41 v1.10 @ 조영욱-PC, prp48 = 110147803244464195761021537297140065029831121169
12/13/09 17:08:42 v1.10 @ 조영욱-PC, prp41 = 34532780382054814199867027222353498860857
12/13/09 17:08:42 v1.10 @ 조영욱-PC, Lanczos elapsed time = 14.0090 seconds.
12/13/09 17:08:42 v1.10 @ 조영욱-PC, Sqrt elapsed time = 1.5600 seconds.
12/13/09 17:08:42 v1.10 @ 조영욱-PC, SIQS elapsed time = 2195.5280 seconds.
12/13/09 17:08:42 v1.10 @ 조영욱-PC, 
12/13/09 17:08:42 v1.10 @ 조영욱-PC,

(68·10¹²⁰-41)/9 = 7(5)₁₁₉1_<121> = 3² · 103 · 640763489 · C110

C110 = P31 · P79

P31 = 7522650767954371464658123338883_<31>

P79 = 1690900338472253717843974265424623024998093155324732145561110307961542934925899_<79>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 12720052729742606071376255874676753059000774246060165339703830758816106561742812070410938974039927844070430817 (110 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=7746665774
Step 1 took 3463ms
Step 2 took 3776ms
********** Factor found in step 2: 7522650767954371464658123338883
Found probable prime factor of 31 digits: 7522650767954371464658123338883
Probable prime cofactor 1690900338472253717843974265424623024998093155324732145561110307961542934925899 has 79 digits

(68·10¹¹⁹-41)/9 = 7(5)₁₁₈1_<120> = 149 · 179 · 12137278595563236544438241_<26> · C91

C91 = P39 · P52

P39 = 693993837679896534923644341171069837383_<39>

P52 = 3363180443604080019397353045243304202704788434190727_<52>

12/13/09 17:12:04 v1.10 @ 조영욱-PC, starting SIQS on c91: 2334026502866772331445982526031065272433160759815583268239268004709042534418333865096547441
12/13/09 17:12:04 v1.10 @ 조영욱-PC, random seeds: 2799027576, 3905644624
12/13/09 17:12:05 v1.10 @ 조영욱-PC, ==== sieve params ====
12/13/09 17:12:05 v1.10 @ 조영욱-PC, n = 91 digits, 303 bits
12/13/09 17:12:05 v1.10 @ 조영욱-PC, factor base: 68495 primes (max prime = 1836641)
12/13/09 17:12:05 v1.10 @ 조영욱-PC, single large prime cutoff: 220396920 (120 * pmax)
12/13/09 17:12:05 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
12/13/09 17:12:05 v1.10 @ 조영욱-PC, double large prime cutoff: 1041765420895216
12/13/09 17:12:05 v1.10 @ 조영욱-PC, using 16 large prime slices of factor base
12/13/09 17:12:05 v1.10 @ 조영욱-PC, buckets hold 1024 elements
12/13/09 17:12:05 v1.10 @ 조영욱-PC, sieve interval: 11 blocks of size 65536
12/13/09 17:12:05 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors
12/13/09 17:12:05 v1.10 @ 조영욱-PC, using multiplier of 5
12/13/09 17:12:05 v1.10 @ 조영욱-PC, using small prime variation correction of 21 bits
12/13/09 17:12:05 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
12/13/09 17:12:05 v1.10 @ 조영욱-PC, trial factoring cutoff at 96 bits
12/13/09 17:12:05 v1.10 @ 조영욱-PC, ==== sieving started ====
12/13/09 18:14:06 v1.10 @ 조영욱-PC, sieve time = 1746.3940, relation time = 734.7870, poly_time = 1239.4730
12/13/09 18:14:06 v1.10 @ 조영욱-PC, 68571 relations found: 18616 full + 49955 from 860287 partial, using 569705 polys (278 A polys)
12/13/09 18:14:06 v1.10 @ 조영욱-PC, on average, sieving found 1.54 rels/poly and 236.14 rels/sec
12/13/09 18:14:06 v1.10 @ 조영욱-PC, trial division touched 32698597 sieve locations out of 821396111360
12/13/09 18:14:06 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
12/13/09 18:14:07 v1.10 @ 조영욱-PC, begin with 878903 relations
12/13/09 18:14:07 v1.10 @ 조영욱-PC, reduce to 165407 relations in 10 passes
12/13/09 18:14:08 v1.10 @ 조영욱-PC, failed to read relation 141413
12/13/09 18:14:09 v1.10 @ 조영욱-PC, recovered 165406 relations
12/13/09 18:14:09 v1.10 @ 조영욱-PC, recovered 143655 polynomials
12/13/09 18:14:09 v1.10 @ 조영욱-PC, attempting to build 68570 cycles
12/13/09 18:14:09 v1.10 @ 조영욱-PC, found 68570 cycles in 4 passes
12/13/09 18:14:09 v1.10 @ 조영욱-PC, distribution of cycle lengths:
12/13/09 18:14:09 v1.10 @ 조영욱-PC,    length 1 : 18616
12/13/09 18:14:09 v1.10 @ 조영욱-PC,    length 2 : 13854
12/13/09 18:14:09 v1.10 @ 조영욱-PC,    length 3 : 12332
12/13/09 18:14:09 v1.10 @ 조영욱-PC,    length 4 : 9209
12/13/09 18:14:09 v1.10 @ 조영욱-PC,    length 5 : 6111
12/13/09 18:14:09 v1.10 @ 조영욱-PC,    length 6 : 3763
12/13/09 18:14:09 v1.10 @ 조영욱-PC,    length 7 : 2224
12/13/09 18:14:09 v1.10 @ 조영욱-PC,    length 9+: 2461
12/13/09 18:14:09 v1.10 @ 조영욱-PC, largest cycle: 19 relations
12/13/09 18:14:09 v1.10 @ 조영욱-PC, matrix is 68495 x 68570 (17.5 MB) with weight 4049507 (59.06/col)
12/13/09 18:14:09 v1.10 @ 조영욱-PC, sparse part has weight 4049507 (59.06/col)
12/13/09 18:14:09 v1.10 @ 조영욱-PC, filtering completed in 3 passes
12/13/09 18:14:09 v1.10 @ 조영욱-PC, matrix is 64145 x 64208 (16.6 MB) with weight 3838689 (59.79/col)
12/13/09 18:14:09 v1.10 @ 조영욱-PC, sparse part has weight 3838689 (59.79/col)
12/13/09 18:14:10 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
12/13/09 18:14:10 v1.10 @ 조영욱-PC, matrix is 64097 x 64208 (11.3 MB) with weight 3041038 (47.36/col)
12/13/09 18:14:10 v1.10 @ 조영욱-PC, sparse part has weight 2315710 (36.07/col)
12/13/09 18:14:10 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
12/13/09 18:14:10 v1.10 @ 조영욱-PC, using block size 25683 for processor cache size 4096 kB
12/13/09 18:14:10 v1.10 @ 조영욱-PC, commencing Lanczos iteration
12/13/09 18:14:10 v1.10 @ 조영욱-PC, memory use: 9.9 MB
12/13/09 18:14:28 v1.10 @ 조영욱-PC, lanczos halted after 1016 iterations (dim = 64097)
12/13/09 18:14:28 v1.10 @ 조영욱-PC, recovered 18 nontrivial dependencies
12/13/09 18:14:30 v1.10 @ 조영욱-PC, prp52 = 3363180443604080019397353045243304202704788434190727
12/13/09 18:14:32 v1.10 @ 조영욱-PC, prp39 = 693993837679896534923644341171069837383
12/13/09 18:14:32 v1.10 @ 조영욱-PC, Lanczos elapsed time = 22.0890 seconds.
12/13/09 18:14:32 v1.10 @ 조영욱-PC, Sqrt elapsed time = 3.6660 seconds.
12/13/09 18:14:32 v1.10 @ 조영욱-PC, SIQS elapsed time = 3747.7380 seconds.
12/13/09 18:14:32 v1.10 @ 조영욱-PC, 
12/13/09 18:14:32 v1.10 @ 조영욱-PC,

2·10¹⁹⁷-1 = 1(9)₁₉₇_<198> = 3489781 · 1544884849_<10> · 99635152957880897351925251119_<29> · C153

C153 = P73 · P81

P73 = 3106715592670622545052652201311870702958135715650492536479382258704707479_<73>

P81 = 119845468875413674461665854674334297323102627345704299514768319724130736097956971_<81>

Number: 19999_197
N=372325786866169441250327851059588119485775841500993243856730119954248515508380134433190793829593497441299946322830257214959074704367324446826072083886109
  ( 153 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=3106715592670622545052652201311870702958135715650492536479382258704707479
 r2=119845468875413674461665854674334297323102627345704299514768319724130736097956971
Version: 
Total time: 263.39 hours.
Scaled time: 628.18 units (timescale=2.385).
Factorization parameters were as follows:
n: 372325786866169441250327851059588119485775841500993243856730119954248515508380134433190793829593497441299946322830257214959074704367324446826072083886109
m: 2000000000000000000000000000000000000000
deg: 5
c5: 25
c0: -4
skew: 0.69
type: snfs
lss: 1
rlim: 14000000
alim: 14000000
lpbr: 29
lpba: 29
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 14000000/14000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 55/55
Sieved rational special-q in [7000000, 13000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 33793998
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2655738 x 2655985
Total sieving time: 232.12 hours.
Total relation processing time: 10.63 hours.
Matrix solve time: 20.22 hours.
Time per square root: 0.41 hours.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,14000000,14000000,29,29,55,55,2.5,2.5,100000
total time: 263.39 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673795)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672307)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

Dec 13, 2009

Factorizations of 755...551 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Dec 12, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 12, 2009

(17·10¹⁸⁴+7)/3 = 5(6)₁₈₃9_<185> = 61 · 39041 · 1909371924869851302649714847256763860533_<40> · C140

C140 = P37 · P103

P37 = 5124172426862591527993743217843926217_<37>

P103 = 2431994737114378672034241234074769137183424168356159641033087179976549773766608679855816455013117557029_<103>

********** Factor found in step 2: 5124172426862591527993743217843926217
Found probable prime factor of 37 digits: 5124172426862591527993743217843926217
Probable prime cofactor 2431994737114378672034241234074769137183424168356159641033087179976549773766608679855816455013117557029 has 103 digits

7·10¹⁷³+3 = 7(0)₁₇₂3_<174> = 37 · 4830247 · 253488539 · 22348446469487_<14> · C144

C144 = P40 · C105

P40 = 4395944156853610582716741443564661893213_<40>

C105 = [157278421733130527374822423031190273787717697677845850752050907400924177459930910588027890386838400438753_<105>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1786388023
Step 1 took 42364ms
********** Factor found in step 1: 4395944156853610582716741443564661893213
Found probable prime factor of 40 digits: 4395944156853610582716741443564661893213
Composite cofactor 157278421733130527374822423031190273787717697677845850752050907400924177459930910588027890386838400438753 has 105 digits

Dec 12, 2009 (2nd)

By Sinkiti Sibata / Msieve / Dec 12, 2009

(61·10¹⁶⁶-43)/9 = 6(7)₁₆₅3_<167> = 3 · 19 · 613 · 4757101 · 6663407 · C149

C149 = P55 · P95

P55 = 1467058864327318536191200519538686958267945548946391343_<55>

P95 = 41712454180418038540092264032930234816532137293588332276077015671466940950225200778451694516853_<95>

Number: 67773_166
N=61194625658229398109012930480802869719547151981450925484771163997284152763997732120947147166743515730911733207086500287913412099184316954874246803579
  ( 149 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=1467058864327318536191200519538686958267945548946391343 (pp55)
 r2=41712454180418038540092264032930234816532137293588332276077015671466940950225200778451694516853 (pp95)
Version: Msieve-1.40
Total time: 46.34 hours.
Scaled time: 152.30 units (timescale=3.287).
Factorization parameters were as follows:
name: 67773_166
n: 61194625658229398109012930480802869719547151981450925484771163997284152763997732120947147166743515730911733207086500287913412099184316954874246803579
m: 1000000000000000000000000000000000
deg: 5
c5: 610
c0: -43
skew: 0.59
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 4600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 836871 x 837119
Total sieving time: 44.68 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.33 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,167.000,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 46.34 hours.
 --------- CPU info (if available) ----------

Dec 12, 2009

According to the progress report from Robert Backstrom, c241 has finally started the Lanczos step today. Msieve requires estimated 515 hours, so it will end early in the new year.

Dec 11, 2009 (4th)

By Lionel Debroux / ggnfs + msieve / Dec 11, 2009

(22·10¹⁶⁶-7)/3 = 7(3)₁₆₅1_<167> = 409 · 419 · 3011 · 115597 · 25852643 · 794728813 · 8492728860754387_<16> · C121

C121 = P43 · P79

P43 = 1104239814695922526636398039119065670197823_<43>

P79 = 6380757027338811217564960531118647618150226218080350862755796008818598741511437_<79>

Number: 73331_166
N=7045885957488314366183623370458357518983247288396398217078479943464251420227362790070367387651860604343780717909807001651
  ( 121 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=1104239814695922526636398039119065670197823 (pp43)
 r2=6380757027338811217564960531118647618150226218080350862755796008818598741511437 (pp79)
Version: Msieve v. 1.44
Total time: 54.51 hours.
Scaled time: 81.55 units (timescale=1.496).
Factorization parameters were as follows:
n: 7045885957488314366183623370458357518983247288396398217078479943464251420227362790070367387651860604343780717909807001651
m: 1000000000000000000000000000000000
deg: 5
c5: 220
c0: -7
skew: 0.50
type: snfs
lss: 1
rlim: 4300000
alim: 4300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4300000/4300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2150000, 3850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 750134 x 750359
Total sieving time: 52.28 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.38 hours.
Time per square root: 0.76 hours.
Prototype def-par.txt line would be:
snfs,167.000,5,0,0,0,0,0,0,0,0,4300000,4300000,27,27,51,51,2.4,2.4,100000
total time: 54.51 hours.
 --------- CPU info (if available) ----------
[    0.030572] CPU0: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.102093] CPU1: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.000000] Memory: 2051108k/2096800k available (7372k kernel code, 452k absent, 44524k reserved, 3466k data, 772k init)
[    0.001009] Calibrating delay loop (skipped), value calculated using timer frequency.. 3989.54 BogoMIPS (lpj=1994771)
[    0.001999] Calibrating delay using timer specific routine.. 5505.93 BogoMIPS (lpj=2752967)
[    0.103024] Total of 2 processors activated (9495.47 BogoMIPS).

Dec 11, 2009 (3rd)

By Dmitry Domanov / ECMNET, GMP-ECM / Dec 11, 2009

(52·10¹⁸⁸-43)/9 = 5(7)₁₈₇3_<189> = 3 · 173 · 2267 · C183

C183 = P32 · P152

P32 = 31978900502670207700576552297793_<32>

P152 = 15356011491672614427520253819593535366479447274276240103542314539618926993708539558051992434641622926845696534507596506662824902117550235921708729961457_<152>

Factor=31978900502670207700576552297793  Method=ECM  B1=11000000  Sigma=590706511

Dec 11, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 11, 2009

(17·10¹⁸⁴+7)/3 = 5(6)₁₈₃9_<185> = 61 · 39041 · C179

C179 = P40 · C140

P40 = 1909371924869851302649714847256763860533_<40>

C140 = [12461960374196436055720590007683928054218374877066989312361949971133799082404460422570765649635829025773078205178509197929750407572765729293_<140>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1534556179
Step 1 took 21297ms
Step 2 took 8517ms
********** Factor found in step 2: 1909371924869851302649714847256763860533
Found probable prime factor of 40 digits: 1909371924869851302649714847256763860533
Composite cofactor 12461960374196436055720590007683928054218374877066989312361949971133799082404460422570765649635829025773078205178509197929750407572765729293 has 140 digits

Dec 11, 2009

By Erik Branger / GMP-ECM / Dec 11, 2009

(23·10¹⁸⁴-41)/9 = 2(5)₁₈₃1_<185> = 3² · 97 · 1061 · C179

C179 = P41 · C139

P41 = 19040340637648210868379117961880200224083_<41>

C139 = [1449042038886457977275736047557847119439134383903865583802730356524462608737631889822415710776695664897224875214083590924322735359677843449_<139>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 
27590254018670444852060458163758234041407213315968267369234491608184324969047933507967645508900436009983833310721320800640381791535957838253215434180030246115862032895499993582267 (179 digits)
Run 585 out of 1000:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1385992420
Step 1 took 66581ms
Step 2 took 20826ms
********** Factor found in step 2: 19040340637648210868379117961880200224083
Found probable prime factor of 41 digits: 19040340637648210868379117961880200224083
Composite cofactor 
1449042038886457977275736047557847119439134383903865583802730356524462608737631889822415710776695664897224875214083590924322735359677843449 has 139 digits

Dec 10, 2009 (4th)

By yoshida / GGNFS / Dec 10, 2009

(59·10¹⁷⁰+13)/9 = 6(5)₁₆₉7_<171> = 3 · 31 · 73 · 229 · 2371 · 136027 · 233155008560892980603136314014073_<33> · C124

C124 = P44 · P80

P44 = 60584128360032301920436560271643813086991257_<44>

P80 = 92556713209596906998848833423411539743687317470367214287086444809227713384971181_<80>

N=5607467793672916357063206022743587336819544589797022881608229298842144002627748832647796629860992889557912488547520943964517
  ( 124 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=60584128360032301920436560271643813086991257 (pp44)
 r2=92556713209596906998848833423411539743687317470367214287086444809227713384971181 (pp80)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 257.03 hours.
Scaled time: 594.77 units (timescale=2.314).
Factorization parameters were as follows:
n: 5607467793672916357063206022743587336819544589797022881608229298842144002627748832647796629860992889557912488547520943964517
m: 10000000000000000000000000000000000
deg: 5
c5: 59
c0: 13
skew: 0.74
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 9500001)
Primes: RFBsize:412849, AFBsize:413701, largePrimes:7914450 encountered
Relations: rels:9994565, finalFF:2581166
Max relations in full relation-set: 32
Initial matrix: 826617 x 2581166 with sparse part having weight 203256814.
Pruned matrix : 465392 x 469589 with weight 138232198.
Total sieving time: 253.71 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 3.07 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 257.03 hours.
 --------- CPU info (if available) ----------
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 32944636k/35127296k available (2460k kernel code, 603560k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5988.95 BogoMIPS (lpj=2994477)
Calibrating delay using timer specific routine.. 5985.01 BogoMIPS (lpj=2992505)
Calibrating delay using timer specific routine.. 5984.97 BogoMIPS (lpj=2992487)
Calibrating delay using timer specific routine.. 5985.05 BogoMIPS (lpj=2992527)
Calibrating delay using timer specific routine.. 5985.21 BogoMIPS (lpj=2992605)
Calibrating delay using timer specific routine.. 5985.02 BogoMIPS (lpj=2992513)
Calibrating delay using timer specific routine.. 5985.05 BogoMIPS (lpj=2992529)
Calibrating delay using timer specific routine.. 5985.00 BogoMIPS (lpj=2992504)

Dec 10, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Dec 10, 2009

(47·10¹⁷²+7)/9 = 5(2)₁₇₁3_<173> = 78889 · 1367259031_<10> · 100846772862529249243_<21> · 288949754807407778795535378837359651_<36> · C104

C104 = P47 · P58

P47 = 12289616516746838106901363670752368934979810153_<47>

P58 = 1351964941985702375077635494737512490391884094055273661193_<58>

N=16615130681090168682484149882073393686384044650429952415437022192442172356711464024014618654692383492529
  ( 104 digits)
Divisors found:
 r1=12289616516746838106901363670752368934979810153 (pp47)
 r2=1351964941985702375077635494737512490391884094055273661193 (pp58)
Version: Msieve-1.40
Total time: 6.33 hours.
Scaled time: 12.01 units (timescale=1.899).
Factorization parameters were as follows:
n: 16615130681090168682484149882073393686384044650429952415437022192442172356711464024014618654692383492529
skew: 5197.87
# norm 1.04e+013
c5: 15960
c4: -184339309
c3: -1695036569856
c2: 5342536944215639
c1: 17116190166354377245
c0: -13677862918281503944854
# alpha -3.45
Y1: 10092556199
Y0: -63605450663550372257
# Murphy_E 2.21e-009
# M 1859835780868646606837778153991172769667025259596543365334539620061107358998462310498137234116573516495
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 274907 x 275135
Polynomial selection time: 0.64 hours.
Total sieving time: 5.47 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 6.33 hours.
 --------- CPU info (if available) ----------

(19·10¹⁷⁷-7)/3 = 6(3)₁₇₆1_<178> = 13 · 47317 · C173

C173 = P38 · C135

P38 = 52374708010720593180983888284200480121_<38>

C135 = [196584909774591899891929740271017992127607138646378613009944940506168200305296645686623671326556823641070931963952390382765248092716091_<135>]

Factor=52374708010720593180983888284200480121  Method=ECM  B1=11000000  Sigma=2413859118

(16·10¹⁸³-1)/3 = 5(3)₁₈₃_<184> = 53 · 9923 · C179

C179 = P35 · P144

P35 = 18627864608408854457971430690578723_<35>

P144 = 544398342498957622062084117964445373269473871781632235659942268003161698603526565536948832419130917001986223882572935713623771914211976408369209_<144>

Factor=18627864608408854457971430690578723  Method=ECM  B1=11000000  Sigma=1934621045

Dec 10, 2009 (2nd)

By Markus Tervooren / GMP-ECM / Dec 10, 2009

(26·10¹⁶⁶-11)/3 = 8(6)₁₆₅3_<167> = 17119841910469978219460966052115200873127_<41> · C127

C127 = P32 · P95

P32 = 96207769849890958637787012089581_<32>

P95 = 52618952197183905165622175960078885504996122246347121928682073766419239235963408943829919813349_<95>

$> echo 5062352042729083324072603410562818478047593167544336937763961405378553912981858058946033962596449849227561328894684469987616769 | ecm -c 0 -I 1 10
GMP-ECM 6.2 [powered by GMP 4.3.0] [ECM]
Input number is 5062352042729083324072603410562818478047593167544336937763961405378553912981858058946033962596449849227561328894684469987616769 (127 digits)
Using B1=10, B2=84, polynomial x^1, sigma=1268245291
Step 1 took 0ms
Step 2 took 0ms
Run 2 out of 0:
Using B1=276, B2=276-7686, polynomial x^1, sigma=1621996872
Step 1 took 0ms
Step 2 took 4ms
Run 3 out of 0:
Using B1=542, B2=542-24246, polynomial x^1, sigma=1027277030
Step 1 took 0ms
Step 2 took 4ms
Run 4 out of 0:
Using B1=808, B2=808-42486, polynomial x^1, sigma=2444484533
Step 1 took 4ms
Step 2 took 4ms
Run 5 out of 0:
Using B1=1074, B2=1074-51606, polynomial x^1, sigma=801533018
Step 1 took 4ms
Step 2 took 8ms
Run 6 out of 0:
Using B1=1340, B2=1340-108636, polynomial x^1, sigma=1628484574
Step 1 took 4ms
Step 2 took 8ms
Run 7 out of 0:
Using B1=1606, B2=1606-109146, polynomial x^1, sigma=3394506902
Step 1 took 4ms
Step 2 took 8ms
Run 8 out of 0:
Using B1=1872, B2=1872-147396, polynomial x^1, sigma=1216102578
Step 1 took 8ms
Step 2 took 8ms
Run 9 out of 0:
Using B1=2138, B2=2138-147906, polynomial x^1, sigma=356966585
Step 1 took 12ms
Step 2 took 8ms
Run 10 out of 0:
Using B1=2540, B2=2540-186156, polynomial x^1, sigma=3077459549
Step 1 took 8ms
Step 2 took 12ms
Run 11 out of 0:
Using B1=2950, B2=2950-224406, polynomial x^1, sigma=485575138
Step 1 took 8ms
Step 2 took 12ms
Run 12 out of 0:
Using B1=3368, B2=3368-294786, polynomial x^1, sigma=2073073101
Step 1 took 16ms
Step 2 took 12ms
Run 13 out of 0:
Using B1=3794, B2=3794-446766, polynomial x^1, sigma=4253881041
Step 1 took 16ms
Step 2 took 12ms
Run 14 out of 0:
Using B1=4228, B2=4228-447786, polynomial x^1, sigma=1490636614
Step 1 took 20ms
Step 2 took 12ms
Run 15 out of 0:
Using B1=4671, B2=4671-447786, polynomial x^1, sigma=4178903842
Step 1 took 20ms
Step 2 took 16ms
********** Factor found in step 2: 96207769849890958637787012089581
Found probable prime factor of 32 digits: 96207769849890958637787012089581
Probable prime cofactor 52618952197183905165622175960078885504996122246347121928682073766419239235963408943829919813349 has 95 digits

After the composite number passed B1=1e6 (level 35) 150 times and B1=11e6 (level 45) 117 times, quite small B1=4671 found P32.

echo 5062352042729083324072603410562818478047593167544336937763961405378553912981858058946033962596449849227561328894684469987616769 | ecm -sigma 4178903842 4671

Dec 10, 2009

By Jo Yeong Uk / GMP-ECM / Dec 10, 2009

5·10¹⁸⁵-1 = 4(9)₁₈₅_<186> = 17 · 31 · 87631 · 30963646453769_<14> · C165

C165 = P38 · P128

P38 = 13467097731105253924325838530156698063_<38>

P128 = 25964233709024130179916331896236768142386809082711053887820914535009226635473159313679197722834392092837158149045577065290385641_<128>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 349662872872685415260187866710169543054711722129687259296757512768829622544293685012492705071389202665843507861957179339289258414384928449524545789244775692467713383 (165 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=575025177
Step 1 took 5506ms
Step 2 took 5102ms
********** Factor found in step 2: 13467097731105253924325838530156698063
Found probable prime factor of 38 digits: 13467097731105253924325838530156698063
Probable prime cofactor 25964233709024130179916331896236768142386809082711053887820914535009226635473159313679197722834392092837158149045577065290385641 has 128 digits

Dec 9, 2009 (5th)

By Sinkiti Sibata / Msieve / Dec 9, 2009

10¹⁹²-3 = (9)₁₉₁7_<192> = 3373 · 1103279 · 30864312787215673925304239_<26> · 728214226699773901950646153594957_<33> · C125

C125 = P43 · P82

P43 = 4461889850767293887261615958368082112572949_<43>

P82 = 2679561266563623732221821991758971715091712588908370052804206440102760114201548833_<82>

Number: 99997_192
N=11955907219789388090396927468596102846705760576688639467787460136053127454112956393569754103555054189544180606793438498318517
  ( 125 digits)
Divisors found:
 r1=4461889850767293887261615958368082112572949 (pp43)
 r2=2679561266563623732221821991758971715091712588908370052804206440102760114201548833 (pp82)
Version: Msieve-1.40
Total time: 74.34 hours.
Scaled time: 245.70 units (timescale=3.305).
Factorization parameters were as follows:
name: 99997_192
# Murphy_E = 1.580662e-10, selected by Jeff Gilchrist
n: 11955907219789388090396927468596102846705760576688639467787460136053127454112956393569754103555054189544180606793438498318517
Y0: -965904624584214002999227
Y1: 29757583127591
c0: -10062534597856893819796369537440
c1: 188270216174299077687152598
c2: -308953642659933419159
c3: -3444590731912942
c4: 12448625118
c5: 14220
skew: 302426.48
type: gnfs
# selected mechanically
rlim: 6800000
alim: 6800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6800000/6800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3400000, 6800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 923005 x 923252
Total sieving time: 72.48 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.64 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,124,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6800000,6800000,27,27,52,52,2.5,2.5,100000
total time: 74.34 hours.
 --------- CPU info (if available) ----------

Dec 9, 2009 (4th)

By yoshida / GGNFS / Dec 9, 2009

(7·10¹⁷⁵+17)/3 = 2(3)₁₇₄9_<176> = 210011 · 53664942222963223_<17> · C154

C154 = P62 · P92

P62 = 26604037908536981465562648809727926589746663642702901812957027_<62>

P92 = 77820948230221907813638916631944197307795299733591181906080936319588979797488625278156383469_<92>

Number: 23339_175
N=2070351456795117553558270718726790833044380782036310828359575179480567729028641533439203231515578311502363046326991595489940095893568406641805115030186663
  ( 154 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=26604037908536981465562648809727926589746663642702901812957027 (pp62)
 r2=77820948230221907813638916631944197307795299733591181906080936319588979797488625278156383469 (pp92)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 340.07 hours.
Scaled time: 786.91 units (timescale=2.314).
Factorization parameters were as follows:
n: 2070351456795117553558270718726790833044380782036310828359575179480567729028641533439203231515578311502363046326991595489940095893568406641805115030186663
m: 100000000000000000000000000000000000
deg: 5
c5: 7
c0: 17
skew: 1.19
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 13400001)
Primes: RFBsize:501962, AFBsize:502556, largePrimes:7532379 encountered
Relations: rels:8852741, finalFF:1897452
Max relations in full relation-set: 32
Initial matrix: 1004583 x 1897452 with sparse part having weight 145358172.
Pruned matrix : 506211 x 511297 with weight 316523678.
Total sieving time: 328.63 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 11.18 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 340.07 hours.
 --------- CPU info (if available) ----------
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 32944636k/35127296k available (2460k kernel code, 603560k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5988.95 BogoMIPS (lpj=2994477)
Calibrating delay using timer specific routine.. 5985.01 BogoMIPS (lpj=2992505)
Calibrating delay using timer specific routine.. 5984.97 BogoMIPS (lpj=2992487)
Calibrating delay using timer specific routine.. 5985.05 BogoMIPS (lpj=2992527)
Calibrating delay using timer specific routine.. 5985.21 BogoMIPS (lpj=2992605)
Calibrating delay using timer specific routine.. 5985.02 BogoMIPS (lpj=2992513)
Calibrating delay using timer specific routine.. 5985.05 BogoMIPS (lpj=2992529)
Calibrating delay using timer specific routine.. 5985.00 BogoMIPS (lpj=2992504)

Dec 9, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 9, 2009

(13·10¹⁸⁸+11)/3 = 4(3)₁₈₇7_<189> = 1543 · 142860607 · 255207723123768259319_<21> · 106516169444251311571441538317907_<33> · C125

C125 = P41 · P85

P41 = 30942293088057381698511237526930241499691_<41>

P85 = 2337124414249729105204220797351745040236609507852691754539000092085018567123113821079_<85>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1831739677
Step 1 took 34209ms
Step 2 took 13653ms
********** Factor found in step 2: 30942293088057381698511237526930241499691
Found probable prime factor of 41 digits: 30942293088057381698511237526930241499691
Probable prime cofactor 2337124414249729105204220797351745040236609507852691754539000092085018567123113821079 has 85 digits

(65·10¹⁷²+7)/9 = 7(2)₁₇₁3_<173> = 257 · 809 · 6563 · 7321 · 1123872308281744993_<19> · C142

C142 = P38 · P40 · P66

P38 = 16755539813811419577324028768476793049_<38>

P40 = 2033261506695711968567171206558801965737_<40>

P66 = 188819897611386026982238522704043786485667381321427555249205867653_<66>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3638956364
Step 1 took 42470ms
Step 2 took 14819ms
********** Factor found in step 2: 16755539813811419577324028768476793049
Found probable prime factor of 38 digits: 16755539813811419577324028768476793049
Composite cofactor
383920229511456818641132015114512787486199837707317822637944375746076797851094768115322811270691062605261
has 105 digits
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2005714314
Step 1 took 26762ms
Step 2 took 11953ms
********** Factor found in step 2: 2033261506695711968567171206558801965737
Found probable prime factor of 40 digits: 2033261506695711968567171206558801965737
Probable prime cofactor 188819897611386026982238522704043786485667381321427555249205867653 has 66 digits

(14·10¹⁸⁹-11)/3 = 4(6)₁₈₈3_<190> = 47 · 48313 · 543227 · 24889499 · 158031581 · 40854831527_<11> · 1413907600387_<13> · 256254713349673_<15> · C125

C125 = P38 · P88

P38 = 56028649144846154576918785107849174457_<38>

P88 = 1159730457435645187988018725993250387128541623197163551356290007640701804261433189154169_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=314256342
Step 1 took 34298ms
********** Factor found in step 1: 56028649144846154576918785107849174457
Found probable prime factor of 38 digits: 56028649144846154576918785107849174457
Probable prime cofactor 1159730457435645187988018725993250387128541623197163551356290007640701804261433189154169 has 88 digits

Dec 9, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve / Dec 9, 2009

(58·10¹⁹⁷+41)/9 = 6(4)₁₉₆9_<198> = 13 · 933299923 · 8436592305409_<13> · 111772795484434550519_<21> · 5087832120754440156018956894208167_<34> · C122

C122 = P56 · P66

P56 = 64694662489083286414695388018448613862933185715531862603_<56>

P66 = 171126198208668315251298457671101379137801125215383625298494188981_<66>

N=11070951636149765536840257253607829444595086747622399008620240727882623901740891490497776510088174513384413377746808577543
  ( 122 digits)
Divisors found:
 r1=64694662489083286414695388018448613862933185715531862603 (pp56)
 r2=171126198208668315251298457671101379137801125215383625298494188981 (pp66)
Version: Msieve-1.40
Total time: 55.80 hours.
Scaled time: 52.29 units (timescale=0.937).
Factorization parameters were as follows:
# Murphy_E = 2.621397e-10, selected by Jeff Gilchrist
n: 11070951636149765536840257253607829444595086747622399008620240727882623901740891490497776510088174513384413377746808577543
Y0: -274680933477785405343845
Y1: 8570518787149
c0: 1350928898463077874422589647232
c1: 19642762067379607582761780
c2: -384503260141907345357
c3: -122711510581868
c4: 4766478592
c5: 7080
skew: 245402.32
type: gnfs
# selected mechanically
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
qintsize: 200000Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2800000, 4800001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 695403 x 695633
Total sieving time: 54.46 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.81 hours.
Time per square root: 0.38 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5600000,5600000,27,27,52,52,2.5,2.5,100000
total time: 55.80 hours.
 --------- CPU info (if available) ----------

(62·10¹⁸³-71)/9 = 6(8)₁₈₂1_<184> = 7 · 307 · 317 · C179

C179 = P45 · P134

P45 = 158335949136530495728829921281768556200044049_<45>

P134 = 63866625867023175938335010351970045440329405009221671936038865883820121592393893151960105634735076570416240607359428554200004909797393_<134>

N=10112382824802804457342625634531634387777586947327696821629147279842416454999814878153126593821627679353303332176933426432496501033991143836086755763283471130859616150258265364257
  ( 179 digits)
SNFS difficulty: 184 digits.
Divisors found:
 r1=158335949136530495728829921281768556200044049 (pp45)
 r2=63866625867023175938335010351970045440329405009221671936038865883820121592393893151960105634735076570416240607359428554200004909797393 (pp134)
Version: Msieve-1.40
Total time: 253.94 hours.
Scaled time: 491.11 units (timescale=1.934).
Factorization parameters were as follows:
n: 10112382824802804457342625634531634387777586947327696821629147279842416454999814878153126593821627679353303332176933426432496501033991143836086755763283471130859616150258265364257
m: 1000000000000000000000000000000000000
deg: 5
c5: 62000
c0: -71
skew: 0.26
type: snfs
lss: 1
rlim: 8400000
alim: 8400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 300000Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4200000, 8400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1833346 x 1833571
Total sieving time: 248.73 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 4.66 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
snfs,184.000,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,54,54,2.5,2.5,100000
total time: 253.94 hours.
 --------- CPU info (if available) ----------

Dec 9, 2009

By Wataru Sakai / Msieve / Dec 9, 2009

(44·10¹⁹⁷-71)/9 = 4(8)₁₉₆1_<198> = 37 · 73 · C195

C195 = P80 · P115

P80 = 52038938123538386499558426521065668429891280877444695007719721706031040955707989_<80>

P115 = 3478220871825907204600143572083807398370519405902086642073165507604921729279187962113161108837292484759222844466529_<115>

Number: 48881_197
N=181002920728948126208400181002920728948126208400181002920728948126208400181002920728948126208400181002920728948126208400181002920728948126208400181002920728948126208400181002920728948126208400181
  ( 195 digits)
SNFS difficulty: 198 digits.
Divisors found:
 r1=52038938123538386499558426521065668429891280877444695007719721706031040955707989
 r2=3478220871825907204600143572083807398370519405902086642073165507604921729279187962113161108837292484759222844466529
Version: 
Total time: 954.48 hours.
Scaled time: 1922.33 units (timescale=2.014).
Factorization parameters were as follows:
n: 181002920728948126208400181002920728948126208400181002920728948126208400181002920728948126208400181002920728948126208400181002920728948126208400181002920728948126208400181002920728948126208400181
m: 2000000000000000000000000000000000000000
deg: 5
c5: 275
c0: -142
skew: 0.88
type: snfs
lss: 1
rlim: 14500000
alim: 14500000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 14500000/14500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [7250000, 17750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2286051 x 2286299
Total sieving time: 954.48 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,198,5,0,0,0,0,0,0,0,0,14500000,14500000,28,28,55,55,2.5,2.5,100000
total time: 954.48 hours.
 --------- CPU info (if available) ----------

(8·10¹⁷²-53)/9 = (8)₁₇₁3_<172> = 3 · 7 · 17 · 19 · 739 · 1530721 · 18210329 · C152

C152 = P50 · P103

P50 = 19072250153851773845855631722459189802972333856393_<50>

P103 = 3335534640447268827772499537443122415609424726507539563699561628396675540925992881380483170481360493007_<103>

Number: 88883_172
N=63616151059448344057594636891100636407831511205135552367798619650654780752786002498411683774793207019413490574485517559732167544208283224904732018743751
  ( 152 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=19072250153851773845855631722459189802972333856393
 r2=3335534640447268827772499537443122415609424726507539563699561628396675540925992881380483170481360493007
Version: 
Total time: 84.29 hours.
Scaled time: 169.68 units (timescale=2.013).
Factorization parameters were as follows:
n: 63616151059448344057594636891100636407831511205135552367798619650654780752786002498411683774793207019413490574485517559732167544208283224904732018743751
m: 20000000000000000000000000000000000
deg: 5
c5: 25
c0: -53
skew: 1.16
type: snfs
lss: 1
rlim: 5300000
alim: 5300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2650000, 5550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 749176 x 749424
Total sieving time: 84.29 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.4,2.4,100000
total time: 84.29 hours.
 --------- CPU info (if available) ----------

Dec 8, 2009 (5th)

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 8, 2009

(47·10¹⁷²+7)/9 = 5(2)₁₇₁3_<173> = 78889 · 1367259031_<10> · 100846772862529249243_<21> · C139

C139 = P36 · C104

P36 = 288949754807407778795535378837359651_<36>

C104 = [16615130681090168682484149882073393686384044650429952415437022192442172356711464024014618654692383492529_<104>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=240630566
Step 1 took 42471ms
Step 2 took 14596ms
********** Factor found in step 2: 288949754807407778795535378837359651
Found probable prime factor of 36 digits: 288949754807407778795535378837359651
Composite cofactor 16615130681090168682484149882073393686384044650429952415437022192442172356711464024014618654692383492529 has 104 digits

Dec 8, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve / Dec 8, 2009

(64·10¹⁷⁸+17)/9 = 7(1)₁₇₇3_<179> = 7 · 23 · 7561 · C173

C173 = P35 · P64 · P75

P35 = 31770331922672269514195751652912853_<35>

P64 = 2820691606995952582774864978273833453721249485749317742014394563_<64>

P75 = 651860990166698295158172796521430338071271034227790252159666126584151543327_<75>

N=58416071940852996958987079916563594245980403781016766416673261293538114524526489817485372478673341798187258012562923921554882492876662039931218726294141899393102650090741153
  ( 173 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=31770331922672269514195751652912853 (pp35)
 r2=2820691606995952582774864978273833453721249485749317742014394563 (pp64)
 r3=651860990166698295158172796521430338071271034227790252159666126584151543327 (pp75)
Version: Msieve-1.40
Total time: 180.40 hours.
Scaled time: 168.85 units (timescale=0.936).
Factorization parameters were as follows:
n: 58416071940852996958987079916563594245980403781016766416673261293538114524526489817485372478673341798187258012562923921554882492876662039931218726294141899393102650090741153
m: 400000000000000000000000000000000000
deg: 5
c5: 125
c0: 34
skew: 0.77
type: snfs
lss: 1
rlim: 7000000
alim: 7000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 300000Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3500000, 5900001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1326304 x 1326539
Total sieving time: 175.81 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 3.12 hours.
Time per square root: 1.19 hours.
Prototype def-par.txt line would be:
snfs,180.000,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,53,53,2.5,2.5,100000
total time: 180.40 hours.
 --------- CPU info (if available) ----------

Dec 8, 2009 (3rd)

By Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve 1.44 SVN / Dec 8, 2009

(32·10¹⁹⁷-23)/9 = 3(5)₁₉₆3_<198> = 11 · 2333 · C194

C194 = P48 · P147

P48 = 120096085869618304491892644395133067385455490461_<48>

P147 = 115364235300837880965021708985205640774020775255855616745497866939437139692350135211083710292284840369791039781831123064423399172513464805436819371_<147>

Msieve v. 1.44
Mon Dec  7 17:40:00 2009
random seeds: ab030b1e 60360f0e
factoring 13854793108972277424913515783640087112011672663194309143730489637047716773391869834218741205453592937519212701381582650335329289465594652049859936700913983382907514926374763494352006996670520031 (194 digits)
searching for 15-digit factors
commencing number field sieve (194-digit input)
R0: -2000000000000000000000000000000000000000
R1:  1
A0: -23
A1:  0
A2:  0
A3:  0
A4:  0
A5:  100
skew 0.75, size 1.190884e-13, alpha -0.297712, combined = 2.194006e-11

commencing linear algebra
read 1593703 cycles
cycles contain 3909055 unique relations
read 3909055 relations
using 20 quadratic characters above 268434578
building initial matrix
memory use: 525.1 MB
read 1593703 cycles
matrix is 1593360 x 1593703 (459.5 MB) with weight 137748177 (86.43/col)
sparse part has weight 102925632 (64.58/col)
filtering completed in 3 passes
matrix is 1589324 x 1589524 (458.9 MB) with weight 137556856 (86.54/col)
sparse part has weight 102814796 (64.68/col)
read 1589524 cycles
matrix is 1589324 x 1589524 (458.9 MB) with weight 137556856 (86.54/col)
sparse part has weight 102814796 (64.68/col)
saving the first 48 matrix rows for later
matrix is 1589276 x 1589524 (437.7 MB) with weight 108725656 (68.40/col)
sparse part has weight 98852707 (62.19/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (2 threads)
memory use: 447.1 MB
linear algebra at 0.0%, ETA 6h24m589524 dimensions (0.0%, ETA 6h24m)
linear algebra completed 2787 of 1589524 dimensions (0.2%, ETA 6h29m)
linear algebra completed 1589125 of 1589524 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 25132 iterations (dim = 1589276)
recovered 39 nontrivial dependencies
BLanczosTime: 24188

commencing square root phase
reading relations for dependency 1
read 795629 cycles
cycles contain 1953244 unique relations
read 1953244 relations
multiplying 1953244 relations
multiply complete, coefficients have about 58.76 million bits
initial square root is modulo 273120781
reading relations for dependency 2
read 794579 cycles
cycles contain 1953628 unique relations
read 1953628 relations
multiplying 1953628 relations
multiply complete, coefficients have about 58.77 million bits
initial square root is modulo 274025231
sqrtTime: 2038
prp48 factor: 120096085869618304491892644395133067385455490461
prp147 factor: 115364235300837880965021708985205640774020775255855616745497866939437139692350135211083710292284840369791039781831123064423399172513464805436819371
elapsed time 07:17:10

Dec 8, 2009 (2nd)

By Sinkiti Sibata / Msieve / Dec 8, 2009

(10²⁰⁷-7)/3 = (3)₂₀₆1_<207> = 42491 · C202

C202 = P73 · P130

P73 = 1894904832363841708654936720234411577262109484929134576621581786833131223_<73>

P130 = 4139943269110878681913041512994527160505437740968307294571520268473274361574028518742477201880838434865365018944874567545447883167_<130>

Number: 33331_207
N=7844798506350364390890619974425956869297812085696578883371380606089132600629152840209299224149427721948961740917684529272865626446384724608348434570458057784785797776784103300306731621598299247683823241
  ( 202 digits)
SNFS difficulty: 207 digits.
Divisors found:
 r1=1894904832363841708654936720234411577262109484929134576621581786833131223 (pp73)
 r2=4139943269110878681913041512994527160505437740968307294571520268473274361574028518742477201880838434865365018944874567545447883167 (pp130)
Version: Msieve v. 1.42
Total time: 56.54 hours.
Scaled time: 57.90 units (timescale=1.024).
Factorization parameters were as follows:
name: 33331_207
n: 7844798506350364390890619974425956869297812085696578883371380606089132600629152840209299224149427721948961740917684529272865626446384724608348434570458057784785797776784103300306731621598299247683823241
m: 200000000000000000000000000000000000000000
deg: 5
c5: 25
c0: -56
skew: 1.18
type: snfs
lss: 1
rlim: 20000000
alim: 20000000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [10000000, 24100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 4023030 x 4023255
Total sieving time: 0.00 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 55.45 hours.
Time per square root: 0.68 hours.
Prototype def-par.txt line would be:
snfs,207.000,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,56,56,2.6,2.6,100000
total time: 56.54 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3057976k/3145344k available (3786k kernel code, 496k absent, 86872k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.88 BogoMIPS (lpj=2393941)
Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393880)
Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393886)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891)
Total of 4 processors activated (19151.19 BogoMIPS).

Total time: 30days 3hours.

(67·10¹⁸⁵+41)/9 = 7(4)₁₈₄9_<186> = 17 · 241 · 251 · C180

C180 = P54 · P127

P54 = 677632651944004039691455516087438517717661638398255957_<54>

P127 = 1068312434596328427520500847735761708190001667063750632770663316658289322784604922836617494449649709779386669313247067392841031_<127>

Number: 74449_185
N=723923388160265401118926242255235289687668116350263524320530370044784926143066926285042348977966041078006202618809063909793527325352672244334300041177194511623454383048177749771667
  ( 180 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=677632651944004039691455516087438517717661638398255957 (pp54)
 r2=1068312434596328427520500847735761708190001667063750632770663316658289322784604922836617494449649709779386669313247067392841031 (pp127)
Version: Msieve v. 1.42
Total time: 13.34 hours.
Scaled time: 10.62 units (timescale=0.796).
Factorization parameters were as follows:
name: 74449_185
n: 723923388160265401118926242255235289687668116350263524320530370044784926143066926285042348977966041078006202618809063909793527325352672244334300041177194511623454383048177749771667
m: 10000000000000000000000000000000000000
deg: 5
c5: 67
c0: 41
skew: 0.91
type: snfs
lss: 1
rlim: 9100000
alim: 9100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 9100000/9100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4550000, 8050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1862951 x 1863182
Total sieving time: 0.00 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 12.31 hours.
Time per square root: 0.81 hours.
Prototype def-par.txt line would be:
snfs,186.000,5,0,0,0,0,0,0,0,0,9100000,9100000,28,28,54,54,2.5,2.5,100000
total time: 13.34 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.33 BogoMIPS (lpj=1860666)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860571)
Total of 2 processors activated (7442.47 BogoMIPS).

Total time: 9 days.

Dec 8, 2009

By matsui / Msieve / Dec 8, 2009

(61·10¹⁷²-43)/9 = 6(7)₁₇₁3_<173> = 3² · 23² · 29 · 484493 · C163

C163 = P71 · P92

P71 = 45877559189501164768877797875928683802683626877074584384877703699129389_<71>

P92 = 22085301644293106916524888744251665456292380269293469527602545567192966951778264232461022321_<92>

N=1013219733404044411721734469880469813759529495196507933262914040634945128375826233118810109979623807613314404653217433898670300606653927616376108259237164596091869
  ( 163 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=45877559189501164768877797875928683802683626877074584384877703699129389 (pp71)
 r2=22085301644293106916524888744251665456292380269293469527602545567192966951778264232461022321 (pp92)
Version: Msieve v. 1.43
Total time: 
Scaled time: 3.82 units (timescale=1.293).
Factorization parameters were as follows:
n: 1013219733404044411721734469880469813759529495196507933262914040634945128375826233118810109979623807613314404653217433898670300606653927616376108259237164596091869
m: 10000000000000000000000000000000000
deg: 5
c5: 6100
c0: -43
skew: 0.37
type: snfs
lss: 1
rlim: 5500000
alim: 5500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2750000, 7450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1120864 x 1121095
Total sieving time: 
Total relation processing time: 
Matrix solve time:
Time per square root: 
Prototype def-par.txt line would be:
snfs,173.000,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,52,52,2.4,2.4,100000
total time:

Dec 7, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.3, GMP-ECM 6.2.1 / Dec 7, 2009

(46·10²⁰⁵+53)/9 = 5(1)₂₀₄7_<206> = 3² · 26988461 · 1312785826004579_<16> · 36944846699201767801_<20> · 8501087904039071003167365661_<28> · C135

C135 = P48 · P87

P48 = 607274900896188899800306385808818802249277400279_<48>

P87 = 840402056184302338438933074944598279441760700448891869373453899535604414870371463267633_<87>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1222432706
Step 1 took 210809ms
Step 2 took 60202ms
********** Factor found in step 2: 607274900896188899800306385808818802249277400279
Found probable prime factor of 48 digits: 607274900896188899800306385808818802249277400279
Probable prime cofactor 840402056184302338438933074944598279441760700448891869373453899535604414870371463267633 has 87 digits

(2·10¹⁷⁴+7)/9 = (2)₁₇₃3_<174> = 32653 · 8605748596807443176651449709360011_<34> · C135

C135 = P38 · P98

P38 = 11120774026941337846943743141659507821_<38>

P98 = 71111645333526043530566149919676115731469180881995789346211441308147356101925837992819399029941861_<98>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3996446347
Step 1 took 41946ms
Step 2 took 14940ms
********** Factor found in step 2: 11120774026941337846943743141659507821
Found probable prime factor of 38 digits: 11120774026941337846943743141659507821
Probable prime cofactor 71111645333526043530566149919676115731469180881995789346211441308147356101925837992819399029941861 has 98 digits

Dec 7, 2009 (3rd)

By yoshida / GGNFS / Dec 7, 2009

(4·10¹⁷⁵-7)/3 = 1(3)₁₇₄1_<176> = 11 · 7198571 · C168

C168 = P46 · P122

P46 = 6641146625152017219757319418286962955580247263_<46>

P122 = 25354595722568226578798768090052792466524658199608562063230132957861080214476755044435971838286795392845251319202194326677_<122>

N=168383587815027749425840380281199160390599913805283315426370207659438535955555791853857122644497249818222550171710637030767928969808203895080304300967679852183457135051
  ( 168 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=6641146625152017219757319418286962955580247263 (pp46)
 r2=25354595722568226578798768090052792466524658199608562063230132957861080214476755044435971838286795392845251319202194326677 (pp122)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 228.69 hours.
Scaled time: 529.18 units (timescale=2.314).
Factorization parameters were as follows:
n: 168383587815027749425840380281199160390599913805283315426370207659438535955555791853857122644497249818222550171710637030767928969808203895080304300967679852183457135051
m: 100000000000000000000000000000000000
deg: 5
c5: 4
c0: -7
skew: 1.12
type: snfs
lss: 1
rlim: 5900000
alim: 5900000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2950000, 6250001)
Primes: RFBsize:406429, AFBsize:405968, largePrimes:16864502 encountered
Relations: rels:18745749, finalFF:2369936
Max relations in full relation-set: 32
Initial matrix: 812461 x 2369934 with sparse part having weight 324211232.
Pruned matrix : 538174 x 542300 with weight 119994356.
Total sieving time: 223.94 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 4.33 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,5900000,5900000,28,28,52,52,2.5,2.5,100000
total time: 228.69 hours.
 --------- CPU info (if available) ----------
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 32944636k/35127296k available (2460k kernel code, 603560k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5988.95 BogoMIPS (lpj=2994477)
Calibrating delay using timer specific routine.. 5985.01 BogoMIPS (lpj=2992505)
Calibrating delay using timer specific routine.. 5984.97 BogoMIPS (lpj=2992487)
Calibrating delay using timer specific routine.. 5985.05 BogoMIPS (lpj=2992527)
Calibrating delay using timer specific routine.. 5985.21 BogoMIPS (lpj=2992605)
Calibrating delay using timer specific routine.. 5985.02 BogoMIPS (lpj=2992513)
Calibrating delay using timer specific routine.. 5985.05 BogoMIPS (lpj=2992529)
Calibrating delay using timer specific routine.. 5985.00 BogoMIPS (lpj=2992504)

Dec 7, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve / Dec 7, 2009

(64·10¹⁸⁶+71)/9 = 7(1)₁₈₅9_<187> = 3 · 109 · C185

C185 = P73 · P112

P73 = 3527800058195301401987694858738253841359278843815495535890073943442102681_<73>

P112 = 6164328136693197517668216069637997130903302377698948344739122252464657975521632190630163982737623010865444415137_<112>

N=21746517159361196058443764865783214407067618076792388718994223581379544682296975874957526333673122663948352021746517159361196058443764865783214407067618076792388718994223581379544682297
  ( 185 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=3527800058195301401987694858738253841359278843815495535890073943442102681 (pp73)
 r2=6164328136693197517668216069637997130903302377698948344739122252464657975521632190630163982737623010865444415137 (pp112)
Version: Msieve-1.40
Total time: 242.25 hours.
Scaled time: 444.28 units (timescale=1.834).
Factorization parameters were as follows:
n: 21746517159361196058443764865783214407067618076792388718994223581379544682296975874957526333673122663948352021746517159361196058443764865783214407067618076792388718994223581379544682297
m: 20000000000000000000000000000000000000
deg: 5
c5: 20
c0: 71
skew: 1.29
type: snfs
lss: 1
rlim: 9400000
alim: 9400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 200000Factor base limits: 9400000/9400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4700000, 8900001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1945351 x 1945576
Total sieving time: 236.87 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.89 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,187.000,5,0,0,0,0,0,0,0,0,9400000,9400000,28,28,54,54,2.5,2.5,100000
total time: 242.25 hours.
 --------- CPU info (if available) ----------

Dec 7, 2009

By Jo Yeong Uk / GMP-ECM / Dec 7, 2009

(5·10¹⁷⁷+1)/3 = 1(6)₁₇₆7_<178> = 17² · 225809 · 1473977 · 205975398179_<12> · C152

C152 = P35 · P118

P35 = 44928186376086850422105844151536019_<35>

P118 = 1872339992492679438794581670820130546867660492569256842639997168734029160890120241815698232929039287868814759633153771_<118>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 84120840142112156160459692364622682411095549541785432669929173279798144770850219502231597393973475703825025357058343212455701873856035812987746872177649 (152 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=7299212132
Step 1 took 4742ms
Step 2 took 4664ms
********** Factor found in step 2: 44928186376086850422105844151536019
Found probable prime factor of 35 digits: 44928186376086850422105844151536019
Probable prime cofactor 1872339992492679438794581670820130546867660492569256842639997168734029160890120241815698232929039287868814759633153771 has 118 digits

Dec 6, 2009 (2nd)

By Sinkiti Sibata / Msieve / Dec 6, 2009

(38·10¹⁸⁵+43)/9 = 4(2)₁₈₄7_<186> = 13² · 47 · 145605431 · 683879683852489637896249_<24> · 52526357427894006525435601_<26> · C125

C125 = P62 · P63

P62 = 12355928475473544330597239983317552083603918386059392690368411_<62>

P63 = 822520210340716770107651062277089751977022102040961398920039521_<63>

Number: 42227_185
N=10163000888601351574091650327076122371330303933857311295882684888886742421333499613627838430705238530881569977996032169971131
  ( 125 digits)
Divisors found:
 r1=12355928475473544330597239983317552083603918386059392690368411 (pp62)
 r2=822520210340716770107651062277089751977022102040961398920039521 (pp63)
Version: Msieve-1.40
Total time: 67.16 hours.
Scaled time: 221.97 units (timescale=3.305).
Factorization parameters were as follows:
name: 42227_185
# Murphy_E = 1.682506e-10, selected by Jeff Gilchrist
n: 10163000888601351574091650327076122371330303933857311295882684888886742421333499613627838430705238530881569977996032169971131
Y0: -923619546624448304172779
Y1: 23021935201633
c0: 79096464115109631933811720529520
c1: 1167382777930674645846480746
c2: 114086121926159006627
c3: -25474691358524626
c4: 6419648568
c5: 15120
skew: 459976.76
type: gnfs
# selected mechanically
rlim: 6700000
alim: 6700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6700000/6700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3350000, 6350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 880662 x 880910
Total sieving time: 65.45 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.49 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,124,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6700000,6700000,27,27,52,52,2.5,2.5,100000
total time: 67.16 hours.
 --------- CPU info (if available) ----------

Dec 6, 2009

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 6, 2009

2·10¹⁷⁴-9 = 1(9)₁₇₃1_<175> = 7 · 67807 · 195697 · 7483601 · 90799214287_<11> · C146

C146 = P36 · P111

P36 = 174469979351152785406123306399771303_<36>

P111 = 181618394791561707872745497404891429823321019239014722523833973110879902107321452734442912936754551424231080727_<111>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3677067375
Step 1 took 47396ms
Step 2 took 15678ms
********** Factor found in step 2: 174469979351152785406123306399771303
Found probable prime factor of 36 digits: 174469979351152785406123306399771303
Probable prime cofactor 181618394791561707872745497404891429823321019239014722523833973110879902107321452734442912936754551424231080727 has 111 digits

Dec 5, 2009 (3rd)

By Dmitry Domanov / ECMNET, GMP-ECM / Dec 5, 2009

(59·10¹⁸³+13)/9 = 6(5)₁₈₂7_<184> = 152837 · C179

C179 = P38 · C142

P38 = 16565676361748490760573183459125786533_<38>

C142 = [2589237124616989862313430226179513606732074304991694656132791636140467706731208512624523960761262512329409853525097262768135108390631536245517_<142>]

Factor=16565676361748490760573183459125786533  Method=ECM  B1=11000000  Sigma=498181646

Dec 5, 2009 (2nd)

By Serge Batalov / PRIMO 3.0.7,3.0.8 / Dec 5, 2009

(47·10²⁰¹⁸+7)/9 = 5(2)₂₀₁₇3_<2019> is prime.

(58·10²⁰³⁶-31)/9 = 6(4)₂₀₃₅1_<2037> is prime.

Dec 5, 2009

By Dmitry Domanov / GGNFS/msieve / Dec 5, 2009

(22·10¹⁹⁷-7)/3 = 7(3)₁₉₆1_<198> = C198

C198 = P85 · P114

P85 = 1691177910918677267446605245592845163445118231338319440072463508348212239791344230793_<85>

P114 = 433622819100666887719364223144800146851804753218297702397853994103761436609576924767421335549798919696781901321467_<114>

N=733333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
  ( 198 digits)
SNFS difficulty: 198 digits.
Divisors found:
 r1=1691177910918677267446605245592845163445118231338319440072463508348212239791344230793 (pp85)
 r2=433622819100666887719364223144800146851804753218297702397853994103761436609576924767421335549798919696781901321467 (pp114)
Version: Msieve-1.40
Total time: 884.76 hours.
Scaled time: 826.37 units (timescale=0.934).
Factorization parameters were as follows:
n: 733333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
m: 2000000000000000000000000000000000000000
deg: 5
c5: 275
c0: -28
skew: 0.63
type: snfs
lss: 1
rlim: 14500000
alim: 14500000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 600000Factor base limits: 14500000/14500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [7250000, 17450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2261830 x 2262055
Total sieving time: 873.62 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 9.77 hours.
Time per square root: 0.89 hours.
Prototype def-par.txt line would be:
snfs,198.000,5,0,0,0,0,0,0,0,0,14500000,14500000,28,28,55,55,2.5,2.5,100000
total time: 884.76 hours.
 --------- CPU info (if available) ----------

Dec 4, 2009 (5th)

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 4, 2009

(55·10¹⁸⁷+53)/9 = 6(1)₁₈₆7_<188> = 2016801382643310733_<19> · 91041909846726201221_<20> · 102340704059336916678649_<24> · C127

C127 = P37 · P90

P37 = 8397437812343835280132655770909271267_<37>

P90 = 387275919082175736508356647496709535387646969166143986070306062251228534714159765453364743_<90>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2229209567
Step 1 took 38497ms
Step 2 took 13868ms
********** Factor found in step 2: 8397437812343835280132655770909271267
Found probable prime factor of 37 digits: 8397437812343835280132655770909271267
Probable prime cofactor 387275919082175736508356647496709535387646969166143986070306062251228534714159765453364743 has 90 digits

Dec 4, 2009 (4th)

By yoshida / GGNFS / Dec 4, 2009

(64·10¹⁶⁹+71)/9 = 7(1)₁₆₈9_<170> = 23 · 61 · 11549 · 23966031393282844036285531597_<29> · C135

C135 = P44 · P91

P44 = 42975927797156758306397330649270731187983431_<44>

P91 = 4261024457333070002753304298392271984643501354942246382861680398744526579464959645375737011_<91>

Number: 64x169p71
N=183121479420265074596121733676477661039260136718147327732153993537840141616263984935289849205491402729831141669703427209999368481464741
  ( 135 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=42975927797156758306397330649270731187983431 (pp44)
 r2=4261024457333070002753304298392271984643501354942246382861680398744526579464959645375737011 (pp91)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 149.69 hours.
Scaled time: 346.24 units (timescale=2.313).
Factorization parameters were as follows:
n: 183121479420265074596121733676477661039260136718147327732153993537840141616263984935289849205491402729831141669703427209999368481464741
m: 20000000000000000000000000000000000
c5: 1
c0: 355
skew: 3.24
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7900001)
Primes: RFBsize:412849, AFBsize:412917, largePrimes:6595493 encountered
Relations: rels:7270557, finalFF:1290130
Max relations in full relation-set: 32
Initial matrix: 825830 x 1290130 with sparse part having weight 91072286.
Pruned matrix : 474578 x 478771 with weight 104728234.
Total sieving time: 146.62 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 2.86 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 149.69 hours.
 --------- CPU info (if available) ----------
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Intel(R) Xeon(R) CPU           E5450  @ 3.00GHz stepping 0a
Memory for crash kernel (0x0 to 0x0) notwithin permissible range
Memory: 32944636k/35127296k available (2460k kernel code, 603560k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5988.97 BogoMIPS (lpj=2994486)
Calibrating delay using timer specific routine.. 5985.01 BogoMIPS (lpj=2992506)
Calibrating delay using timer specific routine.. 5985.03 BogoMIPS (lpj=2992519)
Calibrating delay using timer specific routine.. 5985.06 BogoMIPS (lpj=2992533)
Calibrating delay using timer specific routine.. 5985.01 BogoMIPS (lpj=2992506)
Calibrating delay using timer specific routine.. 5985.01 BogoMIPS (lpj=2992507)
Calibrating delay using timer specific routine.. 5985.04 BogoMIPS (lpj=2992520)
Calibrating delay using timer specific routine.. 5984.89 BogoMIPS (lpj=2992449)

Dec 4, 2009 (3rd)

By Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve / Dec 4, 2009

(16·10²²⁷-7)/9 = 1(7)₂₂₇_<228> = 3 · 6978529417_<10> · 998945248363_<12> · C205

C205 = P89 · P117

P89 = 43313501227448011000083463763352610564812589301818962273432249121716141326899324578414523_<89>

P117 = 196257981736799913361304440989775990019643124662452497442014310394640589026238986779888915065494733438722007484724523_<117>

Thu Nov 26 22:27:46 2009  
Thu Nov 26 22:27:46 2009  
Thu Nov 26 22:27:46 2009  Msieve v. 1.43
Thu Nov 26 22:27:46 2009  random seeds: fb9cbe1d ae67a796
Thu Nov 26 22:27:46 2009  factoring 8500620332853352373100619494859864036219623065828944278551768110817378446210927884562453439711314210424131541144585190430418520177440149893041637577056204111557942429485079430082059275669583801816757447529 (205 digits)
Thu Nov 26 22:27:49 2009  no P-1/P+1/ECM available, skipping
Thu Nov 26 22:27:49 2009  commencing number field sieve (205-digit input)
Thu Nov 26 22:27:49 2009  R0: -100000000000000000000000000000000000000
Thu Nov 26 22:27:49 2009  R1:  1
Thu Nov 26 22:27:49 2009  A0: -35
Thu Nov 26 22:27:49 2009  A1:  0
Thu Nov 26 22:27:49 2009  A2:  0
Thu Nov 26 22:27:49 2009  A3:  0
Thu Nov 26 22:27:49 2009  A4:  0
Thu Nov 26 22:27:49 2009  A5:  0
Thu Nov 26 22:27:49 2009  A6:  8
Thu Nov 26 22:27:49 2009  skew 1.28, size 3.592136e-11, alpha -0.268121, combined = 1.602160e-12
Thu Nov 26 22:27:49 2009  
Thu Nov 26 22:27:49 2009  commencing relation filtering
Thu Nov 26 22:27:49 2009  estimated available RAM is 32159.4 MB
Thu Nov 26 22:27:49 2009  commencing duplicate removal, pass 1
Thu Nov 26 22:28:01 2009  error -9 reading relation 1291015
Thu Nov 26 22:28:01 2009  error -9 reading relation 1342830
Thu Nov 26 22:28:02 2009  error -9 reading relation 1370248
Thu Nov 26 22:28:13 2009  error -1 reading relation 2599430
Thu Nov 26 22:28:13 2009  error -15 reading relation 2626748
Thu Nov 26 22:28:16 2009  error -9 reading relation 2946812
Thu Nov 26 22:28:18 2009  error -1 reading relation 3185545
Thu Nov 26 22:28:19 2009  error -15 reading relation 3219303
Thu Nov 26 22:29:16 2009  error -9 reading relation 9486483
Thu Nov 26 22:29:16 2009  error -9 reading relation 9514482
Thu Nov 26 22:29:17 2009  error -9 reading relation 9556054
Thu Nov 26 22:29:24 2009  error -15 reading relation 10391075
Thu Nov 26 22:29:24 2009  error -1 reading relation 10399383
Thu Nov 26 22:29:27 2009  error -9 reading relation 10711737
Thu Nov 26 22:29:42 2009  error -9 reading relation 12335275
Thu Nov 26 22:29:59 2009  error -15 reading relation 14104824
Thu Nov 26 22:30:04 2009  error -15 reading relation 14711253
Thu Nov 26 22:30:56 2009  error -9 reading relation 20330305
Thu Nov 26 22:30:58 2009  error -15 reading relation 20604086
Thu Nov 26 22:31:59 2009  error -15 reading relation 27248323
Thu Nov 26 22:32:04 2009  error -1 reading relation 27748892
Thu Nov 26 22:32:11 2009  error -9 reading relation 28487866
Thu Nov 26 22:32:16 2009  error -9 reading relation 29006216
Thu Nov 26 22:36:02 2009  error -9 reading relation 51061370
Thu Nov 26 22:36:03 2009  error -15 reading relation 51120025
Thu Nov 26 22:36:46 2009  error -9 reading relation 55851497
Thu Nov 26 22:38:02 2009  error -11 reading relation 64156490
Thu Nov 26 22:38:02 2009  error -15 reading relation 64158279
Thu Nov 26 22:38:07 2009  error -11 reading relation 64707825
Thu Nov 26 22:38:07 2009  error -1 reading relation 64751839
Thu Nov 26 22:38:07 2009  error -15 reading relation 64756725
Thu Nov 26 22:38:12 2009  error -11 reading relation 65315616
Thu Nov 26 22:38:16 2009  error -15 reading relation 65761982
Thu Nov 26 22:38:16 2009  error -11 reading relation 65765885
Thu Nov 26 22:38:27 2009  error -11 reading relation 66855238
Thu Nov 26 22:38:40 2009  error -15 reading relation 68327551
Thu Nov 26 22:39:21 2009  error -15 reading relation 72782069
Thu Nov 26 22:39:23 2009  error -15 reading relation 72922516
Thu Nov 26 22:39:34 2009  error -9 reading relation 74169831
Thu Nov 26 22:39:47 2009  error -15 reading relation 75577775
Thu Nov 26 22:39:58 2009  error -15 reading relation 76730474
Thu Nov 26 22:40:06 2009  error -15 reading relation 77615673
Thu Nov 26 22:40:18 2009  error -11 reading relation 78886058
Thu Nov 26 22:40:29 2009  error -15 reading relation 80065667
Thu Nov 26 22:40:31 2009  error -15 reading relation 80257632
Thu Nov 26 22:40:31 2009  error -15 reading relation 80289278
Thu Nov 26 22:40:35 2009  error -5 reading relation 80739459
Thu Nov 26 22:40:36 2009  error -15 reading relation 80813499
Thu Nov 26 22:40:38 2009  error -9 reading relation 81009455
Thu Nov 26 22:40:38 2009  error -11 reading relation 81009466
Thu Nov 26 22:40:53 2009  error -15 reading relation 82668862
Thu Nov 26 22:40:53 2009  error -9 reading relation 82683063
Thu Nov 26 22:40:58 2009  error -9 reading relation 83225110
Thu Nov 26 22:41:02 2009  error -15 reading relation 83629496
Thu Nov 26 22:41:06 2009  error -9 reading relation 84004849
Thu Nov 26 22:41:06 2009  error -15 reading relation 84019522
Thu Nov 26 22:41:13 2009  error -9 reading relation 84820494
Thu Nov 26 22:41:27 2009  error -9 reading relation 86279356
Thu Nov 26 22:41:27 2009  error -9 reading relation 86286930
Thu Nov 26 22:41:45 2009  error -9 reading relation 88229805
Thu Nov 26 22:41:45 2009  error -5 reading relation 88237485
Thu Nov 26 22:42:04 2009  error -9 reading relation 90292083
Thu Nov 26 22:42:53 2009  error -15 reading relation 95546114
Thu Nov 26 22:42:54 2009  error -11 reading relation 95663440
Thu Nov 26 22:43:11 2009  error -15 reading relation 97555771
Thu Nov 26 22:43:18 2009  found 18531139 hash collisions in 98264717 relations
Thu Nov 26 22:43:41 2009  added 1 free relations
Thu Nov 26 22:43:41 2009  commencing duplicate removal, pass 2
Thu Nov 26 22:44:56 2009  found 18305751 duplicates and 79958967 unique relations
Thu Nov 26 22:44:56 2009  memory use: 660.8 MB
Thu Nov 26 22:44:56 2009  reading ideals above 720000
Thu Nov 26 22:44:57 2009  commencing singleton removal, initial pass
Thu Nov 26 23:03:20 2009  memory use: 2756.0 MB
Thu Nov 26 23:03:21 2009  reading all ideals from disk
Thu Nov 26 23:03:27 2009  memory use: 2944.2 MB
Thu Nov 26 23:03:48 2009  keeping 81907235 ideals with weight <= 200, target excess is 420496
Thu Nov 26 23:04:11 2009  commencing in-memory singleton removal
Thu Nov 26 23:04:29 2009  begin with 79958967 relations and 81907235 unique ideals
Thu Nov 26 23:07:40 2009  reduce to 39200401 relations and 35596299 ideals in 19 passes
Thu Nov 26 23:07:40 2009  max relations containing the same ideal: 134
Thu Nov 26 23:08:24 2009  removing 3629644 relations and 3229644 ideals in 400000 cliques
Thu Nov 26 23:08:28 2009  commencing in-memory singleton removal
Thu Nov 26 23:08:36 2009  begin with 35570757 relations and 35596299 unique ideals
Thu Nov 26 23:09:49 2009  reduce to 35317319 relations and 32109565 ideals in 9 passes
Thu Nov 26 23:09:49 2009  max relations containing the same ideal: 128
Thu Nov 26 23:10:28 2009  removing 2673168 relations and 2273168 ideals in 400000 cliques
Thu Nov 26 23:10:31 2009  commencing in-memory singleton removal
Thu Nov 26 23:10:38 2009  begin with 32644151 relations and 32109565 unique ideals
Thu Nov 26 23:11:45 2009  reduce to 32491803 relations and 29682207 ideals in 9 passes
Thu Nov 26 23:11:45 2009  max relations containing the same ideal: 118
Thu Nov 26 23:12:21 2009  removing 2366440 relations and 1966440 ideals in 400000 cliques
Thu Nov 26 23:12:24 2009  commencing in-memory singleton removal
Thu Nov 26 23:12:30 2009  begin with 30125363 relations and 29682207 unique ideals
Thu Nov 26 23:13:25 2009  reduce to 29993353 relations and 27582220 ideals in 8 passes
Thu Nov 26 23:13:25 2009  max relations containing the same ideal: 110
Thu Nov 26 23:13:58 2009  removing 2206498 relations and 1806498 ideals in 400000 cliques
Thu Nov 26 23:14:01 2009  commencing in-memory singleton removal
Thu Nov 26 23:14:07 2009  begin with 27786855 relations and 27582220 unique ideals
Thu Nov 26 23:15:04 2009  reduce to 27665060 relations and 25652382 ideals in 9 passes
Thu Nov 26 23:15:04 2009  max relations containing the same ideal: 102
Thu Nov 26 23:15:35 2009  removing 2096725 relations and 1696725 ideals in 400000 cliques
Thu Nov 26 23:15:37 2009  commencing in-memory singleton removal
Thu Nov 26 23:15:43 2009  begin with 25568335 relations and 25652382 unique ideals
Thu Nov 26 23:16:29 2009  reduce to 25446757 relations and 23832524 ideals in 8 passes
Thu Nov 26 23:16:29 2009  max relations containing the same ideal: 97
Thu Nov 26 23:16:57 2009  removing 2022002 relations and 1622002 ideals in 400000 cliques
Thu Nov 26 23:17:00 2009  commencing in-memory singleton removal
Thu Nov 26 23:17:05 2009  begin with 23424755 relations and 23832524 unique ideals
Thu Nov 26 23:17:47 2009  reduce to 23300592 relations and 22084668 ideals in 8 passes
Thu Nov 26 23:17:47 2009  max relations containing the same ideal: 89
Thu Nov 26 23:18:13 2009  removing 1974033 relations and 1574033 ideals in 400000 cliques
Thu Nov 26 23:18:15 2009  commencing in-memory singleton removal
Thu Nov 26 23:18:20 2009  begin with 21326559 relations and 22084668 unique ideals
Thu Nov 26 23:18:58 2009  reduce to 21196656 relations and 20378855 ideals in 8 passes
Thu Nov 26 23:18:58 2009  max relations containing the same ideal: 83
Thu Nov 26 23:19:22 2009  removing 1656990 relations and 1326965 ideals in 330025 cliques
Thu Nov 26 23:19:24 2009  commencing in-memory singleton removal
Thu Nov 26 23:19:28 2009  begin with 19539666 relations and 20378855 unique ideals
Thu Nov 26 23:19:59 2009  reduce to 19437929 relations and 18948678 ideals in 7 passes
Thu Nov 26 23:19:59 2009  max relations containing the same ideal: 78
Thu Nov 26 23:20:28 2009  relations with 0 large ideals: 14445
Thu Nov 26 23:20:28 2009  relations with 1 large ideals: 6220
Thu Nov 26 23:20:28 2009  relations with 2 large ideals: 86100
Thu Nov 26 23:20:28 2009  relations with 3 large ideals: 559802
Thu Nov 26 23:20:28 2009  relations with 4 large ideals: 1973251
Thu Nov 26 23:20:28 2009  relations with 5 large ideals: 4114171
Thu Nov 26 23:20:28 2009  relations with 6 large ideals: 5298159
Thu Nov 26 23:20:28 2009  relations with 7+ large ideals: 7385781
Thu Nov 26 23:20:28 2009  commencing 2-way merge
Thu Nov 26 23:20:57 2009  reduce to 12106757 relation sets and 11617506 unique ideals
Thu Nov 26 23:20:57 2009  commencing full merge
Thu Nov 26 23:26:40 2009  memory use: 1424.6 MB
Thu Nov 26 23:26:43 2009  found 6358076 cycles, need 6291706
Thu Nov 26 23:26:47 2009  weight of 6291706 cycles is about 440672317 (70.04/cycle)
Thu Nov 26 23:26:47 2009  distribution of cycle lengths:
Thu Nov 26 23:26:47 2009  1 relations: 826579
Thu Nov 26 23:26:47 2009  2 relations: 770877
Thu Nov 26 23:26:47 2009  3 relations: 748633
Thu Nov 26 23:26:47 2009  4 relations: 676227
Thu Nov 26 23:26:47 2009  5 relations: 612398
Thu Nov 26 23:26:47 2009  6 relations: 533265
Thu Nov 26 23:26:47 2009  7 relations: 463017
Thu Nov 26 23:26:47 2009  8 relations: 390741
Thu Nov 26 23:26:47 2009  9 relations: 318530
Thu Nov 26 23:26:47 2009  10+ relations: 951439
Thu Nov 26 23:26:47 2009  heaviest cycle: 21 relations
Thu Nov 26 23:26:49 2009  commencing cycle optimization
Thu Nov 26 23:27:06 2009  start with 34372455 relations
Thu Nov 26 23:28:31 2009  pruned 753746 relations
Thu Nov 26 23:28:32 2009  memory use: 1143.5 MB
Thu Nov 26 23:28:32 2009  distribution of cycle lengths:
Thu Nov 26 23:28:32 2009  1 relations: 826579
Thu Nov 26 23:28:32 2009  2 relations: 785791
Thu Nov 26 23:28:32 2009  3 relations: 771707
Thu Nov 26 23:28:32 2009  4 relations: 690566
Thu Nov 26 23:28:32 2009  5 relations: 625482
Thu Nov 26 23:28:32 2009  6 relations: 539725
Thu Nov 26 23:28:32 2009  7 relations: 467763
Thu Nov 26 23:28:32 2009  8 relations: 390486
Thu Nov 26 23:28:32 2009  9 relations: 314993
Thu Nov 26 23:28:32 2009  10+ relations: 878614
Thu Nov 26 23:28:32 2009  heaviest cycle: 21 relations
Thu Nov 26 23:28:48 2009  RelProcTime: 3659
Thu Nov 26 23:28:52 2009  elapsed time 01:01:06
Fri Nov 27 06:31:15 2009  
Fri Nov 27 06:31:15 2009  
Fri Nov 27 06:31:15 2009  Msieve v. 1.43
Fri Nov 27 06:31:15 2009  random seeds: a6634281 eaabb899
Fri Nov 27 06:31:15 2009  factoring 8500620332853352373100619494859864036219623065828944278551768110817378446210927884562453439711314210424131541144585190430418520177440149893041637577056204111557942429485079430082059275669583801816757447529 (205 digits)
Fri Nov 27 06:31:18 2009  no P-1/P+1/ECM available, skipping
Fri Nov 27 06:31:18 2009  commencing number field sieve (205-digit input)
Fri Nov 27 06:31:18 2009  R0: -100000000000000000000000000000000000000
Fri Nov 27 06:31:18 2009  R1:  1
Fri Nov 27 06:31:18 2009  A0: -35
Fri Nov 27 06:31:18 2009  A1:  0
Fri Nov 27 06:31:18 2009  A2:  0
Fri Nov 27 06:31:18 2009  A3:  0
Fri Nov 27 06:31:18 2009  A4:  0
Fri Nov 27 06:31:18 2009  A5:  0
Fri Nov 27 06:31:18 2009  A6:  8
Fri Nov 27 06:31:18 2009  skew 1.28, size 3.592136e-11, alpha -0.268121, combined = 1.602160e-12
Fri Nov 27 06:31:18 2009  
Fri Nov 27 06:31:18 2009  commencing linear algebra
Fri Nov 27 06:31:19 2009  read 6291706 cycles
Fri Nov 27 06:31:36 2009  cycles contain 19079877 unique relations
Fri Nov 27 06:34:56 2009  read 19079877 relations
Fri Nov 27 06:35:41 2009  using 20 quadratic characters above 1073739740
Fri Nov 27 06:37:59 2009  building initial matrix
Fri Nov 27 06:44:18 2009  memory use: 2469.6 MB
Fri Nov 27 06:44:25 2009  read 6291706 cycles
Fri Nov 27 06:44:33 2009  matrix is 6291525 x 6291706 (1892.8 MB) with weight 559610983 (88.94/col)
Fri Nov 27 06:44:33 2009  sparse part has weight 426984476 (67.86/col)
Fri Nov 27 06:47:09 2009  filtering completed in 2 passes
Fri Nov 27 06:47:11 2009  matrix is 6285857 x 6286038 (1892.4 MB) with weight 559440693 (89.00/col)
Fri Nov 27 06:47:11 2009  sparse part has weight 426933495 (67.92/col)
Fri Nov 27 06:47:59 2009  read 6286038 cycles
Fri Nov 27 06:48:07 2009  matrix is 6285857 x 6286038 (1892.4 MB) with weight 559440693 (89.00/col)
Fri Nov 27 06:48:07 2009  sparse part has weight 426933495 (67.92/col)
Fri Nov 27 06:48:07 2009  saving the first 48 matrix rows for later
Fri Nov 27 06:48:13 2009  matrix is 6285809 x 6286038 (1807.3 MB) with weight 443908792 (70.62/col)
Fri Nov 27 06:48:13 2009  sparse part has weight 410917321 (65.37/col)
Fri Nov 27 06:48:13 2009  matrix includes 64 packed rows
Fri Nov 27 06:48:13 2009  using block size 65536 for processor cache size 6144 kB
Fri Nov 27 06:48:50 2009  commencing Lanczos iteration (4 threads)
Fri Nov 27 06:48:50 2009  memory use: 1958.3 MB
Fri Nov 27 06:49:32 2009  linear algebra at 0.0%, ETA 90h 4m
Tue Dec  1 00:58:29 2009  lanczos halted after 99407 iterations (dim = 6285808)
Tue Dec  1 00:58:46 2009  recovered 35 nontrivial dependencies
Tue Dec  1 00:58:47 2009  BLanczosTime: 325649
Tue Dec  1 00:58:47 2009  elapsed time 90:27:32
Tue Dec  1 05:38:10 2009  
Tue Dec  1 05:38:10 2009  
Tue Dec  1 05:38:10 2009  Msieve v. 1.43
Tue Dec  1 05:38:10 2009  random seeds: 505cf7ae 6f367940
Tue Dec  1 05:38:10 2009  factoring 8500620332853352373100619494859864036219623065828944278551768110817378446210927884562453439711314210424131541144585190430418520177440149893041637577056204111557942429485079430082059275669583801816757447529 (205 digits)
Tue Dec  1 05:38:13 2009  no P-1/P+1/ECM available, skipping
Tue Dec  1 05:38:13 2009  commencing number field sieve (205-digit input)
Tue Dec  1 05:38:13 2009  R0: -100000000000000000000000000000000000000
Tue Dec  1 05:38:13 2009  R1:  1
Tue Dec  1 05:38:13 2009  A0: -35
Tue Dec  1 05:38:13 2009  A1:  0
Tue Dec  1 05:38:13 2009  A2:  0
Tue Dec  1 05:38:13 2009  A3:  0
Tue Dec  1 05:38:13 2009  A4:  0
Tue Dec  1 05:38:13 2009  A5:  0
Tue Dec  1 05:38:13 2009  A6:  8
Tue Dec  1 05:38:13 2009  skew 1.28, size 3.592136e-11, alpha -0.268121, combined = 1.602160e-12
Tue Dec  1 05:38:13 2009  
Tue Dec  1 05:38:13 2009  commencing square root phase
Tue Dec  1 05:38:13 2009  reading relations for dependency 1
Tue Dec  1 05:38:14 2009  read 3143635 cycles
Tue Dec  1 05:38:23 2009  cycles contain 9541566 unique relations
Tue Dec  1 05:40:18 2009  read 9541566 relations
Tue Dec  1 05:41:36 2009  multiplying 9541566 relations
Tue Dec  1 05:55:44 2009  multiply complete, coefficients have about 259.73 million bits
Tue Dec  1 05:55:47 2009  initial square root is modulo 2093935903
Tue Dec  1 06:21:29 2009  reading relations for dependency 2
Tue Dec  1 06:21:31 2009  read 3142476 cycles
Tue Dec  1 06:21:39 2009  cycles contain 9540940 unique relations
Tue Dec  1 06:23:34 2009  read 9540940 relations
Tue Dec  1 06:24:53 2009  multiplying 9540940 relations
Tue Dec  1 06:39:00 2009  multiply complete, coefficients have about 259.72 million bits
Tue Dec  1 06:39:03 2009  initial square root is modulo 2091413101
Tue Dec  1 07:04:46 2009  sqrtTime: 5193
Tue Dec  1 07:04:46 2009  prp89 factor: 43313501227448011000083463763352610564812589301818962273432249121716141326899324578414523
Tue Dec  1 07:04:46 2009  prp117 factor: 196257981736799913361304440989775990019643124662452497442014310394640589026238986779888915065494733438722007484724523
Tue Dec  1 07:04:46 2009  elapsed time 01:26:36

Dec 4, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Dec 4, 2009

2·10¹⁹⁶-1 = 1(9)₁₉₆_<197> = 7 · 21786481 · C189

C189 = P49 · P141

P49 = 1184519727783750416654949243024504531875874583481_<49>

P141 = 110714007151192388668548159387672871512485358734847066883913445369139729551089568055349728260200404587217820110723312598003341429367614469537_<141>

Number: 19999_196
N=131142925612578605184432623935130099388567747914078328797438322285405208067201989029015614906195399667475309246001814480404483076323471291341504066542130284503364396349408476883308637918297
  ( 189 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=1184519727783750416654949243024504531875874583481
 r2=110714007151192388668548159387672871512485358734847066883913445369139729551089568055349728260200404587217820110723312598003341429367614469537
Version: 
Total time: 216.90 hours.
Scaled time: 517.51 units (timescale=2.386).
Factorization parameters were as follows:
n: 131142925612578605184432623935130099388567747914078328797438322285405208067201989029015614906195399667475309246001814480404483076323471291341504066542130284503364396349408476883308637918297
m: 1000000000000000000000000000000000000000
deg: 5
c5: 20
c0: -1
skew: 0.55
type: snfs
lss: 1
rlim: 13000000
alim: 13000000
lpbr: 29
lpba: 29
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 13000000/13000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 55/55
Sieved rational special-q in [6500000, 11500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 33192013
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2453224 x 2453471
Total sieving time: 190.58 hours.
Total relation processing time: 8.58 hours.
Matrix solve time: 17.00 hours.
Time per square root: 0.74 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,13000000,13000000,29,29,55,55,2.5,2.5,100000
total time: 216.90 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Dec 4, 2009

By Tyler Cadigan / PRIMO 3.0.8 / Dec 4, 2009

(10³¹⁴⁶+71)/9 = (1)₃₁₄₅9_<3146> is prime.

Dec 3, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve / Dec 3, 2009

(67·10¹⁹²-13)/9 = 7(4)₁₉₁3_<193> = 3² · 19 · C191

C191 = P51 · P140

P51 = 787727404219372459895283453175496131491118165296769_<51>

P140 = 55266279425876806713988680815949088304298679361056635098361971746667025608752182148801770835356409734239678567210927995967156095265795663057_<140>

N=43534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833
  ( 191 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=787727404219372459895283453175496131491118165296769 (pp51)
 r2=55266279425876806713988680815949088304298679361056635098361971746667025608752182148801770835356409734239678567210927995967156095265795663057 (pp140)
Version: Msieve-1.40
Total time: 559.66 hours.
Scaled time: 1017.47 units (timescale=1.818).
Factorization parameters were as follows:
n: 43534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833008447043534762833
m: 500000000000000000000000000000000000000
deg: 5
c5: 268
c0: -1625
skew: 1.43
type: snfs
lss: 1
rlim: 12900000
alim: 12900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 12900000/12900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6450000, 15050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2349315 x 2349540
Total sieving time: 550.85 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 7.58 hours.
Time per square root: 0.97 hours.
Prototype def-par.txt line would be:
snfs,195.000,5,0,0,0,0,0,0,0,0,12900000,12900000,28,28,55,55,2.5,2.5,100000
total time: 559.66 hours.
 --------- CPU info (if available) ----------

Dec 3, 2009

By Sinkiti Sibata / Msieve / Dec 3, 2009

(67·10¹⁶⁵-13)/9 = 7(4)₁₆₄3_<166> = 3² · 82021 · 24823583623_<11> · 3186822091492756524752069_<25> · C126

C126 = P47 · P79

P47 = 27450936085202690749136049312900466734576169433_<47>

P79 = 4643925759015711078530301624300186286501864834476494327623680463657883765250197_<79>

Number: 74443_165
N=127480109195166678118588816514385867213041373151950439735287023737133488529901544404868525808710084307279871580450709108628301
  ( 126 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=27450936085202690749136049312900466734576169433 (pp47)
 r2=4643925759015711078530301624300186286501864834476494327623680463657883765250197 (pp79)
Version: Msieve-1.40
Total time: 43.58 hours.
Scaled time: 146.26 units (timescale=3.356).
Factorization parameters were as follows:
name: 74443_165
n: 127480109195166678118588816514385867213041373151950439735287023737133488529901544404868525808710084307279871580450709108628301
m: 1000000000000000000000000000000000
deg: 5
c5: 67
c0: -13
skew: 0.72
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 817860 x 818108
Total sieving time: 41.98 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.26 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 43.58 hours.
 --------- CPU info (if available) ----------

Dec 2, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Dec 2, 2009

(83·10¹⁶⁵+7)/9 = 9(2)₁₆₄3_<166> = 107 · 15031 · 42197 · C156

C156 = P71 · P85

P71 = 43567788308512159678025627034514610908398268888666684424948010635688847_<71>

P85 = 3119010528746029397719209328603357416174022932664142751039778863736466253498609584641_<85>

Number: 92223_165
N=135888390448427588923536357204315898704325886989730889174813579864244032329645737188860895257825731028016278138812310117354155861528825745060357373586198927
  ( 156 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=43567788308512159678025627034514610908398268888666684424948010635688847
 r2=3119010528746029397719209328603357416174022932664142751039778863736466253498609584641
Version: 
Total time: 24.53 hours.
Scaled time: 58.48 units (timescale=2.384).
Factorization parameters were as follows:
n: 135888390448427588923536357204315898704325886989730889174813579864244032329645737188860895257825731028016278138812310117354155861528825745060357373586198927
m: 1000000000000000000000000000000000
deg: 5
c5: 83
c0: 7
skew: 0.61
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 4200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9785094
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 781690 x 781938
Total sieving time: 22.13 hours.
Total relation processing time: 0.96 hours.
Matrix solve time: 1.36 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 24.53 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Dec 1, 2009 (3rd)

By Sinkiti Sibata / Msieve / Dec 1, 2009

(64·10¹⁶⁵+17)/9 = 7(1)₁₆₄3_<166> = 3 · 107 · 109 · 9250127060715581_<16> · C146

C146 = P61 · P86

P61 = 1337660330747353211919119280339282908153321059315073880180853_<61>

P86 = 16425265109434527326510048349197230485054669946738941787287566019735622487230213930669_<86>

Number: 71113_165
N=21971425558899150573132387261603048300262553608841156778721836305533945757037303446237424248823445658589807526596416410732844148519978705723280657
  ( 146 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=1337660330747353211919119280339282908153321059315073880180853 (pp61)
 r2=16425265109434527326510048349197230485054669946738941787287566019735622487230213930669 (pp86)
Version: Msieve-1.40
Total time: 38.63 hours.
Scaled time: 129.65 units (timescale=3.356).
Factorization parameters were as follows:
name: 71113_165
n: 21971425558899150573132387261603048300262553608841156778721836305533945757037303446237424248823445658589807526596416410732844148519978705723280657
m: 2000000000000000000000000000000000
deg: 5
c5: 2
c0: 17
skew: 1.53
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 759798 x 760046
Total sieving time: 37.36 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.09 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 38.63 hours.
 --------- CPU info (if available) ----------

Dec 1, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Dec 1, 2009

(52·10¹⁸⁵-43)/9 = 5(7)₁₈₄3_<186> = 3² · 7 · 30000315797_<11> · 232490372587643_<15> · 174803429130286213921446816952979_<33> · C127

C127 = P43 · P85

P43 = 2498583802588221247133294103735572473992083_<43>

P85 = 3010548420930010766455598533165141367485402944008309486583965145761377674886330486493_<85>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=259561072
Step 1 took 38282ms
Step 2 took 13917ms
********** Factor found in step 2: 2498583802588221247133294103735572473992083
Found probable prime factor of 43 digits: 2498583802588221247133294103735572473992083
Probable prime cofactor 3010548420930010766455598533165141367485402944008309486583965145761377674886330486493 has 85 digits

Dec 1, 2009

By JPascoa / ggnfs, Msieve / Dec 1, 2009

(26·10¹⁸⁵-71)/9 = 2(8)₁₈₄1_<186> = 29 · 5503 · 10169 · 71875359003529_<14> · 1394709746073037_<16> · 2877363597220133641_<19> · C129

C129 = P57 · P73

P57 = 426635400523700719380560824023990687589207990696100701579_<57>

P73 = 1446570433676351806454922108543228604497249940075625639596510848668340941_<73>

Number: 28881_185
N=617158156357253800238573566333189314432699040441120387582829934582368592193389049441631037244285202522375613719835416916069045839
  ( 129 digits)
Divisors found:
 r1=426635400523700719380560824023990687589207990696100701579 (pp57)
 r2=1446570433676351806454922108543228604497249940075625639596510848668340941 (pp73)
Version: Msieve v. 1.43
Total time: 141.61 hours.
Scaled time: 423.57 units (timescale=2.991).
Factorization parameters were as follows:
# Murphy_E = 9.098144e-11, selected by Jeff Gilchrist
n: 617158156357253800238573566333189314432699040441120387582829934582368592193389049441631037244285202522375613719835416916069045839
Y0: -6966184159841423360708233
Y1: 179572073106863
c0: 451869833669647240802733941550960
c1: 6137113730802307406338953288
c2: 909117430681584103700
c3: -61431158639424524
c4: 9830138349
c5: 37620
skew: 580327.33
type: gnfs
# selected mechanically
rlim: 9100000
alim: 9100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 9100000/9100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved algebraic special-q in [4550000, 9150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1356361 x 1356592
Total sieving time: 139.42 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.99 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,128,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,9100000,9100000,28,28,53,53,2.5,2.5,100000
total time: 141.61 hours.
 --------- CPU info (if available) ----------

November 2009

Nov 30, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 30, 2009

(65·10¹⁶⁵-11)/9 = 7(2)₁₆₄1_<166> = 3 · 1627 · 1117427261_<10> · C154

C154 = P45 · P110

P45 = 113006746106565909443027295307940874726468067_<45>

P110 = 11717592946789296253681058279544472082801984835493741742797532427363964872859069731881552804947725855354637643_<110>

Number: 72221_165
N=1324167051117905466116290415486962399951869164503675847313184589279820521464612022488971168097567147466746257583242944662193031062572818924125189995646081
  ( 154 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=113006746106565909443027295307940874726468067
 r2=11717592946789296253681058279544472082801984835493741742797532427363964872859069731881552804947725855354637643
Version: 
Total time: 24.57 hours.
Scaled time: 58.62 units (timescale=2.386).
Factorization parameters were as follows:
n: 1324167051117905466116290415486962399951869164503675847313184589279820521464612022488971168097567147466746257583242944662193031062572818924125189995646081
m: 1000000000000000000000000000000000
deg: 5
c5: 65
c0: -11
skew: 0.70
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 4200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9909831
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 750797 x 751045
Total sieving time: 22.18 hours.
Total relation processing time: 0.97 hours.
Matrix solve time: 1.26 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 24.57 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nov 30, 2009

By Sinkiti Sibata / Msieve / Nov 30, 2009

(62·10¹⁶⁴-71)/9 = 6(8)₁₆₃1_<165> = 3 · 8819 · 51539 · 85667 · 791251537184711_<15> · C136

C136 = P39 · P97

P39 = 992475357917463346229619663566535046949_<39>

P97 = 7509737163976481080866171857101385836152469516008259754713441097351260965314523929224542143986219_<97>

Number: 68881_164
N=7453229079683634188103196101922610125639868950413398574507032854609890070168290130051336575627502110007583354854997020130458699173995831
  ( 136 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=992475357917463346229619663566535046949 (pp39)
 r2=7509737163976481080866171857101385836152469516008259754713441097351260965314523929224542143986219 (pp97)
Version: Msieve-1.40
Total time: 43.13 hours.
Scaled time: 144.79 units (timescale=3.357).
Factorization parameters were as follows:
name: 68881_164
n: 7453229079683634188103196101922610125639868950413398574507032854609890070168290130051336575627502110007583354854997020130458699173995831
m: 1000000000000000000000000000000000
deg: 5
c5: 31
c0: -355
skew: 1.63
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 801871 x 802119
Total sieving time: 41.78 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.21 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 43.13 hours.
 --------- CPU info (if available) ----------

Nov 29, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve / Nov 29, 2009

(5·10¹⁷⁴+31)/9 = (5)₁₇₃9_<174> = 23 · 1259 · 2729 · 92569625550097_<14> · C152

C152 = P36 · P41 · P76

P36 = 319209987870288110798004201214022531_<36>

P41 = 29918625098920000052618788688979657934147_<41>

P76 = 7952135702568029913397518486410342950297753828903848797089446457106865919507_<76>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3191334078
Step 1 took 12315ms
Step 2 took 5559ms
********** Factor found in step 2: 319209987870288110798004201214022531
Found probable prime factor of 36 digits: 319209987870288110798004201214022531
Composite cofactor 237916966820869688084184098718279133319024623800428369609709957288403959046532171004082771755032730649929947208705529 has 117 digits
------------------------------
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1509897548
Step 1 took 10661ms
Step 2 took 4556ms
********** Factor found in step 2: 29918625098920000052618788688979657934147
Found probable prime factor of 41 digits: 29918625098920000052618788688979657934147
Probable prime cofactor 7952135702568029913397518486410342950297753828903848797089446457106865919507 has 76 digits

(47·10²⁰⁰+61)/9 = 5(2)₁₉₉9_<201> = 23 · 29 · C198

C198 = P49 · P150

P49 = 1821402884526033038533370786121841309816963740679_<49>

P150 = 429856496359875945099381474633284382898100856895829070340592911058234885519310144276396296060479619834175215447282578435029435921107042424727017527353_<150>

Number: 52229_200
N=782941862402132267199733466600033316674995835415625520573046809928369148758953856405130767949358654006330168249208728968848908878893886390138264201232716974845910378144261202731967349658504081292687
  ( 198 digits)
SNFS difficulty: 201 digits.
Divisors found:
 r1=1821402884526033038533370786121841309816963740679
 r2=429856496359875945099381474633284382898100856895829070340592911058234885519310144276396296060479619834175215447282578435029435921107042424727017527353
Version: 
Total time: 879.42 hours.
Scaled time: 1768.52 units (timescale=2.011).
Factorization parameters were as follows:
n: 782941862402132267199733466600033316674995835415625520573046809928369148758953856405130767949358654006330168249208728968848908878893886390138264201232716974845910378144261202731967349658504081292687
m: 10000000000000000000000000000000000000000
deg: 5
c5: 47
c0: 61
skew: 1.05
type: snfs
lss: 1
rlim: 16100000
alim: 16100000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 16100000/16100000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [8050000, 17750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3153324 x 3153572
Total sieving time: 879.42 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,201,5,0,0,0,0,0,0,0,0,16100000,16100000,29,29,56,56,2.6,2.6,100000
total time: 879.42 hours.
 --------- CPU info (if available) ----------

Nov 29, 2009 (3rd)

By JPascoa / ggnfs, Msieve / Nov 29, 2009

(65·10¹⁶⁵+7)/9 = 7(2)₁₆₄3_<166> = 709 · 67751 · 1829671 · C152

C152 = P75 · P78

P75 = 312974659587106130775379744870042305659798659750210394695905699474058989043_<75>

P78 = 262558886508076207744801887760311254273758547653064352203241793866965567029249_<78>

Number: 72223_165
N=82174278126434783823391208352460875362453913579954847715282054703599326256843388185088845857667117607706749934491923336032382214386373130028033751518707
  ( 152 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=312974659587106130775379744870042305659798659750210394695905699474058989043 (pp75)
 r2=262558886508076207744801887760311254273758547653064352203241793866965567029249 (pp78)
Version: Msieve v. 1.43
Total time: 48.54 hours.
Scaled time: 138.34 units (timescale=2.850).
Factorization parameters were as follows:
n: 82174278126434783823391208352460875362453913579954847715282054703599326256843388185088845857667117607706749934491923336032382214386373130028033751518707
m: 1000000000000000000000000000000000
deg: 5
c5: 65
c0: 7
skew: 0.64
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4200001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 816606 x 816831
Total sieving time: 47.76 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.67 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 48.54 hours.
 --------- CPU info (if available) ----------

Nov 29, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 29, 2009

(65·10¹⁶⁴+61)/9 = 7(2)₁₆₃9_<165> = 3⁴ · 319001 · 17439599 · C151

C151 = P76 · P76

P76 = 1097127491350443004053837025887267310248050259027019551554425722997887106267_<76>

P76 = 1460831723951703039628220676876044203673473878553552062390817891003524106873_<76>

Number: 72229_164
N=1602718644584274818803163723477909962133415966700972038765533352034751949940452264830643947910679050139435670063108805415833738405346671012673616073091
  ( 151 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=1097127491350443004053837025887267310248050259027019551554425722997887106267
 r2=1460831723951703039628220676876044203673473878553552062390817891003524106873
Version: 
Total time: 28.82 hours.
Scaled time: 68.70 units (timescale=2.384).
Factorization parameters were as follows:
n: 1602718644584274818803163723477909962133415966700972038765533352034751949940452264830643947910679050139435670063108805415833738405346671012673616073091
m: 1000000000000000000000000000000000
deg: 5
c5: 13
c0: 122
skew: 1.56
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 4600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10149598
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 782891 x 783139
Total sieving time: 26.18 hours.
Total relation processing time: 1.18 hours.
Matrix solve time: 1.37 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 28.82 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nice split. :-)

Nov 29, 2009

By Dmitry Domanov / GGNFS/msieve / Nov 29, 2009

(59·10¹⁶⁷+31)/9 = 6(5)₁₆₆9_<168> = 1609 · 1613 · 8969 · C158

C158 = P45 · P114

P45 = 180807571184022017815614490573920266850012827_<45>

P114 = 155760902333919403469684574721889190589532983161655736580938118674989762881341704303010429704566137565650015823529_<114>

Number: s158
N=28162750436427633795391345241974761470071604276095120931948649687067221159896234746405373333713070886324764143370807972283060862326022280203040781466618406483
  ( 158 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=180807571184022017815614490573920266850012827 (pp45)
 r2=155760902333919403469684574721889190589532983161655736580938118674989762881341704303010429704566137565650015823529 (pp114)
Version: Msieve-1.40
Total time: 63.41 hours.
Scaled time: 119.39 units (timescale=1.883).
Factorization parameters were as follows:
n: 28162750436427633795391345241974761470071604276095120931948649687067221159896234746405373333713070886324764143370807972283060862326022280203040781466618406483
m: 2000000000000000000000000000000000
deg: 5
c5: 1475
c0: 248
skew: 0.70
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 5950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1020495 x 1020720
Total sieving time: 61.85 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.31 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,169.000,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000
total time: 63.41 hours.
 --------- CPU info (if available) ----------

Nov 28, 2009 (4th)

By Sinkiti Sibata / Msieve / Nov 28, 2009

(26·10¹⁶³-11)/3 = 8(6)₁₆₂3_<164> = 2239 · 8719 · 195407 · 879139434150694749919804433_<27> · C125

C125 = P46 · P79

P46 = 5211438645737500317674537589757818163406227579_<46>

P79 = 4958791117901422260553490157272046951176263951871311374087740608923515632809707_<79>

Number: 86663_163
N=25842435667971333293845691995925430935046775646627219316454740930177241830087326929025122361662134281077043238993181242309353
  ( 125 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=5211438645737500317674537589757818163406227579 (pp46)
 r2=4958791117901422260553490157272046951176263951871311374087740608923515632809707 (pp79)
Version: Msieve-1.40
Total time: 39.13 hours.
Scaled time: 131.36 units (timescale=3.357).
Factorization parameters were as follows:
name: 86663_163
n: 25842435667971333293845691995925430935046775646627219316454740930177241830087326929025122361662134281077043238993181242309353
m: 500000000000000000000000000000000
deg: 5
c5: 208
c0: -275
skew: 1.06
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 757161 x 757409
Total sieving time: 37.91 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,165.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 39.13 hours.
 --------- CPU info (if available) ----------

(65·10¹⁶⁴-11)/9 = 7(2)₁₆₃1_<165> = 7 · 642113 · 1373173 · 4123318093_<10> · 4443565537_<10> · 4462792390541_<13> · C121

C121 = P52 · P69

P52 = 1551622602733807349047209724184123573558714451797777_<52>

P69 = 922284432714733061874653609820085576890214786673481956403908905108631_<69>

Number: 72221_164
N=1431037371949707131839284966982399894566209201602764234918449603635050483060354978307759067701589405764384099117429313287
  ( 121 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=1551622602733807349047209724184123573558714451797777 (pp52)
 r2=922284432714733061874653609820085576890214786673481956403908905108631 (pp69)
Version: Msieve v. 1.42
Total time: 2.07 hours.
Scaled time: 1.41 units (timescale=0.681).
Factorization parameters were as follows:
name: 72221_163
n: 1431037371949707131839284966982399894566209201602764234918449603635050483060354978307759067701589405764384099117429313287
m: 1000000000000000000000000000000000
deg: 5
c5: 13
c0: -22
skew: 1.11
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 730980 x 731209
Total sieving time: 0.00 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.74 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 2.07 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.19 BogoMIPS (lpj=1860598)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860574)
Total of 2 processors activated (7442.34 BogoMIPS).

Total time: 38 hours.

Nov 28, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 28, 2009

(43·10¹⁸⁸+11)/9 = 4(7)₁₈₇9_<189> = 8387 · 200015330041_<12> · 73294994688491_<14> · 86021662446856582196340817_<26> · C134

C134 = P38 · P96

P38 = 60652757993607889981105524809786581043_<38>

P96 = 744771959182400709766779466077945682530064054931570187406997451913632109458468682650603381975097_<96>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2151625036
Step 1 took 38024ms
Step 2 took 14497ms
********** Factor found in step 2: 60652757993607889981105524809786581043
Found probable prime factor of 38 digits: 60652757993607889981105524809786581043
Probable prime cofactor 744771959182400709766779466077945682530064054931570187406997451913632109458468682650603381975097 has 96 digits

Nov 28, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve 1.42 / Nov 28, 2009

(26·10²⁰⁰-11)/3 = 8(6)₁₉₉3_<201> = C201

C201 = P99 · P103

P99 = 219631702931061976134369747885808367899858190913021959949302323867094375889693220762080723420749513_<99>

P103 = 3945999849296329038851146075899153593764462405886868527184422610760144041919822331667205447984131245551_<103>

Sieving took 39 days on Xeon E5310 1.86GHz (Windows 2003 Server SP2)
Postprocessing took 23.5 hours (8 cores)

Wed Nov 25 07:01:39 2009  Msieve v. 1.42
Wed Nov 25 07:01:39 2009  random seeds: 0016d1ec c3a03c82
Wed Nov 25 07:01:39 2009  factoring 866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 (201 digits)
Wed Nov 25 07:01:42 2009  searching for 15-digit factors
Wed Nov 25 07:01:44 2009  commencing number field sieve (201-digit input)
Wed Nov 25 07:01:44 2009  R0: -10000000000000000000000000000000000000000
Wed Nov 25 07:01:44 2009  R1:  1
Wed Nov 25 07:01:44 2009  A0: -11
Wed Nov 25 07:01:44 2009  A1:  0
Wed Nov 25 07:01:44 2009  A2:  0
Wed Nov 25 07:01:44 2009  A3:  0
Wed Nov 25 07:01:44 2009  A4:  0
Wed Nov 25 07:01:44 2009  A5:  26
Wed Nov 25 07:01:44 2009  skew 0.84, size 5.578690e-014, alpha 1.471114, combined = 1.386997e-011
Wed Nov 25 07:01:44 2009  
Wed Nov 25 07:01:44 2009  commencing relation filtering
Wed Nov 25 07:01:44 2009  estimated available RAM is 4095.0 MB
Wed Nov 25 07:01:44 2009  commencing duplicate removal, pass 1
Wed Nov 25 07:13:10 2009  found 5943338 hash collisions in 42007041 relations
Wed Nov 25 07:14:27 2009  commencing duplicate removal, pass 2
Wed Nov 25 07:18:36 2009  found 5764474 duplicates and 36242567 unique relations
Wed Nov 25 07:18:36 2009  memory use: 197.2 MB
Wed Nov 25 07:18:36 2009  reading ideals above 18284544
Wed Nov 25 07:18:44 2009  commencing singleton removal, initial pass
Wed Nov 25 07:27:59 2009  memory use: 596.8 MB
Wed Nov 25 07:27:59 2009  reading all ideals from disk
Wed Nov 25 07:28:12 2009  memory use: 661.3 MB
Wed Nov 25 07:28:17 2009  commencing in-memory singleton removal
Wed Nov 25 07:28:22 2009  begin with 36242567 relations and 36728595 unique ideals
Wed Nov 25 07:29:15 2009  reduce to 14764672 relations and 11920362 ideals in 21 passes
Wed Nov 25 07:29:15 2009  max relations containing the same ideal: 49
Wed Nov 25 07:29:19 2009  reading ideals above 720000
Wed Nov 25 07:29:20 2009  commencing singleton removal, initial pass
Wed Nov 25 07:34:45 2009  memory use: 298.4 MB
Wed Nov 25 07:34:45 2009  reading all ideals from disk
Wed Nov 25 07:34:54 2009  memory use: 501.5 MB
Wed Nov 25 07:34:59 2009  commencing in-memory singleton removal
Wed Nov 25 07:35:03 2009  begin with 14764763 relations and 14140030 unique ideals
Wed Nov 25 07:35:45 2009  reduce to 14760399 relations and 14135240 ideals in 10 passes
Wed Nov 25 07:35:45 2009  max relations containing the same ideal: 189
Wed Nov 25 07:36:05 2009  removing 2180612 relations and 1935203 ideals in 245409 cliques
Wed Nov 25 07:36:06 2009  commencing in-memory singleton removal
Wed Nov 25 07:36:10 2009  begin with 12579787 relations and 14135240 unique ideals
Wed Nov 25 07:36:49 2009  reduce to 12325260 relations and 11939746 ideals in 11 passes
Wed Nov 25 07:36:49 2009  max relations containing the same ideal: 164
Wed Nov 25 07:37:05 2009  removing 1622619 relations and 1377210 ideals in 245409 cliques
Wed Nov 25 07:37:07 2009  commencing in-memory singleton removal
Wed Nov 25 07:37:10 2009  begin with 10702641 relations and 11939746 unique ideals
Wed Nov 25 07:37:40 2009  reduce to 10529753 relations and 10386055 ideals in 10 passes
Wed Nov 25 07:37:40 2009  max relations containing the same ideal: 149
Wed Nov 25 07:37:54 2009  removing 107501 relations and 98145 ideals in 9356 cliques
Wed Nov 25 07:37:55 2009  commencing in-memory singleton removal
Wed Nov 25 07:37:57 2009  begin with 10422252 relations and 10386055 unique ideals
Wed Nov 25 07:38:15 2009  reduce to 10421333 relations and 10286989 ideals in 6 passes
Wed Nov 25 07:38:15 2009  max relations containing the same ideal: 147
Wed Nov 25 07:38:21 2009  relations with 0 large ideals: 2845
Wed Nov 25 07:38:21 2009  relations with 1 large ideals: 240
Wed Nov 25 07:38:21 2009  relations with 2 large ideals: 6154
Wed Nov 25 07:38:21 2009  relations with 3 large ideals: 65255
Wed Nov 25 07:38:21 2009  relations with 4 large ideals: 363951
Wed Nov 25 07:38:21 2009  relations with 5 large ideals: 1202136
Wed Nov 25 07:38:21 2009  relations with 6 large ideals: 2522194
Wed Nov 25 07:38:21 2009  relations with 7+ large ideals: 6258558
Wed Nov 25 07:38:21 2009  commencing 2-way merge
Wed Nov 25 07:38:42 2009  reduce to 6106240 relation sets and 5971895 unique ideals
Wed Nov 25 07:38:42 2009  commencing full merge
Wed Nov 25 07:42:16 2009  memory use: 632.6 MB
Wed Nov 25 07:42:18 2009  found 3166995 cycles, need 3150095
Wed Nov 25 07:42:18 2009  weight of 3150095 cycles is about 220790303 (70.09/cycle)
Wed Nov 25 07:42:18 2009  distribution of cycle lengths:
Wed Nov 25 07:42:18 2009  1 relations: 431731
Wed Nov 25 07:42:18 2009  2 relations: 392606
Wed Nov 25 07:42:18 2009  3 relations: 386090
Wed Nov 25 07:42:18 2009  4 relations: 345382
Wed Nov 25 07:42:18 2009  5 relations: 293444
Wed Nov 25 07:42:18 2009  6 relations: 254531
Wed Nov 25 07:42:18 2009  7 relations: 215315
Wed Nov 25 07:42:18 2009  8 relations: 176756
Wed Nov 25 07:42:18 2009  9 relations: 145428
Wed Nov 25 07:42:18 2009  10+ relations: 508812
Wed Nov 25 07:42:18 2009  heaviest cycle: 24 relations
Wed Nov 25 07:42:21 2009  commencing cycle optimization
Wed Nov 25 07:42:30 2009  start with 17464318 relations
Wed Nov 25 07:43:23 2009  pruned 322260 relations
Wed Nov 25 07:43:23 2009  memory use: 477.8 MB
Wed Nov 25 07:43:23 2009  distribution of cycle lengths:
Wed Nov 25 07:43:23 2009  1 relations: 431731
Wed Nov 25 07:43:23 2009  2 relations: 400095
Wed Nov 25 07:43:23 2009  3 relations: 397367
Wed Nov 25 07:43:23 2009  4 relations: 350474
Wed Nov 25 07:43:23 2009  5 relations: 298352
Wed Nov 25 07:43:23 2009  6 relations: 255742
Wed Nov 25 07:43:23 2009  7 relations: 215378
Wed Nov 25 07:43:23 2009  8 relations: 175429
Wed Nov 25 07:43:23 2009  9 relations: 143520
Wed Nov 25 07:43:23 2009  10+ relations: 482007
Wed Nov 25 07:43:23 2009  heaviest cycle: 24 relations
Wed Nov 25 07:43:43 2009  RelProcTime: 2519
Wed Nov 25 07:43:43 2009  
Wed Nov 25 07:43:43 2009  commencing linear algebra
Wed Nov 25 07:43:48 2009  read 3150095 cycles
Wed Nov 25 07:43:57 2009  cycles contain 10285527 unique relations
Wed Nov 25 07:55:13 2009  read 10285527 relations
Wed Nov 25 07:55:43 2009  using 20 quadratic characters above 536869410
Wed Nov 25 07:57:06 2009  building initial matrix
Wed Nov 25 08:00:39 2009  memory use: 1151.5 MB
Wed Nov 25 08:00:57 2009  read 3150095 cycles
Wed Nov 25 08:06:32 2009  matrix is 3149918 x 3150095 (902.9 MB) with weight 279978388 (88.88/col)
Wed Nov 25 08:06:32 2009  sparse part has weight 214627921 (68.13/col)
Wed Nov 25 08:08:10 2009  filtering completed in 2 passes
Wed Nov 25 08:08:11 2009  matrix is 3146755 x 3146931 (902.7 MB) with weight 279889156 (88.94/col)
Wed Nov 25 08:08:11 2009  sparse part has weight 214604908 (68.19/col)
Wed Nov 25 08:08:46 2009  read 3146931 cycles
Wed Nov 25 08:37:25 2009  matrix is 3146755 x 3146931 (902.7 MB) with weight 279889156 (88.94/col)
Wed Nov 25 08:37:25 2009  sparse part has weight 214604908 (68.19/col)
Wed Nov 25 08:37:25 2009  saving the first 48 matrix rows for later
Wed Nov 25 08:37:28 2009  matrix is 3146707 x 3146931 (855.2 MB) with weight 221919681 (70.52/col)
Wed Nov 25 08:37:28 2009  sparse part has weight 205309780 (65.24/col)
Wed Nov 25 08:37:28 2009  matrix includes 64 packed rows
Wed Nov 25 08:37:28 2009  using block size 65536 for processor cache size 4096 kB
Wed Nov 25 08:38:02 2009  commencing Lanczos iteration (8 threads)
Wed Nov 25 08:38:02 2009  memory use: 1068.7 MB
Thu Nov 26 05:51:48 2009  lanczos halted after 49761 iterations (dim = 3146707)
Thu Nov 26 05:51:57 2009  recovered 37 nontrivial dependencies
Thu Nov 26 05:51:58 2009  BLanczosTime: 79695
Thu Nov 26 05:51:58 2009  
Thu Nov 26 05:51:58 2009  commencing square root phase
Thu Nov 26 05:51:58 2009  reading relations for dependency 1
Thu Nov 26 05:52:01 2009  read 1574926 cycles
Thu Nov 26 05:52:06 2009  cycles contain 6243919 unique relations
Thu Nov 26 06:01:37 2009  read 6243919 relations
Thu Nov 26 06:02:38 2009  multiplying 5147940 relations
Thu Nov 26 06:13:47 2009  multiply complete, coefficients have about 145.85 million bits
Thu Nov 26 06:13:49 2009  initial square root is modulo 171541
Thu Nov 26 06:32:30 2009  sqrtTime: 2432
Thu Nov 26 06:32:30 2009  prp99 factor: 219631702931061976134369747885808367899858190913021959949302323867094375889693220762080723420749513
Thu Nov 26 06:32:30 2009  prp103 factor: 3945999849296329038851146075899153593764462405886868527184422610760144041919822331667205447984131245551
Thu Nov 26 06:32:30 2009  elapsed time 23:30:51

Nov 28, 2009

By Erik Branger / GGNFS, Msieve / Nov 28, 2009

(64·10²⁰⁵-1)/9 = 7(1)₂₀₅_<206> = 431 · 37940267 · 45453581976434362961_<20> · 3413498540067034957579963393050135213037_<40> · C137

C137 = P52 · P85

P52 = 5021904639112661884279481420515331308570490020937987_<52>

P85 = 5581147687333324553148372632272707694103863113163794664870316102823081173696895306077_<85>

Number: 71111_205
N=28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999
  ( 137 digits)
Divisors found:
 r1=5021904639112661884279481420515331308570490020937987 (pp52)
 r2=5581147687333324553148372632272707694103863113163794664870316102823081173696895306077 (pp85)
Version: Msieve v. 1.43
Total time: 379.42 hours.
Scaled time: 380.18 units (timescale=1.002).
Factorization parameters were as follows:
# Murphy_E = 3.341821e-11, selected by Jeff Gilchrist
n: 28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999
Y0: -200712814366335223924707637
Y1: 1865037990862081
c0: 42756225136356909361925341794202800
c1: 271117863504155830697150367460
c2: -599164415210628480558292
c3: -255405301427474975
c4: 342673420962
c5: 86040
skew: 1286946.34
type: gnfs
# selected mechanically
rlim: 14600000
alim: 14600000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6
Factor base limits: 14600000/14600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved algebraic special-q in [7300000, 18600001)
Primes: , , 
Relations: 23161909 relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2131553 x 2131777
Total sieving time: 365.37 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 12.50 hours.
Time per square root: 0.99 hours.
Prototype def-par.txt line would be:
gnfs,136,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,14600000,14600000,28,28,55,55,2.6,2.6,100000
total time: 379.42 hours.
 --------- CPU info (if available) ----------

Nov 27, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 27, 2009

(22·10¹⁶⁴-7)/3 = 7(3)₁₆₃1_<165> = 23 · 53901767 · 139612857686202560949310679923_<30> · C127

C127 = P49 · P78

P49 = 6754321484568289172985434187887056943790139178677_<49>

P78 = 627282892180425272457203747632461341968295653636265909025507998427062127369821_<78>

Number: 73331_164
N=4236870315556380098039369903323088181940804099761376480634290491976797824420141498514838608126730235966130123927245727176506817
  ( 127 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=6754321484568289172985434187887056943790139178677
 r2=627282892180425272457203747632461341968295653636265909025507998427062127369821
Version: 
Total time: 18.55 hours.
Scaled time: 44.21 units (timescale=2.383).
Factorization parameters were as follows:
n: 4236870315556380098039369903323088181940804099761376480634290491976797824420141498514838608126730235966130123927245727176506817
m: 1000000000000000000000000000000000
deg: 5
c5: 11
c0: -35
skew: 1.26
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 3600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9469802
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 701714 x 701962
Total sieving time: 16.64 hours.
Total relation processing time: 0.71 hours.
Matrix solve time: 1.12 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 18.55 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nov 27, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 27, 2009

(22·10¹⁷²-7)/3 = 7(3)₁₇₁1_<173> = 48214384732603_<14> · 4064286759125334773_<19> · C141

C141 = P34 · P108

P34 = 2528431516575789096617651796309427_<34>

P108 = 148009386868021114014136141181083786229874235422605861967736289169789771857161756134774694674396272086829287_<108>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=897477864
Step 1 took 42495ms
Step 2 took 14659ms
********** Factor found in step 2: 2528431516575789096617651796309427
Found probable prime factor of 34 digits: 2528431516575789096617651796309427
Probable prime cofactor 148009386868021114014136141181083786229874235422605861967736289169789771857161756134774694674396272086829287 has 108 digits

Nov 27, 2009 (2nd)

By Sinkiti Sibata / Msieve / Nov 27, 2009

(59·10¹⁸⁴+31)/9 = 6(5)₁₈₃9_<185> = 3 · 13 · 41 · C182

C182 = P64 · P118

P64 = 6813977917155969100374090114813988981026000167458606630278080087_<64>

P118 = 6016727141523583670134963894843856668867307701321458618205426905018934714457542819286019955552910616372334350104724943_<118>

Number: 65559_184
N=40997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510041
  ( 182 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=6813977917155969100374090114813988981026000167458606630278080087 (pp64)
 r2=6016727141523583670134963894843856668867307701321458618205426905018934714457542819286019955552910616372334350104724943 (pp118)
Version: Msieve v. 1.42
Total time: 12.43 hours.
Scaled time: 9.89 units (timescale=0.796).
Factorization parameters were as follows:
name: 65559_184
n: 40997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510041
m: 10000000000000000000000000000000000000
deg: 5
c5: 59
c0: 310
skew: 1.39
type: snfs
lss: 1
rlim: 9100000
alim: 9100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 9100000/9100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4550000, 8150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1832409 x 1832638
Total sieving time: 0.00 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 11.85 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,186.000,5,0,0,0,0,0,0,0,0,9100000,9100000,28,28,54,54,2.5,2.5,100000
total time: 12.43 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.19 BogoMIPS (lpj=1860598)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860574)
Total of 2 processors activated (7442.34 BogoMIPS).

Total time: 224 hours.

Nov 27, 2009

By Dmitry Domanov / GGNFS/msieve / Nov 27, 2009

(67·10¹⁶⁶-31)/9 = 7(4)₁₆₅1_<167> = 1361 · C164

C164 = P56 · P109

P56 = 36877280473198598114033606344601705893521134287453029239_<56>

P109 = 1483253158041523948079442997084179518478110622805970858351989516224667268559875468140693529675012634339151679_<109>

N=54698342721854845293493346395624132582251612376520532288350069393419871009878357416931994448526410319209731406645440444117887174463221487468364764470569026042942281
  ( 164 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=36877280473198598114033606344601705893521134287453029239 (pp56)
 r2=1483253158041523948079442997084179518478110622805970858351989516224667268559875468140693529675012634339151679 (pp109)
Version: Msieve-1.40
Total time: 71.53 hours.
Scaled time: 66.81 units (timescale=0.934).
Factorization parameters were as follows:
n: 54698342721854845293493346395624132582251612376520532288350069393419871009878357416931994448526410319209731406645440444117887174463221487468364764470569026042942281
m: 2000000000000000000000000000000000
deg: 5
c5: 335
c0: -496
skew: 1.08
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2300000, 5100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 881679 x 881908
Total sieving time: 69.81 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.42 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,169.000,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000
total time: 71.53 hours.
 --------- CPU info (if available) ----------

Nov 26, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 26, 2009

(64·10¹⁶⁴+17)/9 = 7(1)₁₆₃3_<165> = 17597 · 83719 · 553157761307_<12> · C144

C144 = P45 · P100

P45 = 170993170796291589495847649921540863092737789_<45>

P100 = 5103252092711526530908951977517372031589485749269566130240786228969544705813538735808435514565812117_<100>

Number: 71113_164
N=872621256705554537562497017054806961902356913310789643713475531853359484917297314630534101155105898937701858021584802387719938765947681719989313
  ( 144 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=170993170796291589495847649921540863092737789
 r2=5103252092711526530908951977517372031589485749269566130240786228969544705813538735808435514565812117
Version: 
Total time: 19.82 hours.
Scaled time: 47.16 units (timescale=2.379).
Factorization parameters were as follows:
n: 872621256705554537562497017054806961902356913310789643713475531853359484917297314630534101155105898937701858021584802387719938765947681719989313
m: 2000000000000000000000000000000000
deg: 5
c5: 1
c0: 85
skew: 2.43
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 3700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9460398
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 747913 x 748161
Total sieving time: 17.75 hours.
Total relation processing time: 0.75 hours.
Matrix solve time: 1.25 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 19.82 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nov 26, 2009

By Sinkiti Sibata / Msieve / Nov 26, 2009

(64·10¹⁶⁸+17)/9 = 7(1)₁₆₇3_<169> = 3 · 20327 · 127507 · 605117 · 67091077 · 28921206504282603801987443_<26> · C120

C120 = P50 · P71

P50 = 27517303792264798529463417344429815937905759318469_<50>

P71 = 28306260058824912668648377802778355092603705182291293454402273353147913_<71>

Number: 71113_168
N=778911957261536368479252748237453420091363555395653283447916728689860273052859142998360002144908357965800974034629705197
  ( 120 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=27517303792264798529463417344429815937905759318469 (pp50)
 r2=28306260058824912668648377802778355092603705182291293454402273353147913 (pp71)
Version: Msieve-1.40
Total time: 53.36 hours.
Scaled time: 178.43 units (timescale=3.344).
Factorization parameters were as follows:
name: 71113_168
n: 778911957261536368479252748237453420091363555395653283447916728689860273052859142998360002144908357965800974034629705197
m: 4000000000000000000000000000000000
deg: 5
c5: 125
c0: 34
skew: 0.77
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2400000, 5100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 963415 x 963663
Total sieving time: 51.24 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.77 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,170.000,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,52,52,2.4,2.4,100000
total time: 53.36 hours.
 --------- CPU info (if available) ----------

Nov 25, 2009 (5th)

By Lionel Debroux / GMP-ECM 6.2.3 / Nov 25, 2009

(64·10²⁹⁵-1)/9 = 7(1)₂₉₅_<296> = 138283 · 215123 · C286

C286 = P41 · C245

P41 = 27821253425770631779688809196979341911471_<41>

C245 = [85922149607726026782156764348422317355098680473279943458089419000214805543256458905381333491902976675767807884711080103009541396355333130708765008447187044809202021290263519849408848513151067396999960418817775487954720426652016355985801204889849_<245>]

$ echo 2390461899123524468141610636053234044959304079492194303969631663827271671500068555117428139137024327411407816062631071776594231652495314678420709429643785806299647702800471669183303102305194978145426958761047443438144237490094595452807414027153931517127656700294869702783643631664557879 | ecm -c 10 11e7
GMP-ECM 6.2.3 [powered by GMP 4.2.2] [ECM]
Input number is 2390461899123524468141610636053234044959304079492194303969631663827271671500068555117428139137024327411407816062631071776594231652495314678420709429643785806299647702800471669183303102305194978145426958761047443438144237490094595452807414027153931517127656700294869702783643631664557879 (286 digits)
Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=3203913405
Step 1 took 1851787ms
Step 2 took 612963ms
Run 2 out of 10:
Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=4242926597
Step 1 took 1853684ms
Step 2 took 610135ms
Run 3 out of 10:
Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=594201858
Step 1 took 1851104ms
Step 2 took 615097ms
********** Factor found in step 2: 27821253425770631779688809196979341911471
Found probable prime factor of 41 digits: 27821253425770631779688809196979341911471
Composite cofactor 85922149607726026782156764348422317355098680473279943458089419000214805543256458905381333491902976675767807884711080103009541396355333130708765008447187044809202021290263519849408848513151067396999960418817775487954720426652016355985801204889849 has 245 digits

Nov 25, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Nov 25, 2009

(67·10¹⁹⁰-13)/9 = 7(4)₁₈₉3_<191> = 137 · C189

C189 = P67 · P123

P67 = 1071541119796023713943872177373953979517368086289326500970465961839_<67>

P123 = 507110828875460829568417893845099794914673688551241728438396231258250485605676876586330307290817717364311369996839606707501_<123>

N=543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339
  ( 189 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=1071541119796023713943872177373953979517368086289326500970465961839 (pp67)
 r2=507110828875460829568417893845099794914673688551241728438396231258250485605676876586330307290817717364311369996839606707501 (pp123)
Version: Msieve-1.40
Total time: 365.07 hours.
Scaled time: 701.66 units (timescale=1.922).
Factorization parameters were as follows:
n: 543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339
m: 100000000000000000000000000000000000000
deg: 5
c5: 67
c0: -13
skew: 0.72
type: snfs
lss: 1
rlim: 11000000
alim: 11000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5500000, 11300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1986673 x 1986899
Total sieving time: 359.24 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 5.10 hours.
Time per square root: 0.49 hours.
Prototype def-par.txt line would be:
snfs,191.000,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,54,54,2.5,2.5,100000
total time: 365.07 hours.
 --------- CPU info (if available) ----------

(64·10³³⁷-1)/9 = 7(1)₃₃₇_<338> = 641 · 10305987443_<11> · 128091342428974354289_<21> · 1573635359835609855768700526548279_<34> · C272

C272 = P44 · P229

P44 = 23999825294513644566371981203556549145331093_<44>

P229 = 2225142674642345175756085094630621961303073772087561224909653062753168834580195174703734595980867983796542324738572237891366967450081957758673889677981721953767769280970762737157451510595720274177628529785960348826659378796242959_<229>

Factor=23999825294513644566371981203556549145331093  Method=ECM  B1=11000000  Sigma=3143255858

Nov 25, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 25, 2009

2·10¹⁹⁵-1 = 1(9)₁₉₅_<196> = 5899211 · 14379834023187049_<17> · C173

C173 = P61 · P112

P61 = 8005520506168541677107500091857021276142810375469214148691261_<61>

P112 = 2945049630407235486850246768492493463787273516148281573264435077057996480481973645153052764487171176571079917881_<112>

Number: 19999_195
N=23576655207909208424624202624006807544095893996706242465497479933717817335301260997188669857591848828615161079849847110159737109007441407916694060960678075171144655502337941
  ( 173 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=8005520506168541677107500091857021276142810375469214148691261
 r2=2945049630407235486850246768492493463787273516148281573264435077057996480481973645153052764487171176571079917881
Version: 
Total time: 209.06 hours.
Scaled time: 499.43 units (timescale=2.389).
Factorization parameters were as follows:
n: 23576655207909208424624202624006807544095893996706242465497479933717817335301260997188669857591848828615161079849847110159737109007441407916694060960678075171144655502337941
m: 1000000000000000000000000000000000000000
deg: 5
c5: 2
c0: -1
skew: 0.87
type: snfs
lss: 1
rlim: 12000000
alim: 12000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6000000, 11100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 22757439
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2150669 x 2150917
Total sieving time: 189.52 hours.
Total relation processing time: 6.29 hours.
Matrix solve time: 12.68 hours.
Time per square root: 0.57 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,55,55,2.5,2.5,100000
total time: 209.06 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nov 25, 2009 (2nd)

By juno1369 / GMP-ECM + Alpertron ECM (http://www.alpertron.com.ar/ECM.HTM) / Nov 25, 2009

(59·10¹⁵⁸+13)/9 = 6(5)₁₅₇7_<159> = 3 · 547 · 19577 · 20921 · 20562679 · 40037148484895545334741569_<26> · C115

C115 = P33 · P41 · P41

P33 = 714946817551994226795999183397417_<33>

P41 = 18512159506965237722555703148040570906717_<41>

P41 = 89515591408513589807357573543702422736479_<41>

********** Factor found in step 2: 714946817551994226795999183397417
Found probable prime factor of 33 digits: 714946817551994226795999183397417
Composite cofactor 1657126906514730606466839738594265639188592255458992054267231
172851540589382029443 has 82 digits

From Alpertron ECM (http://www.alpertron.com.ar/ECM.HTM)

Factors found for 1657126906514730606466839738594265639188592255458992054267231
172851540589382029443 (82 digits):

prp41: 18512159506965237722555703148040570906717 
prp41: 89515591408513589807357573543702422736479

Nov 25, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 25, 2009

(22·10¹⁶³+17)/3 = 7(3)₁₆₂9_<164> = 41 · 127 · 233861 · 206092781 · 799041773 · C138

C138 = P68 · P70

P68 = 42195990389398706948573405544460493579875597777044234523676722681367_<68>

P70 = 8666676725845304738171565873149213256863607609495312249724267546417367_<70>

Number: 73339_163
N=365699007831793930864297489675417334693538526289939085369313738587375155136237648640690605141401806350384006471083639028582599730736100689
  ( 138 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=42195990389398706948573405544460493579875597777044234523676722681367
 r2=8666676725845304738171565873149213256863607609495312249724267546417367
Version: 
Total time: 23.26 hours.
Scaled time: 55.59 units (timescale=2.390).
Factorization parameters were as follows:
n: 365699007831793930864297489675417334693538526289939085369313738587375155136237648640690605141401806350384006471083639028582599730736100689
m: 1000000000000000000000000000000000
deg: 5
c5: 11
c0: 850
skew: 2.39
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 4100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9997905
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 704228 x 704476
Total sieving time: 20.98 hours.
Total relation processing time: 0.95 hours.
Matrix solve time: 1.17 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 23.26 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nov 24, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve v. 1.43 / Nov 24, 2009

(44·10¹⁸⁸+1)/9 = 4(8)₁₈₇9_<189> = 3 · 67 · 12367047777863_<14> · 57831123768707_<14> · 457613923500905847935719079_<27> · C133

C133 = P43 · P44 · P47

P43 = 3845433339200043771803433770523203501433697_<43>

P44 = 39455414314368368652823846825558613685063769_<44>

P47 = 48981864669302978213702667920212673671860980707_<47>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3869374597
Step 1 took 38192ms
Step 2 took 14250ms
********** Factor found in step 2: 39455414314368368652823846825558613685063769
Found probable prime factor of 44 digits: 39455414314368368652823846825558613685063769
Composite cofactor 188356495415522399273375625775546911031815645086058261222593402241002941614660946956683779 has 90 digits
-------------------------------------
Tue Nov 24 14:30:17 2009  Msieve v. 1.43
Tue Nov 24 14:30:17 2009  random seeds: 05499020 7dd90afa
Tue Nov 24 14:30:17 2009  factoring 188356495415522399273375625775546911031815645086058261222593402241002941614660946956683779 (90 digits)
Tue Nov 24 14:30:18 2009  searching for 15-digit factors
Tue Nov 24 14:30:19 2009  commencing quadratic sieve (90-digit input)
Tue Nov 24 14:30:19 2009  using multiplier of 1
Tue Nov 24 14:30:19 2009  using 64kb Pentium 3 sieve core
Tue Nov 24 14:30:19 2009  sieve interval: 18 blocks of size 65536
Tue Nov 24 14:30:19 2009  processing polynomials in batches of 6
Tue Nov 24 14:30:19 2009  using a sieve bound of 1571777 (59667 primes)
Tue Nov 24 14:30:19 2009  using large prime bound of 125742160 (26 bits)
Tue Nov 24 14:30:19 2009  using double large prime bound of 379372269960400 (42-49 bits)
Tue Nov 24 14:30:19 2009  using trial factoring cutoff of 49 bits
Tue Nov 24 14:30:19 2009  polynomial 'A' values have 11 factors
Tue Nov 24 16:15:50 2009  59769 relations (16430 full + 43339 combined from 626554 partial), need 59763
Tue Nov 24 16:15:51 2009  begin with 642984 relations
Tue Nov 24 16:15:51 2009  reduce to 143182 relations in 9 passes
Tue Nov 24 16:15:51 2009  attempting to read 143182 relations
Tue Nov 24 16:15:53 2009  recovered 143182 relations
Tue Nov 24 16:15:53 2009  recovered 115145 polynomials
Tue Nov 24 16:15:53 2009  attempting to build 59769 cycles
Tue Nov 24 16:15:53 2009  found 59769 cycles in 6 passes
Tue Nov 24 16:15:53 2009  distribution of cycle lengths:
Tue Nov 24 16:15:53 2009     length 1 : 16430
Tue Nov 24 16:15:53 2009     length 2 : 11866
Tue Nov 24 16:15:53 2009     length 3 : 10611
Tue Nov 24 16:15:53 2009     length 4 : 7899
Tue Nov 24 16:15:53 2009     length 5 : 5480
Tue Nov 24 16:15:53 2009     length 6 : 3258
Tue Nov 24 16:15:53 2009     length 7 : 1952
Tue Nov 24 16:15:53 2009     length 9+: 2273
Tue Nov 24 16:15:53 2009  largest cycle: 18 relations
Tue Nov 24 16:15:54 2009  matrix is 59667 x 59769 (14.5 MB) with weight 3574237 (59.80/col)
Tue Nov 24 16:15:54 2009  sparse part has weight 3574237 (59.80/col)
Tue Nov 24 16:15:55 2009  filtering completed in 4 passes
Tue Nov 24 16:15:55 2009  matrix is 55137 x 55201 (13.6 MB) with weight 3340434 (60.51/col)
Tue Nov 24 16:15:55 2009  sparse part has weight 3340434 (60.51/col)
Tue Nov 24 16:15:55 2009  saving the first 48 matrix rows for later
Tue Nov 24 16:15:55 2009  matrix is 55089 x 55201 (9.8 MB) with weight 2725857 (49.38/col)
Tue Nov 24 16:15:55 2009  sparse part has weight 2231393 (40.42/col)
Tue Nov 24 16:15:55 2009  matrix includes 64 packed rows
Tue Nov 24 16:15:55 2009  using block size 22080 for processor cache size 1024 kB
Tue Nov 24 16:15:56 2009  commencing Lanczos iteration
Tue Nov 24 16:15:56 2009  memory use: 9.3 MB
Tue Nov 24 16:16:23 2009  lanczos halted after 872 iterations (dim = 55085)
Tue Nov 24 16:16:23 2009  recovered 15 nontrivial dependencies
Tue Nov 24 16:16:23 2009  prp43 factor: 3845433339200043771803433770523203501433697
Tue Nov 24 16:16:23 2009  prp47 factor: 48981864669302978213702667920212673671860980707
Tue Nov 24 16:16:23 2009  elapsed time 01:46:06

Nov 24, 2009 (2nd)

By Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve 1.44 SVN / Nov 24, 2009

(2·10¹⁹⁰-17)/3 = (6)₁₈₉1_<190> = 586961 · C185

C185 = P73 · P112

P73 = 3522100398505110525113530527897751734365915827795335855724148825683062971_<73>

P112 = 3224762712419591738492616930735227996266954799592039711609720258477080717575085454686644775301672161668689243631_<112>

Mon Nov 23 14:28:19 2009  
Mon Nov 23 14:28:19 2009  
Mon Nov 23 14:28:19 2009  Msieve v. 1.44
Mon Nov 23 14:28:19 2009  random seeds: b070f7b1 fdfdedbf
Mon Nov 23 14:28:19 2009  factoring 11357938034497465192179151028205735417969280184998094705894713050214011947415018487883635653248966569613086161885826599495821130648657520119167485857947404796343652587934576005333687701 (185 digits)
Mon Nov 23 14:28:24 2009  searching for 15-digit factors
Mon Nov 23 14:28:26 2009  commencing number field sieve (185-digit input)
Mon Nov 23 14:28:26 2009  R0: -100000000000000000000000000000000000000
Mon Nov 23 14:28:26 2009  R1:  1
Mon Nov 23 14:28:26 2009  A0: -17
Mon Nov 23 14:28:26 2009  A1:  0
Mon Nov 23 14:28:26 2009  A2:  0
Mon Nov 23 14:28:26 2009  A3:  0
Mon Nov 23 14:28:26 2009  A4:  0
Mon Nov 23 14:28:26 2009  A5:  2
Mon Nov 23 14:28:26 2009  skew 1.53, size 3.675878e-13, alpha 1.784858, combined = 4.412690e-11
Mon Nov 23 14:28:26 2009  
Mon Nov 23 14:28:26 2009  commencing linear algebra
Mon Nov 23 14:28:27 2009  read 1227138 cycles
Mon Nov 23 14:28:32 2009  cycles contain 3011522 unique relations
Mon Nov 23 14:30:07 2009  read 3011522 relations
Mon Nov 23 14:30:19 2009  using 20 quadratic characters above 268432140
Mon Nov 23 14:31:05 2009  building initial matrix
Mon Nov 23 14:33:20 2009  memory use: 395.9 MB
Mon Nov 23 14:33:21 2009  read 1227138 cycles
Mon Nov 23 14:33:28 2009  matrix is 1226938 x 1227138 (388.8 MB) with weight 114097390 (92.98/col)
Mon Nov 23 14:33:28 2009  sparse part has weight 88420184 (72.05/col)
Mon Nov 23 14:33:56 2009  filtering completed in 1 passes
Mon Nov 23 14:33:57 2009  matrix is 1226938 x 1227138 (388.8 MB) with weight 114097390 (92.98/col)
Mon Nov 23 14:33:57 2009  sparse part has weight 88420184 (72.05/col)
Mon Nov 23 14:34:18 2009  read 1227138 cycles
Mon Nov 23 14:34:25 2009  matrix is 1226938 x 1227138 (388.8 MB) with weight 114097390 (92.98/col)
Mon Nov 23 14:34:25 2009  sparse part has weight 88420184 (72.05/col)
Mon Nov 23 14:34:25 2009  saving the first 48 matrix rows for later
Mon Nov 23 14:34:27 2009  matrix is 1226890 x 1227138 (368.4 MB) with weight 91302722 (74.40/col)
Mon Nov 23 14:34:27 2009  sparse part has weight 84297943 (68.69/col)
Mon Nov 23 14:34:27 2009  matrix includes 64 packed rows
Mon Nov 23 14:34:27 2009  using block size 65536 for processor cache size 4096 kB
Mon Nov 23 14:34:42 2009  commencing Lanczos iteration
Mon Nov 23 14:34:42 2009  memory use: 361.6 MB
Mon Nov 23 14:35:04 2009  linear algebra at 0.1%, ETA 9h 0m
Mon Nov 23 14:35:44 2009  lanczos halted after 37 iterations (dim = 2338)
Mon Nov 23 14:35:44 2009  BLanczosTime: 438
Mon Nov 23 14:35:44 2009  elapsed time 00:07:25
Mon Nov 23 14:35:51 2009  
Mon Nov 23 14:35:51 2009  
Mon Nov 23 14:35:51 2009  Msieve v. 1.44
Mon Nov 23 14:35:51 2009  random seeds: 6b3576c1 3d110add
Mon Nov 23 14:35:51 2009  factoring 11357938034497465192179151028205735417969280184998094705894713050214011947415018487883635653248966569613086161885826599495821130648657520119167485857947404796343652587934576005333687701 (185 digits)
Mon Nov 23 14:35:55 2009  searching for 15-digit factors
Mon Nov 23 14:35:57 2009  commencing number field sieve (185-digit input)
Mon Nov 23 14:35:57 2009  R0: -100000000000000000000000000000000000000
Mon Nov 23 14:35:57 2009  R1:  1
Mon Nov 23 14:35:57 2009  A0: -17
Mon Nov 23 14:35:57 2009  A1:  0
Mon Nov 23 14:35:57 2009  A2:  0
Mon Nov 23 14:35:57 2009  A3:  0
Mon Nov 23 14:35:57 2009  A4:  0
Mon Nov 23 14:35:57 2009  A5:  2
Mon Nov 23 14:35:57 2009  skew 1.53, size 3.675878e-13, alpha 1.784858, combined = 4.412690e-11
Mon Nov 23 14:35:57 2009  
Mon Nov 23 14:35:57 2009  commencing linear algebra
Mon Nov 23 14:36:01 2009  read 1227138 cycles
Mon Nov 23 14:36:09 2009  matrix is 1226938 x 1227138 (388.8 MB) with weight 114097390 (92.98/col)
Mon Nov 23 14:36:09 2009  sparse part has weight 88420184 (72.05/col)
Mon Nov 23 14:36:09 2009  saving the first 48 matrix rows for later
Mon Nov 23 14:36:10 2009  matrix is 1226890 x 1227138 (368.4 MB) with weight 91302722 (74.40/col)
Mon Nov 23 14:36:10 2009  sparse part has weight 84297943 (68.69/col)
Mon Nov 23 14:36:10 2009  matrix includes 64 packed rows
Mon Nov 23 14:36:10 2009  using block size 65536 for processor cache size 4096 kB
Mon Nov 23 14:36:25 2009  commencing Lanczos iteration (2 threads)
Mon Nov 23 14:36:25 2009  memory use: 371.0 MB
Mon Nov 23 14:36:25 2009  restarting at iteration 37 (dim = 2338)
Mon Nov 23 14:36:40 2009  linear algebra at 0.3%, ETA 6h44m
Mon Nov 23 21:47:28 2009  lanczos halted after 19405 iterations (dim = 1226888)
Mon Nov 23 21:47:32 2009  recovered 36 nontrivial dependencies
Mon Nov 23 21:47:32 2009  BLanczosTime: 25895
Mon Nov 23 21:47:32 2009  elapsed time 07:11:41
Mon Nov 23 21:49:52 2009  
Mon Nov 23 21:49:52 2009  
Mon Nov 23 21:49:52 2009  Msieve v. 1.44
Mon Nov 23 21:49:52 2009  random seeds: 2800b6ca f4df187c
Mon Nov 23 21:49:52 2009  factoring 11357938034497465192179151028205735417969280184998094705894713050214011947415018487883635653248966569613086161885826599495821130648657520119167485857947404796343652587934576005333687701 (185 digits)
Mon Nov 23 21:49:57 2009  searching for 15-digit factors
Mon Nov 23 21:49:59 2009  commencing number field sieve (185-digit input)
Mon Nov 23 21:49:59 2009  R0: -100000000000000000000000000000000000000
Mon Nov 23 21:49:59 2009  R1:  1
Mon Nov 23 21:49:59 2009  A0: -17
Mon Nov 23 21:49:59 2009  A1:  0
Mon Nov 23 21:49:59 2009  A2:  0
Mon Nov 23 21:49:59 2009  A3:  0
Mon Nov 23 21:49:59 2009  A4:  0
Mon Nov 23 21:49:59 2009  A5:  2
Mon Nov 23 21:49:59 2009  skew 1.53, size 3.675878e-13, alpha 1.784858, combined = 4.412690e-11
Mon Nov 23 21:49:59 2009  
Mon Nov 23 21:49:59 2009  commencing square root phase
Mon Nov 23 21:49:59 2009  reading relations for dependency 1
Mon Nov 23 21:50:03 2009  read 612889 cycles
Mon Nov 23 21:50:05 2009  cycles contain 1503182 unique relations
Mon Nov 23 21:51:23 2009  read 1503182 relations
Mon Nov 23 21:51:43 2009  multiplying 1503182 relations
Mon Nov 23 21:57:34 2009  multiply complete, coefficients have about 37.19 million bits
Mon Nov 23 21:57:35 2009  initial square root is modulo 219041
Mon Nov 23 22:05:37 2009  reading relations for dependency 2
Mon Nov 23 22:05:41 2009  read 613137 cycles
Mon Nov 23 22:05:42 2009  cycles contain 1505808 unique relations
Mon Nov 23 22:06:57 2009  read 1505808 relations
Mon Nov 23 22:07:09 2009  multiplying 1505808 relations
Mon Nov 23 22:10:11 2009  multiply complete, coefficients have about 37.26 million bits
Mon Nov 23 22:10:11 2009  initial square root is modulo 223781
Mon Nov 23 22:16:18 2009  reading relations for dependency 3
Mon Nov 23 22:16:22 2009  read 612903 cycles
Mon Nov 23 22:16:24 2009  cycles contain 1504284 unique relations
Mon Nov 23 22:17:40 2009  read 1504284 relations
Mon Nov 23 22:17:52 2009  multiplying 1504284 relations
Mon Nov 23 22:20:53 2009  multiply complete, coefficients have about 37.22 million bits
Mon Nov 23 22:20:54 2009  initial square root is modulo 221101
Mon Nov 23 22:26:51 2009  reading relations for dependency 4
Mon Nov 23 22:26:56 2009  read 612973 cycles
Mon Nov 23 22:26:58 2009  cycles contain 1504386 unique relations
Mon Nov 23 22:28:13 2009  read 1504386 relations
Mon Nov 23 22:28:24 2009  multiplying 1504386 relations
Mon Nov 23 22:31:25 2009  multiply complete, coefficients have about 37.22 million bits
Mon Nov 23 22:31:25 2009  initial square root is modulo 221201
Mon Nov 23 22:37:27 2009  reading relations for dependency 5
Mon Nov 23 22:37:32 2009  read 614430 cycles
Mon Nov 23 22:37:33 2009  cycles contain 1508298 unique relations
Mon Nov 23 22:38:49 2009  read 1508298 relations
Mon Nov 23 22:39:00 2009  multiplying 1508298 relations
Mon Nov 23 22:42:00 2009  multiply complete, coefficients have about 37.32 million bits
Mon Nov 23 22:42:01 2009  initial square root is modulo 228451
Mon Nov 23 22:48:03 2009  reading relations for dependency 6
Mon Nov 23 22:48:08 2009  read 613942 cycles
Mon Nov 23 22:48:09 2009  cycles contain 1506000 unique relations
Mon Nov 23 22:49:24 2009  read 1506000 relations
Mon Nov 23 22:49:36 2009  multiplying 1506000 relations
Mon Nov 23 22:52:36 2009  multiply complete, coefficients have about 37.27 million bits
Mon Nov 23 22:52:37 2009  initial square root is modulo 224261
Mon Nov 23 22:58:35 2009  sqrtTime: 4116
Mon Nov 23 22:58:35 2009  prp73 factor: 3522100398505110525113530527897751734365915827795335855724148825683062971
Mon Nov 23 22:58:35 2009  prp112 factor: 3224762712419591738492616930735227996266954799592039711609720258477080717575085454686644775301672161668689243631
Mon Nov 23 22:58:35 2009  elapsed time 01:08:43

Nov 24, 2009

By Erik Branger / GGNFS, Msieve / Nov 24, 2009

(65·10¹⁶⁸+61)/9 = 7(2)₁₆₇9_<169> = 7 · 263 · 55893627458327_<14> · C152

C152 = P71 · P82

P71 = 16686719216640258914430547376206697539119714819396999595221215196753619_<71>

P82 = 4206140780347737673879122417993167985752911241206637624428896147475792512758851313_<82>

Number: 72229_168
N=70186690187322848534813391255912423242710432254098754707341062929635389927685614871669166935399377870972333874531367371664986282656059306612965115651747
  ( 152 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=16686719216640258914430547376206697539119714819396999595221215196753619 (pp71)
 r2=4206140780347737673879122417993167985752911241206637624428896147475792512758851313 (pp82)
Version: Msieve v. 1.43
Total time: 123.43 hours.
Scaled time: 97.51 units (timescale=0.790).
Factorization parameters were as follows:
n: 70186690187322848534813391255912423242710432254098754707341062929635389927685614871669166935399377870972333874531367371664986282656059306612965115651747
m: 5000000000000000000000000000000000
deg: 5
c5: 104
c0: 305
skew: 1.24
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 5650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 952088 x 952313
Total sieving time: 116.58 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 5.86 hours.
Time per square root: 0.60 hours.
Prototype def-par.txt line would be:
snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 123.43 hours.
 --------- CPU info (if available) ----------

Nov 23, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 23, 2009

(65·10¹⁶³+7)/9 = 7(2)₁₆₂3_<164> = 23291 · 214849 · 16175813 · C147

C147 = P69 · P79

P69 = 813256512052658243117005216012106187806335489002678159581152113487081_<69>

P79 = 1097123981090889200601269157296277423248544642116547145585024451148021609609649_<79>

Number: 72223_163
N=892243222151303127585237134646888700719111322344662705134948669982776787671783703532461989654078209429613406012214041099368896840129135168614444569
  ( 147 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=813256512052658243117005216012106187806335489002678159581152113487081
 r2=1097123981090889200601269157296277423248544642116547145585024451148021609609649
Version: 
Total time: 24.00 hours.
Scaled time: 57.32 units (timescale=2.388).
Factorization parameters were as follows:
n: 892243222151303127585237134646888700719111322344662705134948669982776787671783703532461989654078209429613406012214041099368896840129135168614444569
m: 1000000000000000000000000000000000
deg: 5
c5: 13
c0: 140
skew: 1.61
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9802166
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 762660 x 762908
Total sieving time: 21.69 hours.
Total relation processing time: 0.96 hours.
Matrix solve time: 1.27 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 24.00 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nov 23, 2009 (3rd)

By Sinkiti Sibata / Msieve / Nov 23, 2009

(65·10¹⁶¹-11)/9 = 7(2)₁₆₀1_<162> = 20084017 · 191866891 · C147

C147 = P69 · P78

P69 = 311840341079435138195582161480994283224403261766637618030009178235597_<69>

P78 = 601018626647427049816918876130796226415550083819651184343799035882306940635219_<78>

Number: 72221_161
N=187421853528827335653389337039146572529035106115131310350823349232846759604043170270164712568736461349957588460504114904477258557263588332817690743
  ( 147 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=311840341079435138195582161480994283224403261766637618030009178235597 (pp69)
 r2=601018626647427049816918876130796226415550083819651184343799035882306940635219 (pp78)
Version: Msieve-1.40
Total time: 29.98 hours.
Scaled time: 100.61 units (timescale=3.356).
Factorization parameters were as follows:
name: 72221_161
n: 187421853528827335653389337039146572529035106115131310350823349232846759604043170270164712568736461349957588460504114904477258557263588332817690743
m: 200000000000000000000000000000000
deg: 5
c5: 325
c0: -176
skew: 0.88
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 3500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 661825 x 662073
Total sieving time: 28.97 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.82 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,164.000,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 29.98 hours.
 --------- CPU info (if available) ----------

Nov 23, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 23, 2009

(67·10¹⁹⁷+41)/9 = 7(4)₁₉₆9_<198> = 6271 · C195

C195 = P32 · C163

P32 = 14804814301257493957368027068209_<32>

C163 = [8018488822340487237390691124028521224201676513048994685760860292500214647027078234420861913727315979617472630756131310269280591852145065737118488621600044708379791_<163>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2933211590
Step 1 took 75324ms
Step 2 took 22413ms
********** Factor found in step 2: 14804814301257493957368027068209
Found probable prime factor of 32 digits: 14804814301257493957368027068209
Composite cofactor 8018488822340487237390691124028521224201676513048994685760860292500214647027078234420861913727315979617472630756131310269280591852145065737118488621600044708379791 has 163 digits

(22·10¹⁹⁵-7)/3 = 7(3)₁₉₄1_<196> = 3137 · C193

C193 = P42 · P151

P42 = 865705014948683820695382200352934286953759_<42>

P151 = 2700330825097480678864281228686638696675856044230083140116407966903315950254431328829179821478217319803331163711026706022488383947812078822791851974157_<151>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2548502624
Step 1 took 70148ms
Step 2 took 21764ms
********** Factor found in step 2: 865705014948683820695382200352934286953759
Found probable prime factor of 42 digits: 865705014948683820695382200352934286953759
Probable prime cofactor 2700330825097480678864281228686638696675856044230083140116407966903315950254431328829179821478217319803331163711026706022488383947812078822791851974157 has 151 digits

Nov 23, 2009

By Dmitry Domanov / ECMNET, GMP-ECM / Nov 23, 2009

(65·10¹⁷¹+61)/9 = 7(2)₁₇₀9_<172> = 59 · 103231 · 288734940313_<12> · C154

C154 = P37 · P117

P37 = 5341730797111883898281272847651922239_<37>

P117 = 768824761082780205497364438889436595941143966789197894042997226025202898341403395396514044299198931236559010774835143_<117>

Factor=5341730797111883898281272847651922239  Method=ECM  B1=11000000  Sigma=3634509346

(26·10¹⁶⁷-11)/3 = 8(6)₁₆₆3_<168> = 7 · 17 · 691 · 229656809 · C155

C155 = P34 · C122

P34 = 1622000506706154937986411401046767_<34>

C122 = [28294157895160621844921147954393461978100031316274893426210418177756993778953017327769043546792385145405456209408807687549_<122>]

Factor=1622000506706154937986411401046767  Method=ECM  B1=11000000  Sigma=420641482

Nov 22, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 22, 2009

(65·10¹⁶²-11)/9 = 7(2)₁₆₁1_<163> = 3 · 59 · 1999 · 4773779 · C151

C151 = P74 · P77

P74 = 70720939585198509430447494622061780717823615546513973846559159308700434243_<74>

P77 = 60460878757510508486907856776275737477095178737018964166774638595681693266091_<77>

Number: 72221_162
N=4275850153877912590311748739884690843676410802291770101508765288141718738539635449718707640413237336721787300567069698882361479787286593316820647154113
  ( 151 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=70720939585198509430447494622061780717823615546513973846559159308700434243
 r2=60460878757510508486907856776275737477095178737018964166774638595681693266091
Version: 
Total time: 24.47 hours.
Scaled time: 58.51 units (timescale=2.391).
Factorization parameters were as follows:
n: 4275850153877912590311748739884690843676410802291770101508765288141718738539635449718707640413237336721787300567069698882361479787286593316820647154113
m: 500000000000000000000000000000000
deg: 5
c5: 52
c0: -275
skew: 1.40
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9691817
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 780277 x 780525
Total sieving time: 21.87 hours.
Total relation processing time: 0.95 hours.
Matrix solve time: 1.40 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 24.47 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nov 22, 2009

By Sinkiti Sibata / Msieve / Nov 22, 2009

(64·10¹⁶¹+17)/9 = 7(1)₁₆₀3_<162> = 13 · 47 · 73 · 971 · 3258491 · 17762837059301_<14> · C135

C135 = P61 · P75

P61 = 1045053944364224676875037140958936245274636458765532056637397_<61>

P75 = 271447969722802002620888132932935879664564355019942468315186681947716233563_<75>

Number: 71113_161
N=283677771448474868630729904666453613625367285272102371126053240308003259939380549919808427192636724065025504641791378151488079652355511
  ( 135 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=1045053944364224676875037140958936245274636458765532056637397 (pp61)
 r2=271447969722802002620888132932935879664564355019942468315186681947716233563 (pp75)
Version: Msieve-1.40
Total time: 27.72 hours.
Scaled time: 93.03 units (timescale=3.356).
Factorization parameters were as follows:
name: 71113_161
n: 283677771448474868630729904666453613625367285272102371126053240308003259939380549919808427192636724065025504641791378151488079652355511
m: 200000000000000000000000000000000
deg: 5
c5: 20
c0: 17
skew: 0.97
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1800000, 3300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 613486 x 613734
Total sieving time: 26.85 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.70 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,162.000,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000
total time: 27.72 hours.
 --------- CPU info (if available) ----------

Nov 21, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM / Nov 20, 2009

(59·10¹⁶¹+31)/9 = 6(5)₁₆₀9_<162> = 210347 · 322840801 · C148

C148 = P44 · P105

P44 = 16143737774649079582774376407801783420888231_<44>

P105 = 597971752607197952577929926186380895991725103128877040652814302508296522632908336217817296076502480481187_<105>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 9653499170737935827020930703101546284142908607431751644711794372056984430617103889827634872490523601821211444382589425755902035305126233259825210197 (148 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5772938245
Step 1 took 4633ms
Step 2 took 4586ms
********** Factor found in step 2: 16143737774649079582774376407801783420888231
Found probable prime factor of 44 digits: 16143737774649079582774376407801783420888231
Probable prime cofactor 597971752607197952577929926186380895991725103128877040652814302508296522632908336217817296076502480481187 has 105 digits

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 21, 2009

(59·10¹⁶¹+13)/9 = 6(5)₁₆₀7_<162> = 3 · 7 · 53 · 743 · 196771241 · 2740438472617133_<16> · C133

C133 = P52 · P81

P52 = 5709310195720236828643845210386126013088462671987029_<52>

P81 = 257489903231838133471085108012293074391834736416021232004557239035900683554813379_<81>

Number: 65557_161
N=1470089729816550615327746631666522054342149372565640256703912340728756124298045838952847268330437311459786713438678509201299203660991
  ( 133 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=5709310195720236828643845210386126013088462671987029
 r2=257489903231838133471085108012293074391834736416021232004557239035900683554813379
Version: 
Total time: 23.22 hours.
Scaled time: 54.90 units (timescale=2.365).
Factorization parameters were as follows:
n: 1470089729816550615327746631666522054342149372565640256703912340728756124298045838952847268330437311459786713438678509201299203660991
m: 100000000000000000000000000000000
deg: 5
c5: 590
c0: 13
skew: 0.47
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 3900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9714777
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 739625 x 739873
Total sieving time: 20.93 hours.
Total relation processing time: 0.95 hours.
Matrix solve time: 1.24 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 23.22 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nov 21, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Nov 21, 2009

(19·10¹⁸⁸+11)/3 = 6(3)₁₈₇7_<189> = 7 · 13 · 43 · C186

C186 = P73 · P113

P73 = 5821078419106027523809386387218682764306133231192700907154676066616935391_<73>

P113 = 27804753444740559479686096411255814898532711759314529476640305709597762933252999828353482262529345803167942993039_<113>

N=161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743249
  ( 186 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=5821078419106027523809386387218682764306133231192700907154676066616935391 (pp73)
 r2=27804753444740559479686096411255814898532711759314529476640305709597762933252999828353482262529345803167942993039 (pp113)
Version: Msieve-1.40
Total time: 302.13 hours.
Scaled time: 570.42 units (timescale=1.888).
Factorization parameters were as follows:
n: 161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743249
m: 50000000000000000000000000000000000000
deg: 5
c5: 152
c0: 275
skew: 1.13
type: snfs
lss: 1
rlim: 10500000
alim: 10500000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10500000/10500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5250000, 9950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1979065 x 1979290
Total sieving time: 295.46 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 5.00 hours.
Time per square root: 1.43 hours.
Prototype def-par.txt line would be:
snfs,190.000,5,0,0,0,0,0,0,0,0,10500000,10500000,28,28,54,54,2.5,2.5,100000
total time: 302.13 hours.
 --------- CPU info (if available) ----------

(22·10¹⁶⁵+17)/3 = 7(3)₁₆₄9_<166> = 862139 · 42698939 · C153

C153 = P39 · P114

P39 = 364142907767587768742722435741327326329_<39>

P114 = 547060294841478817301959720522487529530706748367558955882874997756231160054020556062246281597883447113999513409771_<114>

Factor=364142907767587768742722435741327326329  Method=ECM  B1=11000000  Sigma=2604005257

Nov 21, 2009

By Sinkiti Sibata / Msieve / Nov 21, 2009

(67·10¹⁶⁰+41)/9 = 7(4)₁₅₉9_<161> = 109 · 66347 · 90637257619_<11> · 58054843192433_<14> · C130

C130 = P61 · P69

P61 = 6458162601207874684709389465413979594157825818758560151613079_<61>

P69 = 302921652034106781572164003165353167420092868163923517757663653696611_<69>

Number: 74449_160
N=1956317284262773736098062881121294614246555144986523186725985290723465938887825663867140407665727444773244943801461623492925575269
  ( 130 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=6458162601207874684709389465413979594157825818758560151613079 (pp61)
 r2=302921652034106781572164003165353167420092868163923517757663653696611 (pp69)
Version: Msieve-1.40
Total time: 27.61 hours.
Scaled time: 91.71 units (timescale=3.322).
Factorization parameters were as follows:
name: 74449_160
n: 1956317284262773736098062881121294614246555144986523186725985290723465938887825663867140407665727444773244943801461623492925575269
m: 100000000000000000000000000000000
deg: 5
c5: 67
c0: 41
skew: 0.91
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 621450 x 621698
Total sieving time: 26.76 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.72 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 27.61 hours.
 --------- CPU info (if available) ----------

Nov 20, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 20, 2009

(26·10¹⁶¹-11)/3 = 8(6)₁₆₀3_<162> = 7 · 181 · 17387 · 11596073 · 58262188035421_<14> · C134

C134 = P48 · P87

P48 = 456470417364139674264780752174404710974590776491_<48>

P87 = 127567620784121598321005285879102169613744974602163293210674456685787644756891735053249_<87>

Number: 86663_161
N=58230845101478284843358896477726731596932608490207254663143255682978657099665099256090779442717396787440080924159907391956186142369259
  ( 134 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=456470417364139674264780752174404710974590776491
 r2=127567620784121598321005285879102169613744974602163293210674456685787644756891735053249
Version: 
Total time: 16.77 hours.
Scaled time: 39.99 units (timescale=2.385).
Factorization parameters were as follows:
n: 58230845101478284843358896477726731596932608490207254663143255682978657099665099256090779442717396787440080924159907391956186142369259
m: 100000000000000000000000000000000
deg: 5
c5: 260
c0: -11
skew: 0.53
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 3300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9344646
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 671327 x 671575
Total sieving time: 15.03 hours.
Total relation processing time: 0.64 hours.
Matrix solve time: 0.94 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 16.77 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nov 20, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 20, 2009

(67·10¹⁸¹-13)/9 = 7(4)₁₈₀3_<182> = 127 · 15370583931178846189_<20> · 2253776873153776657897948451534279_<34> · C128

C128 = P41 · P87

P41 = 29200237533398076379310161749061933957963_<41>

P87 = 579483271331262398610183787231750323193470397486915683574230974601792989962677800929853_<87>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4221356910
Step 1 took 38433ms
Step 2 took 13993ms
********** Factor found in step 2: 29200237533398076379310161749061933957963
Found probable prime factor of 41 digits: 29200237533398076379310161749061933957963
Probable prime cofactor 579483271331262398610183787231750323193470397486915683574230974601792989962677800929853 has 87 digits

(64·10¹⁹⁸+71)/9 = 7(1)₁₉₇9_<199> = 3 · 2179 · C196

C196 = P36 · P160

P36 = 650785158455981940062100473969000731_<36>

P160 = 1671557573283360183804878381813370410004043685577428419417647214928170607746446482254417566351134107881259634051566957814751822022316355735422517371501836929077_<160>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=68033887
Step 1 took 75578ms
Step 2 took 22441ms
********** Factor found in step 2: 650785158455981940062100473969000731
Found probable prime factor of 36 digits: 650785158455981940062100473969000731
Probable prime cofactor 1671557573283360183804878381813370410004043685577428419417647214928170607746446482254417566351134107881259634051566957814751822022316355735422517371501836929077 has 160 digits

Nov 20, 2009

By Markus Tervooren / Msieve / Nov 20, 2009

(67·10¹⁶¹+41)/9 = 7(4)₁₆₀9_<162> = 107 · 3701 · 610339 · 33303780809228167275307_<23> · C128

C128 = P38 · P91

P38 = 75535187214103326538317201830040895523_<38>

P91 = 1224377835729844775852488587301078768602817876340329293496172248138770697175289478200468733_<91>

Sieving took ~50 Core2 2,66Ghz-hours.

Msieve v. 1.43
Thu Nov 19 23:37:53 2009
random seeds: 33e3b9eb 433b3587
factoring 92483609042652474194535864343706609135442894008901028868852650839468327428630927857786325232318759223661128228852786657681182359 (128 digits)
searching for 15-digit factors
commencing number field sieve (128-digit input)
R0: -10000000000000000000000000000000000000000
R1:  1
A0:  41
A1:  0
A2:  0
A3:  0
A4:  670
skew 0.49, size 6.343425e-17, alpha -0.256694, combined = 2.982526e-10

commencing relation filtering
estimated available RAM is 8010.2 MB
commencing duplicate removal, pass 1
found 954666 hash collisions in 4340988 relations
added 1374 free relations
commencing duplicate removal, pass 2
found 962823 duplicates and 3379539 unique relations
memory use: 22.6 MB
reading ideals above 100000
commencing singleton removal, initial pass
memory use: 94.1 MB
reading all ideals from disk
memory use: 120.5 MB
keeping 3494492 ideals with weight <= 200, target excess is 20944
commencing in-memory singleton removal
begin with 3379539 relations and 3494492 unique ideals
reduce to 2114129 relations and 1996280 ideals in 11 passes
max relations containing the same ideal: 148
removing 238747 relations and 191970 ideals in 46777 cliques
commencing in-memory singleton removal
begin with 1875382 relations and 1996280 unique ideals
reduce to 1859093 relations and 1787574 ideals in 7 passes
max relations containing the same ideal: 135
removing 178875 relations and 132098 ideals in 46777 cliques
commencing in-memory singleton removal
begin with 1680218 relations and 1787574 unique ideals
reduce to 1669207 relations and 1644169 ideals in 6 passes
max relations containing the same ideal: 128
relations with 0 large ideals: 1163
relations with 1 large ideals: 16
relations with 2 large ideals: 354
relations with 3 large ideals: 4469
relations with 4 large ideals: 29966
relations with 5 large ideals: 168469
relations with 6 large ideals: 284122
relations with 7+ large ideals: 1180648
commencing 2-way merge
reduce to 1229772 relation sets and 1204734 unique ideals
commencing full merge
memory use: 153.3 MB
found 628615 cycles, need 624934
weight of 624934 cycles is about 43940256 (70.31/cycle)
distribution of cycle lengths:
1 relations: 41923
2 relations: 67759
3 relations: 78031
4 relations: 75883
5 relations: 67754
6 relations: 59751
7 relations: 50497
8 relations: 41772
9 relations: 33672
10+ relations: 107892
heaviest cycle: 24 relations
commencing cycle optimization
start with 3747573 relations
pruned 139208 relations
memory use: 109.3 MB
distribution of cycle lengths:
1 relations: 41923
2 relations: 69513
3 relations: 82026
4 relations: 78704
5 relations: 70580
6 relations: 61436
7 relations: 51233
8 relations: 41576
9 relations: 33373
10+ relations: 94570
heaviest cycle: 23 relations
RelProcTime: 129

commencing linear algebra
read 624934 cycles
cycles contain 1653741 unique relations
read 1653741 relations
using 20 quadratic characters above 33554250
building initial matrix
memory use: 212.7 MB
read 624934 cycles
matrix is 624757 x 624934 (186.0 MB) with weight 56594097 (90.56/col)
sparse part has weight 41878845 (67.01/col)
filtering completed in 2 passes
matrix is 624708 x 624885 (186.0 MB) with weight 56592419 (90.56/col)
sparse part has weight 41878378 (67.02/col)
read 624885 cycles
matrix is 624708 x 624885 (186.0 MB) with weight 56592419 (90.56/col)
sparse part has weight 41878378 (67.02/col)
saving the first 48 matrix rows for later
matrix is 624660 x 624885 (177.1 MB) with weight 44687252 (71.51/col)
sparse part has weight 40186863 (64.31/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (4 threads)
memory use: 186.9 MB
linear algebra at 0.2%, ETA 0h27m624885 dimensions (0.2%, ETA 0h27m)
linear algebra completed 624534 of 624885 dimensions (99.9%, ETA 0h 0m)
lanczos halted after 9879 iterations (dim = 624658)
recovered 37 nontrivial dependencies
BLanczosTime: 1716

commencing square root phase
reading relations for dependency 1
read 312907 cycles
cycles contain 828596 unique relations
read 828596 relations
multiplying 828596 relations
multiply complete, coefficients have about 25.82 million bits
initial square root is modulo 26105269
reading relations for dependency 2
read 312740 cycles
cycles contain 828130 unique relations
read 828130 relations
multiplying 828130 relations
multiply complete, coefficients have about 25.81 million bits
initial square root is modulo 25855117
reading relations for dependency 3
read 312584 cycles
cycles contain 827416 unique relations
read 827416 relations
multiplying 827416 relations
multiply complete, coefficients have about 25.79 million bits
initial square root is modulo 25473181
sqrtTime: 243
prp38 factor: 75535187214103326538317201830040895523
prp91 factor: 1224377835729844775852488587301078768602817876340329293496172248138770697175289478200468733
elapsed time 00:34:49

Nov 19, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 19, 2009

(67·10¹⁶⁰-13)/9 = 7(4)₁₅₉3_<161> = 223 · 2790386777_<10> · 1084302893662699352989_<22> · C129

C129 = P51 · P78

P51 = 363065558163129755586591876057933957697079245966993_<51>

P78 = 303897660134854542414694170874725162056604936336714237480477623856561460344929_<78>

Number: 74443_160
N=110334773601330070711761593600846340762094802874387964650626689471684650737015293850889407842085069929569671853321483121928928497
  ( 129 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=363065558163129755586591876057933957697079245966993
 r2=303897660134854542414694170874725162056604936336714237480477623856561460344929
Version: 
Total time: 18.57 hours.
Scaled time: 44.30 units (timescale=2.386).
Factorization parameters were as follows:
n: 110334773601330070711761593600846340762094802874387964650626689471684650737015293850889407842085069929569671853321483121928928497
m: 100000000000000000000000000000000
deg: 5
c5: 67
c0: -13
skew: 0.72
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9630508
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 632716 x 632964
Total sieving time: 16.59 hours.
Total relation processing time: 0.74 hours.
Matrix solve time: 0.86 hours.
Time per square root: 0.38 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 18.57 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nov 19, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve / Nov 19, 2009

(65·10¹⁶⁷+61)/9 = 7(2)₁₆₆9_<168> = 3 · 3163 · 1283549 · 1810364976295258400527_<22> · 6731034634722746219253576990142331_<34> · C103

C103 = P41 · P63

P41 = 43887433213139645955484994448382146047239_<41>

P63 = 110879128047013805011879885468739184560992940355555347685320723_<63>

N=4866200326894477313327351434330702713602820686731038277709376544750901688090575230106979546318423633797
  ( 103 digits)
Divisors found:
 r1=43887433213139645955484994448382146047239 (pp41)
 r2=110879128047013805011879885468739184560992940355555347685320723 (pp63)
Version: Msieve-1.40
Total time: 6.11 hours.
Scaled time: 11.18 units (timescale=1.829).
Factorization parameters were as follows:
name: gg103
n: 4866200326894477313327351434330702713602820686731038277709376544750901688090575230106979546318423633797
skew: 3105.38
# norm 1.91e+014
c5: 1392300
c4: 5986291355
c3: -32719573776586
c2: -35617074683990928
c1: 196103299995263016226
c0: -71023059451757055174092
# alpha -6.16
Y1: 84365831159
Y0: -20355880109292170055
# Murphy_E 2.38e-009
# M 1588861051919919182070347774998276303263568046023222671646578452552654468614274410016547985992962233523
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 220234 x 220457
Polynomial selection time: 0.56 hours.
Total sieving time: 5.26 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 6.11 hours.
 --------- CPU info (if available) ----------

Nov 19, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 19, 2009

(59·10¹⁷⁰+13)/9 = 6(5)₁₆₉7_<171> = 3 · 31 · 73 · 229 · 2371 · 136027 · C157

C157 = P33 · C124

P33 = 233155008560892980603136314014073_<33>

C124 = [5607467793672916357063206022743587336819544589797022881608229298842144002627748832647796629860992889557912488547520943964517_<124>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3871599622
Step 1 took 52361ms
Step 2 took 17180ms
********** Factor found in step 2: 233155008560892980603136314014073
Found probable prime factor of 33 digits: 233155008560892980603136314014073
Composite cofactor 5607467793672916357063206022743587336819544589797022881608229298842144002627748832647796629860992889557912488547520943964517 has 124 digits

(59·10¹⁷¹+31)/9 = 6(5)₁₇₀9_<172> = 7 · 1319207906438579_<16> · C156

C156 = P37 · P120

P37 = 2356463302077488153069650734241665823_<37>

P120 = 301257269819596050498849046453150412524164514988049351771398639204280300958087733288868202951958003834996085783952664261_<120>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2957564567
Step 1 took 52204ms
Step 2 took 17141ms
********** Factor found in step 2: 2356463302077488153069650734241665823
Found probable prime factor of 37 digits: 2356463302077488153069650734241665823
Probable prime cofactor 301257269819596050498849046453150412524164514988049351771398639204280300958087733288868202951958003834996085783952664261 has 120 digits

(22·10¹⁷²+17)/3 = 7(3)₁₇₁9_<173> = 7 · 241 · 3371 · 14678148955213_<14> · C153

C153 = P34 · C120

P34 = 4675036528889963296972072581793651_<34>

C120 = [187919259193893023850805073342750434538681070849906401604520432741490252970095903458623817348949668880171189653291036289_<120>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2243017104
Step 1 took 47067ms
********** Factor found in step 1: 4675036528889963296972072581793651
Found probable prime factor of 34 digits: 4675036528889963296972072581793651
Composite cofactor 187919259193893023850805073342750434538681070849906401604520432741490252970095903458623817348949668880171189653291036289 has 120 digits

Nov 19, 2009 (2nd)

By Sinkiti Sibata / Msieve / Nov 19, 2009

(65·10¹⁶⁰+7)/9 = 7(2)₁₅₉3_<161> = 89 · 691 · 1063 · 30689 · 80147 · 345231714617358424861_<21> · C124

C124 = P47 · P77

P47 = 20357986503829909242696372348001111417687352381_<47>

P77 = 63907821471927606482939461715126003027541213468536152840468146898123845327793_<77>

Number: 72223_160
N=1301034567014673497892919265231793046878598035690062464234773174782366433468283011049257436954506807102849869231615244025133
  ( 124 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=20357986503829909242696372348001111417687352381 (pp47)
 r2=63907821471927606482939461715126003027541213468536152840468146898123845327793 (pp77)
Version: Msieve-1.40
Total time: 26.08 hours.
Scaled time: 86.65 units (timescale=3.322).
Factorization parameters were as follows:
name: 72223_160
n: 1301034567014673497892919265231793046878598035690062464234773174782366433468283011049257436954506807102849869231615244025133
m: 100000000000000000000000000000000
deg: 5
c5: 65
c0: 7
skew: 0.64
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 611722 x 611970
Total sieving time: 25.21 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.69 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 26.08 hours.
 --------- CPU info (if available) ----------

Nov 19, 2009

By Robert Backstrom / Msieve / Nov 19, 2009

(10²²⁹-7)/3 = (3)₂₂₈1_<229> = 3814997 · C222

C222 = P101 · P122

P101 = 32956293259679429768656597360038775832848835783382963927693572571464416807016576796602091743934862861_<101>

P122 = 26512225547078900430922693339363341417936176675074791272188321866779709375923927312831198488509643069134973196513414342243_<122>

Sieving ~ 220 CPU days + 161 hrs Lanczos with Msieve 1.42

Thu Nov 12 23:11:10 2009  
Thu Nov 12 23:11:10 2009  
Thu Nov 12 23:11:10 2009  Msieve v. 1.42
Thu Nov 12 23:11:10 2009  random seeds: a862287b 37faa132
Thu Nov 12 23:11:10 2009  factoring 873744680096297148682773101350625789046055169462343832336783838449501620403196472587877089636855109803057075361614526389754260182467596523230118748018237847456586029643885259499111882219916118763221395281132156416724137223 (222 digits)
Thu Nov 12 23:11:12 2009  no P-1/P+1/ECM available, skipping
Thu Nov 12 23:11:12 2009  commencing number field sieve (222-digit input)
Thu Nov 12 23:11:12 2009  R0: -100000000000000000000000000000000000000
Thu Nov 12 23:11:12 2009  R1:  1
Thu Nov 12 23:11:12 2009  A0: -7
Thu Nov 12 23:11:12 2009  A1:  0
Thu Nov 12 23:11:12 2009  A2:  0
Thu Nov 12 23:11:12 2009  A3:  0
Thu Nov 12 23:11:12 2009  A4:  0
Thu Nov 12 23:11:12 2009  A5:  0
Thu Nov 12 23:11:12 2009  A6:  10
Thu Nov 12 23:11:12 2009  skew 1.00, size 2.833444e-11, alpha 1.102701, combined = 1.358953e-12
Thu Nov 12 23:11:12 2009  
Thu Nov 12 23:11:12 2009  commencing relation filtering
Thu Nov 12 23:11:12 2009  estimated available RAM is 7923.9 MB
Thu Nov 12 23:11:12 2009  commencing duplicate removal, pass 1
Thu Nov 12 23:12:12 2009  error -6 reading relation 9929150
Thu Nov 12 23:13:31 2009  error -11 reading relation 23649746
Thu Nov 12 23:14:21 2009  error -6 reading relation 32916487
Thu Nov 12 23:15:00 2009  error -15 reading relation 40211731
Thu Nov 12 23:15:15 2009  error -11 reading relation 42932952
Thu Nov 12 23:16:49 2009  error -11 reading relation 60575181
Thu Nov 12 23:17:56 2009  error -11 reading relation 69579752
Thu Nov 12 23:18:42 2009  error -6 reading relation 77528636
Thu Nov 12 23:19:27 2009  error -6 reading relation 85390839
Thu Nov 12 23:19:48 2009  found 13696326 hash collisions in 89183073 relations
Thu Nov 12 23:20:04 2009  commencing duplicate removal, pass 2
Thu Nov 12 23:21:33 2009  found 12651851 duplicates and 76531222 unique relations
Thu Nov 12 23:21:33 2009  memory use: 426.4 MB
Thu Nov 12 23:21:33 2009  reading ideals above 91291648
Thu Nov 12 23:21:33 2009  commencing singleton removal, initial pass
Thu Nov 12 23:30:15 2009  memory use: 1193.5 MB
Thu Nov 12 23:30:22 2009  reading all ideals from disk
Thu Nov 12 23:30:27 2009  memory use: 1232.8 MB
Thu Nov 12 23:30:34 2009  commencing in-memory singleton removal
Thu Nov 12 23:30:42 2009  begin with 76531222 relations and 70805144 unique ideals
Thu Nov 12 23:31:54 2009  reduce to 35000016 relations and 23227703 ideals in 19 passes
Thu Nov 12 23:31:54 2009  max relations containing the same ideal: 28
Thu Nov 12 23:31:58 2009  reading ideals above 720000
Thu Nov 12 23:31:58 2009  commencing singleton removal, initial pass
Thu Nov 12 23:37:32 2009  memory use: 596.8 MB
Thu Nov 12 23:37:32 2009  reading all ideals from disk
Thu Nov 12 23:37:41 2009  memory use: 1301.4 MB
Thu Nov 12 23:37:50 2009  keeping 33583094 ideals with weight <= 200, target excess is 181953
Thu Nov 12 23:37:59 2009  commencing in-memory singleton removal
Thu Nov 12 23:38:07 2009  begin with 35000019 relations and 33583094 unique ideals
Thu Nov 12 23:40:13 2009  reduce to 34608397 relations and 33189936 ideals in 15 passes
Thu Nov 12 23:40:13 2009  max relations containing the same ideal: 200
Thu Nov 12 23:40:50 2009  removing 3807449 relations and 3407449 ideals in 400000 cliques
Thu Nov 12 23:40:51 2009  commencing in-memory singleton removal
Thu Nov 12 23:40:59 2009  begin with 30800948 relations and 33189936 unique ideals
Thu Nov 12 23:42:28 2009  reduce to 30471081 relations and 29447150 ideals in 12 passes
Thu Nov 12 23:42:28 2009  max relations containing the same ideal: 190
Thu Nov 12 23:43:00 2009  removing 2782167 relations and 2382167 ideals in 400000 cliques
Thu Nov 12 23:43:02 2009  commencing in-memory singleton removal
Thu Nov 12 23:43:09 2009  begin with 27688914 relations and 29447150 unique ideals
Thu Nov 12 23:44:02 2009  reduce to 27489440 relations and 26862722 ideals in 8 passes
Thu Nov 12 23:44:02 2009  max relations containing the same ideal: 181
Thu Nov 12 23:44:31 2009  removing 2450585 relations and 2050585 ideals in 400000 cliques
Thu Nov 12 23:44:33 2009  commencing in-memory singleton removal
Thu Nov 12 23:44:39 2009  begin with 25038855 relations and 26862722 unique ideals
Thu Nov 12 23:45:51 2009  reduce to 24871942 relations and 24642751 ideals in 12 passes
Thu Nov 12 23:45:51 2009  max relations containing the same ideal: 166
Thu Nov 12 23:46:17 2009  removing 176554 relations and 158429 ideals in 18125 cliques
Thu Nov 12 23:46:18 2009  commencing in-memory singleton removal
Thu Nov 12 23:46:24 2009  begin with 24695388 relations and 24642751 unique ideals
Thu Nov 12 23:46:53 2009  reduce to 24694507 relations and 24483440 ideals in 5 passes
Thu Nov 12 23:46:53 2009  max relations containing the same ideal: 166
Thu Nov 12 23:47:06 2009  relations with 0 large ideals: 6717
Thu Nov 12 23:47:06 2009  relations with 1 large ideals: 1179
Thu Nov 12 23:47:06 2009  relations with 2 large ideals: 8333
Thu Nov 12 23:47:06 2009  relations with 3 large ideals: 89276
Thu Nov 12 23:47:06 2009  relations with 4 large ideals: 546118
Thu Nov 12 23:47:06 2009  relations with 5 large ideals: 2010219
Thu Nov 12 23:47:06 2009  relations with 6 large ideals: 4602823
Thu Nov 12 23:47:06 2009  relations with 7+ large ideals: 17429842
Thu Nov 12 23:47:06 2009  commencing 2-way merge
Thu Nov 12 23:47:41 2009  reduce to 15238596 relation sets and 15027528 unique ideals
Thu Nov 12 23:47:41 2009  commencing full merge
Thu Nov 12 23:54:19 2009  memory use: 1908.0 MB
Thu Nov 12 23:54:22 2009  found 8200658 cycles, need 8173728
Thu Nov 12 23:54:26 2009  weight of 8173728 cycles is about 572210818 (70.01/cycle)
Thu Nov 12 23:54:26 2009  distribution of cycle lengths:
Thu Nov 12 23:54:26 2009  1 relations: 1219496
Thu Nov 12 23:54:26 2009  2 relations: 1113256
Thu Nov 12 23:54:26 2009  3 relations: 1026751
Thu Nov 12 23:54:26 2009  4 relations: 875887
Thu Nov 12 23:54:26 2009  5 relations: 745030
Thu Nov 12 23:54:26 2009  6 relations: 624485
Thu Nov 12 23:54:26 2009  7 relations: 527618
Thu Nov 12 23:54:26 2009  8 relations: 437123
Thu Nov 12 23:54:26 2009  9 relations: 358263
Thu Nov 12 23:54:26 2009  10+ relations: 1245819
Thu Nov 12 23:54:26 2009  heaviest cycle: 24 relations
Thu Nov 12 23:54:29 2009  commencing cycle optimization
Thu Nov 12 23:54:48 2009  start with 43758680 relations
Thu Nov 12 23:56:16 2009  pruned 944312 relations
Thu Nov 12 23:56:16 2009  memory use: 1460.4 MB
Thu Nov 12 23:56:16 2009  distribution of cycle lengths:
Thu Nov 12 23:56:16 2009  1 relations: 1219496
Thu Nov 12 23:56:16 2009  2 relations: 1134660
Thu Nov 12 23:56:16 2009  3 relations: 1058293
Thu Nov 12 23:56:16 2009  4 relations: 890629
Thu Nov 12 23:56:16 2009  5 relations: 757989
Thu Nov 12 23:56:16 2009  6 relations: 628845
Thu Nov 12 23:56:16 2009  7 relations: 528837
Thu Nov 12 23:56:16 2009  8 relations: 434588
Thu Nov 12 23:56:16 2009  9 relations: 353251
Thu Nov 12 23:56:16 2009  10+ relations: 1167140
Thu Nov 12 23:56:16 2009  heaviest cycle: 24 relations
Thu Nov 12 23:56:34 2009  RelProcTime: 2722
Thu Nov 12 23:56:34 2009  
Thu Nov 12 23:56:34 2009  commencing linear algebra
Thu Nov 12 23:56:41 2009  read 8173728 cycles
Thu Nov 12 23:56:58 2009  cycles contain 24518900 unique relations
Thu Nov 12 23:59:32 2009  read 24518900 relations
Fri Nov 13 00:00:18 2009  using 20 quadratic characters above 1073741312
Fri Nov 13 00:02:20 2009  building initial matrix
Fri Nov 13 00:07:17 2009  memory use: 3126.0 MB
Fri Nov 13 00:07:22 2009  read 8173728 cycles
Fri Nov 13 00:07:31 2009  matrix is 8173551 x 8173728 (2459.0 MB) with weight 723523108 (88.52/col)
Fri Nov 13 00:07:31 2009  sparse part has weight 554695601 (67.86/col)
Fri Nov 13 00:09:44 2009  filtering completed in 2 passes
Fri Nov 13 00:09:46 2009  matrix is 8170702 x 8170878 (2458.8 MB) with weight 723445965 (88.54/col)
Fri Nov 13 00:09:46 2009  sparse part has weight 554678395 (67.88/col)
Fri Nov 13 00:10:31 2009  read 8170878 cycles
Fri Nov 13 00:10:36 2009  matrix is 8170702 x 8170878 (2458.8 MB) with weight 723445965 (88.54/col)
Fri Nov 13 00:10:36 2009  sparse part has weight 554678395 (67.88/col)
Fri Nov 13 00:10:36 2009  saving the first 48 matrix rows for later
Fri Nov 13 00:10:39 2009  matrix is 8170654 x 8170878 (2351.5 MB) with weight 572916754 (70.12/col)
Fri Nov 13 00:10:39 2009  sparse part has weight 534727936 (65.44/col)
Fri Nov 13 00:10:39 2009  matrix includes 64 packed rows
Fri Nov 13 00:10:39 2009  using block size 65536 for processor cache size 6144 kB
Fri Nov 13 00:11:12 2009  commencing Lanczos iteration (4 threads)
Fri Nov 13 00:11:12 2009  memory use: 2546.0 MB
Thu Nov 19 17:11:02 2009  lanczos halted after 129209 iterations (dim = 8170651)
Thu Nov 19 17:11:17 2009  recovered 34 nontrivial dependencies
Thu Nov 19 17:11:17 2009  BLanczosTime: 580483
Thu Nov 19 17:11:17 2009  
Thu Nov 19 17:11:17 2009  commencing square root phase
Thu Nov 19 17:11:17 2009  reading relations for dependency 1
Thu Nov 19 17:11:19 2009  read 4087359 cycles
Thu Nov 19 17:11:28 2009  cycles contain 14942110 unique relations
Thu Nov 19 17:13:16 2009  read 14942110 relations
Thu Nov 19 17:14:47 2009  multiplying 12262068 relations
Thu Nov 19 17:52:42 2009  multiply complete, coefficients have about 340.41 million bits
Thu Nov 19 17:52:45 2009  initial square root is modulo 1283017
Thu Nov 19 18:37:22 2009  sqrtTime: 5165
Thu Nov 19 18:37:22 2009  prp101 factor: 32956293259679429768656597360038775832848835783382963927693572571464416807016576796602091743934862861
Thu Nov 19 18:37:22 2009  prp122 factor: 26512225547078900430922693339363341417936176675074791272188321866779709375923927312831198488509643069134973196513414342243
Thu Nov 19 18:37:22 2009  elapsed time 163:26:12

C222 is the fourth largest composite number factored by snfs in our tables so far, and P101 is the third largest prime factor found by nfs in our tables so far. Congratulations!

Nov 18, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Nov 18, 2009

(67·10¹⁶⁰-31)/9 = 7(4)₁₅₉1_<161> = 61982719611999597353_<20> · 143698186760416432999_<21> · C121

C121 = P58 · P64

P58 = 5184273162643458694917399313243984064834873060204015700713_<58>

P64 = 1612213304015942235676505728696547693838364040958693307596122831_<64>

Number: 74441_160
N=8358154164466588821090554087275649937241803372935761744857267124951914706311950912111526869642631543490919504968482278503
  ( 121 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=5184273162643458694917399313243984064834873060204015700713
 r2=1612213304015942235676505728696547693838364040958693307596122831
Version: 
Total time: 17.49 hours.
Scaled time: 41.84 units (timescale=2.392).
Factorization parameters were as follows:
n: 8358154164466588821090554087275649937241803372935761744857267124951914706311950912111526869642631543490919504968482278503
m: 100000000000000000000000000000000
deg: 5
c5: 67
c0: -31
skew: 0.86
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9409654
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 652517 x 652764
Total sieving time: 15.59 hours.
Total relation processing time: 0.68 hours.
Matrix solve time: 0.91 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 17.49 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

(65·10¹⁶²+61)/9 = 7(2)₁₆₁9_<163> = 7 · 433 · 40118289197111849803_<20> · C140

C140 = P35 · P106

P35 = 13579168028242955813092310115106577_<35>

P106 = 4373904977664475284540946690165627879231370447085692210555464579063477417774709742461792175457447644986089_<106>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 59393990631274162535471601057877005972838099309322799817876122604451444243295438344356023518048699407876740752099950221084230446649917407353 (140 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4563230118
Step 1 took 3998ms
********** Factor found in step 1: 13579168028242955813092310115106577
Found probable prime factor of 35 digits: 13579168028242955813092310115106577
Probable prime cofactor 4373904977664475284540946690165627879231370447085692210555464579063477417774709742461792175457447644986089 has 106 digits

Nov 18, 2009 (3rd)

By Sinkiti Sibata / Msieve / Nov 18, 2009

(67·10¹⁵⁸-13)/9 = 7(4)₁₅₇3_<159> = 137 · 367 · 27749 · 723919956530258273_<18> · C132

C132 = P63 · P70

P63 = 323406167861964574204330095340435316519039701961176025430412333_<63>

P70 = 2279079514444156964263123471753688115851723190657786980680661703364237_<70>

Number: 74443_158
N=737068372019091742604361880412597109475278063530233380153041578836135503206432728522468364755483999138828375954292978546680195934921
  ( 132 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=323406167861964574204330095340435316519039701961176025430412333 (pp63)
 r2=2279079514444156964263123471753688115851723190657786980680661703364237 (pp70)
Version: Msieve-1.40
Total time: 27.12 hours.
Scaled time: 89.14 units (timescale=3.287).
Factorization parameters were as follows:
name: 74443_158
n: 737068372019091742604361880412597109475278063530233380153041578836135503206432728522468364755483999138828375954292978546680195934921
m: 50000000000000000000000000000000
deg: 5
c5: 536
c0: -325
skew: 0.90
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 587928 x 588176
Total sieving time: 26.34 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.64 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 27.12 hours.
 --------- CPU info (if available) ----------

Nov 18, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 18, 2009

(65·10¹⁶⁷+61)/9 = 7(2)₁₆₆9_<168> = 3 · 3163 · 1283549 · 1810364976295258400527_<22> · C137

C137 = P34 · C103

P34 = 6731034634722746219253576990142331_<34>

C103 = [4866200326894477313327351434330702713602820686731038277709376544750901688090575230106979546318423633797_<103>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2647962607
Step 1 took 42548ms
Step 2 took 14762ms
********** Factor found in step 2: 6731034634722746219253576990142331
Found probable prime factor of 34 digits: 6731034634722746219253576990142331
Composite cofactor 4866200326894477313327351434330702713602820686731038277709376544750901688090575230106979546318423633797 has 103 digits

Nov 18, 2009

By Erik Branger / GGNFS, Msieve / Nov 18, 2009

(59·10¹⁷²-41)/9 = 6(5)₁₇₁1_<173> = 42787 · 31693768213_<11> · 2536830201015107_<16> · 139446318301636885367_<21> · C123

C123 = P58 · P65

P58 = 6709643923662083287600130339490360747447730333693040348921_<58>

P65 = 20366943698391295213823441988462062034872745975969857861877209429_<65>

Number: 65551_172
N=136654940029478911849727109316279734444197648667253976171378912414680437926200903241898447268360383419731066103731951176109
  ( 123 digits)
Divisors found:
 r1=6709643923662083287600130339490360747447730333693040348921 (pp58)
 r2=20366943698391295213823441988462062034872745975969857861877209429 (pp65)
Version: Msieve v. 1.43
Total time: 60.19 hours.
Scaled time: 58.44 units (timescale=0.971).
Factorization parameters were as follows:
n: 136654940029478911849727109316279734444197648667253976171378912414680437926200903241898447268360383419731066103731951176109
skew: 772856.50
#skew 772856.50, size 9.317641e-012, alpha -7.085631, combined = 2.065199e-010
c5: 600
c4: -431270722
c3: 325013098061919
c2: -1039884277173083768092
c1: -378596922670397322214778260
c0: -1308313376079945581025641373600
Y1: 9213761994587
Y0: -743867510048013670888093
type: gnfs
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3000000, 5400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 880216 x 880442
Total sieving time: 57.70 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 1.86 hours.
Time per square root: 0.37 hours.
Prototype def-par.txt line would be:
gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6000000,6000000,27,27,52,52,2.5,2.5,100000
total time: 60.19 hours.
 --------- CPU info (if available) ----------

Nov 17, 2009 (4th)

By Sinkiti Sibata / Msieve / Nov 17, 2009

(67·10¹⁷⁶+41)/9 = 7(4)₁₇₅9_<177> = 7 · C177

C177 = P36 · P42 · P43 · P57

P36 = 381496638149806557062385644326745051_<36>

P42 = 803770627877673149683896774769690484334047_<42>

P43 = 2540492572298568949029546317256747678065197_<43>

P57 = 136519118946285151795581433335283513926057235634807181623_<57>

Number: 74449_176
N=106349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349207
  ( 177 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=381496638149806557062385644326745051 (pp36)
 r2=803770627877673149683896774769690484334047 (pp42)
 r3=2540492572298568949029546317256747678065197 (pp43)
 r4=136519118946285151795581433335283513926057235634807181623 (pp57)
Version: Msieve-1.40
Total time: 151.29 hours.
Scaled time: 507.89 units (timescale=3.357).
Factorization parameters were as follows:
name: 74449_176
n: 106349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349207
m: 100000000000000000000000000000000000
deg: 5
c5: 670
c0: 41
skew: 0.57
type: snfs
lss: 1
rlim: 6400000
alim: 6400000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6400000/6400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3200000, 8900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1407232 x 1407479
Total sieving time: 146.77 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 3.89 hours.
Time per square root: 0.46 hours.
Prototype def-par.txt line would be:
snfs,177.000,5,0,0,0,0,0,0,0,0,6400000,6400000,28,28,53,53,2.5,2.5,100000
total time: 151.29 hours.
 --------- CPU info (if available) ----------

(62·10¹⁵⁹-71)/9 = 6(8)₁₅₈1_<160> = 7 · 367 · 397 · 1427 · 1295003 · 27044153094400533691_<20> · C126

C126 = P48 · P78

P48 = 637642494412674002793864923763006295921649455939_<48>

P78 = 211957692852734056509800472053686387750176129582452776229614596712235602760093_<78>

Number: 68881_159
N=135153231980572748044136445861801829429050962561946223951226838695412239454479728772981461313692290146394175213660440191042327
  ( 126 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=637642494412674002793864923763006295921649455939 (pp48)
 r2=211957692852734056509800472053686387750176129582452776229614596712235602760093 (pp78)
Version: Msieve v. 1.42
Total time: 1.59 hours.
Scaled time: 1.08 units (timescale=0.681).
Factorization parameters were as follows:
name: 68881_159
n: 135153231980572748044136445861801829429050962561946223951226838695412239454479728772981461313692290146394175213660440191042327
m: 100000000000000000000000000000000
deg: 5
c5: 31
c0: -355
skew: 1.63
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3200001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 652571 x 652797
Total sieving time: 0.00 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.37 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 1.59 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.19 BogoMIPS (lpj=1860598)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860574)
Total of 2 processors activated (7442.34 BogoMIPS).

Total time: 27.7 hours

Nov 17, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 17, 2009

(59·10¹⁵⁹+31)/9 = 6(5)₁₅₈9_<160> = 7 · 41 · 118759055073185934621037_<24> · C135

C135 = P55 · P80

P55 = 2549878433376721403304445956812713905944758972355130839_<55>

P80 = 75429529077254560793474090742639833438562153315193101308443515089992511037341899_<80>

Number: 65559_159
N=192336129433853713462743799811065807296497118520268229199178231611199978210902456189888686092410750956991535069761582060175816921723261
  ( 135 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=2549878433376721403304445956812713905944758972355130839
 r2=75429529077254560793474090742639833438562153315193101308443515089992511037341899
Version: 
Total time: 17.49 hours.
Scaled time: 41.79 units (timescale=2.390).
Factorization parameters were as follows:
n: 192336129433853713462743799811065807296497118520268229199178231611199978210902456189888686092410750956991535069761582060175816921723261
m: 100000000000000000000000000000000
deg: 5
c5: 59
c0: 310
skew: 1.39
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1800000, 3300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9616962
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 621680 x 621928
Total sieving time: 15.89 hours.
Total relation processing time: 0.71 hours.
Matrix solve time: 0.80 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000
total time: 17.49 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Nov 17, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Nov 17, 2009

(64·10¹⁷⁸+71)/9 = 7(1)₁₇₇9_<179> = 229 · C177

C177 = P38 · P139

P38 = 33350205132654546757222414370710831411_<38>

P139 = 9311153207174220903648886531701264110925845510393319781488890048252156953150920948299831365494816188137632384373019136801433203324125922001_<139>

Number: 71119_178
N=310528869480834546336729742843279961183891314895681707908782144590004852013585638039786511402231926249393498301795245026686074721009218825812712275594371664240659873847646773411
  ( 177 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=33350205132654546757222414370710831411 (pp38)
 r2=9311153207174220903648886531701264110925845510393319781488890048252156953150920948299831365494816188137632384373019136801433203324125922001 (pp139)
Version: Msieve v. 1.43
Total time: 134.74 hours.
Scaled time: 234.99 units (timescale=1.744).
Factorization parameters were as follows:
n: 310528869480834546336729742843279961183891314895681707908782144590004852013585638039786511402231926249393498301795245026686074721009218825812712275594371664240659873847646773411
m: 400000000000000000000000000000000000
deg: 5
c5: 125
c0: 142
skew: 1.03
type: snfs
lss: 1
rlim: 7000000
alim: 7000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3500000, 10100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1578565 x 1578790
Total sieving time: 130.38 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.56 hours.
Time per square root: 0.61 hours.
Prototype def-par.txt line would be:
snfs,180.000,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,53,53,2.5,2.5,100000
total time: 134.74 hours.

Nov 17, 2009

By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Nov 17, 2009

(59·10¹⁶⁴+13)/9 = 6(5)₁₆₃7_<165> = 3² · 89 · 967 · C159

C159 = P48 · P112

P48 = 172494834689383932407753106094143525376103225653_<48>

P112 = 4906529533010920434450031087476390453047270898213110900861533572593100963811674429717024242278907331943447184807_<112>

N=846351000695298864469510778997240465389766870465118647651598319519880856730993646199173932733456957959163707665773981534916353983006706399259916257154714253971
  ( 159 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=172494834689383932407753106094143525376103225653 (pp48)
 r2=4906529533010920434450031087476390453047270898213110900861533572593100963811674429717024242278907331943447184807 (pp112)
Version: Msieve-1.40
Total time: 42.70 hours.
Scaled time: 78.56 units (timescale=1.840).
Factorization parameters were as follows:
n: 846351000695298864469510778997240465389766870465118647651598319519880856730993646199173932733456957959163707665773981534916353983006706399259916257154714253971
m: 1000000000000000000000000000000000
deg: 5
c5: 59
c0: 130
skew: 1.17
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4500001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 705092 x 705317
Total sieving time: 41.83 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.64 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 42.70 hours.
 --------- CPU info (if available) ----------

(62·10¹⁹⁰-71)/9 = 6(8)₁₈₉1_<191> = 17 · C190

C190 = P39 · C152

P39 = 159056495352762286480580492048359527989_<39>

C152 = [25477033004606382089474543221740888076315860678491961319226765661507788975891994600263548413995024764740782104709424866797319890147044298005667883592637_<152>]

Factor=159056495352762286480580492048359527989  Method=ECM  B1=11000000  Sigma=3757089473

Nov 16, 2009 (3rd)

By Wataru Sakai / Msieve / Nov 16, 2009

(55·10¹⁸⁹+17)/9 = 6(1)₁₈₈3_<190> = 19 · C189

C189 = P72 · P117

P72 = 743141132482156367337598193227260139629402238122971076355782741496332829_<72>

P117 = 432807999506483598225778604308585057267632076708114307439969977345662831173299530582744403436363128148721417709214863_<117>

Number: 61113_189
N=321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637427
  ( 189 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=743141132482156367337598193227260139629402238122971076355782741496332829
 r2=432807999506483598225778604308585057267632076708114307439969977345662831173299530582744403436363128148721417709214863
Version: 
Total time: 424.41 hours.
Scaled time: 854.34 units (timescale=2.013).
Factorization parameters were as follows:
n: 321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637427
m: 100000000000000000000000000000000000000
deg: 5
c5: 11
c0: 34
skew: 1.25
type: snfs
lss: 1
rlim: 10700000
alim: 10700000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 10700000/10700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5350000, 9650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1681268 x 1681516
Total sieving time: 424.41 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,10700000,10700000,28,28,54,54,2.5,2.5,100000
total time: 424.41 hours.
 --------- CPU info (if available) ----------

Nov 16, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve / Nov 16, 2009

(59·10¹⁶⁰+13)/9 = 6(5)₁₅₉7_<161> = 7039 · 3404279 · C151

C151 = P38 · P113

P38 = 68865197719831614457352449825567313491_<38>

P113 = 39725886046607481763744275688874905087926689678309758721166697739496395380193756474563848842063050364299554448367_<113>

N=2735730997195124102012431130315542645538784010106985048370417728523108614122498641061319159171101423248972776136570302361644318198903522689622662019197
  ( 151 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=68865197719831614457352449825567313491 (pp38)
 r2=39725886046607481763744275688874905087926689678309758721166697739496395380193756474563848842063050364299554448367 (pp113)
Version: Msieve-1.40
Total time: 22.07 hours.
Scaled time: 40.59 units (timescale=1.839).
Factorization parameters were as follows:
n: 2735730997195124102012431130315542645538784010106985048370417728523108614122498641061319159171101423248972776136570302361644318198903522689622662019197
m: 100000000000000000000000000000000
deg: 5
c5: 59
c0: 13
skew: 0.74
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 2950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 582651 x 582876
Total sieving time: 21.30 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 22.07 hours.
 --------- CPU info (if available) ----------

(61·10¹⁶⁹-43)/9 = 6(7)₁₆₈3_<170> = 3 · 7 · 41 · 3907 · C164

C164 = P47 · P56 · P61

P47 = 94208236204350919120277255087982042989012675453_<47>

P56 = 27857142756307349104741327554515339623983588929075998349_<56>

P61 = 7677420362824464519085906573888170277526604508620017795302867_<61>

N=20148409218683335808945252907621888875049243868186728718482231563817460300945227936806529326521585568824108780534707732295551531819144047352328923242917512115387099
  ( 164 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=94208236204350919120277255087982042989012675453 (pp47)
 r2=27857142756307349104741327554515339623983588929075998349 (pp56)
 r3=7677420362824464519085906573888170277526604508620017795302867 (pp61)
Version: Msieve-1.40
Total time: 57.58 hours.
Scaled time: 107.10 units (timescale=1.860).
Factorization parameters were as follows:
n: 20148409218683335808945252907621888875049243868186728718482231563817460300945227936806529326521585568824108780534707732295551531819144047352328923242917512115387099
m: 10000000000000000000000000000000000
deg: 5
c5: 61
c0: -430
skew: 1.48
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 902518 x 902749
Total sieving time: 56.18 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.02 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 57.58 hours.
 --------- CPU info (if available) ----------

(59·10¹⁷¹-41)/9 = 6(5)₁₇₀1_<172> = 17 · 197 · 2423 · C165

C165 = P42 · P124

P42 = 115282334389384451975024500292983441235287_<42>

P124 = 7007743196898658551854826666555383080225449060710447335296189818414329538606806627654954847443983562896198346607513316876499_<124>

N=807868994539805163632974818874059837322843743225111339751729260698680981338459001942486765633904744550249266608995774612382744832948643918636747635542034840979820213
  ( 165 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=115282334389384451975024500292983441235287 (pp42)
 r2=7007743196898658551854826666555383080225449060710447335296189818414329538606806627654954847443983562896198346607513316876499 (pp124)
Version: Msieve-1.40
Total time: 99.95 hours.
Scaled time: 93.55 units (timescale=0.936).
Factorization parameters were as follows:
n: 807868994539805163632974818874059837322843743225111339751729260698680981338459001942486765633904744550249266608995774612382744832948643918636747635542034840979820213
m: 10000000000000000000000000000000000
deg: 5
c5: 590
c0: -41
skew: 0.59
type: snfs
lss: 1
rlim: 5300000
alim: 5300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2650000, 6550001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1033831 x 1034061
Total sieving time: 97.83 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.79 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,172.000,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.4,2.4,100000
total time: 99.95 hours.
 --------- CPU info (if available) ----------

Nov 16, 2009

By Sinkiti Sibata / Msieve / Nov 16, 2009

(41·10¹⁹⁸+13)/9 = 4(5)₁₉₇7_<199> = 3 · 31 · C197

C197 = P66 · P132

P66 = 429273887712751328262058289867997079191088552925834213834435798699_<66>

P132 = 114110058266774921221247378607450666721138374033977704640115321152455033337303110382308778010226239545436861604901232470700565846651_<132>

Number: 45557_198
N=48984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307049
  ( 197 digits)
SNFS difficulty: 201 digits.
Divisors found:
 r1=429273887712751328262058289867997079191088552925834213834435798699 (pp66)
 r2=114110058266774921221247378607450666721138374033977704640115321152455033337303110382308778010226239545436861604901232470700565846651 (pp132)
Version: Msieve v. 1.42
Total time: 51.51 hours.
Scaled time: 43.47 units (timescale=0.844).
Factorization parameters were as follows:
name: 45557_198
n: 48984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307049
m: 5000000000000000000000000000000000000000
deg: 5
c5: 328
c0: 325
skew: 1.00
type: snfs
rlim:  9500000
alim:  9500000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [4750000, 15250001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3000927 x 3001153
Total sieving time: 0.00 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 48.31 hours.
Time per square root: 2.78 hours.
Prototype def-par.txt line would be:
snfs,201.000,5,0,0,0,0,0,0,0,0,9500000,9500000,29,29,56,56,2.6,2.6,100000
total time: 51.51 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583)
Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268)
Total of 2 processors activated (11653.70 BogoMIPS).

Total time: 19 days 1 hour.

(26·10¹⁵⁸-11)/3 = 8(6)₁₅₇3_<159> = 61 · 7727 · 429686857 · 106162330928491_<15> · C131

C131 = P61 · P71

P61 = 2841721909924726851632106444328355405349356896512142306774663_<61>

P71 = 14184278665349773058410239428622656980638132940212009488758588338764809_<71>

Number: 86663_158
N=40307775459802312601143666500637781443565300545471354124635599565639079211034939946642064287574656020645475561982776791182117234367
  ( 131 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=2841721909924726851632106444328355405349356896512142306774663 (pp61)
 r2=14184278665349773058410239428622656980638132940212009488758588338764809 (pp71)
Version: Msieve v. 1.42
Total time: 1.48 hours.
Scaled time: 0.99 units (timescale=0.668).
Factorization parameters were as follows:
name: 86663_158
n: 40307775459802312601143666500637781443565300545471354124635599565639079211034939946642064287574656020645475561982776791182117234367
m: 50000000000000000000000000000000
deg: 5
c5: 208
c0: -275
skew: 1.06
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 626336 x 626562
Total sieving time: 0.00 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.27 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,160.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 1.48 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.19 BogoMIPS (lpj=1860598)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860574)
Total of 2 processors activated (7442.34 BogoMIPS).

Total time: 25 hours 51 min.

Nov 15, 2009 (6th)

By Dmitry Domanov / GGNFS/msieve / Nov 15, 2009

(62·10¹⁷⁰-71)/9 = 6(8)₁₆₉1_<171> = 3⁵ · 5417 · C165

C165 = P83 · P83

P83 = 15602471926924933938592663806430212082428034579139978305230145191169585707783895579_<83>

P83 = 33542131793373349803791167429073588671109887449475537586566666088049681406989340969_<83>

N=523340169675323979218668320421602840690440997658559198931643248460219267713735290659331800959552642070185150155157698853015608451741156964995042195989374168722676051
  ( 165 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=15602471926924933938592663806430212082428034579139978305230145191169585707783895579 (pp83)
 r2=33542131793373349803791167429073588671109887449475537586566666088049681406989340969 (pp83)
Version: Msieve-1.40
Total time: 69.39 hours.
Scaled time: 129.34 units (timescale=1.864).
Factorization parameters were as follows:
n: 523340169675323979218668320421602840690440997658559198931643248460219267713735290659331800959552642070185150155157698853015608451741156964995042195989374168722676051
m: 10000000000000000000000000000000000
deg: 5
c5: 62
c0: -71
skew: 1.03
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 6350001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1047650 x 1047883
Total sieving time: 67.68 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.38 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 69.39 hours.
 --------- CPU info (if available) ----------

Nice split!

Nov 15, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Nov 15, 2009

(59·10¹⁷⁹+13)/9 = 6(5)₁₇₈7_<180> = 3 · 7 · 313 · C176

C176 = P47 · P130

P47 = 34227787132453009430793852808645752930870611989_<47>

P130 = 2913849035609246999052003284781673297721777732911788271360592562809210825744751320660074392479293423943525018257580230618885051381_<130>

Number: 65557_179
N=99734604526936795307402336156329766553408725932687594029447064590834558885677096539716348023057288233007082847338438392751491793025339351217945467146745102016667511875179606809
  ( 176 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=34227787132453009430793852808645752930870611989 (pp47)
 r2=2913849035609246999052003284781673297721777732911788271360592562809210825744751320660074392479293423943525018257580230618885051381 (pp130)
Version: Msieve v. 1.43
Total time: 134.63 hours.
Scaled time: 234.12 units (timescale=1.739).
Factorization parameters were as follows:
n: 99734604526936795307402336156329766553408725932687594029447064590834558885677096539716348023057288233007082847338438392751491793025339351217945467146745102016667511875179606809
m: 1000000000000000000000000000000000000
deg: 5
c5: 59
c0: 130
skew: 1.17
type: snfs
lss: 1
rlim: 7500000
alim: 7500000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7500000/7500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3750000, 10050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1572029 x 1572254
Total sieving time: 129.41 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.56 hours.
Time per square root: 1.46 hours.
Prototype def-par.txt line would be:
snfs,181.000,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,53,53,2.5,2.5,100000
total time: 134.63 hours.

Nov 15, 2009 (4th)

By Sinkiti Sibata / Msieve / Nov 15, 2009

(22·10¹⁵⁸-7)/3 = 7(3)₁₅₇1_<159> = 4938931 · 116721612901_<12> · 1004920243404713858972261_<25> · C118

C118 = P47 · P72

P47 = 12009077923370648080337714781707462324113111259_<47>

P72 = 105408571886886114038898047458864072059719907211055171359755427498953899_<72>

Number: 73331_158
N=1265859753580831970140805253178104479059768213757511408464260680420987308767554609998630957690867230291891172698848841
  ( 118 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=12009077923370648080337714781707462324113111259 (pp47)
 r2=105408571886886114038898047458864072059719907211055171359755427498953899 (pp72)
Version: Msieve v. 1.42
Total time: 1.74 hours.
Scaled time: 1.38 units (timescale=0.796).
Factorization parameters were as follows:
name: 73331_158
n: 1265859753580831970140805253178104479059768213757511408464260680420987308767554609998630957690867230291891172698848841
m: 50000000000000000000000000000000
deg: 5
c5: 176
c0: -175
skew: 1.00
type: snfs
lss: 1
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1650000, 3050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 641091 x 641316
Total sieving time: 0.00 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.32 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,160.000,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000
total time: 1.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
CPU1: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 02
Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.19 BogoMIPS (lpj=1860598)
Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860574)
Total of 2 processors activated (7442.34 BogoMIPS).

Total time: 25 hours 57 min.

Nov 15, 2009 (3rd)

By Markus Tervooren / Msieve / Nov 15, 2009

(59·10¹⁵⁸+31)/9 = 6(5)₁₅₇9_<159> = 6007 · 2562185297819003_<16> · 81019181804777423_<17> · C123

C123 = P58 · P66

P58 = 1812636648515138557638066389371724168451964749993906970903_<58>

P66 = 290029868680170784800973912514904723261070414310744029102462787291_<66>

N=525718769133710523653027683631105261421509093029825731752283277983185064180697266071063641221234058361239671692676215193773
  ( 123 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=1812636648515138557638066389371724168451964749993906970903 (pp58)
 r2=290029868680170784800973912514904723261070414310744029102462787291 (pp66)
Version: Msieve-1.41
Total time: 24.56 hours.
Scaled time: 0.00 units (timescale=0.000).
Factorization parameters were as follows:
n: 525718769133710523653027683631105261421509093029825731752283277983185064180697266071063641221234058361239671692676215193773
m: 50000000000000000000000000000000
deg: 5
c5: 472
c0: 775
skew: 1.10
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5

Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [1000000, 5000001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 543990 x 544236
Total sieving time: 23.95 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2000000,2000000,29,29,56,56,2.5,2.5,800000
total time: 24.56 hours.
 --------- CPU info (if available) ----------
[    0.144009] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.236014] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.333347] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.432500] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197988k/10485760k available (2226k kernel code, 189848k reserved, 1082k data, 392k init)
[    0.083990] Calibrating delay using timer specific routine.. 5337.18 BogoMIPS (lpj=10674366)
[    0.156009] Calibrating delay using timer specific routine.. 5333.33 BogoMIPS (lpj=10666675)
[    0.256016] Calibrating delay using timer specific routine.. 5333.38 BogoMIPS (lpj=10666763)
[    0.352018] Calibrating delay using timer specific routine.. 5333.36 BogoMIPS (lpj=10666735)
[    0.437221] Total of 4 processors activated (21337.26 BogoMIPS).

Nov 15, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Nov 15, 2009

(22·10¹⁵⁷+17)/3 = 7(3)₁₅₆9_<158> = 79² · 89 · 1795517 · 6590261 · 61755013 · C132

C132 = P55 · P77

P55 = 7950796688233200437719771201150520016921625896700384781_<55>

P77 = 22723866813249437260181466059833062612216418676176293743449524658347563807251_<77>

Number: 73339_157
N=180672845002635955973650145697540511621150710038462470711407017816799667146364223424285574886806960321200674321681732470921017847031
  ( 132 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=7950796688233200437719771201150520016921625896700384781
 r2=22723866813249437260181466059833062612216418676176293743449524658347563807251
Version: 
Total time: 13.93 hours.
Scaled time: 33.24 units (timescale=2.386).
Factorization parameters were as follows:
n: 180672845002635955973650145697540511621150710038462470711407017816799667146364223424285574886806960321200674321681732470921017847031
m: 20000000000000000000000000000000
deg: 5
c5: 275
c0: 68
skew: 0.76
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1600000, 2800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8288002
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 569108 x 569356
Total sieving time: 12.50 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 0.78 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000
total time: 13.93 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(26·10¹⁵⁷-11)/3 = 8(6)₁₅₆3_<158> = 13874719638668432738273_<23> · C136

C136 = P46 · P90

P46 = 7990330801087736129609580208900348960160370121_<46>

P90 = 781741409377590402464709803977736132137659344702928238702437054957380692407818254347964111_<90>

Number: 86663_157
N=6246372461835497797590085235144227805300158049988539661664127319813743185508874489362779286942419837673553038815625648251966340584727431
  ( 136 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=7990330801087736129609580208900348960160370121
 r2=781741409377590402464709803977736132137659344702928238702437054957380692407818254347964111
Version: 
Total time: 13.93 hours.
Scaled time: 33.31 units (timescale=2.391).
Factorization parameters were as follows:
n: 6246372461835497797590085235144227805300158049988539661664127319813743185508874489362779286942419837673553038815625648251966340584727431
m: 20000000000000000000000000000000
deg: 5
c5: 325
c0: -44
skew: 0.67
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1600000, 2800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8533070
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 529316 x 529564
Total sieving time: 12.61 hours.
Total relation processing time: 0.52 hours.
Matrix solve time: 0.68 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000
total time: 13.93 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(65·10¹⁵⁷+7)/9 = 7(2)₁₅₆3_<158> = 9679 · 1876797653_<10> · C145

C145 = P72 · P74

P72 = 340269928723054252687708121264854816897562029160532745490903501797972559_<72>

P74 = 11684209505564680196886999355587721293576873890219180545631517614669025331_<74>

Number: 72223_157
N=3975785135643726702230450539778066801184587100157871451338767600314164799713954972226106445526223512112153625343514325724755468276601912413892029
  ( 145 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=340269928723054252687708121264854816897562029160532745490903501797972559
 r2=11684209505564680196886999355587721293576873890219180545631517614669025331
Version: 
Total time: 16.06 hours.
Scaled time: 38.37 units (timescale=2.389).
Factorization parameters were as follows:
n: 3975785135643726702230450539778066801184587100157871451338767600314164799713954972226106445526223512112153625343514325724755468276601912413892029
m: 50000000000000000000000000000000
deg: 5
c5: 52
c0: 175
skew: 1.27
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1600000, 3000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9396692
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 601720 x 601968
Total sieving time: 14.61 hours.
Total relation processing time: 0.65 hours.
Matrix solve time: 0.73 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,51,51,2.4,2.4,100000
total time: 16.06 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(62·10¹⁶²-71)/9 = 6(8)₁₆₁1_<163> = 291727 · 40998522161_<11> · 538331911170192824177_<21> · C127

C127 = P41 · P86

P41 = 13293896052923584707628730999104405807681_<41>

P86 = 80482590851823351939562778795885505113611415145477307256905540960132767325450472770079_<86>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 1069927196854118265491844218314408607974802302696835461705048222248058295906490484465975989906304815245214369775644395405176799 (127 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4381793230
Step 1 took 3319ms
Step 2 took 2107ms
********** Factor found in step 2: 13293896052923584707628730999104405807681
Found probable prime factor of 41 digits: 13293896052923584707628730999104405807681
Probable prime cofactor 80482590851823351939562778795885505113611415145477307256905540960132767325450472770079 has 86 digits

Nov 15, 2009

By juno1369 / GGNFS + Msieve / Nov 15, 2009

(61·10¹⁴⁶+11)/9 = 6(7)₁₄₅9_<147> = 7² · 859 · 5557 · 275800236853_<12> · 43877517103969019_<17> · C111

C111 = P41 · P70

P41 = 47018556761287004919324019214769957965617_<41>

P70 = 5092742427046728561746607640479066938348493902951058681904891312864643_<70>

Number: 67779_146
N=239453398876711150609255320785377692625826392338235113766506874627069551944324667803564622358785358784768979731
  (111 digits)
Divisors found:
 r1=47018556761287004919324019214769957965617 (pp41)
 r2=5092742427046728561746607640479066938348493902951058681904891312864643 (pp70)
Version: Msieve-1.40
Total time: 213.24 hours.
Scaled time: 369.96 units (timescale=1.735).
Factorization parameters were as follows:
name: 67779_146
n: 239453398876711150609255320785377692625826392338235113766506874627069551944324667803564622358785358784768979731
skew: 62268.21
# norm 6.79e+015
c5: 1740
c4: 571107120
c3: 191509397222949
c2: -1689229856928126946
c1: -167460861686685303277376
c0: 366141206224433326132512000
# alpha -5.54
Y1: 357727841273
Y0: -2677506553543671180733
# Murphy_E 7.08e-010
# M 4169860093312916150953838170334394543046091236561083577223534810475410377208532554651542786886462863183822802
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 2
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 466836 x 467084
Total sieving time: 211.86 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.07 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 213.24 hours.
 --------- CPU info (if available) ----------

Nov 14, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / Nov 14, 2009

(22·10¹⁷⁸-7)/3 = 7(3)₁₇₇1_<179> = 17 · C178

C178 = P48 · P62 · P69

P48 = 248547605560480925622741006789238584355839363443_<48>

P62 = 52256505242291123397545087983645084835369273482120400731461829_<62>

P69 = 332125758345610575600565424353848439016390715672904492677915743077469_<69>

Number: n
N=4313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843
  ( 178 digits)
SNFS difficulty: 180 digits.
Divisors found:

Sat Nov 14 06:46:51 2009  prp48 factor: 248547605560480925622741006789238584355839363443
Sat Nov 14 06:46:51 2009  prp62 factor: 52256505242291123397545087983645084835369273482120400731461829
Sat Nov 14 06:46:51 2009  prp69 factor: 332125758345610575600565424353848439016390715672904492677915743077469
Sat Nov 14 06:46:51 2009  elapsed time 05:12:36 (Msieve 1.43 - dependency 5)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 111.82 hours.
Scaled time: 203.84 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_7_3_177_1
n: 4313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843
m: 500000000000000000000000000000000000
deg: 5
c5: 176
c0: -175
skew: 1.00
type: snfs
lss: 1
rlim: 7200000
alim: 7200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 7200000/7200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [3600000, 5400823)
Primes: RFBsize:489319, AFBsize:489694, largePrimes:20744051 encountered
Relations: rels:20484312, finalFF:986940
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1849522 hash collisions in 21701103 relations
Msieve: matrix is 1291973 x 1292197 (348.9 MB)

Total sieving time: 111.13 hours.
Total relation processing time: 0.68 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,56,56,2.5,2.5,100000
total time: 111.82 hours.
 --------- CPU info (if available) ----------

(67·10¹⁵⁴-31)/9 = 7(4)₁₅₃1_<155> = 131 · 397 · 983 · C148

C148 = P38 · P47 · P64

P38 = 19770670872949815347485142394152319553_<38>

P47 = 70311137559137507052774831616250832259377569867_<47>

P64 = 1047541994464449155489159844448139419478733450739365527434608811_<64>

Number: n
N=1456186407891301048633085534526984980452186261655411095560996346126198256401951299349589559407742385341006983633110278828856387112542511922292572761
  ( 148 digits)
SNFS difficulty: 156 digits.
Divisors found:

Sat Nov 14 18:58:09 2009  prp38 factor: 19770670872949815347485142394152319553
Sat Nov 14 18:58:09 2009  prp47 factor: 70311137559137507052774831616250832259377569867
Sat Nov 14 18:58:09 2009  prp64 factor: 1047541994464449155489159844448139419478733450739365527434608811
Sat Nov 14 18:58:09 2009  elapsed time 00:55:11 (Msieve 1.43 - dependency 4)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 21.59 hours.
Scaled time: 39.25 units (timescale=1.818).
Factorization parameters were as follows:
name: KA_7_4_153_1
n: 1456186407891301048633085534526984980452186261655411095560996346126198256401951299349589559407742385341006983633110278828856387112542511922292572761
m: 10000000000000000000000000000000
deg: 5
c5: 67
c0: -310
skew: 1.36
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [1450000, 2750249)
Primes: RFBsize:210109, AFBsize:210215, largePrimes:7718909 encountered
Relations: rels:7439444, finalFF:438767
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 935880 hash collisions in 8065056 relations
Msieve: matrix is 535005 x 535232 (143.1 MB)

Total sieving time: 21.47 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000
total time: 21.59 hours.
 --------- CPU info (if available) ----------

Nov 14, 2009 (5th)

By Sinkiti Sibata / Msieve / Nov 14, 2009

(62·10¹⁵⁸-71)/9 = 6(8)₁₅₇1_<159> = 3 · 17 · 67 · 337 · 3559 · C150

C150 = P54 · P97

P54 = 132575299431508438665738676848358063462718878204534843_<54>

P97 = 1267896186810585277293654903308370039889900735456986092170954192488322227543251134228508640175997_<97>

Number: 68881_158
N=168091716614481103463083594268062800883645758833805202718252499935061086452976721473033496538452942958137049236729866564856854058353995213907038763471
  ( 150 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=132575299431508438665738676848358063462718878204534843 (pp54)
 r2=1267896186810585277293654903308370039889900735456986092170954192488322227543251134228508640175997 (pp97)
Version: Msieve-1.40
Total time: 44.43 hours.
Scaled time: 89.71 units (timescale=2.019).
Factorization parameters were as follows:
name: 68881_158
n: 168091716614481103463083594268062800883645758833805202718252499935061086452976721473033496538452942958137049236729866564856854058353995213907038763471
m: 50000000000000000000000000000000
deg: 5
c5: 496
c0: -1775
skew: 1.29
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 631071 x 631319
Total sieving time: 42.50 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.46 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 44.43 hours.
 --------- CPU info (if available) ----------

Nov 14, 2009 (4th)

By Dmitry Domanov / ggnfs/msieve, GGNFS/msieve / Nov 14, 2009

(67·10¹⁶²-13)/9 = 7(4)₁₆₁3_<163> = 3 · 1951 · 57493 · C155

C155 = P72 · P84

P72 = 173168441496788451919618027345869704057432823437379661717120302268074707_<72>

P84 = 127752688946810654048296217810573665123434033505277792306486178869161540657839807481_<84>

Number: s155
N=22122734041943193454188356756799938477403047488699526672317387471683928142875481754603472922346907701289933796334883132221319974580476696915572905405483067
  ( 155 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=173168441496788451919618027345869704057432823437379661717120302268074707 (pp72)
 r2=127752688946810654048296217810573665123434033505277792306486178869161540657839807481 (pp84)
Version: Msieve-1.40
Total time: 42.12 hours.
Scaled time: 78.35 units (timescale=1.860).
Factorization parameters were as follows:
n: 22122734041943193454188356756799938477403047488699526672317387471683928142875481754603472922346907701289933796334883132221319974580476696915572905405483067
m: 500000000000000000000000000000000
deg: 5
c5: 268
c0: -1625
skew: 1.43
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 794129 x 794355
Total sieving time: 41.11 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.83 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,165.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 42.12 hours.
 --------- CPU info (if available) ----------

(22·10¹⁸⁸-7)/3 = 7(3)₁₈₇1_<189> = C189

C189 = P67 · P123

P67 = 1439804239664097685685896347039690976177416861734275651404144103963_<67>

P123 = 509328499758007349074189685847253363748278305932331944594971040870874995118639499429499748714681777407393380275849433840937_<123>

N=733333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
  ( 189 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=1439804239664097685685896347039690976177416861734275651404144103963 (pp67)
 r2=509328499758007349074189685847253363748278305932331944594971040870874995118639499429499748714681777407393380275849433840937 (pp123)
Version: Msieve-1.40
Total time: 480.46 hours.
Scaled time: 446.35 units (timescale=0.929).
Factorization parameters were as follows:
n: 733333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
m: 50000000000000000000000000000000000000
deg: 5
c5: 176
c0: -175
skew: 1.00
type: snfs
lss: 1
rlim: 10600000
alim: 10600000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 10600000/10600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5300000, 10500001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1872355 x 1872580
Total sieving time: 468.26 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 11.41 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,190.000,5,0,0,0,0,0,0,0,0,10600000,10600000,28,28,54,54,2.5,2.5,100000
total time: 480.46 hours.
 --------- CPU info (if available) ----------

Nov 14, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 14, 2009

(62·10¹⁶⁹-71)/9 = 6(8)₁₆₈1_<170> = 3505219 · 1779396887_<10> · 2788933419652123_<16> · 49618119210892708709_<20> · C119

C119 = P38 · P81

P38 = 82660081394313266012448446052941500919_<38>

P81 = 965577024280041750953286497287634496570237721902454230853822326500051858350496669_<81>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1887201488
Step 1 took 126018ms
Step 2 took 42743ms
********** Factor found in step 2: 82660081394313266012448446052941500919
Found probable prime factor of 38 digits: 82660081394313266012448446052941500919
Probable prime cofactor 965577024280041750953286497287634496570237721902454230853822326500051858350496669 has 81 digits

(62·10¹⁷¹-71)/9 = 6(8)₁₇₀1_<172> = 7 · 19 · 4349 · 9319 · C163

C163 = P40 · P123

P40 = 1600606687685207079981972189175964607847_<40>

P123 = 798461890260203983777865595532676387857491818084310489921571287545918302724829696269195481540944560007643355765101773720401_<123>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=484386855
Step 1 took 52247ms
********** Factor found in step 1: 1600606687685207079981972189175964607847
Found probable prime factor of 40 digits: 1600606687685207079981972189175964607847
Probable prime cofactor 798461890260203983777865595532676387857491818084310489921571287545918302724829696269195481540944560007643355765101773720401 has 123 digits

Nov 14, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 14, 2009

(83·10¹⁵⁶+7)/9 = 9(2)₁₅₅3_<157> = 528078673 · 2354032321_<10> · 54455392027_<11> · C129

C129 = P38 · P91

P38 = 29549430643279790678513909646388049663_<38>

P91 = 4610356690548903466239224249245927737326743875914578310194061475922915915676673744740852531_<91>

Number: 92223_156
N=136233415268155771401978069668754675273317569461066738883978525382951633384097934807394773511147684886619441567552049872987247053
  ( 129 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=29549430643279790678513909646388049663
 r2=4610356690548903466239224249245927737326743875914578310194061475922915915676673744740852531
Version: 
Total time: 13.30 hours.
Scaled time: 31.81 units (timescale=2.392).
Factorization parameters were as follows:
n: 136233415268155771401978069668754675273317569461066738883978525382951633384097934807394773511147684886619441567552049872987247053
m: 10000000000000000000000000000000
deg: 5
c5: 830
c0: 7
skew: 0.38
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8688640
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 495054 x 495302
Total sieving time: 12.20 hours.
Total relation processing time: 0.52 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 13.30 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁵⁶-31)/9 = 7(4)₁₅₅1_<157> = 197 · 100616918774894708640648612559_<30> · C126

C126 = P38 · P44 · P44

P38 = 80153664603958430270698294749615024437_<38>

P44 = 53243536433576582261971256661042578792061799_<44>

P44 = 88004479143123417579377741641004702435368009_<44>

Number: 74441_156
N=375573596903421635313913662354161350696820930953190410603725173618920376118848018490033787713031094858628432879290956933623467
  ( 126 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=80153664603958430270698294749615024437
 r2=53243536433576582261971256661042578792061799
 r3=88004479143123417579377741641004702435368009
Version: 
Total time: 14.44 hours.
Scaled time: 34.20 units (timescale=2.368).
Factorization parameters were as follows:
n: 375573596903421635313913662354161350696820930953190410603725173618920376118848018490033787713031094858628432879290956933623467
m: 10000000000000000000000000000000
deg: 5
c5: 670
c0: -31
skew: 0.54
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8551031
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 530012 x 530260
Total sieving time: 13.13 hours.
Total relation processing time: 0.55 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 14.44 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 14, 2009

By Erik Branger / GGNFS, Msieve / Nov 14, 2009

(59·10¹⁶⁴+31)/9 = 6(5)₁₆₃9_<165> = 41 · 257 · 5763713135701_<13> · 632793202179705926119343697193231_<33> · C116

C116 = P50 · P66

P50 = 34802044557813893139042598653269252013977947167193_<50>

P66 = 490143898602442290601560520700188756718313923047228378482398716229_<66>

Number: 65559_164
N=17058009798902811382752770514092749096039916701396886379742470377517403076500372505435723966037254679924690425475197
  ( 116 digits)
Divisors found:
 r1=34802044557813893139042598653269252013977947167193 (pp50)
 r2=490143898602442290601560520700188756718313923047228378482398716229 (pp66)
Version: Msieve v. 1.43
Total time: 32.74 hours.
Scaled time: 30.19 units (timescale=0.922).
Factorization parameters were as follows:
name: 65559_164
n: 17058009798902811382752770514092749096039916701396886379742470377517403076500372505435723966037254679924690425475197
skew: 28874.31
# norm 6.29e+015
c5: 38700
c4: 4290288453
c3: 226518079060538
c2: -3620472774476150580
c1: -58323442579984867482546
c0: 430888104406967566430909160
# alpha -5.57
Y1: 782134821337
Y0: -13453736550076462582111
# Murphy_E 4.89e-010
# M 1490207370408176870324831131388133250549360282891275986372669753761505327303758919313473708023388505821334417351020
type: gnfs
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved algebraic special-q in [1700000, 3000001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 530195 x 530424
Polynomial selection time: 3.13 hours.
Total sieving time: 28.46 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.62 hours.
Time per square root: 0.38 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3400000,3400000,27,27,53,53,2.5,2.5,100000
total time: 32.74 hours.
 --------- CPU info (if available) ----------

Nov 13, 2009 (5th)

By Erik Branger / GGNFS, Msieve / Nov 13, 2009

(64·10¹⁵⁷+71)/9 = 7(1)₁₅₆9_<158> = 79 · 270163 · 131876297221_<12> · C140

C140 = P67 · P73

P67 = 9964004601390419339148197840705296103238041512903134110631263792189_<67>

P73 = 2535618074861695477526155884291998519175671403992482425103587424791058763_<73>

Number: 71119_157
N=25264910165290650509851238117231571124114862434002665400453091269791075424520683131999659561821303788450380878240060216801402515711719402207
  ( 140 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=9964004601390419339148197840705296103238041512903134110631263792189 (pp67)
 r2=2535618074861695477526155884291998519175671403992482425103587424791058763 (pp73)
Version: Msieve v. 1.43
Total time: 24.74 hours.
Scaled time: 21.77 units (timescale=0.880).
Factorization parameters were as follows:
n: 25264910165290650509851238117231571124114862434002665400453091269791075424520683131999659561821303788450380878240060216801402515711719402207
m: 20000000000000000000000000000000
deg: 5
c5: 200
c0: 71
skew: 0.81
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1550000, 2650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 518813 x 519045
Total sieving time: 23.40 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.62 hours.
Time per square root: 0.60 hours.
Prototype def-par.txt line would be:
snfs,158.000,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000
total time: 24.74 hours.
 --------- CPU info (if available) ----------

Nov 13, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve / Nov 13, 2009

(62·10¹⁹¹-71)/9 = 6(8)₁₉₀1_<192> = 3 · 67 · 887 · 2539 · 9337 · 39719 · 1602440276322618158898151_<25> · 517452552714882800113775903751182527043_<39> · C112

C112 = P54 · P59

P54 = 231966688952782810983569504127235672501575217898942363_<54>

P59 = 21334532365287813355167771978525860077741292728723571466821_<59>

N=4948900833131795948779300436802723663715157264908054857089072914253472322653488429767164518431236683340445838023
  ( 112 digits)
Divisors found:
 r1=231966688952782810983569504127235672501575217898942363 (pp54)
 r2=21334532365287813355167771978525860077741292728723571466821 (pp59)
Version: Msieve-1.40
Total time: 20.06 hours.
Scaled time: 39.49 units (timescale=1.969).
Factorization parameters were as follows:
name: 112-1
n: 4948900833131795948779300436802723663715157264908054857089072914253472322653488429767164518431236683340445838023
skew: 35745.19
# norm 5.68e+015
c5: 20520
c4: 7874928393
c3: -125171518425754
c2: -10002823683309029156
c1: 186591281683383709662296
c0: -10471410601966863892978464
# alpha -6.73
Y1: 577849820273
Y0: -2995434647356879034675
# Murphy_E 7.92e-010
# M 1904396237109010344233056436440516679725570088245749401332422872741388847060985884113432289929434595461246543295
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 392267 x 392493
Polynomial selection time: 1.84 hours.
Total sieving time: 17.36 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.50 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 20.06 hours.
 --------- CPU info (if available) ----------

(65·10¹⁵⁹+7)/9 = 7(2)₁₅₈3_<160> = 23 · 971 · 18793 · C152

C152 = P40 · P112

P40 = 1953853962358201528535638767049885845979_<40>

P112 = 8807153537009589409364235375690005448212234630799533315826453435493873992751942939736651790454264854292839358073_<112>

N=17207891835383235758484443528762219892183657200193172828691880569359507978042076647634841544083820217197423030516824039230894905196218677170418908238467
  ( 152 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=1953853962358201528535638767049885845979 (pp40)
 r2=8807153537009589409364235375690005448212234630799533315826453435493873992751942939736651790454264854292839358073 (pp112)
Version: Msieve-1.40
Total time: 22.98 hours.
Scaled time: 43.39 units (timescale=1.888).
Factorization parameters were as follows:
n: 17207891835383235758484443528762219892183657200193172828691880569359507978042076647634841544083820217197423030516824039230894905196218677170418908238467
m: 100000000000000000000000000000000
deg: 5
c5: 13
c0: 14
skew: 1.01
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3000001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 645407 x 645633
Total sieving time: 22.28 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.55 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 22.98 hours.
 --------- CPU info (if available) ----------

(22·10¹⁶⁰-7)/3 = 7(3)₁₅₉1_<161> = 419726063 · C153

C153 = P38 · P48 · P67

P38 = 62892293150312003950256891682691118047_<38>

P48 = 963980414783305788992504638378182452100686241977_<48>

P67 = 2881839886247664950088754545652096672709151792121416684401536364123_<67>

N=174717130523613286633890384198832402107308102364215903679379884811521302486601441601050476899580413554955564752082915883480253008099078501430427810563037
  ( 153 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=62892293150312003950256891682691118047 (pp38)
 r2=963980414783305788992504638378182452100686241977 (pp48)
 r3=2881839886247664950088754545652096672709151792121416684401536364123 (pp67)
Version: Msieve-1.40
Total time: 19.92 hours.
Scaled time: 36.76 units (timescale=1.845).
Factorization parameters were as follows:
n: 174717130523613286633890384198832402107308102364215903679379884811521302486601441601050476899580413554955564752082915883480253008099078501430427810563037
m: 100000000000000000000000000000000
deg: 5
c5: 22
c0: -7
skew: 0.80
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2800001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 683391 x 683639
Total sieving time: 19.13 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.58 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 19.92 hours.
 --------- CPU info (if available) ----------

Nov 13, 2009 (3rd)

By Wataru Sakai / Msieve / Nov 13, 2009

(22·10¹⁶⁶+17)/3 = 7(3)₁₆₅9_<167> = 7 · 21629000599603_<14> · C153

C153 = P51 · P102

P51 = 641923119296141775585479279443339644024656140218061_<51>

P102 = 754542863764954247166210709332774211904122796445876029066108488793031852354112276874269887328583596219_<102>

Number: 73339_166
N=484358508750643176663936835681906593235838524767765001810069448234657396117754486652019637082863748781456555081996193969222446620209155086837402235111359
  ( 153 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=641923119296141775585479279443339644024656140218061
 r2=754542863764954247166210709332774211904122796445876029066108488793031852354112276874269887328583596219
Version: 
Total time: 64.38 hours.
Scaled time: 129.54 units (timescale=2.012).
Factorization parameters were as follows:
n: 484358508750643176663936835681906593235838524767765001810069448234657396117754486652019637082863748781456555081996193969222446620209155086837402235111359
m: 2000000000000000000000000000000000
deg: 5
c5: 55
c0: 136
skew: 1.20
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 4450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 744654 x 744902
Total sieving time: 64.38 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000
total time: 64.38 hours.
 --------- CPU info (if available) ----------

(25·10¹⁹⁸-43)/9 = 2(7)₁₉₇3_<199> = 5869 · C195

C195 = P58 · P138

P58 = 1451404622524480716557996312602451817462320347463899152439_<58>

P138 = 326095561617768087884395065941298852407265226525174381101383715053134023745318575170785592323285897166994765718293103718772301298550007303_<138>

Number: 27773_198
N=473296605516745233903182446375494594952764998769428825656462391851725639423714053122811003199485053293197781185513337498343461880691391681338861437685768917665322504306999110202381628518960262017
  ( 195 digits)
SNFS difficulty: 199 digits.
Divisors found:
 r1=1451404622524480716557996312602451817462320347463899152439
 r2=326095561617768087884395065941298852407265226525174381101383715053134023745318575170785592323285897166994765718293103718772301298550007303
Version: 
Total time: 721.86 hours.
Scaled time: 1454.54 units (timescale=2.015).
Factorization parameters were as follows:
n: 473296605516745233903182446375494594952764998769428825656462391851725639423714053122811003199485053293197781185513337498343461880691391681338861437685768917665322504306999110202381628518960262017
m: 5000000000000000000000000000000000000000
deg: 5
c5: 8
c0: -43
skew: 1.40
type: snfs
lss: 1
rlim: 14700000
alim: 14700000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 14700000/14700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [7350000, 15150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2531515 x 2531763
Total sieving time: 721.86 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,199,5,0,0,0,0,0,0,0,0,14700000,14700000,28,28,55,55,2.5,2.5,100000
total time: 721.86 hours.
 --------- CPU info (if available) ----------

Nov 13, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Nov 13, 2009

(62·10¹⁶⁸-71)/9 = 6(8)₁₆₇1_<169> = 12579647 · C162

C162 = P69 · P94

P69 = 417996494895948005785248123398354871614766916243498866195380490935959_<69>

P94 = 1310110977341236383525940660843416170256038120437603143534793254416808586880932126433244177097_<94>

Number: 68881_168
N=547621796453341567445325682738862933823889405552388623376227400410272950337071373218094982227155411347304808226247436743565927477049943363982223737191424281531023
  ( 162 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=417996494895948005785248123398354871614766916243498866195380490935959 (pp69)
 r2=1310110977341236383525940660843416170256038120437603143534793254416808586880932126433244177097 (pp94)
Version: Msieve v. 1.43
Total time: 71.81 hours.
Scaled time: 124.87 units (timescale=1.739).
Factorization parameters were as follows:
n: 547621796453341567445325682738862933823889405552388623376227400410272950337071373218094982227155411347304808226247436743565927477049943363982223737191424281531023
m: 5000000000000000000000000000000000
deg: 5
c5: 496
c0: -1775
skew: 1.29
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 6400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1056436 x 1056661
Total sieving time: 69.24 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.46 hours.
Time per square root: 0.98 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 71.81 hours.

Nov 13, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 13, 2009

(65·10¹⁵⁶-11)/9 = 7(2)₁₅₅1_<157> = 3 · 149 · 2909 · 484061 · 1869071 · C139

C139 = P48 · P91

P48 = 924547593040272577001488578136091171063098712873_<48>

P91 = 6639944322588482605733024627603148158770302262895769428985277259280354195849327659562685229_<91>

Number: 72221_156
N=6138944541370604791669877501056223782086626050274386084745206959694754003758284585091174261445808018016007420619027077079856127009549252917
  ( 139 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=924547593040272577001488578136091171063098712873
 r2=6639944322588482605733024627603148158770302262895769428985277259280354195849327659562685229
Version: 
Total time: 12.28 hours.
Scaled time: 28.83 units (timescale=2.347).
Factorization parameters were as follows:
n: 6138944541370604791669877501056223782086626050274386084745206959694754003758284585091174261445808018016007420619027077079856127009549252917
m: 10000000000000000000000000000000
deg: 5
c5: 650
c0: -11
skew: 0.44
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8015116
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 554586 x 554834
Total sieving time: 11.01 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 0.77 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 12.28 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(61·10¹⁶⁰-43)/9 = 6(7)₁₅₉3_<161> = 3 · 258846753455803_<15> · 61739694542088436121217926517233_<32> · C115

C115 = P46 · P69

P46 = 1817926149208691502729521475457905515096473051_<46>

P69 = 777647240937270328992484826480769491945261040621892507628864171690359_<69>

Number: 67773_160
N=1413705254159855371061936185876921103504280730923166822583108539086549753629478508296087325967444560737441760015309
  ( 115 digits)
Divisors found:
 r1=1817926149208691502729521475457905515096473051
 r2=777647240937270328992484826480769491945261040621892507628864171690359
Version: 
Total time: 15.79 hours.
Scaled time: 37.44 units (timescale=2.371).
Factorization parameters were as follows:
name: 67773_160
n: 1413705254159855371061936185876921103504280730923166822583108539086549753629478508296087325967444560737441760015309
skew: 50536.77
# norm 4.80e+15
c5: 25380
c4: -614505552
c3: -47647136645839
c2: 5452395569024831359
c1: 140859291886924652868131
c0: -4324536369697488192023050839
# alpha -6.16
Y1: 2826537573989
Y0: -8895576914842352240720
# Murphy_E 5.57e-10
# M 161569964661124522022265799579816433730413328407547361845111517972008345354236704372972149102516328162387493120225
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1400000, 2450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9221835
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 496281 x 496529
Polynomial selection time: 1.36 hours.
Total sieving time: 12.88 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000
total time: 15.79 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 12, 2009 (6th)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Nov 12, 2009

(59·10¹⁵⁶+31)/9 = 6(5)₁₅₅9_<157> = 211 · 1277 · 204371 · 8456385102374933467647900354881_<31> · C116

C116 = P34 · P82

P34 = 3012983645866773188165757444214891_<34>

P82 = 4672349839242065027594979758740290110260235772594442708775254177171296529449693617_<82>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 14077713653404588690555756672692970008608629107471571113503341492890083842753884124196001195304510019047009059050747 (116 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5651182032
Step 1 took 2692ms
Step 2 took 1917ms
********** Factor found in step 2: 3012983645866773188165757444214891
Found probable prime factor of 34 digits: 3012983645866773188165757444214891
Probable prime cofactor 4672349839242065027594979758740290110260235772594442708775254177171296529449693617 has 82 digits

(64·10¹⁵⁶+17)/9 = 7(1)₁₅₅3_<157> = 3 · 23 · 1476527597_<10> · 4262940271_<10> · 19870321428695636593969_<23> · C114

C114 = P55 · P60

P55 = 1982357395654855011440038146861915074032606554692317687_<55>

P60 = 415671941297055391986742820832969759498307762414593330759457_<60>

Number: 71113_156
N=824010346996428501902929446579336446349065675339870767096387628080340800443117481808771174671282885478191223615959
  ( 114 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=1982357395654855011440038146861915074032606554692317687
 r2=415671941297055391986742820832969759498307762414593330759457
Version: 
Total time: 12.24 hours.
Scaled time: 28.40 units (timescale=2.321).
Factorization parameters were as follows:
n: 824010346996428501902929446579336446349065675339870767096387628080340800443117481808771174671282885478191223615959
m: 20000000000000000000000000000000
deg: 5
c5: 20
c0: 17
skew: 0.97
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8481172
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 485933 x 486180
Total sieving time: 11.15 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 0.51 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 12.24 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(65·10¹⁵⁹+61)/9 = 7(2)₁₅₈9_<160> = 167 · 455921 · 4001016979670712233_<19> · 5379908203555946771_<19> · C115

C115 = P53 · P62

P53 = 96383262843725875562456351579696025282506312998383983_<53>

P62 = 45721228945729185309354981526914135704408442080201681269449463_<62>

Number: 72229_159
N=4406761227014383772744992246241231961679312963933611928862215622302455615422271185419516893972781051599907087151129
  ( 115 digits)
Divisors found:
 r1=96383262843725875562456351579696025282506312998383983
 r2=45721228945729185309354981526914135704408442080201681269449463
Version: 
Total time: 15.08 hours.
Scaled time: 36.03 units (timescale=2.389).
Factorization parameters were as follows:
name: 72229_159
n: 4406761227014383772744992246241231961679312963933611928862215622302455615422271185419516893972781051599907087151129
skew: 17359.92
# norm 2.35e+15
c5: 36540
c4: 5231062026
c3: -130362871646254
c2: -1226930863844106788
c1: 8425729364406378361539
c0: 53716536162268136384847162
# alpha -5.10
Y1: 159695469967
Y0: -10381736553568680581705
# Murphy_E 5.72e-10
# M 827678952077618632955342287148713937231119215230854811599520325539777306026637345719092699824163303916063189669290
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1400000, 2450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9155069
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 523806 x 524054
Polynomial selection time: 1.34 hours.
Total sieving time: 12.38 hours.
Total relation processing time: 0.67 hours.
Matrix solve time: 0.58 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000
total time: 15.08 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(83·10¹⁶¹+7)/9 = 9(2)₁₆₀3_<162> = 1697 · 2711 · 20543 · 1498481 · 53973738457_<11> · 810578820825230269_<18> · C117

C117 = P32 · P85

P32 = 65656961003311514015883035936551_<32>

P85 = 2266995127807532404937686268783558513717904515654110062784739793001401834333714626621_<85>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 148844010701156356756903072727115500377610663976925506749656983744503128054493059428451193698102694635708042011524171 (117 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6209770295
Step 1 took 3580ms
Step 2 took 2050ms
********** Factor found in step 2: 65656961003311514015883035936551
Found probable prime factor of 32 digits: 65656961003311514015883035936551
Probable prime cofactor 2266995127807532404937686268783558513717904515654110062784739793001401834333714626621 has 85 digits

(67·10¹⁶³-31)/9 = 7(4)₁₆₂1_<164> = 1093 · 16633 · 26687 · 14657691415107539107_<20> · C134

C134 = P37 · P38 · P59

P37 = 2379704242579980728400961963262974523_<37>

P38 = 80520601705670054813859962771453621977_<38>

P59 = 54631889004741725520371953058841143590754460348049791924251_<59>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 10468301293755797423881824808300936684163049041001719203135482913387586546663127409790577743604090731829830211783508368815067239088721 (134 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4672242577
Step 1 took 3327ms
Step 2 took 2201ms
********** Factor found in step 2: 80520601705670054813859962771453621977
Found probable prime factor of 38 digits: 80520601705670054813859962771453621977
Composite cofactor 130007738044742485114119405003336802697164449362326732828807416813930485046568036276242158857273 has 96 digits

Number: 74441_163
N=130007738044742485114119405003336802697164449362326732828807416813930485046568036276242158857273
  ( 96 digits)
Divisors found:
 r1=2379704242579980728400961963262974523
 r2=54631889004741725520371953058841143590754460348049791924251
Version: 
Total time: 1.50 hours.
Scaled time: 3.46 units (timescale=2.313).
Factorization parameters were as follows:
name: 74441_163
n: 130007738044742485114119405003336802697164449362326732828807416813930485046568036276242158857273
skew: 1979.38
# norm 1.96e+13
c5: 273300
c4: 304405751
c3: 365710080704
c2: -4895444318937764
c1: -4512394773361583236
c0: 13984228209751842845
# alpha -6.07
Y1: 14191866557
Y0: -861914766383702208
# Murphy_E 6.01e-09
# M 46998393681213226899223521402912408001520722578974367414646002933959646617795624266321907021062
type: gnfs
rlim: 800000
alim: 800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 40000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [400000, 680001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3482298
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 128893 x 129141
Polynomial selection time: 0.10 hours.
Total sieving time: 1.21 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
gnfs,95,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,800000,800000,26,26,48,48,2.5,2.5,40000
total time: 1.50 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 12, 2009 (5th)

By Dmitry Domanov / GGNFS/msieve / Nov 12, 2009

(67·10¹⁷⁵-31)/9 = 7(4)₁₇₄1_<176> = 269 · 3343 · C170

C170 = P57 · P114

P57 = 393007290755296676600975185335423075552050629797117701609_<57>

P114 = 210641059005337681090850353556043252785508344730403422889278293035429519751561094996454076042806528622893752218747_<114>

N=82783471921514349402840807507052348684477963101553203269378776764236255132729705909862637508598052018415492222492812973726873603106134712431841093295366609076552841863923
  ( 170 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=393007290755296676600975185335423075552050629797117701609 (pp57)
 r2=210641059005337681090850353556043252785508344730403422889278293035429519751561094996454076042806528622893752218747 (pp114)
Version: Msieve-1.40
Total time: 82.62 hours.
Scaled time: 155.56 units (timescale=1.883).
Factorization parameters were as follows:
n: 82783471921514349402840807507052348684477963101553203269378776764236255132729705909862637508598052018415492222492812973726873603106134712431841093295366609076552841863923
m: 100000000000000000000000000000000000
deg: 5
c5: 67
c0: -31
skew: 0.86
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3100000, 7200001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1326117 x 1326348
Total sieving time: 79.81 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.19 hours.
Time per square root: 0.45 hours.
Prototype def-par.txt line would be:
snfs,176.000,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,53,53,2.5,2.5,100000
total time: 82.62 hours.
 --------- CPU info (if available) ----------

(65·10¹⁵⁸-11)/9 = 7(2)₁₅₇1_<159> = 7 · 31 · 3607 · C153

C153 = P41 · P50 · P63

P41 = 83363948032550770439971746177796233984623_<41>

P50 = 63165174686566479174510487178756948267564308740641_<50>

P63 = 175230215598453693379399967411213917661767959640494153861891613_<63>

N=922709455401264339082381061686534020794464197524555073049488031109788087707366529012611450881123650022833510138660518298677075964965999576121471718742259
  ( 153 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=83363948032550770439971746177796233984623 (pp41)
 r2=63165174686566479174510487178756948267564308740641 (pp50)
 r3=175230215598453693379399967411213917661767959640494153861891613 (pp63)
Version: Msieve-1.40
Total time: 19.63 hours.
Scaled time: 36.21 units (timescale=1.845).
Factorization parameters were as follows:
n: 922709455401264339082381061686534020794464197524555073049488031109788087707366529012611450881123650022833510138660518298677075964965999576121471718742259
m: 50000000000000000000000000000000
deg: 5
c5: 104
c0: -55
skew: 0.88
type: snfs
lss: 1
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1650000, 2750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 618184 x 618411
Total sieving time: 18.94 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,160.000,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000
total time: 19.63 hours.
 --------- CPU info (if available) ----------

Nov 12, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 12, 2009

(62·10¹⁹²-71)/9 = 6(8)₁₉₁1_<193> = 807571049183_<12> · C181

C181 = P40 · P142

P40 = 2141731664373514704800209804190966929619_<40>

P142 = 3982936487128283963654011022855118528252029474284443258175563324282085584199674797758328510237897814911957350790362026615847538823628063665653_<142>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2276662570
Step 1 took 63985ms
********** Factor found in step 1: 2141731664373514704800209804190966929619
Found probable prime factor of 40 digits: 2141731664373514704800209804190966929619
Probable prime cofactor 3982936487128283963654011022855118528252029474284443258175563324282085584199674797758328510237897814911957350790362026615847538823628063665653 has 142 digits

Nov 12, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Nov 12, 2009

(67·10¹⁶⁴+41)/9 = 7(4)₁₆₃9_<165> = 7 · 97 · 461 · C160

C160 = P44 · P117

P44 = 10965272962460119234911069404341287975741259_<44>

P117 = 216891307273720750758081653250952572647618179283737370490732853103987208380893592346709082214421115917317056152162969_<117>

Number: 74449_164
N=2378272387441159943787579809674315119671471841787381738630704348440332517976367071789394396009329927079328872830225783241414880388872382968587991286293945237971
  ( 160 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=10965272962460119234911069404341287975741259 (pp44)
 r2=216891307273720750758081653250952572647618179283737370490732853103987208380893592346709082214421115917317056152162969 (pp117)
Version: Msieve v. 1.43
Total time: 44.81 hours.
Scaled time: 77.93 units (timescale=1.739).
Factorization parameters were as follows:
n: 2378272387441159943787579809674315119671471841787381738630704348440332517976367071789394396009329927079328872830225783241414880388872382968587991286293945237971
m: 1000000000000000000000000000000000
deg: 5
c5: 67
c0: 410
skew: 1.44
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 794493 x 794718
Total sieving time: 43.79 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.80 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 44.81 hours.

Nov 12, 2009 (2nd)

By Sinkiti Sibata / Msieve / Nov 12, 2009

(62·10¹⁵⁵-71)/9 = 6(8)₁₅₄1_<156> = 3 · 83 · 1054865761_<10> · 5865205252879032365590891631_<28> · C117

C117 = P57 · P60

P57 = 690204344660474179997645180103744985808246178066443143733_<57>

P60 = 647875762848916317184387762028148718967749699167161314240123_<60>

Number: 68881_155
N=447166666318541071021133120076586888737388050135431182917568426080461179199315021134343779030522598595547672164599159
  ( 117 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=690204344660474179997645180103744985808246178066443143733 (pp57)
 r2=647875762848916317184387762028148718967749699167161314240123 (pp60)
Version: Msieve-1.40
Total time: 35.60 hours.
Scaled time: 120.13 units (timescale=3.374).
Factorization parameters were as follows:
name: 68881_155
n: 447166666318541071021133120076586888737388050135431182917568426080461179199315021134343779030522598595547672164599159
m: 10000000000000000000000000000000
deg: 5
c5: 62
c0: -71
skew: 1.03
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1450000, 2750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 507864 x 508112
Total sieving time: 35.01 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.48 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000
total time: 35.60 hours.
 --------- CPU info (if available) ----------

(62·10¹⁵²-71)/9 = 6(8)₁₅₁1_<153> = 3² · 23 · 443 · 1061 · 34279360770581_<14> · C132

C132 = P36 · P96

P36 = 315834675110482422029126787755351387_<36>

P96 = 653984116715282556173259909244692754554281589932741812886644462514507314473058785355215072340543_<96>

Number: 68881_152
N=206550861030187082845434344910136822313692781358486124359562932596625872977417209449469207777000587340003595836995580001075491383141
  ( 132 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=315834675110482422029126787755351387 (pp36)
 r2=653984116715282556173259909244692754554281589932741812886644462514507314473058785355215072340543 (pp96)
Version: Msieve-1.40
Total time: 26.52 hours.
Scaled time: 55.30 units (timescale=2.085).
Factorization parameters were as follows:
name: 68881_152
n: 206550861030187082845434344910136822313692781358486124359562932596625872977417209449469207777000587340003595836995580001075491383141
m: 2000000000000000000000000000000
deg: 5
c5: 775
c0: -284
skew: 0.82
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 503235 x 503483
Total sieving time: 25.38 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.88 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,154.000,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 26.52 hours.
 --------- CPU info (if available) ----------

Nov 12, 2009

By Erik Branger / GGNFS, Msieve / Nov 12, 2009

(65·10¹⁵⁶+61)/9 = 7(2)₁₅₅9_<157> = 7³ · 23041 · 290912309 · C142

C142 = P54 · P88

P54 = 605691835518887929525069079127539502706299835330479941_<54>

P88 = 5186347188194532049169964537904314800100966481543495236359524310108165939442379395721307_<88>

Number: 72229_156
N=3141328148055769408108490574107127310905627536310764350258942664672471270571546787474991776204204338886772516964994368059599955681938189802887
  ( 142 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=605691835518887929525069079127539502706299835330479941 (pp54)
 r2=5186347188194532049169964537904314800100966481543495236359524310108165939442379395721307 (pp88)
Version: Msieve v. 1.43
Total time: 29.78 hours.
Scaled time: 25.49 units (timescale=0.856).
Factorization parameters were as follows:
n: 3141328148055769408108490574107127310905627536310764350258942664672471270571546787474991776204204338886772516964994368059599955681938189802887
m: 10000000000000000000000000000000
deg: 5
c5: 650
c0: 61
skew: 0.62
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2800001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 628739 x 628971
Total sieving time: 28.49 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.91 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,157.000,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 29.78 hours.
 --------- CPU info (if available) ----------

Nov 11, 2009 (6th)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 11, 2009

(62·10¹⁹¹-71)/9 = 6(8)₁₉₀1_<192> = 3 · 67 · 887 · 2539 · 9337 · 39719 · 1602440276322618158898151_<25> · C151

C151 = P39 · C112

P39 = 517452552714882800113775903751182527043_<39>

C112 = [4948900833131795948779300436802723663715157264908054857089072914253472322653488429767164518431236683340445838023_<112>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1659986578
Step 1 took 46926ms
Step 2 took 16405ms
********** Factor found in step 2: 517452552714882800113775903751182527043
Found probable prime factor of 39 digits: 517452552714882800113775903751182527043
Composite cofactor 4948900833131795948779300436802723663715157264908054857089072914253472322653488429767164518431236683340445838023 has 112 digits

Nov 11, 2009 (5th)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Nov 11, 2009

(67·10¹⁹⁷-31)/9 = 7(4)₁₉₆1_<198> = 3² · 62765167725817727_<17> · 569456850647072222011_<21> · 7082290927670325280559_<22> · 143654013588585058279631_<24> · C115

C115 = P39 · P76

P39 = 876417883079711189730801115665794456501_<39>

P76 = 2595419183630539862325486973334714191597155410525075313845472607910755022473_<76>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 2274671786621949951263749654269552518055133473554962856563812879331411196076321546565020576595542670694967075946973 (115 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6695390019
Step 1 took 3447ms
Step 2 took 3775ms
********** Factor found in step 2: 876417883079711189730801115665794456501
Found probable prime factor of 39 digits: 876417883079711189730801115665794456501
Probable prime cofactor 2595419183630539862325486973334714191597155410525075313845472607910755022473 has 76 digits

(67·10¹⁵⁵-13)/9 = 7(4)₁₅₄3_<156> = 7 · 709 · 9293712784931_<13> · 1383499142474187967_<19> · C122

C122 = P49 · P73

P49 = 4878885565302112410069827574733270111997783354663_<49>

P73 = 2391108289919426790093946899475837566572606524440706754396837686596322811_<73>

Number: 74443_155
N=11665943720762109867469144547912706865819403378906466080397791627463020253271963189327366442949178885904585225639650117693
  ( 122 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=4878885565302112410069827574733270111997783354663
 r2=2391108289919426790093946899475837566572606524440706754396837686596322811
Version: 
Total time: 11.86 hours.
Scaled time: 28.30 units (timescale=2.387).
Factorization parameters were as follows:
n: 11665943720762109867469144547912706865819403378906466080397791627463020253271963189327366442949178885904585225639650117693
m: 10000000000000000000000000000000
deg: 5
c5: 67
c0: -13
skew: 0.72
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8097644
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 498919 x 499167
Total sieving time: 10.82 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.54 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 11.86 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(62·10¹⁵⁷-71)/9 = 6(8)₁₅₆1_<158> = 99195219782129_<14> · 862777452673465967877176411389_<30> · C114

C114 = P35 · P80

P35 = 52297659149807374462667474009984713_<35>

P80 = 15391374265113706485561084794199787764149587902549858512746210928097010187565677_<80>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 804932845164033586036914469028264065136979055479450569674957239025392866722070247914821612289988269570817453495701 (114 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=8562617314
Step 1 took 2683ms
Step 2 took 1934ms
********** Factor found in step 2: 52297659149807374462667474009984713
Found probable prime factor of 35 digits: 52297659149807374462667474009984713
Probable prime cofactor 15391374265113706485561084794199787764149587902549858512746210928097010187565677 has 80 digits

(62·10¹⁹³-71)/9 = 6(8)₁₉₂1_<194> = 75960033942817_<14> · 4397607999596779171_<19> · 369309395407669463317213_<24> · 1171702087614980824891741_<25> · C114

C114 = P37 · P39 · P39

P37 = 2525698696521822456119491163260313393_<37>

P39 = 256813952710105392622923287549523616069_<39>

P39 = 734750347974042448663022462026007717303_<39>

Number: 68881_193
N=476584546263894187249410686004100765778612480514835230007919231006638024959787696980937702139804608084591272660451
  ( 114 digits)
Divisors found:
 r1=2525698696521822456119491163260313393
 r2=256813952710105392622923287549523616069
 r3=734750347974042448663022462026007717303
Version: 
Total time: 15.21 hours.
Scaled time: 36.34 units (timescale=2.389).
Factorization parameters were as follows:
name: 68881_193
n: 476584546263894187249410686004100765778612480514835230007919231006638024959787696980937702139804608084591272660451
skew: 81967.32
# norm 9.82e+15
c5: 8820
c4: 2345585976
c3: -323570539152345
c2: -15362443811670735002
c1: 597776664594248966729850
c0: 21149383241086351023669060501
# alpha -6.44
Y1: 162832733239
Y0: -8841660780460233148288
# Murphy_E 6.11e-10
# M 113143934203780989554909325109184190545377095444258272813552631118687650210735975240448943877806470142275656860495
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1400000, 2450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9462558
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 455180 x 455428
Polynomial selection time: 1.15 hours.
Total sieving time: 12.32 hours.
Total relation processing time: 0.70 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.62 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000
total time: 15.21 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁵⁶+41)/9 = 7(4)₁₅₅9_<157> = 3 · 49722859553004683571304633082687_<32> · C125

C125 = P39 · P86

P39 = 977449831415406822625837597217701697963_<39>

P86 = 51057608111162517212283211587392025819225649128369502205593083124860984531588715088543_<86>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 49906250440729710419014031070881432285557829279347790059994308543147408208496821187368869362262186554536134835916248987737909 (125 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4701809730
Step 1 took 3299ms
********** Factor found in step 1: 977449831415406822625837597217701697963
Found probable prime factor of 39 digits: 977449831415406822625837597217701697963
Probable prime cofactor 51057608111162517212283211587392025819225649128369502205593083124860984531588715088543 has 86 digits

Nov 11, 2009 (4th)

By Sinkiti Sibata / Msieve / Nov 11, 2009

(62·10¹⁵¹-71)/9 = 6(8)₁₅₀1_<152> = 331 · 127037 · 11400881 · 134503558337_<12> · C127

C127 = P53 · P74

P53 = 12183800517956357535603106021528312450021649863093099_<53>

P74 = 87687157226222913211851853713756716074490652421247217538196733958337598941_<74>

Number: 68881_151
N=1068362831630975289536719380978717933839318138065193388152189421002793725428131445533649250405126709847471149909608867206808159
  ( 127 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=12183800517956357535603106021528312450021649863093099 (pp53)
 r2=87687157226222913211851853713756716074490652421247217538196733958337598941 (pp74)
Version: Msieve-1.40
Total time: 24.61 hours.
Scaled time: 51.14 units (timescale=2.078).
Factorization parameters were as follows:
name: 68881_151
n: 1068362831630975289536719380978717933839318138065193388152189421002793725428131445533649250405126709847471149909608867206808159
m: 2000000000000000000000000000000
deg: 5
c5: 155
c0: -568
skew: 1.30
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 451516 x 451764
Total sieving time: 23.54 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.71 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,153.000,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 24.61 hours.
 --------- CPU info (if available) ----------

Nov 11, 2009 (3rd)

By Erik Branger / GGNFS, Msieve, GMP-ECM / Nov 11, 2009

(62·10¹⁵⁴-71)/9 = 6(8)₁₅₃1_<155> = 43 · 374993 · 2810836267_<10> · 11225367031078217_<17> · C123

C123 = P50 · P73

P50 = 59456498419297853938720187564291652786173012200777_<50>

P73 = 2277309913700930235171299438349941993910174833496615439903369397888974873_<73>

Number: 68881_154
N=135400873284210690693774015755123458723863999599882657194440727495833755486367006735978429661363061336140811098682184076321
  ( 123 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=59456498419297853938720187564291652786173012200777 (pp50)
 r2=2277309913700930235171299438349941993910174833496615439903369397888974873 (pp73)
Version: Msieve v. 1.43
Total time: 23.11 hours.
Scaled time: 23.09 units (timescale=0.999).
Factorization parameters were as follows:
n: 135400873284210690693774015755123458723863999599882657194440727495833755486367006735978429661363061336140811098682184076321
m: 10000000000000000000000000000000
deg: 5
c5: 31
c0: -355
skew: 1.63
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2500001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 506553 x 506780
Total sieving time: 22.27 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 23.11 hours.
 --------- CPU info (if available) ----------

(67·10¹⁷⁷+41)/9 = 7(4)₁₇₆9_<178> = 3² · 13 · 29 · 83 · 4273 · 5393 · 5722060324567079183_<19> · 151018584602920158933747156833_<30> · C118

C118 = P32 · P86

P32 = 22758430372083446855719889404943_<32>

P86 = 58328645933672237511735506021370981038299449338001585648578106455857959995279721987707_<86>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 1327468427179387889781842707701047813219909890609691053184956887763212589049476886379634400599684315962049865391035701 (118 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3389415600
Step 1 took 35225ms
Step 2 took 12183ms
********** Factor found in step 2: 22758430372083446855719889404943
Found probable prime factor of 32 digits: 22758430372083446855719889404943
Probable prime cofactor 58328645933672237511735506021370981038299449338001585648578106455857959995279721987707 has 86 digits

Nov 11, 2009 (2nd)

By matsui / Msieve / Nov 11, 2009

9·10²²⁹-1 = 8(9)₂₂₉_<230> = 197 · 208440677 · 1189638653569_<13> · 1894742524089853_<16> · 81036479966432843_<17> · 49931612314311537707693_<23> · C153

C153 = P41 · P55 · P57

P41 = 67387210716432592896081650429078156564311_<41>

P55 = 6243050577365052581815882169888181821426803805681795893_<55>

P57 = 571212953652346708852367194795436478812329554530967996239_<57>

N=240310297661166400485936362786332361583251738596432632828490772305058814102347092398830258825622814264893962996338765698926236641973725988355663176866797
  ( 153 digits)
Divisors found:
 r1=67387210716432592896081650429078156564311 (pp41)
 r2=6243050577365052581815882169888181821426803805681795893 (pp55)
 r3=571212953652346708852367194795436478812329554530967996239 (pp57)
Version: Msieve v. 1.43
Total time: 251.99 hours.
Scaled time: 435.68 units (timescale=1.729).
Factorization parameters were as follows:
name: 89999_229
n: 240310297661166400485936362786332361583251738596432632828490772305058814102347092398830258825622814264893962996338765698926236641973725988355663176866797
skew: 767614.43
# norm 1.10e+21
c5: 5687280
c4: -1576344828224
c3: -15992040188510426116
c2: 551458288805369004819659
c1: 3133393285152216531272566657368
c0: 15877934132636447372734593052780585
# alpha -6.25
Y1: 421186069282110373
Y0: -133405467847610273238880604564
# Murphy_E 3.57e-12
# M 94019805174926964203307818923509292211349668657206486672204198932322380976076648921267349291638710915588954585022947785470799284727337408767453363616776
type: gnfs
rlim: 24400000
alim: 24400000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 1600000
Factor base limits: 24400000/24400000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved algebraic special-q in [12200000, 45800001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 4602695 x 4602923
Total sieving time: 218.64 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 28.28 hours.
Time per square root: 4.71 hours.
Prototype def-par.txt line would be:
gnfs,152,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,24400000,24400000,29,29,58,58,2.6,2.6,100000
total time: 251.99 hours.

c153 is the largest composite number which was factored by gnfs in our tables so far. Congratulations!

Nov 11, 2009

By Dmitry Domanov / GGNFS/msieve / Nov 11, 2009

(65·10¹⁵⁶+7)/9 = 7(2)₁₅₅3_<157> = 103 · 5987 · C152

C152 = P34 · P45 · P73

P34 = 7031297053478820252836704940982133_<34>

P45 = 216618954992476495307119418561129767797475183_<45>

P73 = 7689400150761544910067260025642464616112812856275284452144717121553857737_<73>

Number: s152
N=11711819333835319928165105661331302323679010383699021378394648311182679336332640173810606187552354084695192694563499592518778100483445883917131490757843
  ( 152 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=7031297053478820252836704940982133 (pp34)
 r2=216618954992476495307119418561129767797475183 (pp45)
 r3=7689400150761544910067260025642464616112812856275284452144717121553857737 (pp73)
Version: Msieve-1.40
Total time: 20.84 hours.
Scaled time: 39.70 units (timescale=1.905).
Factorization parameters were as follows:
n: 11711819333835319928165105661331302323679010383699021378394648311182679336332640173810606187552354084695192694563499592518778100483445883917131490757843
m: 20000000000000000000000000000000
deg: 5
c5: 325
c0: 112
skew: 0.81
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1550000, 2750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 563522 x 563750
Total sieving time: 19.98 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.39 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
snfs,159.000,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000
total time: 20.84 hours.
 --------- CPU info (if available) ----------

Nov 10, 2009 (7th)

By Lionel Debroux + Jeff Gilchrist / ggnfs + msieve / Nov 10, 2009

(16·10²¹⁸-7)/9 = 1(7)₂₁₈_<219> = 3 · 31 · 47803226827_<11> · 4200791891903_<13> · C193

C193 = P84 · P110

P84 = 268323355950355689735829355470693132255531404134917945907444149722706588875965691187_<84>

P110 = 35477063645140320608508880041657003639745603152097560923338385031351604960423622458603280891900739184876928587_<110>

* Sieving with ggnfs-lasieve4I14e on the RSALS grid
* Relation filtering and matrix creation by Lionel Debroux
* Lanczos iteration and square root phase by Jeff Gilchrist:

Msieve v. 1.43
Sat Nov  7 06:20:12 2009
random seeds: 0a61ba43 4d857a70
factoring 9519324776528409561729990009646664138683276667349926474618191233610006802875690133653956702500176615466439936026117646551454778085624851090212971043848299225331138444034552307364883241094262769
(193 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (193-digit input)
R0: -2000000000000000000000000000000000000
R1:  1
A0: -7
A1:  0
A2:  0
A3:  0
A4:  0
A5:  0
A6:  25
skew 0.81, size 8.982341e-11, alpha 0.442034, combined = 3.092508e-12

commencing square root phase
reading relations for dependency 1
read 2344667 cycles
cycles contain 6788734 unique relations
read 6788734 relations
multiplying 6788734 relations
multiply complete, coefficients have about 194.54 million bits
initial square root is modulo 9585991
reading relations for dependency 2
read 2347128 cycles
cycles contain 6786766 unique relations
read 6786766 relations
multiplying 6786766 relations
multiply complete, coefficients have about 194.49 million bits
initial square root is modulo 9541993
reading relations for dependency 3
read 2345872 cycles
cycles contain 6789410 unique relations
read 6789410 relations
multiplying 6789410 relations
multiply complete, coefficients have about 194.56 million bits
initial square root is modulo 9600571
reading relations for dependency 4
read 2346398 cycles
cycles contain 6788602 unique relations
read 6788602 relations
multiplying 6788602 relations
multiply complete, coefficients have about 194.54 million bits
initial square root is modulo 9582763
reading relations for dependency 5
read 2346536 cycles
cycles contain 6786192 unique relations
read 6786192 relations
multiplying 6786192 relations
multiply complete, coefficients have about 194.48 million bits
initial square root is modulo 9533137
sqrtTime: 9409
prp84 factor: 268323355950355689735829355470693132255531404134917945907444149722706588875965691187
prp110 factor: 35477063645140320608508880041657003639745603152097560923338385031351604960423622458603280891900739184876928587
elapsed time 02:36:51

Nov 10, 2009 (6th)

By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Nov 10, 2009

(22·10¹⁶⁸+17)/3 = 7(3)₁₆₇9_<169> = 13² · 41 · 8713 · 13669 · 214273369 · 114606497028610906462852186626440387_<36> · C114

C114 = P40 · P74

P40 = 4177882563148851956956378400719707432499_<40>

P74 = 86614926782716481655642989173611606205822555745723844164409561209012769799_<74>

Number: g114
N=361866992313925679835060995464419229628238498308302974917150353218753381622582951726188164535961708450542818297701
  ( 114 digits)
Divisors found:
 r1=4177882563148851956956378400719707432499 (pp40)
 r2=86614926782716481655642989173611606205822555745723844164409561209012769799 (pp74)
Version: Msieve-1.40
Total time: 18.28 hours.
Scaled time: 34.22 units (timescale=1.872).
Factorization parameters were as follows:
# Murphy_E = 6.914749e-10, selected by Erik Branger
n: 361866992313925679835060995464419229628238498308302974917150353218753381622582951726188164535961708450542818297701
Y0: -9358848905036098722083
Y1: 1217111908793
c0: 250679101103598290355518496
c1: -98749734681377813022512
c2: -1818902650774914967
c3: -83088339013152
c4: 558203372
c5: 5040
skew: 74097.95
type: gnfs
# selected mechanically
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 421885 x 422119
Total sieving time: 17.91 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.5,2.5,100000
total time: 18.28 hours.
 --------- CPU info (if available) ----------

(65·10¹⁸⁴+61)/9 = 7(2)₁₈₃9_<185> = C185

C185 = P79 · P106

P79 = 7416636363322081411734736677307481195492064107754843900863362332033982448906537_<79>

P106 = 9737867502765395606014252796988801940512562554168295027040851239051448736911790559819965758531428016050317_<106>

Number: s185
N=72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
  ( 185 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=7416636363322081411734736677307481195492064107754843900863362332033982448906537 (pp79)
 r2=9737867502765395606014252796988801940512562554168295027040851239051448736911790559819965758531428016050317 (pp106)
Version: Msieve-1.40
Total time: 356.27 hours.
Scaled time: 332.76 units (timescale=0.934).
Factorization parameters were as follows:
n: 72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
m: 10000000000000000000000000000000000000
deg: 5
c5: 13
c0: 122
skew: 1.56
type: snfs
lss: 1
rlim: 8900000
alim: 8900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 8900000/8900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4450000, 8550001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1689410 x 1689637
Total sieving time: 349.66 hours.
Total relation processing time: 0.66 hours.
Matrix solve time: 5.48 hours.
Time per square root: 0.48 hours.
Prototype def-par.txt line would be:
snfs,186.000,5,0,0,0,0,0,0,0,0,8900000,8900000,28,28,54,54,2.5,2.5,100000
total time: 356.27 hours.
 --------- CPU info (if available) ----------

(59·10¹⁶²+31)/9 = 6(5)₁₆₁9_<163> = 11839 · C159

C159 = P64 · P96

P64 = 1603806001192770510753527225209719940802414193940206966754019963_<64>

P96 = 345257123130058654867239834949430629892606823120856523120868703933491053735726127484325472092987_<96>

Number: s159
N=553725446030539366125141950802901896744282080881455828664207750279209017278110951563101237904853075053260879766496794962036958827228275661420352694953590299481
  ( 159 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=1603806001192770510753527225209719940802414193940206966754019963 (pp64)
 r2=345257123130058654867239834949430629892606823120856523120868703933491053735726127484325472092987 (pp96)
Version: Msieve-1.40
Total time: 42.53 hours.
Scaled time: 77.11 units (timescale=1.813).
Factorization parameters were as follows:
n: 553725446030539366125141950802901896744282080881455828664207750279209017278110951563101237904853075053260879766496794962036958827228275661420352694953590299481
m: 200000000000000000000000000000000
deg: 5
c5: 1475
c0: 248
skew: 0.70
type: snfs
lss: 1
rlim: 3900000
alim: 3900000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 3900000/3900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1950000, 4450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 832432 x 832658
Total sieving time: 41.20 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.90 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
snfs,164.000,5,0,0,0,0,0,0,0,0,3900000,3900000,27,27,51,51,2.4,2.4,100000
total time: 42.53 hours.
 --------- CPU info (if available) ----------

(67·10¹⁷⁶-31)/9 = 7(4)₁₇₅1_<177> = 3 · 13 · 71 · C174

C174 = P38 · C137

P38 = 14585106125382471096943606647246369289_<38>

C137 = [18433157929261372543020550729674096547707466849046376880307345015073860397953606708332537812839756446385684607720942028809690211884235201_<137>]

Factor=14585106125382471096943606647246369289  Method=ECM  B1=11000000  Sigma=2392920153

(22·10¹⁵⁹-7)/3 = 7(3)₁₅₈1_<160> = 13967 · C156

C156 = P45 · P112

P45 = 324485775047405152706505180736142372790996977_<45>

P112 = 1618089837178662448363775067491171510470582401491581751100635227165937052536156327577009094712259852356951106509_<112>

N=525047134913247893845015632085153098971384931147227989785446648051359156106059521252476074556693157681200925992219756091740053936660222906374549533424023293
  ( 156 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=324485775047405152706505180736142372790996977 (pp45)
 r2=1618089837178662448363775067491171510470582401491581751100635227165937052536156327577009094712259852356951106509 (pp112)
Version: Msieve-1.40
Total time: 18.84 hours.
Scaled time: 35.27 units (timescale=1.872).
Factorization parameters were as follows:
n: 525047134913247893845015632085153098971384931147227989785446648051359156106059521252476074556693157681200925992219756091740053936660222906374549533424023293
m: 100000000000000000000000000000000
deg: 5
c5: 11
c0: -35
skew: 1.26
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 637822 x 638049
Total sieving time: 17.98 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 18.84 hours.
 --------- CPU info (if available) ----------

(22·10¹⁸⁰-7)/3 = 7(3)₁₇₉1_<181> = 277 · C179

C179 = P38 · C141

P38 = 28341234128475964035151410109192458499_<38>

C141 = [934120491618255487715617124498006305942083239924591056032626276482155278960222427194169266237177630746177989763840285711539332572356417301997_<141>]

Factor=28341234128475964035151410109192458499  Method=ECM  B1=11000000  Sigma=413036558

Nov 10, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 10, 2009

(64·10¹⁵⁴+17)/9 = 7(1)₁₅₃3_<155> = 7 · 29944451 · 99126724489936082314891547_<26> · C121

C121 = P36 · P85

P36 = 371458155915584869438887303244455043_<36>

P85 = 9213452798851581780246903010130941751346807705140375743997570945393621607222482291029_<85>

Number: 71113_154
N=3422412186276692664840006343775380636492433642471949424208317432860971893505957363340221351729755835795279923807232709247
  ( 121 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=371458155915584869438887303244455043
 r2=9213452798851581780246903010130941751346807705140375743997570945393621607222482291029
Version: 
Total time: 9.13 hours.
Scaled time: 21.70 units (timescale=2.377).
Factorization parameters were as follows:
n: 3422412186276692664840006343775380636492433642471949424208317432860971893505957363340221351729755835795279923807232709247
m: 20000000000000000000000000000000
deg: 5
c5: 1
c0: 85
skew: 2.43
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8251407
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 418737 x 418985
Total sieving time: 8.36 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 0.39 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 9.13 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(26·10¹⁵⁴-11)/3 = 8(6)₁₅₃3_<155> = 71 · 9070459 · 259328111441557_<15> · C132

C132 = P53 · P79

P53 = 99846047824272537592965345005720564798732938551338279_<53>

P79 = 5197374408355423148064024399326141532315371063525619734573070180253227577341089_<79>

Number: 86663_154
N=518937293737305764742350084321901012525716106131552754160789873608663212996406969680024139053939523745253009213500521776057405245831
  ( 132 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=99846047824272537592965345005720564798732938551338279
 r2=5197374408355423148064024399326141532315371063525619734573070180253227577341089
Version: 
Total time: 10.11 hours.
Scaled time: 24.03 units (timescale=2.376).
Factorization parameters were as follows:
n: 518937293737305764742350084321901012525716106131552754160789873608663212996406969680024139053939523745253009213500521776057405245831
m: 10000000000000000000000000000000
deg: 5
c5: 13
c0: -55
skew: 1.33
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7809905
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 491291 x 491539
Total sieving time: 9.02 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.50 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 10.11 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(61·10¹⁵⁵-43)/9 = 6(7)₁₅₄3_<156> = 19207 · 8129724299_<10> · C142

C142 = P50 · P93

P50 = 10773558329235854559383288960393828305859609444921_<50>

P93 = 402895859408850435228560980284998721882290483647477062554586284734865868390478708391490598441_<93>

Number: 67773_155
N=4340622041948858448170164123031439379962172720964831379039893892595501831032998542728524811238685147412778859492166572369332930590658117968161
  ( 142 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=10773558329235854559383288960393828305859609444921
 r2=402895859408850435228560980284998721882290483647477062554586284734865868390478708391490598441
Version: 
Total time: 12.33 hours.
Scaled time: 29.14 units (timescale=2.363).
Factorization parameters were as follows:
n: 4340622041948858448170164123031439379962172720964831379039893892595501831032998542728524811238685147412778859492166572369332930590658117968161
m: 10000000000000000000000000000000
deg: 5
c5: 61
c0: -43
skew: 0.93
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8018085
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 546740 x 546988
Total sieving time: 11.04 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 0.66 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 12.33 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁵⁴+41)/9 = 7(4)₁₅₃9_<155> = 11800182871_<11> · 524297866455971_<15> · C131

C131 = P59 · P72

P59 = 13258140745590103120897332331500375538360937115782994093187_<59>

P72 = 907575659674699981238661788307594336802623003262472252087994176094758447_<72>

Number: 74449_154
N=12032765833238956496135533051537246750802755299151411853583075126019010073293713788119609205211450801525502233723112988192573400589
  ( 131 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=13258140745590103120897332331500375538360937115782994093187
 r2=907575659674699981238661788307594336802623003262472252087994176094758447
Version: 
Total time: 14.37 hours.
Scaled time: 34.37 units (timescale=2.392).
Factorization parameters were as follows:
n: 12032765833238956496135533051537246750802755299151411853583075126019010073293713788119609205211450801525502233723112988192573400589
m: 10000000000000000000000000000000
deg: 5
c5: 67
c0: 410
skew: 1.44
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8669259
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 493382 x 493630
Total sieving time: 13.16 hours.
Total relation processing time: 0.56 hours.
Matrix solve time: 0.53 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 14.37 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 10, 2009 (4th)

By Erik Branger / GGNFS, Msieve / Nov 10, 2009

(22·10¹⁶¹-7)/3 = 7(3)₁₆₀1_<162> = 8988583 · 1473843083_<10> · 43685008931_<11> · 792899578558552316971997_<24> · C112

C112 = P47 · P65

P47 = 97195054545007868780229153979999042837726017679_<47>

P65 = 16442360346075195163255521245258464415073491367475255299473133943_<65>

Number: 73331_161
N=1598116110685453051884152389093381063570392044919000755814313712121566721546816342185364254479151650919152978297
  ( 112 digits)
Divisors found:
 r1=97195054545007868780229153979999042837726017679 (pp47)
 r2=16442360346075195163255521245258464415073491367475255299473133943 (pp65)
Version: Msieve v. 1.43
Total time: 22.37 hours.
Scaled time: 21.93 units (timescale=0.980).
Factorization parameters were as follows:
name: 73331_161
n: 1598116110685453051884152389093381063570392044919000755814313712121566721546816342185364254479151650919152978297
skew: 18801.73
# norm 1.08e+016
c5: 41040
c4: -11257294188
c3: -442650124089326
c2: 2964052129907482063
c1: -8608213059353517719384
c0: 16835718387366714053310855
# alpha -6.76
Y1: 655947863939
Y0: -2080116740162367855658
# Murphy_E 8.38e-010
# M 1271251820443806534114929805329990668883291174007574987231604085600016271988485379380744146412786916036972965427
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2550001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 439313 x 439538
Polynomial selection time: 1.84 hours.
Total sieving time: 19.64 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.46 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 22.37 hours.
 --------- CPU info (if available) ----------

Nov 10, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 10, 2009

(83·10¹⁸⁹+7)/9 = 9(2)₁₈₈3_<190> = 19 · C189

C189 = P34 · C155

P34 = 5990378735789383269628097762672663_<34>

C155 = [81026615906465431938041626994478818515681338940598425649469860858583139654675179162239812855902595745749467893554470062276252107338980178289378117466811059_<155>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3355232220
Step 1 took 69614ms
********** Factor found in step 1: 5990378735789383269628097762672663
Found probable prime factor of 34 digits: 5990378735789383269628097762672663
Composite cofactor 81026615906465431938041626994478818515681338940598425649469860858583139654675179162239812855902595745749467893554470062276252107338980178289378117466811059 has 155 digits

(22·10¹⁹²+17)/3 = 7(3)₁₉₁9_<193> = 13 · 19 · 47 · C189

C189 = P34 · C156

P34 = 1065586090211622938492027332760513_<34>

C156 = [592813482260539816573285099951893028539801844453071033975475976700379685000061841730286610971791510396786665189169314447668289344543691705287196946935621267_<156>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=485063552
Step 1 took 69609ms
Step 2 took 21858ms
********** Factor found in step 2: 1065586090211622938492027332760513
Found probable prime factor of 34 digits: 1065586090211622938492027332760513
Composite cofactor 592813482260539816573285099951893028539801844453071033975475976700379685000061841730286610971791510396786665189169314447668289344543691705287196946935621267 has 156 digits

Nov 10, 2009 (2nd)

By Serge Batalov / GMP-ECM / Nov 10, 2009

(62·10¹⁹⁸-71)/9 = 6(8)₁₉₇1_<199> = 18090491 · 96259713961_<11> · 292004497230977_<15> · C167

C167 = P29 · C138

P29 = 20703814083710017434203941181_<29>

C138 = [654356407770923648465491093265011628500438838155395019040655717408451346641013314886383730589549523068829008515207175565727024831982591463_<138>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=4244008742
Step 1 took 7041ms
Step 2 took 3980ms
********** Factor found in step 2: 20703814083710017434203941181
Found probable prime factor of 29 digits: 20703814083710017434203941181
Composite cofactor has 138 digits

Nov 10, 2009

Factorizations of 688...881 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Nov 9, 2009 (5th)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 9, 2009

(59·10¹⁶⁸+31)/9 = 6(5)₁₆₇9_<169> = 200353029081433643431_<21> · C149

C149 = P36 · P114

P36 = 163345949950143193676363320218134933_<36>

P114 = 200311193457135555149111399446648559579409439169411343631410357357163826821990473660434904444886971998129104305533_<114>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2903774802
Step 1 took 47356ms
Step 2 took 16435ms
********** Factor found in step 2: 163345949950143193676363320218134933
Found probable prime factor of 36 digits: 163345949950143193676363320218134933
Probable prime cofactor 200311193457135555149111399446648559579409439169411343631410357357163826821990473660434904444886971998129104305533 has 114 digits

Nov 9, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Nov 9, 2009

(64·10¹⁵³+71)/9 = 7(1)₁₅₂9_<154> = 3 · 7² · 107 · 5851141 · 28626107 · 28548860107_<11> · C125

C125 = P61 · P65

P61 = 5614634034614379921533744369479856200331498912590870991988599_<61>

P65 = 16839270432055405826800110526516344410089090140539090333981785021_<65>

Number: 71119_153
N=94546340885893875775565511755890916652169251907705803092120211847812361089925446153997345174676984566004539608391284500975579
  ( 125 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=5614634034614379921533744369479856200331498912590870991988599
 r2=16839270432055405826800110526516344410089090140539090333981785021
Version: 
Total time: 12.25 hours.
Scaled time: 29.09 units (timescale=2.374).
Factorization parameters were as follows:
n: 94546340885893875775565511755890916652169251907705803092120211847812361089925446153997345174676984566004539608391284500975579
m: 20000000000000000000000000000000
deg: 5
c5: 1
c0: 3550
skew: 5.13
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8225922
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 512102 x 512350
Total sieving time: 11.13 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 0.59 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 12.25 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(59·10¹⁵²+13)/9 = 6(5)₁₅₁7_<153> = 3 · 1489 · 22639 · 11683159 · 1328096507_<10> · 5450109209_<10> · C119

C119 = P56 · P64

P56 = 59178572867084914379468698280517827432559633138291908257_<56>

P64 = 1295318881695982523785877985646207549117537913160065454433420981_<64>

Number: 65557_152
N=76655122826556645524074443634510586228441763475339929480344042662902252605878456624030665388478094256481641219110940117
  ( 119 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=59178572867084914379468698280517827432559633138291908257
 r2=1295318881695982523785877985646207549117537913160065454433420981
Version: 
Total time: 13.11 hours.
Scaled time: 30.41 units (timescale=2.319).
Factorization parameters were as follows:
n: 76655122826556645524074443634510586228441763475339929480344042662902252605878456624030665388478094256481641219110940117
m: 1000000000000000000000000000000
deg: 5
c5: 5900
c0: 13
skew: 0.29
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8453288
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 459884 x 460132
Total sieving time: 11.78 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 0.46 hours.
Time per square root: 0.38 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 13.11 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(22·10¹⁶⁷-7)/3 = 7(3)₁₆₆1_<168> = 673 · 554010851 · 558911987 · 5945695037_<10> · 109820016330048359322910570503010931_<36> · C103

C103 = P52 · P52

P52 = 1401391479136958593688939741110720276274288575652677_<52>

P52 = 3845750104092990927871071735575755688207468194738649_<52>

Number: 73331_167
N=5389401426765989035878493200566942374516146102706060431089988040720698547959542215951996250572612213373
  ( 103 digits)
Divisors found:
 r1=1401391479136958593688939741110720276274288575652677
 r2=3845750104092990927871071735575755688207468194738649
Version: 
Total time: 3.55 hours.
Scaled time: 8.49 units (timescale=2.390).
Factorization parameters were as follows:
name: 73331_167
n: 5389401426765989035878493200566942374516146102706060431089988040720698547959542215951996250572612213373
skew: 4097.75
# norm 1.64e+14
c5: 40320
c4: -1958361504
c3: -17221716378444
c2: 27188414562676651
c1: 33121214055673416898
c0: -33012256189229942644761
# alpha -5.50
Y1: 45693702307
Y0: -42189907306613412250
# Murphy_E 2.46e-09
# M 1997110600840141969487185735223388600956316936391544059751688593970011381357450945414187330994898656216
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4676874
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 262876 x 263124
Polynomial selection time: 0.25 hours.
Total sieving time: 2.82 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 3.55 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(65·10¹⁵³-11)/9 = 7(2)₁₅₂1_<154> = 3 · 19 · 3191 · 30851 · 1993529 · C138

C138 = P46 · P92

P46 = 8594630348195199186618987496491138043989264641_<46>

P92 = 75119066309768402960586373080898748135184106551828886169635340771025166138551902760422135897_<92>

Number: 72221_153
N=645620607034023065579793268856604425328117343665574488428740228244719430439959533731717952309961769144984088201555673934488542847598917977
  ( 138 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=8594630348195199186618987496491138043989264641
 r2=75119066309768402960586373080898748135184106551828886169635340771025166138551902760422135897
Version: 
Total time: 9.93 hours.
Scaled time: 23.68 units (timescale=2.385).
Factorization parameters were as follows:
n: 645620607034023065579793268856604425328117343665574488428740228244719430439959533731717952309961769144984088201555673934488542847598917977
m: 10000000000000000000000000000000
deg: 5
c5: 13
c0: -220
skew: 1.76
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8428433
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 394554 x 394802
Total sieving time: 9.12 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 9.93 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁵³-13)/9 = 7(4)₁₅₂3_<154> = 3 · 73 · 599 · 6375191 · C142

C142 = P69 · P74

P69 = 630815937238830387707045431729321900960152842180793375602167922900551_<69>

P74 = 14111250397994772249206335757054905306524045262423288625705324246219742983_<74>

Number: 74443_153
N=8901601645422890581068982807068783308967792576347016429003625587988536935014749786660720721784929209055910888848171892379052067704627089083633
  ( 142 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=630815937238830387707045431729321900960152842180793375602167922900551
 r2=14111250397994772249206335757054905306524045262423288625705324246219742983
Version: 
Total time: 12.11 hours.
Scaled time: 28.63 units (timescale=2.364).
Factorization parameters were as follows:
n: 8901601645422890581068982807068783308967792576347016429003625587988536935014749786660720721784929209055910888848171892379052067704627089083633
m: 10000000000000000000000000000000
deg: 5
c5: 67
c0: -1300
skew: 1.81
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8501534
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 447986 x 448234
Total sieving time: 11.02 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 12.11 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(22·10¹⁵⁴-7)/3 = 7(3)₁₅₃1_<155> = 29 · 9311791740963623557_<19> · C135

C135 = P38 · P97

P38 = 65155738369339103941331630969006793233_<38>

P97 = 4167902040813106094398057851557338570627756214904008442532444406520855216370513619157114999436019_<97>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 271562734920253252721963146431377932001653050860753475858443777890484893804596955592971171231575888296804819144102887980271374745659427 (135 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2666678006
Step 1 took 3359ms
Step 2 took 2155ms
********** Factor found in step 2: 65155738369339103941331630969006793233
Found probable prime factor of 38 digits: 65155738369339103941331630969006793233
Probable prime cofactor 4167902040813106094398057851557338570627756214904008442532444406520855216370513619157114999436019 has 97 digits

Nov 9, 2009 (3rd)

By Erik Branger / GGNFS, Msieve / Nov 9, 2009

(59·10¹⁵⁵+13)/9 = 6(5)₁₅₄7_<156> = 3² · 7² · 31² · C151

C151 = P37 · P114

P37 = 3250014503184800505033627409506459859_<37>

P114 = 475950980723268548624810965719672919720034989274501070593621650713069860521169953430677781461307623085322624985823_<114>

Number: 65557_155
N=1546847590155652194203306635792637477390462871856261678371583728107190770091518320050107374818736991077311180378421843165909366791384530842436793578957
  ( 151 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=3250014503184800505033627409506459859 (pp37)
 r2=475950980723268548624810965719672919720034989274501070593621650713069860521169953430677781461307623085322624985823 (pp114)
Version: Msieve v. 1.43
Total time: 19.02 hours.
Scaled time: 19.44 units (timescale=1.022).
Factorization parameters were as follows:
n: 1546847590155652194203306635792637477390462871856261678371583728107190770091518320050107374818736991077311180378421843165909366791384530842436793578957
m: 10000000000000000000000000000000
deg: 5
c5: 59
c0: 13
skew: 0.74
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1450000, 2250001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 456331 x 456559
Total sieving time: 18.33 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000
total time: 19.02 hours.
 --------- CPU info (if available) ----------

Nov 9, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve / Nov 9, 2009

(26·10¹⁸⁸-11)/3 = 8(6)₁₈₇3_<189> = C189

C189 = P62 · P128

P62 = 10259291107232450345127225587209152871731029421866962805442781_<62>

P128 = 84476272055063943325183359642649984717306070885700898533399372021753856257495399877737223250194400158255639618255431995131856723_<128>

N=866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
  ( 189 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=10259291107232450345127225587209152871731029421866962805442781 (pp62)
 r2=84476272055063943325183359642649984717306070885700898533399372021753856257495399877737223250194400158255639618255431995131856723 (pp128)
Version: Msieve-1.40
Total time: 356.05 hours.
Scaled time: 660.47 units (timescale=1.855).
Factorization parameters were as follows:
n: 866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
m: 50000000000000000000000000000000000000
deg: 5
c5: 208
c0: -275
skew: 1.06
type: snfs
lss: 1
rlim: 10600000
alim: 10600000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10600000/10600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5300000, 10600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1915479 x 1915705
Total sieving time: 349.52 hours.
Total relation processing time: 1.02 hours.
Matrix solve time: 4.72 hours.
Time per square root: 0.79 hours.
Prototype def-par.txt line would be:
snfs,190.000,5,0,0,0,0,0,0,0,0,10600000,10600000,28,28,54,54,2.5,2.5,100000
total time: 356.05 hours.
 --------- CPU info (if available) ----------

Nov 9, 2009

By Robert Backstrom / GGNFS, Msieve / Nov 9, 2009

(59·10¹⁷³+31)/9 = 6(5)₁₇₂9_<174> = 17 · C173

C173 = P64 · P109

P64 = 4177250313399903945138253417266710121030087934303335833373800887_<64>

P109 = 9231453374859386654199536787033338094395429597865246821904001952487028953910042143288170856206510706346989121_<109>

Number: n
N=38562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150327
  ( 173 digits)
SNFS difficulty: 176 digits.
Divisors found:

Mon Nov 09 17:57:11 2009  prp64 factor: 4177250313399903945138253417266710121030087934303335833373800887
Mon Nov 09 17:57:11 2009  prp109 factor: 9231453374859386654199536787033338094395429597865246821904001952487028953910042143288170856206510706346989121
Mon Nov 09 17:57:11 2009  elapsed time 03:30:32 (Msieve 1.43 - dependency 3)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 116.60 hours.
Scaled time: 212.56 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_5_172_9
n: 38562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150327
m: 50000000000000000000000000000000000
deg: 5
c5: 472
c0: 775
skew: 1.10
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [3000000, 8200000)
Primes: RFBsize:412849, AFBsize:412487, largePrimes:21228147 encountered
Relations: rels:21095842, finalFF:563665
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 3202566 hash collisions in 24388453 relations
Msieve: matrix is 1106425 x 1106655 (295.8 MB)

Total sieving time: 115.54 hours.
Total relation processing time: 1.06 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,56,56,2.5,2.5,100000
total time: 116.60 hours.
 --------- CPU info (if available) ----------

Nov 8, 2009 (5th)

By Erik Branger / GGNFS, Msieve / Nov 8, 2009

(67·10¹⁵³-31)/9 = 7(4)₁₅₂1_<154> = 7 · 29 · 107 · 1873 · 9283 · 3851031073116400940153_<22> · C121

C121 = P37 · P84

P37 = 6384161033655476762880992360445318917_<37>

P84 = 801762046385247037048308402141985803146797607769907046767693665075239890836475568119_<84>

Number: 74441_153
N=5118578014796569030767959609696286789242595413285599606741445460908841782819618432069526246322988087219996094931712807123
  ( 121 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=6384161033655476762880992360445318917 (pp37)
 r2=801762046385247037048308402141985803146797607769907046767693665075239890836475568119 (pp84)
Version: Msieve-1.40
Total time: 26.48 hours.
Scaled time: 26.27 units (timescale=0.992).
Factorization parameters were as follows:
n: 5118578014796569030767959609696286789242595413285599606741445460908841782819618432069526246322988087219996094931712807123
m: 5000000000000000000000000000000
deg: 5
c5: 536
c0: -775
skew: 1.08
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 517516 x 517745
Total sieving time: 25.51 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.63 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 26.48 hours.
 --------- CPU info (if available) ----------

Nov 8, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 8, 2009

(22·10¹⁶⁷-7)/3 = 7(3)₁₆₆1_<168> = 673 · 554010851 · 558911987 · 5945695037_<10> · C138

C138 = P36 · C103

P36 = 109820016330048359322910570503010931_<36>

C103 = [5389401426765989035878493200566942374516146102706060431089988040720698547959542215951996250572612213373_<103>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4116852324
Step 1 took 42504ms
Step 2 took 14782ms
********** Factor found in step 2: 109820016330048359322910570503010931
Found probable prime factor of 36 digits: 109820016330048359322910570503010931
Composite cofactor 5389401426765989035878493200566942374516146102706060431089988040720698547959542215951996250572612213373 has 103 digits

Nov 8, 2009 (3rd)

By shyguy7129 / GGNFS and Msieve v1.40 / Nov 8, 2009

(65·10¹⁷⁰+61)/9 = 7(2)₁₆₉9_<171> = 3 · 79 · 2293 · 140130990851_<12> · 3757774694852316444096913_<25> · 10144116873340791964390133_<26> · C105

C105 = P38 · P68

P38 = 21971222154598869664832900623562106017_<38>

P68 = 11323613996205652033225521245915447835096235974204481742262021487883_<68>

Yes! My first submitted factors! :D

Number: 72229_170
N=248793638703559462811024537742910133006111369698373954144678461344908746356065631383501263120031326892011
  ( 105 digits)
Divisors found:
 r1=21971222154598869664832900623562106017 (pp38)
 r2=11323613996205652033225521245915447835096235974204481742262021487883 (pp68)
Version: Msieve-1.40
Total time: 21.65 hours.
Scaled time: 38.56 units (timescale=1.781).
Factorization parameters were as follows:
name: 72229_170
n: 248793638703559462811024537742910133006111369698373954144678461344908746356065631383501263120031326892011
skew: 60992.32
# norm 3.41e+014
c5: 960
c4: 182155542
c3: -5698389781438
c2: -468425103552598334
c1: 10463967835739232401989
c0: -997954568530928284717567
# alpha -5.04
Y1: 30184793243
Y0: -191739245141787164928
# Murphy_E 1.68e-009
# M 14245238078513029591920117460774843530496924943504703352168798349066508904664795693381848673546224366040
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 2
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 282011 x 282259
Total sieving time: 21.07 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.41 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 21.65 hours.
 --------- CPU info (if available) ----------

Nov 8, 2009 (2nd)

By Sinkiti Sibata / Msieve / Nov 8, 2009

(67·10¹⁸¹+41)/9 = 7(4)₁₈₀9_<182> = 53 · 911 · 42131 · 4676297 · 8281979 · 141991566527749086929197_<24> · 165108482396811425155660189_<27> · C110

C110 = P48 · P63

P48 = 121710843248256603777008924948983385611121242357_<48>

P63 = 331160752353019654210539187583083132861767802689536904567422471_<63>

Number: 74449_181
N=40305854419613099392933000322931607765920560992330095901788930477410295183773700750837580338887703146798804147
  ( 110 digits)
Divisors found:
 r1=121710843248256603777008924948983385611121242357 (pp48)
 r2=331160752353019654210539187583083132861767802689536904567422471 (pp63)
Version: Msieve-1.40
Total time: 21.25 hours.
Scaled time: 44.16 units (timescale=2.078).
Factorization parameters were as follows:
name: 74449_181
n: 40305854419613099392933000322931607765920560992330095901788930477410295183773700750837580338887703146798804147
skew: 33186.82
# norm 1.64e+15
c5: 30600
c4: 1047455254
c3: -78351538124717
c2: 129431081918751312
c1: 48327712299484053859320
c0: -514868110317796072713683808
# alpha -6.04
Y1: 654077347
Y0: -1056645576467103752827
# Murphy_E 9.67e-10
# M 15796330503120420793036355885019577620524107447618867199386924482341371764583299519964820756277157127611672118
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 394960 x 395208
Polynomial selection time: 1.51 hours.
Total sieving time: 18.66 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.54 hours.
Time per square root: 0.41 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 21.25 hours.
 --------- CPU info (if available) ----------

Nov 8, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Nov 8, 2009

(65·10¹⁵¹-11)/9 = 7(2)₁₅₀1_<152> = 2632819547_<10> · 359828389017095641457_<21> · C122

C122 = P46 · P77

P46 = 4707966628617424628297466037653799757180336867_<46>

P77 = 16192762768567533085113383462849628534669727951104188819800098462441995657197_<77>

Number: 72221_151
N=76234986739534643662491549126650708645656218262843499744778693818048201701410833734282766803893429828567760567175512981799
  ( 122 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=4707966628617424628297466037653799757180336867
 r2=16192762768567533085113383462849628534669727951104188819800098462441995657197
Version: 
Total time: 7.84 hours.
Scaled time: 18.42 units (timescale=2.350).
Factorization parameters were as follows:
n: 76234986739534643662491549126650708645656218262843499744778693818048201701410833734282766803893429828567760567175512981799
m: 1000000000000000000000000000000
deg: 5
c5: 650
c0: -11
skew: 0.44
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1100000, 1800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7347944
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 453651 x 453899
Total sieving time: 7.07 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000
total time: 7.84 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁵¹-31)/9 = 7(4)₁₅₀1_<152> = 1193 · 6254113478800077538215938702699113_<34> · C115

C115 = P55 · P61

P55 = 8228829892112628636884835633777315487804386047416617137_<55>

P61 = 1212517479021868655624024510948004899355487100786836051889177_<61>

Number: 74441_151
N=9977600076084199905958097161900099571496695646133438177125099495316432470281666399300303712370663052339771363026249
  ( 115 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=8228829892112628636884835633777315487804386047416617137
 r2=1212517479021868655624024510948004899355487100786836051889177
Version: 
Total time: 9.71 hours.
Scaled time: 23.17 units (timescale=2.387).
Factorization parameters were as follows:
n: 9977600076084199905958097161900099571496695646133438177125099495316432470281666399300303712370663052339771363026249
m: 1000000000000000000000000000000
deg: 5
c5: 670
c0: -31
skew: 0.54
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1100000, 2000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7894010
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 428637 x 428885
Total sieving time: 8.86 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000
total time: 9.71 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(59·10¹⁵⁵+31)/9 = 6(5)₁₅₄9_<156> = 23 · 31674983 · C147

C147 = P35 · P113

P35 = 82384832793625986764249254072567903_<35>

P113 = 10922398337410720857723866317273548007359511055401276844847935368467831986721558208027076999570364927664168943417_<113>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 899839960732960711222255438670508322602943884295822813523593072688578946213134106435594072781082341661234885691494267087353195443745889379497344551 (147 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3405593309
Step 1 took 4664ms
Step 2 took 4649ms
********** Factor found in step 2: 82384832793625986764249254072567903
Found probable prime factor of 35 digits: 82384832793625986764249254072567903
Probable prime cofactor 10922398337410720857723866317273548007359511055401276844847935368467831986721558208027076999570364927664168943417 has 113 digits

(65·10¹⁵²+7)/9 = 7(2)₁₅₁3_<153> = 3 · 241 · 27347519063_<11> · 1725333177913_<13> · C128

C128 = P38 · P91

P38 = 10514619222825497091683354104111810879_<38>

P91 = 2013483581578352610412684711209758302904144260026256812619717594875763736046702067763469301_<91>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 21171013171707276297284205554612886487286809273598944016623603709651069407896630669000876694960644238838461982364112370634325579 (128 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6792566349
Step 1 took 4196ms
Step 2 took 5756ms
********** Factor found in step 2: 10514619222825497091683354104111810879
Found probable prime factor of 38 digits: 10514619222825497091683354104111810879
Probable prime cofactor 2013483581578352610412684711209758302904144260026256812619717594875763736046702067763469301 has 91 digits

Nov 7, 2009 (6th)

By Dmitry Domanov / GGNFS/msieve / Nov 7, 2009

(65·10¹⁵⁵+7)/9 = 7(2)₁₅₄3_<156> = 3 · 9007 · 1081789 · 8911250809018619_<16> · 142782376236086436331_<21> · C110

C110 = P52 · P58

P52 = 7392507812931635296203627398671630725771305605141003_<52>

P58 = 2626768526217301127090637292882797495139799918052500317901_<58>

N=19418406852824315665554762157458974239206989197334760372678432542908053342430535858752210495531479837429994703
  ( 110 digits)
Divisors found:
 r1=7392507812931635296203627398671630725771305605141003 (pp52)
 r2=2626768526217301127090637292882797495139799918052500317901 (pp58)
Version: Msieve-1.40
Total time: 15.75 hours.
Scaled time: 31.01 units (timescale=1.969).
Factorization parameters were as follows:
name: g110
n: 19418406852824315665554762157458974239206989197334760372678432542908053342430535858752210495531479837429994703
skew: 29767.14
# norm 3.00e+015
c5: 16560
c4: 3825657986
c3: 19567041570883
c2: -2418931829640980736
c1: 30620557498708644779402
c0: -74115411399096749338291340
# alpha -6.43
Y1: 203416736417
Y0: -1032349374499642407141
# Murphy_E 1.04e-009
# M 4165853837495179387505368821618801681724638475605636957434987794044042429718757847059943296685210951731399213
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 391563 x 391788
Polynomial selection time: 1.42 hours.
Total sieving time: 13.33 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 15.75 hours.
 --------- CPU info (if available) ----------

Nov 7, 2009 (5th)

By Sinkiti Sibata / Msieve / Nov 7, 2009

(62·10¹⁵⁰-17)/9 = 6(8)₁₄₉7_<151> = 19 · 96457 · 54014052471186550121_<20> · C125

C125 = P61 · P64

P61 = 7152115416516333263116824921083071837423457619295848531485227_<61>

P64 = 9730172787565460411900025374086137070224048862984493336589028567_<64>

Number: 68887_150
N=69591318799314634387182087997398280009882822525775350033620638088104875270633081216732421635499310384553331373497069641479709
  ( 125 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=7152115416516333263116824921083071837423457619295848531485227 (pp61)
 r2=9730172787565460411900025374086137070224048862984493336589028567 (pp64)
Version: Msieve-1.40
Total time: 17.64 hours.
Scaled time: 36.65 units (timescale=2.078).
Factorization parameters were as follows:
name: 68887_150
n: 69591318799314634387182087997398280009882822525775350033620638088104875270633081216732421635499310384553331373497069641479709
m: 1000000000000000000000000000000
deg: 5
c5: 62
c0: -17
skew: 0.77
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 407535 x 407783
Total sieving time: 16.87 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.57 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 17.64 hours.
 --------- CPU info (if available) ----------

(83·10¹⁹⁰+7)/9 = 9(2)₁₈₉3_<191> = 3 · C191

C191 = P86 · P105

P86 = 31409756452905266401572874729021762403039657905422482493898473135389505774302363727127_<86>

P105 = 978700385239610967893947803706059231473265933390451927236545688516093764875631745635126600791366581119683_<105>

Number: 92223_190
N=30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741
  ( 191 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=31409756452905266401572874729021762403039657905422482493898473135389505774302363727127 (pp86)
 r2=978700385239610967893947803706059231473265933390451927236545688516093764875631745635126600791366581119683 (pp105)
Version: Msieve v. 1.42
Total time: 12.72 hours.
Scaled time: 13.02 units (timescale=1.024).
Factorization parameters were as follows:
name: 92223_190
n: 30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741
m: 100000000000000000000000000000000000000
deg: 5
c5: 83
c0: 7
skew: 0.61
type: snfs
lss: 1
rlim: 11100000
alim: 11100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 11100000/11100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5550000, 10550001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2084496 x 2084721
Total sieving time: 0.00 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 11.53 hours.
Time per square root: 0.98 hours.
Prototype def-par.txt line would be:
snfs,191.000,5,0,0,0,0,0,0,0,0,11100000,11100000,28,28,54,54,2.5,2.5,100000
total time: 12.72 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3057976k/3145344k available (3786k kernel code, 496k absent, 86872k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.88 BogoMIPS (lpj=2393941)
Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393880)
Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393886)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891)
Total of 4 processors activated (19151.19 BogoMIPS).

total time: 9 days 1 hour.

Nov 7, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 7, 2009

(67·10¹⁴⁹+41)/9 = 7(4)₁₄₈9_<150> = 29 · 967 · 10301 · 164117 · 63136961 · 75921228000284137_<17> · C112

C112 = P54 · P58

P54 = 658356174664422161569086775878853672793637262114046597_<54>

P58 = 4975847405368765597872979135265543799568390928601303262351_<58>

Number: 74449_149
N=3275879863512470866831524279102943957767823250262292240603618506109442210271627224143756567808563929798129769547
  ( 112 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=658356174664422161569086775878853672793637262114046597
 r2=4975847405368765597872979135265543799568390928601303262351
Version: 
Total time: 9.16 hours.
Scaled time: 21.88 units (timescale=2.390).
Factorization parameters were as follows:
n: 3275879863512470866831524279102943957767823250262292240603618506109442210271627224143756567808563929798129769547
m: 1000000000000000000000000000000
deg: 5
c5: 67
c0: 410
skew: 1.44
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7095270
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 381891 x 382139
Total sieving time: 8.45 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.31 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000
total time: 9.16 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(26·10¹⁵⁵-11)/3 = 8(6)₁₅₄3_<156> = 7 · 1279 · 83773 · 865854809489_<12> · 1961948617039_<13> · 67938871020299_<14> · C110

C110 = P53 · P57

P53 = 50356743151076883375850389237566626845654858552124607_<53>

P57 = 198824902404933934450436748117874509387381569435016167809_<57>

Number: 86663_155
N=10012174542443186661944529159441458449529896878553572027502711511349648695308726206045539833575579812190176063
  ( 110 digits)
Divisors found:
 r1=50356743151076883375850389237566626845654858552124607
 r2=198824902404933934450436748117874509387381569435016167809
Version: 
Total time: 9.20 hours.
Scaled time: 21.96 units (timescale=2.387).
Factorization parameters were as follows:
name: 86663_155
n: 10012174542443186661944529159441458449529896878553572027502711511349648695308726206045539833575579812190176063
skew: 19361.44
# norm 7.28e+14
c5: 36960
c4: -373375372
c3: 24010419126067
c2: 188419687096119335
c1: -10703912390072075189035
c0: -9921381275227903704194995
# alpha -5.79
Y1: 308100795223
Y0: -770122196696138062932
# Murphy_E 1.05e-09
# M 6923705748279385336736257457255098262017080868569703732932894391890534226799406036569569582345272734642801167
type: gnfs
rlim: 2100000
alim: 2100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1050000, 1700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7841955
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 402815 x 403063
Polynomial selection time: 0.80 hours.
Total sieving time: 7.42 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000
total time: 9.20 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(26·10¹⁵⁶-11)/3 = 8(6)₁₅₅3_<157> = 19 · 439 · 4201 · 22108555559_<11> · 18897188991137_<14> · 19562245823564779_<17> · C110

C110 = P54 · P56

P54 = 694703188931333880775047897831384327876136440996742187_<54>

P56 = 43561789316255219047093334112623127241673869427391777277_<56>

Number: 86663_156
N=30262513953557411191067054802305039488066876688632568417434093173819283820734068340557697961554591668893884799
  ( 110 digits)
Divisors found:
 r1=694703188931333880775047897831384327876136440996742187
 r2=43561789316255219047093334112623127241673869427391777277
Version: 
Total time: 8.76 hours.
Scaled time: 20.90 units (timescale=2.387).
Factorization parameters were as follows:
name: 86663_156
n: 30262513953557411191067054802305039488066876688632568417434093173819283820734068340557697961554591668893884799
skew: 46936.13
# norm 2.00e+15
c5: 4800
c4: -1514434876
c3: -32339594241746
c2: 4238527376382421943
c1: -26343690099191295496866
c0: -124555876330930538048212671
# alpha -6.41
Y1: 329728317391
Y0: -1445236780624805468530
# Murphy_E 1.08e-09
# M 26147608521632649352970030633720039196717174907616904289542536532064184713838448536232324936389216869986608630
type: gnfs
rlim: 2100000
alim: 2100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1050000, 1650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7866072
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 385170 x 385418
Polynomial selection time: 0.66 hours.
Total sieving time: 7.20 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000
total time: 8.76 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(64·10¹⁵¹+17)/9 = 7(1)₁₅₀3_<152> = 29 · 283 · 134839 · 172147 · 757057201 · C129

C129 = P56 · P74

P56 = 13630504369805610897121892199912194495690789284130587631_<56>

P74 = 36174074472493502044830834515488572039115437822520724375951219171660917333_<74>

Number: 71113_151
N=493070880170996278534516753255530271753988214548501769867880630567332323531819123807127232541599603419990823093435241101803308123
  ( 129 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=13630504369805610897121892199912194495690789284130587631
 r2=36174074472493502044830834515488572039115437822520724375951219171660917333
Version: 
Total time: 8.48 hours.
Scaled time: 20.14 units (timescale=2.374).
Factorization parameters were as follows:
n: 493070880170996278534516753255530271753988214548501769867880630567332323531819123807127232541599603419990823093435241101803308123
m: 2000000000000000000000000000000
deg: 5
c5: 20
c0: 17
skew: 0.97
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1000000, 1800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7995257
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 358493 x 358741
Total sieving time: 7.81 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.31 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,50,50,2.4,2.4,100000
total time: 8.48 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 7, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 7, 2009

(26·10¹⁶⁵-11)/3 = 8(6)₁₆₄3_<166> = 83 · 173 · 6255630651772921_<16> · 166231483601086409378491_<24> · C123

C123 = P41 · P83

P41 = 24162374121281115547743488148094071736559_<41>

P83 = 24021709649431187683343098336454103859214433857791311652928195887896967260267801493_<83>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=522846101
Step 1 took 34052ms
Step 2 took 13550ms
********** Factor found in step 2: 24162374121281115547743488148094071736559
Found probable prime factor of 41 digits: 24162374121281115547743488148094071736559
Probable prime cofactor 24021709649431187683343098336454103859214433857791311652928195887896967260267801493 has 83 digits

Nov 7, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Nov 6, 2009

(67·10¹⁸⁴-31)/9 = 7(4)₁₈₃1_<185> = 317 · 809 · 3547 · 33564732315787_<14> · 114897340823411617_<18> · 60403131124295658838209997353451_<32> · C114

C114 = P48 · P67

P48 = 339804285505812771909306394351621065329986786223_<48>

P67 = 1033907895700441246559141545237427637530368994032326666507566286553_<67>

Number: 74441_184
N=351326333777306830594696036569012983844843250127802988338902578492097989153379793913822350569995529157766770559319
  ( 114 digits)
Divisors found:
 r1=339804285505812771909306394351621065329986786223 (pp48)
 r2=1033907895700441246559141545237427637530368994032326666507566286553 (pp67)
Version: Msieve-1.40
Total time: 23.21 hours.
Scaled time: 22.44 units (timescale=0.967).
Factorization parameters were as follows:
n: 351326333777306830594696036569012983844843250127802988338902578492097989153379793913822350569995529157766770559319
c5: 10800
c4: 1941725750
c3: 81144728246589
c2: -2951244695963751041
c1: 4701141700422248571895
c0: 240834821565109408055254255
Y1: 1235140464791
Y0:-7988311196055664378158
skew: 35675.38
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 525895 x 526143
Total sieving time: 22.16 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 23.21 hours.
 --------- CPU info (if available) ----------

Nov 7, 2009

By Erik Branger / PFGW / Nov 7, 2009

7·10¹⁴⁴³⁶+3 = 7(0)₁₄₄₃₅3_<14437> is PRP.

7·10²⁸³³⁸+3 = 7(0)₂₈₃₃₇3_<28339> is PRP.

7·10³²⁷⁹⁶+3 = 7(0)₃₂₇₉₅3_<32797> is PRP.

7·10³⁸⁰⁷⁹+3 = 7(0)₃₈₀₇₈3_<38080> is PRP.

7·10⁵⁶⁷⁷⁹+3 = 7(0)₅₆₇₇₈3_<56780> is PRP.

7·10⁹¹²¹⁵+3 = 7(0)₉₁₂₁₄3_<91216> is PRP.

PRP91216 is the second largest unprovable quasi-repdigit PRP in our tables so far. Congratulations!

Nov 6, 2009 (8th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 6, 2009

(64·10¹⁷⁶+17)/9 = 7(1)₁₇₅3_<177> = 18122431 · 827630411 · 618217711189847_<15> · 51198705749027445793243239875789577253_<38> · C109

C109 = P53 · P56

P53 = 27199328739913350726751375837743051073898498013179701_<53>

P56 = 55071379802039998793236341692499167334341927807025765323_<56>

Number: 71113_176
N=1497904563396310154769792820729281585688689422098966010957032096218297475296578253879252017930370140253308423
  ( 109 digits)
Divisors found:
 r1=27199328739913350726751375837743051073898498013179701
 r2=55071379802039998793236341692499167334341927807025765323
Version: 
Total time: 7.39 hours.
Scaled time: 17.62 units (timescale=2.385).
Factorization parameters were as follows:
name: 71113_176
n: 1497904563396310154769792820729281585688689422098966010957032096218297475296578253879252017930370140253308423
skew: 37228.70
# norm 1.29e+15
c5: 6720
c4: 1929577034
c3: -28048451333417
c2: -2581066827369582849
c1: 23728062558893855083337
c0: 189889730972645309855811835
# alpha -6.65
Y1: 294450677543
Y0: -740650055075990989806
# Murphy_E 1.28e-09
# M 406037342834116125047075340806279652058520344301271931613697935723559786272925786257733844006528099117428762
type: gnfs
rlim: 2100000
alim: 2100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1050000, 2200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8123905
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 371166 x 371414
Polynomial selection time: 0.58 hours.
Total sieving time: 5.59 hours.
Total relation processing time: 0.85 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000
total time: 7.39 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁴⁷-31)/9 = 7(4)₁₄₆1_<148> = 7² · 173 · 1007857 · C138

C138 = P49 · P90

P49 = 3543243945117669927050599146096106098149924350703_<49>

P90 = 245917899090014024113532245535836223215750238360235398952104060053448988922276779413690323_<90>

Number: 74441_147
N=871347106946750342151715673907223653960159603609685187432378536350270402789209264962140023280103965088548237737624848609941132704889347069
  ( 138 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=3543243945117669927050599146096106098149924350703
 r2=245917899090014024113532245535836223215750238360235398952104060053448988922276779413690323
Version: 
Total time: 8.99 hours.
Scaled time: 21.45 units (timescale=2.385).
Factorization parameters were as follows:
n: 871347106946750342151715673907223653960159603609685187432378536350270402789209264962140023280103965088548237737624848609941132704889347069
m: 100000000000000000000000000000
deg: 5
c5: 6700
c0: -31
skew: 0.34
type: snfs
lss: 1
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1650000, 3375001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7066652
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 456862 x 457110
Total sieving time: 7.75 hours.
Total relation processing time: 0.74 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,49,49,2.3,2.3,75000
total time: 8.99 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁴⁷-13)/9 = 7(4)₁₄₆3_<148> = 3⁴ · 23 · 15032488729_<11> · 8212675315501962911_<19> · C116

C116 = P50 · P66

P50 = 35712120107599973268429717906238004919995676811669_<50>

P66 = 906333983462578850099373864796225485410057952884119428606963987551_<66>

Number: 74443_147
N=32367108075015143797053757675227277037681912296576239310580627885454876717201364888999929590596992736623682287532619
  ( 116 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=35712120107599973268429717906238004919995676811669
 r2=906333983462578850099373864796225485410057952884119428606963987551
Version: 
Total time: 8.34 hours.
Scaled time: 19.90 units (timescale=2.385).
Factorization parameters were as follows:
n: 32367108075015143797053757675227277037681912296576239310580627885454876717201364888999929590596992736623682287532619
m: 100000000000000000000000000000
deg: 5
c5: 6700
c0: -13
skew: 0.29
type: snfs
lss: 1
rlim: 3150000
alim: 3150000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 3150000/3150000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1575000, 3150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7259667
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 442603 x 442851
Total sieving time: 7.15 hours.
Total relation processing time: 0.71 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,3150000,3150000,27,27,49,49,2.4,2.4,75000
total time: 8.34 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁴⁹-31)/9 = 7(4)₁₄₈1_<150> = 3 · 127 · 1753489837597_<13> · C136

C136 = P44 · P92

P44 = 20881086487350036134625000283626100896654287_<44>

P92 = 53364319064384742665900100125286466593148958555660756921564191235935418790516441550676542399_<92>

Number: 74441_149
N=1114304961721960173022091383380176976662874322011077839586378960447874153953371814034523514291547521078222901018637342512063392400614513
  ( 136 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=20881086487350036134625000283626100896654287
 r2=53364319064384742665900100125286466593148958555660756921564191235935418790516441550676542399
Version: 
Total time: 10.05 hours.
Scaled time: 23.97 units (timescale=2.386).
Factorization parameters were as follows:
n: 1114304961721960173022091383380176976662874322011077839586378960447874153953371814034523514291547521078222901018637342512063392400614513
m: 1000000000000000000000000000000
deg: 5
c5: 67
c0: -310
skew: 1.36
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7412479
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 371929 x 372177
Total sieving time: 9.35 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000
total time: 10.05 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 6, 2009 (7th)

By Ignacio Santos / GGNFS, Msieve / Nov 6, 2009

5·10¹⁷⁴-7 = 4(9)₁₇₃3_<175> = 876443 · 26652181993_<11> · C159

C159 = P68 · P91

P68 = 46574391450747667692326738358784174396260537130314435096266571242987_<68>

P91 = 4595855531487340412820083355763538183249547281424390205839848914976852602041592456013124361_<91>

Number: 49993_174
N=214049174574575365805581376060199503058514198958035247503679069080324429338324460035489376300752092001338476663839616038201832417706699020583274339297180106307
  ( 159 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=46574391450747667692326738358784174396260537130314435096266571242987 (pp68)
 r2=4595855531487340412820083355763538183249547281424390205839848914976852602041592456013124361 (pp91)
Version: Msieve v. 1.43
Total time: 56.13 hours.
Scaled time: 97.62 units (timescale=1.739).
Factorization parameters were as follows:
n: 214049174574575365805581376060199503058514198958035247503679069080324429338324460035489376300752092001338476663839616038201832417706699020583274339297180106307
m: 100000000000000000000000000000000000
deg: 5
c5: 1
c0: -14
skew: 1.70
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 5500001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 995237 x 995463
Total sieving time: 54.41 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 1.30 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,52,52,2.5,2.5,100000
total time: 56.13 hours.

Nov 6, 2009 (6th)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 6, 2009

(22·10¹⁵⁷-7)/3 = 7(3)₁₅₆1_<158> = 367 · 316304551 · 8534437607_<10> · 2443395325355902608359_<22> · C116

C116 = P38 · P79

P38 = 23693488595112602719126859782566256591_<38>

P79 = 1278592829499304611645554337323796642663523431026589589200118777890584774879621_<79>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=236403890
Step 1 took 31182ms
Step 2 took 13038ms
********** Factor found in step 2: 23693488595112602719126859782566256591
Found probable prime factor of 38 digits: 23693488595112602719126859782566256591
Probable prime cofactor 1278592829499304611645554337323796642663523431026589589200118777890584774879621 has 79 digits

(59·10¹⁶⁴+31)/9 = 6(5)₁₆₃9_<165> = 41 · 257 · 5763713135701_<13> · C149

C149 = P33 · C116

P33 = 632793202179705926119343697193231_<33>

C116 = [17058009798902811382752770514092749096039916701396886379742470377517403076500372505435723966037254679924690425475197_<116>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3331270017
Step 1 took 47229ms
Step 2 took 16627ms
********** Factor found in step 2: 632793202179705926119343697193231
Found probable prime factor of 33 digits: 632793202179705926119343697193231
Composite cofactor 17058009798902811382752770514092749096039916701396886379742470377517403076500372505435723966037254679924690425475197 has 116 digits

(35·10¹⁹⁸+1)/9 = 3(8)₁₉₇9_<199> = 47 · C197

C197 = P82 · P116

P82 = 6326374989656440646106970407770659705730121493408302755378873328843303115001775919_<82>

P116 = 13078945987260134036462322502917867367044969527869559453471699062092522781634351546825345197002805196515382338315673_<116>

Number: 38889_198
N=82742316784869976359338061465721040189125295508274231678486997635933806146572104018912529550827423167848699763593380614657210401891252955082742316784869976359338061465721040189125295508274231678487
  ( 197 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=6326374989656440646106970407770659705730121493408302755378873328843303115001775919
 r2=13078945987260134036462322502917867367044969527869559453471699062092522781634351546825345197002805196515382338315673
Version: 
Total time: 569.79 hours.
Scaled time: 1133.32 units (timescale=1.989).
Factorization parameters were as follows:
n: 82742316784869976359338061465721040189125295508274231678486997635933806146572104018912529550827423167848699763593380614657210401891252955082742316784869976359338061465721040189125295508274231678487
m: 10000000000000000000000000000000000000000
deg: 5
c5: 7
c0: 20
skew: 1.23
type: snfs
lss: 1
rlim: 15600000
alim: 15600000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 15600000/15600000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7800000, 13500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2705232 x 2705480
Total sieving time: 569.79 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15600000,15600000,29,29,56,56,2.6,2.6,100000
total time: 569.79 hours.
 --------- CPU info (if available) ----------

(44·10¹⁹³-71)/9 = 4(8)₁₉₂1_<194> = 6203 · C190

C190 = P43 · P71 · P78

P43 = 1618166115802996840565371152078318243943573_<43>

P71 = 18615892194719893987578001772834971645694757182039038565591672722464263_<71>

P78 = 261638365738076548906793103513491078188631394698342571980380378304781956600273_<78>

Number: 48881_193
N=7881491034803947910509251795726082361581313701255664821681265337560678524728178121697386569222777509090583409461371737689648378024969996596628871334658856825550360936464434771705447185053827
  ( 190 digits)
SNFS difficulty: 194 digits.
Divisors found:
 r1=1618166115802996840565371152078318243943573
 r2=18615892194719893987578001772834971645694757182039038565591672722464263
 r3=261638365738076548906793103513491078188631394698342571980380378304781956600273
Version: 
Total time: 653.71 hours.
Scaled time: 1316.58 units (timescale=2.014).
Factorization parameters were as follows:
n: 7881491034803947910509251795726082361581313701255664821681265337560678524728178121697386569222777509090583409461371737689648378024969996596628871334658856825550360936464434771705447185053827
m: 200000000000000000000000000000000000000
deg: 5
c5: 1375
c0: -71
skew: 0.55
type: snfs
lss: 1
rlim: 12300000
alim: 12300000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 12300000/12300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6150000, 13250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2399210 x 2399457
Total sieving time: 653.71 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,194,5,0,0,0,0,0,0,0,0,12300000,12300000,28,28,55,55,2.5,2.5,100000
total time: 653.71 hours.
 --------- CPU info (if available) ----------

Nov 6, 2009 (5th)

By Sinkiti Sibata / Msieve / Nov 6, 2009

(67·10¹⁴⁰+41)/9 = 7(4)₁₃₉9_<141> = 7 · 3371 · C137

C137 = P30 · P108

P30 = 191509589725032360358047867623_<30>

P108 = 164734656570897235288033852810835623477513274568840397755400314955254385028426104714427625363827448134452979_<108>

Number: 74449_140
N=31548266493386635777617682097065069476816732823852372947596916745537332900133256110710871909329340358708498726297599035658958530509998917
  ( 137 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=191509589725032360358047867623 (pp30)
 r2=164734656570897235288033852810835623477513274568840397755400314955254385028426104714427625363827448134452979 (pp108)
Version: Msieve-1.40
Total time: 7.22 hours.
Scaled time: 14.81 units (timescale=2.051).
Factorization parameters were as follows:
name: 74449_140
n: 31548266493386635777617682097065069476816732823852372947596916745537332900133256110710871909329340358708498726297599035658958530509998917
m: 10000000000000000000000000000
deg: 5
c5: 67
c0: 41
skew: 0.91
type: snfs
lss: 1
rlim: 1620000
alim: 1620000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1620000/1620000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [810000, 1710001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 239634 x 239869
Total sieving time: 6.92 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000
total time: 7.22 hours.
 --------- CPU info (if available) ----------

(67·10¹³¹-31)/9 = 7(4)₁₃₀1_<132> = 3 · 143834439524998271722493_<24> · C109

C109 = P42 · P67

P42 = 323849544307374500128746883591241254838333_<42>

P67 = 5327271893239009943943442287524260619878365564348217121263894689563_<67>

Number: 74441_131
N=1725234575026937588591813062917426515403728981243743236270453675510075150479189227318557947230693458787418479
  ( 109 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=323849544307374500128746883591241254838333 (pp42)
 r2=5327271893239009943943442287524260619878365564348217121263894689563 (pp67)
Version: Msieve-1.40
Total time: 4.53 hours.
Scaled time: 9.44 units (timescale=2.085).
Factorization parameters were as follows:
name: 74441_131
n: 1725234575026937588591813062917426515403728981243743236270453675510075150479189227318557947230693458787418479
m: 200000000000000000000000000
deg: 5
c5: 335
c0: -496
skew: 1.08
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [600000, 1200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 166901 x 167149
Total sieving time: 4.35 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,134.000,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000
total time: 4.53 hours.
 --------- CPU info (if available) ----------

(67·10¹⁴⁴+41)/9 = 7(4)₁₄₃9_<145> = 3 · 79 · 25803630551_<11> · 2084763626306649558391910071_<28> · C105

C105 = P42 · P64

P42 = 423626916383930124653960797887297047400541_<42>

P64 = 1378360327126022364048330167071772464929240931307881983759154457_<64>

Number: 74449_144
N=583910535046342049640391332785757616154332420151820936864626808268428880468476996626812295569863964361237
  ( 105 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=423626916383930124653960797887297047400541 (pp42)
 r2=1378360327126022364048330167071772464929240931307881983759154457 (pp64)
Version: Msieve-1.40
Total time: 15.07 hours.
Scaled time: 29.55 units (timescale=1.961).
Factorization parameters were as follows:
name: 74449_144
n: 583910535046342049640391332785757616154332420151820936864626808268428880468476996626812295569863964361237
m: 100000000000000000000000000000
deg: 5
c5: 67
c0: 410
skew: 1.44
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2480001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 353335 x 353583
Total sieving time: 15.07 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 15.07 hours.
 --------- CPU info (if available) ----------

(67·10¹³⁵+41)/9 = 7(4)₁₃₄9_<136> = 3 · 13 · 163 · 251 · 189043 · C125

C125 = P56 · P69

P56 = 71240130359442359976794234666514935013351341284492389997_<56>

P69 = 346434435442088830363099162339575704342482076530326806769161585968817_<69>

Number: 74449_135
N=24680034341894226799147907831007002424011323440141068996191301321234332937934131467895911287545293909501468601748729044723549
  ( 125 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=71240130359442359976794234666514935013351341284492389997 (pp56)
 r2=346434435442088830363099162339575704342482076530326806769161585968817 (pp69)
Version: Msieve-1.40
Total time: 4.73 hours.
Scaled time: 9.85 units (timescale=2.085).
Factorization parameters were as follows:
name: 74449_135
n: 24680034341894226799147907831007002424011323440141068996191301321234332937934131467895911287545293909501468601748729044723549
m: 1000000000000000000000000000
deg: 5
c5: 67
c0: 41
skew: 0.91
type: snfs
lss: 1
rlim: 1340000
alim: 1340000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1340000/1340000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [670000, 1270001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 189985 x 190228
Total sieving time: 4.52 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1340000,1340000,26,26,48,48,2.3,2.3,75000
total time: 4.73 hours.
 --------- CPU info (if available) ----------

Nov 6, 2009 (4th)

By Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve 1.44 SVN. / Nov 6, 2009

(49·10²⁰¹+41)/9 = 5(4)₂₀₀9_<202> = 1653191 · C196

C196 = P44 · P152

P44 = 37275012028726822642622072954781884705885423_<44>

P152 = 88351259701921852832633429667747775669808345171415609203853358189987067824413888270327700386840290722262317778160874561417235000119736451519483267715993_<152>

Msieve v. 1.44
Thu Nov  5 21:18:46 2009
random seeds: 0f697e6c 28abe295
factoring 3293294268142304455107996864515016380106378781667964829499098679126879135226628045062212681078256804231600852197020455860480999741980475604116187690620408920956165648400241983197612643937962670039 (196 digits)
searching for 15-digit factors
commencing number field sieve (196-digit input)
R0: -10000000000000000000000000000000000000000
R1:  1
A0:  41
A1:  0
A2:  0
A3:  0
A4:  0
A5:  490
skew 0.61, size 2.833956e-14, alpha 1.214899, combined = 9.459428e-12

commencing relation filtering
estimated available RAM is 1148.0 MB
commencing duplicate removal, pass 1
error -9 reading relation 8945276
error -9 reading relation 11307712
error -9 reading relation 11518069
error -15 reading relation 11544804
error -9 reading relation 12509643
error -15 reading relation 12756522
error -15 reading relation 12795024
error -1 reading relation 23489632
error -9 reading relation 23643833
error -15 reading relation 24407655
error -15 reading relation 25776837
error -1 reading relation 26227026
error -15 reading relation 26416665
error -9 reading relation 31485538
found 8862011 hash collisions in 44999986 relations
added 730520 free relations
commencing duplicate removal, pass 2
found 9014662 duplicates and 36715844 unique relations
memory use: 213.2 MB
reading ideals above 19202048
commencing singleton removal, initial pass
memory use: 753.0 MB
removing singletons from LP file
start with 36715844 relations and 36580329 ideals
pass 1: found 14595173 singletons
pruned dataset has 22120671 relations and 19124588 large ideals
reading all ideals from disk
memory use: 382.0 MB
commencing in-memory singleton removal
begin with 22120671 relations and 19124588 unique ideals
reduce to 15684674 relations and 12316705 ideals in 18 passes
max relations containing the same ideal: 30
reading ideals above 720000
commencing singleton removal, initial pass
memory use: 376.5 MB
reading all ideals from disk
memory use: 531.7 MB
keeping 14648359 ideals with weight <= 200, target excess is 116482
commencing in-memory singleton removal
begin with 15684983 relations and 14648359 unique ideals
reduce to 15682203 relations and 14644226 ideals in 9 passes
max relations containing the same ideal: 200
removing 2846610 relations and 2446610 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 12835593 relations and 14644226 unique ideals
reduce to 12465195 relations and 11815179 ideals in 11 passes
max relations containing the same ideal: 175
removing 2135745 relations and 1735745 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 10329450 relations and 11815179 unique ideals
reduce to 10053854 relations and 9795074 ideals in 9 passes
max relations containing the same ideal: 147
removing 792609 relations and 668949 ideals in 123660 cliques
commencing in-memory singleton removal
begin with 9261245 relations and 9795074 unique ideals
reduce to 9216708 relations and 9081049 ideals in 7 passes
max relations containing the same ideal: 139
relations with 0 large ideals: 2906
relations with 1 large ideals: 272
relations with 2 large ideals: 7222
relations with 3 large ideals: 70678
relations with 4 large ideals: 374670
relations with 5 large ideals: 1150194
relations with 6 large ideals: 2257720
relations with 7+ large ideals: 5353046
commencing 2-way merge
reduce to 5570453 relation sets and 5434794 unique ideals
commencing full merge
memory use: 661.0 MB
found 2928967 cycles, need 2910994
weight of 2910994 cycles is about 203790381 (70.01/cycle)
distribution of cycle lengths:
1 relations: 364884
2 relations: 359563
3 relations: 360513
4 relations: 323963
5 relations: 286525
6 relations: 247293
7 relations: 211854
8 relations: 175678
9 relations: 142574
10+ relations: 438147
heaviest cycle: 23 relations
commencing cycle optimization
start with 15939067 relations
pruned 326649 relations
memory use: 540.6 MB
distribution of cycle lengths:
1 relations: 364884
2 relations: 366593
3 relations: 371489
4 relations: 329960
5 relations: 291790
6 relations: 249668
7 relations: 212738
8 relations: 175029
9 relations: 140569
10+ relations: 408274
heaviest cycle: 23 relations
RelProcTime: 1858
elapsed time 00:31:01

Msieve v. 1.44
Thu Nov  5 21:54:39 2009
random seeds: 239a98bf cd32137d
factoring 3293294268142304455107996864515016380106378781667964829499098679126879135226628045062212681078256804231600852197020455860480999741980475604116187690620408920956165648400241983197612643937962670039 (196 digits)
searching for 15-digit factors
commencing number field sieve (196-digit input)
R0: -10000000000000000000000000000000000000000
R1:  1
A0:  41
A1:  0
A2:  0
A3:  0
A4:  0
A5:  490
skew 0.61, size 2.833956e-14, alpha 1.214899, combined = 9.459428e-12

commencing linear algebra
read 2910994 cycles
cycles contain 9097602 unique relations
read 9097602 relations
using 20 quadratic characters above 536868404
building initial matrix
memory use: 1163.2 MB
read 2910994 cycles
matrix is 2910816 x 2910994 (876.2 MB) with weight 256607789 (88.15/col)
sparse part has weight 197667834 (67.90/col)
filtering completed in 2 passes
matrix is 2908807 x 2908984 (876.0 MB) with weight 256551143 (88.19/col)
sparse part has weight 197651271 (67.95/col)
read 2908984 cycles
matrix is 2908807 x 2908984 (876.0 MB) with weight 256551143 (88.19/col)
sparse part has weight 197651271 (67.95/col)
saving the first 48 matrix rows for later
matrix is 2908759 x 2908984 (831.7 MB) with weight 204497989 (70.30/col)
sparse part has weight 188932378 (64.95/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (2 threads)
memory use: 849.9 MB
restarting at iteration 45547 (dim = 2880023)
linear algebra completed 2908597 of 2908984 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 46003 iterations (dim = 2908755)
recovered 35 nontrivial dependencies
BLanczosTime: 102677

commencing square root phase
reading relations for dependency 1
read 1454148 cycles
cycles contain 4549318 unique relations
read 4549318 relations
multiplying 4549318 relations
multiply complete, coefficients have about 146.17 million bits
initial square root is modulo 176051
reading relations for dependency 2
read 1453033 cycles
cycles contain 4546544 unique relations
read 4546544 relations
multiplying 4546544 relations
multiply complete, coefficients have about 146.07 million bits
initial square root is modulo 174721
sqrtTime: 6024
prp44 factor: 37275012028726822642622072954781884705885423
prp152 factor: 88351259701921852832633429667747775669808345171415609203853358189987067824413888270327700386840290722262317778160874561417235000119736451519483267715993
elapsed time 01:57:43

Nov 6, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve / Nov 6, 2009

(67·10¹⁷³-31)/9 = 7(4)₁₇₂1_<174> = 3 · C174

C174 = P84 · P90

P84 = 430710479242399035363062350740645865987466720557004828022753286974516590870289028663_<84>

P90 = 576136778897578548828836762015811405604962956451806450404338507568484460587741229848480869_<90>

N=248148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147
  ( 174 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=430710479242399035363062350740645865987466720557004828022753286974516590870289028663 (pp84)
 r2=576136778897578548828836762015811405604962956451806450404338507568484460587741229848480869 (pp90)
Version: Msieve-1.40
Total time: 104.00 hours.
Scaled time: 197.49 units (timescale=1.899).
Factorization parameters were as follows:
n: 248148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147
m: 50000000000000000000000000000000000
deg: 5
c5: 536
c0: -775
skew: 1.08
type: snfs
lss: 1
rlim: 6100000
alim: 6100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 6100000/6100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3050000, 8350001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1467553 x 1467786
Total sieving time: 100.25 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 2.82 hours.
Time per square root: 0.75 hours.
Prototype def-par.txt line would be:
snfs,176.000,5,0,0,0,0,0,0,0,0,6100000,6100000,28,28,53,53,2.5,2.5,100000
total time: 104.00 hours.
 --------- CPU info (if available) ----------

Nov 6, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Nov 6, 2009

(22·10¹⁵⁶+17)/3 = 7(3)₁₅₅9_<157> = 13 · 19 · 6971 · 470900400663529_<15> · C136

C136 = P32 · P51 · P54

P32 = 22374456972596767383679482063529_<32>

P51 = 828191017353098997423669770686587010084194267524507_<51>

P54 = 488087078674160901172508648961369204695734529976060181_<54>

Number: 73339_156
N=9044411846105054274209815905986355691082748507066852603612928749817550676873652715990888627685568833319637972505812247201723505291521743
  ( 136 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=22374456972596767383679482063529 (pp32)
 r2=828191017353098997423669770686587010084194267524507 (pp51)
 r3=488087078674160901172508648961369204695734529976060181 (pp54)
Version: Msieve-1.40
Total time: 26.33 hours.
Scaled time: 23.30 units (timescale=0.885).
Factorization parameters were as follows:
n: 9044411846105054274209815905986355691082748507066852603612928749817550676873652715990888627685568833319637972505812247201723505291521743
m: 20000000000000000000000000000000
deg: 5
c5: 55
c0: 136
skew: 1.20
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 560422 x 560649
Total sieving time: 24.67 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.80 hours.
Time per square root: 0.74 hours.
Prototype def-par.txt line would be:
snfs,158.000,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 26.33 hours.
 --------- CPU info (if available) ----------

Nov 6, 2009

By Markus Tervooren / Msieve / Nov 6, 2009

(67·10¹⁴⁶+41)/9 = 7(4)₁₄₅9_<147> = 7³ · 2579 · 137933 · C136

C136 = P42 · P95

P42 = 552752232810877924907944618081429138807679_<42>

P95 = 11037942908547355150244790836990039717387364320115120207780436833145912926736258397877527823631_<95>

Sieving time: ~5 hours 

Msieve v. 1.43
Thu Nov  5 15:55:15 2009
random seeds: 22e75df5 c52ae233
factoring 6101247588338546677929745539946244193317898526731142823774618663407511729661540242208206561765864438885995914092862234746612155140462449 (136 digits)
searching for 15-digit factors
commencing number field sieve (136-digit input)
R0:  100000000000000000000000000000
R1: -1
A0:  41
A1:  0
A2:  0
A3:  0
A4:  0
A5:  670
skew 0.57, size 1.339951e-10, alpha 0.971714, combined = 1.477459e-09

commencing relation filtering
estimated available RAM is 8010.2 MB
commencing duplicate removal, pass 1
found 2463214 hash collisions in 18330753 relations
added 379270 free relations
commencing duplicate removal, pass 2
found 2223391 duplicates and 16486632 unique relations
memory use: 98.6 MB
reading ideals above 720000
commencing singleton removal, initial pass
memory use: 344.5 MB
reading all ideals from disk
memory use: 435.9 MB
keeping 12885881 ideals with weight <= 200, target excess is 116169
commencing in-memory singleton removal
begin with 16486632 relations and 12885881 unique ideals
reduce to 11845160 relations and 7680342 ideals in 12 passes
max relations containing the same ideal: 166
removing 1545647 relations and 1145647 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 10299513 relations and 7680342 unique ideals
reduce to 10195507 relations and 6426531 ideals in 7 passes
max relations containing the same ideal: 147
removing 1178313 relations and 778313 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 9017194 relations and 6426531 unique ideals
reduce to 8952428 relations and 5581283 ideals in 6 passes
max relations containing the same ideal: 136
removing 1045750 relations and 645750 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 7906678 relations and 5581283 unique ideals
reduce to 7837859 relations and 4863952 ideals in 5 passes
max relations containing the same ideal: 122
removing 954446 relations and 554446 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 6883413 relations and 4863952 unique ideals
reduce to 6814170 relations and 4236837 ideals in 5 passes
max relations containing the same ideal: 110
removing 927971 relations and 527971 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 5886199 relations and 4236837 unique ideals
reduce to 5819767 relations and 3638595 ideals in 5 passes
max relations containing the same ideal: 98
removing 899906 relations and 499906 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 4919861 relations and 3638595 unique ideals
reduce to 4851525 relations and 3065913 ideals in 7 passes
max relations containing the same ideal: 92
removing 875905 relations and 475905 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 3975620 relations and 3065913 unique ideals
reduce to 3901513 relations and 2509651 ideals in 5 passes
max relations containing the same ideal: 77
removing 854371 relations and 454371 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 3047142 relations and 2509651 unique ideals
reduce to 2976954 relations and 1979149 ideals in 8 passes
max relations containing the same ideal: 60
removing 853727 relations and 453727 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 2123227 relations and 1979149 unique ideals
reduce to 2056703 relations and 1453401 ideals in 6 passes
max relations containing the same ideal: 45
removing 649792 relations and 350445 ideals in 299347 cliques
commencing in-memory singleton removal
begin with 1406911 relations and 1453401 unique ideals
reduce to 1352520 relations and 1044337 ideals in 6 passes
max relations containing the same ideal: 35
removing 361208 relations and 202857 ideals in 158351 cliques
commencing in-memory singleton removal
begin with 991312 relations and 1044337 unique ideals
reduce to 943024 relations and 789269 ideals in 7 passes
max relations containing the same ideal: 28
removing 67885 relations and 48887 ideals in 18998 cliques
commencing in-memory singleton removal
begin with 875139 relations and 789269 unique ideals
reduce to 870935 relations and 736093 ideals in 5 passes
max relations containing the same ideal: 27
relations with 0 large ideals: 2892
relations with 1 large ideals: 12725
relations with 2 large ideals: 78477
relations with 3 large ideals: 199963
relations with 4 large ideals: 264046
relations with 5 large ideals: 196441
relations with 6 large ideals: 93686
relations with 7+ large ideals: 22705
commencing 2-way merge
reduce to 716617 relation sets and 581775 unique ideals
commencing full merge
memory use: 59.6 MB
found 334086 cycles, need 315975
weight of 315975 cycles is about 22212740 (70.30/cycle)
distribution of cycle lengths:
1 relations: 17641
2 relations: 28997
3 relations: 35315
4 relations: 35873
5 relations: 34500
6 relations: 30819
7 relations: 27240
8 relations: 23611
9 relations: 20033
10+ relations: 61946
heaviest cycle: 18 relations
commencing cycle optimization
start with 1977808 relations
pruned 109779 relations
memory use: 55.2 MB
distribution of cycle lengths:
1 relations: 17641
2 relations: 30199
3 relations: 38011
4 relations: 38567
5 relations: 37162
6 relations: 32764
7 relations: 28595
8 relations: 23952
9 relations: 19883
10+ relations: 49201
heaviest cycle: 17 relations
RelProcTime: 483

commencing linear algebra
read 315975 cycles
cycles contain 820073 unique relations
read 820073 relations
using 20 quadratic characters above 134195000
building initial matrix
memory use: 99.5 MB
read 315975 cycles
matrix is 315792 x 315975 (91.9 MB) with weight 27669770 (87.57/col)
sparse part has weight 20606850 (65.22/col)
filtering completed in 2 passes
matrix is 315546 x 315729 (91.8 MB) with weight 27657347 (87.60/col)
sparse part has weight 20599994 (65.25/col)
read 315729 cycles
matrix is 315546 x 315729 (91.8 MB) with weight 27657347 (87.60/col)
sparse part has weight 20599994 (65.25/col)
saving the first 48 matrix rows for later
matrix is 315498 x 315729 (86.7 MB) with weight 21774880 (68.97/col)
sparse part has weight 19583486 (62.03/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (4 threads)
memory use: 90.9 MB
linear algebra at 1.9%, ETA 0h 6m315729 dimensions (1.9%, ETA 0h 6m)
linear algebra completed 313716 of 315729 dimensions (99.4%, ETA 0h 0m)
lanczos halted after 4990 iterations (dim = 315494)
recovered 34 nontrivial dependencies
BLanczosTime: 435

commencing square root phase
reading relations for dependency 1
read 157809 cycles
cycles contain 410208 unique relations
read 410208 relations
multiplying 410208 relations
multiply complete, coefficients have about 12.09 million bits
initial square root is modulo 8837471
sqrtTime: 48
prp42 factor: 552752232810877924907944618081429138807679
prp95 factor: 11037942908547355150244790836990039717387364320115120207780436833145912926736258397877527823631
elapsed time 00:16:07

Nov 5, 2009 (7th)

By Ignacio Santos / GGNFS, Msieve / Nov 5, 2009

(65·10¹⁷⁴+7)/9 = 7(2)₁₇₃3_<175> = 17 · 3919 · C171

C171 = P35 · P136

P35 = 28045218294644002661656500892213117_<35>

P136 = 3865341215601827188809187731591195001845176710932875113565226610209954285454175288779980587070108534688701518416552656964627055137706053_<136>

Number: 72223_174
N=108404338174837852126476175228107743905591495763058136412683641118265797430650409351458538676166222208880149831472948114348231424916653741534038128307374663738081776897201
  ( 171 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=28045218294644002661656500892213117 (pp35)
 r2=3865341215601827188809187731591195001845176710932875113565226610209954285454175288779980587070108534688701518416552656964627055137706053 (pp136)
Version: Msieve-1.40
Total time: 77.49 hours.
Scaled time: 134.75 units (timescale=1.739).
Factorization parameters were as follows:
n: 108404338174837852126476175228107743905591495763058136412683641118265797430650409351458538676166222208880149831472948114348231424916653741534038128307374663738081776897201
m: 100000000000000000000000000000000000
deg: 5
c5: 13
c0: 14
skew: 1.01
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3000000, 6700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1284651 x 1284877
Total sieving time: 74.58 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 2.34 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,176.000,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,53,53,2.5,2.5,100000
total time: 77.49 hours.

Nov 5, 2009 (6th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM v6.2.3, YAFU v1.10 / Nov 5, 2009

(67·10¹⁶⁸-31)/9 = 7(4)₁₆₇1_<169> = 7606561 · 163572667 · 590259537485086986353_<21> · 151964056301483322443154779593_<30> · C104

C104 = P47 · P57

P47 = 97126863769841467874236485364535089605312141371_<47>

P57 = 686767840130450661304870889966446488159378580482101462377_<57>

Number: 74441_168
N=66703606449858545643662707449559166574748186359301268429300565428305734048800989227920948282512461698867
  ( 104 digits)
Divisors found:
 r1=97126863769841467874236485364535089605312141371
 r2=686767840130450661304870889966446488159378580482101462377
Version: 
Total time: 4.22 hours.
Scaled time: 10.06 units (timescale=2.384).
Factorization parameters were as follows:
name: 74441_168
n: 66703606449858545643662707449559166574748186359301268429300565428305734048800989227920948282512461698867
skew: 22384.96
# norm 2.87e+14
c5: 15660
c4: -501824996
c3: -18525148742447
c2: 266426610854246285
c1: 4333073707957086227643
c0: 14764715322523703194493871
# alpha -6.14
Y1: 7300412317
Y0: -84308575724840796752
# Murphy_E 2.08e-09
# M 5388142146302891828223044752647144935689243276179164408869092559758099099626333652594346077847048977290
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4950394
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 255278 x 255526
Polynomial selection time: 0.29 hours.
Total sieving time: 3.36 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 4.22 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁴⁴-31)/9 = 7(4)₁₄₃1_<145> = 1086632116511402147705630873_<28> · C118

C118 = P47 · P72

P47 = 34655482245468834228541408388489501901665410519_<47>

P72 = 197686862953873716181311104410965221646157892429803380406605260036919143_<72>

Number: 74441_144
N=6850933569260401192979346688968304304118740526220941882187274314238921954387217432618656883866956371791087169104665217
  ( 118 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=34655482245468834228541408388489501901665410519
 r2=197686862953873716181311104410965221646157892429803380406605260036919143
Version: 
Total time: 7.05 hours.
Scaled time: 16.85 units (timescale=2.389).
Factorization parameters were as follows:
n: 6850933569260401192979346688968304304118740526220941882187274314238921954387217432618656883866956371791087169104665217
m: 100000000000000000000000000000
deg: 5
c5: 67
c0: -310
skew: 1.36
type: snfs
lss: 1
rlim: 2550000
alim: 2550000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2550000/2550000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1275000, 2775001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4934852
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 407050 x 407298
Total sieving time: 6.06 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.33 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2550000,2550000,26,26,49,49,2.3,2.3,75000
total time: 7.05 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁵⁵+41)/9 = 7(4)₁₅₄9_<156> = 47 · 53 · 241 · 302983 · 14851037 · 252442321 · 79435952371_<11> · 96107273394271_<14> · C105

C105 = P36 · P69

P36 = 513981777262743485425131597124856197_<36>

P69 = 278216723864481525034470316274854133774845275372355082172887637024697_<69>

Number: 74449_155
N=142998326196084153152602303181725148518916237710184541230536160066661148293488886572640010918329062497309
  ( 105 digits)
Divisors found:
 r1=513981777262743485425131597124856197
 r2=278216723864481525034470316274854133774845275372355082172887637024697
Version: 
Total time: 4.48 hours.
Scaled time: 10.70 units (timescale=2.388).
Factorization parameters were as follows:
name: 74449_155
n: 142998326196084153152602303181725148518916237710184541230536160066661148293488886572640010918329062497309
skew: 16634.07
# norm 6.75e+14
c5: 36000
c4: 2507890170
c3: -33754989641093
c2: -411802020026744711
c1: 5598836560479622272525
c0: 714646846507642901515845
# alpha -6.87
Y1: 30603097547
Y0: -83138744797431074138
# Murphy_E 2.01e-09
# M 23638809882836740827105361457170598519475955087418326994978122984763654287971205979734490448061304881821
type: gnfs
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 1700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6901969
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 284502 x 284750
Polynomial selection time: 0.34 hours.
Total sieving time: 3.45 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000
total time: 4.48 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁵⁷+41)/9 = 7(4)₁₅₆9_<158> = 19 · 79 · 569 · 13280256271_<11> · 679103402368889_<15> · 396291799469414089_<18> · C110

C110 = P33 · P38 · P40

P33 = 896016956955767255596724244933401_<33>

P38 = 13950563607253532674032704293646041067_<38>

P40 = 1951074733192853860565440794148429905793_<40>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 24388320126912700619412278763299846909289095649545527020097226863181940482234364839456257636794737384518876531 (110 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5977138773
Step 1 took 3494ms
Step 2 took 3760ms
********** Factor found in step 2: 896016956955767255596724244933401
Found probable prime factor of 33 digits: 896016956955767255596724244933401
Composite cofactor 27218592167912123174017720102720354477066164208529016911587995682062219201131 has 77 digits

11/05/09 08:01:26 v1.10 @ 조영욱-PC, starting SIQS on c77: 27218592167912123174017720102720354477066164208529016911587995682062219201131
11/05/09 08:01:26 v1.10 @ 조영욱-PC, random seeds: 1415046673, 1328948052
11/05/09 08:01:27 v1.10 @ 조영욱-PC, ==== sieve params ====
11/05/09 08:01:27 v1.10 @ 조영욱-PC, n = 77 digits, 258 bits
11/05/09 08:01:27 v1.10 @ 조영욱-PC, factor base: 32200 primes (max prime = 805451)
11/05/09 08:01:27 v1.10 @ 조영욱-PC, single large prime cutoff: 68463335 (85 * pmax)
11/05/09 08:01:27 v1.10 @ 조영욱-PC, using 12 large prime slices of factor base
11/05/09 08:01:27 v1.10 @ 조영욱-PC, buckets hold 1024 elements
11/05/09 08:01:27 v1.10 @ 조영욱-PC, sieve interval: 5 blocks of size 65536
11/05/09 08:01:27 v1.10 @ 조영욱-PC, polynomial A has ~ 10 factors
11/05/09 08:01:27 v1.10 @ 조영욱-PC, using multiplier of 11
11/05/09 08:01:27 v1.10 @ 조영욱-PC, using small prime variation correction of 18 bits
11/05/09 08:01:27 v1.10 @ 조영욱-PC, using SSE2 for trial division and x64 sieve scanning
11/05/09 08:01:27 v1.10 @ 조영욱-PC, trial factoring cutoff at 94 bits
11/05/09 08:01:27 v1.10 @ 조영욱-PC, ==== sieving started ====
11/05/09 08:04:45 v1.10 @ 조영욱-PC, sieve time = 101.5450, relation time = 27.2180, poly_time = 69.2010
11/05/09 08:04:45 v1.10 @ 조영욱-PC, 32279 relations found: 16966 full + 15313 from 161385 partial, using 73331 polys (143 A polys)
11/05/09 08:04:45 v1.10 @ 조영욱-PC, on average, sieving found 2.43 rels/poly and 899.51 rels/sec
11/05/09 08:04:45 v1.10 @ 조영욱-PC, trial division touched 1264882 sieve locations out of 48058204160
11/05/09 08:04:45 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
11/05/09 08:04:45 v1.10 @ 조영욱-PC, begin with 178351 relations
11/05/09 08:04:45 v1.10 @ 조영욱-PC, reduce to 45610 relations in 2 passes
11/05/09 08:04:45 v1.10 @ 조영욱-PC, recovered 45610 relations
11/05/09 08:04:45 v1.10 @ 조영욱-PC, recovered 33913 polynomials
11/05/09 08:04:45 v1.10 @ 조영욱-PC, attempting to build 32279 cycles
11/05/09 08:04:45 v1.10 @ 조영욱-PC, found 32279 cycles in 1 passes
11/05/09 08:04:45 v1.10 @ 조영욱-PC, distribution of cycle lengths:
11/05/09 08:04:45 v1.10 @ 조영욱-PC,    length 1 : 16966
11/05/09 08:04:45 v1.10 @ 조영욱-PC,    length 2 : 15313
11/05/09 08:04:45 v1.10 @ 조영욱-PC, largest cycle: 2 relations
11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix is 32200 x 32279 (4.7 MB) with weight 967198 (29.96/col)
11/05/09 08:04:45 v1.10 @ 조영욱-PC, sparse part has weight 967198 (29.96/col)
11/05/09 08:04:45 v1.10 @ 조영욱-PC, filtering completed in 4 passes
11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix is 27821 x 27885 (4.0 MB) with weight 819515 (29.39/col)
11/05/09 08:04:45 v1.10 @ 조영욱-PC, sparse part has weight 819515 (29.39/col)
11/05/09 08:04:45 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix is 27773 x 27885 (2.8 MB) with weight 596633 (21.40/col)
11/05/09 08:04:45 v1.10 @ 조영욱-PC, sparse part has weight 452964 (16.24/col)
11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
11/05/09 08:04:45 v1.10 @ 조영욱-PC, commencing Lanczos iteration
11/05/09 08:04:45 v1.10 @ 조영욱-PC, memory use: 3.9 MB
11/05/09 08:04:52 v1.10 @ 조영욱-PC, lanczos halted after 441 iterations (dim = 27773)
11/05/09 08:04:52 v1.10 @ 조영욱-PC, recovered 18 nontrivial dependencies
11/05/09 08:04:52 v1.10 @ 조영욱-PC, prp38 = 13950563607253532674032704293646041067
11/05/09 08:04:52 v1.10 @ 조영욱-PC, prp40 = 1951074733192853860565440794148429905793
11/05/09 08:04:52 v1.10 @ 조영욱-PC, Lanczos elapsed time = 7.2070 seconds.
11/05/09 08:04:52 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.2030 seconds.
11/05/09 08:04:52 v1.10 @ 조영욱-PC, SIQS elapsed time = 205.6860 seconds.
11/05/09 08:04:52 v1.10 @ 조영욱-PC, 
11/05/09 08:04:52 v1.10 @ 조영욱-PC,

(67·10¹⁴⁵-31)/9 = 7(4)₁₄₄1_<146> = 709 · 322066412869815736192367293_<27> · C117

C117 = P55 · P62

P55 = 9260894445086141962651210313544909342955325247050444087_<55>

P62 = 35203649447637528618873300517503888994181400098044701486542239_<62>

Number: 74441_145
N=326017281616386218615956963496149396800689269848098363793483088850308834552548967331260168013696545100284199033290793
  ( 117 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=9260894445086141962651210313544909342955325247050444087
 r2=35203649447637528618873300517503888994181400098044701486542239
Version: 
Total time: 6.29 hours.
Scaled time: 15.05 units (timescale=2.391).
Factorization parameters were as follows:
n: 326017281616386218615956963496149396800689269848098363793483088850308834552548967331260168013696545100284199033290793
m: 100000000000000000000000000000
deg: 5
c5: 67
c0: -31
skew: 0.86
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4800623
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 307282 x 307530
Total sieving time: 5.82 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2400000,2400000,26,26,49,49,2.3,2.3,75000
total time: 6.29 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(64·10¹⁹⁹+17)/9 = 7(1)₁₉₈3_<200> = 89 · 179 · 16258282818944805107865067621_<29> · 490563121353478979588912991233_<30> · 5075327543140798696604465814559_<31> · C108

C108 = P52 · P56

P52 = 1407294183161809776961599301547364443542425110383681_<52>

P56 = 78356655111566972388515530318074663443442995516794711409_<56>

Number: 71113_199
N=110270864950524289144339133459841021143400357504267999886887205650991511373184710031303560333324391658116529
  ( 108 digits)
Divisors found:
 r1=1407294183161809776961599301547364443542425110383681
 r2=78356655111566972388515530318074663443442995516794711409
Version: 
Total time: 7.36 hours.
Scaled time: 17.58 units (timescale=2.389).
Factorization parameters were as follows:
name: 71113_199
n: 110270864950524289144339133459841021143400357504267999886887205650991511373184710031303560333324391658116529
skew: 16176.26
# norm 1.23e+15
c5: 35700
c4: -1151299406
c3: -81809870864120
c2: 211043661978170827
c1: 3912276685296992122992
c0: -12446168675693330275146900
# alpha -5.86
Y1: 307474834733
Y0: -314746746576521188279
# Murphy_E 1.37e-09
# M 20791178240142767970955924393944064521478715602414181529369486113938951120512110021307848257334770395712637
type: gnfs
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 1550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7458099
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 288207 x 288455
Polynomial selection time: 0.50 hours.
Total sieving time: 6.22 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000
total time: 7.36 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 5, 2009 (5th)

By Dmitry Domanov / GGNFS, msieve 1.43 / Nov 5, 2009

(67·10¹³⁸-31)/9 = 7(4)₁₃₇1_<139> = 43 · 1487 · 128826294607_<12> · C123

C123 = P52 · P72

P52 = 2155169564333464472349918628266493657340772283669081_<52>

P72 = 419340596308113045083191970050775890985316605601219929324602580966516003_<72>

Number: 123-1
N=903750090252691191717440333954198932390180191786769441344692739715470950187355528108887414276522629304579395374002342803243
  ( 123 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=2155169564333464472349918628266493657340772283669081 (pp52)
 r2=419340596308113045083191970050775890985316605601219929324602580966516003 (pp72)
Version: Msieve-1.40
Total time: 6.21 hours.
Scaled time: 12.23 units (timescale=1.969).
Factorization parameters were as follows:
n: 903750090252691191717440333954198932390180191786769441344692739715470950187355528108887414276522629304579395374002342803243
m: 5000000000000000000000000000
deg: 5
c5: 536
c0: -775
skew: 1.08
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 1990001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 264792 x 265017
Total sieving time: 5.97 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000
total time: 6.21 hours.
 --------- CPU info (if available) ----------

(67·10¹⁴¹+41)/9 = 7(4)₁₄₀9_<142> = 3² · 13 · C140

C140 = P30 · P45 · P67

P30 = 104293407448198211674022417719_<30>

P45 = 266908416852904564619693685732080119715284043_<45>

P67 = 2285742510120211041888511644779295382229835659384985236947755209441_<67>

Number: 140-1
N=63627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294397
  ( 140 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=104293407448198211674022417719 (pp30)
 r2=266908416852904564619693685732080119715284043 (pp45)
 r3=2285742510120211041888511644779295382229835659384985236947755209441 (pp67)
Version: Msieve-1.40
Total time: 6.69 hours.
Scaled time: 12.74 units (timescale=1.905).
Factorization parameters were as follows:
n: 63627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294397
m: 10000000000000000000000000000
deg: 5
c5: 670
c0: 41
skew: 0.57
type: snfs
lss: 1
rlim: 1680000
alim: 1680000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1680000/1680000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [840000, 2040001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 294207 x 294432
Total sieving time: 6.17 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,142.000,5,0,0,0,0,0,0,0,0,1680000,1680000,26,26,48,48,2.3,2.3,100000
total time: 6.69 hours.
 --------- CPU info (if available) ----------

(67·10¹³³+41)/9 = 7(4)₁₃₂9_<134> = 353081 · 7404732168439_<13> · 949521322502583250865947_<24> · C92

C92 = P36 · P57

P36 = 206990362108995995540706786083800799_<36>

P57 = 144875098665335013194730379024627109574296907971431258387_<57>

Thu Nov 05 13:28:38 2009  Msieve v. 1.43
Thu Nov 05 13:28:38 2009  random seeds: b092c728 739803fc
Thu Nov 05 13:28:38 2009  factoring 29987749133314216840538328401109372365462907275873647359634749454350166358605722808406051213 (92 digits)
Thu Nov 05 13:28:39 2009  searching for 15-digit factors
Thu Nov 05 13:28:40 2009  commencing quadratic sieve (92-digit input)
Thu Nov 05 13:28:40 2009  using multiplier of 53
Thu Nov 05 13:28:40 2009  using VC8 32kb sieve core
Thu Nov 05 13:28:40 2009  sieve interval: 36 blocks of size 32768
Thu Nov 05 13:28:40 2009  processing polynomials in batches of 6
Thu Nov 05 13:28:40 2009  using a sieve bound of 1787717 (66930 primes)
Thu Nov 05 13:28:40 2009  using large prime bound of 187710285 (27 bits)
Thu Nov 05 13:28:40 2009  using double large prime bound of 780330238063215 (42-50 bits)
Thu Nov 05 13:28:40 2009  using trial factoring cutoff of 50 bits
Thu Nov 05 13:28:40 2009  polynomial 'A' values have 12 factors
Thu Nov 05 15:11:33 2009  67077 relations (17712 full + 49365 combined from 818509 partial), need 67026
Thu Nov 05 15:11:37 2009  begin with 836221 relations
Thu Nov 05 15:11:37 2009  reduce to 166378 relations in 11 passes
Thu Nov 05 15:11:37 2009  attempting to read 166378 relations
Thu Nov 05 15:11:39 2009  recovered 166378 relations
Thu Nov 05 15:11:39 2009  recovered 145981 polynomials
Thu Nov 05 15:11:40 2009  attempting to build 67077 cycles
Thu Nov 05 15:11:40 2009  found 67077 cycles in 6 passes
Thu Nov 05 15:11:40 2009  distribution of cycle lengths:
Thu Nov 05 15:11:40 2009     length 1 : 17712
Thu Nov 05 15:11:40 2009     length 2 : 12595
Thu Nov 05 15:11:40 2009     length 3 : 11833
Thu Nov 05 15:11:40 2009     length 4 : 8937
Thu Nov 05 15:11:40 2009     length 5 : 6400
Thu Nov 05 15:11:40 2009     length 6 : 4055
Thu Nov 05 15:11:40 2009     length 7 : 2510
Thu Nov 05 15:11:40 2009     length 9+: 3035
Thu Nov 05 15:11:40 2009  largest cycle: 23 relations
Thu Nov 05 15:11:40 2009  matrix is 66930 x 67077 (16.4 MB) with weight 4018873 (59.91/col)
Thu Nov 05 15:11:40 2009  sparse part has weight 4018873 (59.91/col)
Thu Nov 05 15:11:40 2009  filtering completed in 3 passes
Thu Nov 05 15:11:40 2009  matrix is 62762 x 62826 (15.4 MB) with weight 3798024 (60.45/col)
Thu Nov 05 15:11:40 2009  sparse part has weight 3798024 (60.45/col)
Thu Nov 05 15:11:40 2009  saving the first 48 matrix rows for later
Thu Nov 05 15:11:41 2009  matrix is 62714 x 62826 (9.0 MB) with weight 2879392 (45.83/col)
Thu Nov 05 15:11:41 2009  sparse part has weight 1970064 (31.36/col)
Thu Nov 05 15:11:41 2009  matrix includes 64 packed rows
Thu Nov 05 15:11:41 2009  using block size 25130 for processor cache size 6144 kB
Thu Nov 05 15:11:41 2009  commencing Lanczos iteration
Thu Nov 05 15:11:41 2009  memory use: 9.6 MB
Thu Nov 05 15:11:48 2009  linear algebra at 38.3%, ETA 0h 0m
Thu Nov 05 15:11:59 2009  lanczos halted after 993 iterations (dim = 62714)
Thu Nov 05 15:11:59 2009  recovered 18 nontrivial dependencies
Thu Nov 05 15:12:00 2009  prp36 factor: 206990362108995995540706786083800799
Thu Nov 05 15:12:00 2009  prp57 factor: 144875098665335013194730379024627109574296907971431258387
Thu Nov 05 15:12:00 2009  elapsed time 01:43:22

Nov 5, 2009 (4th)

By Sinkiti Sibata / Msieve, GGNFS / Nov 5, 2009

(67·10¹⁵⁰+41)/9 = 7(4)₁₄₉9_<151> = 3² · 23 · 198148463 · C141

C141 = P35 · P106

P35 = 20717939788962621561499247182422137_<35>

P106 = 8760414861837486390460724581872136579955758254687113253234500957057212238208046927618976198274194583616297_<106>

Number: 74449_150
N=181497747633882346312517962380201339855560835063081505846794519711730643938420467789908245811486286339700685380221257507780590325469086766689
  ( 141 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=20717939788962621561499247182422137 (pp35)
 r2=8760414861837486390460724581872136579955758254687113253234500957057212238208046927618976198274194583616297 (pp106)
Version: Msieve-1.40
Total time: 17.61 hours.
Scaled time: 36.48 units (timescale=2.071).
Factorization parameters were as follows:
name: 74449_150
n: 181497747633882346312517962380201339855560835063081505846794519711730643938420467789908245811486286339700685380221257507780590325469086766689
m: 1000000000000000000000000000000
deg: 5
c5: 67
c0: 41
skew: 0.91
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 448148 x 448396
Total sieving time: 16.69 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.69 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 17.61 hours.
 --------- CPU info (if available) ----------

(62·10¹⁵⁰-71)/9 = 6(8)₁₄₉1_<151> = 985483 · 41851752012515441_<17> · C129

C129 = P42 · P87

P42 = 487000537391850390878280007869998072687387_<42>

P87 = 342970652274908800371221025897560617960050601182101051487751425298682261487633167922521_<87>

Number: 68881_150
N=167026891967514041560512106776883305292659958797087512558130233271448139287140102811153939235403213386239930950692215778269942627
  ( 129 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=487000537391850390878280007869998072687387 (pp42)
 r2=342970652274908800371221025897560617960050601182101051487751425298682261487633167922521 (pp87)
Version: GGNFS-0.77.1-20060513-k8
Total time: 28.87 hours.
Scaled time: 56.06 units (timescale=1.942).
Factorization parameters were as follows:
name: 68881_150
n: 167026891967514041560512106776883305292659958797087512558130233271448139287140102811153939235403213386239930950692215778269942627
m: 1000000000000000000000000000000
deg: 5
c5: 62
c0: -71
skew: 1.03
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176285, largePrimes:6922539 encountered
Relations: rels:6824198, finalFF:406801
Max relations in full relation-set: 28
Initial matrix: 352653 x 406801 with sparse part having weight 42278766.
Pruned matrix : 332656 x 334483 with weight 31669257.
Total sieving time: 26.80 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.72 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 28.87 hours.
 --------- CPU info (if available) ----------

Nov 5, 2009 (3rd)

By Serge Batalov / Msieve / Nov 5, 2009

(67·10¹²⁰-31)/9 = 7(4)₁₁₉1_<121> = 72126317 · 10506700696103_<14> · C100

C100 = P48 · P53

P48 = 248173394390078679300038958119545859112216157363_<48>

P53 = 39583751858057050006460477944893403895270269829507257_<53>

SNFS difficulty: 121 digits.
Divisors found:
 r1=248173394390078679300038958119545859112216157363 (pp48)
 r2=39583751858057050006460477944893403895270269829507257 (pp53)
Version: Msieve v. 1.44 SVN130
Total time: 0.86 hours.
Scaled time: 2.06 units (timescale=2.400).
Factorization parameters were as follows:
n: 9823634061308601992262375977557460526603204910482843794627402711296077541420800355402220532262483291
m: 1000000000000000000000000
deg: 5
c5: 67
c0: -31
skew: 0.86
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 675001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 80715 x 80940
Total sieving time: 0.79 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 0.86 hours.

(67·10¹²⁰+41)/9 = 7(4)₁₁₉9_<121> = 3 · 10878293325400967777_<20> · C102

C102 = P44 · P58

P44 = 38149372465301295430054963118277813058918169_<44>

P58 = 5979472529270312373079165688301574540864076057469555901091_<58>

SNFS difficulty: 121 digits.
Divisors found:
 r1=38149372465301295430054963118277813058918169 (pp44)
 r2=5979472529270312373079165688301574540864076057469555901091 (pp58)
Version: Msieve v. 1.44 SVN130
Total time: 0.92 hours.
Scaled time: 2.20 units (timescale=2.400).
Factorization parameters were as follows:
n: 228113124665170349134703467583011286242415225834237151834456021181025487623010089878132800918426822379
m: 1000000000000000000000000
deg: 5
c5: 67
c0: 41
skew: 0.91
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 675001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 78053 x 78278
Total sieving time: 0.86 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 0.92 hours.

Nov 5, 2009 (2nd)

By Robert Backstrom / Msieve / Nov 5, 2009

(8·10²²⁰+7)/3 = 2(6)₂₁₉9_<221> = 23432840917_<11> · C211

C211 = P63 · P72 · P76

P63 = 609079768500831052828490055657690521244152789163817285070668259_<63>

P72 = 796566640808664328548424906689815506613506880016762451255084828876058099_<72>

P76 = 2345565144724188907165081244897249978800113689094388155072548075040871134977_<76>

Sieving ~ 220 CPU days + 117 hrs Lanczos with Msieve 1.42

Sat Oct 31 15:34:27 2009  
Sat Oct 31 15:34:27 2009  
Sat Oct 31 15:34:27 2009  Msieve v. 1.42
Sat Oct 31 15:34:27 2009  random seeds: b45cd8a4 5e8cbb4f
Sat Oct 31 15:34:27 2009  factoring 1138003998794725682926321155405412538979627242039312593634276438708887713594111225991671194456334842477805341329483266540910587391526508465762511226229679040784257745433430779376748272005804726927838540861403257 (211 digits)
Sat Oct 31 15:34:29 2009  no P-1/P+1/ECM available, skipping
Sat Oct 31 15:34:29 2009  commencing number field sieve (211-digit input)
Sat Oct 31 15:34:29 2009  R0: -10000000000000000000000000000000000000
Sat Oct 31 15:34:29 2009  R1:  1
Sat Oct 31 15:34:29 2009  A0:  175
Sat Oct 31 15:34:29 2009  A1:  0
Sat Oct 31 15:34:29 2009  A2:  0
Sat Oct 31 15:34:29 2009  A3:  0
Sat Oct 31 15:34:29 2009  A4:  0
Sat Oct 31 15:34:29 2009  A5:  0
Sat Oct 31 15:34:29 2009  A6:  2
Sat Oct 31 15:34:29 2009  skew 1.00, size 3.489374e-11, alpha 1.918928, combined = 1.519785e-12
Sat Oct 31 15:34:29 2009  
Sat Oct 31 15:34:29 2009  commencing relation filtering
Sat Oct 31 15:34:29 2009  estimated available RAM is 7923.2 MB
Sat Oct 31 15:34:29 2009  commencing duplicate removal, pass 1
Sat Oct 31 15:36:03 2009  error -11 reading relation 17254458
Sat Oct 31 15:36:54 2009  error -11 reading relation 26696095
Sat Oct 31 15:36:58 2009  error -11 reading relation 27363947
Sat Oct 31 15:36:58 2009  error -15 reading relation 27363955
Sat Oct 31 15:38:59 2009  error -11 reading relation 45804540
Sat Oct 31 15:39:03 2009  error -9 reading relation 46551733
Sat Oct 31 15:39:43 2009  found 10149236 hash collisions in 53207787 relations
Sat Oct 31 15:39:58 2009  added 11 free relations
Sat Oct 31 15:39:58 2009  commencing duplicate removal, pass 2
Sat Oct 31 15:40:36 2009  found 10095437 duplicates and 43112361 unique relations
Sat Oct 31 15:40:36 2009  memory use: 330.4 MB
Sat Oct 31 15:40:36 2009  reading ideals above 42532864
Sat Oct 31 15:40:36 2009  commencing singleton removal, initial pass
Sat Oct 31 15:45:48 2009  memory use: 596.8 MB
Sat Oct 31 15:45:52 2009  reading all ideals from disk
Sat Oct 31 15:45:55 2009  memory use: 817.8 MB
Sat Oct 31 15:46:00 2009  commencing in-memory singleton removal
Sat Oct 31 15:46:04 2009  begin with 43112361 relations and 40663350 unique ideals
Sat Oct 31 15:46:48 2009  reduce to 22314083 relations and 17056552 ideals in 16 passes
Sat Oct 31 15:46:48 2009  max relations containing the same ideal: 27
Sat Oct 31 15:46:51 2009  reading ideals above 720000
Sat Oct 31 15:46:51 2009  commencing singleton removal, initial pass
Sat Oct 31 15:50:17 2009  memory use: 532.8 MB
Sat Oct 31 15:50:17 2009  reading all ideals from disk
Sat Oct 31 15:50:18 2009  memory use: 816.4 MB
Sat Oct 31 15:50:24 2009  keeping 22080764 ideals with weight <= 200, target excess is 125696
Sat Oct 31 15:50:29 2009  commencing in-memory singleton removal
Sat Oct 31 15:50:34 2009  begin with 22314094 relations and 22080764 unique ideals
Sat Oct 31 15:51:34 2009  reduce to 22292479 relations and 22059060 ideals in 11 passes
Sat Oct 31 15:51:34 2009  max relations containing the same ideal: 200
Sat Oct 31 15:51:56 2009  removing 650811 relations and 607005 ideals in 43806 cliques
Sat Oct 31 15:51:57 2009  commencing in-memory singleton removal
Sat Oct 31 15:52:02 2009  begin with 21641668 relations and 22059060 unique ideals
Sat Oct 31 15:52:44 2009  reduce to 21625957 relations and 21436291 ideals in 8 passes
Sat Oct 31 15:52:44 2009  max relations containing the same ideal: 200
Sat Oct 31 15:53:06 2009  removing 467462 relations and 423656 ideals in 43806 cliques
Sat Oct 31 15:53:06 2009  commencing in-memory singleton removal
Sat Oct 31 15:53:12 2009  begin with 21158495 relations and 21436291 unique ideals
Sat Oct 31 15:53:52 2009  reduce to 21150366 relations and 21004483 ideals in 8 passes
Sat Oct 31 15:53:52 2009  max relations containing the same ideal: 198
Sat Oct 31 15:54:03 2009  relations with 0 large ideals: 4811
Sat Oct 31 15:54:03 2009  relations with 1 large ideals: 417
Sat Oct 31 15:54:03 2009  relations with 2 large ideals: 3897
Sat Oct 31 15:54:03 2009  relations with 3 large ideals: 44781
Sat Oct 31 15:54:03 2009  relations with 4 large ideals: 304685
Sat Oct 31 15:54:03 2009  relations with 5 large ideals: 1255957
Sat Oct 31 15:54:03 2009  relations with 6 large ideals: 3252807
Sat Oct 31 15:54:03 2009  relations with 7+ large ideals: 16283011
Sat Oct 31 15:54:03 2009  commencing 2-way merge
Sat Oct 31 15:54:34 2009  reduce to 13461304 relation sets and 13315421 unique ideals
Sat Oct 31 15:54:34 2009  commencing full merge
Sat Oct 31 16:00:41 2009  memory use: 1639.9 MB
Sat Oct 31 16:00:43 2009  found 7160180 cycles, need 7153621
Sat Oct 31 16:00:47 2009  weight of 7153621 cycles is about 500859937 (70.01/cycle)
Sat Oct 31 16:00:47 2009  distribution of cycle lengths:
Sat Oct 31 16:00:47 2009  1 relations: 1050682
Sat Oct 31 16:00:47 2009  2 relations: 1061471
Sat Oct 31 16:00:47 2009  3 relations: 984923
Sat Oct 31 16:00:47 2009  4 relations: 812616
Sat Oct 31 16:00:47 2009  5 relations: 657769
Sat Oct 31 16:00:47 2009  6 relations: 527246
Sat Oct 31 16:00:47 2009  7 relations: 421690
Sat Oct 31 16:00:47 2009  8 relations: 331726
Sat Oct 31 16:00:47 2009  9 relations: 261587
Sat Oct 31 16:00:47 2009  10+ relations: 1043911
Sat Oct 31 16:00:47 2009  heaviest cycle: 28 relations
Sat Oct 31 16:00:50 2009  commencing cycle optimization
Sat Oct 31 16:01:06 2009  start with 38264635 relations
Sat Oct 31 16:02:27 2009  pruned 895565 relations
Sat Oct 31 16:02:27 2009  memory use: 1259.8 MB
Sat Oct 31 16:02:27 2009  distribution of cycle lengths:
Sat Oct 31 16:02:27 2009  1 relations: 1050682
Sat Oct 31 16:02:27 2009  2 relations: 1084140
Sat Oct 31 16:02:27 2009  3 relations: 1019860
Sat Oct 31 16:02:27 2009  4 relations: 826893
Sat Oct 31 16:02:27 2009  5 relations: 666675
Sat Oct 31 16:02:27 2009  6 relations: 526965
Sat Oct 31 16:02:27 2009  7 relations: 417613
Sat Oct 31 16:02:27 2009  8 relations: 325306
Sat Oct 31 16:02:27 2009  9 relations: 253971
Sat Oct 31 16:02:27 2009  10+ relations: 981516
Sat Oct 31 16:02:27 2009  heaviest cycle: 28 relations
Sat Oct 31 16:02:43 2009  RelProcTime: 1694
Sat Oct 31 16:02:43 2009  
Sat Oct 31 16:02:43 2009  commencing linear algebra
Sat Oct 31 16:02:48 2009  read 7153621 cycles
Sat Oct 31 16:03:02 2009  cycles contain 20976846 unique relations
Sat Oct 31 16:05:09 2009  read 20976846 relations
Sat Oct 31 16:05:47 2009  using 20 quadratic characters above 536870702
Sat Oct 31 16:07:28 2009  building initial matrix
Sat Oct 31 16:11:42 2009  memory use: 2662.3 MB
Sat Oct 31 16:11:46 2009  read 7153621 cycles
Sat Oct 31 16:11:50 2009  matrix is 7153443 x 7153621 (2122.1 MB) with weight 619248046 (86.56/col)
Sat Oct 31 16:11:50 2009  sparse part has weight 484755663 (67.76/col)
Sat Oct 31 16:13:28 2009  filtering completed in 2 passes
Sat Oct 31 16:13:29 2009  matrix is 7151802 x 7151980 (2122.0 MB) with weight 619201053 (86.58/col)
Sat Oct 31 16:13:29 2009  sparse part has weight 484741960 (67.78/col)
Sat Oct 31 16:14:11 2009  read 7151980 cycles
Sat Oct 31 16:14:15 2009  matrix is 7151802 x 7151980 (2122.0 MB) with weight 619201053 (86.58/col)
Sat Oct 31 16:14:15 2009  sparse part has weight 484741960 (67.78/col)
Sat Oct 31 16:14:15 2009  saving the first 48 matrix rows for later
Sat Oct 31 16:14:18 2009  matrix is 7151754 x 7151980 (2042.1 MB) with weight 494163750 (69.09/col)
Sat Oct 31 16:14:18 2009  sparse part has weight 463811895 (64.85/col)
Sat Oct 31 16:14:18 2009  matrix includes 64 packed rows
Sat Oct 31 16:14:18 2009  using block size 65536 for processor cache size 6144 kB
Sat Oct 31 16:14:46 2009  commencing Lanczos iteration (4 threads)
Sat Oct 31 16:14:46 2009  memory use: 2218.4 MB
Thu Nov  5 10:26:49 2009  lanczos halted after 113099 iterations (dim = 7151754)
Thu Nov  5 10:27:00 2009  recovered 40 nontrivial dependencies
Thu Nov  5 10:27:00 2009  BLanczosTime: 411857
Thu Nov  5 10:27:00 2009  
Thu Nov  5 10:27:00 2009  commencing square root phase
Thu Nov  5 10:27:00 2009  reading relations for dependency 1
Thu Nov  5 10:27:02 2009  read 3576106 cycles
Thu Nov  5 10:27:10 2009  cycles contain 12847903 unique relations
Thu Nov  5 10:28:35 2009  read 12847903 relations
Thu Nov  5 10:29:52 2009  multiplying 10490752 relations
Thu Nov  5 10:49:26 2009  multiply complete, coefficients have about 272.47 million bits
Thu Nov  5 10:49:29 2009  initial square root is modulo 77557
Thu Nov  5 11:21:08 2009  reading relations for dependency 2
Thu Nov  5 11:21:09 2009  read 3577523 cycles
Thu Nov  5 11:21:17 2009  cycles contain 12847085 unique relations
Thu Nov  5 11:22:42 2009  read 12847085 relations
Thu Nov  5 11:24:00 2009  multiplying 10490164 relations
Thu Nov  5 11:43:34 2009  multiply complete, coefficients have about 272.46 million bits
Thu Nov  5 11:43:36 2009  initial square root is modulo 77557
Thu Nov  5 12:15:13 2009  reading relations for dependency 3
Thu Nov  5 12:15:14 2009  read 3574396 cycles
Thu Nov  5 12:15:22 2009  cycles contain 12841056 unique relations
Thu Nov  5 12:16:47 2009  read 12841056 relations
Thu Nov  5 12:18:05 2009  multiplying 10485418 relations
Thu Nov  5 12:37:39 2009  multiply complete, coefficients have about 272.32 million bits
Thu Nov  5 12:37:41 2009  initial square root is modulo 77017
Thu Nov  5 13:09:16 2009  sqrtTime: 9736
Thu Nov  5 13:09:16 2009  prp63 factor: 609079768500831052828490055657690521244152789163817285070668259
Thu Nov  5 13:09:16 2009  prp72 factor: 796566640808664328548424906689815506613506880016762451255084828876058099
Thu Nov  5 13:09:16 2009  prp76 factor: 2345565144724188907165081244897249978800113689094388155072548075040871134977
Thu Nov  5 13:09:16 2009  elapsed time 117:34:49

Nov 5, 2009

By Erik Branger / GGNFS, Msieve / Nov 5, 2009

(67·10¹⁴⁵+41)/9 = 7(4)₁₄₄9_<146> = 563 · C144

C144 = P37 · P38 · P69

P37 = 6082655084179705302299740326973200613_<37>

P38 = 75145263081390269628363377895509391047_<38>

P69 = 289287120475685604509159180322914778804255865863282240870880979061193_<69>

Number: 74449_145
N=132228142885336491020327610025656206828498125123347148213933293862245904874679297414643773435958160647325833826721926189066508782316952832050523
  ( 144 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=6082655084179705302299740326973200613 (pp37)
 r2=75145263081390269628363377895509391047 (pp38)
 r3=289287120475685604509159180322914778804255865863282240870880979061193 (pp69)
Version: Msieve-1.40
Total time: 9.60 hours.
Scaled time: 9.62 units (timescale=1.002).
Factorization parameters were as follows:
n: 132228142885336491020327610025656206828498125123347148213933293862245904874679297414643773435958160647325833826721926189066508782316952832050523
m: 100000000000000000000000000000
deg: 5
c5: 67
c0: 41
skew: 0.91
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2280001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 317816 x 318042
Total sieving time: 9.11 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 9.60 hours.
 --------- CPU info (if available) ----------

Nov 4, 2009 (8th)

By Jo Yeong Uk / GMP-ECM, YAFU v1.10, Msieve, GGNFS / Nov 4, 2009

(67·10¹¹⁴-31)/9 = 7(4)₁₁₃1_<115> = 2179 · C112

C112 = P35 · P78

P35 = 13079519603592591828724136575259833_<35>

P78 = 261206072937066617575379951763202353709110249235984400041972053868280867577163_<78>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 3416449951557799194329712916220488501351282443526592218652796899699148437101626638111264086482076385701901993779 (112 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2024510530
Step 1 took 3463ms
Step 2 took 3791ms
********** Factor found in step 2: 13079519603592591828724136575259833
Found probable prime factor of 35 digits: 13079519603592591828724136575259833
Probable prime cofactor 261206072937066617575379951763202353709110249235984400041972053868280867577163 has 78 digits

(67·10¹²⁸+41)/9 = 7(4)₁₂₇9_<129> = 7 · 23² · 850211 · 156528760163174468436985270573_<30> · C91

C91 = P34 · P57

P34 = 9280978564452803005420807952719117_<34>

P57 = 162766095942852035592368755877316356049781939213380763333_<57>

11/03/09 23:20:43 v1.10 @ 조영욱-PC, starting SIQS on c91: 1510628647465278088780074442873108582826769882337327979799715993558798504460665158401736961
11/03/09 23:20:43 v1.10 @ 조영욱-PC, random seeds: 3179975179, 4127114576
11/03/09 23:20:43 v1.10 @ 조영욱-PC, ==== sieve params ====
11/03/09 23:20:43 v1.10 @ 조영욱-PC, n = 91 digits, 300 bits
11/03/09 23:20:43 v1.10 @ 조영욱-PC, factor base: 67412 primes (max prime = 1795439)
11/03/09 23:20:43 v1.10 @ 조영욱-PC, single large prime cutoff: 215452680 (120 * pmax)
11/03/09 23:20:43 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
11/03/09 23:20:43 v1.10 @ 조영욱-PC, double large prime cutoff: 1000076957903973
11/03/09 23:20:43 v1.10 @ 조영욱-PC, using 16 large prime slices of factor base
11/03/09 23:20:43 v1.10 @ 조영욱-PC, buckets hold 1024 elements
11/03/09 23:20:43 v1.10 @ 조영욱-PC, sieve interval: 11 blocks of size 65536
11/03/09 23:20:43 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors
11/03/09 23:20:43 v1.10 @ 조영욱-PC, using multiplier of 1
11/03/09 23:20:43 v1.10 @ 조영욱-PC, using small prime variation correction of 20 bits
11/03/09 23:20:43 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
11/03/09 23:20:43 v1.10 @ 조영욱-PC, trial factoring cutoff at 96 bits
11/03/09 23:20:43 v1.10 @ 조영욱-PC, ==== sieving started ====
11/04/09 00:02:57 v1.10 @ 조영욱-PC, sieve time = 1131.6620, relation time = 624.9660, poly_time = 777.0980
11/04/09 00:02:57 v1.10 @ 조영욱-PC, 67543 relations found: 20169 full + 47374 from 802231 partial, using 353318 polys (191 A polys)
11/04/09 00:02:57 v1.10 @ 조영욱-PC, on average, sieving found 2.33 rels/poly and 324.47 rels/sec
11/04/09 00:02:57 v1.10 @ 조영욱-PC, trial division touched 22403114 sieve locations out of 509411065856
11/04/09 00:02:57 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
11/04/09 00:02:58 v1.10 @ 조영욱-PC, begin with 822400 relations
11/04/09 00:02:58 v1.10 @ 조영욱-PC, reduce to 153642 relations in 9 passes
11/04/09 00:02:59 v1.10 @ 조영욱-PC, failed to read relation 81905
11/04/09 00:02:59 v1.10 @ 조영욱-PC, recovered 153641 relations
11/04/09 00:02:59 v1.10 @ 조영욱-PC, recovered 124453 polynomials
11/04/09 00:03:00 v1.10 @ 조영욱-PC, attempting to build 67542 cycles
11/04/09 00:03:00 v1.10 @ 조영욱-PC, found 67542 cycles in 5 passes
11/04/09 00:03:00 v1.10 @ 조영욱-PC, distribution of cycle lengths:
11/04/09 00:03:00 v1.10 @ 조영욱-PC,    length 1 : 20169
11/04/09 00:03:00 v1.10 @ 조영욱-PC,    length 2 : 15486
11/04/09 00:03:00 v1.10 @ 조영욱-PC,    length 3 : 12345
11/04/09 00:03:00 v1.10 @ 조영욱-PC,    length 4 : 8239
11/04/09 00:03:00 v1.10 @ 조영욱-PC,    length 5 : 5235
11/04/09 00:03:00 v1.10 @ 조영욱-PC,    length 6 : 2848
11/04/09 00:03:00 v1.10 @ 조영욱-PC,    length 7 : 1600
11/04/09 00:03:00 v1.10 @ 조영욱-PC,    length 9+: 1620
11/04/09 00:03:00 v1.10 @ 조영욱-PC, largest cycle: 17 relations
11/04/09 00:03:00 v1.10 @ 조영욱-PC, matrix is 67412 x 67542 (16.1 MB) with weight 3671773 (54.36/col)
11/04/09 00:03:00 v1.10 @ 조영욱-PC, sparse part has weight 3671773 (54.36/col)
11/04/09 00:03:00 v1.10 @ 조영욱-PC, filtering completed in 3 passes
11/04/09 00:03:00 v1.10 @ 조영욱-PC, matrix is 61730 x 61793 (14.9 MB) with weight 3405157 (55.11/col)
11/04/09 00:03:00 v1.10 @ 조영욱-PC, sparse part has weight 3405157 (55.11/col)
11/04/09 00:03:00 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
11/04/09 00:03:00 v1.10 @ 조영욱-PC, matrix is 61682 x 61793 (10.0 MB) with weight 2620105 (42.40/col)
11/04/09 00:03:00 v1.10 @ 조영욱-PC, sparse part has weight 1998266 (32.34/col)
11/04/09 00:03:00 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
11/04/09 00:03:00 v1.10 @ 조영욱-PC, using block size 24717 for processor cache size 4096 kB
11/04/09 00:03:01 v1.10 @ 조영욱-PC, commencing Lanczos iteration
11/04/09 00:03:01 v1.10 @ 조영욱-PC, memory use: 8.9 MB
11/04/09 00:03:17 v1.10 @ 조영욱-PC, lanczos halted after 977 iterations (dim = 61681)
11/04/09 00:03:17 v1.10 @ 조영욱-PC, recovered 16 nontrivial dependencies
11/04/09 00:03:19 v1.10 @ 조영욱-PC, prp34 = 9280978564452803005420807952719117
11/04/09 00:03:20 v1.10 @ 조영욱-PC, prp57 = 162766095942852035592368755877316356049781939213380763333
11/04/09 00:03:20 v1.10 @ 조영욱-PC, Lanczos elapsed time = 19.4370 seconds.
11/04/09 00:03:20 v1.10 @ 조영욱-PC, Sqrt elapsed time = 2.8390 seconds.
11/04/09 00:03:20 v1.10 @ 조영욱-PC, SIQS elapsed time = 2556.8360 seconds.
11/04/09 00:03:20 v1.10 @ 조영욱-PC, 
11/04/09 00:03:20 v1.10 @ 조영욱-PC,

(67·10¹³⁹+41)/9 = 7(4)₁₃₈9_<140> = 19 · 61 · 786547 · 1674291299_<10> · C122

C122 = P36 · P86

P36 = 534377673459567913254367877976611999_<36>

P86 = 91273531275261258156042651910406956385468817913185449840182337837085448090326006202513_<86>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 48774537291313219904007442623079158405753926520188764791281515395495425389421219582074322630262240994295077354023619753487 (122 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4575964169
Step 1 took 4212ms
Step 2 took 4056ms
********** Factor found in step 2: 534377673459567913254367877976611999
Found probable prime factor of 36 digits: 534377673459567913254367877976611999
Probable prime cofactor 91273531275261258156042651910406956385468817913185449840182337837085448090326006202513 has 86 digits

(65·10¹⁷⁹+61)/9 = 7(2)₁₇₈9_<180> = 3 · 87323 · 1020080559737_<13> · 54796149540726227_<17> · 83447890470698339_<17> · 27708832797767384789479_<23> · C107

C107 = P53 · P55

P53 = 21317743601667445804930194324444375759367676750060383_<53>

P55 = 1000602544242060901983833714061031406596803672213547933_<55>

Number: 72229_179
N=21330588485328361158875002080392748528233289527820690150638446324869293334374003458821833553113928414838339
  ( 107 digits)
Divisors found:
 r1=21317743601667445804930194324444375759367676750060383
 r2=1000602544242060901983833714061031406596803672213547933
Version: 
Total time: 5.92 hours.
Scaled time: 14.12 units (timescale=2.384).
Factorization parameters were as follows:
name: 72229_179
n: 21330588485328361158875002080392748528233289527820690150638446324869293334374003458821833553113928414838339
skew: 9489.31
# norm 3.74e+14
c5: 83520
c4: -436405264
c3: -43730910773101
c2: 49262942741116958
c1: 1251380323824997943208
c0: 1910004788418672326199040
# alpha -5.50
Y1: 141394237039
Y0: -191180153518733060139
# Murphy_E 1.54e-09
# M 1630275644399714633370982263982210328654134408964574373092281722022933840800618587339707463745250196639887
type: gnfs
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7190161
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 325405 x 325653
Polynomial selection time: 0.48 hours.
Total sieving time: 4.47 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000
total time: 5.92 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(62·10¹⁴⁶+1)/9 = 6(8)₁₄₅9_<147> = 13² · 6211201993_<10> · C135

C135 = P44 · P92

P44 = 37581034560382870644756808555485568620305131_<44>

P92 = 17462969313698974114395124223099743671734245518631937018327064999870014820154330993298790107_<92>

Number: 68889_146
N=656276453305026685950132845745911740356925604415194223087379708869983185964276540678527362642992488434795315111654799315241895464139017
  ( 135 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=37581034560382870644756808555485568620305131
 r2=17462969313698974114395124223099743671734245518631937018327064999870014820154330993298790107
Version: 
Total time: 5.79 hours.
Scaled time: 13.84 units (timescale=2.390).
Factorization parameters were as follows:
n: 656276453305026685950132845745911740356925604415194223087379708869983185964276540678527362642992488434795315111654799315241895464139017
m: 100000000000000000000000000000
deg: 5
c5: 620
c0: 1
skew: 0.28
type: snfs
lss: 1
rlim: 2550000
alim: 2550000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2550000/2550000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1275000, 2475001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6418793
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 368564 x 368812
Total sieving time: 4.91 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2550000,2550000,27,27,49,49,2.3,2.3,75000
total time: 5.79 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁷¹-13)/9 = 7(4)₁₇₀3_<172> = 3 · 61 · 83 · 41231 · 19326177205969_<14> · 168398177444718134299_<21> · 2407940199983494858529_<22> · C109

C109 = P46 · P64

P46 = 1214668126324414697566041461258645928187122911_<46>

P64 = 1248799068463420195167977322133851867633591392772046781046404093_<64>

Number: 74443_171
N=1516876424646137080131556036817394582794742250003026910441101316886042947544731337541309623794566063964474723
  ( 109 digits)
Divisors found:
 r1=1214668126324414697566041461258645928187122911
 r2=1248799068463420195167977322133851867633591392772046781046404093
Version: 
Total time: 6.92 hours.
Scaled time: 16.50 units (timescale=2.385).
Factorization parameters were as follows:
name: 74443_171
n: 1516876424646137080131556036817394582794742250003026910441101316886042947544731337541309623794566063964474723
skew: 36638.54
# norm 1.70e+14
c5: 3060
c4: -1398829
c3: -9178005934770
c2: 64214779489920807
c1: 6712137520935301876937
c0: -90999322526528824438261920
# alpha -4.43
Y1: 258078464281
Y0: -869052006919087136947
# Murphy_E 1.27e-09
# M 110391089666132681615043182607453260645570670579022439977078871060208071876625052537906603026807031519173360
type: gnfs
rlim: 2100000
alim: 2100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1050000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7879005
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 383485 x 383733
Polynomial selection time: 0.59 hours.
Total sieving time: 5.13 hours.
Total relation processing time: 0.74 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000
total time: 6.92 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(62·10¹⁴⁶-53)/9 = 6(8)₁₄₅3_<147> = 109 · 3546785903202467_<16> · 185105741159841547_<18> · C112

C112 = P43 · P70

P43 = 7988310259462790706409802227377510746398133_<43>

P70 = 1205071721783088836806307130889214158089504203258137865788043317649411_<70>

Number: 68883_146
N=9626486798508338321166672386969836655287169461778109422543113922006059190158733271959627346684232163256318949663
  ( 112 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=7988310259462790706409802227377510746398133
 r2=1205071721783088836806307130889214158089504203258137865788043317649411
Version: 
Total time: 6.61 hours.
Scaled time: 15.77 units (timescale=2.387).
Factorization parameters were as follows:
n: 9626486798508338321166672386969836655287169461778109422543113922006059190158733271959627346684232163256318949663
m: 100000000000000000000000000000
deg: 5
c5: 620
c0: -53
skew: 0.61
type: snfs
lss: 1
rlim: 2700000
alim: 2700000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2700000/2700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1350000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6538304
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 327576 x 327824
Total sieving time: 6.03 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,49,49,2.3,2.3,75000
total time: 6.61 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁴²+41)/9 = 7(4)₁₄₁9_<143> = 53 · 179 · 78816360949_<11> · C128

C128 = P31 · P32 · P66

P31 = 5118133093176327142512580486229_<31>

P32 = 27674980031210292772854978064813_<32>

P66 = 702891226094754909284926680011670954449302856594259786842594019299_<66>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 99560487302786486582644809814735788246936425457152388359549310276129385428030351314778327957138435828264320333796516810153455923 (128 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1716764280
Step 1 took 3338ms
Step 2 took 2186ms
********** Factor found in step 2: 5118133093176327142512580486229
Found probable prime factor of 31 digits: 5118133093176327142512580486229
Composite cofactor 19452500646285261173250463683416786680393536413987397222165417022651024930736875120889266594826087 has 98 digits

Number: 74449_142
N=19452500646285261173250463683416786680393536413987397222165417022651024930736875120889266594826087
  ( 98 digits)
Divisors found:
 r1=27674980031210292772854978064813
 r2=702891226094754909284926680011670954449302856594259786842594019299
Version: 
Total time: 1.87 hours.
Scaled time: 4.47 units (timescale=2.388).
Factorization parameters were as follows:
name: 74449_142
n: 19452500646285261173250463683416786680393536413987397222165417022651024930736875120889266594826087
skew: 5805.73
# norm 4.06e+13
c5: 35280
c4: 259186874
c3: -2930668561767
c2: 524670497488280
c1: -23868613045324035750
c0: -31419060311344238082400
# alpha -6.08
Y1: 13298192977
Y0: -3534166219473880023
# Murphy_E 4.66e-09
# M 8517735180229158762591976824665689918174103680536278391078828022506025160905842757400524632744508
type: gnfs
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [500000, 850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4177363
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 140601 x 140849
Polynomial selection time: 0.13 hours.
Total sieving time: 1.54 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000
total time: 1.87 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 4, 2009 (7th)

By Erik Branger / GGNFS, Msieve / Nov 4, 2009

(65·10¹⁹⁴+7)/9 = 7(2)₁₉₃3_<195> = 3⁴ · 7884797231020992193_<19> · 2877176822753658311521667_<25> · 7624190601160779016659090250310483321_<37> · C113

C113 = P54 · P60

P54 = 273052063919366325763016102592425759636306414864987143_<54>

P60 = 188794586580741684905644457692277873007482836138123024351931_<60>

Number: 72223_194
N=51550751522675018522266287786788814275048077732851829746459474778039978537603238494488272159493076802130222223133
  ( 113 digits)
Divisors found:
 r1=273052063919366325763016102592425759636306414864987143 (pp54)
 r2=188794586580741684905644457692277873007482836138123024351931 (pp60)
Version: Msieve-1.40
Total time: 26.12 hours.
Scaled time: 26.30 units (timescale=1.007).
Factorization parameters were as follows:
name: 72223_194
n: 51550751522675018522266287786788814275048077732851829746459474778039978537603238494488272159493076802130222223133
skew: 28101.07
# norm 2.49e+015
c5: 87480
c4: 1004856129
c3: -222070576128524
c2: -740136820656606496
c1: 74425772279683296958096
c0: 159258230282416511732846400
# alpha -5.86
Y1: 1063974041153
Y0: -3581499945924918201797
# Murphy_E 7.00e-010
# M 40610620651381900874736357795463379534833466793705614090822895704528946406243335529977265381704063465118931453860
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 432800 x 433031
Polynomial selection time: 2.11 hours.
Total sieving time: 23.07 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 26.12 hours.
 --------- CPU info (if available) ----------

(67·10¹¹⁸-31)/9 = 7(4)₁₁₇1_<119> = 431 · 3539 · 123923 · 1288218067_<10> · C99

C99 = P48 · P51

P48 = 479267594069721891682480549097268372227422319287_<48>

P51 = 637903656034309727455345127696823887454307086504547_<51>

Number: 74441_118
N=305726550475843054138201474310211542232754706418797583515046928519829271317105437137867816611297989
  ( 99 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=479267594069721891682480549097268372227422319287 (pp48)
 r2=637903656034309727455345127696823887454307086504547 (pp51)
Version: Msieve-1.40
Total time: 1.99 hours.
Scaled time: 2.01 units (timescale=1.010).
Factorization parameters were as follows:
n: 305726550475843054138201474310211542232754706418797583515046928519829271317105437137867816611297989
m: 500000000000000000000000
deg: 5
c5: 536
c0: -775
skew: 1.08
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 715001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 95723 x 95968
Total sieving time: 1.93 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.99 hours.
 --------- CPU info (if available) ----------

(67·10¹¹⁹+41)/9 = 7(4)₁₁₈9_<120> = 811 · 853 · 1039 · 333881591 · C103

C103 = P45 · P58

P45 = 727595767725356441642506603221253749877381111_<45>

P58 = 4263479919140776269933631073169481493401714827270904579177_<58>

Number: 74449_119
N=3102089944948873714259994593663261709240030517685023487311603560248802223498469606951297942226303725647
  ( 103 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=727595767725356441642506603221253749877381111 (pp45)
 r2=4263479919140776269933631073169481493401714827270904579177 (pp58)
Version: Msieve-1.40
Total time: 1.69 hours.
Scaled time: 1.67 units (timescale=0.987).
Factorization parameters were as follows:
n: 3102089944948873714259994593663261709240030517685023487311603560248802223498469606951297942226303725647
m: 1000000000000000000000000
deg: 5
c5: 67
c0: 410
skew: 1.44
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 675001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 95333 x 95575
Total sieving time: 1.63 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 1.69 hours.
 --------- CPU info (if available) ----------

(59·10¹⁷⁸+31)/9 = 6(5)₁₇₇9_<179> = 3² · 13² · 10671276340193789_<17> · 290179339919672299_<18> · 169217453948985191765727316229_<30> · C113

C113 = P46 · P67

P46 = 9637005396204158450469257031873149606840099171_<46>

P67 = 8535130676803352925904743730167548657372518054588374638333334952871_<67>

Number: 65559_178
N=82253100389661563231365197085823719682424676832690472227216104481816562001877507221746140576667601734398251169941
  ( 113 digits)
Divisors found:
 r1=9637005396204158450469257031873149606840099171 (pp46)
 r2=8535130676803352925904743730167548657372518054588374638333334952871 (pp67)
Version: Msieve-1.40
Total time: 25.72 hours.
Scaled time: 26.06 units (timescale=1.013).
Factorization parameters were as follows:
name: 65559_178
n: 82253100389661563231365197085823719682424676832690472227216104481816562001877507221746140576667601734398251169941
skew: 12858.02
# norm 8.46e+014
c5: 162060
c4: -2600632228
c3: -43692937574329
c2: 145313605466800506
c1: 4516704750475308887274
c0: 19446884015649887308035447
# alpha -4.68
Y1: 926005928683
Y0: -3476127198522949132180
# Murphy_E 6.68e-010
# M 50982245736449504221446289649068838682897607864980664373131986764254935603578078285367076831133484162907276979025
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 464548 x 464773
Polynomial selection time: 2.10 hours.
Total sieving time: 22.63 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.51 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 25.72 hours.
 --------- CPU info (if available) ----------

Nov 4, 2009 (6th)

By Sinkiti Sibata / Msieve, GGNFS / Nov 4, 2009

(62·10¹⁴⁷-17)/9 = 6(8)₁₄₆7_<148> = 433 · 21503 · 127314740505811_<15> · C127

C127 = P43 · P84

P43 = 7380239265137471589931683785983880322126223_<43>

P84 = 787432068869086227477331279235335612534521397355267720469263971274835068264710154221_<84>

Number: 68887_147
N=5811437073296063859169550612223697098994871055649316965880296678454586156059632707044651861383469849288953521078203648958237283
  ( 127 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=7380239265137471589931683785983880322126223 (pp43)
 r2=787432068869086227477331279235335612534521397355267720469263971274835068264710154221 (pp84)
Version: Msieve-1.40
Total time: 16.55 hours.
Scaled time: 34.61 units (timescale=2.092).
Factorization parameters were as follows:
name: 68887_147
n: 5811437073296063859169550612223697098994871055649316965880296678454586156059632707044651861383469849288953521078203648958237283
m: 200000000000000000000000000000
deg: 5
c5: 775
c0: -68
skew: 0.61
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 3100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 403004 x 403252
Total sieving time: 15.72 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.54 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,149.000,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000
total time: 16.55 hours.
 --------- CPU info (if available) ----------

(65·10¹⁴⁸+61)/9 = 7(2)₁₄₇9_<149> = 107 · 311 · 928044632639367136695800189501_<30> · C115

C115 = P56 · P59

P56 = 50242177561928748451743732864142031671748151278840517047_<56>

P59 = 46546750019341659505338843132529449656489198973335043828091_<59>

Number: 72229_148
N=2338610079402474063205803718148611082030518374643004494619329802098483811535795841671290368340696296730300622967277
  ( 115 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=50242177561928748451743732864142031671748151278840517047 (pp56)
 r2=46546750019341659505338843132529449656489198973335043828091 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 28.48 hours.
Scaled time: 56.48 units (timescale=1.983).
Factorization parameters were as follows:
name: 72229_148
n: 2338610079402474063205803718148611082030518374643004494619329802098483811535795841671290368340696296730300622967277
m: 500000000000000000000000000000
deg: 5
c5: 104
c0: 305
skew: 1.24
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 2050001)
Primes: RFBsize:169511, AFBsize:169717, largePrimes:7420057 encountered
Relations: rels:7854988, finalFF:832362
Max relations in full relation-set: 28
Initial matrix: 339294 x 832362 with sparse part having weight 97295036.
Pruned matrix : 241666 x 243426 with weight 37932161.
Total sieving time: 26.92 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.22 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 28.48 hours.
 --------- CPU info (if available) ----------

(67·10¹⁵⁰-31)/9 = 7(4)₁₄₉1_<151> = 691 · 877 · 32363 · 30693713 · 88802717 · 44229582577_<11> · 5862187185226627723561_<22> · C93

C93 = P41 · P53

P41 = 52149321682005352760460016522007528725573_<41>

P53 = 10299330898577574176970919887050802682776591407979701_<53>

Wed Nov 04 11:38:20 2009  Msieve v. 1.42
Wed Nov 04 11:38:20 2009  random seeds: 089ec948 20f939fa
Wed Nov 04 11:38:20 2009  factoring 537103120139339161837271430024183269497567761442391196882272189956546662230998950851183593673 (93 digits)
Wed Nov 04 11:38:21 2009  searching for 15-digit factors
Wed Nov 04 11:38:21 2009  commencing quadratic sieve (93-digit input)
Wed Nov 04 11:38:21 2009  using multiplier of 5
Wed Nov 04 11:38:21 2009  using 32kb Intel Core sieve core
Wed Nov 04 11:38:21 2009  sieve interval: 36 blocks of size 32768
Wed Nov 04 11:38:21 2009  processing polynomials in batches of 6
Wed Nov 04 11:38:21 2009  using a sieve bound of 1954487 (72941 primes)
Wed Nov 04 11:38:21 2009  using large prime bound of 244310875 (27 bits)
Wed Nov 04 11:38:21 2009  using double large prime bound of 1253998370578250 (42-51 bits)
Wed Nov 04 11:38:21 2009  using trial factoring cutoff of 51 bits
Wed Nov 04 11:38:21 2009  polynomial 'A' values have 12 factors
Wed Nov 04 14:26:40 2009  73249 relations (18003 full + 55246 combined from 1003555 partial), need 73037
Wed Nov 04 14:26:42 2009  begin with 1021558 relations
Wed Nov 04 14:26:43 2009  reduce to 190009 relations in 11 passes
Wed Nov 04 14:26:43 2009  attempting to read 190009 relations
Wed Nov 04 14:26:45 2009  recovered 190009 relations
Wed Nov 04 14:26:45 2009  recovered 173099 polynomials
Wed Nov 04 14:26:46 2009  attempting to build 73249 cycles
Wed Nov 04 14:26:46 2009  found 73249 cycles in 6 passes
Wed Nov 04 14:26:46 2009  distribution of cycle lengths:
Wed Nov 04 14:26:46 2009     length 1 : 18003
Wed Nov 04 14:26:46 2009     length 2 : 12924
Wed Nov 04 14:26:46 2009     length 3 : 12314
Wed Nov 04 14:26:46 2009     length 4 : 9925
Wed Nov 04 14:26:46 2009     length 5 : 7590
Wed Nov 04 14:26:46 2009     length 6 : 5002
Wed Nov 04 14:26:46 2009     length 7 : 3092
Wed Nov 04 14:26:46 2009     length 9+: 4399
Wed Nov 04 14:26:46 2009  largest cycle: 22 relations
Wed Nov 04 14:26:46 2009  matrix is 72941 x 73249 (18.7 MB) with weight 4614755 (63.00/col)
Wed Nov 04 14:26:46 2009  sparse part has weight 4614755 (63.00/col)
Wed Nov 04 14:26:47 2009  filtering completed in 3 passes
Wed Nov 04 14:26:47 2009  matrix is 69394 x 69458 (17.8 MB) with weight 4391238 (63.22/col)
Wed Nov 04 14:26:47 2009  sparse part has weight 4391238 (63.22/col)
Wed Nov 04 14:26:47 2009  saving the first 48 matrix rows for later
Wed Nov 04 14:26:47 2009  matrix is 69346 x 69458 (10.7 MB) with weight 3426212 (49.33/col)
Wed Nov 04 14:26:47 2009  sparse part has weight 2392857 (34.45/col)
Wed Nov 04 14:26:47 2009  matrix includes 64 packed rows
Wed Nov 04 14:26:47 2009  using block size 27783 for processor cache size 1024 kB
Wed Nov 04 14:26:48 2009  commencing Lanczos iteration
Wed Nov 04 14:26:48 2009  memory use: 11.2 MB
Wed Nov 04 14:27:19 2009  lanczos halted after 1098 iterations (dim = 69346)
Wed Nov 04 14:27:19 2009  recovered 18 nontrivial dependencies
Wed Nov 04 14:27:19 2009  prp41 factor: 52149321682005352760460016522007528725573
Wed Nov 04 14:27:19 2009  prp53 factor: 10299330898577574176970919887050802682776591407979701
Wed Nov 04 14:27:19 2009  elapsed time 02:48:59

(67·10¹³⁶-31)/9 = 7(4)₁₃₅1_<137> = 1229 · 2243 · 973091086236793_<15> · 31185773135760457_<17> · C99

C99 = P43 · P57

P43 = 4810783287458379447319665714720974617182731_<43>

P57 = 184980237899848999666716380766074086221876478826386870813_<57>

Number: 74441_136
N=889899836998668686633900800566801256698255608757109609947713814087374076702236000012655652911530303
  ( 99 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=4810783287458379447319665714720974617182731 (pp43)
 r2=184980237899848999666716380766074086221876478826386870813 (pp57)
Version: GGNFS-0.77.1-20060513-k8
Total time: 9.69 hours.
Scaled time: 18.94 units (timescale=1.956).
Factorization parameters were as follows:
name: 74441_136
n: 889899836998668686633900800566801256698255608757109609947713814087374076702236000012655652911530303
m: 2000000000000000000000000000
deg: 5
c5: 335
c0: -496
skew: 1.08
type: snfs
lss: 1
rlim: 1450000
alim: 1450000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1450000/1450000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [725000, 1550001)
Primes: RFBsize:110630, AFBsize:110790, largePrimes:3539552 encountered
Relations: rels:3573888, finalFF:316292
Max relations in full relation-set: 28
Initial matrix: 221487 x 316292 with sparse part having weight 29442668.
Pruned matrix : 194165 x 195336 with weight 14866622.
Total sieving time: 9.16 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000
total time: 9.69 hours.
 --------- CPU info (if available) ----------

(67·10¹⁵⁸-31)/9 = 7(4)₁₅₇1_<159> = 3 · 13 · 47 · 7057 · 8995960241_<10> · 311380275064099_<15> · 693785995312617674467398121_<27> · C101

C101 = P50 · P51

P50 = 93224551460111137035240108268625574954487489831903_<50>

P51 = 317654677042421270612800208132930793843765449092733_<51>

Number: 74441_158
N=29613214786486185544278227521549428503432789847535163482886575624753396192189049354232057714028860899
  ( 101 digits)
Divisors found:
 r1=93224551460111137035240108268625574954487489831903 (pp50)
 r2=317654677042421270612800208132930793843765449092733 (pp51)
Version: Msieve-1.40
Total time: 5.22 hours.
Scaled time: 17.25 units (timescale=3.305).
Factorization parameters were as follows:
name: 74441_158
n: 29613214786486185544278227521549428503432789847535163482886575624753396192189049354232057714028860899
skew: 2475.53
# norm 7.83e+13
c5: 286800
c4: -2941514404
c3: 3174525952836
c2: 18842763152668317
c1: 16056592382406591394
c0: 4443972655071256500177
# alpha -4.91
Y1: 60202425107
Y0: -10064370379691956090
# Murphy_E 3.01e-09
# M 5135300505416392765969601109169315018788510709089396459401407529503863629792793102008601301469075470
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 214611 x 214859
Polynomial selection time: 0.55 hours.
Total sieving time: 4.53 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 5.22 hours.
 --------- CPU info (if available) ----------

(67·10¹⁶⁷-31)/9 = 7(4)₁₆₆1_<168> = 3 · 97 · 1789 · 13892257 · 96862933 · 31292114101_<11> · 51882071872753_<14> · 186886300862329234750824700241_<30> · C94

C94 = P38 · P56

P38 = 84574198791351340668356637482340533647_<38>

P56 = 41412453686437193224539957363738958943723854038718898569_<56>

Wed Nov 04 14:47:54 2009  Msieve v. 1.42
Wed Nov 04 14:47:54 2009  random seeds: b7fa92a0 b09111fb
Wed Nov 04 14:47:54 2009  factoring 3502425090514369839464801792831352863378564620939980353829959014019250494360162188995524651143 (94 digits)
Wed Nov 04 14:47:55 2009  searching for 15-digit factors
Wed Nov 04 14:47:55 2009  commencing quadratic sieve (94-digit input)
Wed Nov 04 14:47:55 2009  using multiplier of 7
Wed Nov 04 14:47:55 2009  using 32kb Intel Core sieve core
Wed Nov 04 14:47:55 2009  sieve interval: 36 blocks of size 32768
Wed Nov 04 14:47:55 2009  processing polynomials in batches of 6
Wed Nov 04 14:47:55 2009  using a sieve bound of 2025253 (75248 primes)
Wed Nov 04 14:47:55 2009  using large prime bound of 271383902 (28 bits)
Wed Nov 04 14:47:55 2009  using double large prime bound of 1515134967946490 (42-51 bits)
Wed Nov 04 14:47:55 2009  using trial factoring cutoff of 51 bits
Wed Nov 04 14:47:55 2009  polynomial 'A' values have 12 factors
Wed Nov 04 17:50:50 2009  75673 relations (18625 full + 57048 combined from 1070859 partial), need 75344
Wed Nov 04 17:50:51 2009  begin with 1089484 relations
Wed Nov 04 17:50:52 2009  reduce to 195943 relations in 11 passes
Wed Nov 04 17:50:52 2009  attempting to read 195943 relations
Wed Nov 04 17:50:55 2009  recovered 195943 relations
Wed Nov 04 17:50:55 2009  recovered 179427 polynomials
Wed Nov 04 17:50:56 2009  attempting to build 75673 cycles
Wed Nov 04 17:50:56 2009  found 75673 cycles in 6 passes
Wed Nov 04 17:50:56 2009  distribution of cycle lengths:
Wed Nov 04 17:50:56 2009     length 1 : 18625
Wed Nov 04 17:50:56 2009     length 2 : 13525
Wed Nov 04 17:50:56 2009     length 3 : 12818
Wed Nov 04 17:50:56 2009     length 4 : 10120
Wed Nov 04 17:50:56 2009     length 5 : 7691
Wed Nov 04 17:50:56 2009     length 6 : 5105
Wed Nov 04 17:50:56 2009     length 7 : 3291
Wed Nov 04 17:50:56 2009     length 9+: 4498
Wed Nov 04 17:50:56 2009  largest cycle: 20 relations
Wed Nov 04 17:50:56 2009  matrix is 75248 x 75673 (19.9 MB) with weight 4909489 (64.88/col)
Wed Nov 04 17:50:56 2009  sparse part has weight 4909489 (64.88/col)
Wed Nov 04 17:50:57 2009  filtering completed in 3 passes
Wed Nov 04 17:50:57 2009  matrix is 71566 x 71630 (18.9 MB) with weight 4655436 (64.99/col)
Wed Nov 04 17:50:57 2009  sparse part has weight 4655436 (64.99/col)
Wed Nov 04 17:50:57 2009  saving the first 48 matrix rows for later
Wed Nov 04 17:50:57 2009  matrix is 71518 x 71630 (12.2 MB) with weight 3691149 (51.53/col)
Wed Nov 04 17:50:57 2009  sparse part has weight 2758033 (38.50/col)
Wed Nov 04 17:50:57 2009  matrix includes 64 packed rows
Wed Nov 04 17:50:57 2009  using block size 28652 for processor cache size 1024 kB
Wed Nov 04 17:50:58 2009  commencing Lanczos iteration
Wed Nov 04 17:50:58 2009  memory use: 12.2 MB
Wed Nov 04 17:51:32 2009  lanczos halted after 1132 iterations (dim = 71517)
Wed Nov 04 17:51:32 2009  recovered 17 nontrivial dependencies
Wed Nov 04 17:51:33 2009  prp38 factor: 84574198791351340668356637482340533647
Wed Nov 04 17:51:33 2009  prp56 factor: 41412453686437193224539957363738958943723854038718898569
Wed Nov 04 17:51:33 2009  elapsed time 03:03:39

(67·10¹³¹+41)/9 = 7(4)₁₃₀9_<132> = 79 · 18493896401067727171723339878571_<32> · C99

C99 = P37 · P63

P37 = 4525308800973640811158291449529412591_<37>

P63 = 112597451591228804139139623565260342727756344221799002605550371_<63>

Number: 74449_131
N=509538238652991184285965430122845534851877702982919855855689867384284811642128713318697751892121261
  ( 99 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=4525308800973640811158291449529412591 (pp37)
 r2=112597451591228804139139623565260342727756344221799002605550371 (pp63)
Version: Msieve-1.40
Total time: 3.42 hours.
Scaled time: 11.42 units (timescale=3.339).
Factorization parameters were as follows:
name: 74449_131
n: 509538238652991184285965430122845534851877702982919855855689867384284811642128713318697751892121261
m: 100000000000000000000000000
deg: 5
c5: 670
c0: 41
skew: 0.57
type: snfs
lss: 1
rlim: 1150000
alim: 1150000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1150000/1150000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [575000, 1175001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 178722 x 178970
Total sieving time: 3.32 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,132.000,5,0,0,0,0,0,0,0,0,1150000,1150000,26,26,47,47,2.3,2.3,50000
total time: 3.42 hours.
 --------- CPU info (if available) ----------

Nov 4, 2009 (5th)

By Dmitry Domanov / GGNFS/msieve / Nov 4, 2009

(65·10¹⁴⁹-11)/9 = 7(2)₁₄₈1_<150> = 229 · 10309737107_<11> · C138

C138 = P61 · P78

P61 = 1760809446734728886340349673660727500140667053250604025945597_<61>

P78 = 173730237829917538457626291929595253008299451778851719371130464180604004301231_<78>

Number: 138-1
N=305905843954389967281676045820831821698738895584262287043064623509243937335538029868173413204853119730514843003514032989035405710006129907
  ( 138 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=1760809446734728886340349673660727500140667053250604025945597 (pp61)
 r2=173730237829917538457626291929595253008299451778851719371130464180604004301231 (pp78)
Version: Msieve-1.40
Total time: 11.49 hours.
Scaled time: 21.02 units (timescale=1.829).
Factorization parameters were as follows:
n: 305905843954389967281676045820831821698738895584262287043064623509243937335538029868173413204853119730514843003514032989035405710006129907
m: 1000000000000000000000000000000
deg: 5
c5: 13
c0: -22
skew: 1.11
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 379854 x 380082
Total sieving time: 11.15 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 11.49 hours.
 --------- CPU info (if available) ----------

(62·10¹⁴⁹+1)/9 = 6(8)₁₄₈9_<150> = 20483 · 1451521 · C140

C140 = P46 · P95

P46 = 2159958576333471630827291022074668095705599543_<46>

P95 = 10727212141443721091591595069382603712040863221467467516173427204992746524141860104161935808261_<95>

Number: 140-1
N=23170333865059911320172901781817463495296432410996862069873982088491668836825268806120304124323254449187510933228247007723728437099297224723
  ( 140 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=2159958576333471630827291022074668095705599543 (pp46)
 r2=10727212141443721091591595069382603712040863221467467516173427204992746524141860104161935808261 (pp95)
Version: Msieve-1.40
Total time: 11.72 hours.
Scaled time: 21.56 units (timescale=1.839).
Factorization parameters were as follows:
n: 23170333865059911320172901781817463495296432410996862069873982088491668836825268806120304124323254449187510933228247007723728437099297224723
m: 1000000000000000000000000000000
deg: 5
c5: 31
c0: 5
skew: 0.69
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 347406 x 347631
Total sieving time: 11.26 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 11.72 hours.
 --------- CPU info (if available) ----------

(62·10¹⁵⁰-53)/9 = 6(8)₁₄₉3_<151> = 29 · 9210591331619_<13> · C137

C137 = P63 · P74

P63 = 661875852763457366391885680418340090691973432419556589889316841_<63>

P74 = 38966117144008027984903360062825590816642015961644316334865082860882091613_<74>

Number: 137-1
N=25790732013571089390629829637694401439543992384512237925102922325233751728027886870816186678957658224553701159626991355378692243745754533
  ( 137 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=661875852763457366391885680418340090691973432419556589889316841 (pp63)
 r2=38966117144008027984903360062825590816642015961644316334865082860882091613 (pp74)
Version: Msieve-1.40
Total time: 14.57 hours.
Scaled time: 27.09 units (timescale=1.860).
Factorization parameters were as follows:
n: 25790732013571089390629829637694401439543992384512237925102922325233751728027886870816186678957658224553701159626991355378692243745754533
m: 1000000000000000000000000000000
deg: 5
c5: 62
c0: -53
skew: 0.97
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 2100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 416838 x 417064
Total sieving time: 14.21 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 14.57 hours.
 --------- CPU info (if available) ----------

(67·10¹¹⁵+41)/9 = 7(4)₁₁₄9_<116> = C116

C116 = P44 · P72

P44 = 75238973175295618288828136185615790213603981_<44>

P72 = 989439931230852392677882277821169072176642871144176663604322784136109029_<72>

Number: s116
N=74444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
  ( 116 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=75238973175295618288828136185615790213603981 (pp44)
 r2=989439931230852392677882277821169072176642871144176663604322784136109029 (pp72)
Version: Msieve-1.40
Total time: 0.85 hours.
Scaled time: 1.52 units (timescale=1.793).
Factorization parameters were as follows:
n: 74444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
m: 100000000000000000000000
deg: 5
c5: 67
c0: 41
skew: 0.91
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 510001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 64899 x 65124
Total sieving time: 0.82 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116.000,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 0.85 hours.
 --------- CPU info (if available) ----------

(22·10¹⁵²+17)/3 = 7(3)₁₅₁9_<153> = 1753 · 95413 · C145

C145 = P68 · P78

P68 = 37075204362561186462930457952094323461588666020443762432927480355047_<68>

P78 = 118257421447605116816883585559520072232239649472035949275385244191705024440833_<78>

Number: 145-1
N=4384418067559486045520299858642176375544954019382081362056620665890389504466832173267132048330947004189612394065907772127770862786533603484434151
  ( 145 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=37075204362561186462930457952094323461588666020443762432927480355047 (pp68)
 r2=118257421447605116816883585559520072232239649472035949275385244191705024440833 (pp78)
Version: Msieve-1.40
Total time: 15.24 hours.
Scaled time: 26.72 units (timescale=1.753).
Factorization parameters were as follows:
n: 4384418067559486045520299858642176375544954019382081362056620665890389504466832173267132048330947004189612394065907772127770862786533603484434151
m: 2000000000000000000000000000000
deg: 5
c5: 275
c0: 68
skew: 0.76
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2200001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 422616 x 422841
Total sieving time: 14.81 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,153.000,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 15.24 hours.
 --------- CPU info (if available) ----------

(67·10¹²²+41)/9 = 7(4)₁₂₁9_<123> = 7 · 6101 · 1433828959_<10> · C110

C110 = P45 · P65

P45 = 799833486774886669446684467145607740034837573_<45>

P65 = 15199744852895041003829511211189301714478486024060607047766140001_<65>

Number: s110
N=12157264923779677503705120562162102877408669455504567715147187442947226381072628485040055315520075129213057573
  ( 110 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=799833486774886669446684467145607740034837573 (pp45)
 r2=15199744852895041003829511211189301714478486024060607047766140001 (pp65)
Version: Msieve-1.40
Total time: 2.10 hours.
Scaled time: 4.13 units (timescale=1.969).
Factorization parameters were as follows:
n: 12157264923779677503705120562162102877408669455504567715147187442947226381072628485040055315520075129213057573
m: 2000000000000000000000000
deg: 5
c5: 1675
c0: 328
skew: 0.72
type: snfs
lss: 1
rlim: 840000
alim: 840000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 840000/840000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [420000, 920001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 109064 x 109289
Total sieving time: 2.03 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,124.000,5,0,0,0,0,0,0,0,0,840000,840000,25,25,46,46,2.2,2.2,50000
total time: 2.10 hours.
 --------- CPU info (if available) ----------

(67·10¹²⁹+41)/9 = 7(4)₁₂₈9_<130> = 3 · 13 · 53 · 12241 · C123

C123 = P50 · P73

P50 = 31174567399065703189714283064966059346296400375499_<50>

P73 = 9437880695028528118480341072386914262636733329993003874835658761941901633_<73>

Number: s123
N=294221847831507912923138279310623104215007700510333942982958894533513082682052414146690573113990857947526921112443321289867
  ( 123 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=31174567399065703189714283064966059346296400375499 (pp50)
 r2=9437880695028528118480341072386914262636733329993003874835658761941901633 (pp73)
Version: Msieve-1.40
Total time: 2.51 hours.
Scaled time: 4.95 units (timescale=1.969).
Factorization parameters were as follows:
n: 294221847831507912923138279310623104215007700510333942982958894533513082682052414146690573113990857947526921112443321289867
m: 100000000000000000000000000
deg: 5
c5: 67
c0: 410
skew: 1.44
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 157655 x 157880
Total sieving time: 2.41 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.51 hours.
 --------- CPU info (if available) ----------

Nov 4, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 4, 2009

(59·10¹⁶³+31)/9 = 6(5)₁₆₂9_<164> = 3 · 32818728326958597007_<20> · 30206450459581731645292633773887341_<35> · C110

C110 = P38 · P72

P38 = 28333720901589950932983121220696385373_<38>

P72 = 777970613242584704317750496597008213030025384705460732425451218674131803_<72>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1029933060
Step 1 took 30438ms
Step 2 took 12835ms
********** Factor found in step 2: 28333720901589950932983121220696385373
Found probable prime factor of 38 digits: 28333720901589950932983121220696385373
Probable prime cofactor 777970613242584704317750496597008213030025384705460732425451218674131803 has 72 digits

Nov 4, 2009 (3rd)

By Robert Backstrom / Msieve, GGNFS / Nov 4, 2009

(67·10¹¹⁵-31)/9 = 7(4)₁₁₄1_<116> = 23 · 1303 · 2584579451_<10> · 10003719409_<11> · C92

C92 = P38 · P55

P38 = 13606100517264678251735534718702197189_<38>

P55 = 7061142524531661338165749232263043327688308648736184639_<55>

Wed Nov 04 03:16:06 2009  
Wed Nov 04 03:16:06 2009  
Wed Nov 04 03:16:06 2009  Msieve v. 1.43
Wed Nov 04 03:16:06 2009  random seeds: 60f2ff78 55277435
Wed Nov 04 03:16:06 2009  factoring 96074614955509853374734392658394094992047014932306016222428043900796653215149734058090779771 (92 digits)
Wed Nov 04 03:16:07 2009  searching for 15-digit factors
Wed Nov 04 03:16:07 2009  commencing quadratic sieve (92-digit input)
Wed Nov 04 03:16:08 2009  using multiplier of 29
Wed Nov 04 03:16:08 2009  using 64kb Opteron sieve core
Wed Nov 04 03:16:08 2009  sieve interval: 18 blocks of size 65536
Wed Nov 04 03:16:08 2009  processing polynomials in batches of 6
Wed Nov 04 03:16:08 2009  using a sieve bound of 1847539 (69412 primes)
Wed Nov 04 03:16:08 2009  using large prime bound of 208771907 (27 bits)
Wed Nov 04 03:16:08 2009  using double large prime bound of 944951756339680 (42-50 bits)
Wed Nov 04 03:16:08 2009  using trial factoring cutoff of 50 bits
Wed Nov 04 03:16:08 2009  polynomial 'A' values have 12 factors
Wed Nov 04 03:16:08 2009  restarting with 2240 full and 114056 partial relations
Wed Nov 04 04:40:28 2009  69576 relations (17880 full + 51696 combined from 889191 partial), need 69508
Wed Nov 04 04:40:29 2009  begin with 907071 relations
Wed Nov 04 04:40:29 2009  reduce to 175853 relations in 12 passes
Wed Nov 04 04:40:29 2009  attempting to read 175853 relations
Wed Nov 04 04:40:31 2009  recovered 175853 relations
Wed Nov 04 04:40:31 2009  recovered 157201 polynomials
Wed Nov 04 04:40:31 2009  attempting to build 69576 cycles
Wed Nov 04 04:40:31 2009  found 69576 cycles in 5 passes
Wed Nov 04 04:40:31 2009  distribution of cycle lengths:
Wed Nov 04 04:40:31 2009     length 1 : 17880
Wed Nov 04 04:40:31 2009     length 2 : 12677
Wed Nov 04 04:40:31 2009     length 3 : 12033
Wed Nov 04 04:40:31 2009     length 4 : 9369
Wed Nov 04 04:40:31 2009     length 5 : 6758
Wed Nov 04 04:40:31 2009     length 6 : 4430
Wed Nov 04 04:40:31 2009     length 7 : 2778
Wed Nov 04 04:40:31 2009     length 9+: 3651
Wed Nov 04 04:40:31 2009  largest cycle: 19 relations
Wed Nov 04 04:40:32 2009  matrix is 69412 x 69576 (17.7 MB) with weight 4370660 (62.82/col)
Wed Nov 04 04:40:32 2009  sparse part has weight 4370660 (62.82/col)
Wed Nov 04 04:40:33 2009  filtering completed in 3 passes
Wed Nov 04 04:40:33 2009  matrix is 65447 x 65511 (16.8 MB) with weight 4148934 (63.33/col)
Wed Nov 04 04:40:33 2009  sparse part has weight 4148934 (63.33/col)
Wed Nov 04 04:40:33 2009  saving the first 48 matrix rows for later
Wed Nov 04 04:40:33 2009  matrix is 65399 x 65511 (10.2 MB) with weight 3230916 (49.32/col)
Wed Nov 04 04:40:33 2009  sparse part has weight 2284762 (34.88/col)
Wed Nov 04 04:40:33 2009  matrix includes 64 packed rows
Wed Nov 04 04:40:33 2009  using block size 26204 for processor cache size 1024 kB
Wed Nov 04 04:40:33 2009  commencing Lanczos iteration
Wed Nov 04 04:40:33 2009  memory use: 10.5 MB
Wed Nov 04 04:40:42 2009  linear algebra at 36.8%, ETA 0h 0m
Wed Nov 04 04:40:58 2009  lanczos halted after 1036 iterations (dim = 65397)
Wed Nov 04 04:40:58 2009  recovered 17 nontrivial dependencies
Wed Nov 04 04:40:59 2009  prp38 factor: 13606100517264678251735534718702197189
Wed Nov 04 04:40:59 2009  prp55 factor: 7061142524531661338165749232263043327688308648736184639
Wed Nov 04 04:40:59 2009  elapsed time 01:24:53

(67·10¹¹⁸+41)/9 = 7(4)₁₁₇9_<119> = 79 · 307 · 14737 · C111

C111 = P51 · P60

P51 = 394121494818965174452737614446926695666843079535589_<51>

P60 = 528478862616451509745863971040078685044093400122478146340481_<60>

Number: n
N=208284879314622401916862034075270093518284946714987602220269436455654582860537149251344762334391880301350878309
  ( 111 digits)
SNFS difficulty: 121 digits.
Divisors found:

Wed Nov 04 16:21:19 2009  prp51 factor: 394121494818965174452737614446926695666843079535589
Wed Nov 04 16:21:19 2009  prp60 factor: 528478862616451509745863971040078685044093400122478146340481
Wed Nov 04 16:21:19 2009  elapsed time 00:03:01 (Msieve 1.43 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.55 hours.
Scaled time: 2.83 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_7_4_117_9
n: 208284879314622401916862034075270093518284946714987602220269436455654582860537149251344762334391880301350878309
m: 500000000000000000000000
deg: 5
c5: 536
c0: 1025
skew: 1.14
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
qintsize: 20000
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved  special-q in [365000, 731243)
Primes: RFBsize:58789, AFBsize:58652, largePrimes:1288707 encountered
Relations: rels:1226476, finalFF:120008
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 114038 hash collisions in 1344703 relations
Msieve: matrix is 96123 x 96371 (25.5 MB)

Total sieving time: 1.53 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.55 hours.
 --------- CPU info (if available) ----------

Nov 4, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Nov 4, 2009

(65·10¹⁶⁹-11)/9 = 7(2)₁₆₈1_<170> = 7283 · C166

C166 = P55 · P112

P55 = 4542588659828027852927753185791967431732095768199561187_<55>

P112 = 2183017035769276937291582142435683590937076880103696235615273791181575193188745388390184796157340731360291701301_<112>

Number: 72221_169
N=9916548430896913665003737775947030375150655255007856957602941400826887576853250339451080903778967763589485407417578226310891421422795856408378720612690130745877004287
  ( 166 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=4542588659828027852927753185791967431732095768199561187 (pp55)
 r2=2183017035769276937291582142435683590937076880103696235615273791181575193188745388390184796157340731360291701301 (pp112)
Version: Msieve v. 1.43
Total time: 55.07 hours.
Scaled time: 95.77 units (timescale=1.739).
Factorization parameters were as follows:
n: 9916548430896913665003737775947030375150655255007856957602941400826887576853250339451080903778967763589485407417578226310891421422795856408378720612690130745877004287
m: 10000000000000000000000000000000000
deg: 5
c5: 13
c0: -22
skew: 1.11
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 948039 x 948264
Total sieving time: 53.64 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.18 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 55.07 hours.

Nov 4, 2009

By Markus Tervooren / Msieve / Nov 4, 2009

(19·10¹⁷¹+71)/9 = 2(1)₁₇₀9_<172> = 13² · 66191 · 54788299 · C157

C157 = P53 · P104

P53 = 36770347511060861410054629572166650094512885628335317_<53>

P104 = 93678492425462393852818727293289502166124539235947642213770088451030209181339994735034641839970928805567_<104>

Sieving: ~200M Rels @ 0.00076secs/rel, 43 Hours total

rlim: 12000000
alim: 12000000
lpbr: 33
lpba: 33
mfbr: 65
mfba: 65
rlambda: 2.6
alambda: 2.6

Msieve v. 1.43
Tue Nov  3 13:48:17 2009
random seeds: dc994ee7 1f3797af
factoring 3444590720796534891970900366617273075288864508894370522444950161612774095027857693356068550244426897682148456369374381691702403566455224593338052625372309739 (157 digits)
searching for 15-digit factors
commencing number field sieve (157-digit input)
R0: -10000000000000000000000000000000000
R1:  1
A0:  71
A1:  0
A2:  0
A3:  0
A4:  0
A5:  190
skew 0.82, size 2.796412e-12, alpha 1.603695, combined = 1.575994e-10

commencing relation filtering
estimated available RAM is 8010.2 MB
commencing duplicate removal, pass 1
error -11 reading relation 42019041
error -9 reading relation 83306597
error -11 reading relation 141242284
error -6 reading relation 141242342
error -11 reading relation 141242368
error -11 reading relation 141242384
error -6 reading relation 141242387
error -6 reading relation 141242425
error -6 reading relation 141242455
error -11 reading relation 141242501
error -11 reading relation 141242542
error -11 reading relation 141242553
error -11 reading relation 180726972
error -11 reading relation 180727060
error -11 reading relation 180727075
error -11 reading relation 180727116
error -11 reading relation 180727119
error -11 reading relation 180727135
error -11 reading relation 180727207
error -6 reading relation 180727245
error -11 reading relation 180727254
error -11 reading relation 180727292
error -6 reading relation 180749356
error -11 reading relation 180749523
error -11 reading relation 189285988
error -11 reading relation 189286082
error -11 reading relation 189286097
error -6 reading relation 189286104
error -11 reading relation 189286184
error -11 reading relation 189286215
error -6 reading relation 197048646
error -6 reading relation 197048659
found 19055345 hash collisions in 203204031 relations
commencing duplicate removal, pass 2
found 12204124 duplicates and 190999907 unique relations
memory use: 788.8 MB
reading ideals above 47775744
commencing singleton removal, initial pass
memory use: 6024.0 MB
reading all ideals from disk
memory use: 3283.9 MB
commencing in-memory singleton removal
begin with 190999907 relations and 224304224 unique ideals
reduce to 35532778 relations and 23616995 ideals in 21 passes
max relations containing the same ideal: 23
reading ideals above 720000
commencing singleton removal, initial pass
memory use: 753.0 MB
reading all ideals from disk
memory use: 1144.1 MB
keeping 29131945 ideals with weight <= 200, target excess is 228616
commencing in-memory singleton removal
begin with 35532778 relations and 29131945 unique ideals
reduce to 35435748 relations and 29034868 ideals in 17 passes
max relations containing the same ideal: 200
removing 3757157 relations and 3357157 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 31678591 relations and 29034868 unique ideals
reduce to 31452550 relations and 25448201 ideals in 9 passes
max relations containing the same ideal: 193
removing 2631341 relations and 2231341 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 28821209 relations and 25448201 unique ideals
reduce to 28692432 relations and 23086444 ideals in 8 passes
max relations containing the same ideal: 189
removing 2262214 relations and 1862214 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 26430218 relations and 23086444 unique ideals
reduce to 26326344 relations and 21119040 ideals in 7 passes
max relations containing the same ideal: 180
removing 2053924 relations and 1653924 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 24272420 relations and 21119040 unique ideals
reduce to 24181657 relations and 19373112 ideals in 8 passes
max relations containing the same ideal: 173
removing 1904878 relations and 1504878 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 22276779 relations and 19373112 unique ideals
reduce to 22189508 relations and 17779698 ideals in 7 passes
max relations containing the same ideal: 162
removing 1798573 relations and 1398573 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 20390935 relations and 17779698 unique ideals
reduce to 20304028 relations and 16292889 ideals in 7 passes
max relations containing the same ideal: 153
removing 1716636 relations and 1316636 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 18587392 relations and 16292889 unique ideals
reduce to 18505170 relations and 14892697 ideals in 6 passes
max relations containing the same ideal: 148
removing 1648470 relations and 1248470 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 16856700 relations and 14892697 unique ideals
reduce to 16772185 relations and 13558246 ideals in 7 passes
max relations containing the same ideal: 143
removing 1586891 relations and 1186891 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 15185294 relations and 13558246 unique ideals
reduce to 15093866 relations and 12278107 ideals in 6 passes
max relations containing the same ideal: 134
removing 1541129 relations and 1141129 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 13552737 relations and 12278107 unique ideals
reduce to 13458160 relations and 11040351 ideals in 6 passes
max relations containing the same ideal: 131
removing 1498638 relations and 1098638 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 11959522 relations and 11040351 unique ideals
reduce to 11854632 relations and 9834292 ideals in 7 passes
max relations containing the same ideal: 119
removing 1469127 relations and 1069127 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 10385505 relations and 9834292 unique ideals
reduce to 10270302 relations and 8646644 ideals in 8 passes
max relations containing the same ideal: 105
removing 1437254 relations and 1037254 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 8833048 relations and 8646644 unique ideals
reduce to 8699917 relations and 7471726 ideals in 7 passes
max relations containing the same ideal: 91
removing 1420498 relations and 1020498 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 7279419 relations and 7471726 unique ideals
reduce to 7131989 relations and 6298123 ideals in 8 passes
max relations containing the same ideal: 80
removing 1400326 relations and 1000326 ideals in 400000 cliques
commencing in-memory singleton removal
begin with 5731663 relations and 6298123 unique ideals
reduce to 5546349 relations and 5103685 ideals in 9 passes
max relations containing the same ideal: 64
removing 757743 relations and 580274 ideals in 177469 cliques
commencing in-memory singleton removal
begin with 4788606 relations and 5103685 unique ideals
reduce to 4717295 relations and 4450118 ideals in 7 passes
max relations containing the same ideal: 59
relations with 0 large ideals: 5175
relations with 1 large ideals: 19840
relations with 2 large ideals: 124171
relations with 3 large ideals: 447449
relations with 4 large ideals: 956838
relations with 5 large ideals: 1277456
relations with 6 large ideals: 1118098
relations with 7+ large ideals: 768268
commencing 2-way merge
reduce to 2954600 relation sets and 2687423 unique ideals
commencing full merge
memory use: 304.6 MB
found 1500953 cycles, need 1463623
weight of 1463623 cycles is about 102593098 (70.10/cycle)
distribution of cycle lengths:
1 relations: 142922
2 relations: 150396
3 relations: 161403
4 relations: 160081
5 relations: 152703
6 relations: 138807
7 relations: 121703
8 relations: 102796
9 relations: 84561
10+ relations: 248251
heaviest cycle: 20 relations
commencing cycle optimization
start with 8578451 relations
pruned 224613 relations
memory use: 278.0 MB
distribution of cycle lengths:
1 relations: 142922
2 relations: 153537
3 relations: 166845
4 relations: 164248
5 relations: 157743
6 relations: 142321
7 relations: 124060
8 relations: 103421
9 relations: 84487
10+ relations: 224039
heaviest cycle: 19 relations
RelProcTime: 5988

commencing linear algebra
read 1463623 cycles
cycles contain 4542980 unique relations
read 4542980 relations
using 20 quadratic characters above 4294609058
building initial matrix
memory use: 570.6 MB
read 1463623 cycles
matrix is 1463440 x 1463623 (438.2 MB) with weight 129707074 (88.62/col)
sparse part has weight 98784045 (67.49/col)
filtering completed in 2 passes
matrix is 1461933 x 1462116 (438.1 MB) with weight 129652551 (88.67/col)
sparse part has weight 98760802 (67.55/col)
read 1462116 cycles
matrix is 1461933 x 1462116 (438.1 MB) with weight 129652551 (88.67/col)
sparse part has weight 98760802 (67.55/col)
saving the first 48 matrix rows for later
matrix is 1461885 x 1462116 (414.7 MB) with weight 102322884 (69.98/col)
sparse part has weight 94100608 (64.36/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (4 threads)
memory use: 444.3 MB
linear algebra at 0.1%, ETA 3h12m462116 dimensions (0.1%, ETA 3h12m)
linear algebra completed 1461694 of 1462116 dimensions (100.0%, ETA 0h 0m)    5m)
lanczos halted after 23120 iterations (dim = 1461880)
recovered 34 nontrivial dependencies
BLanczosTime: 11908

commencing square root phase
reading relations for dependency 1
read 730527 cycles
cycles contain 2268188 unique relations
read 2268188 relations
multiplying 2268188 relations
multiply complete, coefficients have about 70.08 million bits
initial square root is modulo 107251
sqrtTime: 758
prp53 factor: 36770347511060861410054629572166650094512885628335317
prp104 factor: 93678492425462393852818727293289502166124539235947642213770088451030209181339994735034641839970928805567
elapsed time 05:10:56

Nov 3, 2009 (9th)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39, YAFU v1.10 / Nov 3, 2009

(62·10¹⁵⁰+1)/9 = 6(8)₁₄₉9_<151> = 7 · 61 · 335899951 · 631812782018320361_<18> · C122

C122 = P32 · P91

P32 = 12191688122843586596710384365301_<32>

P91 = 6235325251854743704987134113434328800026549545253723826064948248579721224281529557691548137_<91>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 76019140815104174106040378633604961828787051133016498888962165752162413165265840336691286063511280469440153338034833994237 (122 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5303952899
Step 1 took 4180ms
Step 2 took 4072ms
********** Factor found in step 2: 12191688122843586596710384365301
Found probable prime factor of 32 digits: 12191688122843586596710384365301
Probable prime cofactor 6235325251854743704987134113434328800026549545253723826064948248579721224281529557691548137 has 91 digits

2·10¹⁹²-1 = 1(9)₁₉₂_<193> = 13126437311707103_<17> · 151419514294581983_<18> · C160

C160 = P59 · P101

P59 = 34800207118492911860248366555234613008736732153524878679537_<59>

P101 = 28914750508730044277748248804535726260023740804371880053958065619493865157416478604450813537747698223_<101>

Number: 19999_192
N=1006239306483353831476825306401787972745351092928340869203919022242287714541569486966508596822901307295892131075739094628996817962709248807383479467349401362751
  ( 160 digits)
SNFS difficulty: 192 digits.
Divisors found:
 r1=34800207118492911860248366555234613008736732153524878679537
 r2=28914750508730044277748248804535726260023740804371880053958065619493865157416478604450813537747698223
Version: 
Total time: 185.08 hours.
Scaled time: 442.16 units (timescale=2.389).
Factorization parameters were as follows:
n: 1006239306483353831476825306401787972745351092928340869203919022242287714541569486966508596822901307295892131075739094628996817962709248807383479467349401362751
m: 200000000000000000000000000000000000000
deg: 5
c5: 25
c0: -4
skew: 0.69
type: snfs
lss: 1
rlim: 11000000
alim: 11000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [5500000, 10000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 22159829
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2122554 x 2122801
Total sieving time: 166.68 hours.
Total relation processing time: 5.41 hours.
Matrix solve time: 12.11 hours.
Time per square root: 0.89 hours.
Prototype def-par.txt line would be:
snfs,192,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,55,55,2.5,2.5,100000
total time: 185.08 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁰⁴+41)/9 = 7(4)₁₀₃9_<105> = 7² · 8677 · C100

C100 = P30 · P70

P30 = 386165004928233317676708760481_<30>

P70 = 4534127216695181047132731334402401495791222239561382135000425713957373_<70>

Number: 74449_104
N=1750921258980331404967964674248939712645074932896596078406776640201622502944553027695654344100976413
  ( 100 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=386165004928233317676708760481
 r2=4534127216695181047132731334402401495791222239561382135000425713957373
Version: 
Total time: 0.22 hours.
Scaled time: 0.52 units (timescale=2.385).
Factorization parameters were as follows:
n: 1750921258980331404967964674248939712645074932896596078406776640201622502944553027695654344100976413
m: 100000000000000000000000000
deg: 4
c4: 67
c0: 41
skew: 0.88
type: snfs
lss: 1
rlim: 240000
alim: 240000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 240000/240000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [120000, 200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 862464
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 34960 x 35193
Total sieving time: 0.20 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105,4,0,0,0,0,0,0,0,0,240000,240000,25,25,44,44,2.2,2.2,20000
total time: 0.22 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹¹⁰-31)/9 = 7(4)₁₀₉1_<111> = 3 · 13 · 19 · 229016210936117939_<18> · C91

C91 = P36 · P56

P36 = 275211394124960265212782044900640703_<36>

P56 = 15939747957337225794603273784899858020247830193184194553_<56>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 4386800257339265571199285250527432245987346642377889940905440634181278349895045122702690759 (91 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3447484428
Step 1 took 2948ms
Step 2 took 3432ms
********** Factor found in step 2: 275211394124960265212782044900640703
Found probable prime factor of 36 digits: 275211394124960265212782044900640703
Probable prime cofactor 15939747957337225794603273784899858020247830193184194553 has 56 digits

(62·10¹⁴⁵+1)/9 = 6(8)₁₄₄9_<146> = 3 · 53 · 3037 · 6329 · 20233 · 24151 · 289021 · 912403 · C117

C117 = P55 · P62

P55 = 5929006956554283372161105073815933362297298798067922111_<55>

P62 = 29503850915816027505202414387618333019676491925964734615718733_<62>

Number: 68889_145
N=174928537325013691471989457029058752780352462735033025143487876074013410863034271275317125323398497713637324127605363
  ( 117 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=5929006956554283372161105073815933362297298798067922111
 r2=29503850915816027505202414387618333019676491925964734615718733
Version: 
Total time: 4.05 hours.
Scaled time: 9.67 units (timescale=2.386).
Factorization parameters were as follows:
n: 174928537325013691471989457029058752780352462735033025143487876074013410863034271275317125323398497713637324127605363
m: 100000000000000000000000000000
deg: 5
c5: 62
c0: 1
skew: 0.44
type: snfs
lss: 1
rlim: 2250000
alim: 2250000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2250000/2250000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1125000, 2025001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4642203
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 287889 x 288137
Total sieving time: 3.57 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2250000,2250000,26,26,49,49,2.3,2.3,75000
total time: 4.05 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹³³-31)/9 = 7(4)₁₃₂1_<134> = 811 · 30307 · 64765307 · C119

C119 = P34 · P42 · P44

P34 = 8625640909763231199919977502862827_<34>

P42 = 119417958244208526547468954975940805596503_<42>

P44 = 45400961013383699554747369470928758093181399_<44>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 46765551638031908225910312923474405199786280869339065071698203645956926057134044970216126092746638328533578261081259419 (119 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2597803104
Step 1 took 4212ms
Step 2 took 4119ms
********** Factor found in step 2: 8625640909763231199919977502862827
Found probable prime factor of 34 digits: 8625640909763231199919977502862827
Composite cofactor 5421690066543193864230956289682168517981529320315248970797035445413782539943179047697 has 85 digits

11/03/09 22:52:19 v1.10 @ 조영욱-PC, starting SIQS on c85: 5421690066543193864230956289682168517981529320315248970797035445413782539943179047697
11/03/09 22:52:19 v1.10 @ 조영욱-PC, random seeds: 2623786136, 2605774612
11/03/09 22:52:19 v1.10 @ 조영욱-PC, ==== sieve params ====
11/03/09 22:52:19 v1.10 @ 조영욱-PC, n = 85 digits, 282 bits
11/03/09 22:52:19 v1.10 @ 조영욱-PC, factor base: 55732 primes (max prime = 1463621)
11/03/09 22:52:19 v1.10 @ 조영욱-PC, single large prime cutoff: 160998310 (110 * pmax)
11/03/09 22:52:19 v1.10 @ 조영욱-PC, double large prime range from 42 to 50 bits
11/03/09 22:52:19 v1.10 @ 조영욱-PC, double large prime cutoff: 591940930810882
11/03/09 22:52:19 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base
11/03/09 22:52:19 v1.10 @ 조영욱-PC, buckets hold 1024 elements
11/03/09 22:52:19 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536
11/03/09 22:52:19 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors
11/03/09 22:52:19 v1.10 @ 조영욱-PC, using multiplier of 1
11/03/09 22:52:19 v1.10 @ 조영욱-PC, using small prime variation correction of 18 bits
11/03/09 22:52:19 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
11/03/09 22:52:19 v1.10 @ 조영욱-PC, trial factoring cutoff at 94 bits
11/03/09 22:52:19 v1.10 @ 조영욱-PC, ==== sieving started ====
11/03/09 23:12:08 v1.10 @ 조영욱-PC, sieve time = 528.9270, relation time = 286.5150, poly_time = 373.1850
11/03/09 23:12:08 v1.10 @ 조영욱-PC, 55814 relations found: 18396 full + 37418 from 517693 partial, using 211761 polys (207 A polys)
11/03/09 23:12:08 v1.10 @ 조영욱-PC, on average, sieving found 2.53 rels/poly and 450.81 rels/sec
11/03/09 23:12:08 v1.10 @ 조영욱-PC, trial division touched 10174530 sieve locations out of 249803440128
11/03/09 23:12:08 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
11/03/09 23:12:08 v1.10 @ 조영욱-PC, begin with 536089 relations
11/03/09 23:12:08 v1.10 @ 조영욱-PC, reduce to 114934 relations in 9 passes
11/03/09 23:12:09 v1.10 @ 조영욱-PC, recovered 114934 relations
11/03/09 23:12:09 v1.10 @ 조영욱-PC, recovered 88632 polynomials
11/03/09 23:12:09 v1.10 @ 조영욱-PC, attempting to build 55814 cycles
11/03/09 23:12:09 v1.10 @ 조영욱-PC, found 55814 cycles in 4 passes
11/03/09 23:12:09 v1.10 @ 조영욱-PC, distribution of cycle lengths:
11/03/09 23:12:09 v1.10 @ 조영욱-PC,    length 1 : 18396
11/03/09 23:12:09 v1.10 @ 조영욱-PC,    length 2 : 15365
11/03/09 23:12:09 v1.10 @ 조영욱-PC,    length 3 : 10307
11/03/09 23:12:09 v1.10 @ 조영욱-PC,    length 4 : 5958
11/03/09 23:12:09 v1.10 @ 조영욱-PC,    length 5 : 3118
11/03/09 23:12:09 v1.10 @ 조영욱-PC,    length 6 : 1481
11/03/09 23:12:09 v1.10 @ 조영욱-PC,    length 7 : 700
11/03/09 23:12:09 v1.10 @ 조영욱-PC,    length 9+: 489
11/03/09 23:12:09 v1.10 @ 조영욱-PC, largest cycle: 15 relations
11/03/09 23:12:09 v1.10 @ 조영욱-PC, matrix is 55732 x 55814 (11.6 MB) with weight 2587778 (46.36/col)
11/03/09 23:12:09 v1.10 @ 조영욱-PC, sparse part has weight 2587778 (46.36/col)
11/03/09 23:12:10 v1.10 @ 조영욱-PC, filtering completed in 3 passes
11/03/09 23:12:10 v1.10 @ 조영욱-PC, matrix is 49309 x 49373 (10.4 MB) with weight 2337344 (47.34/col)
11/03/09 23:12:10 v1.10 @ 조영욱-PC, sparse part has weight 2337344 (47.34/col)
11/03/09 23:12:10 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
11/03/09 23:12:10 v1.10 @ 조영욱-PC, matrix is 49261 x 49373 (7.0 MB) with weight 1814592 (36.75/col)
11/03/09 23:12:10 v1.10 @ 조영욱-PC, sparse part has weight 1344877 (27.24/col)
11/03/09 23:12:10 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
11/03/09 23:12:10 v1.10 @ 조영욱-PC, using block size 19749 for processor cache size 4096 kB
11/03/09 23:12:10 v1.10 @ 조영욱-PC, commencing Lanczos iteration
11/03/09 23:12:10 v1.10 @ 조영욱-PC, memory use: 6.5 MB
11/03/09 23:12:19 v1.10 @ 조영욱-PC, lanczos halted after 781 iterations (dim = 49258)
11/03/09 23:12:19 v1.10 @ 조영욱-PC, recovered 15 nontrivial dependencies
11/03/09 23:12:19 v1.10 @ 조영욱-PC, prp44 = 45400961013383699554747369470928758093181399
11/03/09 23:12:20 v1.10 @ 조영욱-PC, prp42 = 119417958244208526547468954975940805596503
11/03/09 23:12:20 v1.10 @ 조영욱-PC, Lanczos elapsed time = 11.0290 seconds.
11/03/09 23:12:20 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.5610 seconds.
11/03/09 23:12:20 v1.10 @ 조영욱-PC, SIQS elapsed time = 1200.7470 seconds.
11/03/09 23:12:20 v1.10 @ 조영욱-PC, 
11/03/09 23:12:20 v1.10 @ 조영욱-PC,

(67·10¹¹³+41)/9 = 7(4)₁₁₂9_<114> = 6906511 · 105421943647_<12> · C97

C97 = P45 · P52

P45 = 869590929989825884177330375669983213482524877_<45>

P52 = 1175784051662201321889393008064659953020649677298261_<52>

Number: 74449_113
N=1022451146952139130224967621542222236077630734065060300433981671904917587999691828091026081338897
  ( 97 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=869590929989825884177330375669983213482524877
 r2=1175784051662201321889393008064659953020649677298261
Version: 
Total time: 0.79 hours.
Scaled time: 1.89 units (timescale=2.392).
Factorization parameters were as follows:
n: 1022451146952139130224967621542222236077630734065060300433981671904917587999691828091026081338897
m: 100000000000000000000000
deg: 5
c5: 67
c0: 4100
skew: 2.28
type: snfs
lss: 1
rlim: 450000
alim: 450000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 450000/450000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [225000, 525001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 1168115
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 70222 x 70453
Total sieving time: 0.71 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,450000,450000,25,25,45,45,2.2,2.2,25000
total time: 0.79 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 3, 2009 (8th)

By Ignacio Santos / GGNFS, Msieve / Nov 3, 2009

(59·10¹⁶⁹+13)/9 = 6(5)₁₆₈7_<170> = 397 · 34327 · C163

C163 = P38 · P125

P38 = 48178106573504420424833109041979951647_<38>

P125 = 99846631422582109990143221984485218923595671756459611686870528046668598368786968287093778636678542799792559888673331323201649_<125>

Number: 65557_169
N=4810421649682576174188661850847560828005974804593130827137897528251259835161852058319497459979146740616055698681906147678917334868885149968278530523156754250665903
  ( 163 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=48178106573504420424833109041979951647 (pp38)
 r2=99846631422582109990143221984485218923595671756459611686870528046668598368786968287093778636678542799792559888673331323201649 (pp125)
Version: Msieve-1.40
Total time: 62.49 hours.
Scaled time: 108.68 units (timescale=1.739).
Factorization parameters were as follows:
n: 4810421649682576174188661850847560828005974804593130827137897528251259835161852058319497459979146740616055698681906147678917334868885149968278530523156754250665903
m: 10000000000000000000000000000000000
deg: 5
c5: 59
c0: 130
skew: 1.17
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 990440 x 990665
Total sieving time: 60.96 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.26 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 62.49 hours.

Nov 3, 2009 (7th)

By Dmitry Domanov / GGNFS/msieve / Nov 3, 2009

2·10¹⁹⁴+9 = 2(0)₁₉₃9_<195> = 11 · 83 · 386297 · 30012787171_<11> · 305322490515193_<15> · C161

C161 = P49 · P113

P49 = 2643304814085557167142740766212794564787092479761_<49>

P113 = 23411298965592819498323902257006544390074859563323248495186898066821901827724109659825174326068861411467793246643_<113>

N=61883199259747724562380534631415342215058277850786191528768621756932108340713067029550933363785618882216426350755693966004769148805814527697569597938687958692323
  ( 161 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=2643304814085557167142740766212794564787092479761 (pp49)
 r2=23411298965592819498323902257006544390074859563323248495186898066821901827724109659825174326068861411467793246643 (pp113)
Version: Msieve-1.40
Total time: 376.74 hours.
Scaled time: 352.62 units (timescale=0.936).
Factorization parameters were as follows:
n: 61883199259747724562380534631415342215058277850786191528768621756932108340713067029550933363785618882216426350755693966004769148805814527697569597938687958692323
m: 1000000000000000000000000000000000000000
deg: 5
c5: 1
c0: 45
skew: 2.14
type: snfs
lss: 1
rlim: 12400000
alim: 12400000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 12400000/12400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6200000, 6200000)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2243697 x 2243921
Total sieving time: 371.28 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 3.25 hours.
Time per square root: 1.85 hours.
Prototype def-par.txt line would be:
snfs,195.000,5,0,0,0,0,0,0,0,0,12400000,12400000,28,28,55,55,2.5,2.5,100000
total time: 376.74 hours.
 --------- CPU info (if available) ----------

(65·10¹⁷⁸+7)/9 = 7(2)₁₇₇3_<179> = C179

C179 = P85 · P95

P85 = 4546037810993042721512544690503200646940652284786594915763822514701850550736979210131_<85>

P95 = 15886850313382215611347659103956660765448868131186254125303005503365575849391011481816610070933_<95>

N=72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223
  ( 179 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=4546037810993042721512544690503200646940652284786594915763822514701850550736979210131 (pp85)
 r2=15886850313382215611347659103956660765448868131186254125303005503365575849391011481816610070933 (pp95)
Version: Msieve-1.40
Total time: 138.67 hours.
Scaled time: 255.70 units (timescale=1.844).
Factorization parameters were as follows:
n: 72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223
m: 500000000000000000000000000000000000
deg: 5
c5: 104
c0: 35
skew: 0.80
type: snfs
lss: 1
rlim: 7100000
alim: 7100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7100000/7100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3550000, 5850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1505997 x 1506225
Total sieving time: 135.42 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 2.90 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,180.000,5,0,0,0,0,0,0,0,0,7100000,7100000,28,28,53,53,2.5,2.5,100000
total time: 138.67 hours.
 --------- CPU info (if available) ----------

(67·10¹⁶³-13)/9 = 7(4)₁₆₂3_<164> = 43 · C163

C163 = P46 · P117

P46 = 2669049180343301609996606512118950634407146589_<46>

P117 = 648645278858488499280074851252251346928425857765018089955890174635513009455895281838295786860964371014209079639413509_<117>

Number: s163
N=1731266149870801033591731266149870801033591731266149870801033591731266149870801033591731266149870801033591731266149870801033591731266149870801033591731266149870801
  ( 163 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=2669049180343301609996606512118950634407146589 (pp46)
 r2=648645278858488499280074851252251346928425857765018089955890174635513009455895281838295786860964371014209079639413509 (pp117)
Version: Msieve-1.40
Total time: 36.37 hours.
Scaled time: 66.31 units (timescale=1.823).
Factorization parameters were as follows:
n: 1731266149870801033591731266149870801033591731266149870801033591731266149870801033591731266149870801033591731266149870801033591731266149870801033591731266149870801
m: 500000000000000000000000000000000
deg: 5
c5: 536
c0: -325
skew: 0.90
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 787813 x 788038
Total sieving time: 35.34 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.76 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 36.37 hours.
 --------- CPU info (if available) ----------

(67·10¹⁵⁴-13)/9 = 7(4)₁₅₃3_<155> = 151 · C153

C153 = P46 · P107

P46 = 5070369631976571758208280028273870693194253729_<46>

P107 = 97233456659265110040429583804655748695553519367231505112386341847877549966443762203651496204999326757169917_<107>

Number: s153
N=493009565857247976453274466519499632082413539367181751287711552612214863870493009565857247976453274466519499632082413539367181751287711552612214863870493
  ( 153 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=5070369631976571758208280028273870693194253729 (pp46)
 r2=97233456659265110040429583804655748695553519367231505112386341847877549966443762203651496204999326757169917 (pp107)
Version: Msieve-1.40
Total time: 24.90 hours.
Scaled time: 23.25 units (timescale=0.934).
Factorization parameters were as follows:
n: 493009565857247976453274466519499632082413539367181751287711552612214863870493009565857247976453274466519499632082413539367181751287711552612214863870493
m: 10000000000000000000000000000000
deg: 5
c5: 67
c0: -130
skew: 1.14
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1450000, 2450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 549521 x 549746
Total sieving time: 23.87 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.41 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000
total time: 24.90 hours.
 --------- CPU info (if available) ----------

Nov 3, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Nov 3, 2009

(22·10¹⁴⁶+17)/3 = 7(3)₁₄₅9_<147> = 47 · 307 · 7224559039_<10> · C133

C133 = P62 · P72

P62 = 27842231927103510676920959473150529572734085970185311105905803_<62>

P72 = 252667743244057755987225257364727780951613659443847192687667040767338523_<72>

Number: n
N=7034833907898897215918782067746477148998748541039862569997295891558565179414446486816975422989742881398338017849564728134375451148969
  ( 133 digits)
SNFS difficulty: 148 digits.
Divisors found:

Tue Nov 03 19:38:24 2009  prp62 factor: 27842231927103510676920959473150529572734085970185311105905803
Tue Nov 03 19:38:24 2009  prp72 factor: 252667743244057755987225257364727780951613659443847192687667040767338523
Tue Nov 03 19:38:24 2009  elapsed time 00:30:55 (Msieve 1.43 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.55 hours.
Scaled time: 15.59 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_7_3_145_9
n: 7034833907898897215918782067746477148998748541039862569997295891558565179414446486816975422989742881398338017849564728134375451148969
m: 200000000000000000000000000000
deg: 5
c5: 55
c0: 136
skew: 1.20
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
qintsize: 10000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [1050000, 2565463)
Primes: RFBsize:155805, AFBsize:155943, largePrimes:4072211 encountered
Relations: rels:3998604, finalFF:308817
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 592028 hash collisions in 4536224 relations
Msieve: matrix is 361542 x 361767 (96.3 MB)

Total sieving time: 8.43 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 8.55 hours.
 --------- CPU info (if available) ----------

(65·10¹⁴⁶-11)/9 = 7(2)₁₄₅1_<147> = 7 · 42602801 · C139

C139 = P36 · P104

P36 = 228010369498745966470246714367913773_<36>

P104 = 10621358195754820181708181688331386998838914009256762910359610187203730566466660828760503361669159883911_<104>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 2421779806792590341728343241436242058431195713507268562064137594488286688078903618910014264160110110473796654900099248746653409083938006203 (139 digits)
Using B1=1532000, B2=2140123450, polynomial Dickson(6), sigma=4260663187
Step 1 took 16297ms
Step 2 took 7547ms
********** Factor found in step 2: 228010369498745966470246714367913773
Found probable prime factor of 36 digits: 228010369498745966470246714367913773
Probable prime cofactor 10621358195754820181708181688331386998838914009256762910359610187203730566466660828760503361669159883911 has 104 digits

Nov 3, 2009 (4th)

By Lionel Debroux / GGNFS (gnfs-lasieve4I14e) + msieve 1.43 SVN + msieve 1.44 SVN. / Nov 3, 2009

(16·10²¹⁷-7)/9 = 1(7)₂₁₇_<218> = 2091503 · C211

C211 = P82 · P130

P82 = 7897261403265468514843287619013563217249733055445218350552148477846264432526263073_<82>

P130 = 1076322620591986724257847200110126010314558644320810310385662610774870419875504652264090292435220197925549910589490097242891233983_<130>

Fri Oct 29 15:12:53 2009  Msieve v. 1.43
Fri Oct 29 15:12:53 2009  random seeds: 1be0c4fb f4fd774d
Fri Oct 29 15:12:53 2009  factoring 8500001089062639536150690569307229192488740287619849351293198134441010975254531204486810574872604905552503523914514001547106448223013678573627567246032053397856841600407830052253225444944510133515360856655609759 (211 digits)
Fri Oct 29 15:12:56 2009  searching for 15-digit factors
Fri Oct 29 15:12:57 2009  commencing number field sieve (211-digit input)
Fri Oct 29 15:12:57 2009  R0: -2000000000000000000000000000000000000
Fri Oct 29 15:12:57 2009  R1:  1
Fri Oct 29 15:12:57 2009  A0: -14
Fri Oct 29 15:12:57 2009  A1:  0
Fri Oct 29 15:12:57 2009  A2:  0
Fri Oct 29 15:12:57 2009  A3:  0
Fri Oct 29 15:12:57 2009  A4:  0
Fri Oct 29 15:12:57 2009  A5:  0
Fri Oct 29 15:12:57 2009  A6:  5
Fri Oct 29 15:12:57 2009  skew 1.19, size 9.452967e-11, alpha 0.913323, combined = 3.206796e-12
Fri Oct 29 15:12:57 2009  
Fri Oct 29 15:12:57 2009  commencing relation filtering
Fri Oct 29 15:12:57 2009  estimated available RAM is 1280.0 MB
Fri Oct 29 15:12:57 2009  commencing duplicate removal, pass 1
Fri Oct 29 15:21:42 2009  found 8759283 hash collisions in 53865618 relations
Fri Oct 29 15:22:15 2009  added 1218610 free relations
Fri Oct 29 15:22:15 2009  commencing duplicate removal, pass 2
Fri Oct 29 15:24:28 2009  found 7936035 duplicates and 47148193 unique relations
Fri Oct 29 15:24:28 2009  memory use: 330.4 MB
Fri Oct 29 15:24:28 2009  reading ideals above 44892160
Fri Oct 29 15:24:28 2009  commencing singleton removal, initial pass
Fri Oct 29 15:34:08 2009  memory use: 1065.5 MB
Fri Oct 29 15:34:08 2009  removing singletons from LP file
Fri Oct 29 15:34:08 2009  start with 47148193 relations and 41210405 ideals
Fri Oct 29 15:34:39 2009  pass 1: found 13606580 singletons
Fri Oct 29 15:35:08 2009  pruned dataset has 33541613 relations and 25481673 large ideals
Fri Oct 29 15:35:10 2009  reading all ideals from disk
Fri Oct 29 15:35:18 2009  memory use: 542.1 MB
Fri Oct 29 15:35:23 2009  commencing in-memory singleton removal
Fri Oct 29 15:35:27 2009  begin with 33541613 relations and 25481673 unique ideals
Fri Oct 29 15:36:24 2009  reduce to 27492294 relations and 19190861 ideals in 15 passes
Fri Oct 29 15:36:24 2009  max relations containing the same ideal: 34
Fri Oct 29 15:36:29 2009  reading ideals above 720000
Fri Oct 29 15:36:29 2009  commencing singleton removal, initial pass
Fri Oct 29 15:43:46 2009  memory use: 532.8 MB
Fri Oct 29 15:43:46 2009  reading large ideals from disk
Fri Oct 29 15:44:15 2009  keeping 21950765 ideals with weight <= 20, target excess is 2659545
Fri Oct 29 15:44:53 2009  memory use: 698.7 MB
Fri Oct 29 15:44:53 2009  commencing in-memory singleton removal
Fri Oct 29 15:44:58 2009  begin with 27492304 relations and 21950765 unique ideals
Fri Oct 29 15:45:44 2009  reduce to 27467887 relations and 21926298 ideals in 10 passes
Fri Oct 29 15:45:44 2009  max relations containing the same ideal: 20
Fri Oct 29 15:46:07 2009  removing 2899482 relations and 2499482 ideals in 400000 cliques
Fri Oct 29 15:46:09 2009  commencing in-memory singleton removal
Fri Oct 29 15:46:13 2009  begin with 24568405 relations and 21926298 unique ideals
Fri Oct 29 15:46:50 2009  reduce to 24338001 relations and 19191920 ideals in 9 passes
Fri Oct 29 15:46:50 2009  max relations containing the same ideal: 20
Fri Oct 29 15:47:10 2009  removing 2148119 relations and 1748119 ideals in 400000 cliques
Fri Oct 29 15:47:11 2009  commencing in-memory singleton removal
Fri Oct 29 15:47:15 2009  begin with 22189882 relations and 19191920 unique ideals
Fri Oct 29 15:47:48 2009  reduce to 22052686 relations and 17304302 ideals in 9 passes
Fri Oct 29 15:47:48 2009  max relations containing the same ideal: 20
Fri Oct 29 15:48:06 2009  removing 1906876 relations and 1506876 ideals in 400000 cliques
Fri Oct 29 15:48:07 2009  commencing in-memory singleton removal
Fri Oct 29 15:48:11 2009  begin with 20145810 relations and 17304302 unique ideals
Fri Oct 29 15:48:34 2009  reduce to 20026245 relations and 15675818 ideals in 7 passes
Fri Oct 29 15:48:34 2009  max relations containing the same ideal: 20
Fri Oct 29 15:48:50 2009  removing 1784485 relations and 1384485 ideals in 400000 cliques
Fri Oct 29 15:48:51 2009  commencing in-memory singleton removal
Fri Oct 29 15:48:54 2009  begin with 18241760 relations and 15675818 unique ideals
Fri Oct 29 15:49:18 2009  reduce to 18128520 relations and 14176097 ideals in 8 passes
Fri Oct 29 15:49:18 2009  max relations containing the same ideal: 20
Fri Oct 29 15:49:32 2009  removing 1699578 relations and 1299578 ideals in 400000 cliques
Fri Oct 29 15:49:34 2009  commencing in-memory singleton removal
Fri Oct 29 15:49:36 2009  begin with 16428942 relations and 14176097 unique ideals
Fri Oct 29 15:49:55 2009  reduce to 16315703 relations and 12761159 ideals in 7 passes
Fri Oct 29 15:49:55 2009  max relations containing the same ideal: 20
Fri Oct 29 15:50:08 2009  removing 1641895 relations and 1241895 ideals in 400000 cliques
Fri Oct 29 15:50:09 2009  commencing in-memory singleton removal
Fri Oct 29 15:50:11 2009  begin with 14673808 relations and 12761159 unique ideals
Fri Oct 29 15:50:27 2009  reduce to 14553594 relations and 11396492 ideals in 7 passes
Fri Oct 29 15:50:27 2009  max relations containing the same ideal: 20
Fri Oct 29 15:50:39 2009  removing 403128 relations and 331099 ideals in 72029 cliques
Fri Oct 29 15:50:39 2009  commencing in-memory singleton removal
Fri Oct 29 15:50:42 2009  begin with 14150466 relations and 11396492 unique ideals
Fri Oct 29 15:50:55 2009  reduce to 14143576 relations and 11058472 ideals in 6 passes
Fri Oct 29 15:50:55 2009  max relations containing the same ideal: 19
Fri Oct 29 15:50:59 2009  relations with 0 large ideals: 292627
Fri Oct 29 15:50:59 2009  relations with 1 large ideals: 1412588
Fri Oct 29 15:50:59 2009  relations with 2 large ideals: 3397450
Fri Oct 29 15:50:59 2009  relations with 3 large ideals: 4284035
Fri Oct 29 15:50:59 2009  relations with 4 large ideals: 3066394
Fri Oct 29 15:50:59 2009  relations with 5 large ideals: 1284602
Fri Oct 29 15:50:59 2009  relations with 6 large ideals: 317678
Fri Oct 29 15:50:59 2009  relations with 7+ large ideals: 88202
Fri Oct 29 15:50:59 2009  commencing 2-way merge
Fri Oct 29 15:51:14 2009  reduce to 9477159 relation sets and 6392055 unique ideals
Fri Oct 29 15:51:14 2009  commencing full merge
Fri Oct 29 15:53:33 2009  memory use: 619.5 MB
Fri Oct 29 15:53:34 2009  found 4822262 cycles, need 4400255
Fri Oct 29 15:53:37 2009  weight of 4400255 cycles is about 308133690 (70.03/cycle)
Fri Oct 29 15:53:37 2009  distribution of cycle lengths:
Fri Oct 29 15:53:37 2009  1 relations: 568844
Fri Oct 29 15:53:37 2009  2 relations: 499899
Fri Oct 29 15:53:37 2009  3 relations: 498118
Fri Oct 29 15:53:37 2009  4 relations: 463201
Fri Oct 29 15:53:37 2009  5 relations: 432873
Fri Oct 29 15:53:37 2009  6 relations: 389387
Fri Oct 29 15:53:37 2009  7 relations: 346960
Fri Oct 29 15:53:37 2009  8 relations: 302531
Fri Oct 29 15:53:37 2009  9 relations: 258712
Fri Oct 29 15:53:37 2009  10+ relations: 639730
Fri Oct 29 15:53:37 2009  heaviest cycle: 16 relations
Fri Oct 29 15:53:38 2009  commencing cycle optimization
Fri Oct 29 15:53:49 2009  start with 23784516 relations
Fri Oct 29 15:54:49 2009  pruned 791684 relations
Fri Oct 29 15:54:49 2009  memory use: 766.7 MB
Fri Oct 29 15:54:49 2009  distribution of cycle lengths:
Fri Oct 29 15:54:49 2009  1 relations: 568844
Fri Oct 29 15:54:49 2009  2 relations: 514768
Fri Oct 29 15:54:49 2009  3 relations: 523157
Fri Oct 29 15:54:49 2009  4 relations: 482746
Fri Oct 29 15:54:49 2009  5 relations: 451923
Fri Oct 29 15:54:49 2009  6 relations: 401981
Fri Oct 29 15:54:49 2009  7 relations: 356417
Fri Oct 29 15:54:49 2009  8 relations: 305132
Fri Oct 29 15:54:49 2009  9 relations: 255583
Fri Oct 29 15:54:49 2009  10+ relations: 539704
Fri Oct 29 15:54:49 2009  heaviest cycle: 16 relations
Fri Oct 29 15:55:03 2009  RelProcTime: 2526
Fri Oct 29 15:55:03 2009  elapsed time 00:42:10
Fri Oct 29 15:55:57 2009  
Fri Oct 29 15:55:57 2009  
Fri Oct 29 15:55:57 2009  Msieve v. 1.43
Fri Oct 29 15:55:57 2009  random seeds: 06696a6a 921726f3
Fri Oct 29 15:55:57 2009  factoring 8500001089062639536150690569307229192488740287619849351293198134441010975254531204486810574872604905552503523914514001547106448223013678573627567246032053397856841600407830052253225444944510133515360856655609759 (211 digits)
Fri Oct 29 15:56:00 2009  searching for 15-digit factors
Fri Oct 29 15:56:01 2009  commencing number field sieve (211-digit input)
Fri Oct 29 15:56:01 2009  R0: -2000000000000000000000000000000000000
Fri Oct 29 15:56:01 2009  R1:  1
Fri Oct 29 15:56:01 2009  A0: -14
Fri Oct 29 15:56:01 2009  A1:  0
Fri Oct 29 15:56:01 2009  A2:  0
Fri Oct 29 15:56:01 2009  A3:  0
Fri Oct 29 15:56:01 2009  A4:  0
Fri Oct 29 15:56:01 2009  A5:  0
Fri Oct 29 15:56:01 2009  A6:  5
Fri Oct 29 15:56:01 2009  skew 1.19, size 9.452967e-11, alpha 0.913323, combined = 3.206796e-12
Fri Oct 29 15:56:01 2009  
Fri Oct 29 15:56:01 2009  commencing linear algebra
Fri Oct 29 15:56:02 2009  read 4400255 cycles
Fri Oct 29 15:56:15 2009  cycles contain 12582213 unique relations
Fri Oct 29 16:00:54 2009  read 12582213 relations
Fri Oct 29 16:04:52 2009  using 20 quadratic characters above 536870870
Fri Oct 29 16:06:32 2009  building initial matrix
Fri Oct 29 16:13:53 2009  memory use: 1588.0 MB
Fri Oct 29 16:14:05 2009  read 4400255 cycles
Fri Oct 29 16:14:32 2009  matrix is 4399717 x 4400255 (1290.6 MB) with weight 382534401 (86.93/col)
Fri Oct 29 16:14:32 2009  sparse part has weight 294330484 (66.89/col)
Fri Oct 29 16:16:46 2009  filtering completed in 3 passes
Fri Oct 29 16:16:47 2009  matrix is 4384355 x 4384555 (1288.1 MB) with weight 381708992 (87.06/col)
Fri Oct 29 16:16:47 2009  sparse part has weight 293829804 (67.01/col)
Fri Oct 29 16:17:32 2009  read 4384555 cycles
Fri Oct 29 16:18:02 2009  matrix is 4384355 x 4384555 (1288.1 MB) with weight 381708992 (87.06/col)
Fri Oct 29 16:18:02 2009  sparse part has weight 293829804 (67.01/col)
Fri Oct 29 16:18:02 2009  saving the first 48 matrix rows for later
Fri Oct 29 16:18:05 2009  matrix is 4384307 x 4384555 (1242.3 MB) with weight 301340925 (68.73/col)
Fri Oct 29 16:18:05 2009  sparse part has weight 281805898 (64.27/col)
Fri Oct 29 16:18:05 2009  matrix includes 64 packed rows
Fri Oct 29 16:18:05 2009  using block size 65536 for processor cache size 4096 kB
Fri Oct 29 16:18:30 2009  commencing Lanczos iteration (2 threads)
Fri Oct 29 16:18:30 2009  memory use: 1280.3 MB
Fri Oct 29 16:47:22 2009  lanczos halted after 378 iterations (dim = 23886)
Fri Oct 29 16:47:22 2009  BLanczosTime: 3081
Fri Oct 29 16:47:22 2009  elapsed time 00:51:25
Fri Oct 29 17:03:15 2009  
Fri Oct 29 17:03:15 2009  
Fri Oct 29 17:03:15 2009  Msieve v. 1.43
Fri Oct 29 17:03:15 2009  random seeds: 9d027af2 4992c51d
Fri Oct 29 17:03:15 2009  factoring 8500001089062639536150690569307229192488740287619849351293198134441010975254531204486810574872604905552503523914514001547106448223013678573627567246032053397856841600407830052253225444944510133515360856655609759 (211 digits)
Fri Oct 29 17:03:18 2009  searching for 15-digit factors
Fri Oct 29 17:03:19 2009  commencing number field sieve (211-digit input)
Fri Oct 29 17:03:19 2009  R0: -2000000000000000000000000000000000000
Fri Oct 29 17:03:19 2009  R1:  1
Fri Oct 29 17:03:19 2009  A0: -14
Fri Oct 29 17:03:19 2009  A1:  0
Fri Oct 29 17:03:19 2009  A2:  0
Fri Oct 29 17:03:19 2009  A3:  0
Fri Oct 29 17:03:19 2009  A4:  0
Fri Oct 29 17:03:19 2009  A5:  0
Fri Oct 29 17:03:19 2009  A6:  5
Fri Oct 29 17:03:19 2009  skew 1.19, size 9.452967e-11, alpha 0.913323, combined = 3.206796e-12
Fri Oct 29 17:03:19 2009  
Fri Oct 29 17:03:19 2009  commencing linear algebra
Fri Oct 29 17:03:21 2009  read 4384555 cycles
Fri Oct 29 17:03:50 2009  matrix is 4384355 x 4384555 (1288.1 MB) with weight 381708992 (87.06/col)
Fri Oct 29 17:03:51 2009  sparse part has weight 293829804 (67.01/col)
Fri Oct 29 17:03:51 2009  saving the first 48 matrix rows for later
Fri Oct 29 17:03:54 2009  matrix is 4384307 x 4384555 (1242.3 MB) with weight 301340925 (68.73/col)
Fri Oct 29 17:03:54 2009  sparse part has weight 281805898 (64.27/col)
Fri Oct 29 17:03:54 2009  matrix includes 64 packed rows
Fri Oct 29 17:03:54 2009  using block size 65536 for processor cache size 4096 kB
Fri Oct 29 17:04:19 2009  commencing Lanczos iteration (2 threads)
Fri Oct 29 17:04:19 2009  memory use: 1280.3 MB
Fri Oct 29 17:04:23 2009  restarting at iteration 378 (dim = 23886)
Fri Oct 29 17:09:53 2009  lanczos halted after 455 iterations (dim = 28764)
Fri Oct 29 17:09:53 2009  BLanczosTime: 394
Fri Oct 29 17:09:53 2009  elapsed time 00:06:38
Fri Oct 30 11:29:31 2009  
Fri Oct 30 11:29:32 2009  
Fri Oct 30 11:29:32 2009  Msieve v. 1.44
Fri Oct 30 11:29:32 2009  random seeds: dbcaf00b 6da27e00
Fri Oct 30 11:29:32 2009  factoring 8500001089062639536150690569307229192488740287619849351293198134441010975254531204486810574872604905552503523914514001547106448223013678573627567246032053397856841600407830052253225444944510133515360856655609759 (211 digits)
Fri Oct 30 11:29:34 2009  no P-1/P+1/ECM available, skipping
Fri Oct 30 11:29:34 2009  commencing number field sieve (211-digit input)
Fri Oct 30 11:29:34 2009  R0: -2000000000000000000000000000000000000
Fri Oct 30 11:29:34 2009  R1:  1
Fri Oct 30 11:29:34 2009  A0: -14
Fri Oct 30 11:29:34 2009  A1:  0
Fri Oct 30 11:29:34 2009  A2:  0
Fri Oct 30 11:29:34 2009  A3:  0
Fri Oct 30 11:29:34 2009  A4:  0
Fri Oct 30 11:29:34 2009  A5:  0
Fri Oct 30 11:29:34 2009  A6:  5
Fri Oct 30 11:29:34 2009  skew 1.19, size 9.452967e-11, alpha 0.913323, combined = 3.206796e-12
Fri Oct 30 11:29:34 2009  
Fri Oct 30 11:29:34 2009  commencing linear algebra
Fri Oct 30 11:29:37 2009  read 4384555 cycles
Fri Oct 30 11:31:33 2009  matrix is 4384355 x 4384555 (1288.1 MB) with weight 381708992 (87.06/col)
Fri Oct 30 11:31:33 2009  sparse part has weight 293829804 (67.01/col)
Fri Oct 30 11:31:36 2009  saving the first 48 matrix rows for later
Fri Oct 30 11:31:38 2009  matrix is 4384307 x 4384555 (1242.3 MB) with weight 301340925 (68.73/col)
Fri Oct 30 11:31:39 2009  sparse part has weight 281805898 (64.27/col)
Fri Oct 30 11:31:39 2009  matrix includes 64 packed rows
Fri Oct 30 11:31:39 2009  using block size 65536 for processor cache size 4096 kB
Fri Oct 30 11:32:12 2009  commencing Lanczos iteration (2 threads)
Fri Oct 30 11:32:12 2009  memory use: 1280.3 MB
Fri Oct 30 11:32:29 2009  restarting at iteration 455 (dim = 28764)
Fri Oct 30 11:36:05 2009  linear algebra at 0.7%, ETA 346h33m
Sat Oct 31 08:13:02 2009  
Sat Oct 31 08:13:02 2009  
Sat Oct 31 08:13:02 2009  Msieve v. 1.44
Sat Oct 31 08:13:02 2009  random seeds: 5697b0eb 2dd51323
Sat Oct 31 08:13:02 2009  factoring 8500001089062639536150690569307229192488740287619849351293198134441010975254531204486810574872604905552503523914514001547106448223013678573627567246032053397856841600407830052253225444944510133515360856655609759 (211 digits)
Sat Oct 31 08:13:05 2009  no P-1/P+1/ECM available, skipping
Sat Oct 31 08:13:05 2009  commencing number field sieve (211-digit input)
Sat Oct 31 08:13:05 2009  R0: -2000000000000000000000000000000000000
Sat Oct 31 08:13:05 2009  R1:  1
Sat Oct 31 08:13:05 2009  A0: -14
Sat Oct 31 08:13:05 2009  A1:  0
Sat Oct 31 08:13:05 2009  A2:  0
Sat Oct 31 08:13:05 2009  A3:  0
Sat Oct 31 08:13:05 2009  A4:  0
Sat Oct 31 08:13:05 2009  A5:  0
Sat Oct 31 08:13:05 2009  A6:  5
Sat Oct 31 08:13:05 2009  skew 1.19, size 9.452967e-11, alpha 0.913323, combined = 3.206796e-12
Sat Oct 31 08:13:05 2009  
Sat Oct 31 08:13:05 2009  commencing linear algebra
Sat Oct 31 08:13:07 2009  read 4384555 cycles
Sat Oct 31 08:14:44 2009  matrix is 4384355 x 4384555 (1288.1 MB) with weight 381708992 (87.06/col)
Sat Oct 31 08:14:44 2009  sparse part has weight 293829804 (67.01/col)
Sat Oct 31 08:14:54 2009  saving the first 48 matrix rows for later
Sat Oct 31 08:15:00 2009  matrix is 4384307 x 4384555 (1242.3 MB) with weight 301340925 (68.73/col)
Sat Oct 31 08:15:00 2009  sparse part has weight 281805898 (64.27/col)
Sat Oct 31 08:15:00 2009  matrix includes 64 packed rows
Sat Oct 31 08:15:00 2009  using block size 65536 for processor cache size 4096 kB
Sat Oct 31 08:15:26 2009  commencing Lanczos iteration (2 threads)
Sat Oct 31 08:15:26 2009  memory use: 1280.3 MB
Sat Oct 31 08:15:30 2009  restarting at iteration 17397 (dim = 1100025)
Sat Oct 31 08:16:20 2009  linear algebra at 25.1%, ETA 60h 0m
Sat Oct 31 16:27:58 2009  lanczos halted after 24801 iterations (dim = 1568121)
Sat Oct 31 16:27:58 2009  BLanczosTime: 29693
Sat Oct 31 16:27:58 2009  elapsed time 08:14:56
Sat Oct 31 16:31:56 2009  
Sat Oct 31 16:31:56 2009  
Sat Oct 31 16:31:56 2009  Msieve v. 1.44
Sat Oct 31 16:31:56 2009  random seeds: 9ab3ec5e 2d1353ca
Sat Oct 31 16:31:56 2009  factoring 8500001089062639536150690569307229192488740287619849351293198134441010975254531204486810574872604905552503523914514001547106448223013678573627567246032053397856841600407830052253225444944510133515360856655609759 (211 digits)
Sat Oct 31 16:31:58 2009  no P-1/P+1/ECM available, skipping
Sat Oct 31 16:31:58 2009  commencing number field sieve (211-digit input)
Sat Oct 31 16:31:58 2009  R0: -2000000000000000000000000000000000000
Sat Oct 31 16:31:58 2009  R1:  1
Sat Oct 31 16:31:58 2009  A0: -14
Sat Oct 31 16:31:58 2009  A1:  0
Sat Oct 31 16:31:58 2009  A2:  0
Sat Oct 31 16:31:58 2009  A3:  0
Sat Oct 31 16:31:58 2009  A4:  0
Sat Oct 31 16:31:58 2009  A5:  0
Sat Oct 31 16:31:58 2009  A6:  5
Sat Oct 31 16:31:58 2009  skew 1.19, size 9.452967e-11, alpha 0.913323, combined = 3.206796e-12
Sat Oct 31 16:31:58 2009  
Sat Oct 31 16:31:58 2009  commencing linear algebra
Sat Oct 31 16:32:01 2009  read 4384555 cycles
Sat Oct 31 16:32:28 2009  matrix is 4384355 x 4384555 (1288.1 MB) with weight 381708992 (87.06/col)
Sat Oct 31 16:32:28 2009  sparse part has weight 293829804 (67.01/col)
Sat Oct 31 16:32:28 2009  saving the first 48 matrix rows for later
Sat Oct 31 16:32:31 2009  matrix is 4384307 x 4384555 (1242.3 MB) with weight 301340925 (68.73/col)
Sat Oct 31 16:32:31 2009  sparse part has weight 281805898 (64.27/col)
Sat Oct 31 16:32:31 2009  matrix includes 64 packed rows
Sat Oct 31 16:32:31 2009  using block size 65536 for processor cache size 4096 kB
Sat Oct 31 16:32:55 2009  commencing Lanczos iteration (2 threads)
Sat Oct 31 16:32:55 2009  memory use: 1280.3 MB
Sat Oct 31 16:32:59 2009  restarting at iteration 24801 (dim = 1568121)
Sat Oct 31 16:33:46 2009  linear algebra at 35.8%, ETA 48h22m
Sun Nov  1 12:19:24 2009  lanczos halted after 43056 iterations (dim = 2722803)
Sun Nov  1 12:19:24 2009  BLanczosTime: 71246
Sun Nov  1 12:19:24 2009  elapsed time 19:47:28
Sun Nov  1 19:00:07 2009  
Sun Nov  1 19:00:07 2009  
Sun Nov  1 19:00:07 2009  Msieve v. 1.44
Sun Nov  1 19:00:07 2009  random seeds: 14e84e25 6a7484ee
Sun Nov  1 19:00:07 2009  factoring 8500001089062639536150690569307229192488740287619849351293198134441010975254531204486810574872604905552503523914514001547106448223013678573627567246032053397856841600407830052253225444944510133515360856655609759 (211 digits)
Sun Nov  1 19:00:10 2009  no P-1/P+1/ECM available, skipping
Sun Nov  1 19:00:10 2009  commencing number field sieve (211-digit input)
Sun Nov  1 19:00:10 2009  R0: -2000000000000000000000000000000000000
Sun Nov  1 19:00:10 2009  R1:  1
Sun Nov  1 19:00:10 2009  A0: -14
Sun Nov  1 19:00:10 2009  A1:  0
Sun Nov  1 19:00:10 2009  A2:  0
Sun Nov  1 19:00:10 2009  A3:  0
Sun Nov  1 19:00:10 2009  A4:  0
Sun Nov  1 19:00:10 2009  A5:  0
Sun Nov  1 19:00:10 2009  A6:  5
Sun Nov  1 19:00:10 2009  skew 1.19, size 9.452967e-11, alpha 0.913323, combined = 3.206796e-12
Sun Nov  1 19:00:10 2009  
Sun Nov  1 19:00:10 2009  commencing linear algebra
Sun Nov  1 19:00:12 2009  read 4384555 cycles
Sun Nov  1 19:00:58 2009  matrix is 4384355 x 4384555 (1288.1 MB) with weight 381708992 (87.06/col)
Sun Nov  1 19:00:58 2009  sparse part has weight 293829804 (67.01/col)
Sun Nov  1 19:00:58 2009  saving the first 48 matrix rows for later
Sun Nov  1 19:01:01 2009  matrix is 4384307 x 4384555 (1242.3 MB) with weight 301340925 (68.73/col)
Sun Nov  1 19:01:01 2009  sparse part has weight 281805898 (64.27/col)
Sun Nov  1 19:01:01 2009  matrix includes 64 packed rows
Sun Nov  1 19:01:01 2009  using block size 65536 for processor cache size 4096 kB
Sun Nov  1 19:01:25 2009  commencing Lanczos iteration (2 threads)
Sun Nov  1 19:01:25 2009  memory use: 1280.3 MB
Sun Nov  1 19:01:28 2009  restarting at iteration 43056 (dim = 2722803)
Sun Nov  1 19:02:13 2009  linear algebra at 62.1%, ETA 27h16m
Mon Nov  2 22:49:52 2009  lanczos halted after 69333 iterations (dim = 4384301)
Mon Nov  2 22:50:08 2009  recovered 29 nontrivial dependencies
Mon Nov  2 22:50:08 2009  BLanczosTime: 100198
Mon Nov  2 22:50:08 2009  elapsed time 27:50:01
Tue Nov  3 07:13:41 2009  
Tue Nov  3 07:13:41 2009  
Tue Nov  3 07:13:41 2009  Msieve v. 1.44
Tue Nov  3 07:13:41 2009  random seeds: 1e73deaa db0725d4
Tue Nov  3 07:13:41 2009  factoring 8500001089062639536150690569307229192488740287619849351293198134441010975254531204486810574872604905552503523914514001547106448223013678573627567246032053397856841600407830052253225444944510133515360856655609759 (211 digits)
Tue Nov  3 07:13:44 2009  no P-1/P+1/ECM available, skipping
Tue Nov  3 07:13:44 2009  commencing number field sieve (211-digit input)
Tue Nov  3 07:13:44 2009  R0: -2000000000000000000000000000000000000
Tue Nov  3 07:13:44 2009  R1:  1
Tue Nov  3 07:13:44 2009  A0: -14
Tue Nov  3 07:13:44 2009  A1:  0
Tue Nov  3 07:13:44 2009  A2:  0
Tue Nov  3 07:13:44 2009  A3:  0
Tue Nov  3 07:13:44 2009  A4:  0
Tue Nov  3 07:13:44 2009  A5:  0
Tue Nov  3 07:13:44 2009  A6:  5
Tue Nov  3 07:13:44 2009  skew 1.19, size 9.452967e-11, alpha 0.913323, combined = 3.206796e-12
Tue Nov  3 07:13:44 2009  
Tue Nov  3 07:13:44 2009  commencing square root phase
Tue Nov  3 07:13:44 2009  reading relations for dependency 1
Tue Nov  3 07:13:55 2009  read 2192196 cycles
Tue Nov  3 07:14:01 2009  cycles contain 6282928 unique relations
Tue Nov  3 07:16:39 2009  read 6282928 relations
Tue Nov  3 07:17:34 2009  multiplying 6282928 relations
Tue Nov  3 07:43:49 2009  multiply complete, coefficients have about 166.71 million bits
Tue Nov  3 07:43:51 2009  initial square root is modulo 961063
Tue Nov  3 08:32:47 2009  sqrtTime: 4743
Tue Nov  3 08:32:47 2009  prp82 factor: 7897261403265468514843287619013563217249733055445218350552148477846264432526263073
Tue Nov  3 08:32:47 2009  prp130 factor: 1076322620591986724257847200110126010314558644320810310385662610774870419875504652264090292435220197925549910589490097242891233983
Tue Nov  3 08:32:47 2009  elapsed time 01:19:06

Nov 3, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 3, 2009

(22·10¹⁶⁴+17)/3 = 7(3)₁₆₃9_<165> = 43 · 8807563 · 1054663007_<10> · 20960261227181_<14> · 1061845031479378537_<19> · C116

C116 = P45 · P72

P45 = 269086021530847369814271946140389205816260519_<45>

P72 = 306559325047837647788312601146073338380622501550858942342560398202515871_<72>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=798243210
Step 1 took 34709ms
Step 2 took 13773ms
********** Factor found in step 2: 269086021530847369814271946140389205816260519
Found probable prime factor of 45 digits: 269086021530847369814271946140389205816260519
Probable prime cofactor 306559325047837647788312601146073338380622501550858942342560398202515871 has 72 digits

(83·10¹⁶²+7)/9 = 9(2)₁₆₁3_<163> = 79 · 7163407 · 123782203 · 1379440969_<10> · C137

C137 = P35 · P103

P35 = 77479813795087138515341741319858289_<35>

P103 = 1231796507361522933848450105124016132668124640732119124805549061730851641307686899069575749709590710917_<103>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=33045363
Step 1 took 42515ms
Step 2 took 14795ms
********** Factor found in step 2: 77479813795087138515341741319858289
Found probable prime factor of 35 digits: 77479813795087138515341741319858289
Probable prime cofactor 1231796507361522933848450105124016132668124640732119124805549061730851641307686899069575749709590710917 has 103 digits

Nov 3, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Nov 3, 2009

(65·10¹⁸⁸+7)/9 = 7(2)₁₈₇3_<189> = 3 · 8861 · 65413 · 1138313480230062656887_<22> · 4936904042105335591272083_<25> · 54844619696574357771146978801_<29> · C106

C106 = P46 · P61

P46 = 1138013643656600919904580369595610705548818987_<46>

P61 = 1184144563479191562090572761473075877638386411991788655406931_<61>

Number: 72223_188
N=1347572669301109953949998348172900968329488051278258747576035982677855617296089367339361336974878944198897
  ( 106 digits)
Divisors found:
 r1=1138013643656600919904580369595610705548818987 (pp46)
 r2=1184144563479191562090572761473075877638386411991788655406931 (pp61)
Version: Msieve-1.40
Total time: 9.28 hours.
Scaled time: 9.54 units (timescale=1.028).
Factorization parameters were as follows:
name: 72223_188
n: 1347572669301109953949998348172900968329488051278258747576035982677855617296089367339361336974878944198897
skew: 20299.51
# norm 3.91e+014
c5: 25380
c4: -407224297
c3: -35695951343608
c2: 270716599948667212
c1: 6171660106286066625728
c0: 10630957816144681327805185
# alpha -5.87
Y1: 230111174513
Y0: -139641470087173881524
# Murphy_E 1.71e-009
# M 1023586989596875295902999083337639354687779000129821085247661007333863292560625974576569941944116155178271
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 307925 x 308152
Polynomial selection time: 0.84 hours.
Total sieving time: 8.08 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 9.28 hours.
 --------- CPU info (if available) ----------

Nov 3, 2009

By Lionel Debroux / GMP-ECM

Factorizations of 744...441 and Factorizations of 744...449 have been extended up to n=200. Composite numbers that appeared newly have passed 150 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Nov 2, 2009 (8th)

By Ignacio Santos / GGNFS, Msieve / Nov 2, 2009

(59·10¹⁸⁰+13)/9 = 6(5)₁₇₉7_<181> = 51817 · C177

C177 = P65 · P112

P65 = 95780468341750701326160056307507237638238922434045248449733251961_<65>

P112 = 1320870620450520196921038614538489008181444841181434809163897968164710430144823057566665219559813287555704606661_<112>

Number: 65557_180
N=126513606645609656204634686600064757812215210366396270636191897553998794904289240124969711784849673959425585339860577716879702714467366994529894736390674017321642618359911912221
  ( 177 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=95780468341750701326160056307507237638238922434045248449733251961 (pp65)
 r2=1320870620450520196921038614538489008181444841181434809163897968164710430144823057566665219559813287555704606661 (pp112)
Version: Msieve-1.40
Total time: 133.06 hours.
Scaled time: 231.40 units (timescale=1.739).
Factorization parameters were as follows:
n: 126513606645609656204634686600064757812215210366396270636191897553998794904289240124969711784849673959425585339860577716879702714467366994529894736390674017321642618359911912221
m: 1000000000000000000000000000000000000
deg: 5
c5: 59
c0: 13
skew: 0.74
type: snfs
lss: 1
rlim: 7500000
alim: 7500000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7500000/7500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3750000, 5850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1364571 x 1364796
Total sieving time: 129.77 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.60 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
snfs,181.000,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,53,53,2.5,2.5,100000
total time: 133.06 hours.

Nov 2, 2009 (7th)

By Dmitry Domanov / GGNFS/msieve / Nov 2, 2009

(22·10¹⁵⁹+17)/3 = 7(3)₁₅₈9_<160> = 4987135339_<10> · 264530257997_<12> · 48219886937134417_<17> · 167443476449759357_<18> · C105

C105 = P50 · P56

P50 = 38574187745663264247371938272992130524286949118369_<50>

P56 = 17847759560428889439656259202106657143289384297059785353_<56>

N=688462828123440434779271573945370660625212689440916856718770629482448614016937671446277553177927729449257
  ( 105 digits)
Divisors found:
 r1=38574187745663264247371938272992130524286949118369 (pp50)
 r2=17847759560428889439656259202106657143289384297059785353 (pp56)
Version: Msieve-1.40
Total time: 7.43 hours.
Scaled time: 13.72 units (timescale=1.845).
Factorization parameters were as follows:
name: g105
n: 688462828123440434779271573945370660625212689440916856718770629482448614016937671446277553177927729449257
skew: 11711.95
# norm 3.55e+014
c5: 119280
c4: -33389416
c3: -38876261063554
c2: 57165069223953227
c1: 2940141257243004481354
c0: -7304026992600891397053451
# alpha -6.00
Y1: 135355970453
Y0: -89590634015656412400
# Murphy_E 1.88e-009
# M 59537625610639280219550455181988197619035910092365477801901749653682236582435332856660485432069236618267
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 266780 x 267011
Polynomial selection time: 0.74 hours.
Total sieving time: 6.39 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 7.43 hours.
 --------- CPU info (if available) ----------

(67·10¹⁷³-13)/9 = 7(4)₁₇₂3_<174> = 7 · C174

C174 = P49 · P125

P49 = 3241667577833561934029047613037266732688187964683_<49>

P125 = 32806943894068423044978703902535750856846944093496801328720438946228682490197034377217104129805138286814146349521206468868103_<125>

Number: s174
N=106349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349
  ( 174 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=3241667577833561934029047613037266732688187964683 (pp49)
 r2=32806943894068423044978703902535750856846944093496801328720438946228682490197034377217104129805138286814146349521206468868103 (pp125)
Version: Msieve-1.40
Total time: 79.24 hours.
Scaled time: 153.25 units (timescale=1.934).
Factorization parameters were as follows:
n: 106349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349
m: 50000000000000000000000000000000000
deg: 5
c5: 536
c0: -325
skew: 0.90
type: snfs
lss: 1
rlim: 6100000
alim: 6100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 6100000/6100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3050000, 7050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1268890 x 1269119
Total sieving time: 76.92 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.01 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,176.000,5,0,0,0,0,0,0,0,0,6100000,6100000,28,28,53,53,2.5,2.5,100000
total time: 79.24 hours.
 --------- CPU info (if available) ----------

(61·10¹⁶²-43)/9 = 6(7)₁₆₁3_<163> = 59 · 61175137 · 386218229 · 6104474861_<10> · 103375043945431_<15> · 87828043997778083_<17> · C104

C104 = P47 · P58

P47 = 44852631056757965967627131512225496265304129001_<47>

P58 = 1955881072075677630830269684042401294980535053861409508963_<58>

Number: 104-1
N=87726412116706604176181689442432094886173812740815595253113673769486917695859001854338992189607817735963
  ( 104 digits)
Divisors found:
 r1=44852631056757965967627131512225496265304129001 (pp47)
 r2=1955881072075677630830269684042401294980535053861409508963 (pp58)
Version: Msieve-1.40
Total time: 6.49 hours.
Scaled time: 12.75 units (timescale=1.963).
Factorization parameters were as follows:
name: 104-1
n: 87726412116706604176181689442432094886173812740815595253113673769486917695859001854338992189607817735963
skew: 5632.48
# norm 3.26e+014
c5: 332760
c4: -1844824732
c3: -51516079167636
c2: 54800028999535425
c1: 509268002826041010748
c0: 204082045054914963700680
# alpha -6.10
Y1: 36944582543
Y0: -48328155326484662947
# Murphy_E 2.08e-009
# M 40661182499693352341660221196869806519260094789467311883817922215784162525054796969538126733752536416370
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 283957 x 284182
Polynomial selection time: 0.64 hours.
Total sieving time: 5.53 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 6.49 hours.
 --------- CPU info (if available) ----------

(61·10¹⁵⁸-43)/9 = 6(7)₁₅₇3_<159> = 797 · 30899928821819713155011_<23> · 52479345442178546077447913843_<29> · C105

C105 = P45 · P60

P45 = 538930019607965917593456121461723178381422529_<45>

P60 = 973084915107460761577962192463788650452260933314120111165177_<60>

Number: 105-1
N=524424672379079678588623369392639247096995884972668201702910020068551232364523701651887851582888948072633
  ( 105 digits)
Divisors found:
 r1=538930019607965917593456121461723178381422529 (pp45)
 r2=973084915107460761577962192463788650452260933314120111165177 (pp60)
Version: Msieve-1.40
Total time: 7.43 hours.
Scaled time: 14.55 units (timescale=1.957).
Factorization parameters were as follows:
name: 105-1
n: 524424672379079678588623369392639247096995884972668201702910020068551232364523701651887851582888948072633
skew: 10475.57
# norm 2.35e+014
c5: 33780
c4: 697987307
c3: -22064199777319
c2: -115402330232616307
c1: 654120283538760778254
c0: -688732206002588239770960
# alpha -5.48
Y1: 17799602311
Y0: -109195414579225721363
# Murphy_E 1.89e-009
# M 96514144602388307565875898422554406240271026751061528882716032843747888924680983653499298113795581082078
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 294609 x 294834
Polynomial selection time: 0.74 hours.
Total sieving time: 6.36 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 7.43 hours.
 --------- CPU info (if available) ----------

Nov 2, 2009 (6th)

By Erik Branger / GGNFS, Msieve / Nov 2, 2009

(22·10¹⁶⁵-7)/3 = 7(3)₁₆₄1_<166> = 47 · C165

C165 = P52 · P113

P52 = 1564682708516157729593076746118340115858134618497421_<52>

P113 = 99718855423597857720868501793338779777648696574003544048348780020772616457565445007512772585819256887992072879313_<113>

Number: 73331_165
N=156028368794326241134751773049645390070921985815602836879432624113475177304964539007092198581560283687943262411347517730496453900709219858156028368794326241134751773
  ( 165 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=1564682708516157729593076746118340115858134618497421 (pp52)
 r2=99718855423597857720868501793338779777648696574003544048348780020772616457565445007512772585819256887992072879313 (pp113)
Version: Msieve-1.40
Total time: 38.13 hours.
Scaled time: 37.71 units (timescale=0.989).
Factorization parameters were as follows:
n: 156028368794326241134751773049645390070921985815602836879432624113475177304964539007092198581560283687943262411347517730496453900709219858156028368794326241134751773
m: 1000000000000000000000000000000000
deg: 5
c5: 22
c0: -7
skew: 0.80
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 3650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 805551 x 805782
Total sieving time: 35.57 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 1.49 hours.
Time per square root: 0.94 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 38.13 hours.
 --------- CPU info (if available) ----------

(59·10¹⁵²+31)/9 = 6(5)₁₅₁9_<153> = 20963 · 83107515433_<11> · C138

C138 = P58 · P80

P58 = 5989047883343168355118336561559445805153409691369558165139_<58>

P80 = 62828686959834010448240898643866203654300950428702935348705432337206310724710439_<80>

Number: 65559_152
N=376284014650024403464688154317761647052634033520374653105045692233247804740445138130561820412152041878569194583325890024179836183919186021
  ( 138 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=5989047883343168355118336561559445805153409691369558165139 (pp58)
 r2=62828686959834010448240898643866203654300950428702935348705432337206310724710439 (pp80)
Version: Msieve-1.40
Total time: 24.70 hours.
Scaled time: 24.90 units (timescale=1.008).
Factorization parameters were as follows:
n: 376284014650024403464688154317761647052634033520374653105045692233247804740445138130561820412152041878569194583325890024179836183919186021
m: 2000000000000000000000000000000
deg: 5
c5: 1475
c0: 248
skew: 0.70
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2500001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 543593 x 543818
Total sieving time: 23.50 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.80 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,154.000,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 24.70 hours.
 --------- CPU info (if available) ----------

Nov 2, 2009 (5th)

By Sinkiti Sibata / GGNFS, Msieve / Nov 2, 2009

(62·10¹⁴²-17)/9 = 6(8)₁₄₁7_<143> = 7 · 13 · 2173389745922927702807531_<25> · C117

C117 = P48 · P69

P48 = 358166541419012241609637868825419291785725536283_<48>

P69 = 972490037068366127364333661129741553894152723185471642264624912216109_<69>

Number: 68887_142
N=348313393141223706734704749064438289199394936931752715023824086413973108957877891594866729630631067309563042016582847
  ( 117 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=358166541419012241609637868825419291785725536283 (pp48)
 r2=972490037068366127364333661129741553894152723185471642264624912216109 (pp69)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.57 hours.
Scaled time: 34.21 units (timescale=1.947).
Factorization parameters were as follows:
name: 68887_142
n: 348313393141223706734704749064438289199394936931752715023824086413973108957877891594866729630631067309563042016582847
m: 20000000000000000000000000000
deg: 5
c5: 775
c0: -68
skew: 0.61
type: snfs
lss: 1
rlim: 1790000
alim: 1790000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1790000/1790000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [895000, 2395001)
Primes: RFBsize:134359, AFBsize:134558, largePrimes:4088931 encountered
Relations: rels:4299967, finalFF:392227
Max relations in full relation-set: 28
Initial matrix: 268984 x 392227 with sparse part having weight 42978490.
Pruned matrix : 232463 x 233871 with weight 23727956.
Total sieving time: 16.59 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.74 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1790000,1790000,26,26,49,49,2.3,2.3,100000
total time: 17.57 hours.
 --------- CPU info (if available) ----------

(65·10¹⁴²-11)/9 = 7(2)₁₄₁1_<143> = 14182188136387_<14> · 2301042251793941_<16> · C115

C115 = P47 · P68

P47 = 49683938243911040863561670600066704163687710361_<47>

P68 = 44543772791552787387347470419203004445531100088375155605652133154283_<68>

Number: 72221_142
N=2213110056526313597857792138014442333018479113407539281242501814967691047326942981949448418956015199512081030626163
  ( 115 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=49683938243911040863561670600066704163687710361 (pp47)
 r2=44543772791552787387347470419203004445531100088375155605652133154283 (pp68)
Version: Msieve-1.40
Total time: 10.58 hours.
Scaled time: 21.50 units (timescale=2.032).
Factorization parameters were as follows:
name: 72221_142
n: 2213110056526313597857792138014442333018479113407539281242501814967691047326942981949448418956015199512081030626163
m: 50000000000000000000000000000
deg: 5
c5: 52
c0: -275
skew: 1.40
type: snfs
lss: 1
rlim: 1840000
alim: 1840000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3

*1 These parameters were not fully adjusted. The approximate 
Factor base limits: 1840000/1840000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [920000, 2220001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 293564 x 293799
Total sieving time: 10.16 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,145.000,5,0,0,0,0,0,0,0,0,1840000,1840000,26,26,49,49,2.3,2.3,100000
total time: 10.58 hours.
 --------- CPU info (if available) ----------

(61·10¹⁷⁹-43)/9 = 6(7)₁₇₈3_<180> = 41² · 2671211 · 274287654587_<12> · 89842750365457_<14> · 851082649636320944341_<21> · 1050299838228593445391615122607_<31> · C94

C94 = P33 · P62

P33 = 623546059778895442296480169519561_<33>

P62 = 10989262396970049806453474363931603119465274029106206008787431_<62>

Mon Nov  2 01:27:00 2009  Msieve v. 1.42
Mon Nov  2 01:27:00 2009  random seeds: d6c920ea 1c141072
Mon Nov  2 01:27:00 2009  factoring 6852311267507054493047841489595293852612752095255092259071980445075187069060064528087445437791 (94 digits)
Mon Nov  2 01:27:02 2009  no P-1/P+1/ECM available, skipping
Mon Nov  2 01:27:02 2009  commencing quadratic sieve (94-digit input)
Mon Nov  2 01:27:02 2009  using multiplier of 1
Mon Nov  2 01:27:02 2009  using 64kb Pentium 4 sieve core
Mon Nov  2 01:27:02 2009  sieve interval: 18 blocks of size 65536
Mon Nov  2 01:27:02 2009  processing polynomials in batches of 6
Mon Nov  2 01:27:02 2009  using a sieve bound of 2059517 (76466 primes)
Mon Nov  2 01:27:02 2009  using large prime bound of 284213346 (28 bits)
Mon Nov  2 01:27:02 2009  using double large prime bound of 1646493387513360 (42-51 bits)
Mon Nov  2 01:27:02 2009  using trial factoring cutoff of 51 bits
Mon Nov  2 01:27:02 2009  polynomial 'A' values have 12 factors
Mon Nov  2 07:38:32 2009  76759 relations (18206 full + 58553 combined from 1116861 partial), need 76562
Mon Nov  2 07:38:37 2009  begin with 1135067 relations
Mon Nov  2 07:38:38 2009  reduce to 202625 relations in 11 passes
Mon Nov  2 07:38:38 2009  attempting to read 202625 relations
Mon Nov  2 07:38:44 2009  recovered 202625 relations
Mon Nov  2 07:38:44 2009  recovered 188056 polynomials
Mon Nov  2 07:38:45 2009  attempting to build 76759 cycles
Mon Nov  2 07:38:45 2009  found 76759 cycles in 7 passes
Mon Nov  2 07:38:45 2009  distribution of cycle lengths:
Mon Nov  2 07:38:45 2009     length 1 : 18206
Mon Nov  2 07:38:45 2009     length 2 : 13145
Mon Nov  2 07:38:45 2009     length 3 : 12782
Mon Nov  2 07:38:45 2009     length 4 : 10530
Mon Nov  2 07:38:45 2009     length 5 : 8057
Mon Nov  2 07:38:45 2009     length 6 : 5385
Mon Nov  2 07:38:45 2009     length 7 : 3551
Mon Nov  2 07:38:45 2009     length 9+: 5103
Mon Nov  2 07:38:45 2009  largest cycle: 21 relations
Mon Nov  2 07:38:45 2009  matrix is 76466 x 76759 (20.3 MB) with weight 5004334 (65.20/col)
Mon Nov  2 07:38:45 2009  sparse part has weight 5004334 (65.20/col)
Mon Nov  2 07:38:47 2009  filtering completed in 3 passes
Mon Nov  2 07:38:47 2009  matrix is 73244 x 73308 (19.4 MB) with weight 4800140 (65.48/col)
Mon Nov  2 07:38:47 2009  sparse part has weight 4800140 (65.48/col)
Mon Nov  2 07:38:47 2009  saving the first 48 matrix rows for later
Mon Nov  2 07:38:48 2009  matrix is 73196 x 73308 (12.0 MB) with weight 3773269 (51.47/col)
Mon Nov  2 07:38:48 2009  sparse part has weight 2718479 (37.08/col)
Mon Nov  2 07:38:48 2009  matrix includes 64 packed rows
Mon Nov  2 07:38:48 2009  using block size 21845 for processor cache size 512 kB
Mon Nov  2 07:38:48 2009  commencing Lanczos iteration
Mon Nov  2 07:38:48 2009  memory use: 12.3 MB
Mon Nov  2 07:39:43 2009  lanczos halted after 1159 iterations (dim = 73193)
Mon Nov  2 07:39:44 2009  recovered 15 nontrivial dependencies
Mon Nov  2 07:39:45 2009  prp33 factor: 623546059778895442296480169519561
Mon Nov  2 07:39:45 2009  prp62 factor: 10989262396970049806453474363931603119465274029106206008787431
Mon Nov  2 07:39:45 2009  elapsed time 06:12:45

(22·10¹⁴⁵+17)/3 = 7(3)₁₄₄9_<146> = 2752274513_<10> · 1566730008456407_<16> · 17181518528359567_<17> · C105

C105 = P45 · P61

P45 = 206001556297406951388011103876042896419902713_<45>

P61 = 4804890221710012505146226057101997093818448342097762588344699_<61>

Number: 73339_145
N=989814863510455309432420159547073597905623407332372470876308281179701943588715244504145580284145289268387
  ( 105 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=206001556297406951388011103876042896419902713 (pp45)
 r2=4804890221710012505146226057101997093818448342097762588344699 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 16.48 hours.
Scaled time: 32.29 units (timescale=1.960).
Factorization parameters were as follows:
name: 73339_145
n: 989814863510455309432420159547073597905623407332372470876308281179701943588715244504145580284145289268387
m: 100000000000000000000000000000
deg: 5
c5: 22
c0: 17
skew: 0.95
type: snfs
lss: 1
rlim: 1920000
alim: 1920000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1920000/1920000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [960000, 2260001)
Primes: RFBsize:143414, AFBsize:143078, largePrimes:4258182 encountered
Relations: rels:4535046, finalFF:474607
Max relations in full relation-set: 28
Initial matrix: 286558 x 474607 with sparse part having weight 50088625.
Pruned matrix : 232008 x 233504 with weight 23287895.
Total sieving time: 15.65 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.59 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1920000,1920000,26,26,49,49,2.3,2.3,100000
total time: 16.48 hours.
 --------- CPU info (if available) ----------

(62·10¹⁴⁵-53)/9 = 6(8)₁₄₄3_<146> = 3⁴ · 7 · 4444002491_<10> · 286154403651761_<15> · C119

C119 = P38 · P82

P38 = 20277487323458673341622013549649441909_<38>

P82 = 4711695927599623445659927588915785695966831005489230458903957349220464530717361011_<82>

Number: 68883_145
N=95541354443893219554761713158295632329924591379995392706939600940086281817187950677547878289330951136062210113426009999
  ( 119 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=20277487323458673341622013549649441909 (pp38)
 r2=4711695927599623445659927588915785695966831005489230458903957349220464530717361011 (pp82)
Version: Msieve-1.40
Total time: 12.36 hours.
Scaled time: 25.94 units (timescale=2.099).
Factorization parameters were as follows:
name: 68883_145
n: 95541354443893219554761713158295632329924591379995392706939600940086281817187950677547878289330951136062210113426009999
m: 100000000000000000000000000000
deg: 5
c5: 62
c0: -53
skew: 0.97
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2480001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 360185 x 360433
Total sieving time: 11.70 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.45 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 12.36 hours.
 --------- CPU info (if available) ----------

Nov 2, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.1 / Nov 24, 2009

(61·10¹⁸³-43)/9 = 6(7)₁₈₂3_<184> = 13 · 1153 · 10894858720091063_<17> · 61039604038917041_<17> · 16476593553706548463_<20> · C128

C128 = P32 · P97

P32 = 11030417785044302030364559806857_<32>

P97 = 3741295097064541878566783638460453589780064807775104741236268852291803197624791377605215812186769_<97>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2321782276
Step 1 took 2544ms
Step 2 took 1980ms
********** Factor found in step 2: 11030417785044302030364559806857
Found probable prime factor of 32 digits: 11030417785044302030364559806857
Probable prime cofactor has 97 digits

(61·10¹⁵¹-43)/9 = 6(7)₁₅₀3_<152> = 3 · 7 · 600947 · C145

C145 = P29 · P116

P29 = 83744503330471900677166329923_<29>

P116 = 64132112858217976351724434584972306655962105958394673205655435117315367038933800044622855933622801454864869748712673_<116>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2553111147
Step 1 took 2976ms
Step 2 took 2160ms
********** Factor found in step 2: 83744503330471900677166329923
Found probable prime factor of 29 digits: 83744503330471900677166329923
Probable prime cofactor has 116 digits

(61·10¹⁷⁶-43)/9 = 6(7)₁₇₅3_<177> = 31 · 2442558941_<10> · 4657225973816284327_<19> · C148

C148 = P29 · P119

P29 = 55936980294674513391151031033_<29>

P119 = 34360086679144844121313260956712869553310827453400056575190343859366941459700585511846417879165851191447319575871210593_<119>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3489160518
Step 1 took 2980ms
Step 2 took 2196ms
********** Factor found in step 2: 55936980294674513391151031033
Found probable prime factor of 29 digits: 55936980294674513391151031033
Probable prime cofactor has 119 digits

(61·10¹⁹⁴-43)/9 = 6(7)₁₉₃3_<195> = 23 · 41 · 67 · 95971 · 749939 · 22698602179251101_<17> · C163

C163 = P33 · C131

P33 = 623655988907658070344904037133739_<33>

C131 = [10529085689163555069923502028408334316210581368163244809718003699545475280131011357908335141861212186917544347038254869011830606263_<131>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3314643275
Step 1 took 10664ms
Step 2 took 5561ms
********** Factor found in step 2: 623655988907658070344904037133739
Found probable prime factor of 33 digits: 623655988907658070344904037133739
Composite cofactor has 131 digits

Nov 2, 2009 (3rd)

By Robert Backstrom / Msieve, GMP-ECM / Nov 2, 2009

(61·10¹⁵³-43)/9 = 6(7)₁₅₂3_<154> = 13 · 47 · 115811 · 96593309 · 138654749 · 151234649 · 260725193 · 735770064081398185730057_<24> · C90

C90 = P32 · P58

P32 = 45693359951345274428864482310057_<32>

P58 = 5394919918315846661654873441474430625034440751142940650701_<58>

Mon Nov 02 03:33:12 2009  
Mon Nov 02 03:33:12 2009  
Mon Nov 02 03:33:12 2009  Msieve v. 1.43
Mon Nov 02 03:33:12 2009  random seeds: cc560800 188deb0c
Mon Nov 02 03:33:12 2009  factoring 246512017736288227111883965007638091540411285199799444194590282370792883170754051216399957 (90 digits)
Mon Nov 02 03:33:13 2009  searching for 15-digit factors
Mon Nov 02 03:33:13 2009  commencing quadratic sieve (90-digit input)
Mon Nov 02 03:33:13 2009  using multiplier of 13
Mon Nov 02 03:33:13 2009  using 64kb Opteron sieve core
Mon Nov 02 03:33:13 2009  sieve interval: 18 blocks of size 65536
Mon Nov 02 03:33:13 2009  processing polynomials in batches of 6
Mon Nov 02 03:33:13 2009  using a sieve bound of 1573933 (59667 primes)
Mon Nov 02 03:33:13 2009  using large prime bound of 125914640 (26 bits)
Mon Nov 02 03:33:13 2009  using double large prime bound of 380309430790000 (42-49 bits)
Mon Nov 02 03:33:13 2009  using trial factoring cutoff of 49 bits
Mon Nov 02 03:33:13 2009  polynomial 'A' values have 12 factors
Mon Nov 02 04:18:09 2009  60043 relations (17135 full + 42908 combined from 621739 partial), need 59763
Mon Nov 02 04:18:10 2009  begin with 638874 relations
Mon Nov 02 04:18:11 2009  reduce to 141771 relations in 9 passes
Mon Nov 02 04:18:11 2009  attempting to read 141771 relations
Mon Nov 02 04:18:13 2009  recovered 141771 relations
Mon Nov 02 04:18:13 2009  recovered 114749 polynomials
Mon Nov 02 04:18:13 2009  attempting to build 60043 cycles
Mon Nov 02 04:18:13 2009  found 60043 cycles in 5 passes
Mon Nov 02 04:18:13 2009  distribution of cycle lengths:
Mon Nov 02 04:18:13 2009     length 1 : 17135
Mon Nov 02 04:18:13 2009     length 2 : 12120
Mon Nov 02 04:18:13 2009     length 3 : 10745
Mon Nov 02 04:18:13 2009     length 4 : 7680
Mon Nov 02 04:18:13 2009     length 5 : 5263
Mon Nov 02 04:18:13 2009     length 6 : 3247
Mon Nov 02 04:18:13 2009     length 7 : 1823
Mon Nov 02 04:18:13 2009     length 9+: 2030
Mon Nov 02 04:18:13 2009  largest cycle: 18 relations
Mon Nov 02 04:18:13 2009  matrix is 59667 x 60043 (14.3 MB) with weight 3498442 (58.27/col)
Mon Nov 02 04:18:13 2009  sparse part has weight 3498442 (58.27/col)
Mon Nov 02 04:18:14 2009  filtering completed in 3 passes
Mon Nov 02 04:18:14 2009  matrix is 54812 x 54876 (13.1 MB) with weight 3213472 (58.56/col)
Mon Nov 02 04:18:14 2009  sparse part has weight 3213472 (58.56/col)
Mon Nov 02 04:18:14 2009  saving the first 48 matrix rows for later
Mon Nov 02 04:18:14 2009  matrix is 54764 x 54876 (8.3 MB) with weight 2511809 (45.77/col)
Mon Nov 02 04:18:14 2009  sparse part has weight 1845177 (33.62/col)
Mon Nov 02 04:18:14 2009  matrix includes 64 packed rows
Mon Nov 02 04:18:14 2009  using block size 21950 for processor cache size 1024 kB
Mon Nov 02 04:18:15 2009  commencing Lanczos iteration
Mon Nov 02 04:18:15 2009  memory use: 8.5 MB
Mon Nov 02 04:18:31 2009  lanczos halted after 868 iterations (dim = 54761)
Mon Nov 02 04:18:31 2009  recovered 16 nontrivial dependencies
Mon Nov 02 04:18:31 2009  prp32 factor: 45693359951345274428864482310057
Mon Nov 02 04:18:31 2009  prp58 factor: 5394919918315846661654873441474430625034440751142940650701
Mon Nov 02 04:18:31 2009  elapsed time 00:45:19

(61·10¹⁷⁰-43)/9 = 6(7)₁₆₉3_<171> = 124054861451_<12> · 428268889962110713_<18> · 141351960293925516511_<21> · 117582689526846515424017975289967_<33> · C90

C90 = P35 · P56

P35 = 38211612373060375875899611707596153_<35>

P56 = 20087062029305696571393777932719711095353116697806519111_<56>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 767559027977448817671123325954882817351796463364504665823517850583942819516922282264579983 (90 digits)
Using B1=2354000, B2=3567716890, polynomial Dickson(6), sigma=1412220974
Step 1 took 14609ms
Step 2 took 7110ms
********** Factor found in step 2: 38211612373060375875899611707596153
Found probable prime factor of 35 digits: 38211612373060375875899611707596153
Probable prime cofactor 20087062029305696571393777932719711095353116697806519111 has 56 digits

Nov 2, 2009 (2nd)

By Alexander Mkrtychyan / GGNFS / Nov 1, 2009

The progress report of (64·10²²⁴+53)/9.

I am doing the classic sieving
n: 133391692198670251568394505929677567269013526751287021405198107505366931365805873402947122699514370870589216115383813751849767606661247629171095687696700639863273515496362992142395631422080493549261135079930803059671939807
m: 2000000000000000000000000000000000000000000000
skew: 3.05
c5: 1
c0: 265
type: snfs
a0: -2140000000
a1: 2140000000

Already sieved b in [0; 250000]

GGNFS-0.77.1-VC8(Sat 01/17/2009) : matbuild
largePrimes: 22993308 , relations: 15050039
rels:15050039, initialFF:0, finalFF:2464508

Nov 2, 2009

Factorizations of 677...773 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Nov 1, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve / Nov 1, 2009

(62·10¹⁴¹+1)/9 = 6(8)₁₄₀9_<142> = C142

C142 = P33 · P51 · P60

P33 = 568661993488414430953673552639897_<33>

P51 = 107136670558984692997845953645695662813997409001629_<51>

P60 = 113072457467357463380646477639339817944564509365675623543253_<60>

Number: 142-2
N=6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
  ( 142 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=568661993488414430953673552639897 (pp33)
 r2=107136670558984692997845953645695662813997409001629 (pp51)
 r3=113072457467357463380646477639339817944564509365675623543253 (pp60)
Version: Msieve-1.40
Total time: 6.00 hours.
Scaled time: 11.17 units (timescale=1.860).
Factorization parameters were as follows:
n: 6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
m: 20000000000000000000000000000
deg: 5
c5: 155
c0: 8
skew: 0.55
type: snfs
lss: 1
rlim: 1740000
alim: 1740000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1740000/1740000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [870000, 1870001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 261982 x 262208
Total sieving time: 5.74 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,143.000,5,0,0,0,0,0,0,0,0,1740000,1740000,26,26,48,48,2.3,2.3,100000
total time: 6.00 hours.
 --------- CPU info (if available) ----------

2·10²⁰⁰+9 = 2(0)₁₉₉9_<201> = 11 · 19 · 139 · 1259 · 5326345617905713_<16> · 1991350749169858454527790418207027923203_<40> · C138

C138 = P62 · P77

P62 = 26929252008257191020431416687258193026593735560915113070125073_<62>

P77 = 19144401031633854466395611803227504370594464318406318304124607255623786615883_<77>

N=515544399928007014946837975043806426611470201510365146903403741438897213435687943769990979066673545308632679985149733037848236754218334459
  ( 138 digits)
Divisors found:
 r1=26929252008257191020431416687258193026593735560915113070125073 (pp62)
 r2=19144401031633854466395611803227504370594464318406318304124607255623786615883 (pp77)
Version: Msieve-1.40
Total time: 393.79 hours.
Scaled time: 728.52 units (timescale=1.850).
Factorization parameters were as follows:
name: 138
n: 515544399928007014946837975043806426611470201510365146903403741438897213435687943769990979066673545308632679985149733037848236754218334459
skew: 59396.92
# norm 6.88e+018
c5: 11646900
c4: -656423698046
c3: -91862773336305875
c2: -7446857964439791899471
c1: 144615163516304815228906947
c0: 872413083934548205729822156721
# alpha -5.87
Y1: 3733924185275977
Y0: -134651526480555153942964818
# Murphy_E 2.69e-011
# M 115470477286257391141601787983228737831086354664957529203110934439337617085329047796142281722271255945999979840269516821464770418268211574
type: gnfs
rlim: 11000000
alim: 11000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [5500000, 11700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1968879 x 1969105
Total sieving time: 386.79 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 5.16 hours.
Time per square root: 1.60 hours.
Prototype def-par.txt line would be:
gnfs,137,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,11000000,11000000,28,28,56,56,2.5,2.5,100000
total time: 393.79 hours.
 --------- CPU info (if available) ----------

(62·10¹⁴⁴+1)/9 = 6(8)₁₄₃9_<145> = 7 · 6947 · C141

C141 = P61 · P80

P61 = 4257496835970046328258574077329808655160261495634343872354609_<61>

P80 = 33273578231402606240782600493794607850183398235273622964448002794566112533642949_<80>

Number: s141
N=141662154041598406072279686789547160930491864708073143368954510454438480924733983608317853315694110281702047932075282010505848133601120501941
  ( 141 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=4257496835970046328258574077329808655160261495634343872354609 (pp61)
 r2=33273578231402606240782600493794607850183398235273622964448002794566112533642949 (pp80)
Version: Msieve-1.40
Total time: 6.07 hours.
Scaled time: 10.97 units (timescale=1.808).
Factorization parameters were as follows:
n: 141662154041598406072279686789547160930491864708073143368954510454438480924733983608317853315694110281702047932075282010505848133601120501941
m: 100000000000000000000000000000
deg: 5
c5: 31
c0: 5
skew: 0.69
type: snfs
lss: 1
rlim: 1930000
alim: 1930000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1930000/1930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [965000, 2065001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 295233 x 295458
Total sieving time: 5.87 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000
total time: 6.07 hours.
 --------- CPU info (if available) ----------

Nov 1, 2009 (3rd)

By Sinkiti Sibata / GGNFS, Msieve / Nov 1, 2009

(67·10¹³⁸-13)/9 = 7(4)₁₃₇3_<139> = 3² · 19 · 36017 · C133

C133 = P59 · P74

P59 = 42023764615347595396734863188057129653368717733683543157781_<59>

P74 = 28762967581330039305542481296456056372151385010601032288129901194001326429_<74>

Number: 74443_138
N=1208728179276687315532519722159215010787538185662560653123101947219603160827796952356066497585439176861161313922169054418981232294049
  ( 133 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=42023764615347595396734863188057129653368717733683543157781 (pp59)
 r2=28762967581330039305542481296456056372151385010601032288129901194001326429 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.22 hours.
Scaled time: 19.90 units (timescale=1.948).
Factorization parameters were as follows:
name: 74443_138
n: 1208728179276687315532519722159215010787538185662560653123101947219603160827796952356066497585439176861161313922169054418981232294049
m: 5000000000000000000000000000
deg: 5
c5: 536
c0: -325
skew: 0.90
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 1690001)
Primes: RFBsize:119758, AFBsize:119698, largePrimes:3701668 encountered
Relations: rels:3802277, finalFF:375456
Max relations in full relation-set: 28
Initial matrix: 239523 x 375456 with sparse part having weight 35117704.
Pruned matrix : 200088 x 201349 with weight 15754132.
Total sieving time: 9.66 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000
total time: 10.22 hours.
 --------- CPU info (if available) ----------

(22·10¹⁴⁰+17)/3 = 7(3)₁₃₉9_<141> = 18999512297_<11> · C131

C131 = P50 · P82

P50 = 17503953742095815633532786349291591409121689703227_<50>

P82 = 2205072210500590718176371702165784035293904953432860513137148250438246160864874681_<82>

Number: 73339_140
N=38597481970583306985468424591600627933388333190715549730478080878147992039131304936218139038336670907512891583847234230579436295587
  ( 131 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=17503953742095815633532786349291591409121689703227 (pp50)
 r2=2205072210500590718176371702165784035293904953432860513137148250438246160864874681 (pp82)
Version: Msieve-1.40
Total time: 6.61 hours.
Scaled time: 13.02 units (timescale=1.969).
Factorization parameters were as follows:
name: 73339_140
n: 38597481970583306985468424591600627933388333190715549730478080878147992039131304936218139038336670907512891583847234230579436295587
m: 10000000000000000000000000000
deg: 5
c5: 22
c0: 17
skew: 0.95
type: snfs
lss: 1
rlim: 1590000
alim: 1590000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1590000/1590000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [795000, 1595001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 242040 x 242274
Total sieving time: 6.32 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1590000,1590000,26,26,48,48,2.3,2.3,100000
total time: 6.61 hours.
 --------- CPU info (if available) ----------

(62·10¹⁴⁰-17)/9 = 6(8)₁₃₉7_<141> = 3² · 479 · 2663 · 25237 · 4157699964847379_<16> · C114

C114 = P54 · P61

P54 = 189991277415596029678484840140503978996511068131431747_<54>

P61 = 3010062092706075056003895448693420219313246593121390246857139_<61>

Number: 68887_140
N=571885542093489440362382768505594648425665028980993844375232112444849040293722899734811215715075731527647038191833
  ( 114 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=189991277415596029678484840140503978996511068131431747 (pp54)
 r2=3010062092706075056003895448693420219313246593121390246857139 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.49 hours.
Scaled time: 19.74 units (timescale=1.882).
Factorization parameters were as follows:
name: 68887_140
n: 571885542093489440362382768505594648425665028980993844375232112444849040293722899734811215715075731527647038191833
m: 10000000000000000000000000000
deg: 5
c5: 62
c0: -17
skew: 0.77
type: snfs
lss: 1
rlim: 1620000
alim: 1620000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1620000/1620000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [810000, 1710001)
Primes: RFBsize:122540, AFBsize:122556, largePrimes:3860497 encountered
Relations: rels:4035041, finalFF:430705
Max relations in full relation-set: 28
Initial matrix: 245162 x 430705 with sparse part having weight 41572703.
Pruned matrix : 195424 x 196713 with weight 16613410.
Total sieving time: 9.92 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000
total time: 10.49 hours.
 --------- CPU info (if available) ----------

(22·10¹⁴²+17)/3 = 7(3)₁₄₁9_<143> = 7 · 241 · 4729 · C136

C136 = P61 · P76

P61 = 7890278994627629478652174071224520898225084894273485579113341_<61>

P76 = 1164996631608428630808474583554267570501191000927767091966829090137072008873_<76>

Number: 73339_142
N=9192148451191927087544225201954635159658635361217381400080364446959193420728102557970179751209488269335297779022338968078551421024674693
  ( 136 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=7890278994627629478652174071224520898225084894273485579113341 (pp61)
 r2=1164996631608428630808474583554267570501191000927767091966829090137072008873 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 12.74 hours.
Scaled time: 24.98 units (timescale=1.961).
Factorization parameters were as follows:
name: 73339_142
n: 9192148451191927087544225201954635159658635361217381400080364446959193420728102557970179751209488269335297779022338968078551421024674693
m: 20000000000000000000000000000
deg: 5
c5: 275
c0: 68
skew: 0.76
type: snfs
lss: 1
rlim: 1750000
alim: 1750000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1750000/1750000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [875000, 1975001)
Primes: RFBsize:131608, AFBsize:131403, largePrimes:3900124 encountered
Relations: rels:4052152, finalFF:401107
Max relations in full relation-set: 28
Initial matrix: 263078 x 401107 with sparse part having weight 39060172.
Pruned matrix : 221049 x 222428 with weight 18826482.
Total sieving time: 11.95 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.58 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1750000,1750000,26,26,48,48,2.3,2.3,100000
total time: 12.74 hours.
 --------- CPU info (if available) ----------

(67·10¹³⁹-13)/9 = 7(4)₁₃₈3_<140> = 127 · 314267 · C133

C133 = P58 · P75

P58 = 2566690768266226258423170836580440422708903717424718866809_<58>

P75 = 726701813472812676847611319548437610784202539957759174853069485338437045303_<75>

Number: 74443_139
N=1865218835922993421448331234781188853794100513820184457837996284378290310404457086842036156287198501190320023140071912983276356048127
  ( 133 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=2566690768266226258423170836580440422708903717424718866809 (pp58)
 r2=726701813472812676847611319548437610784202539957759174853069485338437045303 (pp75)
Version: Msieve-1.40
Total time: 7.39 hours.
Scaled time: 15.21 units (timescale=2.058).
Factorization parameters were as follows:
name: 74443_139
n: 1865218835922993421448331234781188853794100513820184457837996284378290310404457086842036156287198501190320023140071912983276356048127
m: 10000000000000000000000000000
deg: 5
c5: 67
c0: -130
skew: 1.14
type: snfs
lss: 1
rlim: 1620000
alim: 1620000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1620000/1620000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [810000, 1710001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 241552 x 241791
Total sieving time: 7.01 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000
total time: 7.39 hours.
 --------- CPU info (if available) ----------

Nov 1, 2009 (2nd)

By juno1369 / GMP-ECM, Msieve v-1.40, Alpertron ECM, GGNFS / Nov 1, 2009

(67·10¹⁴³-13)/9 = 7(4)₁₄₂3_<144> = 7 · 313 · 1129 · 426868832072472269_<18> · 67933898702369285064861293_<26> · C95

C95 = P42 · P53

P42 = 240268262875952563650189119243541705525181_<42>

P53 = 43193518248142142096188006740990085557670555853768681_<53>

Number: 74443_143
N=10378031596981870252939464149157434908883206662215579250592526126932431653369574440179194656261
  ( 95 digits)
Divisors found:
 r1=240268262875952563650189119243541705525181 (pp42)
 r2=43193518248142142096188006740990085557670555853768681 (pp53)
Version: Msieve-1.40
Total time: 4.91 hours.
Scaled time: 8.45 units (timescale=1.720).
Factorization parameters were as follows:
name: 74443_143
n:  10378031596981870252939464149157434908883206662215579250592526126932431653369574440179194656261
m:  4835729701784787971244
deg: 4
c4: 18978720
c3: 78652993
c2: -5560682268093890
c1: 16083300182081943339
c0: -2029851474788969042047
skew: 1635.250
type: gnfs
# adj. I(F,S) = 52.154
# E(F1,F2) = 5.152788e-005
# GGNFS version 0.77.1-20060513-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1256969454.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 2
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1320001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 159725 x 159954
Total sieving time: 4.71 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 4.91 hours.
 --------- CPU info (if available) ----------

(22·10¹⁴⁸+17)/3 = 7(3)₁₄₇9_<149> = 7 · 41 · 74343761 · 360046997 · 2870153148092932417635948631_<28> · C103

C103 = P40 · P64

P40 = 1289700889060485219183727689624462207083_<40>

P64 = 2578824207884392367663721272453581663123001803062041082460324117_<64>

Number: 73339_148
N=3325911873639202393250906590833897427097798202533779599082871166424239204175531089139368010881353120711
  ( 103 digits)
Divisors found:
 r1=1289700889060485219183727689624462207083 (pp40)
 r2=2578824207884392367663721272453581663123001803062041082460324117 (pp64)
Version: Msieve-1.40
Total time: -639.96 hours.
Scaled time: -1146.17 units (timescale=1.791).
Factorization parameters were as follows:
name: 73339_148
n: 3325911873639202393250906590833897427097798202533779599082871166424239204175531089139368010881353120711
skew: 12521.91
# norm 1.49e+014
c5: 7020
c4: 437449634
c3: -11015077232503
c2: -72660396839571297
c1: 387503975999076601291
c0: -163681226940922413934154
# alpha -5.26
Y1: 330796961
Y0: -54339381655504281315
# Murphy_E 2.31e-009
# M 1447140866410042080494015316695201142127604977322561648360653862423286968002221708106929140054468402564
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 2
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 226107 x 226351
Total sieving time: -640.39 hours. (glitch)
Total relation processing time: 0.09 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: -639.96 hours. (glitch)
 --------- CPU info (if available) ----------

Nov 1, 2009

By Jo Yeong Uk / GMP-ECM / Nov 1, 2009

(67·10¹⁴⁸-13)/9 = 7(4)₁₄₇3_<149> = 17 · 71 · 19717 · 10485116375196939239516371649991113_<35> · C108

C108 = P33 · P75

P33 = 493110501797734488620529137369077_<33>

P75 = 605015749007193241077747897233415261264358597396216286880140160508083364397_<75>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 298339619588469240853281754870823326690224613752882667372313547932421348293005050207542165389168819270551569 (108 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3697172534
Step 1 took 3448ms
Step 2 took 3650ms
********** Factor found in step 2: 493110501797734488620529137369077
Found probable prime factor of 33 digits: 493110501797734488620529137369077
Probable prime cofactor 605015749007193241077747897233415261264358597396216286880140160508083364397 has 75 digits

(22·10¹⁷⁴+17)/3 = 7(3)₁₇₃9_<175> = 13 · 19 · 5708523429678096119_<19> · 24284845928264463317467_<23> · 42122343917678177961329_<23> · C109

C109 = P40 · P69

P40 = 5876623023071862162976999206484510040519_<40>

P69 = 865177009851691364199653394697094788721195171472216998317404188606519_<69>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 5084319135126920777631876200778913427885337276529824188767754686508222745647975461621247367668558838837543361 (109 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2954220047
Step 1 took 3495ms
Step 2 took 3806ms
********** Factor found in step 2: 5876623023071862162976999206484510040519
Found probable prime factor of 40 digits: 5876623023071862162976999206484510040519
Probable prime cofactor 865177009851691364199653394697094788721195171472216998317404188606519 has 69 digits

October 2009

Oct 31, 2009 (4th)

By Sinkiti Sibata / GGNFS, Msieve / Oct 30, 2009

(67·10¹³⁵-13)/9 = 7(4)₁₃₄3_<136> = 3 · 6366299 · 343322550875497_<15> · 18427413715447589_<17> · C98

C98 = P39 · P60

P39 = 209356080628475924973631219217832056833_<39>

P60 = 294287428717985459743101905958444395235619064479793257863671_<60>

Number: 74443_135
N=61610862654629425320461097325772360749579711146654232773145044842857294758491948071998405438013943
  ( 98 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=209356080628475924973631219217832056833 (pp39)
 r2=294287428717985459743101905958444395235619064479793257863671 (pp60)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 8.70 hours.
Scaled time: 4.09 units (timescale=0.470).
Factorization parameters were as follows:
name: 74443_135
n: 61610862654629425320461097325772360749579711146654232773145044842857294758491948071998405438013943
m: 1000000000000000000000000000
deg: 5
c5: 67
c0: -13
skew: 0.72
type: snfs
lss: 1
rlim: 1340000
alim: 1340000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1340000/1340000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [670000, 1345001)
Primes: RFBsize:102852, AFBsize:102619, largePrimes:3220602 encountered
Relations: rels:3134916, finalFF:237995
Max relations in full relation-set: 28
Initial matrix: 205536 x 237995 with sparse part having weight 19742667.
Pruned matrix : 195806 x 196897 with weight 13765686.
Total sieving time: 7.72 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.78 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1340000,1340000,26,26,48,48,2.3,2.3,75000
total time: 8.70 hours.
 --------- CPU info (if available) ----------

By Sinkiti Sibata / GGNFS, Msieve / Oct 31, 2009

(62·10¹⁴²-53)/9 = 6(8)₁₄₁3_<143> = 3 · 38231 · C138

C138 = P31 · P108

P31 = 1897221955530729728636794936489_<31>

P108 = 316587764021525936138950181020917122053434327967423987470819925009163201030651339553471066974369806252970879_<108>

Number: 68883_142
N=600637256754020636733618345399360805706441447070779288089847583452249822472939838428577933168448718656665087571943264967250737960371503831
  ( 138 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=1897221955530729728636794936489 (pp31)
 r2=316587764021525936138950181020917122053434327967423987470819925009163201030651339553471066974369806252970879 (pp108)
Version: GGNFS-0.77.1-20060513-k8
Total time: 23.85 hours.
Scaled time: 46.67 units (timescale=1.957).
Factorization parameters were as follows:
name: 68883_142
n: 600637256754020636733618345399360805706441447070779288089847583452249822472939838428577933168448718656665087571943264967250737960371503831
m: 20000000000000000000000000000
deg: 5
c5: 775
c0: -212
skew: 0.77
type: snfs
lss: 1
rlim: 1790000
alim: 1790000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1790000/1790000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [895000, 2995001)
Primes: RFBsize:134359, AFBsize:134018, largePrimes:4285211 encountered
Relations: rels:4611288, finalFF:372028
Max relations in full relation-set: 28
Initial matrix: 268444 x 372028 with sparse part having weight 44790153.
Pruned matrix : 239391 x 240797 with weight 28079612.
Total sieving time: 22.68 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.91 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1790000,1790000,26,26,49,49,2.3,2.3,100000
total time: 23.85 hours.
 --------- CPU info (if available) ----------

(62·10¹⁴⁶-17)/9 = 6(8)₁₄₅7_<147> = 3 · 467 · 8199181 · C137

C137 = P34 · P104

P34 = 1362518920977791402556581436857353_<34>

P104 = 44014728682733656162984696344578934532017463783335918028526772701777175353463305906690407115138338099859_<104>

Number: 68887_146
N=59970900631928507134678788225256830909677272320730651392923130286217054871587593448388419881377479427147482375478201781976233202452413227
  ( 137 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=1362518920977791402556581436857353 (pp34)
 r2=44014728682733656162984696344578934532017463783335918028526772701777175353463305906690407115138338099859 (pp104)
Version: Msieve-1.40
Total time: 13.52 hours.
Scaled time: 28.20 units (timescale=2.085).
Factorization parameters were as follows:
name: 68887_146
n: 59970900631928507134678788225256830909677272320730651392923130286217054871587593448388419881377479427147482375478201781976233202452413227
m: 200000000000000000000000000000
deg: 5
c5: 155
c0: -136
skew: 0.97
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 356196 x 356425
Total sieving time: 12.87 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,148.000,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 13.52 hours.
 --------- CPU info (if available) ----------

(67·10¹³⁶-13)/9 = 7(4)₁₃₅3_<137> = 107071636716652010184212485927_<30> · C108

C108 = P49 · P60

P49 = 1388497017615733774323439876017921362377077183293_<49>

P60 = 500740709756802603000974713552278904512748721414586970310513_<60>

Number: 73339_136
N=695276982096106176900642839859448798309712051367578561086347155086278922700828965871905561126372859625859309
  ( 108 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=1388497017615733774323439876017921362377077183293 (pp49)
 r2=500740709756802603000974713552278904512748721414586970310513 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 9.04 hours.
Scaled time: 17.71 units (timescale=1.960).
Factorization parameters were as follows:
name: 73339_136
n: 695276982096106176900642839859448798309712051367578561086347155086278922700828965871905561126372859625859309
m: 2000000000000000000000000000
deg: 5
c5: 335
c0: -208
skew: 0.91
type: snfs
lss: 1
rlim: 1450000
alim: 1450000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1450000/1450000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [725000, 1550001)
Primes: RFBsize:110630, AFBsize:110649, largePrimes:3508814 encountered
Relations: rels:3522800, finalFF:297635
Max relations in full relation-set: 28
Initial matrix: 221346 x 297635 with sparse part having weight 27324926.
Pruned matrix : 198752 x 199922 with weight 15189467.
Total sieving time: 8.42 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000
total time: 9.04 hours.
 --------- CPU info (if available) ----------

(64·10¹⁸⁵+71)/9 = 7(1)₁₈₄9_<186> = 593707 · 594449 · 4422329046727_<13> · 40284292656009544724056072361587_<32> · 9116432441824664823352631671213357_<34> · C97

C97 = P47 · P50

P47 = 13226685334951086277235559910788997247553626789_<47>

P50 = 93796786332729755561282648937916873301551400163929_<50>

Sat Oct 31 07:48:36 2009  Msieve v. 1.40
Sat Oct 31 07:48:36 2009  random seeds: 95692308 2fbe9ed9
Sat Oct 31 07:48:36 2009  factoring 1240620578252657138397677340020548602052064584196378623862760965588007134959583060094673085893981 (97 digits)
Sat Oct 31 07:48:37 2009  no P-1/P+1/ECM available, skipping
Sat Oct 31 07:48:37 2009  commencing quadratic sieve (97-digit input)
Sat Oct 31 07:48:37 2009  using multiplier of 1
Sat Oct 31 07:48:37 2009  using 32kb Intel Core sieve core
Sat Oct 31 07:48:37 2009  sieve interval: 36 blocks of size 32768
Sat Oct 31 07:48:37 2009  processing polynomials in batches of 6
Sat Oct 31 07:48:37 2009  using a sieve bound of 2319689 (85882 primes)
Sat Oct 31 07:48:37 2009  using large prime bound of 347953350 (28 bits)
Sat Oct 31 07:48:37 2009  using double large prime bound of 2369942626511550 (43-52 bits)
Sat Oct 31 07:48:37 2009  using trial factoring cutoff of 52 bits
Sat Oct 31 07:48:37 2009  polynomial 'A' values have 12 factors
Sat Oct 31 12:43:57 2009  86053 relations (20821 full + 65232 combined from 1294325 partial), need 85978
Sat Oct 31 12:43:58 2009  begin with 1315146 relations
Sat Oct 31 12:43:58 2009  reduce to 225963 relations in 11 passes
Sat Oct 31 12:43:58 2009  attempting to read 225963 relations
Sat Oct 31 12:44:00 2009  recovered 225963 relations
Sat Oct 31 12:44:00 2009  recovered 211772 polynomials
Sat Oct 31 12:44:00 2009  attempting to build 86053 cycles
Sat Oct 31 12:44:00 2009  found 86053 cycles in 6 passes
Sat Oct 31 12:44:00 2009  distribution of cycle lengths:
Sat Oct 31 12:44:00 2009     length 1 : 20821
Sat Oct 31 12:44:00 2009     length 2 : 14726
Sat Oct 31 12:44:00 2009     length 3 : 14389
Sat Oct 31 12:44:00 2009     length 4 : 11723
Sat Oct 31 12:44:00 2009     length 5 : 8681
Sat Oct 31 12:44:00 2009     length 6 : 6191
Sat Oct 31 12:44:00 2009     length 7 : 3942
Sat Oct 31 12:44:00 2009     length 9+: 5580
Sat Oct 31 12:44:00 2009  largest cycle: 21 relations
Sat Oct 31 12:44:00 2009  matrix is 85882 x 86053 (23.8 MB) with weight 5898371 (68.54/col)
Sat Oct 31 12:44:00 2009  sparse part has weight 5898371 (68.54/col)
Sat Oct 31 12:44:01 2009  filtering completed in 3 passes
Sat Oct 31 12:44:01 2009  matrix is 82214 x 82278 (22.9 MB) with weight 5679157 (69.02/col)
Sat Oct 31 12:44:01 2009  sparse part has weight 5679157 (69.02/col)
Sat Oct 31 12:44:01 2009  saving the first 48 matrix rows for later
Sat Oct 31 12:44:01 2009  matrix is 82166 x 82278 (16.5 MB) with weight 4746522 (57.69/col)
Sat Oct 31 12:44:01 2009  sparse part has weight 3827985 (46.53/col)
Sat Oct 31 12:44:01 2009  matrix includes 64 packed rows
Sat Oct 31 12:44:01 2009  using block size 32911 for processor cache size 8192 kB
Sat Oct 31 12:44:01 2009  commencing Lanczos iteration
Sat Oct 31 12:44:01 2009  memory use: 14.7 MB
Sat Oct 31 12:44:26 2009  lanczos halted after 1301 iterations (dim = 82164)
Sat Oct 31 12:44:26 2009  recovered 16 nontrivial dependencies
Sat Oct 31 12:44:27 2009  prp47 factor: 13226685334951086277235559910788997247553626789
Sat Oct 31 12:44:27 2009  prp50 factor: 93796786332729755561282648937916873301551400163929
Sat Oct 31 12:44:27 2009  elapsed time 04:55:51

(59·10¹⁷⁴+31)/9 = 6(5)₁₇₃9_<175> = 41 · 251 · 3754148753_<10> · 182442596131_<12> · 247407888474658786954353161_<27> · 3665302763719338852949381637894473_<34> · C91

C91 = P34 · P57

P34 = 1673659438408664325758148924770227_<34>

P57 = 612806996955643428028548588301906533880212069329060037253_<57>

Sat Oct 31 11:29:05 2009  Msieve v. 1.42
Sat Oct 31 11:29:05 2009  random seeds: 27e0594c 2c6ccd51
Sat Oct 31 11:29:05 2009  factoring 1025630214377682248913408120542627988922255145298292474518193455947066469922875791085266431 (91 digits)
Sat Oct 31 11:29:06 2009  searching for 15-digit factors
Sat Oct 31 11:29:07 2009  commencing quadratic sieve (91-digit input)
Sat Oct 31 11:29:07 2009  using multiplier of 39
Sat Oct 31 11:29:07 2009  using 32kb Intel Core sieve core
Sat Oct 31 11:29:07 2009  sieve interval: 36 blocks of size 32768
Sat Oct 31 11:29:07 2009  processing polynomials in batches of 6
Sat Oct 31 11:29:07 2009  using a sieve bound of 1652503 (62270 primes)
Sat Oct 31 11:29:07 2009  using large prime bound of 145420264 (27 bits)
Sat Oct 31 11:29:07 2009  using double large prime bound of 492861412574344 (42-49 bits)
Sat Oct 31 11:29:07 2009  using trial factoring cutoff of 49 bits
Sat Oct 31 11:29:07 2009  polynomial 'A' values have 12 factors
Sat Oct 31 13:01:36 2009  62513 relations (16385 full + 46128 combined from 695793 partial), need 62366
Sat Oct 31 13:01:37 2009  begin with 712178 relations
Sat Oct 31 13:01:38 2009  reduce to 153635 relations in 10 passes
Sat Oct 31 13:01:38 2009  attempting to read 153635 relations
Sat Oct 31 13:01:40 2009  recovered 153635 relations
Sat Oct 31 13:01:40 2009  recovered 135212 polynomials
Sat Oct 31 13:01:40 2009  attempting to build 62513 cycles
Sat Oct 31 13:01:40 2009  found 62513 cycles in 5 passes
Sat Oct 31 13:01:40 2009  distribution of cycle lengths:
Sat Oct 31 13:01:40 2009     length 1 : 16385
Sat Oct 31 13:01:40 2009     length 2 : 11845
Sat Oct 31 13:01:40 2009     length 3 : 11127
Sat Oct 31 13:01:40 2009     length 4 : 8447
Sat Oct 31 13:01:40 2009     length 5 : 6027
Sat Oct 31 13:01:40 2009     length 6 : 3706
Sat Oct 31 13:01:40 2009     length 7 : 2267
Sat Oct 31 13:01:40 2009     length 9+: 2709
Sat Oct 31 13:01:40 2009  largest cycle: 17 relations
Sat Oct 31 13:01:41 2009  matrix is 62270 x 62513 (15.3 MB) with weight 3763141 (60.20/col)
Sat Oct 31 13:01:41 2009  sparse part has weight 3763141 (60.20/col)
Sat Oct 31 13:01:41 2009  filtering completed in 3 passes
Sat Oct 31 13:01:41 2009  matrix is 58420 x 58484 (14.4 MB) with weight 3545107 (60.62/col)
Sat Oct 31 13:01:42 2009  sparse part has weight 3545107 (60.62/col)
Sat Oct 31 13:01:42 2009  saving the first 48 matrix rows for later
Sat Oct 31 13:01:42 2009  matrix is 58372 x 58484 (8.7 MB) with weight 2731776 (46.71/col)
Sat Oct 31 13:01:42 2009  sparse part has weight 1934628 (33.08/col)
Sat Oct 31 13:01:42 2009  matrix includes 64 packed rows
Sat Oct 31 13:01:42 2009  using block size 23393 for processor cache size 1024 kB
Sat Oct 31 13:01:42 2009  commencing Lanczos iteration
Sat Oct 31 13:01:42 2009  memory use: 9.1 MB
Sat Oct 31 13:02:02 2009  lanczos halted after 925 iterations (dim = 58372)
Sat Oct 31 13:02:03 2009  recovered 19 nontrivial dependencies
Sat Oct 31 13:02:04 2009  prp34 factor: 1673659438408664325758148924770227
Sat Oct 31 13:02:04 2009  prp57 factor: 612806996955643428028548588301906533880212069329060037253
Sat Oct 31 13:02:04 2009  elapsed time 01:32:59

(65·10¹⁸⁷+61)/9 = 7(2)₁₈₆9_<188> = 131 · 5507 · 220729284101_<12> · 2299975915314223_<16> · 1109471659166831215174847_<25> · 1512052274095148841868452958388463932723_<40> · C93

C93 = P42 · P51

P42 = 309843707618510847624745331660074576027487_<42>

P51 = 379380961349370970936336620824720600414315083305277_<51>

Sat Oct 31 13:27:52 2009  Msieve v. 1.42
Sat Oct 31 13:27:52 2009  random seeds: 12ba8844 239eac6d
Sat Oct 31 13:27:52 2009  factoring 117548803664364063729993986270961475590052376474609853792498756031020401498410673032364148899 (93 digits)
Sat Oct 31 13:27:53 2009  searching for 15-digit factors
Sat Oct 31 13:27:53 2009  commencing quadratic sieve (93-digit input)
Sat Oct 31 13:27:54 2009  using multiplier of 59
Sat Oct 31 13:27:54 2009  using 32kb Intel Core sieve core
Sat Oct 31 13:27:54 2009  sieve interval: 36 blocks of size 32768
Sat Oct 31 13:27:54 2009  processing polynomials in batches of 6
Sat Oct 31 13:27:54 2009  using a sieve bound of 1850521 (69412 primes)
Sat Oct 31 13:27:54 2009  using large prime bound of 209108873 (27 bits)
Sat Oct 31 13:27:54 2009  using double large prime bound of 947698977581332 (42-50 bits)
Sat Oct 31 13:27:54 2009  using trial factoring cutoff of 50 bits
Sat Oct 31 13:27:54 2009  polynomial 'A' values have 12 factors
Sat Oct 31 15:05:32 2009  69729 relations (18960 full + 50769 combined from 871863 partial), need 69508
Sat Oct 31 15:05:33 2009  begin with 890823 relations
Sat Oct 31 15:05:34 2009  reduce to 171658 relations in 13 passes
Sat Oct 31 15:05:34 2009  attempting to read 171658 relations
Sat Oct 31 15:05:37 2009  recovered 171658 relations
Sat Oct 31 15:05:37 2009  recovered 148129 polynomials
Sat Oct 31 15:05:37 2009  attempting to build 69729 cycles
Sat Oct 31 15:05:37 2009  found 69729 cycles in 5 passes
Sat Oct 31 15:05:37 2009  distribution of cycle lengths:
Sat Oct 31 15:05:37 2009     length 1 : 18960
Sat Oct 31 15:05:37 2009     length 2 : 13312
Sat Oct 31 15:05:37 2009     length 3 : 12246
Sat Oct 31 15:05:37 2009     length 4 : 9183
Sat Oct 31 15:05:37 2009     length 5 : 6467
Sat Oct 31 15:05:37 2009     length 6 : 4046
Sat Oct 31 15:05:37 2009     length 7 : 2505
Sat Oct 31 15:05:37 2009     length 9+: 3010
Sat Oct 31 15:05:37 2009  largest cycle: 20 relations
Sat Oct 31 15:05:38 2009  matrix is 69412 x 69729 (17.5 MB) with weight 4296010 (61.61/col)
Sat Oct 31 15:05:38 2009  sparse part has weight 4296010 (61.61/col)
Sat Oct 31 15:05:39 2009  filtering completed in 3 passes
Sat Oct 31 15:05:39 2009  matrix is 64555 x 64618 (16.3 MB) with weight 4009614 (62.05/col)
Sat Oct 31 15:05:39 2009  sparse part has weight 4009614 (62.05/col)
Sat Oct 31 15:05:39 2009  saving the first 48 matrix rows for later
Sat Oct 31 15:05:39 2009  matrix is 64507 x 64618 (10.2 MB) with weight 3145901 (48.68/col)
Sat Oct 31 15:05:39 2009  sparse part has weight 2297112 (35.55/col)
Sat Oct 31 15:05:39 2009  matrix includes 64 packed rows
Sat Oct 31 15:05:39 2009  using block size 25847 for processor cache size 1024 kB
Sat Oct 31 15:05:39 2009  commencing Lanczos iteration
Sat Oct 31 15:05:39 2009  memory use: 10.4 MB
Sat Oct 31 15:06:15 2009  lanczos halted after 1022 iterations (dim = 64503)
Sat Oct 31 15:06:15 2009  recovered 15 nontrivial dependencies
Sat Oct 31 15:06:16 2009  prp42 factor: 309843707618510847624745331660074576027487
Sat Oct 31 15:06:16 2009  prp51 factor: 379380961349370970936336620824720600414315083305277
Sat Oct 31 15:06:16 2009  elapsed time 01:38:24

(22·10¹³⁷+17)/3 = 7(3)₁₃₆9_<138> = 99233 · 6090360415818263634173_<22> · C112

C112 = P35 · P77

P35 = 24060802183399412367506978238260797_<35>

P77 = 50430376250228200083232843381013952500349332497781653637769170585369111950243_<77>

Number: 73339_137
N=1213395306991144546783180912710761066871854197431551041872076438143619148233733680631064690192492448101121523671
  ( 112 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=24060802183399412367506978238260797 (pp35)
 r2=50430376250228200083232843381013952500349332497781653637769170585369111950243 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 9.84 hours.
Scaled time: 19.18 units (timescale=1.949).
Factorization parameters were as follows:
name:  73339_137
n: 1213395306991144546783180912710761066871854197431551041872076438143619148233733680631064690192492448101121523671
m: 2000000000000000000000000000
deg: 5
c5: 275
c0: 68
skew: 0.76
type: snfs
lss: 1
rlim: 1450000
alim: 1450000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1450000/1450000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [725000, 1550001)
Primes: RFBsize:110630, AFBsize:110510, largePrimes:3624560 encountered
Relations: rels:3789230, finalFF:422683
Max relations in full relation-set: 28
Initial matrix: 221207 x 422683 with sparse part having weight 40398695.
Pruned matrix : 173233 x 174403 with weight 14551791.
Total sieving time: 9.35 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000
total time: 9.84 hours.
 --------- CPU info (if available) ----------

(62·10¹³⁸-53)/9 = 6(8)₁₃₇3_<139> = 302791 · 77761357942084376053452253_<26> · C108

C108 = P34 · P75

P34 = 2598917760441813104579654155912123_<34>

P75 = 112577044979171717082980452895774413486489534296882540558515482893898057627_<75>

Number: 68883_138
N=292578481614426219363304516419595857892000196250239350859450480767231738398900672852889995261550968201912121
  ( 108 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=2598917760441813104579654155912123 (pp34)
 r2=112577044979171717082980452895774413486489534296882540558515482893898057627 (pp75)
Version: Msieve-1.40
Total time: 9.15 hours.
Scaled time: 30.73 units (timescale=3.357).
Factorization parameters were as follows:
name: 68883_138
n: 292578481614426219363304516419595857892000196250239350859450480767231738398900672852889995261550968201912121
m: 5000000000000000000000000000
deg: 5
c5: 496
c0: -1325
skew: 1.22
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 1990001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 277070 x 277318
Total sieving time: 8.97 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000
total time: 9.15 hours.
 --------- CPU info (if available) ----------

(62·10¹³⁸-17)/9 = 6(8)₁₃₇3_<139> = 127867 · 32744763151_<11> · C124

C124 = P39 · P85

P39 = 971875626191891557665240752440339768261_<39>

P85 = 1692926721964495127439620152695166412870828555923484903620152946476576710419052305151_<85>

Number: 68887_138
N=1645314218006229997445207528172151195583233097326614361854592382318318016040391840164344928471593225843499909801429196612411
  ( 124 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=971875626191891557665240752440339768261 (pp39)
 r2=1692926721964495127439620152695166412870828555923484903620152946476576710419052305151 (pp85)
Version: Msieve-1.40
Total time: 7.31 hours.
Scaled time: 15.09 units (timescale=2.064).
Factorization parameters were as follows:
name: 68887_138
n: 1645314218006229997445207528172151195583233097326614361854592382318318016040391840164344928471593225843499909801429196612411
m: 5000000000000000000000000000
deg: 5
c5: 496
c0: -425
skew: 0.97
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 1690001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 227733 x 227977
Total sieving time: 6.95 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000
total time: 7.31 hours.
 --------- CPU info (if available) ----------

Oct 31, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Oct 31, 2009

(67·10¹⁶⁹-13)/9 = 7(4)₁₆₈3_<170> = 23 · 73 · 409 · 443 · 19531 · 28429 · 307440589 · 230276573803_<12> · 291650412038164334986511683_<27> · C107

C107 = P42 · P65

P42 = 393857077963053849631651147459903660023143_<42>

P65 = 54194634030097109172706023869603113274357441497744516636274957483_<65>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=750763233
Step 1 took 31013ms
Step 2 took 12299ms
********** Factor found in step 2: 393857077963053849631651147459903660023143
Found probable prime factor of 42 digits: 393857077963053849631651147459903660023143
Probable prime cofactor 54194634030097109172706023869603113274357441497744516636274957483 has 65 digits

Oct 31, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve / Oct 31, 2009

(67·10¹⁷⁴-13)/9 = 7(4)₁₇₃3_<175> = 3³ · 19 · 137 · 31440401 · 4039164379_<10> · 21853548229100149169939_<23> · 6941387106858984105338581430971_<31> · C100

C100 = P41 · P60

P41 = 45447270246285945938556880752125388129671_<41>

P60 = 120987005656784401807364834160943893119911420811939979029743_<60>

Number: g100
N=5498529142372807175182476307775514287810474350786223541016287633379554796119682890402386436049804553
  ( 100 digits)
Divisors found:
 r1=45447270246285945938556880752125388129671 (pp41)
 r2=120987005656784401807364834160943893119911420811939979029743 (pp60)
Version: Msieve-1.40
Total time: 3.76 hours.
Scaled time: 7.40 units (timescale=1.969).
Factorization parameters were as follows:
name: g100
n: 5498529142372807175182476307775514287810474350786223541016287633379554796119682890402386436049804553
skew: 28871.49
# norm 5.18e+013
c5: 1860
c4: -19207852
c3: -4079387662045
c2: 20205124276853681
c1: 1594619980425421631937
c0: -8929492543484694695004813
# alpha -5.55
Y1: 7628741191
Y0: -19685527873587608852
# Murphy_E 3.35e-009
# M 1964019609939265345418848352462673916351410918179450993688452056155422116082900383504670895533042190
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 233609 x 233857
Polynomial selection time: 0.38 hours.
Total sieving time: 3.13 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 3.76 hours.
 --------- CPU info (if available) ----------

(67·10¹⁶⁴-13)/9 = 7(4)₁₆₃3_<165> = 17 · 2859771989_<10> · 263447695627_<12> · 398722735777_<12> · 151262176674730970257358082173_<30> · C102

C102 = P39 · P64

P39 = 224280627189667359179586493987006022837_<39>

P64 = 4296991075348987428139366522540260942980725114590177648731306909_<64>

Number: g102
N=963731853407674093877908577792914764065479764108496015908002087521494488533136960353559408101309880833
  ( 102 digits)
Divisors found:
 r1=224280627189667359179586493987006022837 (pp39)
 r2=4296991075348987428139366522540260942980725114590177648731306909 (pp64)
Version: Msieve-1.40
Total time: 5.24 hours.
Scaled time: 10.31 units (timescale=1.969).
Factorization parameters were as follows:
name: g102
n: 963731853407674093877908577792914764065479764108496015908002087521494488533136960353559408101309880833
skew: 1562.33
# norm 1.03e+014
c5: 1528560
c4: 13594030180
c3: 3000195359306
c2: -30653164647004551
c1: 3594495509332078518
c0: 7733172680002833841155
# alpha -5.72
Y1: 89251703579
Y0: -14452067262770819782
# Murphy_E 2.76e-009
# M 129344431061528792284070628029008878021022211209342795954905427200961353231646508782196747326379618063
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 276517 x 276742
Polynomial selection time: 0.50 hours.
Total sieving time: 4.33 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 5.24 hours.
 --------- CPU info (if available) ----------

Oct 31, 2009

By Serge Batalov / Msieve / Oct 31, 2009

(67·10¹⁴⁴-13)/9 = 7(4)₁₄₃3_<145> = 3 · 29 · C143

C143 = P59 · P85

P59 = 43105680901206764377509983041410360068255898727809426039017_<59>

P85 = 1985082364056607809703148754055340488055249934086925223804597770313599535606384757717_<85>

SNFS difficulty: 146 digits.
Divisors found:
 r1=43105680901206764377509983041410360068255898727809426039017 (pp59)
 r2=1985082364056607809703148754055340488055249934086925223804597770313599535606384757717 (pp85)
Version: Msieve v. 1.44 SVN130
Total time: 5.35 hours.
Scaled time: 12.83 units (timescale=2.400).
Factorization parameters were as follows:
n: 85568326947637292464878671775223499361430395913154533844189016602809706257982120051085568326947637292464878671775223499361430395913154533844189
m: 100000000000000000000000000000
deg: 5
c5: 67
c0: -130
skew: 1.14
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1225000, 2525001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 323954 x 324180
Total sieving time: 5.00 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 5.35 hours.

(22·10¹⁴⁴+17)/3 = 7(3)₁₄₃9_<145> = 13 · 79 · C142

C142 = P39 · P49 · P55

P39 = 355704369772481560789194645513945473203_<39>

P49 = 5325835763078243037856500964485555354952804736467_<49>

P55 = 3769241919049291518517227454568595454414179901716545857_<55>

SNFS difficulty: 146 digits.
Divisors found:
 r1=355704369772481560789194645513945473203 (pp39)
 r2=5325835763078243037856500964485555354952804736467 (pp49)
 r3=3769241919049291518517227454568595454414179901716545857 (pp55)
Version: Msieve v. 1.44 SVN130
Total time: 5.14 hours.
Scaled time: 12.33 units (timescale=2.400).
Factorization parameters were as follows:
n: 7140538786108406361570918532943849399545602077247646867900032456994482310938007140538786108406361570918532943849399545602077247646867900032457
m: 100000000000000000000000000000
deg: 5
c5: 11
c0: 85
skew: 1.51
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1187500, 2387501)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 328823 x 329048
Total sieving time: 4.60 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.41 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 5.14 hours.

Oct 30, 2009 (11th)

By Ignacio Santos / GGNFS, Msieve / Oct 30, 2009

(26·10¹⁷⁰-11)/3 = 8(6)₁₆₉3_<171> = 1574849 · C165

C165 = P64 · P101

P64 = 6879741969361830247705267902282155696253164397146995711289478697_<64>

P101 = 79990981245460272814684156404787112141167933425430834180983411533442461790764746144400168831077267471_<101>

Number: 86663_170
N=550317310844828086163604679983075626086479825473214680687905104976201951213523751589305810694654958454217938778045810529559765200769512928964406534637077374825565287
  ( 165 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=6879741969361830247705267902282155696253164397146995711289478697 (pp64)
 r2=79990981245460272814684156404787112141167933425430834180983411533442461790764746144400168831077267471 (pp101)
Version: Msieve-1.40
Total time: 58.86 hours.
Scaled time: 102.35 units (timescale=1.739).
Factorization parameters were as follows:
n: 550317310844828086163604679983075626086479825473214680687905104976201951213523751589305810694654958454217938778045810529559765200769512928964406534637077374825565287
m: 10000000000000000000000000000000000
deg: 5
c5: 26
c0: -11
skew: 0.84
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1074714 x 1074941
Total sieving time: 57.03 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.54 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 58.86 hours.

(83·10¹⁷⁰+7)/9 = 9(2)₁₆₉3_<171> = 13² · 1303 · C166

C166 = P44 · P46 · P76

P44 = 75175740784686081593779300770475028296195771_<44>

P46 = 7924410550370980851226220768780461448204670107_<46>

P76 = 7030072093617251150883355788994421962121941534602600580932819909233991111337_<76>

Number: 92223_170
N=4187978684702222101124043387459173515020967645089494077037615617224803127158638109697794448960397363490816469150491229716685764858620399089139864864523935307334563489
  ( 166 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=75175740784686081593779300770475028296195771 (pp44)
 r2=7924410550370980851226220768780461448204670107 (pp46)
 r3=7030072093617251150883355788994421962121941534602600580932819909233991111337 (pp76)
Version: Msieve-1.40
Total time: 54.19 hours.
Scaled time: 94.23 units (timescale=1.739).
Factorization parameters were as follows:
n: 4187978684702222101124043387459173515020967645089494077037615617224803127158638109697794448960397363490816469150491229716685764858620399089139864864523935307334563489
m: 10000000000000000000000000000000000
deg: 5
c5: 83
c0: 7
skew: 0.61
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5350001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 982004 x 982229
Total sieving time: 52.51 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.25 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 54.19 hours.

Oct 30, 2009 (10th)

By Robert Backstrom / GGNFS / Oct 30, 2009

(62·10¹³⁹+1)/9 = 6(8)₁₃₈9_<140> = 3 · 17 · 45022889 · C131

C131 = P36 · P95

P36 = 484214506163729990618092275284042969_<36>

P95 = 61959492079224298660493435009803532533981674214668390763156707898945653153181452537824772870179_<95>

Number: n
N=30001684859297133695920447411646111254476339752905477978706189100135479668056060999868132384792574078543187957473551055021294721451
  ( 131 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=484214506163729990618092275284042969 (pp36)
 r2=61959492079224298660493435009803532533981674214668390763156707898945653153181452537824772870179 (pp95)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.64 hours.
Scaled time: 8.46 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_8_138_9
n: 30001684859297133695920447411646111254476339752905477978706189100135479668056060999868132384792574078543187957473551055021294721451
m: 10000000000000000000000000000
deg: 5
c5: 31
c0: 5
skew: 0.69
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
qintsize: 10000
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1540001)
Primes: RFBsize:121127, AFBsize:121136, largePrimes:3480094 encountered
Relations: rels:3388656, finalFF:277961
Max relations in full relation-set: 48
Initial matrix: 242328 x 277961 with sparse part having weight 26767212.
Pruned matrix : 230728 x 232003 with weight 17588153.
Total sieving time: 4.07 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.43 hours.
Total square root time: 0.07 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 4.64 hours.
 --------- CPU info (if available) ----------

(67·10¹²⁴-13)/9 = 7(4)₁₂₃3_<125> = 167 · 2098015493895221_<16> · C108

C108 = P50 · P59

P50 = 18413459563540298067804775297170844243589025668543_<50>

P59 = 11539094725850237919675966907571710452758307093471194899943_<59>

Number: n
N=212474654134304477312475815582067521840594360125311988630953593272073000222223112697185992344600977567593049
  ( 108 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=18413459563540298067804775297170844243589025668543 (pp50)
 r2=11539094725850237919675966907571710452758307093471194899943 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.71 hours.
Scaled time: 3.11 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_7_4_123_3
n: 212474654134304477312475815582067521840594360125311988630953593272073000222223112697185992344600977567593049
m: 10000000000000000000000000
deg: 5
c5: 67
c0: -130
skew: 1.14
type: snfs
lss: 1
rlim: 910000
alim: 910000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
qintsize: 10000
Factor base limits: 910000/910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [455000, 735001)
Primes: RFBsize:72026, AFBsize:72442, largePrimes:2399626 encountered
Relations: rels:2237187, finalFF:162283
Max relations in full relation-set: 48
Initial matrix: 144533 x 162283 with sparse part having weight 13056975.
Pruned matrix : 138055 x 138841 with weight 8687947.
Total sieving time: 1.51 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Total square root time: 0.06 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000
total time: 1.71 hours.
 --------- CPU info (if available) ----------

Oct 30, 2009 (9th)

By Wataru Sakai / GMP-ECM 6.2.1 / Oct 30, 2009

(65·10¹⁸⁷+61)/9 = 7(2)₁₈₆9_<188> = 131 · 5507 · 220729284101_<12> · 2299975915314223_<16> · 1109471659166831215174847_<25> · C132

C132 = P40 · C93

P40 = 1512052274095148841868452958388463932723_<40>

C93 = [117548803664364063729993986270961475590052376474609853792498756031020401498410673032364148899_<93>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2945990577
Step 1 took 38221ms
Step 2 took 14029ms
********** Factor found in step 2: 1512052274095148841868452958388463932723
Found probable prime factor of 40 digits: 1512052274095148841868452958388463932723
Composite cofactor 117548803664364063729993986270961475590052376474609853792498756031020401498410673032364148899 has 93 digits

(64·10¹⁸⁵+71)/9 = 7(1)₁₈₄9_<186> = 593707 · 594449 · 4422329046727_<13> · 40284292656009544724056072361587_<32> · C131

C131 = P34 · C97

P34 = 9116432441824664823352631671213357_<34>

C97 = [1240620578252657138397677340020548602052064584196378623862760965588007134959583060094673085893981_<97>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=630455973
Step 1 took 38243ms
Step 2 took 13952ms
********** Factor found in step 2: 9116432441824664823352631671213357
Found probable prime factor of 34 digits: 9116432441824664823352631671213357
Composite cofactor 1240620578252657138397677340020548602052064584196378623862760965588007134959583060094673085893981 has 97 digits

(59·10¹⁶⁶+31)/9 = 6(5)₁₆₅9_<167> = 3 · 13 · 7259437319_<10> · 8758021819_<10> · 3392702120053749464840779_<25> · C121

C121 = P35 · P86

P35 = 80699902067736399108835652452339219_<35>

P86 = 96564428551450245513740093588018269772203313974459102582096055520689780511463138067621_<86>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1299118853
Step 1 took 34255ms
Step 2 took 13280ms
********** Factor found in step 2: 80699902067736399108835652452339219
Found probable prime factor of 35 digits: 80699902067736399108835652452339219
Probable prime cofactor 96564428551450245513740093588018269772203313974459102582096055520689780511463138067621 has 86 digits

Oct 30, 2009 (8th)

By Erik Branger / GGNFS, Msieve, YAFU / Oct 30, 2009

(67·10¹⁰⁵-13)/9 = 7(4)₁₀₄3_<106> = 3 · 73 · 5669 · 569057 · C95

C95 = P41 · P54

P41 = 60058359933313649972243137470065257329163_<41>

P54 = 175449640663427204253932925983205548218359311006550343_<54>

Number: 74443_105
N=10537217669134653717350764785332255258069098699759163662633735476197589541582812554582281552909
  ( 95 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=60058359933313649972243137470065257329163 (pp41)
 r2=175449640663427204253932925983205548218359311006550343 (pp54)
Version: Msieve v. 1.43
Total time: 0.80 hours.
Scaled time: 0.63 units (timescale=0.788).
Factorization parameters were as follows:
n: 10537217669134653717350764785332255258069098699759163662633735476197589541582812554582281552909
m: 200000000000000000000000000
deg: 4
c4: 335
c0: -104
skew: 0.75
type: snfs
lss: 1
rlim: 440000
alim: 440000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 440000/440000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [220000, 300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 36011 x 36238
Total sieving time: 0.78 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107.000,4,0,0,0,0,0,0,0,0,440000,440000,25,25,44,44,2.2,2.2,20000
total time: 0.80 hours.
 --------- CPU info (if available) ----------

(22·10¹¹¹+17)/3 = 7(3)₁₁₀9_<112> = 4561 · C109

C109 = P41 · P69

P41 = 10353494998124320950439689240019536224501_<41>

P69 = 155293892497221396344263249494507201244620736494605530331157572978399_<69>

Number: 73339_111
N=1607834539209237740261638529562230505006212087992399327632829057955126799678433092158152451947672294087553899
  ( 109 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=10353494998124320950439689240019536224501 (pp41)
 r2=155293892497221396344263249494507201244620736494605530331157572978399 (pp69)
Version: Msieve v. 1.43
Total time: 1.33 hours.
Scaled time: 1.05 units (timescale=0.788).
Factorization parameters were as follows:
n: 1607834539209237740261638529562230505006212087992399327632829057955126799678433092158152451947672294087553899
m: 20000000000000000000000
deg: 5
c5: 55
c0: 136
skew: 1.20
type: snfs
lss: 1
rlim: 540000
alim: 540000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 540000/540000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [270000, 420001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 64236 x 64465
Total sieving time: 1.28 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,113.000,5,0,0,0,0,0,0,0,0,540000,540000,25,25,45,45,2.2,2.2,50000
total time: 1.33 hours.
 --------- CPU info (if available) ----------

(62·10¹³⁷-53)/9 = 6(8)₁₃₆3_<138> = 13 · 379 · 9913338693829_<13> · C122

C122 = P41 · P81

P41 = 92016598929517614098722805673273505224217_<41>

P81 = 153278236964167015210420723223931171496148765949262538905208174029503679220103953_<81>

Number: 68883_137
N=14104142055355317759668354177413145279996340994172427429184656761606188941098694112179225964159993307036446344359313029801
  ( 122 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=92016598929517614098722805673273505224217 (pp41)
 r2=153278236964167015210420723223931171496148765949262538905208174029503679220103953 (pp81)
Version: Msieve-1.40
Total time: 7.17 hours.
Scaled time: 6.96 units (timescale=0.970).
Factorization parameters were as follows:
n: 14104142055355317759668354177413145279996340994172427429184656761606188941098694112179225964159993307036446344359313029801
m: 2000000000000000000000000000
deg: 5
c5: 775
c0: -212
skew: 0.77
type: snfs
lss: 1
rlim: 1470000
alim: 1470000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1470000/1470000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [735000, 1860001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 261076 x 261302
Total sieving time: 6.82 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,139.000,5,0,0,0,0,0,0,0,0,1470000,1470000,26,26,48,48,2.3,2.3,75000
total time: 7.17 hours.
 --------- CPU info (if available) ----------

(22·10¹⁷³-7)/3 = 7(3)₁₇₂1_<174> = 97 · 541859 · 65483111511553_<14> · 29019575156728627496451041059487_<32> · 7085999215281227635840096984763449_<34> · C88

C88 = P43 · P45

P43 = 2918897382864143812189601638526072779141423_<43>

P45 = 354979371562529997440931835199505599882907401_<45>

10/29/09 19:43:40 v1.12 @ ERIK-DATOR, starting SIQS on c88: 1036148358624627286217516372248460715568726928814760434392187296717805689495977792371623
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, random seeds: 1579246471, 485612288
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, ==== sieve params ====
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, n = 88 digits, 291 bits
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, factor base: 60488 primes (max prime = 1595317)
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, single large prime cutoff: 175484870 (110 * pmax)
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, double large prime range from 43 to 50 bits
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, double large prime cutoff: 691244073679672
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, using 0 large prime slices of factor base
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, buckets hold 1024 elements
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, polynomial A has ~ 0 factors
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, using multiplier of 3
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, using small prime variation correction of 20 bits
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, trial factoring cutoff at 97 bits
10/29/09 19:43:40 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ====
10/29/09 20:04:47 v1.12 @ ERIK-DATOR, sieve time = 379.8600, relation time = 165.2976, poly_time = 696.2156
10/29/09 20:04:47 v1.12 @ ERIK-DATOR, 60850 relations found: 20164 full + 40686 from 522236 partial, using 48318116 polys (613 A polys)
10/29/09 20:04:47 v1.12 @ ERIK-DATOR, on average, sieving found 0.01 rels/poly and 428.14 rels/sec
10/29/09 20:04:47 v1.12 @ ERIK-DATOR, trial division touched 13914331 sieve locations out of 56998368903168
10/29/09 20:04:47 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ====
10/29/09 20:04:47 v1.12 @ ERIK-DATOR, begin with 542400 relations
10/29/09 20:04:47 v1.12 @ ERIK-DATOR, reduce to 123655 relations in 8 passes
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, recovered 123655 relations
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, recovered 102177 polynomials
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, attempting to build 60850 cycles
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, found 60850 cycles in 4 passes
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, distribution of cycle lengths:
10/29/09 20:04:54 v1.12 @ ERIK-DATOR,    length 1 : 20164
10/29/09 20:04:54 v1.12 @ ERIK-DATOR,    length 2 : 16960
10/29/09 20:04:54 v1.12 @ ERIK-DATOR,    length 3 : 11354
10/29/09 20:04:54 v1.12 @ ERIK-DATOR,    length 4 : 6358
10/29/09 20:04:54 v1.12 @ ERIK-DATOR,    length 5 : 3250
10/29/09 20:04:54 v1.12 @ ERIK-DATOR,    length 6 : 1545
10/29/09 20:04:54 v1.12 @ ERIK-DATOR,    length 7 : 694
10/29/09 20:04:54 v1.12 @ ERIK-DATOR,    length 9+: 525
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, largest cycle: 15 relations
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, matrix is 60488 x 60850 (12.1 MB) with weight 2920285 (47.99/col)
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, sparse part has weight 2920285 (47.99/col)
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, filtering completed in 3 passes
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, matrix is 53491 x 53554 (10.8 MB) with weight 2626833 (49.05/col)
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, sparse part has weight 2626833 (49.05/col)
10/29/09 20:04:54 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later
10/29/09 20:04:55 v1.12 @ ERIK-DATOR, matrix is 53443 x 53554 (9.2 MB) with weight 2268111 (42.35/col)
10/29/09 20:04:55 v1.12 @ ERIK-DATOR, sparse part has weight 2086592 (38.96/col)
10/29/09 20:04:55 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows
10/29/09 20:04:55 v1.12 @ ERIK-DATOR, using block size 21421 for processor cache size 2048 kB
10/29/09 20:04:55 v1.12 @ ERIK-DATOR, commencing Lanczos iteration
10/29/09 20:04:55 v1.12 @ ERIK-DATOR, memory use: 8.3 MB
10/29/09 20:05:13 v1.12 @ ERIK-DATOR, lanczos halted after 847 iterations (dim = 53443)
10/29/09 20:05:13 v1.12 @ ERIK-DATOR, recovered 18 nontrivial dependencies
10/29/09 20:05:14 v1.12 @ ERIK-DATOR, prp43 = 2918897382864143812189601638526072779141423
10/29/09 20:05:21 v1.12 @ ERIK-DATOR, prp45 = 354979371562529997440931835199505599882907401
10/29/09 20:05:21 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 26.7540 seconds.
10/29/09 20:05:21 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 7.7850 seconds.
10/29/09 20:05:21 v1.12 @ ERIK-DATOR, SIQS elapsed time = 1301.4064 seconds.

(22·10¹¹³+17)/3 = 7(3)₁₁₂9_<114> = 41 · 89 · 30226562196724237_<17> · C94

C94 = P40 · P55

P40 = 4742658220612723377993912832802326986709_<40>

P55 = 1401899815697364732864295246904507767152298674388612267_<55>

Number: 73339_113
N=6648731685392568673340087143484735074721518359722676856044541286039486751148900577046263359303
  ( 94 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=4742658220612723377993912832802326986709 (pp40)
 r2=1401899815697364732864295246904507767152298674388612267 (pp55)
Version: Msieve v. 1.43
Total time: 1.39 hours.
Scaled time: 1.10 units (timescale=0.788).
Factorization parameters were as follows:
n: 6648731685392568673340087143484735074721518359722676856044541286039486751148900577046263359303
m: 50000000000000000000000
deg: 5
c5: 176
c0: 425
skew: 1.19
type: snfs
lss: 1
rlim: 590000
alim: 590000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 590000/590000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [295000, 445001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 63916 x 64141
Total sieving time: 1.34 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115.000,5,0,0,0,0,0,0,0,0,590000,590000,25,25,45,45,2.2,2.2,50000
total time: 1.39 hours.
 --------- CPU info (if available) ----------

(67·10¹¹⁵-13)/9 = 7(4)₁₁₄3_<116> = 934023203657_<12> · C104

C104 = P46 · P59

P46 = 2363136207298356542813024663867821003977095941_<46>

P59 = 33727633771518272875025217406971537221298425870762282057639_<59>

Number: 74443_115
N=79702992551973656202412085387411627658370929220796610067063903154859269670308077208497397166333194943299
  ( 104 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=2363136207298356542813024663867821003977095941 (pp46)
 r2=33727633771518272875025217406971537221298425870762282057639 (pp59)
Version: Msieve-1.40
Total time: 1.15 hours.
Scaled time: 1.12 units (timescale=0.969).
Factorization parameters were as follows:
n: 79702992551973656202412085387411627658370929220796610067063903154859269670308077208497397166333194943299
m: 100000000000000000000000
deg: 5
c5: 67
c0: -13
skew: 0.72
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 510001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 68923 x 69148
Total sieving time: 1.12 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116.000,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 1.15 hours.
 --------- CPU info (if available) ----------

(22·10¹¹⁹+17)/3 = 7(3)₁₁₈9_<120> = 4871 · 88395289 · C109

C109 = P35 · P36 · P39

P35 = 50397412484330388603542395361078269_<35>

P36 = 284229425704179960225725802324609161_<36>

P39 = 118898643426182964310318249358540813809_<39>

Number: 73339_119
N=1703155010376173589245963363912844479505898920513548079792184363384189269662871013342757311335327814133864981
  ( 109 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=50397412484330388603542395361078269 (pp35)
 r2=284229425704179960225725802324609161 (pp36)
 r3=118898643426182964310318249358540813809 (pp39)
Version: Msieve-1.40
Total time: 1.44 hours.
Scaled time: 1.45 units (timescale=1.003).
Factorization parameters were as follows:
n: 1703155010376173589245963363912844479505898920513548079792184363384189269662871013342757311335327814133864981
m: 1000000000000000000000000
deg: 5
c5: 11
c0: 85
skew: 1.51
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2

Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 615001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 86095 x 86343
Total sieving time: 1.37 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.44 hours.
 --------- CPU info (if available) ----------

(67·10¹²³-13)/9 = 7(4)₁₂₂3_<124> = 3 · 36172259 · 12953224991209_<14> · C103

C103 = P37 · P67

P37 = 1598370800869751930125360162910027197_<37>

P67 = 3313446482445314661395426297353620629334616744119570057380870392583_<67>

Number: 74443_123
N=5296116107785180025060234384281114220424865461631383972660953328631925645912935715468651123228597079851
  ( 103 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=1598370800869751930125360162910027197 (pp37)
 r2=3313446482445314661395426297353620629334616744119570057380870392583 (pp67)
Version: Msieve-1.40
Total time: 1.93 hours.
Scaled time: 1.73 units (timescale=0.894).
Factorization parameters were as follows:
n: 5296116107785180025060234384281114220424865461631383972660953328631925645912935715468651123228597079851
m: 5000000000000000000000000
deg: 5
c5: 536
c0: -325
skew: 0.90
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 745001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 120758 x 120983
Total sieving time: 1.83 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 1.93 hours.
 --------- CPU info (if available) ----------

(65·10¹³⁸+61)/9 = 7(2)₁₃₇9_<139> = 7 · 820888039693842689_<18> · C121

C121 = P39 · P82

P39 = 231983952017062808710371389960379972197_<39>

P82 = 5417899396106871046513719119689905295688836403624747656508338369048000425620143559_<82>

Number: 72229_138
N=1256865713539729940732436596428989152859916869094343065781795420088325741227881969351681537465013212501751088675568629123
  ( 121 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=231983952017062808710371389960379972197 (pp39)
 r2=5417899396106871046513719119689905295688836403624747656508338369048000425620143559 (pp82)
Version: Msieve-1.40
Total time: 5.96 hours.
Scaled time: 5.98 units (timescale=1.003).
Factorization parameters were as follows:
n: 1256865713539729940732436596428989152859916869094343065781795420088325741227881969351681537465013212501751088675568629123
m: 5000000000000000000000000000
deg: 5
c5: 104
c0: 305
skew: 1.24
type: snfs
lss: 1
rlim: 1540000
alim: 1540000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1540000/1540000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [770000, 1670001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 260716 x 260941
Total sieving time: 5.73 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,140.000,5,0,0,0,0,0,0,0,0,1540000,1540000,26,26,48,48,2.3,2.3,100000
total time: 5.96 hours.
 --------- CPU info (if available) ----------

(22·10¹³²+17)/3 = 7(3)₁₃₁9_<133> = 13 · 12133421 · 30027659 · 3606149550515935321_<19> · C99

C99 = P47 · P53

P47 = 12453067396570738943402028834555057839784395671_<47>

P53 = 34477300948705518718980721337704600617529621152055447_<53>

Number: 73339_132
N=429348152366082101879424461334080508049160634782916238895467141839271983897081546365941358378769937
  ( 99 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=12453067396570738943402028834555057839784395671 (pp47)
 r2=34477300948705518718980721337704600617529621152055447 (pp53)
Version: Msieve v. 1.43
Total time: 5.61 hours.
Scaled time: 4.43 units (timescale=0.789).
Factorization parameters were as follows:
n: 429348152366082101879424461334080508049160634782916238895467141839271983897081546365941358378769937
m: 200000000000000000000000000
deg: 5
c5: 275
c0: 68
skew: 0.76
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [600000, 1125001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 163998 x 164223
Total sieving time: 5.36 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,133.000,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000
total time: 5.61 hours.
 --------- CPU info (if available) ----------

(22·10¹³⁶+17)/3 = 7(3)₁₃₅9_<137> = 7 · 8980812433_<10> · C127

C127 = P61 · P66

P61 = 4113360418876992191345184069972901753084088769096918837906397_<61>

P66 = 283590053967020542468512853768491642154157101023860518632668590177_<66>

Number: 73339_136
N=1166508103175132439655105140329176295856416365286589900933541796885056511509952662674708395223890149826768594586479376279662269
  ( 127 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=4113360418876992191345184069972901753084088769096918837906397 (pp61)
 r2=283590053967020542468512853768491642154157101023860518632668590177 (pp66)
Version: Msieve-1.40
Total time: 4.90 hours.
Scaled time: 4.82 units (timescale=0.983).
Factorization parameters were as follows:
n: 1166508103175132439655105140329176295856416365286589900933541796885056511509952662674708395223890149826768594586479376279662269
m: 2000000000000000000000000000
deg: 5
c5: 55
c0: 136
skew: 1.20
type: snfs
lss: 1
rlim: 1410000
alim: 1410000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1410000/1410000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [705000, 1455001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 214678 x 214903
Total sieving time: 4.73 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,138.000,5,0,0,0,0,0,0,0,0,1410000,1410000,26,26,48,48,2.3,2.3,75000
total time: 4.90 hours.
 --------- CPU info (if available) ----------

Oct 30, 2009 (7th)

By Sinkiti Sibata / Msieve, GGNFS / Oct 30, 2009

(62·10¹⁴⁸-53)/9 = 6(8)₁₄₇3_<149> = 3 · 2957 · 554396173829032040309_<21> · 80618323734034493160877932323_<29> · C96

C96 = P41 · P56

P41 = 15649311336687670483003413809050773543817_<41>

P56 = 11102668729253886618598862637858746443379270194714314067_<56>

Number: 68883_148
N=173749119612200540250170808346984527455185833744652662545780871322071342123571560550077923973739
  ( 96 digits)
Divisors found:
 r1=15649311336687670483003413809050773543817 (pp41)
 r2=11102668729253886618598862637858746443379270194714314067 (pp56)
Version: Msieve-1.40
Total time: 7.06 hours.
Scaled time: 14.35 units (timescale=2.032).
Factorization parameters were as follows:
name: 68883_148
n:  173749119612200540250170808346984527455185833744652662545780871322071342123571560550077923973739
m:  6500700344411699054074
deg: 4
c4: 97293096
c3: -223649123332
c2: -642136958186635483
c1: 738328517650567800
c0: 471523111539404624724519
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.605
# E(F1,F2) = 2.998325e-05
# GGNFS version 0.77.1-20060722-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1256814568.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 179842 x 180070
Polynomial selection time: 0.17 hours.
Total sieving time: 6.60 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 7.06 hours.
 --------- CPU info (if available) ----------

(62·10¹⁴⁸+1)/9 = 6(8)₁₄₇9_<149> = 3 · 968893963 · 1010325931287078378105743_<25> · 26271799596027579924616943_<26> · C90

C90 = P40 · P51

P40 = 1154296887283017820556565817700236598461_<40>

P51 = 773540093204736296456243349622971513303636130557709_<51>

Fri Oct 30 07:07:22 2009  Msieve v. 1.42
Fri Oct 30 07:07:22 2009  random seeds: dc8593b8 2e6a889f
Fri Oct 30 07:07:22 2009  factoring 892894921774842591947278084980579648441470220219533682231568136751789747957843249021085849 (90 digits)
Fri Oct 30 07:07:23 2009  searching for 15-digit factors
Fri Oct 30 07:07:24 2009  commencing quadratic sieve (90-digit input)
Fri Oct 30 07:07:24 2009  using multiplier of 1
Fri Oct 30 07:07:24 2009  using 32kb Intel Core sieve core
Fri Oct 30 07:07:24 2009  sieve interval: 36 blocks of size 32768
Fri Oct 30 07:07:24 2009  processing polynomials in batches of 6
Fri Oct 30 07:07:24 2009  using a sieve bound of 1606249 (61176 primes)
Fri Oct 30 07:07:24 2009  using large prime bound of 134924916 (27 bits)
Fri Oct 30 07:07:24 2009  using double large prime bound of 430690990940364 (42-49 bits)
Fri Oct 30 07:07:24 2009  using trial factoring cutoff of 49 bits
Fri Oct 30 07:07:24 2009  polynomial 'A' values have 11 factors
Fri Oct 30 08:13:01 2009  61413 relations (16479 full + 44934 combined from 660424 partial), need 61272
Fri Oct 30 08:13:02 2009  begin with 676903 relations
Fri Oct 30 08:13:03 2009  reduce to 149572 relations in 11 passes
Fri Oct 30 08:13:03 2009  attempting to read 149572 relations
Fri Oct 30 08:13:05 2009  recovered 149572 relations
Fri Oct 30 08:13:05 2009  recovered 125294 polynomials
Fri Oct 30 08:13:05 2009  attempting to build 61413 cycles
Fri Oct 30 08:13:05 2009  found 61413 cycles in 5 passes
Fri Oct 30 08:13:05 2009  distribution of cycle lengths:
Fri Oct 30 08:13:05 2009     length 1 : 16479
Fri Oct 30 08:13:05 2009     length 2 : 11841
Fri Oct 30 08:13:05 2009     length 3 : 10776
Fri Oct 30 08:13:05 2009     length 4 : 8279
Fri Oct 30 08:13:05 2009     length 5 : 5761
Fri Oct 30 08:13:05 2009     length 6 : 3579
Fri Oct 30 08:13:05 2009     length 7 : 2062
Fri Oct 30 08:13:05 2009     length 9+: 2636
Fri Oct 30 08:13:05 2009  largest cycle: 19 relations
Fri Oct 30 08:13:05 2009  matrix is 61176 x 61413 (15.1 MB) with weight 3709126 (60.40/col)
Fri Oct 30 08:13:05 2009  sparse part has weight 3709126 (60.40/col)
Fri Oct 30 08:13:06 2009  filtering completed in 3 passes
Fri Oct 30 08:13:06 2009  matrix is 57171 x 57235 (14.2 MB) with weight 3482985 (60.85/col)
Fri Oct 30 08:13:06 2009  sparse part has weight 3482985 (60.85/col)
Fri Oct 30 08:13:06 2009  saving the first 48 matrix rows for later
Fri Oct 30 08:13:06 2009  matrix is 57123 x 57235 (10.6 MB) with weight 2895121 (50.58/col)
Fri Oct 30 08:13:06 2009  sparse part has weight 2423000 (42.33/col)
Fri Oct 30 08:13:06 2009  matrix includes 64 packed rows
Fri Oct 30 08:13:06 2009  using block size 22894 for processor cache size 1024 kB
Fri Oct 30 08:13:07 2009  commencing Lanczos iteration
Fri Oct 30 08:13:07 2009  memory use: 9.9 MB
Fri Oct 30 08:13:29 2009  lanczos halted after 905 iterations (dim = 57121)
Fri Oct 30 08:13:30 2009  recovered 15 nontrivial dependencies
Fri Oct 30 08:13:30 2009  prp40 factor: 1154296887283017820556565817700236598461
Fri Oct 30 08:13:30 2009  prp51 factor: 773540093204736296456243349622971513303636130557709
Fri Oct 30 08:13:30 2009  elapsed time 01:06:08

(62·10¹⁴⁸-17)/9 = 6(8)₁₄₇7_<149> = 7² · 13 · 33403 · 2587105617619_<13> · 248476266691661817327986323_<27> · C103

C103 = P44 · P59

P44 = 77534847850900282536204141003399873814651531_<44>

P59 = 64957344590901786161929874304410491618727520507584961391411_<59>

Number: 68887_148
N=5036457829654070447291851666637862041967460202109673946848020460954015526291427291729686600891861400241
  ( 103 digits)
Divisors found:
 r1=77534847850900282536204141003399873814651531 (pp44)
 r2=64957344590901786161929874304410491618727520507584961391411 (pp59)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 12.94 hours.
Scaled time: 6.08 units (timescale=0.470).
Factorization parameters were as follows:
name: 68887_148
n: 5036457829654070447291851666637862041967460202109673946848020460954015526291427291729686600891861400241
skew: 5250.84
# norm 1.51e+14
c5: 158400
c4: -2369595480
c3: -9089246452964
c2: 12488829579152730
c1: 148149926348795334669
c0: 243869513540266992110835
# alpha -5.95
Y1: 46917187199
Y0: -31657450076936910292
# Murphy_E 2.45e-09
# M 4472840802460327703162608013156768940227082287739066635374172230098893954410321033694631482111869343000
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: RFBsize:169511, AFBsize:170119, largePrimes:4420988 encountered
Relations: rels:4544685, finalFF:508022
Max relations in full relation-set: 28
Initial matrix: 339708 x 508022 with sparse part having weight 36322270.
Pruned matrix : 211251 x 213013 with weight 16139750.
Polynomial selection time: 0.70 hours.
Total sieving time: 10.80 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 1.00 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 12.94 hours.
 --------- CPU info (if available) ----------

(22·10¹³⁶-7)/3 = 7(3)₁₃₅1_<137> = 19389191 · 4895993365661197097_<19> · C111

C111 = P46 · P66

P46 = 6443188619669826476280091645257651931718381011_<46>

P66 = 119894723769212387435501631561188909687989725490025836640734845023_<66>

Number: 73331_136
N=772504319748246697665149190240682725304722032243784064764023030120508817790677757304825249856253631163551058253
  ( 111 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=6443188619669826476280091645257651931718381011 (pp46)
 r2=119894723769212387435501631561188909687989725490025836640734845023 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.27 hours.
Scaled time: 12.36 units (timescale=1.972).
Factorization parameters were as follows:
name: 73331_136
n: 772504319748246697665149190240682725304722032243784064764023030120508817790677757304825249856253631163551058253
m: 2000000000000000000000000000
deg: 5
c5: 55
c0: -56
skew: 1.00
type: snfs
lss: 1
rlim: 1410000
alim: 1410000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1410000/1410000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [705000, 1230001)
Primes: RFBsize:107805, AFBsize:107265, largePrimes:3428918 encountered
Relations: rels:3561302, finalFF:431806
Max relations in full relation-set: 28
Initial matrix: 215137 x 431806 with sparse part having weight 35153928.
Pruned matrix : 155036 x 156175 with weight 10589950.
Total sieving time: 5.94 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1410000,1410000,26,26,48,48,2.3,2.3,75000
total time: 6.27 hours.
 --------- CPU info (if available) ----------

(22·10¹²⁶+17)/3 = 7(3)₁₂₅9_<127> = 13 · 191 · 840251492083_<12> · 1895876995008967_<16> · C97

C97 = P47 · P50

P47 = 62954221240549700803517895855591515615873618567_<47>

P50 = 29449667885623623024571417153719273982755349467859_<50>

Number: 73339_126
N=1853980907532261085359289430354461486793949958322168440086644145089512112616560650231980192138053
  ( 97 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=62954221240549700803517895855591515615873618567 (pp47)
 r2=29449667885623623024571417153719273982755349467859 (pp50)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 4.65 hours.
Scaled time: 2.18 units (timescale=0.470).
Factorization parameters were as follows:
name: 73339_126
n: 1853980907532261085359289430354461486793949958322168440086644145089512112616560650231980192138053
m: 20000000000000000000000000
deg: 5
c5: 55
c0: 136
skew: 1.20
type: snfs
lss: 1
rlim: 960000
alim: 960000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 960000/960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [480000, 880001)
Primes: RFBsize:75618, AFBsize:75331, largePrimes:2684351 encountered
Relations: rels:2649373, finalFF:258875
Max relations in full relation-set: 28
Initial matrix: 151016 x 258875 with sparse part having weight 20919788.
Pruned matrix : 123819 x 124638 with weight 7186531.
Total sieving time: 4.30 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,960000,960000,26,26,47,47,2.3,2.3,50000
total time: 4.65 hours.
 --------- CPU info (if available) ----------

(22·10¹³⁰+17)/3 = 7(3)₁₂₉9_<131> = 7 · 2543 · 783371639 · 23314400769738955085791_<23> · C96

C96 = P46 · P50

P46 = 5668358868056523752203461746253003242713937413_<46>

P50 = 39793082832407892372132468962834943667647868416847_<50>

Fri Oct 30 10:44:12 2009  Msieve v. 1.40
Fri Oct 30 10:44:12 2009  random seeds: 4f9e5c6b 8f5e88a9
Fri Oct 30 10:44:12 2009  factoring 225561473960387088874197487909377436905992883142405706677354077914645400486794949390462152796811 (96 digits)
Fri Oct 30 10:44:12 2009  no P-1/P+1/ECM available, skipping
Fri Oct 30 10:44:12 2009  commencing quadratic sieve (96-digit input)
Fri Oct 30 10:44:12 2009  using multiplier of 19
Fri Oct 30 10:44:12 2009  using 32kb Intel Core sieve core
Fri Oct 30 10:44:12 2009  sieve interval: 36 blocks of size 32768
Fri Oct 30 10:44:12 2009  processing polynomials in batches of 6
Fri Oct 30 10:44:12 2009  using a sieve bound of 2225473 (82353 primes)
Fri Oct 30 10:44:12 2009  using large prime bound of 333820950 (28 bits)
Fri Oct 30 10:44:12 2009  using double large prime bound of 2199502175184600 (43-51 bits)
Fri Oct 30 10:44:12 2009  using trial factoring cutoff of 51 bits
Fri Oct 30 10:44:12 2009  polynomial 'A' values have 12 factors
Fri Oct 30 13:12:19 2009  82483 relations (20939 full + 61544 combined from 1214119 partial), need 82449
Fri Oct 30 13:12:20 2009  begin with 1235058 relations
Fri Oct 30 13:12:20 2009  reduce to 211848 relations in 10 passes
Fri Oct 30 13:12:20 2009  attempting to read 211848 relations
Fri Oct 30 13:12:22 2009  recovered 211848 relations
Fri Oct 30 13:12:22 2009  recovered 194844 polynomials
Fri Oct 30 13:12:22 2009  attempting to build 82483 cycles
Fri Oct 30 13:12:22 2009  found 82483 cycles in 6 passes
Fri Oct 30 13:12:22 2009  distribution of cycle lengths:
Fri Oct 30 13:12:22 2009     length 1 : 20939
Fri Oct 30 13:12:22 2009     length 2 : 14842
Fri Oct 30 13:12:22 2009     length 3 : 13930
Fri Oct 30 13:12:22 2009     length 4 : 10990
Fri Oct 30 13:12:22 2009     length 5 : 8283
Fri Oct 30 13:12:22 2009     length 6 : 5570
Fri Oct 30 13:12:22 2009     length 7 : 3442
Fri Oct 30 13:12:22 2009     length 9+: 4487
Fri Oct 30 13:12:22 2009  largest cycle: 21 relations
Fri Oct 30 13:12:22 2009  matrix is 82353 x 82483 (22.5 MB) with weight 5580538 (67.66/col)
Fri Oct 30 13:12:22 2009  sparse part has weight 5580538 (67.66/col)
Fri Oct 30 13:12:23 2009  filtering completed in 3 passes
Fri Oct 30 13:12:23 2009  matrix is 78173 x 78237 (21.6 MB) with weight 5337663 (68.22/col)
Fri Oct 30 13:12:23 2009  sparse part has weight 5337663 (68.22/col)
Fri Oct 30 13:12:23 2009  saving the first 48 matrix rows for later
Fri Oct 30 13:12:23 2009  matrix is 78125 x 78237 (15.9 MB) with weight 4472451 (57.17/col)
Fri Oct 30 13:12:23 2009  sparse part has weight 3699137 (47.28/col)
Fri Oct 30 13:12:23 2009  matrix includes 64 packed rows
Fri Oct 30 13:12:23 2009  using block size 31294 for processor cache size 8192 kB
Fri Oct 30 13:12:24 2009  commencing Lanczos iteration
Fri Oct 30 13:12:24 2009  memory use: 14.0 MB
Fri Oct 30 13:12:45 2009  lanczos halted after 1238 iterations (dim = 78125)
Fri Oct 30 13:12:45 2009  recovered 18 nontrivial dependencies
Fri Oct 30 13:12:46 2009  prp46 factor: 5668358868056523752203461746253003242713937413
Fri Oct 30 13:12:46 2009  prp50 factor: 39793082832407892372132468962834943667647868416847
Fri Oct 30 13:12:46 2009  elapsed time 02:28:34

(59·10¹⁹⁰+31)/9 = 6(5)₁₈₉9_<191> = 3 · 13 · 431 · 6199 · 19576751 · 104183263 · 36559727551187_<14> · 135004420102133_<15> · 12932888608664243860259_<23> · 490648692732801719123587_<24> · C94

C94 = P31 · P63

P31 = 9865405008537377442324456789611_<31>

P63 = 998332882065300959385122964248060387944996253698508642405943101_<63>

Number: 65559_190
N=9848958214914575038497851680581147805444684312048313010541252541165888436426497955577193923711
  ( 94 digits)
Divisors found:
 r1=9865405008537377442324456789611 (pp31)
 r2=998332882065300959385122964248060387944996253698508642405943101 (pp63)
Version: Msieve-1.40
Total time: 5.33 hours.
Scaled time: 10.87 units (timescale=2.038).
Factorization parameters were as follows:
name: 65559_190
n:  9848958214914575038497851680581147805444684312048313010541252541165888436426497955577193923711
m:  4626552704081064038673
deg: 4
c4: 21496128
c3: 80594542214
c2: -148327043924384507
c1: -201872463427757100
c0: 35697740878523611215328
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.239
# E(F1,F2) = 4.784960e-05
# GGNFS version 0.77.1-20060722-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1256859102.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1260001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 160364 x 160593
Polynomial selection time: 0.17 hours.
Total sieving time: 5.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 5.33 hours.
 --------- CPU info (if available) ----------

(67·10¹²⁵-13)/9 = 7(4)₁₂₄3_<126> = 7 · 23 · 383 · 2112973088280065635622951_<25> · C97

C97 = P34 · P64

P34 = 3637308040834686028487388657126347_<34>

P64 = 1570845943462575746091980845703965709073524066171708229509776313_<64>

Number: 74443_125
N=5713650581068975362283662920696280343317363639223493296916903514253804648431669229237353348818611
  ( 97 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=3637308040834686028487388657126347 (pp34)
 r2=1570845943462575746091980845703965709073524066171708229509776313 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.85 hours.
Scaled time: 5.61 units (timescale=1.967).
Factorization parameters were as follows:
name: 74443_125
n: 5713650581068975362283662920696280343317363639223493296916903514253804648431669229237353348818611
m: 10000000000000000000000000
deg: 5
c5: 67
c0: -13
skew: 0.72
type: snfs
lss: 1
rlim: 910000
alim: 910000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 910000/910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [455000, 705001)
Primes: RFBsize:72026, AFBsize:71722, largePrimes:2409478 encountered
Relations: rels:2267940, finalFF:164897
Max relations in full relation-set: 28
Initial matrix: 143813 x 164897 with sparse part having weight 11603791.
Pruned matrix : 135848 x 136631 with weight 7820050.
Total sieving time: 2.65 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000
total time: 2.85 hours.
 --------- CPU info (if available) ----------

(67·10¹²⁸-13)/9 = 7(4)₁₂₇3_<129> = 97 · 3307 · 102539 · 14264757233_<11> · C109

C109 = P41 · P68

P41 = 16848849103457524845559641834441573294541_<41>

P68 = 94167851235718598569337274009848709690744380558238621290057509744751_<68>

Number: 74443_128
N=1586619915867458882658700891790336634603941150882959229493854020939935382701589118280696639658681911051704291
  ( 109 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=16848849103457524845559641834441573294541 (pp41)
 r2=94167851235718598569337274009848709690744380558238621290057509744751 (pp68)
Version: Msieve-1.40
Total time: 3.09 hours.
Scaled time: 6.24 units (timescale=2.019).
Factorization parameters were as follows:
name: 74443_128
n: 1586619915867458882658700891790336634603941150882959229493854020939935382701589118280696639658681911051704291
m: 50000000000000000000000000
deg: 5
c5: 536
c0: -325
skew: 0.90
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 940001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 167097 x 167345
Total sieving time: 2.89 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 3.09 hours.
 --------- CPU info (if available) ----------

(67·10¹⁵²-13)/9 = 7(4)₁₅₁3_<153> = 173 · 385193 · 59290667 · 1714313748613543313_<19> · 197788961175491971099981_<24> · C96

C96 = P47 · P49

P47 = 97221051417449319448358224662337021824557951429_<47>

P49 = 5715691719482093033732344844964775540735095156253_<49>

Fri Oct 30 14:37:10 2009  Msieve v. 1.40
Fri Oct 30 14:37:10 2009  random seeds: 58df9d7d a63c1257
Fri Oct 30 14:37:10 2009  factoring 555685558546057878893653180212330583409127836210597174985850701280488576149477345118354339635537 (96 digits)
Fri Oct 30 14:37:11 2009  no P-1/P+1/ECM available, skipping
Fri Oct 30 14:37:11 2009  commencing quadratic sieve (96-digit input)
Fri Oct 30 14:37:11 2009  using multiplier of 3
Fri Oct 30 14:37:11 2009  using 32kb Intel Core sieve core
Fri Oct 30 14:37:11 2009  sieve interval: 36 blocks of size 32768
Fri Oct 30 14:37:11 2009  processing polynomials in batches of 6
Fri Oct 30 14:37:11 2009  using a sieve bound of 2299949 (84350 primes)
Fri Oct 30 14:37:11 2009  using large prime bound of 344992350 (28 bits)
Fri Oct 30 14:37:11 2009  using double large prime bound of 2333764230167400 (43-52 bits)
Fri Oct 30 14:37:11 2009  using trial factoring cutoff of 52 bits
Fri Oct 30 14:37:11 2009  polynomial 'A' values have 12 factors
Fri Oct 30 18:38:25 2009  84448 relations (20475 full + 63973 combined from 1281737 partial), need 84446
Fri Oct 30 18:38:26 2009  begin with 1302212 relations
Fri Oct 30 18:38:26 2009  reduce to 222956 relations in 11 passes
Fri Oct 30 18:38:26 2009  attempting to read 222956 relations
Fri Oct 30 18:38:28 2009  recovered 222956 relations
Fri Oct 30 18:38:28 2009  recovered 209931 polynomials
Fri Oct 30 18:38:28 2009  attempting to build 84448 cycles
Fri Oct 30 18:38:28 2009  found 84448 cycles in 5 passes
Fri Oct 30 18:38:28 2009  distribution of cycle lengths:
Fri Oct 30 18:38:28 2009     length 1 : 20475
Fri Oct 30 18:38:28 2009     length 2 : 14393
Fri Oct 30 18:38:28 2009     length 3 : 13940
Fri Oct 30 18:38:28 2009     length 4 : 11339
Fri Oct 30 18:38:28 2009     length 5 : 8544
Fri Oct 30 18:38:28 2009     length 6 : 6044
Fri Oct 30 18:38:28 2009     length 7 : 3948
Fri Oct 30 18:38:28 2009     length 9+: 5765
Fri Oct 30 18:38:28 2009  largest cycle: 20 relations
Fri Oct 30 18:38:28 2009  matrix is 84350 x 84448 (24.0 MB) with weight 5954508 (70.51/col)
Fri Oct 30 18:38:28 2009  sparse part has weight 5954508 (70.51/col)
Fri Oct 30 18:38:29 2009  filtering completed in 3 passes
Fri Oct 30 18:38:29 2009  matrix is 80666 x 80730 (23.1 MB) with weight 5735368 (71.04/col)
Fri Oct 30 18:38:29 2009  sparse part has weight 5735368 (71.04/col)
Fri Oct 30 18:38:29 2009  saving the first 48 matrix rows for later
Fri Oct 30 18:38:29 2009  matrix is 80618 x 80730 (17.1 MB) with weight 4813504 (59.62/col)
Fri Oct 30 18:38:29 2009  sparse part has weight 3986473 (49.38/col)
Fri Oct 30 18:38:29 2009  matrix includes 64 packed rows
Fri Oct 30 18:38:29 2009  using block size 32292 for processor cache size 8192 kB
Fri Oct 30 18:38:29 2009  commencing Lanczos iteration
Fri Oct 30 18:38:29 2009  memory use: 14.9 MB
Fri Oct 30 18:38:53 2009  lanczos halted after 1276 iterations (dim = 80614)
Fri Oct 30 18:38:54 2009  recovered 16 nontrivial dependencies
Fri Oct 30 18:38:55 2009  prp47 factor: 97221051417449319448358224662337021824557951429
Fri Oct 30 18:38:55 2009  prp49 factor: 5715691719482093033732344844964775540735095156253
Fri Oct 30 18:38:55 2009  elapsed time 04:01:45

Oct 30, 2009 (6th)

By Serge Batalov / GMP-ECM / Oct 30, 2009

(59·10¹⁵⁴+31)/9 = 6(5)₁₅₃9_<155> = 3 · 13 · 41 · 561602387 · 1468996097_<10> · 629373674601490057_<18> · C116

C116 = P32 · P85

P32 = 11515653024662605644224396059681_<32>

P85 = 6856686724641505888344919729757159600810076382419241778190435348457495481603278102507_<85>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3333432130
Step 1 took 2768ms
Step 2 took 1908ms
********** Factor found in step 2: 11515653024662605644224396059681
Found probable prime factor of 32 digits: 11515653024662605644224396059681
Probable prime cofactor has 85 digits

(59·10¹⁷⁴+31)/9 = 6(5)₁₇₃9_<175> = 41 · 251 · 3754148753_<10> · 182442596131_<12> · 247407888474658786954353161_<27> · C124

C124 = P34 · C91

P34 = 3665302763719338852949381637894473_<34>

C91 = [1025630214377682248913408120542627988922255145298292474518193455947066469922875791085266431_<91>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1424803983
Step 1 took 2564ms
********** Factor found in step 1: 3665302763719338852949381637894473
Found probable prime factor of 34 digits: 3665302763719338852949381637894473
Composite cofactor has 91 digits

(59·10¹⁹⁹+31)/9 = 6(5)₁₉₈9_<200> = 3 · 23 · 41 · 151760533 · 458867159 · 30185840183_<11> · C170

C170 = P28 · P142

P28 = 1602687943698543126131675611_<28>

P142 = 6878258551729128554685038747479659603886933282297464944457396121908040776440780280432667254915111985042970315141255881530546102872883667527461_<142>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2091762947
Step 1 took 3492ms
Step 2 took 2452ms
********** Factor found in step 2: 1602687943698543126131675611
Found probable prime factor of 28 digits: 1602687943698543126131675611
Probable prime cofactor has 142 digits

(59·10²⁰⁰+31)/9 = 6(5)₁₉₉9_<201> = 647 · 59141 · 357238529 · C185

C185 = P28 · P158

P28 = 2286251887838065901353298057_<28>

P158 = 20976556125252658394173548582655076279566955914498617474180556805568901829064519383634511266481239826594839102020809479854759222807301826314172217673409387589_<158>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=741387217
Step 1 took 4080ms
********** Factor found in step 1: 2286251887838065901353298057
Found probable prime factor of 28 digits: 2286251887838065901353298057
Probable prime cofactor has 158 digits

(67·10¹⁶¹-13)/9 = 7(4)₁₆₀3_<162> = 7 · 73 · 5280887 · 354444281 · 5910599194139687430907_<22> · 65963915942544805370686211_<26> · C97

C97 = P34 · P63

P34 = 2668794540328995477716550306660659_<34>

P63 = 748003215572714369503951702881054047348463244791006660340612553_<63>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3974447949
Step 1 took 2048ms
Step 2 took 1480ms
********** Factor found in step 2: 2668794540328995477716550306660659
Found probable prime factor of 34 digits: 2668794540328995477716550306660659
Probable prime cofactor has 63 digits

(22·10¹⁸³+17)/3 = 7(3)₁₈₂9_<184> = 29 · 41 · 79 · 457 · 176257138459_<12> · C165

C165 = P31 · C135

P31 = 8048080087752238884475113802981_<31>

C135 = [120430718000717344755122639668146818766081866163800205532918460738996973886808495543748787636747999455799416767695465023104549925150223_<135>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1294281311
Step 1 took 3488ms
Step 2 took 2468ms
********** Factor found in step 2: 8048080087752238884475113802981
Found probable prime factor of 31 digits: 8048080087752238884475113802981
Composite cofactor has 135 digits

(67·10¹⁸¹-13)/9 = 7(4)₁₈₀3_<182> = 127 · 15370583931178846189_<20> · C161

C161 = P34 · C128

P34 = 2253776873153776657897948451534279_<34>

C128 = [16921049169503429770691052650078474147642338224813289853061010395893828071230552899451200517984291274406940600654599798013769439_<128>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=736395422
Step 1 took 3560ms
Step 2 took 2413ms
********** Factor found in step 2: 2253776873153776657897948451534279
Found probable prime factor of 34 digits: 2253776873153776657897948451534279
Composite cofactor has 128 digits

(22·10¹⁹⁷+17)/3 = 7(3)₁₉₆9_<198> = 2999609 · 17526737 · C185

C185 = P32 · C153

P32 = 85768965380696892224398060458083_<32>

C153 = [162631825549783751295866446947190481527542400941976286560382655837239566893610989918569146348381161296601343514990401403459613148506298287882369753536801_<153>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4294209017
Step 1 took 4064ms
Step 2 took 2681ms
********** Factor found in step 2: 85768965380696892224398060458083
Found probable prime factor of 32 digits: 85768965380696892224398060458083
Composite cofactor has 153 digits

(22·10¹⁷⁹+17)/3 = 7(3)₁₇₈9_<180> = 15559 · 184211 · 8689564994090088209_<19> · 60523080194263634333609_<23> · 61570408566381724845907_<23> · C106

C106 = P33 · P74

P33 = 446056747541793215384851975393451_<33>

P74 = 17714258502083168870661444117316394335176926736315549830701596471827794183_<74>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1545800992
Step 1 took 2365ms
Step 2 took 1700ms
********** Factor found in step 2: 446056747541793215384851975393451
Found probable prime factor of 33 digits: 446056747541793215384851975393451
Probable prime cofactor has 74 digits

(67·10¹⁵⁶-13)/9 = 7(4)₁₅₅3_<157> = 3² · 19 · 47 · 139 · 33161 · C147

C147 = P36 · P112

P36 = 134467084183425554399242168453850521_<36>

P112 = 1494444938340149006807751226662925392418214556242644418555585617423575237956535769730952159502701461363114458621_<112>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2881240165
Step 1 took 2980ms
********** Factor found in step 1: 134467084183425554399242168453850521
Found probable prime factor of 36 digits: 134467084183425554399242168453850521
Probable prime cofactor has 112 digits

(67·10¹⁹⁵-13)/9 = 7(4)₁₉₄3_<196> = 3 · 173 · 4373 · 31069 · 125294581708453_<15> · 1784960739592187_<16> · 87066488362644079096453_<23> · 5741354370893543162557514479_<28> · C105

C105 = P36 · P70

P36 = 123426397951350582174645249823462411_<36>

P70 = 7651098400206075515266178289261247157235344735713694647781980737240803_<70>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=26946518
Step 1 took 2156ms
Step 2 took 1684ms
********** Factor found in step 2: 123426397951350582174645249823462411
Found probable prime factor of 36 digits: 123426397951350582174645249823462411
Probable prime cofactor has 70 digits

Oct 30, 2009 (5th)

By Dmitry Domanov / GGNFS/msieve / Oct 30, 2009

(22·10¹⁴⁷-7)/3 = 7(3)₁₄₆1_<148> = 877 · 2089 · 125294657 · 1955716477250593_<16> · 5297185565183853217_<19> · C100

C100 = P34 · P66

P34 = 5357601451931949330338251285732117_<34>

P66 = 575584852032572576040227977297423130731945405191587010014254749643_<66>

Number: g100
N=3083754238959747050060530712204481731076920353986016215023861867048446187911390233584704185799384231
  ( 100 digits)
Divisors found:
 r1=5357601451931949330338251285732117 (pp34)
 r2=575584852032572576040227977297423130731945405191587010014254749643 (pp66)
Version: Msieve-1.40
Total time: 3.29 hours.
Scaled time: 6.46 units (timescale=1.963).
Factorization parameters were as follows:
name: g100
n: 3083754238959747050060530712204481731076920353986016215023861867048446187911390233584704185799384231
skew: 2378.52
# norm 6.26e+013
c5: 716040
c4: 768401206
c3: -3347407358048
c2: -21666142625728748
c1: -5359048822522704315
c0: 22498539625274014910685
# alpha -6.46
Y1: 3195251251
Y0: -5331242520959992304
# Murphy_E 3.76e-009
# M 2889047347447943462753756483416340182973701438603636079111165743841444508017748937466511011496473051
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 228951 x 229176
Polynomial selection time: 0.38 hours.
Total sieving time: 2.65 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 3.29 hours.
 --------- CPU info (if available) ----------

(65·10¹⁵⁷+61)/9 = 7(2)₁₅₆9_<158> = 79 · 153773771 · 85677699739844835667027_<23> · 1389841419191345191370059_<25> · C101

C101 = P50 · P51

P50 = 70655337767515623403718126937284154445695756983599_<50>

P51 = 706615998528579354350895287081083417163425558047983_<51>

Number: g101
N=49926192047967097030608276609867645116088896365617729035992426846122079146222535243827882930586030817
  ( 101 digits)
Divisors found:
 r1=70655337767515623403718126937284154445695756983599 (pp50)
 r2=706615998528579354350895287081083417163425558047983 (pp51)
Version: Msieve-1.40
Total time: 4.53 hours.
Scaled time: 8.43 units (timescale=1.860).
Factorization parameters were as follows:
name: g101
n: 49926192047967097030608276609867645116088896365617729035992426846122079146222535243827882930586030817
skew: 1704.10
# norm 3.47e+013
c5: 755040
c4: -778190204
c3: -4882519895824
c2: 9111802450446
c1: -4465344687580793315
c0: 612530740196218749242
# alpha -5.35
Y1: 11385808801
Y0: -9206017737240624105
# Murphy_E 3.21e-009
# M 42391844600785429460091656032734960392745250527381026440482151276186691213655918782772522577390152249
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 182786 x 183011
Polynomial selection time: 0.43 hours.
Total sieving time: 3.77 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 4.53 hours.
 --------- CPU info (if available) ----------

(22·10¹⁶²-7)/3 = 7(3)₁₆₁1_<163> = 17 · 6151 · 32670611801_<11> · 2202000923674657459_<19> · 6467789994663449185869367399_<28> · C102

C102 = P45 · P57

P45 = 199209648585588769622820458941437925059772499_<45>

P57 = 756598949668130460359016509976391729974682603903888934227_<57>

Number: g102
N=150721810883613833860276412458540167568640519018256430521087768408836448415786099602290956392194423273
  ( 102 digits)
Divisors found:
 r1=199209648585588769622820458941437925059772499 (pp45)
 r2=756598949668130460359016509976391729974682603903888934227 (pp57)
Version: Msieve-1.40
Total time: 4.99 hours.
Scaled time: 9.77 units (timescale=1.957).
Factorization parameters were as follows:
name: g102
n: 150721810883613833860276412458540167568640519018256430521087768408836448415786099602290956392194423273
skew: 5475.89
# norm 1.34e+014
c5: 68040
c4: -664173246
c3: -7626252806023
c2: -37813406180968319
c1: 52258057748767061759
c0: 107057378213323747343421
# alpha -5.71
Y1: 17409096199
Y0: -18581602017512027734
# Murphy_E 2.75e-009
# M 67503055058093048970044476777557095622419620092815774496828876992418422713533293625409912225975661918
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 262112 x 262337
Polynomial selection time: 0.50 hours.
Total sieving time: 4.23 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 4.99 hours.
 --------- CPU info (if available) ----------

(62·10¹⁴⁷+1)/9 = 6(8)₁₄₆9_<148> = C148

C148 = P38 · P47 · P64

P38 = 14609058570850068072790171345251209857_<38>

P47 = 54119127478220719186968454440445122879267586001_<47>

P64 = 8713169520734770932259156884452356918743245463266750664655868777_<64>

N=6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
  ( 148 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=14609058570850068072790171345251209857 (pp38)
 r2=54119127478220719186968454440445122879267586001 (pp47)
 r3=8713169520734770932259156884452356918743245463266750664655868777 (pp64)
Version: Msieve-1.40
Total time: 14.47 hours.
Scaled time: 13.52 units (timescale=0.934).
Factorization parameters were as follows:
n: 6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
m: 500000000000000000000000000000
deg: 5
c5: 248
c0: 125
skew: 0.87
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1750001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 304330 x 304556
Total sieving time: 14.04 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,150.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 14.47 hours.

(22·10¹¹⁶+17)/3 = 7(3)₁₁₅9_<117> = 643 · C115

C115 = P45 · P70

P45 = 127199283710829473583831003888420738835436659_<45>

P70 = 8966145609054367047114636580013011049277494734917626941664754253624147_<70>

Number: s115
N=1140487299118714359771902540176257128045619491964748574390876101607050285121824779678589942975635044064282011404873
  ( 115 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=127199283710829473583831003888420738835436659 (pp45)
 r2=8966145609054367047114636580013011049277494734917626941664754253624147 (pp70)
Version: Msieve-1.40
Total time: 1.46 hours.
Scaled time: 1.36 units (timescale=0.934).
Factorization parameters were as follows:
n: 1140487299118714359771902540176257128045619491964748574390876101607050285121824779678589942975635044064282011404873
m: 200000000000000000000000
deg: 5
c5: 55
c0: 136
skew: 1.20
type: snfs
lss: 1
rlim: 650000
alim: 650000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 650000/650000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [325000, 575001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 71229 x 71454
Total sieving time: 1.42 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,118.000,5,0,0,0,0,0,0,0,0,650000,650000,25,25,45,45,2.2,2.2,50000
total time: 1.46 hours.
 --------- CPU info (if available) ----------

(22·10¹⁵⁴+17)/3 = 7(3)₁₅₃9_<155> = 7 · C155

C155 = P39 · P116

P39 = 184686752453367787287809095416797694533_<39>

P116 = 56724103580930346666691668641253433479051981833696382842269072327040745086396602948789182818404047086941094879036969_<116>

Number: s154
N=10476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190477
  ( 155 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=184686752453367787287809095416797694533 (pp39)
 r2=56724103580930346666691668641253433479051981833696382842269072327040745086396602948789182818404047086941094879036969 (pp116)
Version: Msieve-1.40
Total time: 23.76 hours.
Scaled time: 22.19 units (timescale=0.934).
Factorization parameters were as follows:
n: 10476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190477
m: 10000000000000000000000000000000
deg: 5
c5: 11
c0: 85
skew: 1.51
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 481528 x 481757
Total sieving time: 23.09 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 23.76 hours.
 --------- CPU info (if available) ----------

(22·10¹⁵³-7)/3 = 7(3)₁₅₂1_<154> = C154

C154 = P41 · P53 · P62

P41 = 16102595691756429004184189289923007311587_<41>

P53 = 16804048553475014199523698985582044088874738998911019_<53>

P62 = 27101392731833721574475833973613757042141875062514354080413427_<62>

Number: s154
N=7333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
  ( 154 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=16102595691756429004184189289923007311587 (pp41)
 r2=16804048553475014199523698985582044088874738998911019 (pp53)
 r3=27101392731833721574475833973613757042141875062514354080413427 (pp62)
Version: Msieve-1.40
Total time: 17.81 hours.
Scaled time: 34.95 units (timescale=1.963).
Factorization parameters were as follows:
n: 7333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
m: 5000000000000000000000000000000
deg: 5
c5: 176
c0: -175
skew: 1.00
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 499206 x 499433
Total sieving time: 16.85 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.71 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,155.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 17.81 hours.
 --------- CPU info (if available) ----------

Oct 30, 2009 (4th)

By Jo Yeong Uk / GMP-ECM / Oct 30, 2009

(62·10¹⁴¹-17)/9 = 6(8)₁₄₀7_<142> = 449 · 643 · 739570927 · 2076569140741_<13> · C116

C116 = P29 · P88

P29 = 12449586199568989558573448867_<29>

P88 = 1247988902077611754486563333046373100040151974373538545203846142963842189794646273724189_<88>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 15536945412520690380033798617839461767749986899777529309993270411105848832394342125721382926624823181351370052543863 (116 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5231726309
Step 1 took 3478ms
Step 2 took 1358ms
********** Factor found in step 2: 12449586199568989558573448867
Found probable prime factor of 29 digits: 12449586199568989558573448867
Probable prime cofactor 1247988902077611754486563333046373100040151974373538545203846142963842189794646273724189 has 88 digits

Oct 30, 2009 (3rd)

By Lionel Debroux / GGNFS + Msieve / Oct 30, 2009

(22·10¹⁰³+17)/3 = 7(3)₁₀₂9_<104> = 41 · C103

C103 = P37 · P66

P37 = 1968440256387558857469214196952117053_<37>

P66 = 908647280695882845564443412045563169110619998478775609933242429343_<66>

Number: 73339_103
N=1788617886178861788617886178861788617886178861788617886178861788617886178861788617886178861788617886179
  ( 103 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=1968440256387558857469214196952117053 (pp37)
 r2=908647280695882845564443412045563169110619998478775609933242429343 (pp66)
Version: Msieve v. 1.44
Total time: 1.48 hours.
Scaled time: 2.20 units (timescale=1.485).
Factorization parameters were as follows:
n: 1788617886178861788617886178861788617886178861788617886178861788617886178861788617886178861788617886179
m: 100000000000000000000000000
deg: 4
c4: 11
c0: 85
skew: 1.67
type: snfs
lss: 1
rlim: 390000
alim: 390000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 390000/390000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [195000, 355001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 62433 x 62681
Total sieving time: 1.45 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105.000,4,0,0,0,0,0,0,0,0,390000,390000,25,25,44,44,2.2,2.2,20000
total time: 1.48 hours.
 --------- CPU info (if available) ----------
[    0.029106] CPU0: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.101090] CPU1: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.000000] Memory: 2051108k/2096800k available (7368k kernel code, 452k absent, 44504k reserved, 3461k data, 768k init)
[    0.001009] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.00 BogoMIPS (lpj=1995001)
[    0.001999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913)
[    0.102026] Total of 2 processors activated (7979.82 BogoMIPS).

(22·10¹⁰⁵+17)/3 = 7(3)₁₀₄9_<106> = 23 · 79 · 941 · C100

C100 = P42 · P58

P42 = 667319846833294484773950178480591643333119_<42>

P58 = 6427215088318733045674430056423147409336405409180529236673_<58>

Number: 73339_105
N=4289008188301496220506488976956523688679611283288795882396175296443573905752164340757021642530273087
  ( 100 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=667319846833294484773950178480591643333119 (pp42)
 r2=6427215088318733045674430056423147409336405409180529236673 (pp58)
Version: Msieve v. 1.44
Total time: 2.09 hours.
Scaled time: 3.01 units (timescale=1.441).
Factorization parameters were as follows:
n: 4289008188301496220506488976956523688679611283288795882396175296443573905752164340757021642530273087
m: 200000000000000000000000000
deg: 4
c4: 55
c0: 68
skew: 1.05
type: snfs
lss: 1
rlim: 420000
alim: 420000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 420000/420000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [210000, 450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 68749 x 68997
Total sieving time: 2.06 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,106.000,4,0,0,0,0,0,0,0,0,420000,420000,25,25,44,44,2.2,2.2,20000
total time: 2.09 hours.
 --------- CPU info (if available) ----------
[    0.029106] CPU0: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.101090] CPU1: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.000000] Memory: 2051108k/2096800k available (7368k kernel code, 452k absent, 44504k reserved, 3461k data, 768k init)
[    0.001009] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.00 BogoMIPS (lpj=1995001)
[    0.001999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913)
[    0.102026] Total of 2 processors activated (7979.82 BogoMIPS).

Oct 30, 2009 (2nd)

Factorizations of 655...559 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 30, 2009

By Lionel Debroux / GMP-ECM

Factorizations of 733...339 and Factorizations of 744...443 have been extended up to n=200. Composite numbers that appeared newly have passed 150 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 29, 2009 (9th)

By Erik Branger / GGNFS, Msieve / Oct 29, 2009

(22·10¹⁴⁴-7)/3 = 7(3)₁₄₃1_<145> = 35933501 · 33082734446491157_<17> · C121

C121 = P61 · P61

P61 = 1611222895107357825861684897891027348379434665936113039177013_<61>

P61 = 3828642978160722759423548127980286671936987166408740855033191_<61>

Number: 73331_144
N=6168797223604576285866739275513559616412539375347282679742557779151130854164360406427707025619267418222104317849439238483
  ( 121 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1611222895107357825861684897891027348379434665936113039177013 (pp61)
 r2=3828642978160722759423548127980286671936987166408740855033191 (pp61)
Version: Msieve-1.40
Total time: 6.72 hours.
Scaled time: 6.67 units (timescale=0.992).
Factorization parameters were as follows:
n: 6168797223604576285866739275513559616412539375347282679742557779151130854164360406427707025619267418222104317849439238483
m: 100000000000000000000000000000
deg: 5
c5: 11
c0: -35
skew: 1.26
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3

Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [950000, 1850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 270431 x 270656
Total sieving time: 6.48 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 6.72 hours.
 --------- CPU info (if available) ----------

(65·10¹⁴⁸+7)/9 = 7(2)₁₄₇3_<149> = 701 · C147

C147 = P34 · P47 · P66

P34 = 3755550574749161555183061499920779_<34>

P47 = 46814150630339904680428759046932495299316986541_<47>

P66 = 586006004706828862487443318948487124438444839144237964283793539957_<66>

Number: 72223_148
N=103027421144396893326993184339831986051672214297035980345538120145823426850530987478205737834839118719289903312727849104453954667934696465366936123
  ( 147 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=3755550574749161555183061499920779 (pp34)
 r2=46814150630339904680428759046932495299316986541 (pp47)
 r3=586006004706828862487443318948487124438444839144237964283793539957 (pp66)
Version: Msieve v. 1.43
Total time: 25.27 hours.
Scaled time: 19.91 units (timescale=0.788).
Factorization parameters were as follows:
n: 103027421144396893326993184339831986051672214297035980345538120145823426850530987478205737834839118719289903312727849104453954667934696465366936123
m: 500000000000000000000000000000
deg: 5
c5: 104
c0: 35
skew: 0.80
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 363568 x 363798
Total sieving time: 23.94 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.74 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,150.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 25.27 hours.
 --------- CPU info (if available) ----------

(65·10¹⁴⁵+7)/9 = 7(2)₁₄₄3_<146> = 73 · 127 · C142

C142 = P33 · P110

P33 = 215020535686146100995565648128067_<33>

P110 = 36229665693495144004165159106176063374327069676193814029155021451148871281621766835872766224697315800096474339_<110>

Number: 72223_145
N=7790122125145315739642133774374093649252747516149522405589712244873500401490909526720118889248432986972518846103141216936923980392861851172713
  ( 142 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=215020535686146100995565648128067 (pp33)
 r2=36229665693495144004165159106176063374327069676193814029155021451148871281621766835872766224697315800096474339 (pp110)
Version: Msieve-1.40
Total time: 8.81 hours.
Scaled time: 9.16 units (timescale=1.039).
Factorization parameters were as follows:
n: 7790122125145315739642133774374093649252747516149522405589712244873500401490909526720118889248432986972518846103141216936923980392861851172713
m: 100000000000000000000000000000
deg: 5
c5: 65
c0: 7
skew: 0.64
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2180001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 308284 x 308510
Total sieving time: 8.34 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 8.81 hours.
 --------- CPU info (if available) ----------

(62·10¹³¹-53)/9 = 6(8)₁₃₀3_<132> = 13 · 19 · 199 · 10513 · 81899 · C119

C119 = P52 · P67

P52 = 2213322253356502762971124059611562807329201224533739_<52>

P67 = 7354433687504421692647292079401137480439947289067440673701943894427_<67>

Number: 68883_131
N=16277731741388260497915416758923984903955258653210841577364643431610859290705103072764367923074919035554697010915572553
  ( 119 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=2213322253356502762971124059611562807329201224533739 (pp52)
 r2=7354433687504421692647292079401137480439947289067440673701943894427 (pp67)
Version: Msieve v. 1.43
Total time: 4.98 hours.
Scaled time: 3.91 units (timescale=0.785).
Factorization parameters were as follows:
n: 16277731741388260497915416758923984903955258653210841577364643431610859290705103072764367923074919035554697010915572553
m: 200000000000000000000000000
deg: 5
c5: 155
c0: -424
skew: 1.22
type: snfs
lss: 1
rlim: 1180000
alim: 1180000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1180000/1180000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [590000, 1040001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 161442 x 161667
Total sieving time: 4.69 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,133.000,5,0,0,0,0,0,0,0,0,1180000,1180000,26,26,47,47,2.3,2.3,75000
total time: 4.98 hours.
 --------- CPU info (if available) ----------

(62·10¹⁴⁰+1)/9 = 6(8)₁₃₉9_<141> = 13 · 12015911326813_<14> · C127

C127 = P53 · P75

P53 = 10098947505940741188253378705758426820362239035432097_<53>

P75 = 436689750002543719167336765795082713550194093289913311609891257071910504673_<75>

Number: 68889_140
N=4410106861658074670653860173486054163974219973878488208662754414022560015885316271061355644080305761472103499186111823892689281
  ( 127 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=10098947505940741188253378705758426820362239035432097 (pp53)
 r2=436689750002543719167336765795082713550194093289913311609891257071910504673 (pp75)
Version: Msieve-1.40
Total time: 5.09 hours.
Scaled time: 5.12 units (timescale=1.006).
Factorization parameters were as follows:
n: 4410106861658074670653860173486054163974219973878488208662754414022560015885316271061355644080305761472103499186111823892689281
m: 20000000000000000000000000000
deg: 5
c5: 31
c0: 16
skew: 0.88
type: snfs
lss: 1
rlim: 1690000
alim: 1690000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1690000/1690000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [845000, 1545001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 219150 x 219377
Total sieving time: 4.88 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,142.000,5,0,0,0,0,0,0,0,0,1690000,1690000,26,26,48,48,2.3,2.3,100000
total time: 5.09 hours.
 --------- CPU info (if available) ----------

(65·10¹³⁰+61)/9 = 7(2)₁₂₉9_<131> = 5309 · 133853 · 11432210892981839783_<20> · C103

C103 = P44 · P60

P44 = 88242340891347424067333022942264527163159569_<44>

P60 = 100744829127432112190700097504794978919085457423286387865851_<60>

Number: 72229_130
N=8889959554903411701690137669062704823054606208746224362590409854700706089629534587027889575236078978219
  ( 103 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=88242340891347424067333022942264527163159569 (pp44)
 r2=100744829127432112190700097504794978919085457423286387865851 (pp60)
Version: Msieve v. 1.43
Total time: 5.60 hours.
Scaled time: 4.35 units (timescale=0.776).
Factorization parameters were as follows:
n: 8889959554903411701690137669062704823054606208746224362590409854700706089629534587027889575236078978219
m: 100000000000000000000000000
deg: 5
c5: 65
c0: 61
skew: 0.99
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 170836 x 171061
Total sieving time: 5.33 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 5.60 hours.
 --------- CPU info (if available) ----------

Oct 29, 2009 (8th)

By Wataru Sakai / GMP-ECM 6.2.1 / Oct 29, 2009

(83·10¹⁸³+7)/9 = 9(2)₁₈₂3_<184> = 197 · 187504159 · 103695324197_<12> · 10933903999027_<14> · 231095300840004022549_<21> · C129

C129 = P42 · P88

P42 = 224437963133592964448686504282443534327677_<42>

P88 = 4245575694068388034155339395025821288916179217836087032692125228590049200357040943403523_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4111386264
Step 1 took 38383ms
Step 2 took 14033ms
********** Factor found in step 2: 224437963133592964448686504282443534327677
Found probable prime factor of 42 digits: 224437963133592964448686504282443534327677
Probable prime cofactor 4245575694068388034155339395025821288916179217836087032692125228590049200357040943403523 has 88 digits

(22·10¹⁷³-7)/3 = 7(3)₁₇₂1_<174> = 97 · 541859 · 65483111511553_<14> · 29019575156728627496451041059487_<32> · C121

C121 = P34 · C88

P34 = 7085999215281227635840096984763449_<34>

C88 = [1036148358624627286217516372248460715568726928814760434392187296717805689495977792371623_<88>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2752642412
Step 1 took 34284ms
Step 2 took 13203ms
********** Factor found in step 2: 7085999215281227635840096984763449
Found probable prime factor of 34 digits: 7085999215281227635840096984763449
Composite cofactor 1036148358624627286217516372248460715568726928814760434392187296717805689495977792371623 has 88 digits

Oct 29, 2009 (7th)

By Sinkiti Sibata / Msieve, GGNFS / Oct 29, 2009

(65·10¹¹⁹+61)/9 = 7(2)₁₁₈9_<120> = 3² · 7761437 · C113

C113 = P50 · P63

P50 = 61337291745830448794575516401101672468419237064719_<50>

P63 = 168562748737289305529363034257681167433141794253215672631853727_<63>

Number: 72229_119
N=10339182496778227225222199649400866563787983279416803045653390419872880960091142088797076312060113814007240357713
  ( 113 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=61337291745830448794575516401101672468419237064719 (pp50)
 r2=168562748737289305529363034257681167433141794253215672631853727 (pp63)
Version: Msieve-1.40
Total time: 1.93 hours.
Scaled time: 3.95 units (timescale=2.045).
Factorization parameters were as follows:
name: 72229_119
n: 10339182496778227225222199649400866563787983279416803045653390419872880960091142088797076312060113814007240357713
m: 1000000000000000000000000
deg: 5
c5: 13
c0: 122
skew: 1.56
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 665001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 87883 x 88110
Total sieving time: 1.87 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.93 hours.
 --------- CPU info (if available) ----------

(64·10¹⁸³+17)/9 = 7(1)₁₈₂3_<184> = 3 · 59 · C182

C182 = P33 · P46 · P104

P33 = 384410432843509184562551441772217_<33>

P46 = 5960154262873601562601591019221235861490470119_<46>

P104 = 17535232633606003339861798618760092993549136117476670102764910728473797048681628830125019112178672954103_<104>

Number: 71113_183
N=40175768989328311362209667294413057124921531701192718141870684243565599497802887633396107972379158819836785938480853735091023226616446955430006277463904582548650345260514752040175769
  ( 182 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=384410432843509184562551441772217 (pp33)
 r2=5960154262873601562601591019221235861490470119 (pp46)
 r3=17535232633606003339861798618760092993549136117476670102764910728473797048681628830125019112178672954103 (pp104)
Version: Msieve v. 1.42
Total time: 12.89 hours.
Scaled time: 10.99 units (timescale=0.853).
Factorization parameters were as follows:
name: 71113_183
n: 40175768989328311362209667294413057124921531701192718141870684243565599497802887633396107972379158819836785938480853735091023226616446955430006277463904582548650345260514752040175769
m: 4000000000000000000000000000000000000
deg: 5
c5: 125
c0: 34
skew: 0.77
type: snfs
lss: 1
rlim: 8500000
alim: 8500000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4250000, 7450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1649596 x 1649831
Total sieving time: 0.00 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 11.71 hours.
Time per square root: 0.97 hours.
Prototype def-par.txt line would be:
snfs,185.000,5,0,0,0,0,0,0,0,0,8500000,8500000,28,28,54,54,2.5,2.5,100000
total time: 12.89 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583)
Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268)
Total of 2 processors activated (11653.70 BogoMIPS).

Total time: 125hours 39min

(62·10¹²⁸-17)/9 = 6(8)₁₂₇7_<129> = 3 · 1657 · 105522593823052741_<18> · 4736156499474908470847_<22> · C87

C87 = P41 · P47

P41 = 19238524155145887995567897573406759382183_<41>

P47 = 14413258025958972317973107989704103083120550217_<47>

Thu Oct 29 08:01:12 2009  Msieve v. 1.42
Thu Oct 29 08:01:12 2009  random seeds: 0947fb50 3b7d3568
Thu Oct 29 08:01:12 2009  factoring 277289812686762027301312045381903076962595440431498977011201304744729183842977946583711 (87 digits)
Thu Oct 29 08:01:13 2009  searching for 15-digit factors
Thu Oct 29 08:01:13 2009  commencing quadratic sieve (87-digit input)
Thu Oct 29 08:01:13 2009  using multiplier of 35
Thu Oct 29 08:01:13 2009  using 32kb Intel Core sieve core
Thu Oct 29 08:01:13 2009  sieve interval: 20 blocks of size 32768
Thu Oct 29 08:01:13 2009  processing polynomials in batches of 11
Thu Oct 29 08:01:13 2009  using a sieve bound of 1484803 (56667 primes)
Thu Oct 29 08:01:13 2009  using large prime bound of 118784240 (26 bits)
Thu Oct 29 08:01:13 2009  using double large prime bound of 342425267860000 (42-49 bits)
Thu Oct 29 08:01:13 2009  using trial factoring cutoff of 49 bits
Thu Oct 29 08:01:13 2009  polynomial 'A' values have 11 factors
Thu Oct 29 08:50:06 2009  56767 relations (15620 full + 41147 combined from 598038 partial), need 56763
Thu Oct 29 08:50:07 2009  begin with 613658 relations
Thu Oct 29 08:50:08 2009  reduce to 136464 relations in 11 passes
Thu Oct 29 08:50:08 2009  attempting to read 136464 relations
Thu Oct 29 08:50:09 2009  recovered 136464 relations
Thu Oct 29 08:50:09 2009  recovered 117722 polynomials
Thu Oct 29 08:50:10 2009  attempting to build 56767 cycles
Thu Oct 29 08:50:10 2009  found 56767 cycles in 5 passes
Thu Oct 29 08:50:10 2009  distribution of cycle lengths:
Thu Oct 29 08:50:10 2009     length 1 : 15620
Thu Oct 29 08:50:10 2009     length 2 : 11099
Thu Oct 29 08:50:10 2009     length 3 : 10028
Thu Oct 29 08:50:10 2009     length 4 : 7451
Thu Oct 29 08:50:10 2009     length 5 : 5227
Thu Oct 29 08:50:10 2009     length 6 : 3205
Thu Oct 29 08:50:10 2009     length 7 : 1902
Thu Oct 29 08:50:10 2009     length 9+: 2235
Thu Oct 29 08:50:10 2009  largest cycle: 22 relations
Thu Oct 29 08:50:10 2009  matrix is 56667 x 56767 (13.5 MB) with weight 3322806 (58.53/col)
Thu Oct 29 08:50:10 2009  sparse part has weight 3322806 (58.53/col)
Thu Oct 29 08:50:11 2009  filtering completed in 4 passes
Thu Oct 29 08:50:11 2009  matrix is 52465 x 52529 (12.7 MB) with weight 3116575 (59.33/col)
Thu Oct 29 08:50:11 2009  sparse part has weight 3116575 (59.33/col)
Thu Oct 29 08:50:11 2009  saving the first 48 matrix rows for later
Thu Oct 29 08:50:11 2009  matrix is 52417 x 52529 (8.7 MB) with weight 2519016 (47.95/col)
Thu Oct 29 08:50:11 2009  sparse part has weight 1975140 (37.60/col)
Thu Oct 29 08:50:11 2009  matrix includes 64 packed rows
Thu Oct 29 08:50:11 2009  using block size 21011 for processor cache size 1024 kB
Thu Oct 29 08:50:11 2009  commencing Lanczos iteration
Thu Oct 29 08:50:11 2009  memory use: 8.6 MB
Thu Oct 29 08:50:29 2009  lanczos halted after 831 iterations (dim = 52415)
Thu Oct 29 08:50:29 2009  recovered 18 nontrivial dependencies
Thu Oct 29 08:50:29 2009  prp41 factor: 19238524155145887995567897573406759382183
Thu Oct 29 08:50:29 2009  prp47 factor: 14413258025958972317973107989704103083120550217
Thu Oct 29 08:50:29 2009  elapsed time 00:49:17

(62·10¹³⁰-17)/9 = 6(8)₁₂₉7_<131> = 7 · 13 · 151² · 619 · 1091 · 4691 · 3632610707018230033248932603_<28> · C88

C88 = P40 · P49

P40 = 2216843675469889748033783817831646405793_<40>

P49 = 1301424962816481848646950520141595158687854696197_<49>

Thu Oct 29 09:38:44 2009  Msieve v. 1.42
Thu Oct 29 09:38:44 2009  random seeds: 844858f0 9939bf40
Thu Oct 29 09:38:44 2009  factoring 2885055697918354219788012698586494272919721129686201143026490798695353880043070995869221 (88 digits)
Thu Oct 29 09:38:45 2009  searching for 15-digit factors
Thu Oct 29 09:38:45 2009  commencing quadratic sieve (88-digit input)
Thu Oct 29 09:38:46 2009  using multiplier of 5
Thu Oct 29 09:38:46 2009  using 32kb Intel Core sieve core
Thu Oct 29 09:38:46 2009  sieve interval: 25 blocks of size 32768
Thu Oct 29 09:38:46 2009  processing polynomials in batches of 9
Thu Oct 29 09:38:46 2009  using a sieve bound of 1517707 (57351 primes)
Thu Oct 29 09:38:46 2009  using large prime bound of 121416560 (26 bits)
Thu Oct 29 09:38:46 2009  using double large prime bound of 356205104400640 (42-49 bits)
Thu Oct 29 09:38:46 2009  using trial factoring cutoff of 49 bits
Thu Oct 29 09:38:46 2009  polynomial 'A' values have 11 factors
Thu Oct 29 10:19:57 2009  57823 relations (16380 full + 41443 combined from 602864 partial), need 57447
Thu Oct 29 10:19:58 2009  begin with 619244 relations
Thu Oct 29 10:19:59 2009  reduce to 137627 relations in 10 passes
Thu Oct 29 10:19:59 2009  attempting to read 137627 relations
Thu Oct 29 10:20:01 2009  recovered 137627 relations
Thu Oct 29 10:20:01 2009  recovered 111021 polynomials
Thu Oct 29 10:20:01 2009  attempting to build 57823 cycles
Thu Oct 29 10:20:01 2009  found 57823 cycles in 5 passes
Thu Oct 29 10:20:01 2009  distribution of cycle lengths:
Thu Oct 29 10:20:01 2009     length 1 : 16380
Thu Oct 29 10:20:01 2009     length 2 : 11364
Thu Oct 29 10:20:01 2009     length 3 : 10278
Thu Oct 29 10:20:01 2009     length 4 : 7544
Thu Oct 29 10:20:01 2009     length 5 : 5180
Thu Oct 29 10:20:01 2009     length 6 : 3069
Thu Oct 29 10:20:01 2009     length 7 : 1919
Thu Oct 29 10:20:01 2009     length 9+: 2089
Thu Oct 29 10:20:01 2009  largest cycle: 18 relations
Thu Oct 29 10:20:01 2009  matrix is 57351 x 57823 (13.7 MB) with weight 3355406 (58.03/col)
Thu Oct 29 10:20:01 2009  sparse part has weight 3355406 (58.03/col)
Thu Oct 29 10:20:02 2009  filtering completed in 3 passes
Thu Oct 29 10:20:02 2009  matrix is 52428 x 52492 (12.5 MB) with weight 3061277 (58.32/col)
Thu Oct 29 10:20:02 2009  sparse part has weight 3061277 (58.32/col)
Thu Oct 29 10:20:02 2009  saving the first 48 matrix rows for later
Thu Oct 29 10:20:02 2009  matrix is 52380 x 52492 (8.7 MB) with weight 2464760 (46.95/col)
Thu Oct 29 10:20:02 2009  sparse part has weight 1969615 (37.52/col)
Thu Oct 29 10:20:02 2009  matrix includes 64 packed rows
Thu Oct 29 10:20:02 2009  using block size 20996 for processor cache size 1024 kB
Thu Oct 29 10:20:03 2009  commencing Lanczos iteration
Thu Oct 29 10:20:03 2009  memory use: 8.5 MB
Thu Oct 29 10:20:20 2009  lanczos halted after 830 iterations (dim = 52377)
Thu Oct 29 10:20:20 2009  recovered 16 nontrivial dependencies
Thu Oct 29 10:20:21 2009  prp40 factor: 2216843675469889748033783817831646405793
Thu Oct 29 10:20:21 2009  prp49 factor: 1301424962816481848646950520141595158687854696197
Thu Oct 29 10:20:21 2009  elapsed time 00:41:37

(62·10¹⁴⁹-17)/9 = 6(8)₁₄₈7_<150> = 3⁴ · 53 · 563 · 3259 · 12479 · 27827 · 1543019 · 317866189 · 30231364087_<11> · 1303276091026529_<16> · C92

C92 = P44 · P48

P44 = 14990515629278420189522772956896539661364399_<44>

P48 = 869406757400744216491505254904358858761686953217_<48>

Thu Oct 29 10:31:36 2009  Msieve v. 1.42
Thu Oct 29 10:31:36 2009  random seeds: 10de91b8 65f02773
Thu Oct 29 10:31:36 2009  factoring 13032855585016127987715163764187861752979788193972047216203105388131327964051192003502321583 (92 digits)
Thu Oct 29 10:31:37 2009  searching for 15-digit factors
Thu Oct 29 10:31:37 2009  commencing quadratic sieve (92-digit input)
Thu Oct 29 10:31:37 2009  using multiplier of 3
Thu Oct 29 10:31:37 2009  using 32kb Intel Core sieve core
Thu Oct 29 10:31:37 2009  sieve interval: 36 blocks of size 32768
Thu Oct 29 10:31:37 2009  processing polynomials in batches of 6
Thu Oct 29 10:31:37 2009  using a sieve bound of 1748623 (65882 primes)
Thu Oct 29 10:31:37 2009  using large prime bound of 176610923 (27 bits)
Thu Oct 29 10:31:37 2009  using double large prime bound of 699248562996980 (42-50 bits)
Thu Oct 29 10:31:37 2009  using trial factoring cutoff of 50 bits
Thu Oct 29 10:31:37 2009  polynomial 'A' values have 12 factors
Thu Oct 29 12:23:28 2009  66409 relations (16846 full + 49563 combined from 801134 partial), need 65978
Thu Oct 29 12:23:29 2009  begin with 817980 relations
Thu Oct 29 12:23:30 2009  reduce to 167485 relations in 11 passes
Thu Oct 29 12:23:30 2009  attempting to read 167485 relations
Thu Oct 29 12:23:32 2009  recovered 167485 relations
Thu Oct 29 12:23:32 2009  recovered 148683 polynomials
Thu Oct 29 12:23:32 2009  attempting to build 66409 cycles
Thu Oct 29 12:23:32 2009  found 66409 cycles in 6 passes
Thu Oct 29 12:23:32 2009  distribution of cycle lengths:
Thu Oct 29 12:23:32 2009     length 1 : 16846
Thu Oct 29 12:23:32 2009     length 2 : 12029
Thu Oct 29 12:23:32 2009     length 3 : 11566
Thu Oct 29 12:23:32 2009     length 4 : 9050
Thu Oct 29 12:23:32 2009     length 5 : 6594
Thu Oct 29 12:23:32 2009     length 6 : 4335
Thu Oct 29 12:23:32 2009     length 7 : 2615
Thu Oct 29 12:23:33 2009     length 9+: 3374
Thu Oct 29 12:23:33 2009  largest cycle: 19 relations
Thu Oct 29 12:23:33 2009  matrix is 65882 x 66409 (16.6 MB) with weight 4091728 (61.61/col)
Thu Oct 29 12:23:33 2009  sparse part has weight 4091728 (61.61/col)
Thu Oct 29 12:23:34 2009  filtering completed in 3 passes
Thu Oct 29 12:23:34 2009  matrix is 62231 x 62295 (15.6 MB) with weight 3839753 (61.64/col)
Thu Oct 29 12:23:34 2009  sparse part has weight 3839753 (61.64/col)
Thu Oct 29 12:23:34 2009  saving the first 48 matrix rows for later
Thu Oct 29 12:23:34 2009  matrix is 62183 x 62295 (9.7 MB) with weight 3001449 (48.18/col)
Thu Oct 29 12:23:34 2009  sparse part has weight 2164215 (34.74/col)
Thu Oct 29 12:23:34 2009  matrix includes 64 packed rows
Thu Oct 29 12:23:34 2009  using block size 24918 for processor cache size 1024 kB
Thu Oct 29 12:23:35 2009  commencing Lanczos iteration
Thu Oct 29 12:23:35 2009  memory use: 10.0 MB
Thu Oct 29 12:23:59 2009  lanczos halted after 984 iterations (dim = 62181)
Thu Oct 29 12:23:59 2009  recovered 16 nontrivial dependencies
Thu Oct 29 12:24:00 2009  prp44 factor: 14990515629278420189522772956896539661364399
Thu Oct 29 12:24:00 2009  prp48 factor: 869406757400744216491505254904358858761686953217
Thu Oct 29 12:24:00 2009  elapsed time 01:52:24

(62·10¹³⁶-17)/9 = 6(8)₁₃₅7_<137> = 7 · 13 · 53 · 69581581 · 1013310464338031_<16> · C111

C111 = P44 · P67

P44 = 21445140596559027674445600227216279078028913_<44>

P67 = 9446397147569998958870814273587432081956274848493168972552660851483_<67>

Number: 68887_136
N=202579314960572784853853841483578465366236882142762231912399875722301397628634517434793217876549853255872927979
  ( 111 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=21445140596559027674445600227216279078028913 (pp44)
 r2=9446397147569998958870814273587432081956274848493168972552660851483 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.69 hours.
Scaled time: 15.12 units (timescale=1.967).
Factorization parameters were as follows:
name: 68887_136
n: 202579314960572784853853841483578465366236882142762231912399875722301397628634517434793217876549853255872927979
m: 2000000000000000000000000000
deg: 5
c5: 155
c0: -136
skew: 0.97
type: snfs
lss: 1
rlim: 1430000
alim: 1430000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1430000/1430000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [715000, 1390001)
Primes: RFBsize:109205, AFBsize:109105, largePrimes:3313683 encountered
Relations: rels:3256308, finalFF:265958
Max relations in full relation-set: 28
Initial matrix: 218377 x 265958 with sparse part having weight 21751660.
Pruned matrix : 202781 x 203936 with weight 13649675.
Total sieving time: 7.13 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1430000,1430000,26,26,48,48,2.3,2.3,75000
total time: 7.69 hours.
 --------- CPU info (if available) ----------

(62·10¹²⁶+1)/9 = 6(8)₁₂₅9_<127> = 7 · 47 · 83 · 1541963399_<10> · 660931435820087_<15> · C99

C99 = P41 · P59

P41 = 24438968728948515381731252918147334447671_<41>

P59 = 10128889662287420283252120128975774558249253186011221512749_<59>

Number: 68889_126
N=247539617715612152894729759876354338742558857147054971673720876347783084339220280796770906999857579
  ( 99 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=24438968728948515381731252918147334447671 (pp41)
 r2=10128889662287420283252120128975774558249253186011221512749 (pp59)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 4.21 hours.
Scaled time: 1.98 units (timescale=0.470).
Factorization parameters were as follows:
name: 68889_126
n: 247539617715612152894729759876354338742558857147054971673720876347783084339220280796770906999857579
m: 20000000000000000000000000
deg: 5
c5: 155
c0: 8
skew: 0.55
type: snfs
lss: 1
rlim: 980000
alim: 980000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 980000/980000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [490000, 840001)
Primes: RFBsize:77067, AFBsize:76704, largePrimes:2697581 encountered
Relations: rels:2682573, finalFF:279654
Max relations in full relation-set: 28
Initial matrix: 153838 x 279654 with sparse part having weight 21371172.
Pruned matrix : 119190 x 120023 with weight 6566874.
Total sieving time: 3.90 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,980000,980000,26,26,47,47,2.3,2.3,50000
total time: 4.21 hours.
 --------- CPU info (if available) ----------

(22·10¹²⁵-7)/3 = 7(3)₁₂₄1_<126> = 139 · 1753 · 29813712015624763_<17> · C105

C105 = P46 · P59

P46 = 5835514109274418429331289019347933750642074023_<46>

P59 = 17298543348572175255854507216815323864835034117825029046357_<59>

Number: 73331_125
N=100945893780488072805794054903888609442778207215050028770210697409559135193502458841115087258636292484211
  ( 105 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=5835514109274418429331289019347933750642074023 (pp46)
 r2=17298543348572175255854507216815323864835034117825029046357 (pp59)
Version: Msieve v. 1.42
Total time: 0.06 hours.
Scaled time: 0.06 units (timescale=1.024).
Factorization parameters were as follows:
name: 73331_125
n: 100945893780488072805794054903888609442778207215050028770210697409559135193502458841115087258636292484211
m: 10000000000000000000000000
deg: 5
c5: 22
c0: -7
skew: 0.80
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 695001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 102874 x 103106
Total sieving time: 0.00 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 0.06 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3057976k/3145344k available (3786k kernel code, 496k absent, 86872k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.88 BogoMIPS (lpj=2393941)
Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393880)
Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393886)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891)
Total of 4 processors activated (19151.19 BogoMIPS).

total time: 57 min

(62·10¹²⁷-53)/9 = 6(8)₁₂₆3_<128> = 3² · 7 · 4373075016167159_<16> · C111

C111 = P40 · P71

P40 = 5453325435685665821475301936816985008441_<40>

P71 = 45852211565333095184206412202116635585191607632222241319520518384375539_<71>

Number: 68883_127
N=250047031611671426524712294764192025608047985060941485564187383018891286802343657348586214528075249412428924699
  ( 111 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=5453325435685665821475301936816985008441 (pp40)
 r2=45852211565333095184206412202116635585191607632222241319520518384375539 (pp71)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.22 hours.
Scaled time: 10.27 units (timescale=1.967).
Factorization parameters were as follows:
name: 68883_127
n: 250047031611671426524712294764192025608047985060941485564187383018891286802343657348586214528075249412428924699
m: 20000000000000000000000000
deg: 5
c5: 775
c0: -212
skew: 0.77
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 1050001)
Primes: RFBsize:78498, AFBsize:78237, largePrimes:2790052 encountered
Relations: rels:2715447, finalFF:211136
Max relations in full relation-set: 28
Initial matrix: 156802 x 211136 with sparse part having weight 18694044.
Pruned matrix : 143833 x 144681 with weight 10166225.
Total sieving time: 4.95 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 5.22 hours.
 --------- CPU info (if available) ----------

(62·10¹³⁰+1)/9 = 6(8)₁₂₉9_<131> = 3 · 1021 · 4517 · 97829 · C119

C119 = P36 · P84

P36 = 172646517491005006256239973571080363_<36>

P84 = 294799441210256853477729159395431700808480725079520017412819392555476174232512350517_<84>

Number: 68889_130
N=50896096883245111904087491066818110988048098986769458408393871306471379148082206150305806791176779739197015576231597671
  ( 119 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=172646517491005006256239973571080363 (pp36)
 r2=294799441210256853477729159395431700808480725079520017412819392555476174232512350517 (pp84)
Version: Msieve v. 1.42
Total time: 0.11 hours.
Scaled time: 0.11 units (timescale=1.025).
Factorization parameters were as follows:
name: 68889_130
n: 50896096883245111904087491066818110988048098986769458408393871306471379148082206150305806791176779739197015576231597671
m: 200000000000000000000000000
deg: 5
c5: 31
c0: 16
skew: 0.88
type: snfs
lss: 1
rlim: 1150000
alim: 1150000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1150000/1150000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [575000, 875001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 165872 x 166120
Total sieving time: 0.00 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,132.000,5,0,0,0,0,0,0,0,0,1150000,1150000,26,26,47,47,2.3,2.3,50000
total time: 0.11 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3057976k/3145344k available (3786k kernel code, 496k absent, 86872k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.88 BogoMIPS (lpj=2393941)
Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393880)
Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393886)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891)
Total of 4 processors activated (19151.19 BogoMIPS).

total time: 1 hour 17 min

(62·10¹³⁰-53)/9 = 6(8)₁₂₉3_<131> = 3 · 827 · 209767934901885224303739917497_<30> · C99

C99 = P38 · P61

P38 = 27526445632823402801555781212943586751_<38>

P61 = 4808760820477327944086801289662261340494201135301405931889669_<61>

Number: 68883_130
N=132368093286120427073132380496392850742543712691797795425763461226071196035292063716102728062175419
  ( 99 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=27526445632823402801555781212943586751 (pp38)
 r2=4808760820477327944086801289662261340494201135301405931889669 (pp61)
Version: Msieve v. 1.42
Total time: 0.12 hours.
Scaled time: 0.13 units (timescale=1.025).
Factorization parameters were as follows:
name: 68883_130
n: 132368093286120427073132380496392850742543712691797795425763461226071196035292063716102728062175419
m: 100000000000000000000000000
deg: 5
c5: 62
c0: -53
skew: 0.97
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 180005 x 180230
Total sieving time: 0.00 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 0.12 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3057976k/3145344k available (3786k kernel code, 496k absent, 86872k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.88 BogoMIPS (lpj=2393941)
Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393880)
Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393886)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891)
Total of 4 processors activated (19151.19 BogoMIPS).

total time: 1 hour 55 min

(62·10¹³⁹-17)/9 = 6(8)₁₃₈7_<140> = 23 · 757 · 18719 · 30161 · 130303 · 696107 · 2665811 · 5686673 · C103

C103 = P39 · P64

P39 = 926007323380718041367848667604976818917_<39>

P64 = 5503825234459097628568763534609341243640504139868724244565262153_<64>

Number: 68887_139
N=5096582473716721911320817165106487433415795470035694878499516371602090541767465977942766273924114548301
  ( 103 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=926007323380718041367848667604976818917 (pp39)
 r2=5503825234459097628568763534609341243640504139868724244565262153 (pp64)
Version: Msieve-1.40
Total time: 6.59 hours.
Scaled time: 13.64 units (timescale=2.071).
Factorization parameters were as follows:
name: 68887_139
n: 5096582473716721911320817165106487433415795470035694878499516371602090541767465977942766273924114548301
m: 10000000000000000000000000000
deg: 5
c5: 31
c0: -85
skew: 1.22
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 227013 x 227254
Total sieving time: 6.28 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 6.59 hours.
 --------- CPU info (if available) ----------

Oct 29, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / Oct 29, 2009

(22·10¹²⁷-7)/3 = 7(3)₁₂₆1_<128> = 479 · 44075527 · C118

C118 = P46 · P72

P46 = 6577399073481143560931762320945836405658976407_<46>

P72 = 528097615006827450101667740710985593710548414937408630323507149175477101_<72>

Number: n
N=3473508763653508525973618996598802094452506079093510872225215128682143135403106733322106848803942284172130817527756107
  ( 118 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=6577399073481143560931762320945836405658976407 (pp46)
 r2=528097615006827450101667740710985593710548414937408630323507149175477101 (pp72)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.95 hours.
Scaled time: 3.55 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_7_3_126_1
n: 3473508763653508525973618996598802094452506079093510872225215128682143135403106733322106848803942284172130817527756107
m: 20000000000000000000000000
deg: 5
c5: 275
c0: -28
skew: 0.63
type: snfs
lss: 1
rlim: 990000
alim: 990000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
qintsize: 10000
Factor base limits: 990000/990000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [495000, 835001)
Primes: RFBsize:77777, AFBsize:77453, largePrimes:2595907 encountered
Relations: rels:2454373, finalFF:189776
Max relations in full relation-set: 48
Initial matrix: 155297 x 189776 with sparse part having weight 16134020.
Pruned matrix : 143607 x 144447 with weight 8818753.
Total sieving time: 1.77 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.11 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,990000,990000,26,26,47,47,2.3,2.3,50000
total time: 1.95 hours.
 --------- CPU info (if available) ----------

(62·10¹²⁶-17)/9 = 6(8)₁₂₅7_<127> = 126222973133549_<15> · C113

C113 = P44 · P70

P44 = 17478016109900362123148044512875872521564383_<44>

P70 = 3122616420509176390118982265005374742402752146903093305407083770722861_<70>

Number: n
N=54577140102698788478968629476910731542323421602049717663968754282023809748791855193804422746495616416174461459763
  ( 113 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=17478016109900362123148044512875872521564383 (pp44)
 r2=3122616420509176390118982265005374742402752146903093305407083770722861 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.44 hours.
Scaled time: 4.44 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_8_125_7
n: 54577140102698788478968629476910731542323421602049717663968754282023809748791855193804422746495616416174461459763
m: 20000000000000000000000000
deg: 5
c5: 155
c0: -136
skew: 0.97
type: snfs
lss: 1
rlim: 980000
alim: 980000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
qintsize: 10000
Factor base limits: 980000/980000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [490000, 850001)
Primes: RFBsize:77067, AFBsize:77074, largePrimes:2525068 encountered
Relations: rels:2371743, finalFF:176884
Max relations in full relation-set: 48
Initial matrix: 154208 x 176884 with sparse part having weight 15357027.
Pruned matrix : 146855 x 147690 with weight 9842125.
Total sieving time: 2.24 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.12 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,980000,980000,26,26,47,47,2.3,2.3,50000
total time: 2.44 hours.
 --------- CPU info (if available) ----------

(62·10¹²⁸+1)/9 = 6(8)₁₂₇9_<129> = 13 · 97 · 197 · 1571 · C121

C121 = P54 · P67

P54 = 221839062921055719484107373612660853699302142746356139_<54>

P67 = 7957078823320286782689262399302302972074139970168996053248181231993_<67>

Number: n
N=1765190909754349106047805048835653555356153326809056765104083714705035874397650631344173890587328534974454782088558755027
  ( 121 digits)
SNFS difficulty: 131 digits.
Divisors found:

Thu Oct 29 22:10:41 2009  prp54 factor: 221839062921055719484107373612660853699302142746356139
Thu Oct 29 22:10:41 2009  prp67 factor: 7957078823320286782689262399302302972074139970168996053248181231993
Thu Oct 29 22:10:41 2009  elapsed time 00:08:18 (Msieve 1.43 - dependency 2)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.84 hours.
Scaled time: 3.36 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_6_8_127_9
n: 1765190909754349106047805048835653555356153326809056765104083714705035874397650631344173890587328534974454782088558755027
m: 100000000000000000000000000
deg: 5
c5: 31
c0: 50
skew: 1.10
type: snfs
lss: 1
rlim: 1090000
alim: 1090000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
qintsize: 10000
Factor base limits: 1090000/1090000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved  special-q in [545000, 885331)
Primes: RFBsize:84976, AFBsize:85149, largePrimes:2650390 encountered
Relations: rels:2480173, finalFF:181106
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 234173 hash collisions in 2642513 relations
Msieve: matrix is 158517 x 158742 (42.6 MB)

Total sieving time: 1.79 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000
total time: 1.84 hours.
 --------- CPU info (if available) ----------

Oct 29, 2009 (5th)

By matsui / Msieve / Oct 29, 2009

(64·10³³³-1)/9 = 7(1)₃₃₃_<334> = 13 · 4999 · 228777281 · 1541677987_<10> · 1103253089147723_<16> · 897821565552123255197697079_<27> · 1138685703753966317205547366328393186964066889_<46> · 3426549570671671064841267094850481127005282543233354557266456990784769879505493_<79> · C146

C146 = P56 · P91

P56 = 12174361251367883129391909180738935636343765462088551283_<56>

P91 = 6593745087362144980904245668229480104648255993069991196974660634291764657660612015236166117_<91>

N=80274634692979035236916096891593763332243932346695290164007809815885473899897686446683991310308022576677193511877133845257360068833629111661478111
  ( 146 digits)
Divisors found:
 r1=12174361251367883129391909180738935636343765462088551283 (pp56)
 r2=6593745087362144980904245668229480104648255993069991196974660634291764657660612015236166117 (pp91)
Version: Msieve v. 1.43
Total time: 6730.09 hours.
Scaled time: 12289.14 units (timescale=1.826).
Factorization parameters were as follows:
name: 71111_333
n: 80274634692979035236916096891593763332243932346695290164007809815885473899897686446683991310308022576677193511877133845257360068833629111661478111
skew: 377073.07
# norm 6.21e+19
c5: 1288500
c4: 68290971667
c3: 619913143244182622
c2: -26447842285036047361452
c1: -55420844824743942680919908090
c0: 1642140321092668673121090476858417
# alpha -5.93
Y1: 7265089991871023
Y0: -9097012245689260132720497456
# Murphy_E 8.85e-12
# M 51307725631548334216899866953555587407604198005490433969505896061629967361718503918766814953119299580128428318493399064108307143252143563690561581
type: gnfs
rlim: 16800000
alim: 16800000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 800000
Factor base limits: 16800000/16800000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved algebraic special-q in [8400000, 23600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3285994 x 3286224
Total sieving time: 6713.90 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 14.23 hours.
Time per square root: 1.66 hours.
Prototype def-par.txt line would be:
gnfs,145,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,16800000,16800000,29,29,58,58,2.6,2.6,100000
total time: 6730.09 hours.

c146 is the second largest composite number which was factored by gnfs in our tables so far. Congratulations!

Oct 29, 2009 (4th)

By juno1369 / GGNFS, Msieve v1.41 / Oct 29, 2009

(62·10¹⁴⁹-71)/9 = 6(8)₁₄₈1_<150> = 3 · 2417 · 74029477891_<11> · 3497744479903_<13> · 382748316025440940507_<21> · C102

C102 = P35 · P68

P35 = 43565025495414996045361762082014639_<35>

P68 = 22004284299797228251633148946891172189744868497880149030614978474539_<68>

Number: 68881_149
N=958617206529026163078164168986373017228530684647348271505022568050178553786224842053248585300086776421
  ( 102 digits)
Divisors found:
 r1=43565025495414996045361762082014639 (pp35)
 r2=22004284299797228251633148946891172189744868497880149030614978474539 (pp68)
Version: Msieve-1.40
Total time: 8.42 hours.
Scaled time: 14.82 units (timescale=1.761).
Factorization parameters were as follows:
name: 68881_149
n: 958617206529026163078164168986373017228530684647348271505022568050178553786224842053248585300086776421
skew: 22580.98
# norm 2.26e+014
c5: 6720
c4: 338199084
c3: -10505707699312
c2: -4051122316080619
c1: 2503178937575702048042
c0: -9365976316249819726224600
# alpha -6.53
Y1: 38483326871
Y0: -42741647054392727347
# Murphy_E 2.68e-009
# M 52154113368020348603538907067962726876078627937292628552976680809307400113998793692763656046280578354
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 2
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 280615 x 280863
Total sieving time: 7.77 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 8.42 hours.
 --------- CPU info (if available) ----------

Oct 29, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve / Oct 29, 2009

(65·10¹³⁴+61)/9 = 7(2)₁₃₃9_<135> = 3 · 17 · 137 · 14707723 · C124

C124 = P58 · P66

P58 = 8170620663352175538141363624278865919798181514357283034749_<58>

P66 = 860160735400974356984124869352479240710535091232943755301407369921_<66>

Number: s124
N=7028047078471404241385538249417286890637656454374573587608436511688677005460215314566301659645079212232217122710089340384829
  ( 124 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=8170620663352175538141363624278865919798181514357283034749 (pp58)
 r2=860160735400974356984124869352479240710535091232943755301407369921 (pp66)
Version: Msieve-1.40
Total time: 3.37 hours.
Scaled time: 6.60 units (timescale=1.957).
Factorization parameters were as follows:
n: 7028047078471404241385538249417286890637656454374573587608436511688677005460215314566301659645079212232217122710089340384829
m: 1000000000000000000000000000
deg: 5
c5: 13
c0: 122
skew: 1.56
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1325001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 196084 x 196310
Total sieving time: 3.24 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 3.37 hours.
 --------- CPU info (if available) ----------

(62·10¹³⁵-17)/9 = 6(8)₁₃₄7_<136> = C136

C136 = P34 · P103

P34 = 3006133944868273649904641611835927_<34>

P103 = 2291610758279353520262479427436718759759968530711012838648548023370471952701819314481826902624062304481_<103>

Number: 136-2
N=6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
  ( 136 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=3006133944868273649904641611835927 (pp34)
 r2=2291610758279353520262479427436718759759968530711012838648548023370471952701819314481826902624062304481 (pp103)
Version: Msieve-1.40
Total time: 4.00 hours.
Scaled time: 7.87 units (timescale=1.969).
Factorization parameters were as follows:
n: 6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
m: 1000000000000000000000000000
deg: 5
c5: 62
c0: -17
skew: 0.77
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1415001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 166629 x 166854
Total sieving time: 3.88 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 4.00 hours.
 --------- CPU info (if available) ----------

Oct 29, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Oct 29, 2009

(64·10¹⁶⁷+17)/9 = 7(1)₁₆₆3_<168> = 13 · 19 · 31 · C164

C164 = P66 · P99

P66 = 147801285874676743702605376197388769702296463745069614255372510569_<66>

P99 = 628348532318111008341516309337363050902767140223828818956120842657819837747040849338498348275327161_<99>

Number: 71113_167
N=92870721054082683963838462989566554931580398473437522673515882344405264608999753312147200092870721054082683963838462989566554931580398473437522673515882344405264609
  ( 164 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=147801285874676743702605376197388769702296463745069614255372510569 (pp66)
 r2=628348532318111008341516309337363050902767140223828818956120842657819837747040849338498348275327161 (pp99)
Version: Msieve-1.40
Total time: 37.66 hours.
Scaled time: 65.68 units (timescale=1.744).
Factorization parameters were as follows:
n: 92870721054082683963838462989566554931580398473437522673515882344405264608999753312147200092870721054082683963838462989566554931580398473437522673515882344405264609
m: 4000000000000000000000000000000000
deg: 5
c5: 25
c0: 68
skew: 1.22
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 4250001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 799987 x 800213
Total sieving time: 36.03 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.81 hours.
Time per square root: 0.72 hours.
Prototype def-par.txt line would be:
snfs,169.000,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000
total time: 37.66 hours.

Oct 29, 2009

Factorizations of 688...883, Factorizations of 688...887 and Factorizations of 688...889 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 28, 2009 (8th)

By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Oct 28, 2009

(62·10¹⁴²-71)/9 = 6(8)₁₄₁1_<143> = 17 · 127 · C140

C140 = P32 · P39 · P70

P32 = 88605204287423670249671527649293_<32>

P39 = 282298075240783523797463502563785239997_<39>

P70 = 1275643702644799867268139877864205097833015033358005502736075772881079_<70>

Number: s140
N=31907776233853121301013843857753074983274149554835057382533065719726210694251453862384848952704441356595131490916576604395038855437187998559
  ( 140 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=88605204287423670249671527649293 (pp32)
 r2=282298075240783523797463502563785239997 (pp39)
 r3=1275643702644799867268139877864205097833015033358005502736075772881079 (pp70)
Version: Msieve-1.40
Total time: 7.72 hours.
Scaled time: 15.16 units (timescale=1.963).
Factorization parameters were as follows:
n: 31907776233853121301013843857753074983274149554835057382533065719726210694251453862384848952704441356595131490916576604395038855437187998559
m: 20000000000000000000000000000
deg: 5
c5: 775
c0: -284
skew: 0.82
type: snfs
lss: 1
rlim: 1790000
alim: 1790000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1790000/1790000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [895000, 2295001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 313997 x 314222
Total sieving time: 7.26 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,144.000,5,0,0,0,0,0,0,0,0,1790000,1790000,26,26,49,49,2.3,2.3,100000
total time: 7.72 hours.
 --------- CPU info (if available) ----------

(61·10¹⁴⁴+11)/9 = 6(7)₁₄₃9_<145> = 139 · C143

C143 = P32 · P36 · P76

P32 = 35451613663413251648447982109961_<32>

P36 = 902835582445713727649667691606922077_<36>

P76 = 1523448755300188337671604898103869412215946977128520856830739463707719389413_<76>

Number: s143
N=48760991207034372501998401278976818545163868904876099120703437250199840127897681854516386890487609912070343725019984012789768185451638689048761
  ( 143 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=35451613663413251648447982109961 (pp32)
 r2=902835582445713727649667691606922077 (pp36)
 r3=1523448755300188337671604898103869412215946977128520856830739463707719389413 (pp76)
Version: Msieve-1.40
Total time: 8.06 hours.
Scaled time: 15.04 units (timescale=1.866).
Factorization parameters were as follows:
n: 48760991207034372501998401278976818545163868904876099120703437250199840127897681854516386890487609912070343725019984012789768185451638689048761
m: 100000000000000000000000000000
deg: 5
c5: 61
c0: 110
skew: 1.13
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2480001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 325579 x 325804
Total sieving time: 7.78 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 8.06 hours.
 --------- CPU info (if available) ----------

(59·10¹⁶⁶+13)/9 = 6(5)₁₆₅7_<167> = 17 · 67 · C164

C164 = P64 · P101

P64 = 1520300600803178723554489839762734450050310979284651413036412657_<64>

P101 = 37857881804580042766073071926977642450283485731120277261311868008262073402242471720348178440977797559_<101>

Number: 164-1
N=57555360452638766949565896010145351673007511462296361330601892498292849478099697590478977660716027704614183982050531655448248951321822261242805579943420154131304263
  ( 164 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=1520300600803178723554489839762734450050310979284651413036412657 (pp64)
 r2=37857881804580042766073071926977642450283485731120277261311868008262073402242471720348178440977797559 (pp101)
Version: Msieve-1.40
Total time: 54.33 hours.
Scaled time: 101.39 units (timescale=1.866).
Factorization parameters were as follows:
n: 57555360452638766949565896010145351673007511462296361330601892498292849478099697590478977660716027704614183982050531655448248951321822261242805579943420154131304263
m: 2000000000000000000000000000000000
deg: 5
c5: 295
c0: 208
skew: 0.93
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2300000, 5400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 963749 x 963974
Total sieving time: 52.94 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.17 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,168.000,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000
total time: 54.33 hours.
 --------- CPU info (if available) ----------

(59·10¹⁶⁵+13)/9 = 6(5)₁₆₄7_<166> = 23² · C164

C164 = P81 · P84

P81 = 110196508485120959229584433888099581893885727408622561715778078112344496125474827_<81>

P84 = 112456871072618870945836117361013701928460846350502379302614333335364545406654278879_<84>

Number: 164-2
N=12392354547363999159840369670237345095568157950010501995379122033186305398025624868725057760974585171182524679689140936777987817685360218441503885738290275152278933
  ( 164 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=110196508485120959229584433888099581893885727408622561715778078112344496125474827 (pp81)
 r2=112456871072618870945836117361013701928460846350502379302614333335364545406654278879 (pp84)
Version: Msieve-1.40
Total time: 30.84 hours.
Scaled time: 58.75 units (timescale=1.905).
Factorization parameters were as follows:
n: 12392354547363999159840369670237345095568157950010501995379122033186305398025624868725057760974585171182524679689140936777987817685360218441503885738290275152278933
m: 1000000000000000000000000000000000
deg: 5
c5: 59
c0: 13
skew: 0.74
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 3800001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 716975 x 717202
Total sieving time: 30.05 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.63 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 30.84 hours.
 --------- CPU info (if available) ----------

(65·10¹⁷⁶+7)/9 = 7(2)₁₇₅3_<177> = 3² · C176

C176 = P37 · P140

P37 = 4442942910712936991397591050639207179_<37>

P140 = 18061657597884841998286548530250959539096033255123941595949495422393933276866461274947045522461378351677425535396899275108324213821248779493_<140>

Factor=4442942910712936991397591050639207179  Method=ECM  B1=11000000  Sigma=1661063128

(65·10¹³¹+61)/9 = 7(2)₁₃₀9_<132> = 3 · 79 · C130

C130 = P52 · P79

P52 = 1280509510648682082491308652467981505699141252049001_<52>

P79 = 2379795794779564354598086165038364450138527040490957073655723750806221001915617_<79>

Number: s130-1
N=3047351148616971401781528363806844819503047351148616971401781528363806844819503047351148616971401781528363806844819503047351148617
  ( 130 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=1280509510648682082491308652467981505699141252049001 (pp52)
 r2=2379795794779564354598086165038364450138527040490957073655723750806221001915617 (pp79)
Version: Msieve-1.40
Total time: 3.55 hours.
Scaled time: 6.62 units (timescale=1.866).
Factorization parameters were as follows:
n: 3047351148616971401781528363806844819503047351148616971401781528363806844819503047351148616971401781528363806844819503047351148617
m: 100000000000000000000000000
deg: 5
c5: 650
c0: 61
skew: 0.62
type: snfs
lss: 1
rlim: 1140000
alim: 1140000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1140000/1140000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [570000, 1320001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 149370 x 149595
Total sieving time: 3.44 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,132.000,5,0,0,0,0,0,0,0,0,1140000,1140000,26,26,47,47,2.3,2.3,50000
total time: 3.55 hours.
 --------- CPU info (if available) ----------

(65·10¹⁵²+61)/9 = 7(2)₁₅₁9_<153> = 3 · C153

C153 = P35 · P118

P35 = 31146531695975924298765364037305309_<35>

P118 = 7729295290102686139699794454856781365379879804351612416391812646752847109285668325511683064669740001403032177197768627_<118>

Factor=31146531695975924298765364037305309  Method=ECM  B1=11000000  Sigma=190775455

(22·10¹⁴³-7)/3 = 7(3)₁₄₂1_<144> = C144

C144 = P43 · P44 · P58

P43 = 3107752485792958896855128352023536341050509_<43>

P44 = 59206074072516662497430087693127541112104321_<44>

P58 = 3985554382642451971682452172996902377956999045276349984479_<58>

Number: s144
N=733333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
  ( 144 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=3107752485792958896855128352023536341050509 (pp43)
 r2=59206074072516662497430087693127541112104321 (pp44)
 r3=3985554382642451971682452172996902377956999045276349984479 (pp58)
Version: Msieve-1.40
Total time: 6.51 hours.
Scaled time: 12.04 units (timescale=1.850).
Factorization parameters were as follows:
n: 733333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
m: 50000000000000000000000000000
deg: 5
c5: 176
c0: -175
skew: 1.00
type: snfs
lss: 1
rlim: 1880000
alim: 1880000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1880000/1880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [940000, 2140001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 331290 x 331538
Total sieving time: 6.24 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,145.000,5,0,0,0,0,0,0,0,0,1880000,1880000,26,26,49,49,2.3,2.3,100000
total time: 6.51 hours.
 --------- CPU info (if available) ----------

(65·10¹³⁷-11)/9 = 7(2)₁₃₆1_<138> = C138

C138 = P40 · P99

P40 = 3856127651773716445077580043028022865033_<40>

P99 = 187292093893732785337096962993710590056537036033026265546665061444636987452833698017865574966552037_<99>

Number: s138-2
N=722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
  ( 138 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=3856127651773716445077580043028022865033 (pp40)
 r2=187292093893732785337096962993710590056537036033026265546665061444636987452833698017865574966552037 (pp99)
Version: Msieve-1.40
Total time: 4.39 hours.
Scaled time: 8.15 units (timescale=1.855).
Factorization parameters were as follows:
n: 722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 5000000000000000000000000000
deg: 5
c5: 52
c0: -275
skew: 1.40
type: snfs
lss: 1
rlim: 1520000
alim: 1520000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1520000/1520000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [760000, 1585001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 262716 x 262964
Total sieving time: 4.26 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140.000,5,0,0,0,0,0,0,0,0,1520000,1520000,26,26,48,48,2.3,2.3,75000
total time: 4.39 hours.
 --------- CPU info (if available) ----------

(65·10¹⁸⁵+61)/9 = 7(2)₁₈₄9_<186> = 3 · C186

C186 = P38 · C148

P38 = 35141952992942757477971514122621284567_<38>

C148 = [6850522530409352594617032385273079677147742201520609487175172835765408849862204938465321362129623843494992872240521378843361310626504793995366334929_<148>]

Factor=35141952992942757477971514122621284567  Method=ECM  B1=11000000  Sigma=2647286449

(22·10¹⁵⁰-7)/3 = 7(3)₁₄₉1_<151> = C151

C151 = P63 · P89

P63 = 557437416104319050904396406476585854891860424980271017156626667_<63>

P89 = 13155437940608153459755208722920934403344534831120327715310189648982331381764859489159993_<89>

Number: s151-1
N=7333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
  ( 151 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=557437416104319050904396406476585854891860424980271017156626667 (pp63)
 r2=13155437940608153459755208722920934403344534831120327715310189648982331381764859489159993 (pp89)
Version: Msieve-1.40
Total time: 10.22 hours.
Scaled time: 19.13 units (timescale=1.872).
Factorization parameters were as follows:
n: 7333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
m: 1000000000000000000000000000000
deg: 5
c5: 22
c0: -7
skew: 0.80
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 352545 x 352780
Total sieving time: 9.85 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 10.22 hours.
 --------- CPU info (if available) ----------

(65·10¹⁶³-11)/9 = 7(2)₁₆₂1_<164> = C164

C164 = P42 · P47 · P77

P42 = 382159282100879841810432048201209139152111_<42>

P47 = 12134760941028933954849302273360311799514764407_<47>

P77 = 15573822111719989074008727773441965485234326451554657360445839721618992013973_<77>

Number: 164-3
N=72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
  ( 164 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=382159282100879841810432048201209139152111 (pp42)
 r2=12134760941028933954849302273360311799514764407 (pp47)
 r3=15573822111719989074008727773441965485234326451554657360445839721618992013973 (pp77)
Version: Msieve-1.40
Total time: 30.58 hours.
Scaled time: 55.93 units (timescale=1.829).
Factorization parameters were as follows:
n: 72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 500000000000000000000000000000000
deg: 5
c5: 104
c0: -55
skew: 0.88
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 3700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 743661 x 743886
Total sieving time: 29.67 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.68 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,165.000,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 30.58 hours.
 --------- CPU info (if available) ----------

Oct 28, 2009 (7th)

By Sinkiti Sibata / Msieve, GGNFS / Oct 28, 2009

(65·10¹⁴⁸-11)/9 = 7(2)₁₄₇1_<149> = 821 · 15121 · 434867 · 2659663 · 4831786039_<10> · 5683466138107710514513519_<25> · C96

C96 = P39 · P57

P39 = 939723580029040882857358260430399230301_<39>

P57 = 194913992192781453472395092670134360915528563343150609321_<57>

Tue Oct 27 22:38:26 2009  Msieve v. 1.42
Tue Oct 27 22:38:26 2009  random seeds: a4cc6856 2144dfb9
Tue Oct 27 22:38:26 2009  factoring 183165274541153112029213156380438260588196891503607577322934423409998681788864687052077556235621 (96 digits)
Tue Oct 27 22:38:28 2009  no P-1/P+1/ECM available, skipping
Tue Oct 27 22:38:28 2009  commencing quadratic sieve (96-digit input)
Tue Oct 27 22:38:28 2009  using multiplier of 5
Tue Oct 27 22:38:28 2009  using 64kb Pentium 4 sieve core
Tue Oct 27 22:38:28 2009  sieve interval: 18 blocks of size 65536
Tue Oct 27 22:38:28 2009  processing polynomials in batches of 6
Tue Oct 27 22:38:28 2009  using a sieve bound of 2231357 (82234 primes)
Tue Oct 27 22:38:28 2009  using large prime bound of 334703550 (28 bits)
Tue Oct 27 22:38:28 2009  using double large prime bound of 2209980934643550 (43-51 bits)
Tue Oct 27 22:38:28 2009  using trial factoring cutoff of 51 bits
Tue Oct 27 22:38:28 2009  polynomial 'A' values have 12 factors
Wed Oct 28 06:29:56 2009  82388 relations (19397 full + 62991 combined from 1246766 partial), need 82330
Wed Oct 28 06:30:01 2009  begin with 1266163 relations
Wed Oct 28 06:30:02 2009  reduce to 217857 relations in 11 passes
Wed Oct 28 06:30:03 2009  attempting to read 217857 relations
Wed Oct 28 06:30:10 2009  recovered 217857 relations
Wed Oct 28 06:30:10 2009  recovered 205011 polynomials
Wed Oct 28 06:30:10 2009  attempting to build 82388 cycles
Wed Oct 28 06:30:10 2009  found 82388 cycles in 6 passes
Wed Oct 28 06:30:10 2009  distribution of cycle lengths:
Wed Oct 28 06:30:10 2009     length 1 : 19397
Wed Oct 28 06:30:10 2009     length 2 : 13993
Wed Oct 28 06:30:10 2009     length 3 : 13942
Wed Oct 28 06:30:10 2009     length 4 : 11324
Wed Oct 28 06:30:10 2009     length 5 : 8561
Wed Oct 28 06:30:10 2009     length 6 : 5904
Wed Oct 28 06:30:10 2009     length 7 : 3771
Wed Oct 28 06:30:10 2009     length 9+: 5496
Wed Oct 28 06:30:10 2009  largest cycle: 21 relations
Wed Oct 28 06:30:11 2009  matrix is 82234 x 82388 (22.9 MB) with weight 5663813 (68.75/col)
Wed Oct 28 06:30:11 2009  sparse part has weight 5663813 (68.75/col)
Wed Oct 28 06:30:13 2009  filtering completed in 3 passes
Wed Oct 28 06:30:13 2009  matrix is 78854 x 78918 (22.0 MB) with weight 5462402 (69.22/col)
Wed Oct 28 06:30:13 2009  sparse part has weight 5462402 (69.22/col)
Wed Oct 28 06:30:13 2009  saving the first 48 matrix rows for later
Wed Oct 28 06:30:14 2009  matrix is 78806 x 78918 (15.6 MB) with weight 4513875 (57.20/col)
Wed Oct 28 06:30:14 2009  sparse part has weight 3618396 (45.85/col)
Wed Oct 28 06:30:14 2009  matrix includes 64 packed rows
Wed Oct 28 06:30:14 2009  using block size 21845 for processor cache size 512 kB
Wed Oct 28 06:30:15 2009  commencing Lanczos iteration
Wed Oct 28 06:30:15 2009  memory use: 14.7 MB
Wed Oct 28 06:31:23 2009  lanczos halted after 1248 iterations (dim = 78806)
Wed Oct 28 06:31:24 2009  recovered 18 nontrivial dependencies
Wed Oct 28 06:31:26 2009  prp39 factor: 939723580029040882857358260430399230301
Wed Oct 28 06:31:26 2009  prp57 factor: 194913992192781453472395092670134360915528563343150609321
Wed Oct 28 06:31:26 2009  elapsed time 07:53:00

(62·10¹⁴¹-71)/9 = 6(8)₁₄₀1_<142> = 7 · 965308026157_<12> · 39824757917563793_<17> · C113

C113 = P47 · P66

P47 = 67396829659826934567187683042527026494165158749_<47>

P66 = 379832927230764651413352296349336303801716583716324523571650614767_<66>

Number: 68881_141
N=25599535095765284772907421390742729405999308114306671311586277227479931833907608502472969991698711464297998646483
  ( 113 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=67396829659826934567187683042527026494165158749 (pp47)
 r2=379832927230764651413352296349336303801716583716324523571650614767 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 15.56 hours.
Scaled time: 30.54 units (timescale=1.963).
Factorization parameters were as follows:
name: 68881_141
n: 25599535095765284772907421390742729405999308114306671311586277227479931833907608502472969991698711464297998646483
m: 20000000000000000000000000000
deg: 5
c5: 155
c0: -568
skew: 1.30
type: snfs
lss: 1
rlim: 1740000
alim: 1740000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1740000/1740000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [870000, 2170001)
Primes: RFBsize:130902, AFBsize:130802, largePrimes:3951723 encountered
Relations: rels:4084666, finalFF:353287
Max relations in full relation-set: 28
Initial matrix: 261771 x 353287 with sparse part having weight 36947158.
Pruned matrix : 232903 x 234275 with weight 21833316.
Total sieving time: 14.65 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.68 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1740000,1740000,26,26,48,48,2.3,2.3,100000
total time: 15.56 hours.
 --------- CPU info (if available) ----------

(22·10¹²⁰-7)/3 = 7(3)₁₁₉1_<121> = 23 · 5569172379466719569647_<22> · C98

C98 = P38 · P61

P38 = 12467268040968644200593760852105178561_<38>

P61 = 4592103128437975144998245779741025244221395688765409799392491_<61>

Number: 73331_120
N=57250980574006896711440906216273061639096909115796536426296321791734696445274584207837732877585451
  ( 98 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=12467268040968644200593760852105178561 (pp38)
 r2=4592103128437975144998245779741025244221395688765409799392491 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.72 hours.
Scaled time: 3.40 units (timescale=1.981).
Factorization parameters were as follows:
name: 73331_120
n: 57250980574006896711440906216273061639096909115796536426296321791734696445274584207837732877585451
m: 1000000000000000000000000
deg: 5
c5: 22
c0: -7
skew: 0.80
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 520001)
Primes: RFBsize:59531, AFBsize:59739, largePrimes:1304416 encountered
Relations: rels:1281725, finalFF:153417
Max relations in full relation-set: 28
Initial matrix: 119336 x 153417 with sparse part having weight 6853124.
Pruned matrix : 101139 x 101799 with weight 3462450.
Total sieving time: 1.62 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 1.72 hours.
 --------- CPU info (if available) ----------

(65·10¹¹⁴-11)/9 = 7(2)₁₁₃1_<115> = 3² · 233 · 409 · 558040613659747_<15> · C95

C95 = P39 · P56

P39 = 160981721112651612109794172448162077483_<39>

P56 = 93736068617683451547390765327106178850798232594071318277_<56>

Wed Oct 28 07:53:02 2009  Msieve v. 1.42
Wed Oct 28 07:53:02 2009  random seeds: 2df2b7a0 fd14a991
Wed Oct 28 07:53:02 2009  factoring 15089793656408292305935405066824835096685463605339172081455823016898078435395327872084828056791 (95 digits)
Wed Oct 28 07:53:04 2009  no P-1/P+1/ECM available, skipping
Wed Oct 28 07:53:04 2009  commencing quadratic sieve (95-digit input)
Wed Oct 28 07:53:04 2009  using multiplier of 1
Wed Oct 28 07:53:04 2009  using 64kb Pentium 4 sieve core
Wed Oct 28 07:53:04 2009  sieve interval: 18 blocks of size 65536
Wed Oct 28 07:53:04 2009  processing polynomials in batches of 6
Wed Oct 28 07:53:04 2009  using a sieve bound of 2083057 (77647 primes)
Wed Oct 28 07:53:04 2009  using large prime bound of 295794094 (28 bits)
Wed Oct 28 07:53:04 2009  using double large prime bound of 1769216945767030 (42-51 bits)
Wed Oct 28 07:53:04 2009  using trial factoring cutoff of 51 bits
Wed Oct 28 07:53:04 2009  polynomial 'A' values have 12 factors
Wed Oct 28 12:47:27 2009  77846 relations (19670 full + 58176 combined from 1126255 partial), need 77743
Wed Oct 28 12:47:32 2009  begin with 1145925 relations
Wed Oct 28 12:47:33 2009  reduce to 200673 relations in 12 passes
Wed Oct 28 12:47:33 2009  attempting to read 200673 relations
Wed Oct 28 12:47:39 2009  recovered 200673 relations
Wed Oct 28 12:47:40 2009  recovered 182034 polynomials
Wed Oct 28 12:47:40 2009  attempting to build 77846 cycles
Wed Oct 28 12:47:40 2009  found 77846 cycles in 5 passes
Wed Oct 28 12:47:40 2009  distribution of cycle lengths:
Wed Oct 28 12:47:40 2009     length 1 : 19670
Wed Oct 28 12:47:40 2009     length 2 : 13856
Wed Oct 28 12:47:40 2009     length 3 : 13168
Wed Oct 28 12:47:40 2009     length 4 : 10392
Wed Oct 28 12:47:40 2009     length 5 : 7815
Wed Oct 28 12:47:40 2009     length 6 : 5267
Wed Oct 28 12:47:40 2009     length 7 : 3239
Wed Oct 28 12:47:40 2009     length 9+: 4439
Wed Oct 28 12:47:40 2009  largest cycle: 22 relations
Wed Oct 28 12:47:40 2009  matrix is 77647 x 77846 (20.2 MB) with weight 4991551 (64.12/col)
Wed Oct 28 12:47:40 2009  sparse part has weight 4991551 (64.12/col)
Wed Oct 28 12:47:42 2009  filtering completed in 3 passes
Wed Oct 28 12:47:42 2009  matrix is 73601 x 73665 (19.3 MB) with weight 4757494 (64.58/col)
Wed Oct 28 12:47:42 2009  sparse part has weight 4757494 (64.58/col)
Wed Oct 28 12:47:43 2009  saving the first 48 matrix rows for later
Wed Oct 28 12:47:43 2009  matrix is 73553 x 73665 (12.1 MB) with weight 3744511 (50.83/col)
Wed Oct 28 12:47:43 2009  sparse part has weight 2717431 (36.89/col)
Wed Oct 28 12:47:43 2009  matrix includes 64 packed rows
Wed Oct 28 12:47:43 2009  using block size 21845 for processor cache size 512 kB
Wed Oct 28 12:47:44 2009  commencing Lanczos iteration
Wed Oct 28 12:47:44 2009  memory use: 12.3 MB
Wed Oct 28 12:48:38 2009  lanczos halted after 1165 iterations (dim = 73552)
Wed Oct 28 12:48:38 2009  recovered 17 nontrivial dependencies
Wed Oct 28 12:48:40 2009  prp39 factor: 160981721112651612109794172448162077483
Wed Oct 28 12:48:40 2009  prp56 factor: 93736068617683451547390765327106178850798232594071318277
Wed Oct 28 12:48:40 2009  elapsed time 04:55:38

(22·10¹³⁰-7)/3 = 7(3)₁₂₉1_<131> = 17 · 7433 · 3557979273660185577548488019_<28> · C99

C99 = P39 · P61

P39 = 134460901537550527043746602103014314371_<39>

P61 = 1213078594105218010976731081776468633605124806837098291598179_<61>

Number: 73331_130
N=163111641399291940164106253116807208918321091467924877033762537156128353415965974233879839517130409
  ( 99 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=134460901537550527043746602103014314371 (pp39)
 r2=1213078594105218010976731081776468633605124806837098291598179 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.02 hours.
Scaled time: 7.72 units (timescale=1.919).
Factorization parameters were as follows:
name: 73331_130
n: 163111641399291940164106253116807208918321091467924877033762537156128353415965974233879839517130409
m: 100000000000000000000000000
deg: 5
c5: 22
c0: -7
skew: 0.80
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 890001)
Primes: RFBsize:84270, AFBsize:84284, largePrimes:3048064 encountered
Relations: rels:3176662, finalFF:414631
Max relations in full relation-set: 28
Initial matrix: 168620 x 414631 with sparse part having weight 33226394.
Pruned matrix : 113770 x 114677 with weight 7927149.
Total sieving time: 3.83 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 4.02 hours.
 --------- CPU info (if available) ----------

(65·10¹⁴⁹+7)/9 = 7(2)₁₄₈3_<150> = 3² · C149

C149 = P36 · P114

P36 = 105819244784386683109998203139936629_<36>

P114 = 758339503780763218629421606198547022990365677947048506292345087129713241005798463428316768844290881088734441938843_<114>

Number: 72223_149
N=80246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247
  ( 149 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=105819244784386683109998203139936629 (pp36)
 r2=758339503780763218629421606198547022990365677947048506292345087129713241005798463428316768844290881088734441938843 (pp114)
Version: Msieve-1.40
Total time: 17.34 hours.
Scaled time: 34.91 units (timescale=2.013).
Factorization parameters were as follows:
name: 72223_149
n: 80246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247
m: 1000000000000000000000000000000
deg: 5
c5: 13
c0: 14
skew: 1.01
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 373221 x 373469
Total sieving time: 16.65 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.49 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 17.34 hours.
 --------- CPU info (if available) ----------

(22·10¹¹⁸-7)/3 = 7(3)₁₁₇1_<119> = 235522201 · C111

C111 = P33 · P78

P33 = 677750033164238962514135169268793_<33>

P78 = 459409558976066599817050888415589308499006600496142633440871915604917908812067_<78>

Number: 73331_118
N=311364843831997533571509606151028341202251813761426819093514387347854877312960120194076028243865355747644925131
  ( 111 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=677750033164238962514135169268793 (pp33)
 r2=459409558976066599817050888415589308499006600496142633440871915604917908812067 (pp78)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.39 hours.
Scaled time: 4.76 units (timescale=1.989).
Factorization parameters were as follows:
name: 73331_118
n: 311364843831997533571509606151028341202251813761426819093514387347854877312960120194076028243865355747644925131
m: 500000000000000000000000
deg: 5
c5: 176
c0: -175
skew: 1.00
type: snfs
lss: 1
rlim: 720000
alim: 720000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 720000/720000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [360000, 610001)
Primes: RFBsize:58029, AFBsize:57998, largePrimes:1411373 encountered
Relations: rels:1434070, finalFF:193473
Max relations in full relation-set: 28
Initial matrix: 116094 x 193473 with sparse part having weight 9266838.
Pruned matrix : 90589 x 91233 with weight 3277602.
Total sieving time: 2.29 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,720000,720000,25,25,46,46,2.2,2.2,50000
total time: 2.39 hours.
 --------- CPU info (if available) ----------

(22·10¹²²-7)/3 = 7(3)₁₂₁1_<123> = 1530693038761_<13> · C111

C111 = P37 · P75

P37 = 1563778519534554459376784440862037907_<37>

P75 = 306364243034504327427694743241261865971138614286892595581588786721014964953_<75>

Number: 73331_122
N=479085822410821615351658824263053170082524325756116963166672692714955311750266379072262180668088864623762473371
  ( 111 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=1563778519534554459376784440862037907 (pp37)
 r2=306364243034504327427694743241261865971138614286892595581588786721014964953 (pp75)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.26 hours.
Scaled time: 6.24 units (timescale=1.914).
Factorization parameters were as follows:
name: 73331_122
n: 479085822410821615351658824263053170082524325756116963166672692714955311750266379072262180668088864623762473371
m: 2000000000000000000000000
deg: 5
c5: 275
c0: -28
skew: 0.63
type: snfs
lss: 1
rlim: 810000
alim: 810000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 810000/810000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [405000, 755001)
Primes: RFBsize:64683, AFBsize:64458, largePrimes:1606389 encountered
Relations: rels:1722493, finalFF:278867
Max relations in full relation-set: 28
Initial matrix: 129208 x 278867 with sparse part having weight 14688172.
Pruned matrix : 91624 x 92334 with weight 4159609.
Total sieving time: 3.15 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,810000,810000,25,25,46,46,2.2,2.2,50000
total time: 3.26 hours.
 --------- CPU info (if available) ----------

(65·10¹²³+61)/9 = 7(2)₁₂₂9_<124> = 205592060411_<12> · C113

C113 = P53 · P60

P53 = 43832229960417833389559695476524062451127923298934897_<53>

P60 = 801439867065015004955353448349678622394919140325219877510687_<60>

Number: 72229_123
N=35128896552640436304237638852300777831238242048760563711369157626269703401120520531589052046752787199110834744239
  ( 113 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=43832229960417833389559695476524062451127923298934897 (pp53)
 r2=801439867065015004955353448349678622394919140325219877510687 (pp60)
Version: Msieve-1.40
Total time: 2.23 hours.
Scaled time: 4.63 units (timescale=2.078).
Factorization parameters were as follows:
name: 72229_123
n: 35128896552640436304237638852300777831238242048760563711369157626269703401120520531589052046752787199110834744239
m: 5000000000000000000000000
deg: 5
c5: 104
c0: 305
skew: 1.24
type: snfs
lss: 1
rlim: 860000
alim: 860000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 860000/860000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [430000, 730001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 138461 x 138703
Total sieving time: 2.08 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,125.000,5,0,0,0,0,0,0,0,0,860000,860000,26,26,46,46,2.3,2.3,50000
total time: 2.23 hours.
 --------- CPU info (if available) ----------

(65·10¹²¹+61)/9 = 7(2)₁₂₀9_<122> = 179 · 7207 · 7309 · 801733 · 9292867 · C100

C100 = P41 · P59

P41 = 20970409353518247468689112397010047726039_<41>

P59 = 49025151298473527075633438557521717012039531437304980040413_<59>

Number: 72229_121
N=1028077491347156507372296855523252062931863952111775925648980556755371523816490127643897432972414107
  ( 100 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=20970409353518247468689112397010047726039 (pp41)
 r2=49025151298473527075633438557521717012039531437304980040413 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.16 hours.
Scaled time: 6.05 units (timescale=1.916).
Factorization parameters were as follows:
name: 72229_121
n: 1028077491347156507372296855523252062931863952111775925648980556755371523816490127643897432972414107
m: 1000000000000000000000000
deg: 5
c5: 650
c0: 61
skew: 0.62
type: snfs
lss: 1
rlim: 780000
alim: 780000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 780000/780000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [390000, 740001)
Primes: RFBsize:62468, AFBsize:62166, largePrimes:1452590 encountered
Relations: rels:1463616, finalFF:183399
Max relations in full relation-set: 28
Initial matrix: 124701 x 183399 with sparse part having weight 9655301.
Pruned matrix : 106872 x 107559 with weight 4217800.
Total sieving time: 3.03 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,780000,780000,25,25,46,46,2.2,2.2,50000
total time: 3.16 hours.
 --------- CPU info (if available) ----------

Oct 28, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / Oct 28, 2009

(65·10¹¹⁶+61)/9 = 7(2)₁₁₅9_<117> = 3 · C117

C117 = P47 · P70

P47 = 34527480997338766455831224411614972334483833577_<47>

P70 = 6972438584769506590625189732568805545326881025591814765362809896626159_<70>

Number: n
N=240740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
  ( 117 digits)
SNFS difficulty: 117 digits.
Divisors found:

Wed Oct 28 16:56:37 2009  prp47 factor: 34527480997338766455831224411614972334483833577
Wed Oct 28 16:56:37 2009  prp70 factor: 6972438584769506590625189732568805545326881025591814765362809896626159
Wed Oct 28 16:56:37 2009  elapsed time 00:02:19 (Msieve 1.43 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.05 hours.
Scaled time: 1.92 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_2_115_9
n: 240740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
m: 100000000000000000000000
deg: 5
c5: 650
c0: 61
skew: 0.62
type: snfs
lss: 1
rlim: 640000
alim: 640000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
qintsize: 10000
Factor base limits: 640000/640000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved  special-q in [320000, 561061)
Primes: RFBsize:52074, AFBsize:51702, largePrimes:1210995 encountered
Relations: rels:1144261, finalFF:109583
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 87777 hash collisions in 1223142 relations
Msieve: matrix is 79909 x 80151 (21.9 MB)

Total sieving time: 1.03 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,640000,640000,25,25,45,45,2.2,2.2,50000
total time: 1.05 hours.
 --------- CPU info (if available) ----------

(22·10¹²⁴-7)/3 = 7(3)₁₂₃1_<125> = 75534607 · C117

C117 = P37 · P81

P37 = 8115001058452151810981501720352816797_<37>

P81 = 119637373860289775776679722919530050967368885966201837192042266522620691868053089_<81>

Number: n
N=970857415506687329866339720723420634641460878102315847533744808301356930781851202765023101706656570455623517486935933
  ( 117 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=8115001058452151810981501720352816797 (pp37)
 r2=119637373860289775776679722919530050967368885966201837192042266522620691868053089 (pp81)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.22 hours.
Scaled time: 2.22 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_7_3_123_1
n: 970857415506687329866339720723420634641460878102315847533744808301356930781851202765023101706656570455623517486935933
m: 10000000000000000000000000
deg: 5
c5: 11
c0: -35
skew: 1.26
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
qintsize: 10000
Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 640001)
Primes: RFBsize:69823, AFBsize:69714, largePrimes:2298551 encountered
Relations: rels:2160546, finalFF:174436
Max relations in full relation-set: 48
Initial matrix: 139602 x 174436 with sparse part having weight 12948806.
Pruned matrix : 125159 x 125921 with weight 6476055.
Total sieving time: 1.10 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 1.22 hours.
 --------- CPU info (if available) ----------

Oct 28, 2009 (5th)

By Wataru Sakai / GMP-ECM 6.2.1 / Oct 28, 2009

(65·10¹⁸⁵-11)/9 = 7(2)₁₈₄1_<186> = 3673 · 145459 · 51028247 · 523181223872965338269_<21> · 1045359163418150399691709_<25> · C125

C125 = P32 · P93

P32 = 61950651458183075429960343799297_<32>

P93 = 781871016839220677109463407665525311825701689960463807826403466950410272126295951203562513177_<93>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2064621114
Step 1 took 34199ms
Step 2 took 13550ms
********** Factor found in step 2: 61950651458183075429960343799297
Found probable prime factor of 32 digits: 61950651458183075429960343799297
Probable prime cofactor 781871016839220677109463407665525311825701689960463807826403466950410272126295951203562513177 has 93 digits

(65·10¹⁹⁴+7)/9 = 7(2)₁₉₃3_<195> = 3⁴ · 7884797231020992193_<19> · 2877176822753658311521667_<25> · C150

C150 = P37 · C113

P37 = 7624190601160779016659090250310483321_<37>

C113 = [51550751522675018522266287786788814275048077732851829746459474778039978537603238494488272159493076802130222223133_<113>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1441488083
Step 1 took 47275ms
Step 2 took 16303ms
********** Factor found in step 2: 7624190601160779016659090250310483321
Found probable prime factor of 37 digits: 7624190601160779016659090250310483321
Composite cofactor 51550751522675018522266287786788814275048077732851829746459474778039978537603238494488272159493076802130222223133 has 113 digits

(65·10¹⁸⁴+7)/9 = 7(2)₁₈₃3_<185> = 60719 · 171726193 · 51058810193_<11> · 228486884552752127332609_<24> · C138

C138 = P38 · P101

P38 = 21849812748236144008464710337280850879_<38>

P101 = 27172525737692482212391401687104134737901694575685983842308802500321577962738259082419630105067070303_<101>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3570817345
Step 1 took 42646ms
Step 2 took 14810ms
********** Factor found in step 2: 21849812748236144008464710337280850879
Found probable prime factor of 38 digits: 21849812748236144008464710337280850879
Probable prime cofactor 27172525737692482212391401687104134737901694575685983842308802500321577962738259082419630105067070303 has 101 digits

Oct 28, 2009 (4th)

By Serge Batalov / Msieve / Oct 28, 2009

(65·10¹⁰²+61)/9 = 7(2)₁₀₁9_<103> = 7 · 17 · 137 · 38468687 · C92

C92 = P42 · P50

P42 = 175788552003242654918707023394121127082163_<42>

P50 = 65509663177054239063561837808654735019636969220503_<50>

SNFS difficulty: 104 digits.
Divisors found:
 r1=175788552003242654918707023394121127082163 (pp42)
 r2=65509663177054239063561837808654735019636969220503 (pp50)
Version: Msieve v. 1.44 SVN130
Total time: 0.26 hours.
Scaled time: 0.63 units (timescale=2.400).
Factorization parameters were as follows:
n: 11515848832114509541969286728301648150391951381143915818708913267971130126036386168945187989
m: 50000000000000000000000000
deg: 4
c4: 52
c0: 305
skew: 1.56
type: snfs
lss: 1
rlim: 390000
alim: 390000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 390000/390000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [195000, 275001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 31248 x 31496
Total sieving time: 0.25 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,104.000,4,0,0,0,0,0,0,0,0,390000,390000,25,25,44,44,2.2,2.2,10000
total time: 0.26 hours.

(22·10¹⁰⁹-7)/3 = 7(3)₁₀₈1_<110> = C110

C110 = P36 · P75

P36 = 366976113897403798134036390219247147_<36>

P75 = 199831352930603192222342071083610479760495108319628605228753948824443242873_<75>

SNFS difficulty: 111 digits.
Divisors found:
 r1=366976113897403798134036390219247147 (pp36)
 r2=199831352930603192222342071083610479760495108319628605228753948824443242873 (pp75)
Version: Msieve v. 1.44 SVN130
Total time: 0.46 hours.
Scaled time: 1.12 units (timescale=2.400).
Factorization parameters were as follows:
n: 73333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
m: 10000000000000000000000
deg: 5
c5: 11
c0: -35
skew: 1.26
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [250000, 400001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 37502 x 37737
Total sieving time: 0.44 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 0.46 hours.

(65·10¹¹²-11)/9 = 7(2)₁₁₁1_<113> = 349 · 1609 · C108

C108 = P41 · P67

P41 = 70607932059021754016721120546462990586001_<41>

P67 = 1821528136121762022116250471027322875569923541409150218970043515481_<67>

SNFS difficulty: 115 digits.
Divisors found:
 r1=70607932059021754016721120546462990586001 (pp41)
 r2=1821528136121762022116250471027322875569923541409150218970043515481 (pp67)
Version: Msieve v. 1.44 SVN130
Total time: 0.72 hours.
Scaled time: 1.73 units (timescale=2.400).
Factorization parameters were as follows:
n: 128614334878881902162481853012019108528535266743162515688475502629767411858122954908407796086523018305381481
m: 50000000000000000000000
deg: 5
c5: 52
c0: -275
skew: 1.40
type: snfs
lss: 1
rlim: 580000
alim: 580000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 580000/580000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [362500, 612501)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 64101 x 64332
Total sieving time: 0.68 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115.000,5,0,0,0,0,0,0,0,0,580000,580000,25,25,45,45,2.2,2.2,50000
total time: 0.72 hours.

(65·10¹²³+7)/9 = 7(2)₁₂₂3_<124> = 31 · 433341079 · C114

C114 = P47 · P68

P47 = 31760089599647095470964140303933168837398685341_<47>

P68 = 16927685203118105408193075223017693529147950521552388939439515578947_<68>

SNFS difficulty: 125 digits.
Divisors found:
 r1=31760089599647095470964140303933168837398685341 (pp47)
 r2=16927685203118105408193075223017693529147950521552388939439515578947 (pp68)
Version: Msieve v. 1.44 SVN130
Total time: 1.07 hours.
Scaled time: 2.57 units (timescale=2.400).
Factorization parameters were as follows:
n: 537624798765651370372182957215632388524131277277257415040186469316725900027661524584873859219275425292106297115927
m: 5000000000000000000000000
deg: 5
c5: 104
c0: 35
skew: 0.80
type: snfs
lss: 1
rlim: 860000
alim: 860000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 860000/860000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [537500, 837501)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 114687 x 114917
Total sieving time: 0.98 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,125.000,5,0,0,0,0,0,0,0,0,860000,860000,26,26,46,46,2.3,2.3,50000
total time: 1.07 hours.

(65·10¹²⁴+7)/9 = 7(2)₁₂₃3_<125> = 23627 · 122179984837067_<15> · C107

C107 = P52 · P55

P52 = 2779713843164198342229108373215405036999849001718309_<52>

P55 = 9000406178344471728392191196472373929710255397699359483_<55>

SNFS difficulty: 126 digits.
Divisors found:
 r1=2779713843164198342229108373215405036999849001718309 (pp52)
 r2=9000406178344471728392191196472373929710255397699359483 (pp55)
Version: Msieve v. 1.44 SVN130
Total time: 1.10 hours.
Scaled time: 2.64 units (timescale=2.400).
Factorization parameters were as follows:
n: 25018553648044706659806696982403245276792059272573860134171871212230208677668993529533362509883455693874247
m: 10000000000000000000000000
deg: 5
c5: 13
c0: 14
skew: 1.01
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [556250, 856251)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 121199 x 121429
Total sieving time: 1.01 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 1.10 hours.

Oct 28, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM v6.2.3, YAFU v1.10, Msieve / Oct 28, 2009

(65·10¹⁴⁵-11)/9 = 7(2)₁₄₄1_<146> = 47 · 607 · 351457 · 10203519393642125535430984893281_<32> · C105

C105 = P41 · P65

P41 = 70454049702556330053008041614724445605807_<41>

P65 = 10019732907879640889882400544847060911821000275230632388769933171_<65>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 705930760298091485229453256487302969635908437931309773233506439012655251426409443017893127773611999523997 (105 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1037193634
Step 1 took 3494ms
Step 2 took 3588ms
********** Factor found in step 2: 70454049702556330053008041614724445605807
Found probable prime factor of 41 digits: 70454049702556330053008041614724445605807
Probable prime cofactor 10019732907879640889882400544847060911821000275230632388769933171 has 65 digits

(65·10¹³⁷+7)/9 = 7(2)₁₃₆3_<138> = 3 · 23 · 73 · 30871 · 1386083 · 720941959457_<12> · C112

C112 = P30 · P31 · P53

P30 = 190061403203275865525088244967_<30>

P31 = 1244841026681448907106941991207_<31>

P53 = 19644945785038727533820766473773169516200342274306591_<53>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 4647920156400974489982688051665613882176378983480078042769794813814236946086858104526358893394750640417706768879 (112 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6061696595
Step 1 took 3495ms
Step 2 took 3822ms
********** Factor found in step 2: 190061403203275865525088244967
Found probable prime factor of 30 digits: 190061403203275865525088244967
Composite cofactor 24454834480149011868325660087316764591350057434391682905368504067395322836744145337 has 83 digits

10/27/09 21:28:44 v1.10 @ 조영욱-PC, starting SIQS on c83: 24454834480149011868325660087316764591350057434391682905368504067395322836744145337
10/27/09 21:28:44 v1.10 @ 조영욱-PC, random seeds: 2880975533, 481832920
10/27/09 21:28:45 v1.10 @ 조영욱-PC, ==== sieve params ====
10/27/09 21:28:45 v1.10 @ 조영욱-PC, n = 83 digits, 274 bits
10/27/09 21:28:45 v1.10 @ 조영욱-PC, factor base: 49771 primes (max prime = 1295131)
10/27/09 21:28:45 v1.10 @ 조영욱-PC, single large prime cutoff: 123037445 (95 * pmax)
10/27/09 21:28:45 v1.10 @ 조영욱-PC, double large prime range from 42 to 49 bits
10/27/09 21:28:45 v1.10 @ 조영욱-PC, double large prime cutoff: 364810346638489
10/27/09 21:28:45 v1.10 @ 조영욱-PC, using 14 large prime slices of factor base
10/27/09 21:28:45 v1.10 @ 조영욱-PC, buckets hold 1024 elements
10/27/09 21:28:45 v1.10 @ 조영욱-PC, sieve interval: 7 blocks of size 65536
10/27/09 21:28:45 v1.10 @ 조영욱-PC, polynomial A has ~ 10 factors
10/27/09 21:28:45 v1.10 @ 조영욱-PC, using multiplier of 1
10/27/09 21:28:45 v1.10 @ 조영욱-PC, using small prime variation correction of 18 bits
10/27/09 21:28:45 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
10/27/09 21:28:45 v1.10 @ 조영욱-PC, trial factoring cutoff at 94 bits
10/27/09 21:28:45 v1.10 @ 조영욱-PC, ==== sieving started ====
10/27/09 21:40:57 v1.10 @ 조영욱-PC, sieve time = 340.0500, relation time = 136.3560, poly_time = 255.6500
10/27/09 21:40:57 v1.10 @ 조영욱-PC, 49848 relations found: 21802 full + 28046 from 290299 partial, using 172944 polys (244 A polys)
10/27/09 21:40:57 v1.10 @ 조영욱-PC, on average, sieving found 1.80 rels/poly and 426.07 rels/sec
10/27/09 21:40:57 v1.10 @ 조영욱-PC, trial division touched 6239436 sieve locations out of 158676811776
10/27/09 21:40:57 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
10/27/09 21:40:57 v1.10 @ 조영욱-PC, begin with 312101 relations
10/27/09 21:40:57 v1.10 @ 조영욱-PC, reduce to 79841 relations in 7 passes
10/27/09 21:40:58 v1.10 @ 조영욱-PC, recovered 79841 relations
10/27/09 21:40:58 v1.10 @ 조영욱-PC, recovered 63984 polynomials
10/27/09 21:40:58 v1.10 @ 조영욱-PC, attempting to build 49848 cycles
10/27/09 21:40:58 v1.10 @ 조영욱-PC, found 49848 cycles in 3 passes
10/27/09 21:40:58 v1.10 @ 조영욱-PC, distribution of cycle lengths:
10/27/09 21:40:58 v1.10 @ 조영욱-PC,    length 1 : 21802
10/27/09 21:40:58 v1.10 @ 조영욱-PC,    length 2 : 20836
10/27/09 21:40:58 v1.10 @ 조영욱-PC,    length 3 : 5377
10/27/09 21:40:58 v1.10 @ 조영욱-PC,    length 4 : 1388
10/27/09 21:40:58 v1.10 @ 조영욱-PC,    length 5 : 329
10/27/09 21:40:58 v1.10 @ 조영욱-PC,    length 6 : 97
10/27/09 21:40:58 v1.10 @ 조영욱-PC,    length 7 : 16
10/27/09 21:40:58 v1.10 @ 조영욱-PC,    length 9+: 3
10/27/09 21:40:58 v1.10 @ 조영욱-PC, largest cycle: 9 relations
10/27/09 21:40:58 v1.10 @ 조영욱-PC, matrix is 49771 x 49848 (8.2 MB) with weight 1749155 (35.09/col)
10/27/09 21:40:58 v1.10 @ 조영욱-PC, sparse part has weight 1749155 (35.09/col)
10/27/09 21:40:58 v1.10 @ 조영욱-PC, filtering completed in 3 passes
10/27/09 21:40:58 v1.10 @ 조영욱-PC, matrix is 38980 x 39042 (6.8 MB) with weight 1458401 (37.35/col)
10/27/09 21:40:58 v1.10 @ 조영욱-PC, sparse part has weight 1458401 (37.35/col)
10/27/09 21:40:58 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
10/27/09 21:40:58 v1.10 @ 조영욱-PC, matrix is 38932 x 39042 (4.7 MB) with weight 1118471 (28.65/col)
10/27/09 21:40:58 v1.10 @ 조영욱-PC, sparse part has weight 846197 (21.67/col)
10/27/09 21:40:58 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
10/27/09 21:40:58 v1.10 @ 조영욱-PC, using block size 15616 for processor cache size 4096 kB
10/27/09 21:40:58 v1.10 @ 조영욱-PC, commencing Lanczos iteration
10/27/09 21:40:58 v1.10 @ 조영욱-PC, memory use: 4.6 MB
10/27/09 21:41:03 v1.10 @ 조영욱-PC, lanczos halted after 617 iterations (dim = 38926)
10/27/09 21:41:03 v1.10 @ 조영욱-PC, recovered 13 nontrivial dependencies
10/27/09 21:41:03 v1.10 @ 조영욱-PC, prp31 = 1244841026681448907106941991207
10/27/09 21:41:03 v1.10 @ 조영욱-PC, prp53 = 19644945785038727533820766473773169516200342274306591
10/27/09 21:41:03 v1.10 @ 조영욱-PC, Lanczos elapsed time = 6.0210 seconds.
10/27/09 21:41:03 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.5150 seconds.
10/27/09 21:41:03 v1.10 @ 조영욱-PC, SIQS elapsed time = 739.0400 seconds.
10/27/09 21:41:03 v1.10 @ 조영욱-PC, 
10/27/09 21:41:03 v1.10 @ 조영욱-PC,

(22·10¹⁰⁸-7)/3 = 7(3)₁₀₇1_<109> = 197 · 2311 · 315155716987_<12> · 2708183643299_<13> · C80

C80 = P33 · P48

P33 = 133878894470440665305883428582177_<33>

P48 = 140967772262343217162849205986846194637148762593_<48>

10/28/09 01:14:46 v1.10 @ 조영욱-PC, starting SIQS on c80: 18872609506443360331949072625824394175999049219789808838348481048176363964104961
10/28/09 01:14:46 v1.10 @ 조영욱-PC, random seeds: 2953276341, 473520796
10/28/09 01:14:47 v1.10 @ 조영욱-PC, ==== sieve params ====
10/28/09 01:14:47 v1.10 @ 조영욱-PC, n = 80 digits, 264 bits
10/28/09 01:14:47 v1.10 @ 조영욱-PC, factor base: 41901 primes (max prime = 1074701)
10/28/09 01:14:47 v1.10 @ 조영욱-PC, single large prime cutoff: 91349585 (85 * pmax)
10/28/09 01:14:47 v1.10 @ 조영욱-PC, using 13 large prime slices of factor base
10/28/09 01:14:47 v1.10 @ 조영욱-PC, buckets hold 1024 elements
10/28/09 01:14:47 v1.10 @ 조영욱-PC, sieve interval: 5 blocks of size 65536
10/28/09 01:14:47 v1.10 @ 조영욱-PC, polynomial A has ~ 10 factors
10/28/09 01:14:47 v1.10 @ 조영욱-PC, using multiplier of 1
10/28/09 01:14:47 v1.10 @ 조영욱-PC, using small prime variation correction of 17 bits
10/28/09 01:14:47 v1.10 @ 조영욱-PC, using SSE2 for trial division and x64 sieve scanning
10/28/09 01:14:47 v1.10 @ 조영욱-PC, trial factoring cutoff at 95 bits
10/28/09 01:14:47 v1.10 @ 조영욱-PC, ==== sieving started ====
10/28/09 01:21:38 v1.10 @ 조영욱-PC, sieve time = 193.1750, relation time = 50.4470, poly_time = 167.9450
10/28/09 01:21:38 v1.10 @ 조영욱-PC, 42077 relations found: 21186 full + 20891 from 219340 partial, using 140092 polys (274 A polys)
10/28/09 01:21:38 v1.10 @ 조영욱-PC, on average, sieving found 1.72 rels/poly and 583.88 rels/sec
10/28/09 01:21:38 v1.10 @ 조영욱-PC, trial division touched 2486400 sieve locations out of 91810693120
10/28/09 01:21:38 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
10/28/09 01:21:38 v1.10 @ 조영욱-PC, begin with 240526 relations
10/28/09 01:21:38 v1.10 @ 조영욱-PC, reduce to 60274 relations in 2 passes
10/28/09 01:21:39 v1.10 @ 조영욱-PC, recovered 60274 relations
10/28/09 01:21:39 v1.10 @ 조영욱-PC, recovered 49064 polynomials
10/28/09 01:21:39 v1.10 @ 조영욱-PC, attempting to build 42077 cycles
10/28/09 01:21:39 v1.10 @ 조영욱-PC, found 42077 cycles in 1 passes
10/28/09 01:21:39 v1.10 @ 조영욱-PC, distribution of cycle lengths:
10/28/09 01:21:39 v1.10 @ 조영욱-PC,    length 1 : 21186
10/28/09 01:21:39 v1.10 @ 조영욱-PC,    length 2 : 20891
10/28/09 01:21:39 v1.10 @ 조영욱-PC, largest cycle: 2 relations
10/28/09 01:21:39 v1.10 @ 조영욱-PC, matrix is 41901 x 42077 (6.1 MB) with weight 1266037 (30.09/col)
10/28/09 01:21:39 v1.10 @ 조영욱-PC, sparse part has weight 1266037 (30.09/col)
10/28/09 01:21:39 v1.10 @ 조영욱-PC, filtering completed in 4 passes
10/28/09 01:21:39 v1.10 @ 조영욱-PC, matrix is 30689 x 30753 (4.9 MB) with weight 1028952 (33.46/col)
10/28/09 01:21:39 v1.10 @ 조영욱-PC, sparse part has weight 1028952 (33.46/col)
10/28/09 01:21:39 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
10/28/09 01:21:39 v1.10 @ 조영욱-PC, matrix is 30641 x 30753 (3.6 MB) with weight 811519 (26.39/col)
10/28/09 01:21:39 v1.10 @ 조영욱-PC, sparse part has weight 632898 (20.58/col)
10/28/09 01:21:39 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
10/28/09 01:21:39 v1.10 @ 조영욱-PC, using block size 12301 for processor cache size 4096 kB
10/28/09 01:21:39 v1.10 @ 조영욱-PC, commencing Lanczos iteration
10/28/09 01:21:39 v1.10 @ 조영욱-PC, memory use: 3.5 MB
10/28/09 01:21:42 v1.10 @ 조영욱-PC, lanczos halted after 486 iterations (dim = 30639)
10/28/09 01:21:42 v1.10 @ 조영욱-PC, recovered 15 nontrivial dependencies
10/28/09 01:21:42 v1.10 @ 조영욱-PC, prp48 = 140967772262343217162849205986846194637148762593
10/28/09 01:21:43 v1.10 @ 조영욱-PC, prp33 = 133878894470440665305883428582177
10/28/09 01:21:43 v1.10 @ 조영욱-PC, Lanczos elapsed time = 3.7600 seconds.
10/28/09 01:21:43 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.7330 seconds.
10/28/09 01:21:43 v1.10 @ 조영욱-PC, SIQS elapsed time = 416.4350 seconds.
10/28/09 01:21:43 v1.10 @ 조영욱-PC, 
10/28/09 01:21:43 v1.10 @ 조영욱-PC,

(65·10¹⁸⁴-11)/9 = 7(2)₁₈₃1_<185> = 691 · 219621875269_<12> · 2157276602733659502141754392473_<31> · 1366875469678489414121668461325082477_<37> · C105

C105 = P34 · P71

P34 = 4503477033199215094729890033147187_<34>

P71 = 35837232906713279419812768310828169169378234147431171772663813102526637_<71>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 161392155328794403131606385552815547402281189086153913445436817927538091137682507550470946122430609120119 (105 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4945725169
Step 1 took 3478ms
Step 2 took 3698ms
********** Factor found in step 2: 4503477033199215094729890033147187
Found probable prime factor of 34 digits: 4503477033199215094729890033147187
Probable prime cofactor 35837232906713279419812768310828169169378234147431171772663813102526637 has 71 digits

(59·10¹⁵³+13)/9 = 6(5)₁₅₂7_<154> = 61 · 14431 · 448464904859558179943943527591218691_<36> · C113

C113 = P34 · P79

P34 = 1945389686705257859216885747713751_<34>

P79 = 8535877402069090294321958359979736349858550365095150663138218416934201553637547_<79>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 16605607864965677941097681100617903499359254644723048816511846628405008244182350794304630346346316241452961808797 (113 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2517939697
Step 1 took 3448ms
Step 2 took 3775ms
********** Factor found in step 2: 1945389686705257859216885747713751
Found probable prime factor of 34 digits: 1945389686705257859216885747713751
Probable prime cofactor 8535877402069090294321958359979736349858550365095150663138218416934201553637547 has 79 digits

Oct 28, 2009 (2nd)

By Erik Branger / GGNFS, Msieve, YAFU / Oct 28, 2009

(65·10¹³⁸+7)/9 = 7(2)₁₃₇3_<139> = 31 · 229 · 33461 · 1259007165190111865378078821_<28> · C104

C104 = P51 · P54

P51 = 241431719926832113054176853658594117687436004218661_<51>

P54 = 100025844120941294664361239378525121327867816498537297_<54>

Number: 72223_138
N=24149411583252065135541995261870948312801057540026010846855723972400408737150851077914404918027851899317
  ( 104 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=241431719926832113054176853658594117687436004218661 (pp51)
 r2=100025844120941294664361239378525121327867816498537297 (pp54)
Version: Msieve-1.40
Total time: 5.45 hours.
Scaled time: 5.30 units (timescale=0.971).
Factorization parameters were as follows:
n: 24149411583252065135541995261870948312801057540026010846855723972400408737150851077914404918027851899317
m: 5000000000000000000000000000
deg: 5
c5: 104
c0: 35
skew: 0.80
type: snfs
lss: 1
rlim: 1540000
alim: 1540000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1540000/1540000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [770000, 1570001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 229296 x 229521
Total sieving time: 5.25 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,140.000,5,0,0,0,0,0,0,0,0,1540000,1540000,26,26,48,48,2.3,2.3,100000
total time: 5.45 hours.
 --------- CPU info (if available) ----------

(65·10¹⁰⁴+61)/9 = 7(2)₁₀₃9_<105> = 3 · 743 · 4139 · 158017 · 318523367 · C85

C85 = P38 · P47

P38 = 40936918812214106518239018554059251721_<38>

P47 = 37993131474820395090146307173650064397787555261_<47>

10/27/09 17:32:06 v1.12 @ ERIK-DATOR, starting SIQS on c85: 1555321738606498913184153860786756010560527305346283314428864765623009053835596854181
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, random seeds: 3962589134, 1153892920
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, ==== sieve params ====
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, n = 85 digits, 280 bits
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, factor base: 54371 primes (max prime = 1426717)
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, single large prime cutoff: 135538115 (95 * pmax)
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, double large prime range from 42 to 49 bits
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, double large prime cutoff: 434220771349436
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, using 0 large prime slices of factor base
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, buckets hold 1024 elements
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, sieve interval: 14 blocks of size 32768
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, polynomial A has ~ -1878638032 factors
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, using multiplier of 1
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, using small prime variation correction of 19 bits
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, trial factoring cutoff at 91 bits
10/27/09 17:32:06 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ====
10/27/09 17:45:18 v1.12 @ ERIK-DATOR, sieve time = 169.0812, relation time = 175.8406, poly_time = 323.7462
10/27/09 17:45:18 v1.12 @ ERIK-DATOR, 54712 relations found: 17242 full + 37470 from 548555 partial, using 22772460 polys (501 A polys)
10/27/09 17:45:18 v1.12 @ ERIK-DATOR, on average, sieving found 0.02 rels/poly and 714.15 rels/sec
10/27/09 17:45:18 v1.12 @ ERIK-DATOR, trial division touched 13327686 sieve locations out of 20893823139840
10/27/09 17:45:18 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ====
10/27/09 17:45:19 v1.12 @ ERIK-DATOR, begin with 565797 relations
10/27/09 17:45:19 v1.12 @ ERIK-DATOR, reduce to 119482 relations in 11 passes
10/27/09 17:45:24 v1.12 @ ERIK-DATOR, recovered 119482 relations
10/27/09 17:45:24 v1.12 @ ERIK-DATOR, recovered 87233 polynomials
10/27/09 17:45:24 v1.12 @ ERIK-DATOR, attempting to build 54712 cycles
10/27/09 17:45:24 v1.12 @ ERIK-DATOR, found 54712 cycles in 5 passes
10/27/09 17:45:24 v1.12 @ ERIK-DATOR, distribution of cycle lengths:
10/27/09 17:45:24 v1.12 @ ERIK-DATOR,    length 1 : 17242
10/27/09 17:45:24 v1.12 @ ERIK-DATOR,    length 2 : 12987
10/27/09 17:45:24 v1.12 @ ERIK-DATOR,    length 3 : 10242
10/27/09 17:45:24 v1.12 @ ERIK-DATOR,    length 4 : 6560
10/27/09 17:45:24 v1.12 @ ERIK-DATOR,    length 5 : 3769
10/27/09 17:45:24 v1.12 @ ERIK-DATOR,    length 6 : 1911
10/27/09 17:45:24 v1.12 @ ERIK-DATOR,    length 7 : 1038
10/27/09 17:45:24 v1.12 @ ERIK-DATOR,    length 9+: 963
10/27/09 17:45:24 v1.12 @ ERIK-DATOR, largest cycle: 16 relations
10/27/09 17:45:25 v1.12 @ ERIK-DATOR, matrix is 54371 x 54712 (11.1 MB) with weight 2693387 (49.23/col)
10/27/09 17:45:25 v1.12 @ ERIK-DATOR, sparse part has weight 2693387 (49.23/col)
10/27/09 17:45:25 v1.12 @ ERIK-DATOR, filtering completed in 3 passes
10/27/09 17:45:25 v1.12 @ ERIK-DATOR, matrix is 48327 x 48390 (10.0 MB) with weight 2415324 (49.91/col)
10/27/09 17:45:25 v1.12 @ ERIK-DATOR, sparse part has weight 2415324 (49.91/col)
10/27/09 17:45:25 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later
10/27/09 17:45:25 v1.12 @ ERIK-DATOR, matrix is 48279 x 48390 (8.4 MB) with weight 2085580 (43.10/col)
10/27/09 17:45:25 v1.12 @ ERIK-DATOR, sparse part has weight 1899415 (39.25/col)
10/27/09 17:45:25 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows
10/27/09 17:45:25 v1.12 @ ERIK-DATOR, using block size 19356 for processor cache size 2048 kB
10/27/09 17:45:26 v1.12 @ ERIK-DATOR, commencing Lanczos iteration
10/27/09 17:45:26 v1.12 @ ERIK-DATOR, memory use: 7.5 MB
10/27/09 17:45:42 v1.12 @ ERIK-DATOR, lanczos halted after 764 iterations (dim = 48277)
10/27/09 17:45:42 v1.12 @ ERIK-DATOR, recovered 15 nontrivial dependencies
10/27/09 17:45:43 v1.12 @ ERIK-DATOR, prp38 = 40936918812214106518239018554059251721
10/27/09 17:45:50 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 23.2130 seconds.
10/27/09 17:45:50 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 8.6580 seconds.
10/27/09 17:45:50 v1.12 @ ERIK-DATOR, SIQS elapsed time = 824.1340 seconds.

(65·10¹⁰⁷+61)/9 = 7(2)₁₀₆9_<108> = 3 · 23 · C107

C107 = P47 · P60

P47 = 79042814270215615286909496928517614545370473299_<47>

P60 = 132421761857768186465514068388207008726242724827202973362059_<60>

Number: 72229_107
N=10466988727858293075684380032206119162640901771336553945249597423510466988727858293075684380032206119162641
  ( 107 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=79042814270215615286909496928517614545370473299 (pp47)
 r2=132421761857768186465514068388207008726242724827202973362059 (pp60)
Version: Msieve-1.40
Total time: 0.81 hours.
Scaled time: 0.81 units (timescale=1.005).
Factorization parameters were as follows:
n: 10466988727858293075684380032206119162640901771336553945249597423510466988727858293075684380032206119162641
m: 5000000000000000000000
deg: 5
c5: 52
c0: 1525
skew: 1.97
type: snfs
lss: 1
rlim: 480000
alim: 480000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 480000/480000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [240000, 390001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 46369 x 46594
Total sieving time: 0.79 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,110.000,5,0,0,0,0,0,0,0,0,480000,480000,25,25,44,44,2.2,2.2,50000
total time: 0.81 hours.
 --------- CPU info (if available) ----------

(65·10¹³⁵-11)/9 = 7(2)₁₃₄1_<136> = 3 · 19 · 8053 · 180391 · 10080019 · C118

C118 = P47 · P72

P47 = 47143046448625917952027767536030904815495237561_<47>

P72 = 183545791821273701961220689454604108763314382917801245535477001041814229_<72>

Number: 72221_135
N=8652907789280129252198822257687729096160252806243514414209614921213401995731190366456215067084773588979155172785055469
  ( 118 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=47143046448625917952027767536030904815495237561 (pp47)
 r2=183545791821273701961220689454604108763314382917801245535477001041814229 (pp72)
Version: Msieve v. 1.43
Total time: 6.58 hours.
Scaled time: 5.15 units (timescale=0.782).
Factorization parameters were as follows:
n: 8652907789280129252198822257687729096160252806243514414209614921213401995731190366456215067084773588979155172785055469
m: 1000000000000000000000000000
deg: 5
c5: 65
c0: -11
skew: 0.70
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1190001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 201818 x 202043
Total sieving time: 5.65 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.61 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 6.58 hours.
 --------- CPU info (if available) ----------

(65·10¹¹¹+61)/9 = 7(2)₁₁₀9_<112> = C112

C112 = P32 · P32 · P50

P32 = 14428621383131545651735579585663_<32>

P32 = 18758370112130867494247173697377_<32>

P50 = 26683998610560713798271832980145381354268977407179_<50>

Number: 72229_111
N=7222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
  ( 112 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=14428621383131545651735579585663 (pp32)
 r2=18758370112130867494247173697377 (pp32)
 r3=26683998610560713798271832980145381354268977407179 (pp50)
Version: Msieve-1.40
Total time: 1.11 hours.
Scaled time: 1.06 units (timescale=0.954).
Factorization parameters were as follows:
n: 7222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
m: 10000000000000000000000
deg: 5
c5: 650
c0: 61
skew: 0.62
type: snfs
lss: 1
rlim: 530000
alim: 530000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 530000/530000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [265000, 465001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 57157 x 57383
Total sieving time: 1.07 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,112.000,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000
total time: 1.11 hours.
 --------- CPU info (if available) ----------

(22·10¹¹⁷-7)/3 = 7(3)₁₁₆1_<118> = 131 · 2340703 · 874029479 · C101

C101 = P32 · P69

P32 = 73599418399459784738905045672909_<32>

P69 = 371777716502150259894247513418601899164271481551734543209609930979997_<69>

Number: 73331_117
N=27362623708437501481435967480647416522582967037243405954798475215929239453117920160504986430683801273
  ( 101 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=73599418399459784738905045672909 (pp32)
 r2=371777716502150259894247513418601899164271481551734543209609930979997 (pp69)
Version: Msieve-1.40
Total time: 1.12 hours.
Scaled time: 1.10 units (timescale=0.985).
Factorization parameters were as follows:
n: 27362623708437501481435967480647416522582967037243405954798475215929239453117920160504986430683801273
m: 200000000000000000000000
deg: 5
c5: 275
c0: -28
skew: 0.63
type: snfs
lss: 1
rlim: 670000
alim: 670000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 670000/670000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [335000, 535001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 79136 x 79384
Total sieving time: 1.08 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,118.000,5,0,0,0,0,0,0,0,0,670000,670000,25,25,45,45,2.2,2.2,50000
total time: 1.12 hours.
 --------- CPU info (if available) ----------

(65·10¹¹⁵+61)/9 = 7(2)₁₁₄9_<116> = 205397 · C111

C111 = P42 · P70

P42 = 328435207543886906309884067988371073769559_<42>

P70 = 1070599521074343091789542842721123619754026479476702613661538459978023_<70>

Number: 72229_115
N=351622575900437797154886498937288384067061457675731496673379953077319640609269961207915511045547024650906401857
  ( 111 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=328435207543886906309884067988371073769559 (pp42)
 r2=1070599521074343091789542842721123619754026479476702613661538459978023 (pp70)
Version: Msieve v. 1.43
Total time: 2.15 hours.
Scaled time: 1.69 units (timescale=0.786).
Factorization parameters were as follows:
n: 351622575900437797154886498937288384067061457675731496673379953077319640609269961207915511045547024650906401857
m: 100000000000000000000000
deg: 5
c5: 65
c0: 61
skew: 0.99
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 560001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 71961 x 72186
Total sieving time: 2.09 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,116.000,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 2.15 hours.
 --------- CPU info (if available) ----------

(65·10¹¹⁷+61)/9 = 7(2)₁₁₆9_<118> = 47 · 55405520323687_<14> · C103

C103 = P38 · P65

P38 = 42093341119931891329454249457027079313_<38>

P65 = 65888034547824796575698532984997713657408166425194274082537404797_<65>

Number: 72229_117
N=2773447513943446569817561422303395282509228786333955391050715933373497446320373021357915263447705664461
  ( 103 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=42093341119931891329454249457027079313 (pp38)
 r2=65888034547824796575698532984997713657408166425194274082537404797 (pp65)
Version: Msieve-1.40
Total time: 1.41 hours.
Scaled time: 1.34 units (timescale=0.948).
Factorization parameters were as follows:
n: 2773447513943446569817561422303395282509228786333955391050715933373497446320373021357915263447705664461
m: 500000000000000000000000
deg: 5
c5: 52
c0: 1525
skew: 1.97
type: snfs
lss: 1
rlim: 710000
alim: 710000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 710000/710000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [355000, 605001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 90219 x 90444
Total sieving time: 1.34 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,120.000,5,0,0,0,0,0,0,0,0,710000,710000,25,25,46,46,2.2,2.2,50000
total time: 1.41 hours.
 --------- CPU info (if available) ----------

Oct 28, 2009

By Lionel Debroux / GMP-ECM

Factorizations of 722...229 and Factorizations of 733...331 have been extended up to n=200. Composite numbers that appeared newly have passed 150 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 27, 2009 (8th)

By Robert Backstrom / Msieve, GGNFS / Oct 27, 2009

(73·10²²⁸-1)/9 = 8(1)₂₂₈_<229> = C229

C229 = P95 · P134

P95 = 82040674460345276418092109635781689113066914859498489130035782209201051170000071099537504824993_<95>

P134 = 98866948187166021079702228415749082839158698719028540432556084739146464048408908049274520025910320723752161628884636948875147203809127_<134>

Sieving ~ 240 CPU days + 203 hrs Lanczos with Msieve 1.42

Sun Oct 18 23:45:19 2009  
Sun Oct 18 23:45:19 2009  
Sun Oct 18 23:45:19 2009  Msieve v. 1.42
Sun Oct 18 23:45:19 2009  random seeds: 6d66a88d 9990fcd1
Sun Oct 18 23:45:19 2009  factoring 8111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 (229 digits)
Sun Oct 18 23:45:21 2009  no P-1/P+1/ECM available, skipping
Sun Oct 18 23:45:21 2009  commencing number field sieve (229-digit input)
Sun Oct 18 23:45:21 2009  R0: -100000000000000000000000000000000000000
Sun Oct 18 23:45:21 2009  R1:  1
Sun Oct 18 23:45:21 2009  A0: -1
Sun Oct 18 23:45:21 2009  A1:  0
Sun Oct 18 23:45:21 2009  A2:  0
Sun Oct 18 23:45:21 2009  A3:  0
Sun Oct 18 23:45:21 2009  A4:  0
Sun Oct 18 23:45:21 2009  A5:  0
Sun Oct 18 23:45:21 2009  A6:  73
Sun Oct 18 23:45:21 2009  skew 1.00, size 2.476818e-11, alpha 1.224717, combined = 1.221636e-12
Sun Oct 18 23:45:21 2009  
Sun Oct 18 23:45:21 2009  commencing relation filtering
Sun Oct 18 23:45:21 2009  estimated available RAM is 7924.4 MB
Sun Oct 18 23:45:21 2009  commencing duplicate removal, pass 1
Sun Oct 18 23:45:36 2009  error -11 reading relation 2694508
Sun Oct 18 23:45:37 2009  error -15 reading relation 2872732
Sun Oct 18 23:46:12 2009  error -11 reading relation 9214336
Sun Oct 18 23:46:56 2009  error -11 reading relation 17266893
Sun Oct 18 23:47:08 2009  error -11 reading relation 19445707
Sun Oct 18 23:47:49 2009  error -11 reading relation 26762938
Sun Oct 18 23:48:17 2009  error -11 reading relation 31897864
Sun Oct 18 23:48:20 2009  error -11 reading relation 32438426
Sun Oct 18 23:48:24 2009  error -11 reading relation 33197093
Sun Oct 18 23:48:36 2009  error -11 reading relation 35426385
Sun Oct 18 23:49:25 2009  error -11 reading relation 43496383
Sun Oct 18 23:50:28 2009  error -11 reading relation 55107936
Sun Oct 18 23:51:15 2009  error -11 reading relation 60505135
Sun Oct 18 23:51:38 2009  error -6 reading relation 64394186
Sun Oct 18 23:51:50 2009  error -11 reading relation 66647536
Sun Oct 18 23:52:00 2009  error -11 reading relation 68358255
Sun Oct 18 23:52:09 2009  error -6 reading relation 70104845
Sun Oct 18 23:52:57 2009  error -11 reading relation 78093580
Sun Oct 18 23:53:09 2009  error -11 reading relation 80154003
Sun Oct 18 23:53:26 2009  error -11 reading relation 83269566
Sun Oct 18 23:53:38 2009  error -11 reading relation 85439373
Sun Oct 18 23:53:57 2009  error -11 reading relation 88668784
Sun Oct 18 23:54:02 2009  error -11 reading relation 89540526
Sun Oct 18 23:54:06 2009  found 15179751 hash collisions in 90256777 relations
Sun Oct 18 23:54:22 2009  commencing duplicate removal, pass 2
Sun Oct 18 23:55:57 2009  found 14787900 duplicates and 75468877 unique relations
Sun Oct 18 23:55:57 2009  memory use: 426.4 MB
Sun Oct 18 23:55:57 2009  reading ideals above 83951616
Sun Oct 18 23:55:57 2009  commencing singleton removal, initial pass
Mon Oct 19 00:04:47 2009  memory use: 1193.5 MB
Mon Oct 19 00:04:47 2009  reading all ideals from disk
Mon Oct 19 00:04:55 2009  memory use: 1253.5 MB
Mon Oct 19 00:05:02 2009  commencing in-memory singleton removal
Mon Oct 19 00:05:09 2009  begin with 75468877 relations and 71429593 unique ideals
Mon Oct 19 00:06:20 2009  reduce to 33368308 relations and 23102541 ideals in 19 passes
Mon Oct 19 00:06:20 2009  max relations containing the same ideal: 28
Mon Oct 19 00:06:25 2009  reading ideals above 720000
Mon Oct 19 00:06:25 2009  commencing singleton removal, initial pass
Mon Oct 19 00:11:51 2009  memory use: 596.8 MB
Mon Oct 19 00:11:52 2009  reading all ideals from disk
Mon Oct 19 00:11:59 2009  memory use: 1246.6 MB
Mon Oct 19 00:12:08 2009  keeping 32677867 ideals with weight <= 200, target excess is 174639
Mon Oct 19 00:12:16 2009  commencing in-memory singleton removal
Mon Oct 19 00:12:24 2009  begin with 33368308 relations and 32677867 unique ideals
Mon Oct 19 00:14:33 2009  reduce to 33118187 relations and 32426869 ideals in 16 passes
Mon Oct 19 00:14:33 2009  max relations containing the same ideal: 200
Mon Oct 19 00:15:09 2009  removing 2785840 relations and 2541472 ideals in 244368 cliques
Mon Oct 19 00:15:10 2009  commencing in-memory singleton removal
Mon Oct 19 00:15:18 2009  begin with 30332347 relations and 32426869 unique ideals
Mon Oct 19 00:16:45 2009  reduce to 30140693 relations and 29691582 ideals in 12 passes
Mon Oct 19 00:16:45 2009  max relations containing the same ideal: 196
Mon Oct 19 00:17:17 2009  removing 2018847 relations and 1774479 ideals in 244368 cliques
Mon Oct 19 00:17:18 2009  commencing in-memory singleton removal
Mon Oct 19 00:17:25 2009  begin with 28121846 relations and 29691582 unique ideals
Mon Oct 19 00:18:19 2009  reduce to 28011472 relations and 27805669 ideals in 8 passes
Mon Oct 19 00:18:19 2009  max relations containing the same ideal: 187
Mon Oct 19 00:18:58 2009  relations with 0 large ideals: 6501
Mon Oct 19 00:18:58 2009  relations with 1 large ideals: 1045
Mon Oct 19 00:18:58 2009  relations with 2 large ideals: 6849
Mon Oct 19 00:18:58 2009  relations with 3 large ideals: 76396
Mon Oct 19 00:18:58 2009  relations with 4 large ideals: 501001
Mon Oct 19 00:18:58 2009  relations with 5 large ideals: 1974881
Mon Oct 19 00:18:58 2009  relations with 6 large ideals: 4825536
Mon Oct 19 00:18:58 2009  relations with 7+ large ideals: 20619263
Mon Oct 19 00:18:58 2009  commencing 2-way merge
Mon Oct 19 00:19:39 2009  reduce to 16924970 relation sets and 16719168 unique ideals
Mon Oct 19 00:19:39 2009  ignored 1 oversize relation sets
Mon Oct 19 00:19:39 2009  commencing full merge
Mon Oct 19 00:27:27 2009  memory use: 2107.1 MB
Mon Oct 19 00:27:30 2009  found 8999888 cycles, need 8981368
Mon Oct 19 00:27:36 2009  weight of 8981368 cycles is about 629038424 (70.04/cycle)
Mon Oct 19 00:27:36 2009  distribution of cycle lengths:
Mon Oct 19 00:27:36 2009  1 relations: 1407270
Mon Oct 19 00:27:36 2009  2 relations: 1249187
Mon Oct 19 00:27:36 2009  3 relations: 1131311
Mon Oct 19 00:27:36 2009  4 relations: 950440
Mon Oct 19 00:27:36 2009  5 relations: 792936
Mon Oct 19 00:27:36 2009  6 relations: 650379
Mon Oct 19 00:27:36 2009  7 relations: 540476
Mon Oct 19 00:27:36 2009  8 relations: 441114
Mon Oct 19 00:27:36 2009  9 relations: 358546
Mon Oct 19 00:27:36 2009  10+ relations: 1459709
Mon Oct 19 00:27:36 2009  heaviest cycle: 28 relations
Mon Oct 19 00:27:38 2009  commencing cycle optimization
Mon Oct 19 00:28:01 2009  start with 49064201 relations
Mon Oct 19 00:29:42 2009  pruned 1034355 relations
Mon Oct 19 00:29:42 2009  memory use: 1642.5 MB
Mon Oct 19 00:29:43 2009  distribution of cycle lengths:
Mon Oct 19 00:29:43 2009  1 relations: 1407270
Mon Oct 19 00:29:43 2009  2 relations: 1273515
Mon Oct 19 00:29:43 2009  3 relations: 1165835
Mon Oct 19 00:29:43 2009  4 relations: 965226
Mon Oct 19 00:29:43 2009  5 relations: 804038
Mon Oct 19 00:29:43 2009  6 relations: 654272
Mon Oct 19 00:29:43 2009  7 relations: 539463
Mon Oct 19 00:29:43 2009  8 relations: 435494
Mon Oct 19 00:29:43 2009  9 relations: 353137
Mon Oct 19 00:29:43 2009  10+ relations: 1383118
Mon Oct 19 00:29:43 2009  heaviest cycle: 28 relations
Mon Oct 19 00:30:03 2009  RelProcTime: 2682
Mon Oct 19 00:30:03 2009  
Mon Oct 19 00:30:03 2009  commencing linear algebra
Mon Oct 19 00:30:10 2009  read 8981368 cycles
Mon Oct 19 00:30:29 2009  cycles contain 27737847 unique relations
Mon Oct 19 00:33:24 2009  read 27737847 relations
Mon Oct 19 00:34:16 2009  using 20 quadratic characters above 1073741672
Mon Oct 19 00:36:34 2009  building initial matrix
Mon Oct 19 00:42:04 2009  memory use: 3378.6 MB
Mon Oct 19 00:42:10 2009  read 8981368 cycles
Mon Oct 19 00:42:15 2009  matrix is 8981191 x 8981368 (2704.3 MB) with weight 782303917 (87.10/col)
Mon Oct 19 00:42:15 2009  sparse part has weight 610125085 (67.93/col)
Mon Oct 19 00:44:22 2009  filtering completed in 2 passes
Mon Oct 19 00:44:24 2009  matrix is 8977172 x 8977349 (2704.0 MB) with weight 782193362 (87.13/col)
Mon Oct 19 00:44:24 2009  sparse part has weight 610095193 (67.96/col)
Mon Oct 19 00:45:05 2009  read 8977349 cycles
Mon Oct 19 00:45:10 2009  matrix is 8977172 x 8977349 (2704.0 MB) with weight 782193362 (87.13/col)
Mon Oct 19 00:45:10 2009  sparse part has weight 610095193 (67.96/col)
Mon Oct 19 00:45:10 2009  saving the first 48 matrix rows for later
Mon Oct 19 00:45:14 2009  matrix is 8977124 x 8977349 (2578.3 MB) with weight 627869172 (69.94/col)
Mon Oct 19 00:45:14 2009  sparse part has weight 586117479 (65.29/col)
Mon Oct 19 00:45:14 2009  matrix includes 64 packed rows
Mon Oct 19 00:45:14 2009  using block size 65536 for processor cache size 6144 kB
Mon Oct 19 00:45:49 2009  commencing Lanczos iteration (4 threads)
Mon Oct 19 00:45:49 2009  memory use: 2813.4 MB
Tue Oct 27 11:21:10 2009  lanczos halted after 141967 iterations (dim = 8977122)
Tue Oct 27 11:21:29 2009  recovered 30 nontrivial dependencies
Tue Oct 27 11:21:30 2009  BLanczosTime: 730287
Tue Oct 27 11:21:30 2009  
Tue Oct 27 11:21:30 2009  commencing square root phase
Tue Oct 27 11:21:30 2009  reading relations for dependency 1
Tue Oct 27 11:21:32 2009  read 4490596 cycles
Tue Oct 27 11:21:42 2009  cycles contain 16870428 unique relations
Tue Oct 27 11:23:42 2009  read 16870428 relations
Tue Oct 27 11:25:27 2009  multiplying 13873600 relations
Tue Oct 27 12:05:42 2009  multiply complete, coefficients have about 419.03 million bits
Tue Oct 27 12:05:46 2009  initial square root is modulo 33011653
Tue Oct 27 13:04:31 2009  sqrtTime: 6181
Tue Oct 27 13:04:31 2009  prp95 factor: 82040674460345276418092109635781689113066914859498489130035782209201051170000071099537504824993
Tue Oct 27 13:04:31 2009  prp134 factor: 98866948187166021079702228415749082839158698719028540432556084739146464048408908049274520025910320723752161628884636948875147203809127
Tue Oct 27 13:04:31 2009  elapsed time 205:19:12

c229 is the largest composite number which was factored by SNFS in our tables so far. Congratulations!

(14·10¹⁷³-17)/3 = 4(6)₁₇₂1_<174> = 13 · 859 · 5998697 · 13845991 · 409103341929942277576340139824293_<33> · C124

C124 = P55 · P69

P55 = 4187044847170696975495032484814703095237037002928822757_<55>

P69 = 293730235942494492861511218837078094643977016140350496314412187630029_<69>

Number: n
N=1229861670861254617548494925913918290044304120418280776400992158432398260682671962391119989681635502520909226281982831769953
  ( 124 digits)
Divisors found:

Wed Oct 28 01:20:11 2009  prp55 factor: 4187044847170696975495032484814703095237037002928822757
Wed Oct 28 01:20:11 2009  prp69 factor: 293730235942494492861511218837078094643977016140350496314412187630029
Wed Oct 28 01:20:11 2009  elapsed time 02:55:22 (Msieve 1.43 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.12 hours.
Scaled time: 44.11 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_6_172_1
n: 1229861670861254617548494925913918290044304120418280776400992158432398260682671962391119989681635502520909226281982831769953
Y0: -679980794164857001434425
Y1:  20228359617079
c0:  574058941022120395736367581472
c1:  15189963738966010296654600
c2: -20437377482172436876
c3: -1303581716936282
c4:  1749624141
c5:  8460
skew: 186678.04
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 5100269)
Primes: RFBsize:348513, AFBsize:349151, largePrimes:15654479 encountered
Relations: rels:14625624, finalFF:735763
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1637074 hash collisions in 15982632 relations
Msieve: matrix is 846990 x 847215 (231.9 MB)

Total sieving time: 23.66 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,28,28,56,56,2.4,2.4,60000
total time: 24.12 hours.
 --------- CPU info (if available) ----------

Oct 27, 2009 (7th)

By Sinkiti Sibata / Msieve, GGNFS / Oct 27, 2009

(65·10¹⁵⁷-11)/9 = 7(2)₁₅₆1_<158> = 467 · 881 · 34893421 · 76139466457_<11> · 45062034422087_<14> · 16026975876783402520793945195297_<32> · C89

C89 = P37 · P53

P37 = 2781337945606846567176996666297459217_<37>

P53 = 32893382824650786898544395629261720525621863468742293_<53>

ue Oct 27 07:50:11 2009  Msieve v. 1.42
Tue Oct 27 07:50:11 2009  random seeds: f5d8dff7 b54d31b6
Tue Oct 27 07:50:11 2009  factoring 91487613809573751425008504937197311213425423081348495271434108401057020019688124450564581 (89 digits)
Tue Oct 27 07:50:13 2009  no P-1/P+1/ECM available, skipping
Tue Oct 27 07:50:13 2009  commencing quadratic sieve (89-digit input)
Tue Oct 27 07:50:13 2009  using multiplier of 5
Tue Oct 27 07:50:13 2009  using 64kb Pentium 4 sieve core
Tue Oct 27 07:50:13 2009  sieve interval: 17 blocks of size 65536
Tue Oct 27 07:50:13 2009  processing polynomials in batches of 6
Tue Oct 27 07:50:13 2009  using a sieve bound of 1561823 (59333 primes)
Tue Oct 27 07:50:13 2009  using large prime bound of 124945840 (26 bits)
Tue Oct 27 07:50:13 2009  using double large prime bound of 375058674136800 (42-49 bits)
Tue Oct 27 07:50:13 2009  using trial factoring cutoff of 49 bits
Tue Oct 27 07:50:13 2009  polynomial 'A' values have 11 factors
Tue Oct 27 09:57:07 2009  59872 relations (15645 full + 44227 combined from 638789 partial), need 59429
Tue Oct 27 09:57:09 2009  begin with 654434 relations
Tue Oct 27 09:57:10 2009  reduce to 147759 relations in 9 passes
Tue Oct 27 09:57:10 2009  attempting to read 147759 relations
Tue Oct 27 09:57:14 2009  recovered 147759 relations
Tue Oct 27 09:57:14 2009  recovered 127871 polynomials
Tue Oct 27 09:57:14 2009  attempting to build 59872 cycles
Tue Oct 27 09:57:14 2009  found 59872 cycles in 6 passes
Tue Oct 27 09:57:14 2009  distribution of cycle lengths:
Tue Oct 27 09:57:14 2009     length 1 : 15645
Tue Oct 27 09:57:14 2009     length 2 : 11335
Tue Oct 27 09:57:14 2009     length 3 : 10329
Tue Oct 27 09:57:14 2009     length 4 : 8029
Tue Oct 27 09:57:14 2009     length 5 : 5649
Tue Oct 27 09:57:14 2009     length 6 : 3678
Tue Oct 27 09:57:14 2009     length 7 : 2279
Tue Oct 27 09:57:14 2009     length 9+: 2928
Tue Oct 27 09:57:14 2009  largest cycle: 18 relations
Tue Oct 27 09:57:14 2009  matrix is 59333 x 59872 (15.0 MB) with weight 3697274 (61.75/col)
Tue Oct 27 09:57:14 2009  sparse part has weight 3697274 (61.75/col)
Tue Oct 27 09:57:16 2009  filtering completed in 3 passes
Tue Oct 27 09:57:16 2009  matrix is 55708 x 55771 (14.0 MB) with weight 3439964 (61.68/col)
Tue Oct 27 09:57:16 2009  sparse part has weight 3439964 (61.68/col)
Tue Oct 27 09:57:16 2009  saving the first 48 matrix rows for later
Tue Oct 27 09:57:16 2009  matrix is 55660 x 55771 (10.7 MB) with weight 2917754 (52.32/col)
Tue Oct 27 09:57:16 2009  sparse part has weight 2471995 (44.32/col)
Tue Oct 27 09:57:16 2009  matrix includes 64 packed rows
Tue Oct 27 09:57:16 2009  using block size 21845 for processor cache size 512 kB
Tue Oct 27 09:57:17 2009  commencing Lanczos iteration
Tue Oct 27 09:57:17 2009  memory use: 9.9 MB
Tue Oct 27 09:57:50 2009  lanczos halted after 881 iterations (dim = 55654)
Tue Oct 27 09:57:50 2009  recovered 15 nontrivial dependencies
Tue Oct 27 09:57:54 2009  prp37 factor: 2781337945606846567176996666297459217
Tue Oct 27 09:57:54 2009  prp53 factor: 32893382824650786898544395629261720525621863468742293
Tue Oct 27 09:57:54 2009  elapsed time 02:07:43

(62·10¹⁴³-71)/9 = 6(8)₁₄₂1_<144> = 3³ · 213480877273187_<15> · C129

C129 = P51 · P79

P51 = 103755478159889828751485057885748821715212892879557_<51>

P79 = 1151901651383832725319629282005586242558015694434569307514321563885225997402317_<79>

Number: 68881_143
N=119516106632496283665894694538282365100792261988213590436675492772858536245889750978063107224994882728409718860150351667953733569
  ( 129 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=103755478159889828751485057885748821715212892879557 (pp51)
 r2=1151901651383832725319629282005586242558015694434569307514321563885225997402317 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 21.93 hours.
Scaled time: 43.67 units (timescale=1.991).
Factorization parameters were as follows:
name: 68881_143
n: 119516106632496283665894694538282365100792261988213590436675492772858536245889750978063107224994882728409718860150351667953733569
m: 50000000000000000000000000000
deg: 5
c5: 496
c0: -1775
skew: 1.29
type: snfs
lss: 1
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [955000, 2855001)
Primes: RFBsize:142718, AFBsize:142742, largePrimes:4317703 encountered
Relations: rels:4561580, finalFF:361745
Max relations in full relation-set: 28
Initial matrix: 285527 x 361745 with sparse part having weight 41726282.
Pruned matrix : 260885 x 262376 with weight 28387579.
Total sieving time: 20.68 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.99 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 21.93 hours.
 --------- CPU info (if available) ----------

(61·10¹⁴²+11)/9 = 6(7)₁₄₁9_<143> = 3 · 33353 · 19906792880765389_<17> · C122

C122 = P34 · P88

P34 = 6333596761890210427769088539424107_<34>

P88 = 5372537550577884027041044748259697776204681547417165620095560642583786697767311429280647_<88>

Number: 67779_142
N=34027486433473648903006226725877484429114615245532918207296038291178904927843612374299078287204050202839724770542660357229
  ( 122 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=6333596761890210427769088539424107 (pp34)
 r2=5372537550577884027041044748259697776204681547417165620095560642583786697767311429280647 (pp88)
Version: Msieve-1.40
Total time: 11.35 hours.
Scaled time: 23.67 units (timescale=2.085).
Factorization parameters were as follows:
name: 67779_142
n: 34027486433473648903006226725877484429114615245532918207296038291178904927843612374299078287204050202839724770542660357229
m: 50000000000000000000000000000
deg: 5
c5: 244
c0: 1375
skew: 1.41
type: snfs
lss: 1
rlim: 1890000
alim: 1890000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1890000/1890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [945000, 2345001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 315046 x 315276
Total sieving time: 10.88 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,145.000,5,0,0,0,0,0,0,0,0,1890000,1890000,26,26,49,49,2.3,2.3,100000
total time: 11.35 hours.
 --------- CPU info (if available) ----------

(65·10¹⁰⁹-11)/9 = 7(2)₁₀₈1_<110> = 52391597 · 2542076848723_<13> · C90

C90 = P33 · P58

P33 = 137580139588561846772155174238321_<33>

P58 = 3941529571374024940821143658563287380985182879516137168171_<58>

Tue Oct 27 14:22:59 2009  Msieve v. 1.42
Tue Oct 27 14:22:59 2009  random seeds: e7404b6c 37a5d6c9
Tue Oct 27 14:22:59 2009  factoring 542276188622082695982597047253643601927608428763762474084725223935309903592111092809680891 (90 digits)
Tue Oct 27 14:22:59 2009  searching for 15-digit factors
Tue Oct 27 14:23:00 2009  commencing quadratic sieve (90-digit input)
Tue Oct 27 14:23:00 2009  using multiplier of 1
Tue Oct 27 14:23:00 2009  using 32kb Intel Core sieve core
Tue Oct 27 14:23:00 2009  sieve interval: 36 blocks of size 32768
Tue Oct 27 14:23:00 2009  processing polynomials in batches of 6
Tue Oct 27 14:23:00 2009  using a sieve bound of 1618559 (61176 primes)
Tue Oct 27 14:23:00 2009  using large prime bound of 135958956 (27 bits)
Tue Oct 27 14:23:00 2009  using double large prime bound of 436650541653060 (42-49 bits)
Tue Oct 27 14:23:00 2009  using trial factoring cutoff of 49 bits
Tue Oct 27 14:23:00 2009  polynomial 'A' values have 11 factors
Tue Oct 27 15:37:19 2009  61746 relations (16189 full + 45557 combined from 673042 partial), need 61272
Tue Oct 27 15:37:20 2009  begin with 689231 relations
Tue Oct 27 15:37:21 2009  reduce to 152393 relations in 13 passes
Tue Oct 27 15:37:21 2009  attempting to read 152393 relations
Tue Oct 27 15:37:22 2009  recovered 152393 relations
Tue Oct 27 15:37:23 2009  recovered 129486 polynomials
Tue Oct 27 15:37:23 2009  attempting to build 61746 cycles
Tue Oct 27 15:37:23 2009  found 61746 cycles in 6 passes
Tue Oct 27 15:37:23 2009  distribution of cycle lengths:
Tue Oct 27 15:37:23 2009     length 1 : 16189
Tue Oct 27 15:37:23 2009     length 2 : 11482
Tue Oct 27 15:37:23 2009     length 3 : 10776
Tue Oct 27 15:37:23 2009     length 4 : 8189
Tue Oct 27 15:37:23 2009     length 5 : 6077
Tue Oct 27 15:37:23 2009     length 6 : 3830
Tue Oct 27 15:37:23 2009     length 7 : 2326
Tue Oct 27 15:37:23 2009     length 9+: 2877
Tue Oct 27 15:37:23 2009  largest cycle: 18 relations
Tue Oct 27 15:37:23 2009  matrix is 61176 x 61746 (15.6 MB) with weight 3833340 (62.08/col)
Tue Oct 27 15:37:23 2009  sparse part has weight 3833340 (62.08/col)
Tue Oct 27 15:37:24 2009  filtering completed in 3 passes
Tue Oct 27 15:37:24 2009  matrix is 57219 x 57282 (14.4 MB) with weight 3554565 (62.05/col)
Tue Oct 27 15:37:24 2009  sparse part has weight 3554565 (62.05/col)
Tue Oct 27 15:37:24 2009  saving the first 48 matrix rows for later
Tue Oct 27 15:37:24 2009  matrix is 57171 x 57282 (10.9 MB) with weight 2991811 (52.23/col)
Tue Oct 27 15:37:24 2009  sparse part has weight 2516615 (43.93/col)
Tue Oct 27 15:37:24 2009  matrix includes 64 packed rows
Tue Oct 27 15:37:24 2009  using block size 22912 for processor cache size 1024 kB
Tue Oct 27 15:37:25 2009  commencing Lanczos iteration
Tue Oct 27 15:37:25 2009  memory use: 10.1 MB
Tue Oct 27 15:37:47 2009  lanczos halted after 906 iterations (dim = 57169)
Tue Oct 27 15:37:47 2009  recovered 17 nontrivial dependencies
Tue Oct 27 15:37:48 2009  prp33 factor: 137580139588561846772155174238321
Tue Oct 27 15:37:48 2009  prp58 factor: 3941529571374024940821143658563287380985182879516137168171
Tue Oct 27 15:37:48 2009  elapsed time 01:14:49

(65·10¹²²+7)/9 = 7(2)₁₂₁3_<123> = 3² · 103 · 241 · 1237726493_<10> · 38487393601_<11> · C98

C98 = P44 · P55

P44 = 11234321827921433174867669812024514743374959_<44>

P55 = 6040654844216834979500238535767959586811972858326905147_<55>

Number: 72223_122
N=67862660571324533702443114986666233918366106026626913499884976055568855064095612384649480248013973
  ( 98 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=11234321827921433174867669812024514743374959 (pp44)
 r2=6040654844216834979500238535767959586811972858326905147 (pp55)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.78 hours.
Scaled time: 5.49 units (timescale=1.977).
Factorization parameters were as follows:
name: 72223_122
n: 67862660571324533702443114986666233918366106026626913499884976055568855064095612384649480248013973
m: 5000000000000000000000000
deg: 5
c5: 52
c0: 175
skew: 1.27
type: snfs
lss: 1
rlim: 850000
alim: 850000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 850000/850000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [425000, 675001)
Primes: RFBsize:67617, AFBsize:67460, largePrimes:2468450 encountered
Relations: rels:2389203, finalFF:214856
Max relations in full relation-set: 28
Initial matrix: 135144 x 214856 with sparse part having weight 16202448.
Pruned matrix : 112573 x 113312 with weight 5963078.
Total sieving time: 2.61 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,850000,850000,26,26,46,46,2.3,2.3,50000
total time: 2.78 hours.
 --------- CPU info (if available) ----------

(65·10¹⁶¹+7)/9 = 7(2)₁₆₀3_<162> = 3 · 73 · 4787 · 197829613 · 123623015233_<12> · 46276777179460717_<17> · 63995894158538638194695901113_<29> · C91

C91 = P40 · P52

P40 = 2848409643006055036625993604980263881331_<40>

P52 = 3339296686306871044335539412177570631478147640034229_<52>

Tue Oct 27 16:31:08 2009  Msieve v. 1.42
Tue Oct 27 16:31:08 2009  random seeds: b1198b50 756956c1
Tue Oct 27 16:31:08 2009  factoring 9511684882134657103583478171233840687877877382184865824492238380051531346401527161234078799 (91 digits)
Tue Oct 27 16:31:09 2009  searching for 15-digit factors
Tue Oct 27 16:31:10 2009  commencing quadratic sieve (91-digit input)
Tue Oct 27 16:31:10 2009  using multiplier of 23
Tue Oct 27 16:31:10 2009  using 32kb Intel Core sieve core
Tue Oct 27 16:31:10 2009  sieve interval: 36 blocks of size 32768
Tue Oct 27 16:31:10 2009  processing polynomials in batches of 6
Tue Oct 27 16:31:10 2009  using a sieve bound of 1753553 (65751 primes)
Tue Oct 27 16:31:10 2009  using large prime bound of 177108853 (27 bits)
Tue Oct 27 16:31:10 2009  using double large prime bound of 702801048059511 (42-50 bits)
Tue Oct 27 16:31:10 2009  using trial factoring cutoff of 50 bits
Tue Oct 27 16:31:10 2009  polynomial 'A' values have 12 factors
Tue Oct 27 18:27:20 2009  65975 relations (16850 full + 49125 combined from 800521 partial), need 65847
Tue Oct 27 18:27:21 2009  begin with 817371 relations
Tue Oct 27 18:27:22 2009  reduce to 165324 relations in 10 passes
Tue Oct 27 18:27:22 2009  attempting to read 165324 relations
Tue Oct 27 18:27:24 2009  recovered 165324 relations
Tue Oct 27 18:27:24 2009  recovered 147877 polynomials
Tue Oct 27 18:27:25 2009  attempting to build 65975 cycles
Tue Oct 27 18:27:25 2009  found 65975 cycles in 6 passes
Tue Oct 27 18:27:25 2009  distribution of cycle lengths:
Tue Oct 27 18:27:25 2009     length 1 : 16850
Tue Oct 27 18:27:25 2009     length 2 : 12355
Tue Oct 27 18:27:25 2009     length 3 : 11631
Tue Oct 27 18:27:25 2009     length 4 : 8792
Tue Oct 27 18:27:25 2009     length 5 : 6353
Tue Oct 27 18:27:25 2009     length 6 : 4131
Tue Oct 27 18:27:25 2009     length 7 : 2598
Tue Oct 27 18:27:25 2009     length 9+: 3265
Tue Oct 27 18:27:25 2009  largest cycle: 22 relations
Tue Oct 27 18:27:25 2009  matrix is 65751 x 65975 (16.1 MB) with weight 3946793 (59.82/col)
Tue Oct 27 18:27:25 2009  sparse part has weight 3946793 (59.82/col)
Tue Oct 27 18:27:26 2009  filtering completed in 3 passes
Tue Oct 27 18:27:26 2009  matrix is 62108 x 62171 (15.2 MB) with weight 3745410 (60.24/col)
Tue Oct 27 18:27:26 2009  sparse part has weight 3745410 (60.24/col)
Tue Oct 27 18:27:26 2009  saving the first 48 matrix rows for later
Tue Oct 27 18:27:26 2009  matrix is 62060 x 62171 (8.8 MB) with weight 2840677 (45.69/col)
Tue Oct 27 18:27:26 2009  sparse part has weight 1934538 (31.12/col)
Tue Oct 27 18:27:26 2009  matrix includes 64 packed rows
Tue Oct 27 18:27:26 2009  using block size 24868 for processor cache size 1024 kB
Tue Oct 27 18:27:27 2009  commencing Lanczos iteration
Tue Oct 27 18:27:27 2009  memory use: 9.5 MB
Tue Oct 27 18:27:49 2009  lanczos halted after 983 iterations (dim = 62058)
Tue Oct 27 18:27:49 2009  recovered 16 nontrivial dependencies
Tue Oct 27 18:27:50 2009  prp40 factor: 2848409643006055036625993604980263881331
Tue Oct 27 18:27:50 2009  prp52 factor: 3339296686306871044335539412177570631478147640034229
Tue Oct 27 18:27:50 2009  elapsed time 01:56:42

(65·10¹⁴¹-11)/9 = 7(2)₁₄₀1_<142> = 3² · 71 · 145991 · 3380926859_<10> · 12718567937_<11> · 6088571724331250328637_<22> · C93

C93 = P34 · P59

P34 = 6943388399896641031086000361099687_<34>

P59 = 42587586623151738614250628439153952183704337824580960958877_<59>

Tue Oct 27 18:51:10 2009  Msieve v. 1.42
Tue Oct 27 18:51:10 2009  random seeds: 8c180bf0 06ebb811
Tue Oct 27 18:51:10 2009  factoring 295702154938785144292115280791360472969719657708376609043932299246578073523096330409704571499 (93 digits)
Tue Oct 27 18:51:11 2009  searching for 15-digit factors
Tue Oct 27 18:51:11 2009  commencing quadratic sieve (93-digit input)
Tue Oct 27 18:51:11 2009  using multiplier of 59
Tue Oct 27 18:51:11 2009  using 32kb Intel Core sieve core
Tue Oct 27 18:51:11 2009  sieve interval: 36 blocks of size 32768
Tue Oct 27 18:51:11 2009  processing polynomials in batches of 6
Tue Oct 27 18:51:11 2009  using a sieve bound of 1914637 (71765 primes)
Tue Oct 27 18:51:11 2009  using large prime bound of 231671077 (27 bits)
Tue Oct 27 18:51:11 2009  using double large prime bound of 1139644007123941 (42-51 bits)
Tue Oct 27 18:51:11 2009  using trial factoring cutoff of 51 bits
Tue Oct 27 18:51:11 2009  polynomial 'A' values have 12 factors
Tue Oct 27 21:14:42 2009  71939 relations (18409 full + 53530 combined from 952627 partial), need 71861
Tue Oct 27 21:14:43 2009  begin with 971036 relations
Tue Oct 27 21:14:44 2009  reduce to 182111 relations in 11 passes
Tue Oct 27 21:14:44 2009  attempting to read 182111 relations
Tue Oct 27 21:14:47 2009  recovered 182111 relations
Tue Oct 27 21:14:47 2009  recovered 164123 polynomials
Tue Oct 27 21:14:47 2009  attempting to build 71939 cycles
Tue Oct 27 21:14:47 2009  found 71939 cycles in 6 passes
Tue Oct 27 21:14:47 2009  distribution of cycle lengths:
Tue Oct 27 21:14:47 2009     length 1 : 18409
Tue Oct 27 21:14:47 2009     length 2 : 13122
Tue Oct 27 21:14:47 2009     length 3 : 12329
Tue Oct 27 21:14:47 2009     length 4 : 9818
Tue Oct 27 21:14:47 2009     length 5 : 6996
Tue Oct 27 21:14:47 2009     length 6 : 4630
Tue Oct 27 21:14:47 2009     length 7 : 2874
Tue Oct 27 21:14:47 2009     length 9+: 3761
Tue Oct 27 21:14:47 2009  largest cycle: 21 relations
Tue Oct 27 21:14:48 2009  matrix is 71765 x 71939 (18.4 MB) with weight 4526395 (62.92/col)
Tue Oct 27 21:14:48 2009  sparse part has weight 4526395 (62.92/col)
Tue Oct 27 21:14:49 2009  filtering completed in 3 passes
Tue Oct 27 21:14:49 2009  matrix is 67785 x 67848 (17.4 MB) with weight 4302286 (63.41/col)
Tue Oct 27 21:14:49 2009  sparse part has weight 4302286 (63.41/col)
Tue Oct 27 21:14:49 2009  saving the first 48 matrix rows for later
Tue Oct 27 21:14:49 2009  matrix is 67737 x 67848 (10.8 MB) with weight 3365472 (49.60/col)
Tue Oct 27 21:14:49 2009  sparse part has weight 2433869 (35.87/col)
Tue Oct 27 21:14:49 2009  matrix includes 64 packed rows
Tue Oct 27 21:14:49 2009  using block size 27139 for processor cache size 1024 kB
Tue Oct 27 21:14:50 2009  commencing Lanczos iteration
Tue Oct 27 21:14:50 2009  memory use: 11.1 MB
Tue Oct 27 21:15:20 2009  lanczos halted after 1073 iterations (dim = 67735)
Tue Oct 27 21:15:20 2009  recovered 17 nontrivial dependencies
Tue Oct 27 21:15:21 2009  prp34 factor: 6943388399896641031086000361099687
Tue Oct 27 21:15:21 2009  prp59 factor: 42587586623151738614250628439153952183704337824580960958877
Tue Oct 27 21:15:21 2009  elapsed time 02:24:11

Oct 27, 2009 (6th)

By Jo Yeong Uk / GMP-ECM / Oct 27, 2009

(64·10¹⁵²+17)/9 = 7(1)₁₅₁3_<153> = 31 · 2963 · 10369 · C144

C144 = P36 · P109

P36 = 283694462391482906919275678331316889_<36>

P109 = 2631821231403694835169657384499841538907632715198481209702013976288681679080749181540420214573026569499688181_<109>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 746633109353561737237420791374811444472516566080481664330335589383152179299440880191222604195404494840956714093295250625621585698340692598988909 (144 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5550384773
Step 1 took 4836ms
Step 2 took 4587ms
********** Factor found in step 2: 283694462391482906919275678331316889
Found probable prime factor of 36 digits: 283694462391482906919275678331316889
Probable prime cofactor 2631821231403694835169657384499841538907632715198481209702013976288681679080749181540420214573026569499688181 has 109 digits

(65·10¹³⁶-11)/9 = 7(2)₁₃₅1_<137> = 123427 · 1375629339975159871097_<22> · C111

C111 = P35 · P76

P35 = 62806303538900550603721255401770903_<35>

P76 = 6772609105223622686935968347184377631672554842728485633440352400986340351953_<76>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 425362543212996505062160779945012195556672752416538326291513581129682622441372293849259290070706914884494623559 (111 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6175954588
Step 1 took 2668ms
Step 2 took 1914ms
********** Factor found in step 2: 62806303538900550603721255401770903
Found probable prime factor of 35 digits: 62806303538900550603721255401770903
Probable prime cofactor 6772609105223622686935968347184377631672554842728485633440352400986340351953 has 76 digits

(65·10¹³⁸-11)/9 = 7(2)₁₃₇1_<139> = 3 · 17 · 103 · 773 · 5441 · C129

C129 = P33 · P97

P33 = 112083887363024514430569516904031_<33>

P97 = 2916500408302875083987535970330480585387768895593985589434940784587907313673484732150584806331979_<97>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 326892703258434457249483455127619453214466851802822900044820676463512268062759713949088227925259582699844814203345266405269307349 (129 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2474648913
Step 1 took 4228ms
Step 2 took 4227ms
********** Factor found in step 2: 112083887363024514430569516904031
Found probable prime factor of 33 digits: 112083887363024514430569516904031
Probable prime cofactor 2916500408302875083987535970330480585387768895593985589434940784587907313673484732150584806331979 has 97 digits

(65·10¹⁴⁰+7)/9 = 7(2)₁₃₉3_<141> = 3³ · 62547324597825074395248779_<26> · C114

C114 = P35 · P80

P35 = 22106601597297777135014061131159201_<35>

P80 = 19345339717907152871106612963136797155474171896145552677486729052119091953982231_<80>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 427659717908154394995200702825198766565175314645691050004375381571272656253058536994853204719480586679929186157431 (114 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=534140875
Step 1 took 3510ms
Step 2 took 3729ms
********** Factor found in step 2: 22106601597297777135014061131159201
Found probable prime factor of 35 digits: 22106601597297777135014061131159201
Probable prime cofactor 19345339717907152871106612963136797155474171896145552677486729052119091953982231 has 80 digits

Oct 27, 2009 (5th)

By Erik Branger / YAFU, Msieve, GGNFS / Oct 27, 2009

(65·10¹²¹-11)/9 = 7(2)₁₂₀1_<122> = 7963 · 534570376243_<12> · 73739065922107105379_<20> · C87

C87 = P42 · P45

P42 = 947352483431407184943321232710242057202163_<42>

P45 = 242873434001740665351347420833894420438989397_<45>

10/26/09 22:29:21 v1.12 @ ERIK-DATOR, starting SIQS on c87: 230086750861062990102879505215238593179218694592354480636195783944430374045677042465711
10/26/09 22:29:21 v1.12 @ ERIK-DATOR, random seeds: 678843804, 631501508
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, ==== sieve params ====
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, n = 88 digits, 290 bits
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, factor base: 58705 primes (max prime = 1550441)
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, single large prime cutoff: 170548510 (110 * pmax)
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, double large prime range from 43 to 50 bits
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, double large prime cutoff: 656638394910403
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, using 0 large prime slices of factor base
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, buckets hold 1024 elements
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, polynomial A has ~ 16860432 factors
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, using multiplier of 7
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, using small prime variation correction of 19 bits
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, trial factoring cutoff at 97 bits
10/26/09 22:29:22 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ====
10/26/09 22:53:27 v1.12 @ ERIK-DATOR, sieve time = 428.5008, relation time = 216.6216, poly_time = 749.0964
10/26/09 22:53:27 v1.12 @ ERIK-DATOR, 58825 relations found: 19764 full + 39061 from 557035 partial, using 39156060 polys (551 A polys)
10/26/09 22:53:27 v1.12 @ ERIK-DATOR, on average, sieving found 0.01 rels/poly and 398.98 rels/sec
10/26/09 22:53:27 v1.12 @ ERIK-DATOR, trial division touched 11945439 sieve locations out of 46190367866880
10/26/09 22:53:27 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ====
10/26/09 22:53:27 v1.12 @ ERIK-DATOR, begin with 576799 relations
10/26/09 22:53:28 v1.12 @ ERIK-DATOR, reduce to 121036 relations in 8 passes
10/26/09 22:53:33 v1.12 @ ERIK-DATOR, recovered 121036 relations
10/26/09 22:53:33 v1.12 @ ERIK-DATOR, recovered 98465 polynomials
10/26/09 22:53:33 v1.12 @ ERIK-DATOR, attempting to build 58825 cycles
10/26/09 22:53:33 v1.12 @ ERIK-DATOR, found 58825 cycles in 4 passes
10/26/09 22:53:33 v1.12 @ ERIK-DATOR, distribution of cycle lengths:
10/26/09 22:53:33 v1.12 @ ERIK-DATOR,    length 1 : 19764
10/26/09 22:53:33 v1.12 @ ERIK-DATOR,    length 2 : 15983
10/26/09 22:53:33 v1.12 @ ERIK-DATOR,    length 3 : 10840
10/26/09 22:53:33 v1.12 @ ERIK-DATOR,    length 4 : 6126
10/26/09 22:53:33 v1.12 @ ERIK-DATOR,    length 5 : 3262
10/26/09 22:53:33 v1.12 @ ERIK-DATOR,    length 6 : 1595
10/26/09 22:53:33 v1.12 @ ERIK-DATOR,    length 7 : 705
10/26/09 22:53:33 v1.12 @ ERIK-DATOR,    length 9+: 550
10/26/09 22:53:33 v1.12 @ ERIK-DATOR, largest cycle: 18 relations
10/26/09 22:53:33 v1.12 @ ERIK-DATOR, matrix is 58705 x 58825 (11.7 MB) with weight 2823437 (48.00/col)
10/26/09 22:53:33 v1.12 @ ERIK-DATOR, sparse part has weight 2823437 (48.00/col)
10/26/09 22:53:34 v1.12 @ ERIK-DATOR, filtering completed in 4 passes
10/26/09 22:53:34 v1.12 @ ERIK-DATOR, matrix is 51811 x 51875 (10.6 MB) with weight 2563413 (49.42/col)
10/26/09 22:53:34 v1.12 @ ERIK-DATOR, sparse part has weight 2563413 (49.42/col)
10/26/09 22:53:34 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later
10/26/09 22:53:34 v1.12 @ ERIK-DATOR, matrix is 51763 x 51875 (9.0 MB) with weight 2223575 (42.86/col)
10/26/09 22:53:34 v1.12 @ ERIK-DATOR, sparse part has weight 2036371 (39.26/col)
10/26/09 22:53:34 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows
10/26/09 22:53:34 v1.12 @ ERIK-DATOR, using block size 20750 for processor cache size 2048 kB
10/26/09 22:53:34 v1.12 @ ERIK-DATOR, commencing Lanczos iteration
10/26/09 22:53:34 v1.12 @ ERIK-DATOR, memory use: 8.0 MB
10/26/09 22:53:51 v1.12 @ ERIK-DATOR, lanczos halted after 820 iterations (dim = 51759)
10/26/09 22:53:51 v1.12 @ ERIK-DATOR, recovered 16 nontrivial dependencies
10/26/09 22:53:52 v1.12 @ ERIK-DATOR, prp45 = 242873434001740665351347420833894420438989397
10/26/09 22:53:56 v1.12 @ ERIK-DATOR, prp42 = 947352483431407184943321232710242057202163
10/26/09 22:53:56 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 23.8370 seconds.
10/26/09 22:53:56 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 5.6940 seconds.
10/26/09 22:53:56 v1.12 @ ERIK-DATOR, SIQS elapsed time = 1475.2452 seconds.

(65·10¹⁴⁰-11)/9 = 7(2)₁₃₉1_<141> = 7 · 241 · C138

C138 = P61 · P78

P61 = 1977175504445211461870746854270739911051029758911560186271011_<61>

P78 = 216526244460396024191855897937745004522218028630947175795677723021683328286153_<78>

Number: 72221_140
N=428110386616610683000724494500428110386616610683000724494500428110386616610683000724494500428110386616610683000724494500428110386616610683
  ( 138 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=1977175504445211461870746854270739911051029758911560186271011 (pp61)
 r2=216526244460396024191855897937745004522218028630947175795677723021683328286153 (pp78)
Version: Msieve-1.40
Total time: 5.60 hours.
Scaled time: 4.90 units (timescale=0.875).
Factorization parameters were as follows:
n: 428110386616610683000724494500428110386616610683000724494500428110386616610683000724494500428110386616610683000724494500428110386616610683
m: 10000000000000000000000000000
deg: 5
c5: 65
c0: -11
skew: 0.70
type: snfs
lss: 1
rlim: 1620000
alim: 1620000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3

Factor base limits: 1620000/1620000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [810000, 1610001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 234432 x 234658
Total sieving time: 5.39 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000
total time: 5.60 hours.
 --------- CPU info (if available) ----------

(65·10¹²⁹+7)/9 = 7(2)₁₂₈3_<130> = 73 · 2221 · 2567729 · C119

C119 = P44 · P75

P44 = 85683277507409068791600540542053437197885827_<44>

P75 = 202466964608723252374887795280215191067174586508857815139998546556449041857_<75>

Number: 72223_129
N=17348033114652005022752627590558703019224037688666980158306193742390894985894433406088781202803253598064633340230060739
  ( 119 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=85683277507409068791600540542053437197885827 (pp44)
 r2=202466964608723252374887795280215191067174586508857815139998546556449041857 (pp75)
Version: Msieve-1.40
Total time: 2.64 hours.
Scaled time: 2.63 units (timescale=0.995).
Factorization parameters were as follows:
n: 17348033114652005022752627590558703019224037688666980158306193742390894985894433406088781202803253598064633340230060739
m: 100000000000000000000000000
deg: 5
c5: 13
c0: 14
skew: 1.01
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 935001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 145078 x 145303
Total sieving time: 2.52 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 2.64 hours.
 --------- CPU info (if available) ----------

(65·10¹⁴¹+7)/9 = 7(2)₁₄₀3_<142> = 1407927869_<10> · C133

C133 = P53 · P81

P53 = 12049710125367851790960582688070194854908188364815339_<53>

P81 = 425709990455910147905908526532864228292366077716772356573508558892819462447043953_<81>

Number: 72223_141
N=5129681982466832057731092630443713606341165636960782557122762815502036363357349113047653027331489112118869650858670674003273261595067
  ( 133 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=12049710125367851790960582688070194854908188364815339 (pp53)
 r2=425709990455910147905908526532864228292366077716772356573508558892819462447043953 (pp81)
Version: Msieve v. 1.43
Total time: 11.54 hours.
Scaled time: 9.10 units (timescale=0.789).
Factorization parameters were as follows:
n: 5129681982466832057731092630443713606341165636960782557122762815502036363357349113047653027331489112118869650858670674003273261595067
m: 20000000000000000000000000000
deg: 5
c5: 325
c0: 112
skew: 0.81
type: snfs
lss: 1
rlim: 1760000
alim: 1760000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1760000/1760000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [880000, 1880001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 304431 x 304677
Total sieving time: 10.67 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.46 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,144.000,5,0,0,0,0,0,0,0,0,1760000,1760000,26,26,49,49,2.3,2.3,100000
total time: 11.54 hours.
 --------- CPU info (if available) ----------

(65·10¹⁰⁸-11)/9 = 7(2)₁₀₇1_<109> = 3 · 23 · 9033556013789_<13> · C95

C95 = P45 · P50

P45 = 135554491375990857956197246460694492102127861_<45>

P50 = 85476966858717394152054163418298515138093927220521_<50>

Number: 72221_108
N=11586786766895863381830670020753519733562146967072224373606260076037382144838546474453485035581
  ( 95 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=135554491375990857956197246460694492102127861 (pp45)
 r2=85476966858717394152054163418298515138093927220521 (pp50)
Version: Msieve-1.40
Total time: 0.59 hours.
Scaled time: 0.59 units (timescale=1.002).
Factorization parameters were as follows:
n: 11586786766895863381830670020753519733562146967072224373606260076037382144838546474453485035581
m: 5000000000000000000000
deg: 5
c5: 104
c0: -55
skew: 0.88
type: snfs
lss: 1
rlim: 490000
alim: 490000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 490000/490000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [245000, 345001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 45830 x 46055
Total sieving time: 0.56 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,110.000,5,0,0,0,0,0,0,0,0,490000,490000,25,25,44,44,2.2,2.2,50000
total time: 0.59 hours.
 --------- CPU info (if available) ----------

Oct 27, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve / Oct 27, 2009

(59·10¹⁸⁹+13)/9 = 6(5)₁₈₈7_<190> = 225241963 · 31687580934872183_<17> · 261849580258534788772143093627569_<33> · C133

C133 = P44 · P89

P44 = 84827586340642371205886492540524983243965279_<44>

P89 = 41350629053536239606694402476456416541139861065143806414400328891246290212348829620411783_<89>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2453899015
Step 1 took 38020ms
Step 2 took 14078ms
********** Factor found in step 2: 84827586340642371205886492540524983243965279
Found probable prime factor of 44 digits: 84827586340642371205886492540524983243965279
Probable prime cofactor 41350629053536239606694402476456416541139861065143806414400328891246290212348829620411783 has 89 digits

(11·10¹⁹³+1)/3 = 3(6)₁₉₂7_<194> = 37 · 1949 · C189

C189 = P49 · P65 · P76

P49 = 3877282014566842518519492328248181190291969603383_<49>

P65 = 92484341434178074305109486526779408950878040850072954005996360127_<65>

P76 = 1417954412002055454225203117654102106991785323552900390351400853029752285699_<76>

Number: 36667_193
N=508461257563361206254997943043094402766029241144684962027188810154433551047199071827086193427907127240118517696762950739348892247814772186244736270390452022057973828112360693171365310924059
  ( 189 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=3877282014566842518519492328248181190291969603383
 r2=92484341434178074305109486526779408950878040850072954005996360127
 r3=1417954412002055454225203117654102106991785323552900390351400853029752285699
Version: 
Total time: 548.33 hours.
Scaled time: 1104.89 units (timescale=2.015).
Factorization parameters were as follows:
n: 508461257563361206254997943043094402766029241144684962027188810154433551047199071827086193427907127240118517696762950739348892247814772186244736270390452022057973828112360693171365310924059
m: 500000000000000000000000000000000000000
deg: 5
c5: 88
c0: 25
skew: 0.78
type: snfs
lss: 1
rlim: 12700000
alim: 12700000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 12700000/12700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6350000, 12050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1962220 x 1962468
Total sieving time: 548.33 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,12700000,12700000,28,28,55,55,2.5,2.5,100000
total time: 548.33 hours.
 --------- CPU info (if available) ----------

(65·10¹⁸⁹+43)/9 = 7(2)₁₈₈7_<190> = 3 · 11 · C189

C189 = P93 · P96

P93 = 344169962009931548308268017081595995989862134133897845813087998330100327017231481133237154389_<93>

P96 = 635892852406752029790139607998304098096231541911114002251357000552628373073014289921768913242471_<96>

Number: 72227_189
N=218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855219
  ( 189 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=344169962009931548308268017081595995989862134133897845813087998330100327017231481133237154389
 r2=635892852406752029790139607998304098096231541911114002251357000552628373073014289921768913242471
Version: 
Total time: 327.17 hours.
Scaled time: 656.96 units (timescale=2.008).
Factorization parameters were as follows:
n: 218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855219
m: 100000000000000000000000000000000000000
deg: 5
c5: 13
c0: 86
skew: 1.46
type: snfs
lss: 1
rlim: 10700000
alim: 10700000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10700000/10700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5350000, 8950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1761109 x 1761357
Total sieving time: 327.17 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,10700000,10700000,28,28,54,54,2.5,2.5,100000
total time: 327.17 hours.
 --------- CPU info (if available) ----------

7·10¹⁷³-9 = 6(9)₁₇₂1_<174> = 17 · 23 · 16421 · 951988489 · 967778104050840161_<18> · C141

C141 = P61 · P80

P61 = 5822198849636541604216008139984546047314947195596463077900521_<61>

P80 = 20324841068780494305293498995060419802226786782151713853158153045709315773873709_<80>

Number: 69991_173
N=118335266289699330717287805739976609910028642379095256867623958931583444124800011987668345641662168237014794505569635206720802429547119302389
  ( 141 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=5822198849636541604216008139984546047314947195596463077900521
 r2=20324841068780494305293498995060419802226786782151713853158153045709315773873709
Version: 
Total time: 117.44 hours.
Scaled time: 236.63 units (timescale=2.015).
Factorization parameters were as follows:
n: 118335266289699330717287805739976609910028642379095256867623958931583444124800011987668345641662168237014794505569635206720802429547119302389
m: 50000000000000000000000000000000000
deg: 5
c5: 56
c0: -225
skew: 1.32
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 6500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1100358 x 1100606
Total sieving time: 117.44 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,52,52,2.5,2.5,100000
total time: 117.44 hours.
 --------- CPU info (if available) ----------

(19·10¹⁸⁹+53)/9 = 2(1)₁₈₈7_<190> = 137 · C188

C188 = P53 · P135

P53 = 50276311039073491284553796865897030204461721150551647_<53>

P135 = 306497629512232293365247269171182637897810549798966215737832495828240735616622890851416942888914546319515586789212490295293970999607803_<135>

Number: 21117_189
N=15409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701541
  ( 188 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=50276311039073491284553796865897030204461721150551647
 r2=306497629512232293365247269171182637897810549798966215737832495828240735616622890851416942888914546319515586789212490295293970999607803
Version: 
Total time: 526.99 hours.
Scaled time: 1061.88 units (timescale=2.015).
Factorization parameters were as follows:
n: 15409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701541
m: 50000000000000000000000000000000000000
deg: 5
c5: 304
c0: 265
skew: 0.97
type: snfs
lss: 1
rlim: 10700000
alim: 10700000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 10700000/10700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5350000, 11050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1964631 x 1964879
Total sieving time: 526.99 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,10700000,10700000,28,28,54,54,2.5,2.5,100000
total time: 526.99 hours.
 --------- CPU info (if available) ----------

(11·10¹⁹⁴-17)/3 = 3(6)₁₉₃1_<195> = 43 · 53 · C192

C192 = P44 · P61 · P87

P44 = 78977963478275827768612875134173255212037391_<44>

P61 = 7989706671541663001611625673535523086770395124467865271255451_<61>

P87 = 254970736930429047359472790175682836301063560469885661449512858357441037849002410792199_<87>

Number: 36661_194
N=160889278923504461020915606260055579932719028813807225391253473745794939300862951586953342109112183706303934474184583881819511481643995904636536492613719467602749744039783530788357466725171859
  ( 192 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=78977963478275827768612875134173255212037391
 r2=7989706671541663001611625673535523086770395124467865271255451
 r3=254970736930429047359472790175682836301063560469885661449512858357441037849002410792199
Version: 
Total time: 613.96 hours.
Scaled time: 1235.91 units (timescale=2.013).
Factorization parameters were as follows:
n: 160889278923504461020915606260055579932719028813807225391253473745794939300862951586953342109112183706303934474184583881819511481643995904636536492613719467602749744039783530788357466725171859
m: 1000000000000000000000000000000000000000
deg: 5
c5: 11
c0: -170
skew: 1.73
type: snfs
lss: 1
rlim: 13000000
alim: 13000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 13000000/13000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6500000, 13800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2233237 x 2233485
Total sieving time: 613.96 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,55,55,2.5,2.5,100000
total time: 613.96 hours.
 --------- CPU info (if available) ----------

Oct 27, 2009 (3rd)

By Dmitry Domanov / msieve/SIQS, GGNFS/msieve / Oct 27, 2009

(65·10¹⁰⁷-11)/9 = 7(2)₁₀₆1_<108> = 36749656866201527263_<20> · C89

C89 = P36 · P54

P36 = 174577584931942788813973330285134439_<36>

P54 = 112571661871895252862906862024566402469110010962824053_<54>

Tue Oct 27 00:50:36 2009  Msieve v. 1.43
Tue Oct 27 00:50:36 2009  random seeds: cb1332a0 13eb75b0
Tue Oct 27 00:50:36 2009  factoring 19652488861370739252193054495891224009287472706110752921759607452304062429675176207861267 (89 digits)
Tue Oct 27 00:50:37 2009  searching for 15-digit factors
Tue Oct 27 00:50:37 2009  commencing quadratic sieve (89-digit input)
Tue Oct 27 00:50:37 2009  using multiplier of 3
Tue Oct 27 00:50:37 2009  using VC8 32kb sieve core
Tue Oct 27 00:50:37 2009  sieve interval: 30 blocks of size 32768
Tue Oct 27 00:50:37 2009  processing polynomials in batches of 7
Tue Oct 27 00:50:37 2009  using a sieve bound of 1544869 (58667 primes)
Tue Oct 27 00:50:37 2009  using large prime bound of 123589520 (26 bits)
Tue Oct 27 00:50:37 2009  using double large prime bound of 367761997746960 (42-49 bits)
Tue Oct 27 00:50:37 2009  using trial factoring cutoff of 49 bits
Tue Oct 27 00:50:37 2009  polynomial 'A' values have 11 factors
Tue Oct 27 01:40:58 2009  58889 relations (15988 full + 42901 combined from 620648 partial), need 58763
Tue Oct 27 01:41:02 2009  begin with 636636 relations
Tue Oct 27 01:41:02 2009  reduce to 142394 relations in 11 passes
Tue Oct 27 01:41:02 2009  attempting to read 142394 relations
Tue Oct 27 01:41:03 2009  recovered 142394 relations
Tue Oct 27 01:41:03 2009  recovered 118558 polynomials
Tue Oct 27 01:41:04 2009  attempting to build 58889 cycles
Tue Oct 27 01:41:04 2009  found 58889 cycles in 5 passes
Tue Oct 27 01:41:04 2009  distribution of cycle lengths:
Tue Oct 27 01:41:04 2009     length 1 : 15988
Tue Oct 27 01:41:04 2009     length 2 : 11412
Tue Oct 27 01:41:04 2009     length 3 : 10470
Tue Oct 27 01:41:04 2009     length 4 : 7779
Tue Oct 27 01:41:04 2009     length 5 : 5448
Tue Oct 27 01:41:04 2009     length 6 : 3426
Tue Oct 27 01:41:04 2009     length 7 : 2061
Tue Oct 27 01:41:04 2009     length 9+: 2305
Tue Oct 27 01:41:04 2009  largest cycle: 18 relations
Tue Oct 27 01:41:04 2009  matrix is 58667 x 58889 (14.3 MB) with weight 3504276 (59.51/col)
Tue Oct 27 01:41:04 2009  sparse part has weight 3504276 (59.51/col)
Tue Oct 27 01:41:04 2009  filtering completed in 3 passes
Tue Oct 27 01:41:04 2009  matrix is 54552 x 54616 (13.4 MB) with weight 3281370 (60.08/col)
Tue Oct 27 01:41:04 2009  sparse part has weight 3281370 (60.08/col)
Tue Oct 27 01:41:04 2009  saving the first 48 matrix rows for later
Tue Oct 27 01:41:04 2009  matrix is 54504 x 54616 (9.7 MB) with weight 2701329 (49.46/col)
Tue Oct 27 01:41:04 2009  sparse part has weight 2208475 (40.44/col)
Tue Oct 27 01:41:04 2009  matrix includes 64 packed rows
Tue Oct 27 01:41:04 2009  using block size 21846 for processor cache size 6144 kB
Tue Oct 27 01:41:05 2009  commencing Lanczos iteration
Tue Oct 27 01:41:05 2009  memory use: 9.2 MB
Tue Oct 27 01:41:20 2009  lanczos halted after 863 iterations (dim = 54500)
Tue Oct 27 01:41:20 2009  recovered 15 nontrivial dependencies
Tue Oct 27 01:41:20 2009  prp36 factor: 174577584931942788813973330285134439
Tue Oct 27 01:41:20 2009  prp54 factor: 112571661871895252862906862024566402469110010962824053
Tue Oct 27 01:41:20 2009  elapsed time 00:50:44

2·10¹⁹¹+9 = 2(0)₁₉₀9_<192> = 139787422364207720750158040677389843257571643_<45> · C148

C148 = P68 · P80

P68 = 46096944919325148346223203940223926055682830814085225169569170904023_<68>

P80 = 31037716041925551555377656141714970107015368138481092969610634477807320110383981_<80>

Number: 209-191
N=1430743886806296706788516093667434949145159858014350886258366962866810355411884866166709798529837275207436439253831768696683312353651987615427655563
  ( 148 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=46096944919325148346223203940223926055682830814085225169569170904023 (pp68)
 r2=31037716041925551555377656141714970107015368138481092969610634477807320110383981 (pp80)
Version: Msieve-1.40
Total time: 245.12 hours.
Scaled time: 458.63 units (timescale=1.871).
Factorization parameters were as follows:
n: 1430743886806296706788516093667434949145159858014350886258366962866810355411884866166709798529837275207436439253831768696683312353651987615427655563
m: 100000000000000000000000000000000000000
deg: 5
c5: 20
c0: 9
skew: 0.85
type: snfs
lss: 1
rlim: 10800000
alim: 10800000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10800000/10800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5400000, 9300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1851073 x 1851298
Total sieving time: 240.25 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 4.45 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,191.000,5,0,0,0,0,0,0,0,0,10800000,10800000,28,28,54,54,2.5,2.5,100000
total time: 245.12 hours.
 --------- CPU info (if available) ----------

(65·10¹²⁵-11)/9 = 7(2)₁₂₄1_<126> = C126

C126 = P41 · P85

P41 = 91555041401965548538648038653167603029653_<41>

P85 = 7888393813851928434485152622480874620149146146332238895830736022441467295327701644057_<85>

Number: s126
N=722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
  ( 126 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=91555041401965548538648038653167603029653 (pp41)
 r2=7888393813851928434485152622480874620149146146332238895830736022441467295327701644057 (pp85)
Version: Msieve-1.40
Total time: 1.50 hours.
Scaled time: 2.94 units (timescale=1.963).
Factorization parameters were as follows:
n: 722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 10000000000000000000000000
deg: 5
c5: 65
c0: -11
skew: 0.70
type: snfs
lss: 1
rlim: 910000
alim: 910000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 910000/910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [455000, 755001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 110745 x 110974
Total sieving time: 1.41 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000
total time: 1.50 hours.
 --------- CPU info (if available) ----------

(62·10¹³²-71)/9 = 6(8)₁₃₁1_<133> = 5717 · C130

C130 = P41 · P89

P41 = 14196147689937141374294318249731425936067_<41>

P89 = 84880998342609810093756094165793232255873270007284083264233059727258303257959873758507279_<89>

Number: s130
N=1204983188540998581229471556566186616912522107554467183643324976191864419956076419256408761393893456163877713641575807047208131693
  ( 130 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=14196147689937141374294318249731425936067 (pp41)
 r2=84880998342609810093756094165793232255873270007284083264233059727258303257959873758507279 (pp89)
Version: Msieve-1.40
Total time: 3.18 hours.
Scaled time: 5.79 units (timescale=1.823).
Factorization parameters were as follows:
n: 1204983188540998581229471556566186616912522107554467183643324976191864419956076419256408761393893456163877713641575807047208131693
m: 200000000000000000000000000
deg: 5
c5: 775
c0: -284
skew: 0.82
type: snfs
lss: 1
rlim: 1220000
alim: 1220000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1220000/1220000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [610000, 1285001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 206175 x 206400
Total sieving time: 3.08 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,134.000,5,0,0,0,0,0,0,0,0,1220000,1220000,26,26,47,47,2.3,2.3,75000
total time: 3.18 hours.
 --------- CPU info (if available) ----------

(65·10¹³⁰+7)/9 = 7(2)₁₂₉3_<131> = C131

C131 = P53 · P79

P53 = 46485863897376296550853545500186122961951356602030151_<53>

P79 = 1553638378791073916029398963967193954361536667650255332339812815429978361841273_<79>

Number: s131
N=72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223
  ( 131 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=46485863897376296550853545500186122961951356602030151 (pp53)
 r2=1553638378791073916029398963967193954361536667650255332339812815429978361841273 (pp79)
Version: Msieve-1.40
Total time: 2.03 hours.
Scaled time: 3.81 units (timescale=1.877).
Factorization parameters were as follows:
n: 72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223
m: 100000000000000000000000000
deg: 5
c5: 65
c0: 7
skew: 0.64
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 157737 x 157962
Total sieving time: 1.93 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.03 hours.
 --------- CPU info (if available) ----------

Oct 27, 2009 (2nd)

By Norbert Schneider / Msieve / Oct 27, 2009

(61·10¹³⁰+11)/9 = 6(7)₁₂₉9_<131> = 3³ · 12141019215809417_<17> · 258286671235162236352303_<24> · C90

C90 = P40 · P51

P40 = 2603800835257585405318811667397972553087_<40>

P51 = 307438786873328469652390333446782493394750798060721_<51>

Mon Oct 26 19:16:40 2009  
Mon Oct 26 19:16:40 2009  
Mon Oct 26 19:16:40 2009  Msieve v. 1.43
Mon Oct 26 19:16:40 2009  random seeds: a73f8f44 bd2ae005
Mon Oct 26 19:16:40 2009  factoring 800509370051351453037656179793997623801994692989397392614271301898208518060262904821995727 (90 digits)
Mon Oct 26 19:16:45 2009  searching for 15-digit factors
Mon Oct 26 19:16:46 2009  commencing quadratic sieve (90-digit input)
Mon Oct 26 19:16:48 2009  using multiplier of 13
Mon Oct 26 19:16:48 2009  using 64kb Pentium 4 sieve core
Mon Oct 26 19:16:48 2009  sieve interval: 18 blocks of size 65536
Mon Oct 26 19:16:48 2009  processing polynomials in batches of 6
Mon Oct 26 19:16:48 2009  using a sieve bound of 1618703 (61070 primes)
Mon Oct 26 19:16:49 2009  using large prime bound of 135971052 (27 bits)
Mon Oct 26 19:16:49 2009  using double large prime bound of 436720526960928 (42-49 bits)
Mon Oct 26 19:16:49 2009  using trial factoring cutoff of 49 bits
Mon Oct 26 19:16:49 2009  polynomial 'A' values have 12 factors
Mon Oct 26 22:15:13 2009  61446 relations (16348 full + 45098 combined from 666206 partial), need 61166
Mon Oct 26 22:15:15 2009  begin with 682554 relations
Mon Oct 26 22:15:16 2009  reduce to 150056 relations in 10 passes
Mon Oct 26 22:15:16 2009  attempting to read 150056 relations
Mon Oct 26 22:15:19 2009  recovered 150056 relations
Mon Oct 26 22:15:19 2009  recovered 129311 polynomials
Mon Oct 26 22:15:19 2009  attempting to build 61446 cycles
Mon Oct 26 22:15:19 2009  found 61446 cycles in 6 passes
Mon Oct 26 22:15:19 2009  distribution of cycle lengths:
Mon Oct 26 22:15:19 2009     length 1 : 16348
Mon Oct 26 22:15:19 2009     length 2 : 11864
Mon Oct 26 22:15:19 2009     length 3 : 10847
Mon Oct 26 22:15:19 2009     length 4 : 8262
Mon Oct 26 22:15:19 2009     length 5 : 5686
Mon Oct 26 22:15:19 2009     length 6 : 3736
Mon Oct 26 22:15:19 2009     length 7 : 2192
Mon Oct 26 22:15:19 2009     length 9+: 2511
Mon Oct 26 22:15:19 2009  largest cycle: 20 relations
Mon Oct 26 22:15:19 2009  matrix is 61070 x 61446 (15.3 MB) with weight 3754514 (61.10/col)
Mon Oct 26 22:15:19 2009  sparse part has weight 3754514 (61.10/col)
Mon Oct 26 22:15:21 2009  filtering completed in 3 passes
Mon Oct 26 22:15:21 2009  matrix is 57065 x 57129 (14.3 MB) with weight 3510750 (61.45/col)
Mon Oct 26 22:15:21 2009  sparse part has weight 3510750 (61.45/col)
Mon Oct 26 22:15:22 2009  saving the first 48 matrix rows for later
Mon Oct 26 22:15:22 2009  matrix is 57017 x 57129 (9.2 MB) with weight 2773047 (48.54/col)
Mon Oct 26 22:15:22 2009  sparse part has weight 2059967 (36.06/col)
Mon Oct 26 22:15:22 2009  matrix includes 64 packed rows
Mon Oct 26 22:15:22 2009  using block size 10922 for processor cache size 256 kB
Mon Oct 26 22:15:22 2009  commencing Lanczos iteration
Mon Oct 26 22:15:22 2009  memory use: 9.3 MB
Mon Oct 26 22:15:54 2009  lanczos halted after 904 iterations (dim = 57015)
Mon Oct 26 22:15:54 2009  recovered 17 nontrivial dependencies
Mon Oct 26 22:15:56 2009  prp40 factor: 2603800835257585405318811667397972553087
Mon Oct 26 22:15:56 2009  prp51 factor: 307438786873328469652390333446782493394750798060721
Mon Oct 26 22:15:56 2009  elapsed time 02:59:16

Oct 27, 2009

By Lionel Debroux / GMP-ECM

Factorizations of 722...221 and Factorizations of 722...223 have been extended up to n=200. Composite numbers that appeared newly have passed 150 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 26, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Oct 26, 2009

(83·10¹⁴⁶+7)/9 = 9(2)₁₄₅3_<147> = 13 · 6112473163_<10> · 70315458832223316419214342764791_<32> · C105

C105 = P52 · P53

P52 = 5791378332563386734299789562740645717003706558548593_<52>

P53 = 28499846000487846733642226699203988710334388566768759_<53>

Number: 92223_146
N=165053390608618612168814333894623116123683611767851606138040337603496776755267221271940941504830895806087
  ( 105 digits)
Divisors found:
 r1=5791378332563386734299789562740645717003706558548593
 r2=28499846000487846733642226699203988710334388566768759
Version: 
Total time: 4.39 hours.
Scaled time: 10.46 units (timescale=2.385).
Factorization parameters were as follows:
name: 92223_146
n: 165053390608618612168814333894623116123683611767851606138040337603496776755267221271940941504830895806087
skew: 19553.75
# norm 1.36e+14
c5: 5700
c4: 235810005
c3: 245079180905
c2: -154319593207427431
c1: -148483831425267567230
c0: -814720965704383267381256
# alpha -5.81
Y1: 82920931379
Y0: -123693679908535878411
# Murphy_E 2.07e-09
# M 16105943711929144827060288703611641223991067736201404894401156909521716930802385512633608291851676404138
type: gnfs
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 1650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6891219
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 274339 x 274587
Polynomial selection time: 0.36 hours.
Total sieving time: 3.24 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000
total time: 4.39 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(62·10¹⁴⁴-71)/9 = 6(8)₁₄₃1_<145> = 173 · 617 · 1283 · 92610038086816262454859531913_<29> · C108

C108 = P35 · P74

P35 = 45060620799576548736690063731376301_<35>

P74 = 12054134222394110709717782635167614241122684394866782704597181919381457779_<74>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 543166771262499552479231555893942724170566107989350047498766678598794980817702546211216551464640875392695479 (108 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4831068078
Step 1 took 2670ms
Step 2 took 1844ms
********** Factor found in step 2: 45060620799576548736690063731376301
Found probable prime factor of 35 digits: 45060620799576548736690063731376301
Probable prime cofactor 12054134222394110709717782635167614241122684394866782704597181919381457779 has 74 digits

(26·10¹⁸⁰-11)/3 = 8(6)₁₇₉3_<181> = 3540853596198710609_<19> · 750709090610386998791821_<24> · 311104155382289880239512627969_<30> · C110

C110 = P41 · P69

P41 = 72785908957299479303025193305881070533587_<41>

P69 = 143985688074871851263884561113056280933967878093323444574394933207489_<69>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 10480129183371743899045412556645811521917224266909621512471309641624950039890299342336256862579936558614433043 (110 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5524291184
Step 1 took 3526ms
Step 2 took 3900ms
********** Factor found in step 2: 72785908957299479303025193305881070533587
Found probable prime factor of 41 digits: 72785908957299479303025193305881070533587
Probable prime cofactor 143985688074871851263884561113056280933967878093323444574394933207489 has 69 digits

Oct 26, 2009 (6th)

By Sinkiti Sibata / Msieve, GGNFS / Oct 26, 2009

(83·10¹⁴⁰+7)/9 = 9(2)₁₃₉3_<141> = 13 · 59 · 179 · 196835519 · 780759681572696281_<18> · C110

C110 = P54 · P56

P54 = 950945206033983716590046745708439382556184867498061651_<54>

P56 = 45963262403462441886100482311242817697783998352022258799_<56>

Number: 92223_140
N=43708544036254649395714070133193976331990037910375971143155353250353772955674359691405658669750880139179217149
  ( 110 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=950945206033983716590046745708439382556184867498061651 (pp54)
 r2=45963262403462441886100482311242817697783998352022258799 (pp56)
Version: Msieve-1.40
Total time: 6.58 hours.
Scaled time: 13.36 units (timescale=2.032).
Factorization parameters were as follows:
name: 92223_140
n: 43708544036254649395714070133193976331990037910375971143155353250353772955674359691405658669750880139179217149
m: 10000000000000000000000000000
deg: 5
c5: 83
c0: 7
skew: 0.61
type: snfs
lss: 1
rlim: 1620000
alim: 1620000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1620000/1620000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [810000, 1610001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 235126 x 235372
Total sieving time: 6.28 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000
total time: 6.58 hours.
 --------- CPU info (if available) ----------

(61·10¹³⁶+11)/9 = 6(7)₁₃₅9_<137> = 3 · 2213363 · 20975235357953_<14> · C117

C117 = P38 · P79

P38 = 56099438243208509545785301147285196647_<38>

P79 = 8674572279336327283237021925543194621541044909983854234310679612701120002673821_<79>

Number: 67779_136
N=486638631870876768578237462710217409611440936923179732511602138246948855664505898321050283688239457736079891783878187
  ( 117 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=56099438243208509545785301147285196647 (pp38)
 r2=8674572279336327283237021925543194621541044909983854234310679612701120002673821 (pp79)
Version: Msieve-1.40
Total time: 5.94 hours.
Scaled time: 12.39 units (timescale=2.085).
Factorization parameters were as follows:
name: 67779_136
n: 486638631870876768578237462710217409611440936923179732511602138246948855664505898321050283688239457736079891783878187
m: 2000000000000000000000000000
deg: 5
c5: 305
c0: 176
skew: 0.90
type: snfs
lss: 1
rlim: 1450000
alim: 1450000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1450000/1450000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [725000, 1475001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 247395 x 247643
Total sieving time: 5.59 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,138.000,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000
total time: 5.94 hours.
 --------- CPU info (if available) ----------

(62·10¹³⁶-71)/9 = 6(8)₁₃₅1_<137> = 797 · 91957 · 141665756784889_<15> · C115

C115 = P41 · P74

P41 = 87940173824683258876381753531354451770847_<41>

P74 = 75449064368628461623561903771559610802465731814491611535253595307663468583_<74>

SNFS difficulty: 138 digits.
Divisors found:
 r1=87940173824683258876381753531354451770847 (pp41)
 r2=75449064368628461623561903771559610802465731814491611535253595307663468583 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.91 hours.
Scaled time: 17.36 units (timescale=1.949).
Factorization parameters were as follows:
name: 68881_136
n: 6635003835486902970594310750805950658360102961790601430840554603116519491417799716317124902425292622802174699799801
m: 2000000000000000000000000000
deg: 5
c5: 155
c0: -568
skew: 1.30
type: snfs
lss: 1
rlim: 1430000
alim: 1430000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1430000/1430000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [715000, 1540001)
Primes: RFBsize:109205, AFBsize:109291, largePrimes:3393933 encountered
Relations: rels:3341469, finalFF:248129
Max relations in full relation-set: 28
Initial matrix: 218563 x 248129 with sparse part having weight 22264177.
Pruned matrix : 209570 x 210726 with weight 16662072.
Total sieving time: 8.30 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1430000,1430000,26,26,48,48,2.3,2.3,75000
total time: 8.91 hours.
 --------- CPU info (if available) ----------

(61·10¹⁴⁰+11)/9 = 6(7)₁₃₉9_<141> = 7 · 173 · 4668508477118735351_<19> · 11868308233560420583480229_<26> · C95

C95 = P38 · P57

P38 = 34654709996381233356360236722003259611_<38>

P57 = 291483479342020082267398383224796794589186280350551363081_<57>

Number: 67779_140
N=10101275445333886072937871136953074721594155330052969136352011175659007415845411001561163821491
  ( 95 digits)
Divisors found:
 r1=34654709996381233356360236722003259611 (pp38)
 r2=291483479342020082267398383224796794589186280350551363081 (pp57)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 10.42 hours.
Scaled time: 4.92 units (timescale=0.472).
Factorization parameters were as follows:
name: 67779_140
n:  10101275445333886072937871136953074721594155330052969136352011175659007415845411001561163821491
m:  7926501998682499714959
deg: 4
c4: 2558880
c3: 12052800
c2: -345390808657415679
c1: 764061773339347700034
c0: -2640085652055857279596
skew: 1635.250
type: gnfs
# adj. I(F,S) = 57.775
# E(F1,F2) = 3.595557e-05
# GGNFS version 0.77.1-20050930-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1256504580.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1440001)
Primes: RFBsize:92938, AFBsize:93122, largePrimes:1879615 encountered
Relations: rels:1950424, finalFF:223451
Max relations in full relation-set: 28
Initial matrix: 186133 x 223451 with sparse part having weight 18769959.
Pruned matrix : 169528 x 170522 with weight 12045876.
Polynomial selection time: 0.17 hours.
Total sieving time: 9.52 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.54 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 10.42 hours.
 --------- CPU info (if available) ----------

(61·10¹³⁷+11)/9 = 6(7)₁₃₆9_<138> = 41854649 · C131

C131 = P43 · P89

P43 = 1497100862179284466393211599484926776042967_<43>

P89 = 10816644611377158968597922580922419233088088735788862949569901953744310105884107215906413_<89>

Number: 67779_137
N=16193607973579656056314742426290034776728811601735754080216460010876635897192156067962194063024582472971587404251742208560338847371
  ( 131 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=1497100862179284466393211599484926776042967 (pp43)
 r2=10816644611377158968597922580922419233088088735788862949569901953744310105884107215906413 (pp89)
Version: Msieve-1.40
Total time: 7.87 hours.
Scaled time: 16.35 units (timescale=2.078).
Factorization parameters were as follows:
name: 67779_137
n: 16193607973579656056314742426290034776728811601735754080216460010876635897192156067962194063024582472971587404251742208560338847371
m: 5000000000000000000000000000
deg: 5
c5: 244
c0: 1375
skew: 1.41
type: snfs
lss: 1
rlim: 1560000
alim: 1560000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1560000/1560000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [780000, 1780001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 240232 x 240464
Total sieving time: 7.52 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,140.000,5,0,0,0,0,0,0,0,0,1560000,1560000,26,26,48,48,2.3,2.3,100000
total time: 7.87 hours.
 --------- CPU info (if available) ----------

(62·10¹³⁸-71)/9 = 6(8)₁₃₇1_<139> = 178973 · 371864911123_<12> · C123

C123 = P42 · P81

P42 = 586223530914985362890505263147233484304329_<42>

P81 = 176568494706771364851457868738726420430749628421559284794116630853036260388793391_<81>

Number: 68881_138
N=103508606415347412610445012420502440976795110134999813227178254855128575837561314714804310858344623651363750600965347889639
  ( 123 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=586223530914985362890505263147233484304329 (pp42)
 r2=176568494706771364851457868738726420430749628421559284794116630853036260388793391 (pp81)
Version: GGNFS-0.77.1-20060513-k8
Total time: 14.59 hours.
Scaled time: 28.97 units (timescale=1.985).
Factorization parameters were as follows:
name: 68881_138
n: 103508606415347412610445012420502440976795110134999813227178254855128575837561314714804310858344623651363750600965347889639
m: 5000000000000000000000000000
deg: 5
c5: 496
c0: -1775
skew: 1.29
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 2090001)
Primes: RFBsize:119758, AFBsize:119825, largePrimes:3944588 encountered
Relations: rels:4138860, finalFF:373069
Max relations in full relation-set: 28
Initial matrix: 239650 x 373069 with sparse part having weight 41359806.
Pruned matrix : 204694 x 205956 with weight 20997592.
Total sieving time: 13.95 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000
total time: 14.59 hours.
 --------- CPU info (if available) ----------

Oct 26, 2009 (5th)

By Erik Branger / GGNFS, Msieve, YAFU / Oct 26, 2009

(64·10¹³⁸+17)/9 = 7(1)₁₃₇3_<139> = 3 · 293 · 1997 · 8020147355672225249324209607_<28> · C105

C105 = P40 · P66

P40 = 1025076302214321651403303364378397080819_<40>

P66 = 492756070518680163420363928894391737927860973928594193525801851047_<66>

Number: 71113_138
N=505112570660948178612268467748518628903549911512652796501301806603729962592526334904318991700411458767493
  ( 105 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=1025076302214321651403303364378397080819 (pp40)
 r2=492756070518680163420363928894391737927860973928594193525801851047 (pp66)
Version: Msieve-1.40
Total time: 5.34 hours.
Scaled time: 5.21 units (timescale=0.977).
Factorization parameters were as follows:
n: 505112570660948178612268467748518628903549911512652796501301806603729962592526334904318991700411458767493
m: 4000000000000000000000000000
deg: 5
c5: 125
c0: 34
skew: 0.77
type: snfs
lss: 1
rlim: 1510000
alim: 1510000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1510000/1510000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [755000, 1505001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 240146 x 240371
Total sieving time: 5.01 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,140.000,5,0,0,0,0,0,0,0,0,1510000,1510000,26,26,48,48,2.3,2.3,75000
total time: 5.34 hours.
 --------- CPU info (if available) ----------

(62·10¹³⁵-71)/9 = 6(8)₁₃₄1_<136> = 7² · 19 · 3908604569_<10> · 4071319992583851580553_<22> · 6092834482135211337409_<22> · C80

C80 = P34 · P47

P34 = 3023609198798573489557559745506843_<34>

P47 = 25240472910189074574471536572739850312627201889_<47>

10/25/09 16:58:59 v1.12 @ ERIK-DATOR, starting SIQS on c80: 76317326073273886332452818555423918091234042295879702293589897638297267192026427
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, random seeds: 2974791847, 2559185332
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, ==== sieve params ====
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, n = 81 digits, 267 bits
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, factor base: 43638 primes (max prime = 1126361)
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, single large prime cutoff: 107004295 (95 * pmax)
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, using 0 large prime slices of factor base
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, buckets hold 1024 elements
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, sieve interval: 14 blocks of size 32768
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, polynomial A has ~ 568396561 factors
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, using multiplier of 2
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, using small prime variation correction of 21 bits
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x64 sieve scanning
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, trial factoring cutoff at 92 bits
10/25/09 16:58:59 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ====
10/25/09 17:04:18 v1.12 @ ERIK-DATOR, sieve time = 94.7714, relation time = 39.4308, poly_time = 161.4446
10/25/09 17:04:18 v1.12 @ ERIK-DATOR, 43726 relations found: 22156 full + 21570 from 236834 partial, using 7943760 polys (351 A polys)
10/25/09 17:04:18 v1.12 @ ERIK-DATOR, on average, sieving found 0.03 rels/poly and 811.84 rels/sec
10/25/09 17:04:18 v1.12 @ ERIK-DATOR, trial division touched 4575910 sieve locations out of 7288431575040
10/25/09 17:04:18 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ====
10/25/09 17:04:26 v1.12 @ ERIK-DATOR, begin with 258990 relations
10/25/09 17:04:26 v1.12 @ ERIK-DATOR, reduce to 62563 relations in 2 passes
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, recovered 62563 relations
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, recovered 44959 polynomials
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, attempting to build 43726 cycles
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, found 43726 cycles in 1 passes
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, distribution of cycle lengths:
10/25/09 17:04:34 v1.12 @ ERIK-DATOR,    length 1 : 22156
10/25/09 17:04:34 v1.12 @ ERIK-DATOR,    length 2 : 21570
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, largest cycle: 2 relations
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, matrix is 43638 x 43726 (5.7 MB) with weight 1316031 (30.10/col)
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, sparse part has weight 1316031 (30.10/col)
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, filtering completed in 3 passes
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, matrix is 31257 x 31321 (4.5 MB) with weight 1063089 (33.94/col)
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, sparse part has weight 1063089 (33.94/col)
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, matrix is 31209 x 31321 (3.8 MB) with weight 875970 (27.97/col)
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, sparse part has weight 800848 (25.57/col)
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, using block size 12528 for processor cache size 2048 kB
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, commencing Lanczos iteration
10/25/09 17:04:34 v1.12 @ ERIK-DATOR, memory use: 3.8 MB
10/25/09 17:04:39 v1.12 @ ERIK-DATOR, lanczos halted after 495 iterations (dim = 31207)
10/25/09 17:04:39 v1.12 @ ERIK-DATOR, recovered 16 nontrivial dependencies
10/25/09 17:04:40 v1.12 @ ERIK-DATOR, prp34 = 3023609198798573489557559745506843
10/25/09 17:04:41 v1.12 @ ERIK-DATOR, prp47 = 25240472910189074574471536572739850312627201889
10/25/09 17:04:41 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 21.1420 seconds.
10/25/09 17:04:41 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 1.4820 seconds.
10/25/09 17:04:41 v1.12 @ ERIK-DATOR, SIQS elapsed time = 341.6886 seconds.

(61·10¹⁴⁸+11)/9 = 6(7)₁₄₇9_<149> = 3² · 17 · 15319 · 159589 · 97217642812415666311_<20> · 268978493809359271513416809599_<30> · C88

C88 = P41 · P48

P41 = 15778348857742482280322540725154142893917_<41>

P48 = 439175725135905508379395921376984663405910180421_<48>

10/25/09 17:09:43 v1.12 @ ERIK-DATOR, starting SIQS on c88: 6929467801046341041659258046990532322098586303429838696777373698294583310076464533399057
10/25/09 17:09:43 v1.12 @ ERIK-DATOR, random seeds: 2974791847, 2559185332
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, ==== sieve params ====
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, n = 88 digits, 292 bits
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, factor base: 61677 primes (max prime = 1631843)
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, single large prime cutoff: 179502730 (110 * pmax)
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, double large prime range from 43 to 50 bits
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, double large prime cutoff: 719992387123441
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, using 3224628 large prime slices of factor base
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, buckets hold 1024 elements
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, polynomial A has ~ 24220 factors
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, using multiplier of 1
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, using small prime variation correction of 18 bits
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, trial factoring cutoff at 99 bits
10/25/09 17:09:44 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ====
10/25/09 17:41:01 v1.12 @ ERIK-DATOR, sieve time = 533.6376, relation time = 233.5958, poly_time = 958.4928
10/25/09 17:41:01 v1.12 @ ERIK-DATOR, 62052 relations found: 18755 full + 43297 from 625600 partial, using 72681032 polys (751 A polys)
10/25/09 17:41:01 v1.12 @ ERIK-DATOR, on average, sieving found 0.01 rels/poly and 343.14 rels/sec
10/25/09 17:41:01 v1.12 @ ERIK-DATOR, trial division touched 13403412 sieve locations out of 85738034036736
10/25/09 17:41:01 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ====
10/25/09 17:41:04 v1.12 @ ERIK-DATOR, begin with 644355 relations
10/25/09 17:41:04 v1.12 @ ERIK-DATOR, reduce to 134988 relations in 10 passes
10/25/09 17:41:14 v1.12 @ ERIK-DATOR, recovered 134988 relations
10/25/09 17:41:14 v1.12 @ ERIK-DATOR, recovered 113960 polynomials
10/25/09 17:41:14 v1.12 @ ERIK-DATOR, attempting to build 62052 cycles
10/25/09 17:41:14 v1.12 @ ERIK-DATOR, found 62052 cycles in 5 passes
10/25/09 17:41:14 v1.12 @ ERIK-DATOR, distribution of cycle lengths:
10/25/09 17:41:14 v1.12 @ ERIK-DATOR,    length 1 : 18755
10/25/09 17:41:14 v1.12 @ ERIK-DATOR,    length 2 : 15491
10/25/09 17:41:14 v1.12 @ ERIK-DATOR,    length 3 : 11875
10/25/09 17:41:14 v1.12 @ ERIK-DATOR,    length 4 : 7479
10/25/09 17:41:14 v1.12 @ ERIK-DATOR,    length 5 : 4105
10/25/09 17:41:14 v1.12 @ ERIK-DATOR,    length 6 : 2226
10/25/09 17:41:14 v1.12 @ ERIK-DATOR,    length 7 : 1131
10/25/09 17:41:14 v1.12 @ ERIK-DATOR,    length 9+: 990
10/25/09 17:41:14 v1.12 @ ERIK-DATOR, largest cycle: 16 relations
10/25/09 17:41:15 v1.12 @ ERIK-DATOR, matrix is 61677 x 62052 (13.1 MB) with weight 3173720 (51.15/col)
10/25/09 17:41:15 v1.12 @ ERIK-DATOR, sparse part has weight 3173720 (51.15/col)
10/25/09 17:41:15 v1.12 @ ERIK-DATOR, filtering completed in 4 passes
10/25/09 17:41:15 v1.12 @ ERIK-DATOR, matrix is 55966 x 56030 (11.9 MB) with weight 2905052 (51.85/col)
10/25/09 17:41:15 v1.12 @ ERIK-DATOR, sparse part has weight 2905052 (51.85/col)
10/25/09 17:41:16 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later
10/25/09 17:41:16 v1.12 @ ERIK-DATOR, matrix is 55918 x 56030 (10.4 MB) with weight 2572396 (45.91/col)
10/25/09 17:41:16 v1.12 @ ERIK-DATOR, sparse part has weight 2378132 (42.44/col)
10/25/09 17:41:16 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows
10/25/09 17:41:16 v1.12 @ ERIK-DATOR, using block size 22412 for processor cache size 2048 kB
10/25/09 17:41:16 v1.12 @ ERIK-DATOR, commencing Lanczos iteration
10/25/09 17:41:16 v1.12 @ ERIK-DATOR, memory use: 9.1 MB
10/25/09 17:42:19 v1.12 @ ERIK-DATOR, lanczos halted after 886 iterations (dim = 55914)
10/25/09 17:42:19 v1.12 @ ERIK-DATOR, recovered 14 nontrivial dependencies
10/25/09 17:42:20 v1.12 @ ERIK-DATOR, prp41 = 15778348857742482280322540725154142893917
10/25/09 17:42:22 v1.12 @ ERIK-DATOR, prp48 = 439175725135905508379395921376984663405910180421
10/25/09 17:42:22 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 77.8740 seconds.
10/25/09 17:42:22 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 3.1200 seconds.
10/25/09 17:42:22 v1.12 @ ERIK-DATOR, SIQS elapsed time = 1958.8982 seconds.

(62·10¹²⁹-71)/9 = 6(8)₁₂₈1_<130> = 7 · 74507 · 863695087070633_<15> · 446537572767580550602547_<24> · C86

C86 = P29 · P58

P29 = 27413652247099964745959987129_<29>

P58 = 1249305658838193522558789938622451015178573054392034321111_<58>

Sun Oct 25 17:00:39 2009  Msieve v. 1.43
Sun Oct 25 17:00:39 2009  random seeds: 312f2c38 e5b608c2
Sun Oct 25 17:00:39 2009  factoring 34248030881724345791926751354933118415888088772687415035676269296160679100087812980319 (86 digits)
Sun Oct 25 17:00:40 2009  searching for 15-digit factors
Sun Oct 25 17:00:41 2009  commencing quadratic sieve (86-digit input)
Sun Oct 25 17:00:41 2009  using multiplier of 1
Sun Oct 25 17:00:41 2009  using 64kb Pentium 4 sieve core
Sun Oct 25 17:00:41 2009  sieve interval: 8 blocks of size 65536
Sun Oct 25 17:00:41 2009  processing polynomials in batches of 13
Sun Oct 25 17:00:41 2009  using a sieve bound of 1461403 (55559 primes)
Sun Oct 25 17:00:41 2009  using large prime bound of 116912240 (26 bits)
Sun Oct 25 17:00:41 2009  using double large prime bound of 332772803587280 (41-49 bits)
Sun Oct 25 17:00:41 2009  using trial factoring cutoff of 49 bits
Sun Oct 25 17:00:41 2009  polynomial 'A' values have 11 factors
Sun Oct 25 17:52:41 2009  55902 relations (16079 full + 39823 combined from 580400 partial), need 55655
Sun Oct 25 17:52:43 2009  begin with 596479 relations
Sun Oct 25 17:52:44 2009  reduce to 132644 relations in 9 passes
Sun Oct 25 17:52:44 2009  attempting to read 132644 relations
Sun Oct 25 17:52:48 2009  recovered 132644 relations
Sun Oct 25 17:52:48 2009  recovered 108900 polynomials
Sun Oct 25 17:52:48 2009  attempting to build 55902 cycles
Sun Oct 25 17:52:48 2009  found 55902 cycles in 5 passes
Sun Oct 25 17:52:48 2009  distribution of cycle lengths:
Sun Oct 25 17:52:48 2009     length 1 : 16079
Sun Oct 25 17:52:48 2009     length 2 : 11136
Sun Oct 25 17:52:48 2009     length 3 : 9863
Sun Oct 25 17:52:48 2009     length 4 : 7144
Sun Oct 25 17:52:48 2009     length 5 : 4967
Sun Oct 25 17:52:48 2009     length 6 : 3039
Sun Oct 25 17:52:48 2009     length 7 : 1735
Sun Oct 25 17:52:48 2009     length 9+: 1939
Sun Oct 25 17:52:48 2009  largest cycle: 18 relations
Sun Oct 25 17:52:49 2009  matrix is 55559 x 55902 (12.1 MB) with weight 2954402 (52.85/col)
Sun Oct 25 17:52:49 2009  sparse part has weight 2954402 (52.85/col)
Sun Oct 25 17:52:50 2009  filtering completed in 3 passes
Sun Oct 25 17:52:50 2009  matrix is 50604 x 50668 (11.1 MB) with weight 2695723 (53.20/col)
Sun Oct 25 17:52:50 2009  sparse part has weight 2695723 (53.20/col)
Sun Oct 25 17:52:50 2009  saving the first 48 matrix rows for later
Sun Oct 25 17:52:50 2009  matrix is 50556 x 50668 (6.1 MB) with weight 1989485 (39.27/col)
Sun Oct 25 17:52:50 2009  sparse part has weight 1292326 (25.51/col)
Sun Oct 25 17:52:50 2009  matrix includes 64 packed rows
Sun Oct 25 17:52:50 2009  using block size 20267 for processor cache size 512 kB
Sun Oct 25 17:52:50 2009  commencing Lanczos iteration
Sun Oct 25 17:52:50 2009  memory use: 7.0 MB
Sun Oct 25 17:53:10 2009  lanczos halted after 801 iterations (dim = 50550)
Sun Oct 25 17:53:11 2009  recovered 15 nontrivial dependencies
Sun Oct 25 17:53:11 2009  prp29 factor: 27413652247099964745959987129
Sun Oct 25 17:53:11 2009  prp58 factor: 1249305658838193522558789938622451015178573054392034321111
Sun Oct 25 17:53:11 2009  elapsed time 00:52:32

(61·10¹²⁶+11)/9 = 6(7)₁₂₅9_<127> = 4583 · 6317 · 17909 · 3879167 · 10801069060460037677_<20> · C90

C90 = P43 · P48

P43 = 2195586039900908690698168329609801270916603_<43>

P48 = 142101798548019649379224996185134551483183791973_<48>

10/25/09 17:45:35 v1.12 @ ERIK-DATOR, starting SIQS on c90: 311996725136843158550452678007225947321786519109975065421192818805281768398691918983827719
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, random seeds: 2974791847, 2559185332
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, ==== sieve params ====
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, n = 90 digits, 298 bits
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, factor base: 65244 primes (max prime = 1734011)
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, single large prime cutoff: 190741210 (110 * pmax)
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, double large prime range from 43 to 50 bits
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, double large prime cutoff: 803156465804099
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, using 3750192 large prime slices of factor base
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, buckets hold 1024 elements
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, polynomial A has ~ 112967 factors
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, using multiplier of 1
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, using small prime variation correction of 19 bits
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, trial factoring cutoff at 97 bits
10/25/09 17:45:35 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ====
10/25/09 18:24:28 v1.12 @ ERIK-DATOR, sieve time = 658.7142, relation time = 356.6018, poly_time = 1203.0792
10/25/09 18:24:28 v1.12 @ ERIK-DATOR, 65578 relations found: 18773 full + 46805 from 764136 partial, using 103699520 polys (895 A polys)
10/25/09 18:24:28 v1.12 @ ERIK-DATOR, on average, sieving found 0.01 rels/poly and 335.54 rels/sec
10/25/09 18:24:28 v1.12 @ ERIK-DATOR, trial division touched 24098010 sieve locations out of 122328931368960
10/25/09 18:24:28 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ====
10/25/09 18:24:28 v1.12 @ ERIK-DATOR, begin with 782909 relations
10/25/09 18:24:29 v1.12 @ ERIK-DATOR, reduce to 153559 relations in 9 passes
10/25/09 18:24:38 v1.12 @ ERIK-DATOR, recovered 153559 relations
10/25/09 18:24:38 v1.12 @ ERIK-DATOR, recovered 130881 polynomials
10/25/09 18:24:38 v1.12 @ ERIK-DATOR, attempting to build 65578 cycles
10/25/09 18:24:38 v1.12 @ ERIK-DATOR, found 65578 cycles in 5 passes
10/25/09 18:24:38 v1.12 @ ERIK-DATOR, distribution of cycle lengths:
10/25/09 18:24:38 v1.12 @ ERIK-DATOR,    length 1 : 18773
10/25/09 18:24:38 v1.12 @ ERIK-DATOR,    length 2 : 13847
10/25/09 18:24:38 v1.12 @ ERIK-DATOR,    length 3 : 12128
10/25/09 18:24:38 v1.12 @ ERIK-DATOR,    length 4 : 8263
10/25/09 18:24:38 v1.12 @ ERIK-DATOR,    length 5 : 5490
10/25/09 18:24:38 v1.12 @ ERIK-DATOR,    length 6 : 3283
10/25/09 18:24:38 v1.12 @ ERIK-DATOR,    length 7 : 1832
10/25/09 18:24:38 v1.12 @ ERIK-DATOR,    length 9+: 1962
10/25/09 18:24:38 v1.12 @ ERIK-DATOR, largest cycle: 17 relations
10/25/09 18:24:39 v1.12 @ ERIK-DATOR, matrix is 65244 x 65578 (15.3 MB) with weight 3744054 (57.09/col)
10/25/09 18:24:39 v1.12 @ ERIK-DATOR, sparse part has weight 3744054 (57.09/col)
10/25/09 18:24:39 v1.12 @ ERIK-DATOR, filtering completed in 4 passes
10/25/09 18:24:39 v1.12 @ ERIK-DATOR, matrix is 60363 x 60427 (14.2 MB) with weight 3485480 (57.68/col)
10/25/09 18:24:39 v1.12 @ ERIK-DATOR, sparse part has weight 3485480 (57.68/col)
10/25/09 18:24:39 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later
10/25/09 18:24:39 v1.12 @ ERIK-DATOR, matrix is 60315 x 60427 (12.3 MB) with weight 3066599 (50.75/col)
10/25/09 18:24:39 v1.12 @ ERIK-DATOR, sparse part has weight 2853662 (47.22/col)
10/25/09 18:24:39 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows
10/25/09 18:24:39 v1.12 @ ERIK-DATOR, using block size 24170 for processor cache size 2048 kB
10/25/09 18:24:40 v1.12 @ ERIK-DATOR, commencing Lanczos iteration
10/25/09 18:24:40 v1.12 @ ERIK-DATOR, memory use: 10.5 MB
10/25/09 18:25:48 v1.12 @ ERIK-DATOR, lanczos halted after 955 iterations (dim = 60312)
10/25/09 18:25:49 v1.12 @ ERIK-DATOR, recovered 16 nontrivial dependencies
10/25/09 18:25:49 v1.12 @ ERIK-DATOR, prp48 = 142101798548019649379224996185134551483183791973
10/25/09 18:25:50 v1.12 @ ERIK-DATOR, prp43 = 2195586039900908690698168329609801270916603
10/25/09 18:25:50 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 80.6840 seconds.
10/25/09 18:25:50 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 1.4040 seconds.
10/25/09 18:25:50 v1.12 @ ERIK-DATOR, SIQS elapsed time = 2415.3788 seconds.

(64·10¹⁴⁸+71)/9 = 7(1)₁₄₇9_<149> = 178488573881573_<15> · C135

C135 = P54 · P81

P54 = 975169651366129558075327576737355940889743354566764389_<54>

P81 = 408551555183519006487997988119774128669000839667774060646809837018531358174074727_<81>

Number: 71119_148
N=398407077633402270859097355117764757231141518424162589329272214800757115653354785873245636091652410515292878810302450340483976288496803
  ( 135 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=975169651366129558075327576737355940889743354566764389 (pp54)
 r2=408551555183519006487997988119774128669000839667774060646809837018531358174074727 (pp81)
Version: Msieve-1.40
Total time: 16.08 hours.
Scaled time: 15.11 units (timescale=0.940).
Factorization parameters were as follows:
n: 398407077633402270859097355117764757231141518424162589329272214800757115653354785873245636091652410515292878810302450340483976288496803
m: 400000000000000000000000000000
deg: 5
c5: 125
c0: 142
skew: 1.03
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 1900001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 410063 x 410289
Total sieving time: 15.38 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,150.000,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,49,49,2.4,2.4,100000
total time: 16.08 hours.
 --------- CPU info (if available) ----------

(62·10¹³³-71)/9 = 6(8)₁₃₂1_<134> = 43 · 163 · 2767 · 3169 · C124

C124 = P54 · P70

P54 = 660658928585086985809163336350428170481943780205911441_<54>

P70 = 1696619339049209242025102064325212037235881003135077451714444644950863_<70>

Number: 68881_133
N=1120886714752989012233833245860000318452629651590483870856165594382614990996828653825284052587494909528216045838705574523583
  ( 124 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=660658928585086985809163336350428170481943780205911441 (pp54)
 r2=1696619339049209242025102064325212037235881003135077451714444644950863 (pp70)
Version: Msieve v. 1.43
Total time: 7.68 hours.
Scaled time: 6.05 units (timescale=0.788).
Factorization parameters were as follows:
n: 1120886714752989012233833245860000318452629651590483870856165594382614990996828653825284052587494909528216045838705574523583
m: 500000000000000000000000000
deg: 5
c5: 496
c0: -1775
skew: 1.29
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 211824 x 212049
Total sieving time: 7.30 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 7.68 hours.
 --------- CPU info (if available) ----------

Oct 26, 2009 (4th)

By Dmitry Domanov / ECMNET, GMP-ECM / Oct 26, 2009

(64·10¹⁸⁷+71)/9 = 7(1)₁₈₆9_<188> = C188

C188 = P40 · C148

P40 = 7275715586058467200945112931785663485369_<40>

C148 = [9773761806656149658840124430630023407923748725432364869224515384214314070359484134600992488023678710746726151284389176767268774084013256015079671751_<148>]

Factor=7275715586058467200945112931785663485369  Method=ECM  B1=11000000  Sigma=3065088127

Oct 26, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Oct 26, 2009

(64·10¹⁴⁵+71)/9 = 7(1)₁₄₄9_<146> = 195178673 · 13433198376877_<14> · C125

C125 = P58 · P67

P58 = 3985975919104421112065980519315938875570010459634054863923_<58>

P67 = 6804418311733872599573710011672467323159706487887800210790835847993_<67>

Number: n
N=27122247534084376245588110450780566165130294252738929924863032247137344769809668138430297488719079932927938298601631927656539
  ( 125 digits)
SNFS difficulty: 146 digits.
Divisors found:

Mon Oct 26 05:47:24 2009  prp58 factor: 3985975919104421112065980519315938875570010459634054863923
Mon Oct 26 05:47:24 2009  prp67 factor: 6804418311733872599573710011672467323159706487887800210790835847993
Mon Oct 26 05:47:24 2009  elapsed time 00:38:06 (Msieve 1.42 - dependency 6)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.17 hours.
Scaled time: 13.11 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_1_144_9
n: 27122247534084376245588110450780566165130294252738929924863032247137344769809668138430297488719079932927938298601631927656539
m: 200000000000000000000000000000
deg: 5
c5: 2
c0: 71
skew: 2.04
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [980000, 2260327)
Primes: RFBsize:146186, AFBsize:145537, largePrimes:3949671 encountered
Relations: rels:3857064, finalFF:293739
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 617581 hash collisions in 4330650 relations
Msieve: matrix is 336970 x 337195 (89.4 MB)

Total sieving time: 7.09 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 7.17 hours.
 --------- CPU info (if available) ----------

(61·10¹³⁴+11)/9 = 6(7)₁₃₃9_<135> = 7 · 956689 · 147489889 · C120

C120 = P40 · P81

P40 = 1605024511121898730823739355562491316477_<40>

P81 = 427537867971104787643044373647126483897763339452030506462774083723736087616393641_<81>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 686208757526421347401301256515966628463717052016141591646519249049878232120521785773458876968529245559700231093141322757 (120 digits)
Using B1=2118000, B2=2854078510, polynomial Dickson(6), sigma=3579718577
Step 1 took 18312ms
Step 2 took 7875ms
********** Factor found in step 2: 1605024511121898730823739355562491316477
Found probable prime factor of 40 digits: 1605024511121898730823739355562491316477
Probable prime cofactor 427537867971104787643044373647126483897763339452030506462774083723736087616393641 has 81 digits

Oct 26, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Oct 26, 2009

(26·10¹⁹²-11)/3 = 8(6)₁₉₁3_<193> = 19 · 31 · C191

C191 = P39 · P153

P39 = 101077267653156631307592584180426757637_<39>

P153 = 145573828899862454232548939907903440117030008911903381461583149437913645824448129191836349310485548267196198682523833675203109703598164258322341355722791_<153>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=97527106
Step 1 took 69743ms
Step 2 took 21801ms
********** Factor found in step 2: 101077267653156631307592584180426757637
Found probable prime factor of 39 digits: 101077267653156631307592584180426757637
Probable prime cofactor 145573828899862454232548939907903440117030008911903381461583149437913645824448129191836349310485548267196198682523833675203109703598164258322341355722791 has 153 digits

(26·10¹⁸⁹-11)/3 = 8(6)₁₈₈3_<190> = 71 · C189

C189 = P39 · P150

P39 = 141538917737574835614928365545711650133_<39>

P150 = 862418122525500258553228011718122233569703757701307710205000528958821534542694199458423775010924655490594982609345756497272737613083229460774392256541_<150>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4145718496
Step 1 took 70088ms
Step 2 took 21780ms
********** Factor found in step 2: 141538917737574835614928365545711650133
Found probable prime factor of 39 digits: 141538917737574835614928365545711650133
Probable prime cofactor 862418122525500258553228011718122233569703757701307710205000528958821534542694199458423775010924655490594982609345756497272737613083229460774392256541 has 150 digits

Oct 26, 2009

Factorizations of 677...779 and Factorizations of 688...881 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 25, 2009 (8th)

By Jo Yeong Uk / GMP-ECM v6.2.3, YAFU v1.10, GGNFS, Msieve v1.39 / Oct 25, 2009

(83·10¹⁴¹+7)/9 = 9(2)₁₄₀3_<142> = 61 · 91303 · 45529459 · 61880267 · C120

C120 = P32 · P35 · P54

P32 = 90583254195064513964951551233389_<32>

P35 = 32008672599379556241790724929001261_<35>

P54 = 202703127076465420436501533853575825089948645698619413_<54>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 587727526365835134078809853742617748922618069947582969642059147943446920904864207550850301733379285639847576970969808477 (120 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=8461231021
Step 1 took 4243ms
Step 2 took 4087ms
********** Factor found in step 2: 90583254195064513964951551233389
Found probable prime factor of 32 digits: 90583254195064513964951551233389
Composite cofactor 6488258029461010918009232216393658197894504657730103080991528610887031948984672636079793 has 88 digits
10/24/09 23:23:31 v1.10 @ 조영욱-PC, starting SIQS on c88: 6488258029461010918009232216393658197894504657730103080991528610887031948984672636079793

10/24/09 23:23:31 v1.10 @ 조영욱-PC, random seeds: 170176739, 2015898184
10/24/09 23:23:31 v1.10 @ 조영욱-PC, ==== sieve params ====
10/24/09 23:23:31 v1.10 @ 조영욱-PC, n = 88 digits, 292 bits
10/24/09 23:23:31 v1.10 @ 조영욱-PC, factor base: 61677 primes (max prime = 1636883)
10/24/09 23:23:31 v1.10 @ 조영욱-PC, single large prime cutoff: 180057130 (110 * pmax)
10/24/09 23:23:31 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
10/24/09 23:23:31 v1.10 @ 조영욱-PC, double large prime cutoff: 724000026774137
10/24/09 23:23:31 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base
10/24/09 23:23:31 v1.10 @ 조영욱-PC, buckets hold 1024 elements
10/24/09 23:23:31 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536
10/24/09 23:23:31 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors
10/24/09 23:23:31 v1.10 @ 조영욱-PC, using multiplier of 1
10/24/09 23:23:31 v1.10 @ 조영욱-PC, using small prime variation correction of 18 bits
10/24/09 23:23:31 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
10/24/09 23:23:31 v1.10 @ 조영욱-PC, trial factoring cutoff at 99 bits
10/24/09 23:23:31 v1.10 @ 조영욱-PC, ==== sieving started ====
10/24/09 23:59:49 v1.10 @ 조영욱-PC, sieve time = 1044.0410, relation time = 341.2810, poly_time = 792.4710
10/24/09 23:59:49 v1.10 @ 조영욱-PC, 61780 relations found: 20672 full + 41108 from 551741 partial, using 422103 polys (412 A polys)
10/24/09 23:59:49 v1.10 @ 조영욱-PC, on average, sieving found 1.36 rels/poly and 262.74 rels/sec
10/24/09 23:59:49 v1.10 @ 조영욱-PC, trial division touched 11670223 sieve locations out of 497932959744
10/24/09 23:59:49 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
10/24/09 23:59:50 v1.10 @ 조영욱-PC, begin with 572413 relations
10/24/09 23:59:50 v1.10 @ 조영욱-PC, reduce to 125508 relations in 9 passes
10/24/09 23:59:51 v1.10 @ 조영욱-PC, recovered 125508 relations
10/24/09 23:59:51 v1.10 @ 조영욱-PC, recovered 108512 polynomials
10/24/09 23:59:51 v1.10 @ 조영욱-PC, attempting to build 61780 cycles
10/24/09 23:59:51 v1.10 @ 조영욱-PC, found 61780 cycles in 4 passes
10/24/09 23:59:51 v1.10 @ 조영욱-PC, distribution of cycle lengths:
10/24/09 23:59:51 v1.10 @ 조영욱-PC,    length 1 : 20672
10/24/09 23:59:51 v1.10 @ 조영욱-PC,    length 2 : 17282
10/24/09 23:59:51 v1.10 @ 조영욱-PC,    length 3 : 11476
10/24/09 23:59:51 v1.10 @ 조영욱-PC,    length 4 : 6357
10/24/09 23:59:51 v1.10 @ 조영욱-PC,    length 5 : 3343
10/24/09 23:59:51 v1.10 @ 조영욱-PC,    length 6 : 1500
10/24/09 23:59:51 v1.10 @ 조영욱-PC,    length 7 : 675
10/24/09 23:59:51 v1.10 @ 조영욱-PC,    length 9+: 475
10/24/09 23:59:51 v1.10 @ 조영욱-PC, largest cycle: 15 relations
10/24/09 23:59:51 v1.10 @ 조영욱-PC, matrix is 61677 x 61780 (13.0 MB) with weight 2901214 (46.96/col)
10/24/09 23:59:51 v1.10 @ 조영욱-PC, sparse part has weight 2901214 (46.96/col)
10/24/09 23:59:51 v1.10 @ 조영욱-PC, filtering completed in 3 passes
10/24/09 23:59:51 v1.10 @ 조영욱-PC, matrix is 55117 x 55181 (11.8 MB) with weight 2649715 (48.02/col)
10/24/09 23:59:51 v1.10 @ 조영욱-PC, sparse part has weight 2649715 (48.02/col)
10/24/09 23:59:52 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
10/24/09 23:59:52 v1.10 @ 조영욱-PC, matrix is 55069 x 55181 (8.3 MB) with weight 2124201 (38.50/col)
10/24/09 23:59:52 v1.10 @ 조영욱-PC, sparse part has weight 1633043 (29.59/col)
10/24/09 23:59:52 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
10/24/09 23:59:52 v1.10 @ 조영욱-PC, using block size 22072 for processor cache size 4096 kB
10/24/09 23:59:52 v1.10 @ 조영욱-PC, commencing Lanczos iteration
10/24/09 23:59:52 v1.10 @ 조영욱-PC, memory use: 7.6 MB
10/25/09 00:00:04 v1.10 @ 조영욱-PC, lanczos halted after 872 iterations (dim = 55067)
10/25/09 00:00:04 v1.10 @ 조영욱-PC, recovered 15 nontrivial dependencies
10/25/09 00:00:04 v1.10 @ 조영욱-PC, prp35 = 32008672599379556241790724929001261
10/25/09 00:00:05 v1.10 @ 조영욱-PC, prp54 = 202703127076465420436501533853575825089948645698619413
10/25/09 00:00:05 v1.10 @ 조영욱-PC, Lanczos elapsed time = 14.2900 seconds.
10/25/09 00:00:05 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.9510 seconds.
10/25/09 00:00:05 v1.10 @ 조영욱-PC, SIQS elapsed time = 2193.8590 seconds.
10/25/09 00:00:05 v1.10 @ 조영욱-PC, 
10/25/09 00:00:05 v1.10 @ 조영욱-PC,

(2·10¹⁹¹+1)/3 = (6)₁₉₀7_<191> = 107 · 434363 · C184

C184 = P50 · P51 · P84

P50 = 15883788275518933823378174648633065329129145471009_<50>

P51 = 129154159023019835829280546025015851553267122632403_<51>

P84 = 699213257067203864864521928555707071916884215419505461497175542943038439663014948481_<84>

Number: 66667_191
N=1434406152231100789889456270633080821191497646465831588396179221102111192683398311573427864141340128230028944236263102878843823887829783153004453694834093105998031722221970005807121587
  ( 184 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=15883788275518933823378174648633065329129145471009
 r2=129154159023019835829280546025015851553267122632403
 r3=699213257067203864864521928555707071916884215419505461497175542943038439663014948481
Version: 
Total time: 149.38 hours.
Scaled time: 353.14 units (timescale=2.364).
Factorization parameters were as follows:
n: 1434406152231100789889456270633080821191497646465831588396179221102111192683398311573427864141340128230028944236263102878843823887829783153004453694834093105998031722221970005807121587
m: 100000000000000000000000000000000000000
deg: 5
c5: 20
c0: 1
skew: 0.55
type: snfs
lss: 1
rlim: 10000000
alim: 10000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [5000000, 8700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 21632821
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1981244 x 1981491
Total sieving time: 133.97 hours.
Total relation processing time: 4.32 hours.
Matrix solve time: 10.51 hours.
Time per square root: 0.59 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,55,55,2.5,2.5,100000
total time: 149.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(64·10¹⁴⁶+71)/9 = 7(1)₁₄₅9_<147> = 29 · 43 · 2942688563887_<13> · C132

C132 = P38 · P94

P38 = 20922248714492232747363242068574188327_<38>

P94 = 9262289457946675998505921238040544871349507594919771113867620230027339113642857153369700991273_<94>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 193787923704779801177073863032680063432689263509288681043015945411329156407124011875072237800285489154167790197935985497233285470271 (132 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5589003022
Step 1 took 3281ms
Step 2 took 2185ms
********** Factor found in step 2: 20922248714492232747363242068574188327
Found probable prime factor of 38 digits: 20922248714492232747363242068574188327
Probable prime cofactor 9262289457946675998505921238040544871349507594919771113867620230027339113642857153369700991273 has 94 digits

(26·10¹⁴⁹-11)/3 = 8(6)₁₄₈3_<150> = 7 · 367 · 437964631187_<12> · 2462434045223432635184577368617_<31> · C105

C105 = P32 · P74

P32 = 14879455248887629252872247910309_<32>

P74 = 21023126856417165892087401739868084915754062458746846717606000991769788457_<74>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 312812675251746883894906550322388849288538455287149121253041175155208857123669318024554523653217239503213 (105 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=7586851862
Step 1 took 2674ms
Step 2 took 1850ms
********** Factor found in step 2: 14879455248887629252872247910309
Found probable prime factor of 32 digits: 14879455248887629252872247910309
Probable prime cofactor 21023126856417165892087401739868084915754062458746846717606000991769788457 has 74 digits

(64·10¹⁴⁷+71)/9 = 7(1)₁₄₆9_<148> = 3³ · 7 · 23 · 1361 · 34037098252908254717_<20> · C122

C122 = P31 · P43 · P49

P31 = 9092679240857687203699489343863_<31>

P43 = 1133692009344949981305377259795459982489171_<43>

P49 = 3425706994020588576485113095334514017387044260077_<49>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 35313207866128717054296738530445351859223418556327577583962195210110904762886801944682119343082073509336326076720727163121 (122 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=7176917761
Step 1 took 4196ms
Step 2 took 16ms
********** Factor found in step 2: 9092679240857687203699489343863
Found probable prime factor of 31 digits: 9092679240857687203699489343863
Composite cofactor 3883696645478249614182960181405500086959054640731065811210010188998322859496291566360126167 has 91 digits

10/25/09 09:34:43 v1.10 @ 조영욱-PC, starting SIQS on c91: 3883696645478249614182960181405500086959054640731065811210010188998322859496291566360126167
10/25/09 09:34:43 v1.10 @ 조영욱-PC, random seeds: 2850916953, 456782072
10/25/09 09:34:44 v1.10 @ 조영욱-PC, ==== sieve params ====
10/25/09 09:34:44 v1.10 @ 조영욱-PC, n = 91 digits, 304 bits
10/25/09 09:34:44 v1.10 @ 조영욱-PC, factor base: 68495 primes (max prime = 1822187)
10/25/09 09:34:44 v1.10 @ 조영욱-PC, single large prime cutoff: 218662440 (120 * pmax)
10/25/09 09:34:44 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
10/25/09 09:34:44 v1.10 @ 조영욱-PC, double large prime cutoff: 1027054623429564
10/25/09 09:34:44 v1.10 @ 조영욱-PC, using 16 large prime slices of factor base
10/25/09 09:34:44 v1.10 @ 조영욱-PC, buckets hold 1024 elements
10/25/09 09:34:44 v1.10 @ 조영욱-PC, sieve interval: 11 blocks of size 65536
10/25/09 09:34:44 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors
10/25/09 09:34:44 v1.10 @ 조영욱-PC, using multiplier of 7
10/25/09 09:34:44 v1.10 @ 조영욱-PC, using small prime variation correction of 21 bits
10/25/09 09:34:44 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
10/25/09 09:34:44 v1.10 @ 조영욱-PC, trial factoring cutoff at 96 bits
10/25/09 09:34:44 v1.10 @ 조영욱-PC, ==== sieving started ====
10/25/09 10:24:05 v1.10 @ 조영욱-PC, sieve time = 1336.7250, relation time = 691.6450, poly_time = 932.2880
10/25/09 10:24:05 v1.10 @ 조영욱-PC, 68584 relations found: 19869 full + 48715 from 829684 partial, using 424594 polys (207 A polys)
10/25/09 10:24:05 v1.10 @ 조영욱-PC, on average, sieving found 2.00 rels/poly and 286.83 rels/sec
10/25/09 10:24:05 v1.10 @ 조영욱-PC, trial division touched 25510065 sieve locations out of 612176232448
10/25/09 10:24:05 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
10/25/09 10:24:06 v1.10 @ 조영욱-PC, begin with 849553 relations
10/25/09 10:24:06 v1.10 @ 조영욱-PC, reduce to 159157 relations in 9 passes
10/25/09 10:24:07 v1.10 @ 조영욱-PC, recovered 159157 relations
10/25/09 10:24:07 v1.10 @ 조영욱-PC, recovered 132584 polynomials
10/25/09 10:24:08 v1.10 @ 조영욱-PC, attempting to build 68584 cycles
10/25/09 10:24:08 v1.10 @ 조영욱-PC, found 68584 cycles in 5 passes
10/25/09 10:24:08 v1.10 @ 조영욱-PC, distribution of cycle lengths:
10/25/09 10:24:08 v1.10 @ 조영욱-PC,    length 1 : 19869
10/25/09 10:24:08 v1.10 @ 조영욱-PC,    length 2 : 14935
10/25/09 10:24:08 v1.10 @ 조영욱-PC,    length 3 : 12558
10/25/09 10:24:08 v1.10 @ 조영욱-PC,    length 4 : 8791
10/25/09 10:24:08 v1.10 @ 조영욱-PC,    length 5 : 5600
10/25/09 10:24:08 v1.10 @ 조영욱-PC,    length 6 : 3169
10/25/09 10:24:08 v1.10 @ 조영욱-PC,    length 7 : 1793
10/25/09 10:24:08 v1.10 @ 조영욱-PC,    length 9+: 1869
10/25/09 10:24:08 v1.10 @ 조영욱-PC, largest cycle: 16 relations
10/25/09 10:24:08 v1.10 @ 조영욱-PC, matrix is 68495 x 68584 (16.9 MB) with weight 3885812 (56.66/col)
10/25/09 10:24:08 v1.10 @ 조영욱-PC, sparse part has weight 3885812 (56.66/col)
10/25/09 10:24:08 v1.10 @ 조영욱-PC, filtering completed in 3 passes
10/25/09 10:24:08 v1.10 @ 조영욱-PC, matrix is 63408 x 63471 (15.8 MB) with weight 3643439 (57.40/col)
10/25/09 10:24:08 v1.10 @ 조영욱-PC, sparse part has weight 3643439 (57.40/col)
10/25/09 10:24:08 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
10/25/09 10:24:08 v1.10 @ 조영욱-PC, matrix is 63360 x 63471 (10.5 MB) with weight 2826606 (44.53/col)
10/25/09 10:24:08 v1.10 @ 조영욱-PC, sparse part has weight 2120045 (33.40/col)
10/25/09 10:24:08 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
10/25/09 10:24:08 v1.10 @ 조영욱-PC, using block size 25388 for processor cache size 4096 kB
10/25/09 10:24:09 v1.10 @ 조영욱-PC, commencing Lanczos iteration
10/25/09 10:24:09 v1.10 @ 조영욱-PC, memory use: 9.4 MB
10/25/09 10:24:26 v1.10 @ 조영욱-PC, lanczos halted after 1004 iterations (dim = 63356)
10/25/09 10:24:26 v1.10 @ 조영욱-PC, recovered 15 nontrivial dependencies
10/25/09 10:24:29 v1.10 @ 조영욱-PC, prp49 = 3425706994020588576485113095334514017387044260077
10/25/09 10:24:30 v1.10 @ 조영욱-PC, prp43 = 1133692009344949981305377259795459982489171
10/25/09 10:24:30 v1.10 @ 조영욱-PC, Lanczos elapsed time = 20.9670 seconds.
10/25/09 10:24:30 v1.10 @ 조영욱-PC, Sqrt elapsed time = 3.5410 seconds.
10/25/09 10:24:30 v1.10 @ 조영욱-PC, SIQS elapsed time = 2986.4140 seconds.
10/25/09 10:24:30 v1.10 @ 조영욱-PC, 
10/25/09 10:24:30 v1.10 @ 조영욱-PC,

(83·10¹⁴⁴+7)/9 = 9(2)₁₄₃3_<145> = 89 · 607 · 530743 · 26578672453_<11> · C125

C125 = P37 · P88

P37 = 7620243200305720178433627196673681023_<37>

P88 = 1588073113575697728528935879433186144051276413419026749657921230265554117895252647777853_<88>

Number: 92223_144
N=12101503345313544296726077856879492583269902651699773591285503600604622679901120704345584900671105410790856437888630685783619
  ( 125 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=7620243200305720178433627196673681023
 r2=1588073113575697728528935879433186144051276413419026749657921230265554117895252647777853
Version: 
Total time: 7.02 hours.
Scaled time: 16.72 units (timescale=2.383).
Factorization parameters were as follows:
n: 12101503345313544296726077856879492583269902651699773591285503600604622679901120704345584900671105410790856437888630685783619
m: 100000000000000000000000000000
deg: 5
c5: 83
c0: 70
skew: 0.97
type: snfs
lss: 1
rlim: 2550000
alim: 2550000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2550000/2550000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1275000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4760461
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 349434 x 349682
Total sieving time: 6.52 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2550000,2550000,26,26,49,49,2.3,2.3,75000
total time: 7.02 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(64·10¹⁴⁵+17)/9 = 7(1)₁₄₄3_<146> = 73 · 7109 · 9487363 · 211475533 · 146365173826136249057_<21> · C105

C105 = P49 · P57

P49 = 1169813637472724608879846874031360720284904573943_<49>

P57 = 398883444547249357116524080979030956658275082357933999821_<57>

Number: 71113_145
N=466619293193467609106637409577082544935587703521242296864100906176497819573361078885346853164715843264203
  ( 105 digits)
Divisors found:
 r1=1169813637472724608879846874031360720284904573943
 r2=398883444547249357116524080979030956658275082357933999821
Version: 
Total time: 4.96 hours.
Scaled time: 11.85 units (timescale=2.387).
Factorization parameters were as follows:
name: 71113_145
n: 466619293193467609106637409577082544935587703521242296864100906176497819573361078885346853164715843264203
skew: 6309.61
# norm 1.33e+14
c5: 31200
c4: -790565510
c3: -11376259783517
c2: 23289595609209357
c1: 16856853205610039493
c0: 20770263123537894491952
# alpha -4.99
Y1: 71362036229
Y0: -108383474337977239085
# Murphy_E 1.96e-09
# M 165076693542715147816953182526660278637643445471452452355295693622258007479330605559673783801438412873209
type: gnfs
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 1800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7220317
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 288024 x 288272
Polynomial selection time: 0.33 hours.
Total sieving time: 3.86 hours.
Total relation processing time: 0.53 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000
total time: 4.96 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(59·10¹⁵³+13)/9 = 6(5)₁₅₂7_<154> = 61 · 14431 · C148

C148 = P36 · C113

P36 = 448464904859558179943943527591218691_<36>

C113 = [16605607864965677941097681100617903499359254644723048816511846628405008244182350794304630346346316241452961808797_<113>]

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 7447032351296963794422021303813801976341409324366096615273307980605908223025744390838433603837316927647284313432212252034333595998999825688954624727 (148 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3255258886
Step 1 took 4664ms
Step 2 took 4586ms
********** Factor found in step 2: 448464904859558179943943527591218691
Found probable prime factor of 36 digits: 448464904859558179943943527591218691
Composite cofactor 16605607864965677941097681100617903499359254644723048816511846628405008244182350794304630346346316241452961808797 has 113 digits

Oct 25, 2009 (7th)

By Sinkiti Sibata / GGNFS, Msieve / Oct 25, 2009

(26·10¹²⁸-11)/3 = 8(6)₁₂₇3_<129> = 534716673012120673637_<21> · C109

C109 = P53 · P56

P53 = 28231457338923355714210349805249384803656629093653461_<53>

P56 = 57410994463621940343419240971956483368602008129962515759_<56>

Number: 86663_128
N=1620796040984907771562505445804590777389195101791022914125100946213000619690680554239828560158443812097391899
  ( 109 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=28231457338923355714210349805249384803656629093653461 (pp53)
 r2=57410994463621940343419240971956483368602008129962515759 (pp56)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.82 hours.
Scaled time: 9.40 units (timescale=1.949).
Factorization parameters were as follows:
name: 86663_128
n: 1620796040984907771562505445804590777389195101791022914125100946213000619690680554239828560158443812097391899
m: 50000000000000000000000000
deg: 5
c5: 208
c0: -275
skew: 1.06
type: snfs
lss: 1
rlim: 1060000
alim: 1060000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1060000/1060000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [530000, 980001)
Primes: RFBsize:82832, AFBsize:83234, largePrimes:2781623 encountered
Relations: rels:2702185, finalFF:229580
Max relations in full relation-set: 28
Initial matrix: 166133 x 229580 with sparse part having weight 17710428.
Pruned matrix : 146994 x 147888 with weight 8493934.
Total sieving time: 4.56 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1060000,1060000,26,26,47,47,2.3,2.3,50000
total time: 4.82 hours.
 --------- CPU info (if available) ----------

(64·10¹³⁹+17)/9 = 7(1)₁₃₈3_<140> = 113 · 2066992703_<10> · 732894075941_<12> · 3316020366531589_<16> · C102

C102 = P41 · P61

P41 = 35340792430636249735607064473287711611151_<41>

P61 = 3544748225760749980193652509393545530287763093943914933592433_<61>

Number: 71113_139
N=125274211265476789012584372600934384359407136184462238841338702440456197293391775672309177070812020383
  ( 102 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=35340792430636249735607064473287711611151 (pp41)
 r2=3544748225760749980193652509393545530287763093943914933592433 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.57 hours.
Scaled time: 16.96 units (timescale=1.979).
Factorization parameters were as follows:
name: 71113_139
n: 125274211265476789012584372600934384359407136184462238841338702440456197293391775672309177070812020383
m: 20000000000000000000000000000
deg: 5
c5: 1
c0: 85
skew: 2.43
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1500001)
Primes: RFBsize:121127, AFBsize:121640, largePrimes:3807169 encountered
Relations: rels:4056948, finalFF:533305
Max relations in full relation-set: 28
Initial matrix: 242831 x 533305 with sparse part having weight 45727150.
Pruned matrix : 171742 x 173020 with weight 14020652.
Total sieving time: 8.12 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 8.57 hours.
 --------- CPU info (if available) ----------

(59·10¹⁶²+13)/9 = 6(5)₁₆₁7_<163> = 73² · 97 · 727 · 110119 · 187420399057_<12> · 2334523065937_<13> · 382716642977363_<15> · 12076827793624644509443_<23> · C89

C89 = P29 · P61

P29 = 69516819691144244489845582123_<29>

P61 = 1126834753234250582167665892728317395683413561745942050448631_<61>

Sun Oct 25 15:43:55 2009  Msieve v. 1.42
Sun Oct 25 15:43:55 2009  random seeds: eca55479 eedbe34a
Sun Oct 25 15:43:55 2009  factoring 78333968362300416510181956690557714648145208117374814352621832119111721264997885503423613 (89 digits)
Sun Oct 25 15:43:56 2009  no P-1/P+1/ECM available, skipping
Sun Oct 25 15:43:56 2009  commencing quadratic sieve (89-digit input)
Sun Oct 25 15:43:56 2009  using multiplier of 1
Sun Oct 25 15:43:56 2009  using 64kb Pentium 4 sieve core
Sun Oct 25 15:43:56 2009  sieve interval: 17 blocks of size 65536
Sun Oct 25 15:43:56 2009  processing polynomials in batches of 6
Sun Oct 25 15:43:56 2009  using a sieve bound of 1565017 (59333 primes)
Sun Oct 25 15:43:56 2009  using large prime bound of 125201360 (26 bits)
Sun Oct 25 15:43:56 2009  using double large prime bound of 376440425084800 (42-49 bits)
Sun Oct 25 15:43:56 2009  using trial factoring cutoff of 49 bits
Sun Oct 25 15:43:56 2009  polynomial 'A' values have 11 factors
Sun Oct 25 17:47:06 2009  59646 relations (15545 full + 44101 combined from 638233 partial), need 59429
Sun Oct 25 17:47:08 2009  begin with 653778 relations
Sun Oct 25 17:47:09 2009  reduce to 147069 relations in 10 passes
Sun Oct 25 17:47:09 2009  attempting to read 147069 relations
Sun Oct 25 17:47:12 2009  recovered 147069 relations
Sun Oct 25 17:47:12 2009  recovered 125914 polynomials
Sun Oct 25 17:47:13 2009  attempting to build 59646 cycles
Sun Oct 25 17:47:13 2009  found 59646 cycles in 5 passes
Sun Oct 25 17:47:13 2009  distribution of cycle lengths:
Sun Oct 25 17:47:13 2009     length 1 : 15545
Sun Oct 25 17:47:13 2009     length 2 : 11194
Sun Oct 25 17:47:13 2009     length 3 : 10420
Sun Oct 25 17:47:13 2009     length 4 : 8120
Sun Oct 25 17:47:13 2009     length 5 : 5800
Sun Oct 25 17:47:13 2009     length 6 : 3610
Sun Oct 25 17:47:13 2009     length 7 : 2239
Sun Oct 25 17:47:13 2009     length 9+: 2718
Sun Oct 25 17:47:13 2009  largest cycle: 18 relations
Sun Oct 25 17:47:13 2009  matrix is 59333 x 59646 (14.8 MB) with weight 3630587 (60.87/col)
Sun Oct 25 17:47:13 2009  sparse part has weight 3630587 (60.87/col)
Sun Oct 25 17:47:14 2009  filtering completed in 3 passes
Sun Oct 25 17:47:14 2009  matrix is 55723 x 55787 (13.9 MB) with weight 3413972 (61.20/col)
Sun Oct 25 17:47:15 2009  sparse part has weight 3413972 (61.20/col)
Sun Oct 25 17:47:15 2009  saving the first 48 matrix rows for later
Sun Oct 25 17:47:15 2009  matrix is 55675 x 55787 (10.3 MB) with weight 2849057 (51.07/col)
Sun Oct 25 17:47:15 2009  sparse part has weight 2368968 (42.46/col)
Sun Oct 25 17:47:15 2009  matrix includes 64 packed rows
Sun Oct 25 17:47:15 2009  using block size 21845 for processor cache size 512 kB
Sun Oct 25 17:47:15 2009  commencing Lanczos iteration
Sun Oct 25 17:47:15 2009  memory use: 9.7 MB
Sun Oct 25 17:47:48 2009  lanczos halted after 881 iterations (dim = 55671)
Sun Oct 25 17:47:48 2009  recovered 14 nontrivial dependencies
Sun Oct 25 17:47:51 2009  prp29 factor: 69516819691144244489845582123
Sun Oct 25 17:47:51 2009  prp61 factor: 1126834753234250582167665892728317395683413561745942050448631
Sun Oct 25 17:47:51 2009  elapsed time 02:03:56

(26·10¹³⁹-11)/3 = 8(6)₁₃₈3_<140> = 1693 · 6888904706941_<13> · C124

C124 = P61 · P63

P61 = 8870595788892487911104375936030780894093930167133280256610899_<61>

P63 = 837707045164910241217663948652115615923423788814338069923561749_<63>

Number: 86663_139
N=7430960587165421962000123662758431206353926455170965852483838812840294402028743639310757689822470021911230605916761692902351
  ( 124 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=8870595788892487911104375936030780894093930167133280256610899 (pp61)
 r2=837707045164910241217663948652115615923423788814338069923561749 (pp63)
Version: Msieve-1.40
Total time: 6.51 hours.
Scaled time: 13.48 units (timescale=2.071).
Factorization parameters were as follows:
name: 86663_139
n: 7430960587165421962000123662758431206353926455170965852483838812840294402028743639310757689822470021911230605916761692902351
m: 10000000000000000000000000000
deg: 5
c5: 13
c0: -55
skew: 1.33
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1585001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 229759 x 229996
Total sieving time: 6.20 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 6.51 hours.
 --------- CPU info (if available) ----------

(64·10¹⁴¹+17)/9 = 7(1)₁₄₀3_<142> = 3 · 3631 · 23774027 · 38210935379_<11> · C120

C120 = P47 · P74

P47 = 23562641469567864876337026588185070376527483949_<47>

P74 = 30498295302175290423634367739758902230843046755702055066361643029047633073_<74>

SNFS difficulty: 142 digits.
Divisors found:
 r1=23562641469567864876337026588185070376527483949 (pp47)
 r2=30498295302175290423634367739758902230843046755702055066361643029047633073 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.53 hours.
Scaled time: 20.20 units (timescale=1.919).
Factorization parameters were as follows:
name: 71113_141
n: 718620397638162294733305621236272925576662114980663962005049956604711481492309440291240165113252665825820512650449045277
m: 20000000000000000000000000000
deg: 5
c5: 20
c0: 17
skew: 0.97
type: snfs
lss: 1
rlim: 1680000
alim: 1680000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1680000/1680000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [840000, 1740001)
Primes: RFBsize:126753, AFBsize:126821, largePrimes:3769249 encountered
Relations: rels:3815360, finalFF:333077
Max relations in full relation-set: 28
Initial matrix: 253640 x 333077 with sparse part having weight 30096722.
Pruned matrix : 227339 x 228671 with weight 17309106.
Total sieving time: 9.84 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.49 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1680000,1680000,26,26,48,48,2.3,2.3,100000
total time: 10.53 hours.
 --------- CPU info (if available) ----------

Oct 25, 2009 (6th)

By Norbert Schneider / Msieve / Oct 25, 2009

(26·10¹⁴⁷-11)/3 = 8(6)₁₄₆3_<148> = 31 · 79 · 167 · 1353459067381824712130681_<25> · 21398446694347252792235023_<26> · C93

C93 = P42 · P52

P42 = 126483774862839140088316862326098266953543_<42>

P52 = 5784750647104411502104764644569097235027045860205329_<52>

Sat Oct 24 19:10:22 2009  
Sat Oct 24 19:10:22 2009  
Sat Oct 24 19:10:22 2009  Msieve v. 1.43
Sat Oct 24 19:10:22 2009  random seeds: b616bf80 3a42ab57
Sat Oct 24 19:10:22 2009  factoring 731677098486017412808124512800179508883325488052549521445809992284550135852428581537284030647 (93 digits)
Sat Oct 24 19:10:24 2009  searching for 15-digit factors
Sat Oct 24 19:10:24 2009  commencing quadratic sieve (93-digit input)
Sat Oct 24 19:10:25 2009  using multiplier of 47
Sat Oct 24 19:10:25 2009  using 64kb Pentium 4 sieve core
Sat Oct 24 19:10:25 2009  sieve interval: 18 blocks of size 65536
Sat Oct 24 19:10:25 2009  processing polynomials in batches of 6
Sat Oct 24 19:10:25 2009  using a sieve bound of 1956901 (72705 primes)
Sat Oct 24 19:10:25 2009  using large prime bound of 244612625 (27 bits)
Sat Oct 24 19:10:25 2009  using double large prime bound of 1256787622996125 (42-51 bits)
Sat Oct 24 19:10:25 2009  using trial factoring cutoff of 51 bits
Sat Oct 24 19:10:25 2009  polynomial 'A' values have 12 factors
Sat Oct 24 23:59:39 2009  73218 relations (18983 full + 54235 combined from 989961 partial), need 72801
Sat Oct 24 23:59:45 2009  begin with 1008944 relations
Sat Oct 24 23:59:47 2009  reduce to 185654 relations in 13 passes
Sat Oct 24 23:59:47 2009  attempting to read 185654 relations
Sat Oct 24 23:59:53 2009  recovered 185654 relations
Sat Oct 24 23:59:53 2009  recovered 166490 polynomials
Sat Oct 24 23:59:53 2009  attempting to build 73218 cycles
Sat Oct 24 23:59:54 2009  found 73218 cycles in 6 passes
Sat Oct 24 23:59:54 2009  distribution of cycle lengths:
Sat Oct 24 23:59:54 2009     length 1 : 18983
Sat Oct 24 23:59:54 2009     length 2 : 13497
Sat Oct 24 23:59:54 2009     length 3 : 12531
Sat Oct 24 23:59:54 2009     length 4 : 9663
Sat Oct 24 23:59:54 2009     length 5 : 7152
Sat Oct 24 23:59:54 2009     length 6 : 4604
Sat Oct 24 23:59:54 2009     length 7 : 2958
Sat Oct 24 23:59:54 2009     length 9+: 3830
Sat Oct 24 23:59:54 2009  largest cycle: 21 relations
Sat Oct 24 23:59:54 2009  matrix is 72705 x 73218 (19.0 MB) with weight 4700937 (64.20/col)
Sat Oct 24 23:59:54 2009  sparse part has weight 4700937 (64.20/col)
Sat Oct 24 23:59:58 2009  filtering completed in 3 passes
Sat Oct 24 23:59:58 2009  matrix is 68396 x 68460 (17.8 MB) with weight 4402031 (64.30/col)
Sat Oct 24 23:59:58 2009  sparse part has weight 4402031 (64.30/col)
Sat Oct 24 23:59:58 2009  saving the first 48 matrix rows for later
Sat Oct 24 23:59:58 2009  matrix is 68348 x 68460 (11.8 MB) with weight 3524777 (51.49/col)
Sat Oct 24 23:59:58 2009  sparse part has weight 2669452 (38.99/col)
Sat Oct 24 23:59:58 2009  matrix includes 64 packed rows
Sat Oct 24 23:59:59 2009  using block size 10922 for processor cache size 256 kB
Sun Oct 25 00:00:00 2009  commencing Lanczos iteration
Sun Oct 25 00:00:00 2009  memory use: 11.6 MB
Sun Oct 25 00:00:23 2009  linear algebra at 35.2%, ETA 0h 0m
Sun Oct 25 00:01:04 2009  lanczos halted after 1082 iterations (dim = 68345)
Sun Oct 25 00:01:04 2009  recovered 16 nontrivial dependencies
Sun Oct 25 00:01:05 2009  prp42 factor: 126483774862839140088316862326098266953543
Sun Oct 25 00:01:05 2009  prp52 factor: 5784750647104411502104764644569097235027045860205329
Sun Oct 25 00:01:05 2009  elapsed time 04:50:43

Oct 25, 2009 (5th)

By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Oct 25, 2009

(64·10¹⁵⁰+17)/9 = 7(1)₁₄₉3_<151> = 3 · 163 · 593 · C146

C146 = P45 · P102

P45 = 181460493643859860267546457615776892302547113_<45>

P102 = 135142461223855023769374585953390591400230384542853999743362412572020686220483774158288305519116127913_<102>

Number: s146
N=24523017725926922173521041707139225218245278456950417140363239536622253182532101204961466292537377485494060256886274122123861930812137207816865169
  ( 146 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=181460493643859860267546457615776892302547113 (pp45)
 r2=135142461223855023769374585953390591400230384542853999743362412572020686220483774158288305519116127913 (pp102)
Version: Msieve-1.40
Total time: 11.57 hours.
Scaled time: 21.45 units (timescale=1.855).
Factorization parameters were as follows:
n: 24523017725926922173521041707139225218245278456950417140363239536622253182532101204961466292537377485494060256886274122123861930812137207816865169
m: 2000000000000000000000000000000
deg: 5
c5: 2
c0: 17
skew: 1.53
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1900001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 385402 x 385626
Total sieving time: 11.29 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 11.57 hours.
 --------- CPU info (if available) ----------

(64·10¹⁵⁰+71)/9 = 7(1)₁₄₉9_<151> = 3 · 37589 · 1608992995552909_<16> · 38743674467950353459894799_<26> · C106

C106 = P47 · P59

P47 = 60033171818637036837946345942978850104908263861_<47>

P59 = 16850360145293193596749837297116847910388052640299429895407_<59>

Number: gnfs106
N=1011580565808300035324835095269093337415387040964529896988277350606665747712644305132003455465229187986427
  ( 106 digits)
Divisors found:
 r1=60033171818637036837946345942978850104908263861 (pp47)
 r2=16850360145293193596749837297116847910388052640299429895407 (pp59)
Version: Msieve-1.40
Total time: 7.46 hours.
Scaled time: 14.39 units (timescale=1.928).
Factorization parameters were as follows:
name: gnfs106
n: 1011580565808300035324835095269093337415387040964529896988277350606665747712644305132003455465229187986427
skew: 12656.69
# norm 7.40e+014
c5: 92400
c4: 839948774
c3: -73701608093115
c2: -18833223482297583
c1: 3377810069304610720235
c0: 488844492386143255374089
# alpha -6.62
Y1: 273354832543
Y0: -101827148467019791260
# Murphy_E 1.89e-009
# M 301070719605173866416940685340759894911051254330603743674021012391945810541977611780615421200839662171667
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 241887 x 242112
Polynomial selection time: 0.85 hours.
Total sieving time: 6.35 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 7.46 hours.
 --------- CPU info (if available) ----------

(83·10¹⁵⁷+7)/9 = 9(2)₁₅₆3_<158> = 3³ · 23 · 139 · 677 · C151

C151 = P36 · P40 · P76

P36 = 626045116755851438475264246925740973_<36>

P40 = 1012848459600439964833165666804565900201_<40>

P76 = 2488802357902899188563060987762312568445426174233937076223149292666541768377_<76>

Number: s151
N=1578121780566208685648783175796566047694410946908300383814237710890474095105303759855938548409399934460792588239638370389847815575334517088184990675021
  ( 151 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=626045116755851438475264246925740973 (pp36)
 r2=1012848459600439964833165666804565900201 (pp40)
 r3=2488802357902899188563060987762312568445426174233937076223149292666541768377 (pp76)
Version: Msieve-1.40
Total time: 25.44 hours.
Scaled time: 49.04 units (timescale=1.928).
Factorization parameters were as follows:
n: 1578121780566208685648783175796566047694410946908300383814237710890474095105303759855938548409399934460792588239638370389847815575334517088184990675021
m: 50000000000000000000000000000000
deg: 5
c5: 332
c0: 875
skew: 1.21
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3200001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 703919 x 704146
Total sieving time: 24.62 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.59 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 25.44 hours.
 --------- CPU info (if available) ----------

(26·10¹⁹⁴-11)/3 = 8(6)₁₉₃3_<195> = C195

C195 = P39 · C157

P39 = 195721309769165290517468167522075066993_<39>

C157 = [4428064923992271188897172141909552065313113376249145079122632080472355721315498754192989009423534511274168794443365639986065578670493920034925645440231447191_<157>]

Factor=195721309769165290517468167522075066993  Method=ECM  B1=11000000  Sigma=1337364280

Oct 25, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Oct 25, 2009

(64·10¹⁴⁶+17)/9 = 7(1)₁₄₅3_<147> = 131 · 409831 · C140

C140 = P46 · P94

P46 = 2851884250413709181276276969836114316460554033_<46>

P94 = 4644398416732077928294402657397906910999332994134532480822741775205785263948309822994189042901_<94>

Number: n
N=13245286697324579779982501279220476135398858805552173350901633259539081117631248358192387495398840924415131962718930283162354169988465569733
  ( 140 digits)
SNFS difficulty: 147 digits.
Divisors found:

Sun Oct 25 04:44:32 2009  prp46 factor: 2851884250413709181276276969836114316460554033
Sun Oct 25 04:44:32 2009  prp94 factor: 4644398416732077928294402657397906910999332994134532480822741775205785263948309822994189042901
Sun Oct 25 04:44:32 2009  elapsed time 00:02:10 (Msieve 1.42 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.35 hours.
Scaled time: 13.44 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_1_145_3
n: 13245286697324579779982501279220476135398858805552173350901633259539081117631248358192387495398840924415131962718930283162354169988465569733
m: 200000000000000000000000000000
deg: 5
c5: 20
c0: 17
skew: 0.97
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [1000000, 2300323)
Primes: RFBsize:148933, AFBsize:148990, largePrimes:3965971 encountered
Relations: rels:3886206, finalFF:306420
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 553406 hash collisions in 4547224 relations
Msieve: matrix is 338967 x 339192 (89.4 MB)

Total sieving time: 7.26 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000
total time: 7.35 hours.
 --------- CPU info (if available) ----------

(83·10¹³⁸+7)/9 = 9(2)₁₃₇3_<139> = 29 · 296315088385031_<15> · C124

C124 = P50 · P74

P50 = 93988310201234862601570372294932527271313227418747_<50>

P74 = 11418524212125215153704901048888926793883689926626226465167573286606626391_<74>

Number: n
N=1073207795689535631622836147825278952552729693717888979960708463097569132782518985104571996377844886200285553772238738352077
  ( 124 digits)
SNFS difficulty: 141 digits.
Divisors found:

Sun Oct 25 18:47:01 2009  prp50 factor: 93988310201234862601570372294932527271313227418747
Sun Oct 25 18:47:01 2009  prp74 factor: 11418524212125215153704901048888926793883689926626226465167573286606626391
Sun Oct 25 18:47:01 2009  elapsed time 00:20:23 (Msieve 1.42 - dependency 2)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.21 hours.
Scaled time: 9.50 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_9_2_137_3
n: 1073207795689535631622836147825278952552729693717888979960708463097569132782518985104571996377844886200285553772238738352077
m: 5000000000000000000000000000
deg: 5
c5: 664
c0: 175
skew: 0.77
type: snfs
lss: 1
rlim: 1590000
alim: 1590000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 1590000/1590000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved  special-q in [795000, 1787953)
Primes: RFBsize:120451, AFBsize:120228, largePrimes:3468598 encountered
Relations: rels:3326883, finalFF:241527
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 497871 hash collisions in 3752395 relations
Msieve: matrix is 266381 x 266606 (71.1 MB)

Total sieving time: 5.14 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1590000,1590000,26,26,48,48,2.3,2.3,100000
total time: 5.21 hours.
 --------- CPU info (if available) ----------

Oct 25, 2009 (3rd)

By Serge Batalov / Msieve / Oct 25, 2009

(26·10¹¹⁹-11)/3 = 8(6)₁₁₈3_<120> = 7 · 17 · 71 · 3803 · C113

C113 = P55 · P59

P55 = 1274995380145892465903774193098344924077906451577513651_<55>

P59 = 21154942370976421697486933878627177564197928329200354011079_<59>

SNFS difficulty: 121 digits.
Divisors found:
 r1=1274995380145892465903774193098344924077906451577513651 (pp55)
 r2=21154942370976421697486933878627177564197928329200354011079 (pp59)
Version: Msieve v. 1.44 SVN130
Total time: 0.74 hours.
Scaled time: 1.77 units (timescale=2.400).
Factorization parameters were as follows:
n: 26972453790247530461781583895312188568657048061416609249055660677236196149119949520845251137975605926059727739429
m: 1000000000000000000000000
deg: 5
c5: 13
c0: -55
skew: 1.33
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
name: 86663_119
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [456250, 706251)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 76157 x 76382
Total sieving time: 0.70 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 0.74 hours.

(83·10¹¹⁸+7)/9 = 9(2)₁₁₇3_<119> = 3 · 1092919 · C113

C113 = P42 · P71

P42 = 705070381600235455186991830596638083559201_<42>

P71 = 39892741314093663141511170138983554044263787963680068665654734350406339_<71>

SNFS difficulty: 121 digits.
Divisors found:
 r1=705070381600235455186991830596638083559201 (pp42)
 r2=39892741314093663141511170138983554044263787963680068665654734350406339 (pp71)
Version: Msieve v. 1.44 SVN130
Total time: 1.05 hours.
Scaled time: 2.52 units (timescale=2.400).
Factorization parameters were as follows:
name: 92223_118
n: 28127190341407497482192862179851151586476894207842246992449340473301992865656778535958054293813851475489712175139
m: 500000000000000000000000
deg: 5
c5: 664
c0: 175
skew: 0.77
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [462500, 812501)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 88790 x 89015
Total sieving time: 0.96 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 1.05 hours.

Oct 25, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Oct 25, 2009

(64·10¹³⁵+71)/9 = 7(1)₁₃₄9_<136> = 3 · 7 · 17 · 47 · 59 · 71705902740581_<14> · C117

C117 = P44 · P73

P44 = 49396726635866252941349225764082311779594253_<44>

P73 = 2027992294691125275972524809223849871442123743225447567390794349798850103_<73>

Number: 71119_135
N=1001761810005006313080634948875632238963927787480139812249508104174234067865331438566434001609614270508832793072

58059
  ( 117 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=49396726635866252941349225764082311779594253 (pp44)
 r2=2027992294691125275972524809223849871442123743225447567390794349798850103 (pp73)
Version: Msieve-1.40
Total time: 4.15 hours.
Scaled time: 4.18 units (timescale=1.006).
Factorization parameters were as follows:
n: 

100176181000500631308063494887563223896392778748013981224950810417423406786533143856643400160961427050883279307258

059
m: 2000000000000000000000000000
deg: 5
c5: 2
c0: 71
skew: 2.04
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1265001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 183913 x 184139
Total sieving time: 3.98 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 4.15 hours.
 --------- CPU info (if available) ----------

Oct 25, 2009

Factorizations of 655...557 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 24, 2009 (12th)

By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Oct 24, 2009

(83·10¹⁵³+7)/9 = 9(2)₁₅₂3_<154> = 19 · C153

C153 = P41 · P50 · P63

P41 = 11845787618552744408592793547872783337647_<41>

P50 = 99267096564836654377879865186188878175450767609761_<50>

P63 = 412774367410497933703892824746397001142527586353054293958148251_<63>

Number: s153
N=485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380117
  ( 153 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=11845787618552744408592793547872783337647 (pp41)
 r2=99267096564836654377879865186188878175450767609761 (pp50)
 r3=412774367410497933703892824746397001142527586353054293958148251 (pp63)
Version: Msieve-1.40
Total time: 19.76 hours.
Scaled time: 37.09 units (timescale=1.877).
Factorization parameters were as follows:
n: 485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380117
m: 5000000000000000000000000000000
deg: 5
c5: 664
c0: 175
skew: 0.77
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 496610 x 496839
Total sieving time: 19.17 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 19.76 hours.
 --------- CPU info (if available) ----------

(64·10¹⁷⁰+17)/9 = 7(1)₁₆₉3_<171> = C171

C171 = P41 · C131

P41 = 20144781073759431713450953582651849027061_<41>

C131 = [35300016838475530194639813738214629072622370366721985133667932037689576825363959054040956101074677617174755632664566964527186992133_<131>]

Factor=20144781073759431713450953582651849027061  Method=ECM  B1=11000000  Sigma=2496299565

(64·10¹⁴⁷+17)/9 = 7(1)₁₄₆3_<148> = 3 · 57503 · 216157 · C138

C138 = P48 · P91

P48 = 107549954987785579928593402880636566882663688597_<48>

P91 = 1773152830631860446188329106257338288543867985415407300744686996376641282910154550813699133_<91>

Number: s138
N=190702507120921179029693498224047177003466422091042164816733207692270771454237644049874031134578027075937711938152210610862622491960886401
  ( 138 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=107549954987785579928593402880636566882663688597 (pp48)
 r2=1773152830631860446188329106257338288543867985415407300744686996376641282910154550813699133 (pp91)
Version: Msieve-1.40
Total time: 6.95 hours.
Scaled time: 13.17 units (timescale=1.894).
Factorization parameters were as follows:
n: 190702507120921179029693498224047177003466422091042164816733207692270771454237644049874031134578027075937711938152210610862622491960886401
m: 400000000000000000000000000000
deg: 5
c5: 25
c0: 68
skew: 1.22
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 2300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 324891 x 325117
Total sieving time: 6.76 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,149.000,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000
total time: 6.95 hours.
 --------- CPU info (if available) ----------

Oct 24, 2009 (11th)

By Erik Branger / GGNFS, Msieve / Oct 24, 2009

(26·10¹³⁴-11)/3 = 8(6)₁₃₃3_<135> = 79 · 971 · C131

C131 = P40 · P91

P40 = 5793892158320044697483839891106768191867_<40>

P91 = 1950003382206205302748093895603935525675119062485432522884303420606445893015445347133372321_<91>

Number: 86663_134
N=11298109304862097885080846662929599742750741981601463539697645213295267395829259495843599403807462835738526987272245325407275113307
  ( 131 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=5793892158320044697483839891106768191867 (pp40)
 r2=1950003382206205302748093895603935525675119062485432522884303420606445893015445347133372321 (pp91)
Version: Msieve-1.40
Total time: 3.59 hours.
Scaled time: 3.70 units (timescale=1.029).
Factorization parameters were as follows:
n: 11298109304862097885080846662929599742750741981601463539697645213295267395829259495843599403807462835738526987272245325407275113307
m: 1000000000000000000000000000
deg: 5
c5: 13
c0: -55
skew: 1.33
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1175001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 190282 x 190507
Total sieving time: 3.43 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 3.59 hours.
 --------- CPU info (if available) ----------

(83·10¹²²+7)/9 = 9(2)₁₂₁3_<123> = 13 · 108887 · 128563 · 1114283 · C106

C106 = P50 · P57

P50 = 15088320696223135169809198089153969811751774911547_<50>

P57 = 301414255803061414574888662754994760101373439276969078791_<57>

Number: 92223_122
N=4547834953970025762840857831440101814378063031264673061402797428646893129342321038178952983343358098699677
  ( 106 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=15088320696223135169809198089153969811751774911547 (pp50)
 r2=301414255803061414574888662754994760101373439276969078791 (pp57)
Version: Msieve v. 1.41
Total time: 3.72 hours.
Scaled time: 2.90 units (timescale=0.780).
Factorization parameters were as follows:
n: 4547834953970025762840857831440101814378063031264673061402797428646893129342321038178952983343358098699677
m: 5000000000000000000000000
deg: 5
c5: 332
c0: 875
skew: 1.21
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 790001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 114621 x 114866
Total sieving time: 3.38 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 3.72 hours.
 --------- CPU info (if available) ----------

(61·10¹³⁵-43)/9 = 6(7)₁₃₄3_<136> = 13 · 113 · 2237 · 2689 · 48222969881785793_<17> · C110

C110 = P36 · P74

P36 = 344359163910943223401461453853061057_<36>

P74 = 46189487683276597744389391866230132568115599033739994894011952870193891269_<74>

Number: 67773_135
N=15905773360087939094211704956938899126912493543414565319868815848987679577477410100590419453658538537876211333
  ( 110 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=344359163910943223401461453853061057 (pp36)
 r2=46189487683276597744389391866230132568115599033739994894011952870193891269 (pp74)
Version: Msieve-1.40
Total time: 4.16 hours.
Scaled time: 4.09 units (timescale=0.982).
Factorization parameters were as follows:
n: 15905773360087939094211704956938899126912493543414565319868815848987679577477410100590419453658538537876211333
m: 1000000000000000000000000000
deg: 5
c5: 61
c0: -43
skew: 0.93
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1265001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 222182 x 222426
Total sieving time: 3.99 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 4.16 hours.
 --------- CPU info (if available) ----------

Oct 24, 2009 (10th)

By Sinkiti Sibata / GGNFS, Msieve / Oct 24, 2009

(26·10¹²²-11)/3 = 8(6)₁₂₁3_<123> = 29 · 173 · 694609010965955053_<18> · C102

C102 = P39 · P64

P39 = 120746948127208544826323464254407158937_<39>

P64 = 2059640468687729008837858895651778106818536471694582461670919699_<64>

Number: 86663_122
N=248695300833336709755409333590044888311569315534462185870771869373467855384404691791683714454457199963
  ( 102 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=120746948127208544826323464254407158937 (pp39)
 r2=2059640468687729008837858895651778106818536471694582461670919699 (pp64)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.28 hours.
Scaled time: 1.54 units (timescale=0.469).
Factorization parameters were as follows:
name: 86663_122
n: 248695300833336709755409333590044888311569315534462185870771869373467855384404691791683714454457199963
m: 2000000000000000000000000
deg: 5
c5: 325
c0: -44
skew: 0.67
type: snfs
lss: 1
rlim: 820000
alim: 820000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 820000/820000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [410000, 710001)
Primes: RFBsize:65416, AFBsize:65484, largePrimes:1429398 encountered
Relations: rels:1437565, finalFF:182524
Max relations in full relation-set: 28
Initial matrix: 130967 x 182524 with sparse part having weight 8950961.
Pruned matrix : 108472 x 109190 with weight 4019574.
Total sieving time: 3.09 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,46,46,2.2,2.2,50000
total time: 3.28 hours.
 --------- CPU info (if available) ----------

(61·10¹³²-43)/9 = 6(7)₁₃₁3_<133> = C133

C133 = P64 · P70

P64 = 4725606646772188984100152280396967524259863324041339868262971543_<64>

P70 = 1434266176683858768188100131193185398372991118836079821228326791155611_<70>

Number: 67773_132
N=6777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
  ( 133 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=4725606646772188984100152280396967524259863324041339868262971543 (pp64)
 r2=1434266176683858768188100131193185398372991118836079821228326791155611 (pp70)
Version: Msieve-1.40
Total time: 5.14 hours.
Scaled time: 10.57 units (timescale=2.058).
Factorization parameters were as follows:
name: 67773_132
n: 6777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
m: 200000000000000000000000000
deg: 5
c5: 1525
c0: -344
skew: 0.74
type: snfs
lss: 1
rlim: 1230000
alim: 1230000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1230000/1230000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [615000, 1290001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 209854 x 210102
Total sieving time: 4.89 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,134.000,5,0,0,0,0,0,0,0,0,1230000,1230000,26,26,47,47,2.3,2.3,75000
total time: 5.14 hours.
 --------- CPU info (if available) ----------

Oct 24, 2009 (9th)

By Norbert Schneider / Msieve / Oct 24, 2009

(26·10¹⁸⁴-11)/3 = 8(6)₁₈₃3_<185> = 997 · 3359 · 7535765227_<10> · 71533389013_<11> · 7870346972320838175697646839916923_<34> · 343812931207218909137926438686226411_<36> · C89

C89 = P39 · P50

P39 = 876770922639554917353142630986272212417_<39>

P50 = 20235248676411114188095713258897648593212272464731_<50>

Sat Oct 24 11:22:12 2009  
Sat Oct 24 11:22:12 2009  
Sat Oct 24 11:22:12 2009  Msieve v. 1.43
Sat Oct 24 11:22:12 2009  random seeds: 38021554 97df5c5b
Sat Oct 24 11:22:12 2009  factoring 17741677651857805032606358886945695648559407609858617356573827167385163195236452972764827 (89 digits)
Sat Oct 24 11:22:14 2009  searching for 15-digit factors
Sat Oct 24 11:22:14 2009  commencing quadratic sieve (89-digit input)
Sat Oct 24 11:22:15 2009  using multiplier of 3
Sat Oct 24 11:22:15 2009  using 64kb Pentium 4 sieve core
Sat Oct 24 11:22:15 2009  sieve interval: 15 blocks of size 65536
Sat Oct 24 11:22:15 2009  processing polynomials in batches of 7
Sat Oct 24 11:22:15 2009  using a sieve bound of 1533841 (58667 primes)
Sat Oct 24 11:22:15 2009  using large prime bound of 122707280 (26 bits)
Sat Oct 24 11:22:15 2009  using double large prime bound of 363050102703040 (42-49 bits)
Sat Oct 24 11:22:15 2009  using trial factoring cutoff of 49 bits
Sat Oct 24 11:22:15 2009  polynomial 'A' values have 11 factors
Sat Oct 24 13:21:58 2009  59137 relations (15514 full + 43623 combined from 623536 partial), need 58763
Sat Oct 24 13:22:00 2009  begin with 639050 relations
Sat Oct 24 13:22:01 2009  reduce to 143799 relations in 11 passes
Sat Oct 24 13:22:01 2009  attempting to read 143799 relations
Sat Oct 24 13:22:03 2009  recovered 143799 relations
Sat Oct 24 13:22:03 2009  recovered 121653 polynomials
Sat Oct 24 13:22:03 2009  attempting to build 59137 cycles
Sat Oct 24 13:22:03 2009  found 59137 cycles in 5 passes
Sat Oct 24 13:22:03 2009  distribution of cycle lengths:
Sat Oct 24 13:22:03 2009     length 1 : 15514
Sat Oct 24 13:22:03 2009     length 2 : 11441
Sat Oct 24 13:22:03 2009     length 3 : 10453
Sat Oct 24 13:22:03 2009     length 4 : 7982
Sat Oct 24 13:22:03 2009     length 5 : 5575
Sat Oct 24 13:22:03 2009     length 6 : 3626
Sat Oct 24 13:22:03 2009     length 7 : 2155
Sat Oct 24 13:22:03 2009     length 9+: 2391
Sat Oct 24 13:22:03 2009  largest cycle: 17 relations
Sat Oct 24 13:22:04 2009  matrix is 58667 x 59137 (14.2 MB) with weight 3493263 (59.07/col)
Sat Oct 24 13:22:04 2009  sparse part has weight 3493263 (59.07/col)
Sat Oct 24 13:22:06 2009  filtering completed in 3 passes
Sat Oct 24 13:22:06 2009  matrix is 54726 x 54790 (13.2 MB) with weight 3244734 (59.22/col)
Sat Oct 24 13:22:06 2009  sparse part has weight 3244734 (59.22/col)
Sat Oct 24 13:22:06 2009  saving the first 48 matrix rows for later
Sat Oct 24 13:22:06 2009  matrix is 54678 x 54790 (8.9 MB) with weight 2562127 (46.76/col)
Sat Oct 24 13:22:06 2009  sparse part has weight 2001405 (36.53/col)
Sat Oct 24 13:22:06 2009  matrix includes 64 packed rows
Sat Oct 24 13:22:06 2009  using block size 10922 for processor cache size 256 kB
Sat Oct 24 13:22:07 2009  commencing Lanczos iteration
Sat Oct 24 13:22:07 2009  memory use: 8.9 MB
Sat Oct 24 13:22:36 2009  lanczos halted after 867 iterations (dim = 54676)
Sat Oct 24 13:22:37 2009  recovered 16 nontrivial dependencies
Sat Oct 24 13:22:38 2009  prp39 factor: 876770922639554917353142630986272212417
Sat Oct 24 13:22:38 2009  prp50 factor: 20235248676411114188095713258897648593212272464731
Sat Oct 24 13:22:38 2009  elapsed time 02:00:26

Oct 24, 2009 (8th)

By Jo Yeong Uk / GMP-ECM / Oct 24, 2009

(26·10¹³³-11)/3 = 8(6)₁₃₂3_<134> = 8009 · 80177 · 32126005968869790559_<20> · C106

C106 = P45 · P61

P45 = 550163656152061301729216721644787738922797889_<45>

P61 = 7636166060905673296895325749165505687838183112138994178407041_<61>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 4201141039052149243603287764147523672856402177150099821931686403318057752296883188700119512080564817536449 (106 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3051414086
Step 1 took 3463ms
Step 2 took 3744ms
********** Factor found in step 2: 550163656152061301729216721644787738922797889
Found probable prime factor of 45 digits: 550163656152061301729216721644787738922797889
Probable prime cofactor 7636166060905673296895325749165505687838183112138994178407041 has 61 digits

(26·10¹³⁷-11)/3 = 8(6)₁₃₆3_<138> = 7 · 23 · 1621 · 12781 · 818398784008789836734085037_<27> · C102

C102 = P34 · P69

P34 = 2800432686063638191873112356083593_<34>

P69 = 113367417640850910889863553364828353318982821587846623336743491667163_<69>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 317477821896066397184834973712219743381652191068754392191236772976186795003721381583904453464961156659 (102 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6788081729
Step 1 took 3494ms
Step 2 took 3666ms
********** Factor found in step 2: 2800432686063638191873112356083593
Found probable prime factor of 34 digits: 2800432686063638191873112356083593
Probable prime cofactor 113367417640850910889863553364828353318982821587846623336743491667163 has 69 digits

Oct 24, 2009 (7th)

By Erik Branger / GGNFS, Msieve / Oct 24, 2009

(64·10¹³³+71)/9 = 7(1)₁₃₂9_<134> = 97 · 277 · 28460161 · 8090129964135488682227_<22> · C101

C101 = P43 · P58

P43 = 1664789434755203812778700766914906617226821_<43>

P58 = 6904524884467902638231307540947107049825316235236603917773_<58>

Number: 71119_133
N=11494580079666558542443783728928619354494775302497272662571411224326978098568361652889243341174189633
  ( 101 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1664789434755203812778700766914906617226821 (pp43)
 r2=6904524884467902638231307540947107049825316235236603917773 (pp58)
Version: Msieve-1.40
Total time: 4.57 hours.
Scaled time: 4.67 units (timescale=1.022).
Factorization parameters were as follows:
n: 11494580079666558542443783728928619354494775302497272662571411224326978098568361652889243341174189633
m: 400000000000000000000000000
deg: 5
c5: 125
c0: 142
skew: 1.03
type: snfs
lss: 1
rlim: 1250000
alim: 1250000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1250000/1250000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [625000, 1300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 192195 x 192420
Total sieving time: 4.37 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135.000,5,0,0,0,0,0,0,0,0,1250000,1250000,26,26,47,47,2.3,2.3,75000
total time: 4.57 hours.
 --------- CPU info (if available) ----------

(64·10¹³⁰+17)/9 = 7(1)₁₂₉3_<131> = 7 · 157 · 165063455625212909_<18> · C111

C111 = P54 · P57

P54 = 501311136493860382206840311242822408732912729612367501_<54>

P57 = 781954506321762288842405664687450652305558751607526123043_<57>

Number: 71113_130
N=392002502250658185901973161083526625449589937750275737553700107399876492854647059016885556452815419107060425543
  ( 111 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=501311136493860382206840311242822408732912729612367501 (pp54)
 r2=781954506321762288842405664687450652305558751607526123043 (pp57)
Version: Msieve v. 1.41
Total time: 4.37 hours.
Scaled time: 3.45 units (timescale=0.789).
Factorization parameters were as follows:
n: 392002502250658185901973161083526625449589937750275737553700107399876492854647059016885556452815419107060425543
m: 200000000000000000000000000
deg: 5
c5: 2
c0: 17
skew: 1.53
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 145871 x 146108
Total sieving time: 4.17 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 4.37 hours.
 --------- CPU info (if available) ----------

(26·10¹⁰⁷-11)/3 = 8(6)₁₀₆3_<108> = 7 · 131289139 · 697721177 · C91

C91 = P28 · P63

P28 = 3978386986036076319565900111_<28>

P63 = 339731895873013988365966755540530078047599588313131089726670973_<63>

Number: 86663_107
N=1351584953282562236353361499271620221383262966791354356378814555478909569263862450281178003
  ( 91 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=3978386986036076319565900111 (pp28)
 r2=339731895873013988365966755540530078047599588313131089726670973 (pp63)
Version: Msieve-1.40
Total time: 0.60 hours.
Scaled time: 0.55 units (timescale=0.922).
Factorization parameters were as follows:
n: 1351584953282562236353361499271620221383262966791354356378814555478909569263862450281178003
m: 2000000000000000000000
deg: 5
c5: 325
c0: -44
skew: 0.67
type: snfs
lss: 1
rlim: 460000
alim: 460000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 460000/460000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [230000, 330001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 44372 x 44597
Total sieving time: 0.58 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,109.000,5,0,0,0,0,0,0,0,0,460000,460000,25,25,44,44,2.2,2.2,50000
total time: 0.60 hours.
 --------- CPU info (if available) ----------

(26·10¹¹⁰-11)/3 = 8(6)₁₀₉3_<111> = 5700415541281_<13> · C99

C99 = P47 · P53

P47 = 12272738724182301305612091265295950998101974637_<47>

P53 = 12388082508652856169851007015980590350203785032347779_<53>

Number: 86663_110
N=152035699922309336604290501684473783819776715715277959163551715561100466551758956332833140021281223
  ( 99 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=12272738724182301305612091265295950998101974637 (pp47)
 r2=12388082508652856169851007015980590350203785032347779 (pp53)
Version: Msieve-1.40
Total time: 0.82 hours.
Scaled time: 0.75 units (timescale=0.920).
Factorization parameters were as follows:
n: 152035699922309336604290501684473783819776715715277959163551715561100466551758956332833140021281223
m: 10000000000000000000000
deg: 5
c5: 26
c0: -11
skew: 0.84
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [250000, 400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 51155 x 51381
Total sieving time: 0.79 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 0.82 hours.
 --------- CPU info (if available) ----------

(83·10¹¹⁰+7)/9 = 9(2)₁₀₉3_<111> = 13 · 29 · 79 · 571 · 62260951271_<11> · C93

C93 = P42 · P52

P42 = 393854541172230339186777355842066105426479_<42>

P52 = 2211461708879282181705305020872043074904345739338579_<52>

Number: 92223_110
N=870994236670606108303870557022767515535183065838195376207590467620873957918857961332172833341
  ( 93 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=393854541172230339186777355842066105426479 (pp42)
 r2=2211461708879282181705305020872043074904345739338579 (pp52)
Version: Msieve-1.40
Total time: 0.61 hours.
Scaled time: 0.60 units (timescale=0.991).
Factorization parameters were as follows:
n: 870994236670606108303870557022767515535183065838195376207590467620873957918857961332172833341
m: 10000000000000000000000
deg: 5
c5: 83
c0: 7
skew: 0.61
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [255000, 355001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 56979 x 57211
Total sieving time: 0.57 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.61 hours.
 --------- CPU info (if available) ----------

(26·10¹⁴⁶-11)/3 = 8(6)₁₄₅3_<147> = C147

C147 = P72 · P76

P72 = 131158134929014941897991043155494762191194655999220655657005466227475003_<72>

P76 = 6607799562991054291615354621323538605634856746762653073904905905353439897221_<76>

Number: 86663_146
N=866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
  ( 147 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=131158134929014941897991043155494762191194655999220655657005466227475003 (pp72)
 r2=6607799562991054291615354621323538605634856746762653073904905905353439897221 (pp76)
Version: Msieve-1.40
Total time: 9.56 hours.
Scaled time: 9.83 units (timescale=1.029).
Factorization parameters were as follows:
n: 866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
m: 200000000000000000000000000000
deg: 5
c5: 65
c0: -88
skew: 1.06
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2350001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 344320 x 344545
Total sieving time: 9.20 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,148.000,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 9.56 hours.
 --------- CPU info (if available) ----------

(64·10¹⁴¹+71)/9 = 7(1)₁₄₀9_<142> = 3 · 7 · 57847 · 30874858832399_<14> · C123

C123 = P37 · P86

P37 = 6510739734848601425260429916535506287_<37>

P86 = 29120713619885368879626705765668284768909292908607215351267930881138585180884368345349_<86>

Number: 71119_141
N=189597387272134522772268193701446398461691904062379603481427004394227700656471441219573544266601776458865910529642176709163
  ( 123 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=6510739734848601425260429916535506287 (pp37)
 r2=29120713619885368879626705765668284768909292908607215351267930881138585180884368345349 (pp86)
Version: Msieve v. 1.41
Total time: 10.10 hours.
Scaled time: 7.97 units (timescale=0.789).
Factorization parameters were as follows:
n: 189597387272134522772268193701446398461691904062379603481427004394227700656471441219573544266601776458865910529642176709163
m: 20000000000000000000000000000
deg: 5
c5: 20
c0: 71
skew: 1.29
type: snfs
lss: 1
rlim: 1680000
alim: 1680000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1680000/1680000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [840000, 1740001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 287547 x 287795
Total sieving time: 9.54 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.40 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,142.000,5,0,0,0,0,0,0,0,0,1680000,1680000,26,26,48,48,2.3,2.3,100000
total time: 10.10 hours.
 --------- CPU info (if available) ----------

(26·10¹²⁴-11)/3 = 8(6)₁₂₃3_<125> = 83 · 27431 · 381461 · 2016101 · C107

C107 = P45 · P63

P45 = 438878110517843642539991775562600262919496931_<45>

P63 = 112778421637215029419777137694092275643046196593126789882595041_<63>

Number: 86663_124
N=49495980595325626435872640529294835369469109074742694477217163577982039477317528441557433297428732515319171
  ( 107 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=438878110517843642539991775562600262919496931 (pp45)
 r2=112778421637215029419777137694092275643046196593126789882595041 (pp63)
Version: Msieve-1.40
Total time: 1.72 hours.
Scaled time: 1.70 units (timescale=0.994).
Factorization parameters were as follows:
n: 49495980595325626435872640529294835369469109074742694477217163577982039477317528441557433297428732515319171
m: 10000000000000000000000000
deg: 5
c5: 13
c0: -55
skew: 1.33
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 695001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 123067 x 123293
Total sieving time: 1.62 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 1.72 hours.
 --------- CPU info (if available) ----------

Oct 24, 2009 (6th)

By Sinkiti Sibata / Msieve, GGNFS / Oct 23, 2009

(64·10¹²⁹+17)/9 = 7(1)₁₂₈3_<130> = 3 · 73 · 12269 · 39990589935139_<14> · 95328430487254801_<17> · C93

C93 = P44 · P49

P44 = 90121920285179397280256156598295853120418907_<44>

P49 = 7703241133517384550461381620028772328027196622071_<49>

Fri Oct 23 19:53:21 2009  Msieve v. 1.42
Fri Oct 23 19:53:21 2009  random seeds: 2d359c10 ab5736ee
Fri Oct 23 19:53:21 2009  factoring 694230883372368712626881565996878478687550383836869743633600004878384701569568055066881896397 (93 digits)
Fri Oct 23 19:53:22 2009  searching for 15-digit factors
Fri Oct 23 19:53:23 2009  commencing quadratic sieve (93-digit input)
Fri Oct 23 19:53:23 2009  using multiplier of 5
Fri Oct 23 19:53:23 2009  using 32kb Intel Core sieve core
Fri Oct 23 19:53:23 2009  sieve interval: 36 blocks of size 32768
Fri Oct 23 19:53:23 2009  processing polynomials in batches of 6
Fri Oct 23 19:53:23 2009  using a sieve bound of 1944721 (72941 primes)
Fri Oct 23 19:53:23 2009  using large prime bound of 243090125 (27 bits)
Fri Oct 23 19:53:23 2009  using double large prime bound of 1242742353333750 (42-51 bits)
Fri Oct 23 19:53:23 2009  using trial factoring cutoff of 51 bits
Fri Oct 23 19:53:23 2009  polynomial 'A' values have 12 factors
Fri Oct 23 22:31:03 2009  73411 relations (18165 full + 55246 combined from 994698 partial), need 73037
Fri Oct 23 22:31:05 2009  begin with 1012863 relations
Fri Oct 23 22:31:06 2009  reduce to 188691 relations in 10 passes
Fri Oct 23 22:31:06 2009  attempting to read 188691 relations
Fri Oct 23 22:31:09 2009  recovered 188691 relations
Fri Oct 23 22:31:09 2009  recovered 170591 polynomials
Fri Oct 23 22:31:09 2009  attempting to build 73411 cycles
Fri Oct 23 22:31:09 2009  found 73411 cycles in 5 passes
Fri Oct 23 22:31:09 2009  distribution of cycle lengths:
Fri Oct 23 22:31:09 2009     length 1 : 18165
Fri Oct 23 22:31:09 2009     length 2 : 13171
Fri Oct 23 22:31:09 2009     length 3 : 12398
Fri Oct 23 22:31:09 2009     length 4 : 10001
Fri Oct 23 22:31:09 2009     length 5 : 7388
Fri Oct 23 22:31:09 2009     length 6 : 4931
Fri Oct 23 22:31:09 2009     length 7 : 3103
Fri Oct 23 22:31:09 2009     length 9+: 4254
Fri Oct 23 22:31:09 2009  largest cycle: 22 relations
Fri Oct 23 22:31:09 2009  matrix is 72941 x 73411 (18.4 MB) with weight 4529616 (61.70/col)
Fri Oct 23 22:31:09 2009  sparse part has weight 4529616 (61.70/col)
Fri Oct 23 22:31:10 2009  filtering completed in 3 passes
Fri Oct 23 22:31:10 2009  matrix is 69213 x 69277 (17.4 MB) with weight 4281226 (61.80/col)
Fri Oct 23 22:31:10 2009  sparse part has weight 4281226 (61.80/col)
Fri Oct 23 22:31:11 2009  saving the first 48 matrix rows for later
Fri Oct 23 22:31:11 2009  matrix is 69165 x 69277 (10.2 MB) with weight 3257486 (47.02/col)
Fri Oct 23 22:31:11 2009  sparse part has weight 2253122 (32.52/col)
Fri Oct 23 22:31:11 2009  matrix includes 64 packed rows
Fri Oct 23 22:31:11 2009  using block size 27710 for processor cache size 1024 kB
Fri Oct 23 22:31:11 2009  commencing Lanczos iteration
Fri Oct 23 22:31:11 2009  memory use: 10.9 MB
Fri Oct 23 22:31:42 2009  lanczos halted after 1095 iterations (dim = 69159)
Fri Oct 23 22:31:42 2009  recovered 13 nontrivial dependencies
Fri Oct 23 22:31:43 2009  prp44 factor: 90121920285179397280256156598295853120418907
Fri Oct 23 22:31:43 2009  prp49 factor: 7703241133517384550461381620028772328027196622071
Fri Oct 23 22:31:43 2009  elapsed time 02:38:22

(64·10¹²⁰+71)/9 = 7(1)₁₁₉9_<121> = 3³ · 25056137 · 39405479110031809_<17> · C96

C96 = P31 · P66

P31 = 1909784723324945661063074631191_<31>

P66 = 139674960799589269574939897676758027913533545895886397551579842899_<66>

Number: 71119_120
N=266749106366066224179930490595843183605440843999355589847519042761546631831691215229244145262709
  ( 96 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=1909784723324945661063074631191 (pp31)
 r2=139674960799589269574939897676758027913533545895886397551579842899 (pp66)
Version: Msieve v. 1.42
Total time: 0.05 hours.
Scaled time: 0.04 units (timescale=0.854).
Factorization parameters were as follows:
name: 71119_120
n: 266749106366066224179930490595843183605440843999355589847519042761546631831691215229244145262709
m: 2000000000000000000000000
deg: 5
c5: 2
c0: 71
skew: 2.04
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 625001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 94388 x 94615
Total sieving time: 0.00 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 0.05 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583)
Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268)
Total of 2 processors activated (11653.70 BogoMIPS).

Total time: 42 min.

By Sinkiti Sibata / Msieve, GGNFS / Oct 24, 2009

(64·10¹²⁸+71)/9 = 7(1)₁₂₇9_<129> = 4493 · 35149 · C121

C121 = P33 · P33 · P56

P33 = 219246084445885541879554806930967_<33>

P33 = 226366253431612444268772260693243_<33>

P56 = 90728669742939326666422767939725447916165155744870994707_<56>

Number: 71119_128
N=4502856141598834885410504283773545671340260559585847498662674592011490095616482702936322973148554888563657439779014792567
  ( 121 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=219246084445885541879554806930967 (pp33)
 r2=226366253431612444268772260693243 (pp33)
 r3=90728669742939326666422767939725447916165155744870994707 (pp56)
Version: Msieve-1.40
Total time: 3.48 hours.
Scaled time: 6.96 units (timescale=1.999).
Factorization parameters were as follows:
name: 71119_128
n: 4502856141598834885410504283773545671340260559585847498662674592011490095616482702936322973148554888563657439779014792567
m: 40000000000000000000000000
deg: 5
c5: 125
c0: 142
skew: 1.03
type: snfs
lss: 1
rlim: 1030000
alim: 1030000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1030000/1030000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [515000, 965001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 170055 x 170303
Total sieving time: 3.22 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,130.000,5,0,0,0,0,0,0,0,0,1030000,1030000,26,26,47,47,2.3,2.3,50000
total time: 3.48 hours.
 --------- CPU info (if available) ----------

(7·10¹⁷¹+11)/9 = (7)₁₇₀9_<171> = 79 · 38849977 · 203457481442417_<15> · 81709955186191980351449_<23> · C125

C125 = P44 · P81

P44 = 98257468015187235416827038555249763862904983_<44>

P81 = 155139886054848009277581492355401445786172323675067944033931354665035918101197867_<81>

Number: 77779_171
N=15243652391914020488510365474725098887583903365784101043635177021944272391291910540061456099835261086105261271359058703271261
  ( 125 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=98257468015187235416827038555249763862904983 (pp44)
 r2=155139886054848009277581492355401445786172323675067944033931354665035918101197867 (pp81)
Version: Msieve-1.40
Total time: 59.76 hours.
Scaled time: 198.54 units (timescale=3.322).
Factorization parameters were as follows:
name: 77779_171
n: 15243652391914020488510365474725098887583903365784101043635177021944272391291910540061456099835261086105261271359058703271261
m: 10000000000000000000000000000000000
deg: 5
c5: 70
c0: 11
skew: 0.69
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 950870 x 951118
Total sieving time: 57.71 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.71 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 59.76 hours.
 --------- CPU info (if available) ----------

(83·10¹¹⁷+7)/9 = 9(2)₁₁₆3_<118> = 19 · 16547 · C113

C113 = P38 · P75

P38 = 36779934795762142506535701356535567163_<38>

P75 = 797538689045240465818445964027040354448230908021748469854654299849630902597_<75>

Number: 92223_117
N=29333420980181563273426005738748070797448487155319050431218959144199209976755914483535645584418934970633004622311
  ( 113 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=36779934795762142506535701356535567163 (pp38)
 r2=797538689045240465818445964027040354448230908021748469854654299849630902597 (pp75)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.04 hours.
Scaled time: 1.43 units (timescale=0.470).
Factorization parameters were as follows:
name: 92223_117
n: 29333420980181563273426005738748070797448487155319050431218959144199209976755914483535645584418934970633004622311
m: 500000000000000000000000
deg: 5
c5: 332
c0: 875
skew: 1.21
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 665001)
Primes: RFBsize:58789, AFBsize:58546, largePrimes:1331675 encountered
Relations: rels:1305723, finalFF:150232
Max relations in full relation-set: 28
Initial matrix: 117402 x 150232 with sparse part having weight 7226670.
Pruned matrix : 103906 x 104557 with weight 3808187.
Total sieving time: 2.87 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 3.04 hours.
 --------- CPU info (if available) ----------

(83·10¹¹⁵+7)/9 = 9(2)₁₁₄3_<116> = 3 · 1331261 · C110

C110 = P36 · P74

P36 = 448998983579618286682910369713303867_<36>

P74 = 51428725407187141859088119824597898798122680510169179933669682357162579243_<74>

Number: 92223_115
N=23091445434622317292206968235936259486863012392566702352687219666722559093025891046714912207854613588725832681
  ( 110 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=448998983579618286682910369713303867 (pp36)
 r2=51428725407187141859088119824597898798122680510169179933669682357162579243 (pp74)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.08 hours.
Scaled time: 0.98 units (timescale=0.470).
Factorization parameters were as follows:
name: 92223_115
n: 23091445434622317292206968235936259486863012392566702352687219666722559093025891046714912207854613588725832681
m: 100000000000000000000000
deg: 5
c5: 83
c0: 7
skew: 0.61
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 510001)
Primes: RFBsize:50612, AFBsize:50913, largePrimes:1330235 encountered
Relations: rels:1344098, finalFF:182266
Max relations in full relation-set: 28
Initial matrix: 101590 x 182266 with sparse part having weight 8528252.
Pruned matrix : 74591 x 75162 with weight 2650532.
Total sieving time: 1.97 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 2.08 hours.
 --------- CPU info (if available) ----------

(61·10¹⁴⁰-43)/9 = 6(7)₁₃₉3_<141> = C141

C141 = P54 · P88

P54 = 325989444321476741768568655839830941695732012474364613_<54>

P88 = 2079140259245273419208476348596406001746636489082295143446360245837532934734529053949321_<88>

Number: 67773_140
N=677777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
  ( 141 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=325989444321476741768568655839830941695732012474364613 (pp54)
 r2=2079140259245273419208476348596406001746636489082295143446360245837532934734529053949321 (pp88)
Version: Msieve-1.40
Total time: 8.13 hours.
Scaled time: 16.63 units (timescale=2.047).
Factorization parameters were as follows:
name: 67773_140
n: 677777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
m: 10000000000000000000000000000
deg: 5
c5: 61
c0: -43
skew: 0.93
type: snfs
lss: 1
rlim: 1620000
alim: 1620000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1620000/1620000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [810000, 1810001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 248303 x 248545
Total sieving time: 7.81 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000
total time: 8.13 hours.
 --------- CPU info (if available) ----------

(26·10¹²¹-11)/3 = 8(6)₁₂₀3_<122> = 79 · 336307 · 6093956023_<10> · C105

C105 = P39 · P66

P39 = 789884894421491276071791572937175094431_<39>

P66 = 677682031517397071638948408764507850205264432110583575670993308667_<66>

Number: 86663_121
N=535290799916460909322632937046079933332540413019329214648720061719617671786879004686665942761564855733477
  ( 105 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=789884894421491276071791572937175094431 (pp39)
 r2=677682031517397071638948408764507850205264432110583575670993308667 (pp66)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.21 hours.
Scaled time: 1.50 units (timescale=0.469).
Factorization parameters were as follows:
name: 86663_121
n: 535290799916460909322632937046079933332540413019329214648720061719617671786879004686665942761564855733477
m: 2000000000000000000000000
deg: 5
c5: 65
c0: -88
skew: 1.06
type: snfs
lss: 1
rlim: 800000
alim: 800000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [400000, 700001)
Primes: RFBsize:63951, AFBsize:64009, largePrimes:1439328 encountered
Relations: rels:1469098, finalFF:201631
Max relations in full relation-set: 28
Initial matrix: 128027 x 201631 with sparse part having weight 9518384.
Pruned matrix : 99188 x 99892 with weight 3617086.
Total sieving time: 3.03 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,800000,800000,25,25,46,46,2.2,2.2,50000
total time: 3.21 hours.
 --------- CPU info (if available) ----------

Oct 24, 2009 (5th)

By Jo Yeong Uk / GMP-ECM / Oct 24, 2009

(83·10¹²⁹+7)/9 = 9(2)₁₂₈3_<130> = 370756134989_<12> · C119

C119 = P32 · P88

P32 = 13462314290065597650967239163411_<32>

P88 = 1847683206138391614740683802658317179021351885853039473016213575460366458036348637474537_<88>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 24874092029511088830793977824159149728669959484925561047172970971177927785079482037048683023491324655978050891694565707 (119 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2972610773
Step 1 took 4305ms
Step 2 took 4056ms
********** Factor found in step 2: 13462314290065597650967239163411
Found probable prime factor of 32 digits: 13462314290065597650967239163411
Probable prime cofactor 1847683206138391614740683802658317179021351885853039473016213575460366458036348637474537 has 88 digits

Oct 24, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve / Oct 23, 2009

(61·10¹²⁷-43)/9 = 6(7)₁₂₆3_<128> = 3³ · 7 · C126

C126 = P42 · P84

P42 = 407477037943091526384154945619729486878481_<42>

P84 = 880080464521505363745973815942538725788188776246941876761082167649369496854560358497_<84>

Number: s126
N=358612580834803057025279247501469723691945914168136390358612580834803057025279247501469723691945914168136390358612580834803057
  ( 126 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=407477037943091526384154945619729486878481 (pp42)
 r2=880080464521505363745973815942538725788188776246941876761082167649369496854560358497 (pp84)
Version: Msieve-1.40
Total time: 2.34 hours.
Scaled time: 4.27 units (timescale=1.823).
Factorization parameters were as follows:
n: 358612580834803057025279247501469723691945914168136390358612580834803057025279247501469723691945914168136390358612580834803057
m: 20000000000000000000000000
deg: 5
c5: 1525
c0: -344
skew: 0.74
type: snfs
lss: 1
rlim: 1020000
alim: 1020000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1020000/1020000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [510000, 960001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 164071 x 164319
Total sieving time: 2.14 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,129.000,5,0,0,0,0,0,0,0,0,1020000,1020000,26,26,47,47,2.3,2.3,50000
total time: 2.34 hours.
 --------- CPU info (if available) ----------

By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Oct 24, 2009

(61·10¹²⁹-43)/9 = 6(7)₁₂₈3_<130> = 13 · 41 · C128

C128 = P49 · P79

P49 = 2287528054637314045109190267051066417529641653837_<49>

P79 = 5558961772374893628056239196627218661806824030916893112945718861901654135077213_<79>

Number: s128
N=12716281008963935793204085887012716281008963935793204085887012716281008963935793204085887012716281008963935793204085887012716281
  ( 128 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=2287528054637314045109190267051066417529641653837 (pp49)
 r2=5558961772374893628056239196627218661806824030916893112945718861901654135077213 (pp79)
Version: Msieve-1.40
Total time: 2.30 hours.
Scaled time: 4.36 units (timescale=1.894).
Factorization parameters were as follows:
n: 12716281008963935793204085887012716281008963935793204085887012716281008963935793204085887012716281008963935793204085887012716281
m: 100000000000000000000000000
deg: 5
c5: 61
c0: -430
skew: 1.48
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 157778 x 158003
Total sieving time: 2.18 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.30 hours.
 --------- CPU info (if available) ----------

(61·10¹⁴⁴-43)/9 = 6(7)₁₄₃3_<145> = 29 · 41 · C142

C142 = P50 · P92

P50 = 71125248172047812172367744106022257084097146704433_<50>

P92 = 80145967544683774899184978886451319499171988890775611014685828126239600820562577193465265529_<92>

Number: s142
N=5700401831604522941781141949350527988038501074665919072983833286608728156247079712176432109148677693673488459022521259695355574245397626390057
  ( 142 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=71125248172047812172367744106022257084097146704433 (pp50)
 r2=80145967544683774899184978886451319499171988890775611014685828126239600820562577193465265529 (pp92)
Version: Msieve-1.40
Total time: 8.24 hours.
Scaled time: 14.82 units (timescale=1.798).
Factorization parameters were as follows:
n: 5700401831604522941781141949350527988038501074665919072983833286608728156247079712176432109148677693673488459022521259695355574245397626390057
m: 100000000000000000000000000000
deg: 5
c5: 61
c0: -430
skew: 1.48
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2480001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 269112 x 269338
Total sieving time: 8.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 8.24 hours.
 --------- CPU info (if available) ----------

(64·10¹⁹⁰+17)/9 = 7(1)₁₈₉3_<191> = 7 · 6691 · 290494829 · 1380866687_<10> · 4086027269_<10> · 9660969623051_<13> · 3941138284671811_<16> · 5842416003241847136942269089_<28> · C103

C103 = P32 · P71

P32 = 78312274930106768612277915759019_<32>

P71 = 53173135201406687225987643466447677679826748068879261893091308053037777_<71>

Number: gnfs103
N=4164109182788298634637983560598824442861592984170310779241065618584708338011804829543687064903635460763
  ( 103 digits)
Divisors found:
 r1=78312274930106768612277915759019 (pp32)
 r2=53173135201406687225987643466447677679826748068879261893091308053037777 (pp71)
Version: Msieve-1.40
Total time: 5.84 hours.
Scaled time: 11.16 units (timescale=1.911).
Factorization parameters were as follows:
name: gnfs103
n: 4164109182788298634637983560598824442861592984170310779241065618584708338011804829543687064903635460763
skew: 2491.34
# norm 7.07e+013
c5: 744120
c4: -3420269382
c3: -5627753013815
c2: 15061763833701973
c1: -8412804937219830845
c0: -17049204468924793063920
# alpha -5.55
Y1: 56538318353
Y0: -22365408527022715867
# Murphy_E 2.54e-009
# M 1237890708516201371853183408783352573063846900088206779982914609995757268982164069799294337788323393398
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 258653 x 258879
Polynomial selection time: 0.56 hours.
Total sieving time: 5.00 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 5.84 hours.
 --------- CPU info (if available) ----------

(26·10¹⁴²-11)/3 = 8(6)₁₄₁3_<143> = C143

C143 = P55 · P88

P55 = 9115691638023963245342223206652254475126670948607632921_<55>

P88 = 9507415356741232292647529763366614856021224385838795802922228204646406610693093895859903_<88>

Number: snfs144
N=86666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
  ( 143 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=9115691638023963245342223206652254475126670948607632921 (pp55)
 r2=9507415356741232292647529763366614856021224385838795802922228204646406610693093895859903 (pp88)
Version: Msieve-1.40
Total time: 6.14 hours.
Scaled time: 11.17 units (timescale=1.818).
Factorization parameters were as follows:
n: 86666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
m: 20000000000000000000000000000
deg: 5
c5: 325
c0: -44
skew: 0.67
type: snfs
lss: 1
rlim: 1760000
alim: 1760000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1760000/1760000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [880000, 1980001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 250506 x 250735
Total sieving time: 5.88 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,144.000,5,0,0,0,0,0,0,0,0,1760000,1760000,26,26,49,49,2.3,2.3,100000
total time: 6.14 hours.
 --------- CPU info (if available) ----------

(64·10¹⁶³+17)/9 = 7(1)₁₆₂3_<164> = C164

C164 = P43 · P59 · P64

P43 = 2888653647017384944658914318490351960163173_<43>

P59 = 11446809117705912722904058389563035914239392318736582956591_<59>

P64 = 2150589649330390921462700175523316447389381808394324271813972091_<64>

Number: snfs164
N=71111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
  ( 164 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=2888653647017384944658914318490351960163173 (pp43)
 r2=11446809117705912722904058389563035914239392318736582956591 (pp59)
 r3=2150589649330390921462700175523316447389381808394324271813972091 (pp64)
Version: Msieve-1.40
Total time: 33.78 hours.
Scaled time: 63.40 units (timescale=1.877).
Factorization parameters were as follows:
n: 71111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
m: 400000000000000000000000000000000
deg: 5
c5: 125
c0: 34
skew: 0.77
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 3900001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 747981 x 748207
Total sieving time: 32.73 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.68 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,165.000,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 33.78 hours.
 --------- CPU info (if available) ----------

(64·10¹⁶⁰+17)/9 = 7(1)₁₅₉3_<161> = 7 · C161

C161 = P36 · P125

P36 = 131913096460266010557621868043636567_<36>

P125 = 77010777787254081793969654885395836435882049747648388057048074731510796864579726325788840724789541809298412181124172069193577_<125>

C161=P36*P125
C161=131913096460266010557621868043636567<36>*77010777787254081793969654885395836435882049747648388057048074731510796864579726325788840724789541809298412181124172069193577<125>

(26·10¹⁶⁶-11)/3 = 8(6)₁₆₅3_<167> = C167

C167 = P41 · C127

P41 = 17119841910469978219460966052115200873127_<41>

C127 = [5062352042729083324072603410562818478047593167544336937763961405378553912981858058946033962596449849227561328894684469987616769_<127>]

C167=P41*C127
C167=17119841910469978219460966052115200873127<41>*5062352042729083324072603410562818478047593167544336937763961405378553912981858058946033962596449849227561328894684469987616769<127>

(61·10¹³⁸-43)/9 = 6(7)₁₃₇3_<139> = 1913 · C136

C136 = P35 · P38 · P64

P35 = 19822961305870189378473837722701931_<35>

P38 = 49642245410591432336300254111585192267_<38>

P64 = 3600413696042753233794529585243447232275463312210167503100777373_<64>

Number: s136
N=3543009815879653830516350119068362664808038566533077771969564964860312481849334959632920950223616193297322413893245048498576987860835221
  ( 136 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=19822961305870189378473837722701931 (pp35)
 r2=49642245410591432336300254111585192267 (pp38)
 r3=3600413696042753233794529585243447232275463312210167503100777373 (pp64)
Version: Msieve-1.40
Total time: 6.18 hours.
Scaled time: 11.18 units (timescale=1.808).
Factorization parameters were as follows:
n: 3543009815879653830516350119068362664808038566533077771969564964860312481849334959632920950223616193297322413893245048498576987860835221
m: 5000000000000000000000000000
deg: 5
c5: 488
c0: -1075
skew: 1.17
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 1990001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 240685 x 240913
Total sieving time: 6.03 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000
total time: 6.18 hours.
 --------- CPU info (if available) ----------

(26·10¹⁶²-11)/3 = 8(6)₁₆₁3_<163> = 31 · C162

C162 = P46 · P117

P46 = 2196424621818773603600345463796839158507351567_<46>

P117 = 127284082365465995552850204415842628504762600410597057869464777586572822332556289495204674872568853707859104015568119_<117>

Factor=2196424621818773603600345463796839158507351567  Method=ECM  B1=11000000  Sigma=2633918174

(26·10¹⁵²-11)/3 = 8(6)₁₅₁3_<153> = 63149 · C149

C149 = P33 · P116

P33 = 232675221140264800583789692746517_<33>

P116 = 58984171040930859733047313827260929303323028868561821673181544466560112712053036164869422569370489494475243023777111_<116>

Number: s149
N=13724155040723790822763094691391259824647526748906026487619228596916287932772754385131461569726625388631121105111192048435710251415963303720829572387
  ( 149 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=232675221140264800583789692746517 (pp33)
 r2=58984171040930859733047313827260929303323028868561821673181544466560112712053036164869422569370489494475243023777111 (pp116)
Version: Msieve-1.40
Total time: 13.58 hours.
Scaled time: 25.79 units (timescale=1.899).
Factorization parameters were as follows:
n: 13724155040723790822763094691391259824647526748906026487619228596916287932772754385131461569726625388631121105111192048435710251415963303720829572387
m: 2000000000000000000000000000000
deg: 5
c5: 325
c0: -44
skew: 0.67
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 458985 x 459215
Total sieving time: 13.15 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,154.000,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 13.58 hours.
 --------- CPU info (if available) ----------

Oct 24, 2009 (3rd)

By Serge Batalov / Msieve, GMP-ECM / Oct 24, 2009

(64·10¹¹²+17)/9 = 7(1)₁₁₁3_<113> = 7 · 23 · 107 · 58217 · C104

C104 = P44 · P61

P44 = 29421594806177130768713735992366864817252927_<44>

P61 = 2409970790474565626502863955858891453277441083926831383294141_<61>

SNFS difficulty: 114 digits.
Divisors found:
 r1=29421594806177130768713735992366864817252927 (pp44)
 r2=2409970790474565626502863955858891453277441083926831383294141 (pp61)
Version: Msieve v. 1.44 SVN130
Total time: 0.49 hours.
Scaled time: 1.17 units (timescale=2.400).
Factorization parameters were as follows:
#res 5444
n: 70905184092065074290517207895425949239199622454800155665817260340412126130088665932279295576419634200707
m: 40000000000000000000000
deg: 5
c5: 25
c0: 68
skew: 1.22
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [350000, 500001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 52873 x 53108
Total sieving time: 0.43 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,114.000,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000
total time: 0.49 hours.

(26·10¹⁸⁷-11)/3 = 8(6)₁₈₆3_<188> = 337 · 43665343 · 5821288230130187_<16> · C163

C163 = P34 · P129

P34 = 9991165980682396704453204886294931_<34>

P129 = 101262825097714124221150710784145645266502910002869015154872310194798802000025178431518800026396746555000440686019072606961525369_<129>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=610105107
Step 1 took 3540ms
Step 2 took 2388ms
********** Factor found in step 2: 9991165980682396704453204886294931
Found probable prime factor of 34 digits: 9991165980682396704453204886294931
Probable prime cofactor has 129 digits

(83·10¹⁴²+7)/9 = 9(2)₁₄₁3_<143> = 3 · 43 · 71 · 557 · 3493359870103_<13> · 391944702424322680440077_<24> · C101

C101 = P34 · P67

P34 = 1535181644225391274770405393769327_<34>

P67 = 8600118470782546419223756731522576547964652510173823240589849178233_<67>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4109546562
Step 1 took 2184ms
Step 2 took 1692ms
********** Factor found in step 2: 1535181644225391274770405393769327
Found probable prime factor of 34 digits: 1535181644225391274770405393769327
Probable prime cofactor has 67 digits

(26·10¹³⁵-11)/3 = 8(6)₁₃₄3_<136> = 17 · 193573 · 192815039 · C122

C122 = P37 · P85

P37 = 5454710823688942334175811855714794721_<37>

P85 = 2504065903217569708844174464681505132806673398424266096733702746000918751373630975797_<85>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=765632283
Step 1 took 5037ms
Step 2 took 3092ms
********** Factor found in step 2: 5454710823688942334175811855714794721
Found probable prime factor of 37 digits: 5454710823688942334175811855714794721
Probable prime cofactor 2504065903217569708844174464681505132806673398424266096733702746000918751373630975797 has 85 digits

(26·10¹⁸³-11)/3 = 8(6)₁₈₂3_<184> = 17 · 48989 · 53857 · 90797663536907_<14> · 567087650203225062437861_<24> · C136

C136 = P32 · P104

P32 = 61186619953122149431960957214347_<32>

P104 = 61331150820779255676079631245412342285786210808138765086237596311374322119595871484930746172259468195647_<104>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=1343869211
Step 1 took 6509ms
Step 2 took 3392ms
********** Factor found in step 2: 61186619953122149431960957214347
Found probable prime factor of 32 digits: 61186619953122149431960957214347
Probable prime cofactor has 104 digits

(83·10¹⁴⁶+7)/9 = 9(2)₁₄₅3_<147> = 13 · 6112473163_<10> · C137

C137 = P32 · C105

P32 = 70315458832223316419214342764791_<32>

C105 = [165053390608618612168814333894623116123683611767851606138040337603496776755267221271940941504830895806087_<105>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=4092763463
Step 1 took 6060ms
********** Factor found in step 1: 70315458832223316419214342764791
Found probable prime factor of 32 digits: 70315458832223316419214342764791
Composite cofactor has 105 digits

Oct 24, 2009 (2nd)

By Robert Backstrom / GGNFS / Oct 24, 2009

(64·10¹⁴⁸+17)/9 = 7(1)₁₄₇3_<149> = 7 · 311 · C146

C146 = P65 · P82

P65 = 13862318111733729004439259370064720101102185805867897760100165383_<65>

P82 = 2356368316987349258771784289940244839436834125337731025218453398175647281594404143_<82>

Number: n
N=32664727198489256367069871893023018424947685397846169550349614658296330322053794722605011994079518195273822283468585719389577910478232021640381769
  ( 146 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=13862318111733729004439259370064720101102185805867897760100165383 (pp65)
 r2=2356368316987349258771784289940244839436834125337731025218453398175647281594404143 (pp82)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 12.47 hours.
Scaled time: 22.81 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_1_147_3
n: 32664727198489256367069871893023018424947685397846169550349614658296330322053794722605011994079518195273822283468585719389577910478232021640381769
m: 400000000000000000000000000000
deg: 5
c5: 125
c0: 34
skew: 0.77
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 20000
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved  special-q in [1100000, 1100000)
Primes: RFBsize:162662, AFBsize:162170, largePrimes:6640238 encountered
Relations: rels:6390194, finalFF:415657
Max relations in full relation-set: 28
Initial matrix: 324897 x 415657 with sparse part having weight 56474105.
Pruned matrix : 293478 x 295166 with weight 32001067.
Total sieving time: 11.21 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.07 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,49,49,2.4,2.4,100000
total time: 12.47 hours.
 --------- CPU info (if available) ----------

Oct 24, 2009

By Lionel Debroux / GMP-ECM

Factorizations of 866...663 and Factorizations of 922...223 have been extended up to n=200. Composite numbers that appeared newly have passed 150 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 23, 2009 (9th)

By Sinkiti Sibata / Msieve / Oct 23, 2009

(62·10¹¹¹-17)/9 = 6(8)₁₁₀7_<112> = 3962587 · 482246250193_<12> · C94

C94 = P45 · P49

P45 = 660147994517388539314411545518085157537248401_<45>

P49 = 5460849429187019232147638751889511274742905293557_<49>

Thu Oct 22 20:45:19 2009  Msieve v. 1.42
Thu Oct 22 20:45:19 2009  random seeds: 280bcafc e7ff4b71
Thu Oct 22 20:45:19 2009  factoring 3604968799039236706524693981054537071333612156402064636673186885165658800240706988506933852357 (94 digits)
Thu Oct 22 20:45:20 2009  searching for 15-digit factors
Thu Oct 22 20:45:21 2009  commencing quadratic sieve (94-digit input)
Thu Oct 22 20:45:21 2009  using multiplier of 29
Thu Oct 22 20:45:21 2009  using 32kb Intel Core sieve core
Thu Oct 22 20:45:21 2009  sieve interval: 36 blocks of size 32768
Thu Oct 22 20:45:21 2009  processing polynomials in batches of 6
Thu Oct 22 20:45:21 2009  using a sieve bound of 2023369 (75294 primes)
Thu Oct 22 20:45:21 2009  using large prime bound of 271131446 (28 bits)
Thu Oct 22 20:45:21 2009  using double large prime bound of 1512598956202640 (42-51 bits)
Thu Oct 22 20:45:21 2009  using trial factoring cutoff of 51 bits
Thu Oct 22 20:45:21 2009  polynomial 'A' values have 12 factors
Thu Oct 22 23:57:17 2009  75593 relations (18708 full + 56885 combined from 1066860 partial), need 75390
Thu Oct 22 23:57:19 2009  begin with 1085568 relations
Thu Oct 22 23:57:20 2009  reduce to 195381 relations in 11 passes
Thu Oct 22 23:57:20 2009  attempting to read 195381 relations
Thu Oct 22 23:57:23 2009  recovered 195381 relations
Thu Oct 22 23:57:23 2009  recovered 179758 polynomials
Thu Oct 22 23:57:23 2009  attempting to build 75593 cycles
Thu Oct 22 23:57:23 2009  found 75593 cycles in 5 passes
Thu Oct 22 23:57:23 2009  distribution of cycle lengths:
Thu Oct 22 23:57:23 2009     length 1 : 18708
Thu Oct 22 23:57:23 2009     length 2 : 13355
Thu Oct 22 23:57:23 2009     length 3 : 12883
Thu Oct 22 23:57:23 2009     length 4 : 10340
Thu Oct 22 23:57:23 2009     length 5 : 7585
Thu Oct 22 23:57:23 2009     length 6 : 5128
Thu Oct 22 23:57:23 2009     length 7 : 3230
Thu Oct 22 23:57:23 2009     length 9+: 4364
Thu Oct 22 23:57:23 2009  largest cycle: 20 relations
Thu Oct 22 23:57:24 2009  matrix is 75294 x 75593 (20.3 MB) with weight 5015048 (66.34/col)
Thu Oct 22 23:57:24 2009  sparse part has weight 5015048 (66.34/col)
Thu Oct 22 23:57:25 2009  filtering completed in 4 passes
Thu Oct 22 23:57:25 2009  matrix is 71654 x 71718 (19.3 MB) with weight 4778097 (66.62/col)
Thu Oct 22 23:57:25 2009  sparse part has weight 4778097 (66.62/col)
Thu Oct 22 23:57:25 2009  saving the first 48 matrix rows for later
Thu Oct 22 23:57:25 2009  matrix is 71606 x 71718 (13.2 MB) with weight 3887217 (54.20/col)
Thu Oct 22 23:57:25 2009  sparse part has weight 3026218 (42.20/col)
Thu Oct 22 23:57:25 2009  matrix includes 64 packed rows
Thu Oct 22 23:57:25 2009  using block size 28687 for processor cache size 1024 kB
Thu Oct 22 23:57:26 2009  commencing Lanczos iteration
Thu Oct 22 23:57:26 2009  memory use: 12.7 MB
Thu Oct 22 23:58:03 2009  lanczos halted after 1134 iterations (dim = 71604)
Thu Oct 22 23:58:03 2009  recovered 16 nontrivial dependencies
Thu Oct 22 23:58:04 2009  prp45 factor: 660147994517388539314411545518085157537248401
Thu Oct 22 23:58:04 2009  prp49 factor: 5460849429187019232147638751889511274742905293557
Thu Oct 22 23:58:04 2009  elapsed time 03:12:45

(11·10¹⁷¹+7)/9 = 1(2)₁₇₀3_<172> = 50222149146929_<14> · 143622706373009_<15> · 75094583901802513_<17> · C127

C127 = P41 · P86

P41 = 24901499544721371734264989415030097233317_<41>

P86 = 90614492030344526375011699819556672642162000003956105269511487846415420194738095567283_<86>

Number: 12223_171
N=2256436732038782590955720508896276694051180539535330232627385110920722833921004383641867215954888860165018041347441759922767711
  ( 127 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=24901499544721371734264989415030097233317 (pp41)
 r2=90614492030344526375011699819556672642162000003956105269511487846415420194738095567283 (pp86)
Version: Msieve v. 1.42
Total time: 4.35 hours.
Scaled time: 3.72 units (timescale=0.854).
Factorization parameters were as follows:
name: 12223_171
n: 2256436732038782590955720508896276694051180539535330232627385110920722833921004383641867215954888860165018041347441759922767711
m: 10000000000000000000000000000000000
deg: 5
c5: 110
c0: 7
skew: 0.58
type: snfs
lss: 1
rlim: 5200000
alim: 5200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2600000, 6100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1055791 x 1056020
Total sieving time: 0.00 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 4.11 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,172.000,5,0,0,0,0,0,0,0,0,5200000,5200000,27,27,52,52,2.4,2.4,100000
total time: 4.35 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583)
Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268)
Total of 2 processors activated (11653.70 BogoMIPS).

(61·10¹⁴³-43)/9 = 6(7)₁₄₂3_<144> = C144

C144 = P46 · P99

P46 = 1200283367986996913095104606977284717546493557_<46>

P99 = 564681470938386259483663674816910554996872081880213418373669960124803403134080700332834602060881689_<99>

Number: 67773_143
N=677777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
  ( 144 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1200283367986996913095104606977284717546493557 (pp46)
 r2=564681470938386259483663674816910554996872081880213418373669960124803403134080700332834602060881689 (pp99)
Version: Msieve-1.40
Total time: 13.06 hours.
Scaled time: 27.23 units (timescale=2.085).
Factorization parameters were as follows:
name: 67773_143
n: 677777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
m: 50000000000000000000000000000
deg: 5
c5: 488
c0: -1075
skew: 1.17
type: snfs
lss: 1
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [955000, 2555001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 328328 x 328560
Total sieving time: 12.55 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 13.06 hours.
 --------- CPU info (if available) ----------

(64·10¹²⁶+71)/9 = 7(1)₁₂₅9_<127> = 3 · C127

C127 = P41 · P86

P41 = 83875743501839534174392033664726057850617_<41>

P86 = 28260499059759562269210391206123758704930814197669847316807229716561932184297190743469_<86>

Number: 71119_126
N=2370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370373
  ( 127 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=83875743501839534174392033664726057850617 (pp41)
 r2=28260499059759562269210391206123758704930814197669847316807229716561932184297190743469 (pp86)
Version: Msieve v. 1.42
Total time: 0.10 hours.
Scaled time: 0.08 units (timescale=0.854).
Factorization parameters were as follows:
name: 71119_126
n: 2370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370373
m: 20000000000000000000000000
deg: 5
c5: 20
c0: 71
skew: 1.29
type: snfs
lss: 1
rlim: 940000
alim: 940000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 940000/940000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [470000, 770001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 148947 x 149195
Total sieving time: 0.00 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,127.000,5,0,0,0,0,0,0,0,0,940000,940000,26,26,46,46,2.3,2.3,50000
total time: 0.10 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583)
Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268)
Total of 2 processors activated (11653.70 BogoMIPS).

(64·10¹⁵²+71)/9 = 7(1)₁₅₁9_<153> = 19 · 2131 · 5581 · 2583903677_<10> · 964660848422868911_<18> · 244287028094134326208459_<24> · C94

C94 = P31 · P64

P31 = 3928758742686927379474311715139_<31>

P64 = 1315472132328471305168939778776883400661078541357517237138695553_<64>

Fri Oct 23 14:56:27 2009  Msieve v. 1.42
Fri Oct 23 14:56:27 2009  random seeds: f194aed4 464868b8
Fri Oct 23 14:56:27 2009  factoring 5168172640646496280310503746779910476782570941333542739924774727373152267839256863568582076867 (94 digits)
Fri Oct 23 14:56:28 2009  searching for 15-digit factors
Fri Oct 23 14:56:29 2009  commencing quadratic sieve (94-digit input)
Fri Oct 23 14:56:29 2009  using multiplier of 2
Fri Oct 23 14:56:29 2009  using 32kb Intel Core sieve core
Fri Oct 23 14:56:29 2009  sieve interval: 36 blocks of size 32768
Fri Oct 23 14:56:29 2009  processing polynomials in batches of 6
Fri Oct 23 14:56:29 2009  using a sieve bound of 2056211 (76471 primes)
Fri Oct 23 14:56:29 2009  using large prime bound of 283757118 (28 bits)
Fri Oct 23 14:56:29 2009  using double large prime bound of 1641738948997842 (42-51 bits)
Fri Oct 23 14:56:29 2009  using trial factoring cutoff of 51 bits
Fri Oct 23 14:56:29 2009  polynomial 'A' values have 12 factors
Fri Oct 23 18:15:47 2009  76840 relations (18623 full + 58217 combined from 1108711 partial), need 76567
Fri Oct 23 18:15:50 2009  begin with 1127334 relations
Fri Oct 23 18:15:51 2009  reduce to 200273 relations in 11 passes
Fri Oct 23 18:15:51 2009  attempting to read 200273 relations
Fri Oct 23 18:15:54 2009  recovered 200273 relations
Fri Oct 23 18:15:54 2009  recovered 184455 polynomials
Fri Oct 23 18:15:54 2009  attempting to build 76840 cycles
Fri Oct 23 18:15:54 2009  found 76840 cycles in 6 passes
Fri Oct 23 18:15:54 2009  distribution of cycle lengths:
Fri Oct 23 18:15:54 2009     length 1 : 18623
Fri Oct 23 18:15:54 2009     length 2 : 13514
Fri Oct 23 18:15:54 2009     length 3 : 12946
Fri Oct 23 18:15:54 2009     length 4 : 10395
Fri Oct 23 18:15:54 2009     length 5 : 7844
Fri Oct 23 18:15:54 2009     length 6 : 5278
Fri Oct 23 18:15:54 2009     length 7 : 3534
Fri Oct 23 18:15:54 2009     length 9+: 4706
Fri Oct 23 18:15:54 2009  largest cycle: 22 relations
Fri Oct 23 18:15:55 2009  matrix is 76471 x 76840 (20.2 MB) with weight 4987394 (64.91/col)
Fri Oct 23 18:15:55 2009  sparse part has weight 4987394 (64.91/col)
Fri Oct 23 18:15:56 2009  filtering completed in 3 passes
Fri Oct 23 18:15:56 2009  matrix is 72965 x 73029 (19.2 MB) with weight 4748338 (65.02/col)
Fri Oct 23 18:15:56 2009  sparse part has weight 4748338 (65.02/col)
Fri Oct 23 18:15:56 2009  saving the first 48 matrix rows for later
Fri Oct 23 18:15:56 2009  matrix is 72917 x 73029 (12.0 MB) with weight 3734396 (51.14/col)
Fri Oct 23 18:15:56 2009  sparse part has weight 2704773 (37.04/col)
Fri Oct 23 18:15:56 2009  matrix includes 64 packed rows
Fri Oct 23 18:15:56 2009  using block size 29211 for processor cache size 1024 kB
Fri Oct 23 18:15:57 2009  commencing Lanczos iteration
Fri Oct 23 18:15:57 2009  memory use: 12.2 MB
Fri Oct 23 18:16:32 2009  lanczos halted after 1154 iterations (dim = 72917)
Fri Oct 23 18:16:32 2009  recovered 18 nontrivial dependencies
Fri Oct 23 18:16:33 2009  prp31 factor: 3928758742686927379474311715139
Fri Oct 23 18:16:33 2009  prp64 factor: 1315472132328471305168939778776883400661078541357517237138695553
Fri Oct 23 18:16:33 2009  elapsed time 03:20:06

(64·10¹³⁷+71)/9 = 7(1)₁₃₆9_<138> = C138

C138 = P52 · P87

P52 = 4678254969758935869078035834515686537386950155297113_<52>

P87 = 152003496112943519578771055918308270279589141828614745466191423566662228372256519561063_<87>

Number: 71119_137
N=711111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119
  ( 138 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=4678254969758935869078035834515686537386950155297113 (pp52)
 r2=152003496112943519578771055918308270279589141828614745466191423566662228372256519561063 (pp87)
Version: Msieve v. 1.42
Total time: 0.16 hours.
Scaled time: 0.14 units (timescale=0.854).
Factorization parameters were as follows:
name: 71119_137
n: 711111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119
m: 2000000000000000000000000000
deg: 5
c5: 200
c0: 71
skew: 0.81
type: snfs
lss: 1
rlim: 1440000
alim: 1440000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1440000/1440000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [720000, 1395001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 199344 x 199572
Total sieving time: 0.00 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138.000,5,0,0,0,0,0,0,0,0,1440000,1440000,26,26,48,48,2.3,2.3,75000
total time: 0.16 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583)
Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268)
Total of 2 processors activated (11653.70 BogoMIPS).

Total time: 2 hours 24 min.

(64·10¹⁴²+71)/9 = 7(1)₁₄₁9_<143> = C143

C143 = P67 · P77

P67 = 2751554361959943194224637967034286786872683258385468032588376648693_<67>

P77 = 25843978259785636875135096179738241197288805889331674506170937558923404767283_<77>

Number: 71119_142
N=71111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119
  ( 143 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=2751554361959943194224637967034286786872683258385468032588376648693 (pp67)
 r2=25843978259785636875135096179738241197288805889331674506170937558923404767283 (pp77)
Version: Msieve v. 1.42
Total time: 0.35 hours.
Scaled time: 0.30 units (timescale=0.854).
Factorization parameters were as follows:
name: 71119_142
n: 71111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119
m: 20000000000000000000000000000
deg: 5
c5: 200
c0: 71
skew: 0.81
type: snfs
lss: 1
rlim: 1750000
alim: 1750000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1750000/1750000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [875000, 1775001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 279652 x 279877
Total sieving time: 0.00 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,143.000,5,0,0,0,0,0,0,0,0,1750000,1750000,26,26,48,48,2.3,2.3,100000
total time: 0.35 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583)
Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268)
Total of 2 processors activated (11653.70 BogoMIPS).

Total time: 3 hours 26 min.

(64·10¹¹⁷+71)/9 = 7(1)₁₁₆9_<118> = 3 · 7 · 701 · 7515499 · 23743504943_<11> · C97

C97 = P37 · P60

P37 = 4516580461486691478502658597295084017_<37>

P60 = 599359992790028012792514906989104429264325175899011050976531_<60>

Number: 71119_117
N=2707057632832244799267652406416240543325923557196933707581792296587876751972688319636553540205027
  ( 97 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=4516580461486691478502658597295084017 (pp37)
 r2=599359992790028012792514906989104429264325175899011050976531 (pp60)
Version: Msieve v. 1.42
Total time: 0.03 hours.
Scaled time: 0.02 units (timescale=0.854).
Factorization parameters were as follows:
name: 71119_117
n: 2707057632832244799267652406416240543325923557196933707581792296587876751972688319636553540205027
m: 200000000000000000000000
deg: 5
c5: 200
c0: 71
skew: 0.81
type: snfs
lss: 1
rlim: 670000
alim: 670000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 670000/670000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [335000, 535001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 65411 x 65637
Total sieving time: 0.00 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,118.000,5,0,0,0,0,0,0,0,0,670000,670000,25,25,45,45,2.2,2.2,50000
total time: 0.03 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583)
Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268)
Total of 2 processors activated (11653.70 BogoMIPS).

Total time: 34 min

Oct 23, 2009 (8th)

By Erik Branger / GGNFS, Msieve / Oct 23, 2009

(61·10¹³⁰-43)/9 = 6(7)₁₂₉3_<131> = 3 · 19 · 104561 · C125

C125 = P41 · P84

P41 = 24361422306134632500392015614068389799001_<41>

P84 = 466809946821758952510988775171027699846042995590601360581498213062383282235577864749_<84>

Number: 67773_130
N=11372154251229120142204873907697593091009877685396735218571779350453496343656658033710159918029512157140502014987268873315749
  ( 125 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=24361422306134632500392015614068389799001 (pp41)
 r2=466809946821758952510988775171027699846042995590601360581498213062383282235577864749 (pp84)
Version: Msieve-1.40
Total time: 2.99 hours.
Scaled time: 3.03 units (timescale=1.016).
Factorization parameters were as follows:
n: 11372154251229120142204873907697593091009877685396735218571779350453496343656658033710159918029512157140502014987268873315749
m: 100000000000000000000000000
deg: 5
c5: 61
c0: -43
skew: 0.93
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1000001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 158677 x 158902
Total sieving time: 2.87 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.99 hours.
 --------- CPU info (if available) ----------

(64·10¹²⁴+71)/9 = 7(1)₁₂₃9_<125> = 783406759 · 1633240943_<10> · C107

C107 = P52 · P56

P52 = 4300286476281171151258495079275806409526889381253159_<52>

P56 = 12924165284242435730941431622919751804153543973171327793_<56>

Number: 71119_124
N=55577613189050344711092134103356742462283334416640186952779668783769271578241242367317453883505946305748087
  ( 107 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=4300286476281171151258495079275806409526889381253159 (pp52)
 r2=12924165284242435730941431622919751804153543973171327793 (pp56)
Version: Msieve-1.40
Total time: 1.42 hours.
Scaled time: 1.41 units (timescale=0.988).
Factorization parameters were as follows:
n: 55577613189050344711092134103356742462283334416640186952779668783769271578241242367317453883505946305748087
m: 20000000000000000000000000
deg: 5
c5: 1
c0: 355
skew: 3.24
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 131335 x 131571
Total sieving time: 1.34 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 1.42 hours.
 --------- CPU info (if available) ----------

(64·10¹²⁸+17)/9 = 7(1)₁₂₇3_<129> = 121313 · C124

C124 = P34 · P90

P34 = 9945734072532744106094589386357869_<34>

P90 = 589377128997571574070207750719380203511023715515564916726810532898128176314108510769595629_<90>

Number: 71113_128
N=5861788193442674001229143711812510704632736072070685838377676845112321936734819113459490006109082382853536810655998212154601
  ( 124 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=9945734072532744106094589386357869 (pp34)
 r2=589377128997571574070207750719380203511023715515564916726810532898128176314108510769595629 (pp90)
Version: Msieve-1.40
Total time: 2.34 hours.
Scaled time: 2.06 units (timescale=0.882).
Factorization parameters were as follows:
n: 5861788193442674001229143711812510704632736072070685838377676845112321936734819113459490006109082382853536810655998212154601
m: 40000000000000000000000000
deg: 5
c5: 125
c0: 34
skew: 0.77
type: snfs
lss: 1
rlim: 1030000
alim: 1030000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1030000/1030000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [515000, 865001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 168923 x 169147
Total sieving time: 2.19 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130.000,5,0,0,0,0,0,0,0,0,1030000,1030000,26,26,47,47,2.3,2.3,50000
total time: 2.34 hours.
 --------- CPU info (if available) ----------

(64·10¹²⁰+17)/9 = 7(1)₁₁₉3_<121> = 3 · 317069430763113141972035184913_<30> · C91

C91 = P43 · P49

P43 = 2483220410140889475298484044606681873376039_<43>

P49 = 3010555013680947198263188604057952229055006361653_<49>

Number: 71113_120
N=7475871655824512827094195598536550953335744647383126234581928937795878542508172953298632467
  ( 91 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=2483220410140889475298484044606681873376039 (pp43)
 r2=3010555013680947198263188604057952229055006361653 (pp49)
Version: Msieve v. 1.41
Total time: 2.33 hours.
Scaled time: 1.82 units (timescale=0.778).
Factorization parameters were as follows:
n: 7475871655824512827094195598536550953335744647383126234581928937795878542508172953298632467
m: 2000000000000000000000000
deg: 5
c5: 2
c0: 17
skew: 1.53
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 625001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 83122 x 83348
Total sieving time: 2.26 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 2.33 hours.
 --------- CPU info (if available) ----------

Oct 23, 2009 (7th)

By Jo Yeong Uk / GMP-ECM v6.2.3, YAFU v1.10, Msieve / Oct 23, 2009

(64·10¹⁴⁰+71)/9 = 7(1)₁₃₉9_<141> = 4261 · 290870269 · 605275506321521939515134243439_<30> · C99

C99 = P40 · P60

P40 = 4365243825947720194516559610136906553161_<40>

P60 = 217152578872431638637153816457693436327459716445307037022729_<60>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 947923954211507557584220578170638095302115735929727807120717193980875431937747867188809643003796369 (99 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3295075564
Step 1 took 2713ms
Step 2 took 1770ms
********** Factor found in step 2: 4365243825947720194516559610136906553161
Found probable prime factor of 40 digits: 4365243825947720194516559610136906553161
Probable prime cofactor 217152578872431638637153816457693436327459716445307037022729 has 60 digits

(64·10¹⁵⁶+71)/9 = 7(1)₁₅₅9_<157> = 3² · 191 · 12568412159_<11> · 1665303397181_<13> · 790909645848014343691_<21> · C111

C111 = P34 · P37 · P41

P34 = 1509622802506911568366078614272501_<34>

P37 = 3540605850217335430143189930721214149_<37>

P41 = 46753583509719466111127548763912412200641_<41>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 249896937284161970702752522215730960916460132881437417396746833828803352253291147384499572487883163961983272009 (111 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3636675759
Step 1 took 3447ms
Step 2 took 3775ms
********** Factor found in step 2: 1509622802506911568366078614272501
Found probable prime factor of 34 digits: 1509622802506911568366078614272501
Composite cofactor 165536011293137483754755380980026119736404254846460957351992023020952516069509 has 78 digits

10/23/09 18:51:26 v1.10 @ 조영욱-PC, starting SIQS on c78: 165536011293137483754755380980026119736404254846460957351992023020952516069509
10/23/09 18:51:26 v1.10 @ 조영욱-PC, random seeds: 3287229736, 2548667776
10/23/09 18:51:27 v1.10 @ 조영욱-PC, ==== sieve params ====
10/23/09 18:51:27 v1.10 @ 조영욱-PC, n = 78 digits, 257 bits
10/23/09 18:51:27 v1.10 @ 조영욱-PC, factor base: 35111 primes (max prime = 879097)
10/23/09 18:51:27 v1.10 @ 조영욱-PC, single large prime cutoff: 74723245 (85 * pmax)
10/23/09 18:51:27 v1.10 @ 조영욱-PC, using 12 large prime slices of factor base
10/23/09 18:51:27 v1.10 @ 조영욱-PC, buckets hold 1024 elements
10/23/09 18:51:27 v1.10 @ 조영욱-PC, sieve interval: 5 blocks of size 65536
10/23/09 18:51:27 v1.10 @ 조영욱-PC, polynomial A has ~ 10 factors
10/23/09 18:51:27 v1.10 @ 조영욱-PC, using multiplier of 1
10/23/09 18:51:27 v1.10 @ 조영욱-PC, using small prime variation correction of 18 bits
10/23/09 18:51:27 v1.10 @ 조영욱-PC, using SSE2 for trial division and x64 sieve scanning
10/23/09 18:51:27 v1.10 @ 조영욱-PC, trial factoring cutoff at 91 bits
10/23/09 18:51:27 v1.10 @ 조영욱-PC, ==== sieving started ====
10/23/09 18:55:46 v1.10 @ 조영욱-PC, sieve time = 124.7190, relation time = 44.5060, poly_time = 89.7600
10/23/09 18:55:46 v1.10 @ 조영욱-PC, 35322 relations found: 17489 full + 17833 from 185428 partial, using 88776 polys (173 A polys)
10/23/09 18:55:46 v1.10 @ 조영욱-PC, on average, sieving found 2.29 rels/poly and 782.63 rels/sec
10/23/09 18:55:46 v1.10 @ 조영욱-PC, trial division touched 2499810 sieve locations out of 58180239360
10/23/09 18:55:46 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
10/23/09 18:55:46 v1.10 @ 조영욱-PC, begin with 202917 relations
10/23/09 18:55:46 v1.10 @ 조영욱-PC, reduce to 50918 relations in 2 passes
10/23/09 18:55:46 v1.10 @ 조영욱-PC, recovered 50918 relations
10/23/09 18:55:46 v1.10 @ 조영욱-PC, recovered 38684 polynomials
10/23/09 18:55:46 v1.10 @ 조영욱-PC, attempting to build 35322 cycles
10/23/09 18:55:46 v1.10 @ 조영욱-PC, found 35322 cycles in 1 passes
10/23/09 18:55:46 v1.10 @ 조영욱-PC, distribution of cycle lengths:
10/23/09 18:55:46 v1.10 @ 조영욱-PC,    length 1 : 17489
10/23/09 18:55:46 v1.10 @ 조영욱-PC,    length 2 : 17833
10/23/09 18:55:46 v1.10 @ 조영욱-PC, largest cycle: 2 relations
10/23/09 18:55:46 v1.10 @ 조영욱-PC, matrix is 35111 x 35322 (5.1 MB) with weight 1049121 (29.70/col)
10/23/09 18:55:46 v1.10 @ 조영욱-PC, sparse part has weight 1049121 (29.70/col)
10/23/09 18:55:46 v1.10 @ 조영욱-PC, filtering completed in 3 passes
10/23/09 18:55:46 v1.10 @ 조영욱-PC, matrix is 26735 x 26799 (4.1 MB) with weight 861999 (32.17/col)
10/23/09 18:55:46 v1.10 @ 조영욱-PC, sparse part has weight 861999 (32.17/col)
10/23/09 18:55:46 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
10/23/09 18:55:46 v1.10 @ 조영욱-PC, matrix is 26687 x 26799 (2.8 MB) with weight 634513 (23.68/col)
10/23/09 18:55:46 v1.10 @ 조영욱-PC, sparse part has weight 469328 (17.51/col)
10/23/09 18:55:46 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
10/23/09 18:55:46 v1.10 @ 조영욱-PC, commencing Lanczos iteration
10/23/09 18:55:46 v1.10 @ 조영욱-PC, memory use: 3.8 MB
10/23/09 18:55:53 v1.10 @ 조영욱-PC, lanczos halted after 424 iterations (dim = 26685)
10/23/09 18:55:53 v1.10 @ 조영욱-PC, recovered 15 nontrivial dependencies
10/23/09 18:55:53 v1.10 @ 조영욱-PC, prp37 = 3540605850217335430143189930721214149
10/23/09 18:55:54 v1.10 @ 조영욱-PC, prp41 = 46753583509719466111127548763912412200641
10/23/09 18:55:54 v1.10 @ 조영욱-PC, Lanczos elapsed time = 7.4720 seconds.
10/23/09 18:55:54 v1.10 @ 조영욱-PC, Sqrt elapsed time = 1.1390 seconds.
10/23/09 18:55:54 v1.10 @ 조영욱-PC, SIQS elapsed time = 267.8880 seconds.
10/23/09 18:55:54 v1.10 @ 조영욱-PC, 
10/23/09 18:55:54 v1.10 @ 조영욱-PC,

(64·10¹³²+71)/9 = 7(1)₁₃₁9_<133> = 3 · 40621759 · 15607242535519221001_<20> · C106

C106 = P32 · P75

P32 = 33406633458733228036889158768693_<32>

P75 = 111917652785707680031519794663165296371462657267249967130393240919514596279_<75>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 3738792004173910248793834600429365849248846138515661337826580068398171638128399400957869379586676639493347 (106 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=8392278160
Step 1 took 3541ms
Step 2 took 3791ms
********** Factor found in step 2: 33406633458733228036889158768693
Found probable prime factor of 32 digits: 33406633458733228036889158768693
Probable prime cofactor 111917652785707680031519794663165296371462657267249967130393240919514596279 has 75 digits

(64·10¹³⁴+17)/9 = 7(1)₁₃₃3_<135> = 23 · 14221 · 975649 · 34880230928998141_<17> · C107

C107 = P35 · P73

P35 = 10208742076409209802516091161404393_<35>

P73 = 6257981936958239643101695299355915454578456422592818381228632246736931903_<73>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 63886123513234388051995446841980835995324452787258192996393457188745439536452888704414805133551897486049879 (107 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6549767235
Step 1 took 3573ms
Step 2 took 3556ms
********** Factor found in step 2: 10208742076409209802516091161404393
Found probable prime factor of 35 digits: 10208742076409209802516091161404393
Probable prime cofactor 6257981936958239643101695299355915454578456422592818381228632246736931903 has 73 digits

Oct 23, 2009 (6th)

By Dmitry Domanov / GGNFS/msieve / Oct 23, 2009

(62·10¹²²+1)/9 = 6(8)₁₂₁9_<123> = 13 · 43 · 71 · 12852950743_<11> · C109

C109 = P45 · P64

P45 = 298297116435961716457125618861217437142706371_<45>

P64 = 4527173357582149631512924797923598004872719944155101719816241917_<64>

Number: snfs109
N=1350442758172466235831250671045390216870069256104474538043817178620260152392578018490262908301541399833153207
  ( 109 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=298297116435961716457125618861217437142706371 (pp45)
 r2=4527173357582149631512924797923598004872719944155101719816241917 (pp64)
Version: Msieve-1.40
Total time: 1.11 hours.
Scaled time: 2.16 units (timescale=1.957).
Factorization parameters were as follows:
n: 1350442758172466235831250671045390216870069256104474538043817178620260152392578018490262908301541399833153207
m: 5000000000000000000000000
deg: 5
c5: 248
c0: 125
skew: 0.87
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 640001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 102486 x 102715
Total sieving time: 1.05 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,125.000,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 1.11 hours.
 --------- CPU info (if available) ----------

(64·10¹³⁶+17)/9 = 7(1)₁₃₅3_<137> = 7 · 77093 · 5547661787_<10> · 66111733711_<11> · 3770592903491924639_<19> · C92

C92 = P46 · P47

P46 = 5422249164127684148858996648996091821227445417_<46>

P47 = 17573037645400070249428839877166074647419899393_<47>

Number: 92
N=95285388683954857710126813040472911888407431629029171998566805703742921828445711644538931881
  ( 92 digits)
Divisors found:
 r1=5422249164127684148858996648996091821227445417 (pp46)
 r2=17573037645400070249428839877166074647419899393 (pp47)
Version: Msieve-1.40
Total time: 2.77 hours.
Scaled time: 5.44 units (timescale=1.963).
Factorization parameters were as follows:
name: 92
n:  95285388683954857710126813040472911888407431629029171998566805703742921828445711644538931881
m:  1219925083891547904536
deg: 4
c4: 43022304
c3: 117357957168
c2: -116549645048442254
c1: -345234638576714221
c0: 178970559087716997950049
skew: 1635.250
type: gnfs
# adj. I(F,S) = 53.624
# E(F1,F2) = 8.591379e-005
# GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=58.00000000, seed=1256249799.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 700000
alim: 700000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.4
alambda: 2.4
qintsize: 40000

type: gnfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [350000, 910001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 130314 x 130562
Polynomial selection time: 0.17 hours.
Total sieving time: 2.52 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
gnfs,91,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000
total time: 2.77 hours.
 --------- CPU info (if available) ----------

(64·10¹⁰¹+71)/9 = 7(1)₁₀₀9_<102> = 3250990037_<10> · C93

C93 = P38 · P56

P38 = 10748647274212289142063536058100292177_<38>

P56 = 20350168736847131287336811282510747218369900720674640931_<56>

Number: snfs93
N=218736785723072060928346398100976742892156427457889226103190026820470108721871518645663296787
  ( 93 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=10748647274212289142063536058100292177 (pp38)
 r2=20350168736847131287336811282510747218369900720674640931 (pp56)
Version: Msieve-1.40
Total time: 0.21 hours.
Scaled time: 0.40 units (timescale=1.951).
Factorization parameters were as follows:
n: 218736785723072060928346398100976742892156427457889226103190026820470108721871518645663296787
m: 20000000000000000000000000
deg: 4
c4: 40
c0: 71
skew: 1.15
type: snfs
lss: 1
rlim: 360000
alim: 360000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [180000, 220001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 31327 x 31552
Total sieving time: 0.20 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,102.000,4,0,0,0,0,0,0,0,0,360000,360000,25,25,43,43,2.2,2.2,10000
total time: 0.21 hours.
 --------- CPU info (if available) ----------

(64·10¹⁰⁸+17)/9 = 7(1)₁₀₇3_<109> = 3² · 1399 · 890949611 · C96

C96 = P45 · P52

P45 = 433190132097380420384996916362442135529201421_<45>

P52 = 1463341007385146117446818610976026834508899289208553_<52>

Number: snfs96
N=633904884292685183921845263177093156427638567190056943304369860206601718459519750575711212953813
  ( 96 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=433190132097380420384996916362442135529201421 (pp45)
 r2=1463341007385146117446818610976026834508899289208553 (pp52)
Version: Msieve-1.40
Total time: 0.66 hours.
Scaled time: 1.29 units (timescale=1.963).
Factorization parameters were as follows:
n: 633904884292685183921845263177093156427638567190056943304369860206601718459519750575711212953813
m: 4000000000000000000000
deg: 5
c5: 125
c0: 34
skew: 0.77
type: snfs
lss: 1
rlim: 480000
alim: 480000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2Factor base limits: 480000/480000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [240000, 390001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 45435 x 45665
Total sieving time: 0.64 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,110.000,5,0,0,0,0,0,0,0,0,480000,480000,25,25,44,44,2.2,2.2,50000
total time: 0.66 hours.
 --------- CPU info (if available) ----------

(64·10¹¹¹+17)/9 = 7(1)₁₁₀3_<112> = 3 · 89 · 417370571 · C101

C101 = P47 · P55

P47 = 54782810780936906708981933325626845098262652917_<47>

P55 = 1164823351692625310889945891417246864769307437537167277_<55>

Number: snfs101
N=63812297268993815940902221849348184534482795624962936864923878115416909012601683655932390427220997009
  ( 101 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=54782810780936906708981933325626845098262652917 (pp47)
 r2=1164823351692625310889945891417246864769307437537167277 (pp55)
Version: Msieve-1.40
Total time: 0.66 hours.
Scaled time: 1.30 units (timescale=1.963).
Factorization parameters were as follows:
n: 63812297268993815940902221849348184534482795624962936864923878115416909012601683655932390427220997009
m: 20000000000000000000000
deg: 5
c5: 20
c0: 17
skew: 0.97
type: snfs
lss: 1
rlim: 530000
alim: 530000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 530000/530000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [265000, 415001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 50310 x 50535
Total sieving time: 0.64 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,112.000,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000
total time: 0.66 hours.
 --------- CPU info (if available) ----------

(64·10¹¹⁹+17)/9 = 7(1)₁₁₈3_<120> = 13 · C119

C119 = P45 · P75

P45 = 488727793725958700489283586125677588925075041_<45>

P75 = 111924992609539966693906747228138885053736779654620027718067011364684909261_<75>

Number: s119
N=54700854700854700854700854700854700854700854700854700854700854700854700854700854700854700854700854700854700854700854701
  ( 119 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=488727793725958700489283586125677588925075041 (pp45)
 r2=111924992609539966693906747228138885053736779654620027718067011364684909261 (pp75)
Version: Msieve-1.40
Total time: 1.49 hours.
Scaled time: 2.93 units (timescale=1.975).
Factorization parameters were as follows:
n: 54700854700854700854700854700854700854700854700854700854700854700854700854700854700854700854700854700854700854700854701
m: 2000000000000000000000000
deg: 5
c5: 1
c0: 85
skew: 2.43
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 670001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 63745 x 63970
Total sieving time: 1.46 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 1.49 hours.
 --------- CPU info (if available) ----------

Oct 23, 2009 (5th)

By Serge Batalov / Msieve, GMP-ECM 6.2.1 / Oct 23, 2009

(62·10¹¹⁹+1)/9 = 6(8)₁₁₈9_<120> = 53 · C119

C119 = P59 · P60

P59 = 81639827347528296394011236911324937968186783394226152874541_<59>

P60 = 159210326457590438894678389977581407772306683697429931033193_<60>

SNFS difficulty: 121 digits.
Divisors found:
 r1=81639827347528296394011236911324937968186783394226152874541 (pp59)
 r2=159210326457590438894678389977581407772306683697429931033193 (pp60)
Version: Msieve v. 1.44 SVN130
Total time: 0.77 hours.
Scaled time: 1.84 units (timescale=2.400).
Factorization parameters were as follows:
n: 12997903563941299790356394129979035639412997903563941299790356394129979035639412997903563941299790356394129979035639413
m: 1000000000000000000000000
deg: 5
c5: 31
c0: 5
skew: 0.69
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [462500, 712501)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 80641 x 80867
Total sieving time: 0.73 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 0.77 hours.

(62·10¹⁰⁸-17)/9 = 6(8)₁₀₇7_<109> = 71 · 6691 · C104

C104 = P44 · P60

P44 = 46859901000776781131465690847842935612263181_<44>

P60 = 309455663057323235274691052519448169795958335578466652421607_<60>

SNFS difficulty: 111 digits.
Divisors found:
 r1=46859901000776781131465690847842935612263181 (pp44)
 r2=309455663057323235274691052519448169795958335578466652421607 (pp60)
Version: Msieve v. 1.44 SVN130
Total time: 0.57 hours.
Scaled time: 1.36 units (timescale=2.400).
Factorization parameters were as follows:
n: 14501061734995903450059863657275358088516819711339993998431546451695443088127396037327604010619454951867
m: 5000000000000000000000
deg: 5
c5: 496
c0: -425
skew: 0.97
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [312500, 512501)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 46087 x 46312
Total sieving time: 0.54 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 0.57 hours.

(64·10¹⁸³+71)/9 = 7(1)₁₈₂9_<184> = 3² · 7 · 17 · 79 · 193 · 293 · 5011 · C171

C171 = P35 · P137

P35 = 17301463376975847179315279150325763_<35>

P137 = 17143075290875582464063217144806230401728131829237471188559245402738466206829167056208532345413386033226412355136311495896727090101119163_<137>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=238477675
Step 1 took 3528ms
Step 2 took 2501ms
********** Factor found in step 2: 17301463376975847179315279150325763
Found probable prime factor of 35 digits: 17301463376975847179315279150325763
Probable prime cofactor has 137 digits

(64·10¹⁸⁵+71)/9 = 7(1)₁₈₄9_<186> = 593707 · 594449 · 4422329046727_<13> · C162

C162 = P32 · C131

P32 = 40284292656009544724056072361587_<32>

C131 = [11310033687577798780951179717781239801201300667676599750525383725016871763434743855775671472835920548897294389560503214459333104217_<131>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1330655251
Step 1 took 3552ms
Step 2 took 2400ms
********** Factor found in step 2: 40284292656009544724056072361587
Found probable prime factor of 32 digits: 40284292656009544724056072361587
Composite cofactor has 131 digits

Oct 23, 2009 (4th)

By Sinkiti Sibata / Msieve / Oct 23, 2009

(64·10¹²³+71)/9 = 7(1)₁₂₂9_<124> = 3 · 7 · 15583 · 15881 · 105885567595491756562319_<24> · C92

C92 = P34 · P59

P34 = 1136814553249137324245558559567913_<34>

P59 = 11367444950762975702690695066334498127534988253058760353619_<59>

Number: 71119_123
N=12922676853285774050945956342016639234286997338578012703264913559170745694076371843725827147
  ( 92 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=1136814553249137324245558559567913 (pp34)
 r2=11367444950762975702690695066334498127534988253058760353619 (pp59)
Version: Msieve v. 1.42
Total time: 0.10 hours.
Scaled time: 0.08 units (timescale=0.854).
Factorization parameters were as follows:
name: 71119_123
n: 12922676853285774050945956342016639234286997338578012703264913559170745694076371843725827147
m: 4000000000000000000000000
deg: 5
c5: 125
c0: 142
skew: 1.03
type: snfs
lss: 1
rlim: 850000
alim: 850000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 850000/850000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [425000, 725001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 135545 x 135793
Total sieving time: 0.00 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,125.000,5,0,0,0,0,0,0,0,0,850000,850000,26,26,46,46,2.3,2.3,50000
total time: 0.10 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02
Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583)
Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268)
Total of 2 processors activated (11653.70 BogoMIPS).

Oct 23, 2009 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Oct 23, 2009

(64·10¹¹⁰+17)/9 = 7(1)₁₀₉3_<111> = 2269 · C108

C108 = P34 · P74

P34 = 6107263899343395071821741879117103_<34>

P74 = 51316411859772317742603311829444405836304533254101354511869738454046382259_<74>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 313402869595024729445178982420057783654081582684491454874883698153861221291807453111992556681847118162675677 (108 digits)
Using B1=1636000, B2=2140202620, polynomial Dickson(6), sigma=2170076982
Step 1 took 12735ms
Step 2 took 5781ms
********** Factor found in step 2: 6107263899343395071821741879117103
Found probable prime factor of 34 digits: 6107263899343395071821741879117103
Probable prime cofactor 51316411859772317742603311829444405836304533254101354511869738454046382259 has 74 digits

(64·10¹¹⁹+71)/9 = 7(1)₁₁₈9_<120> = 17 · C119

C119 = P36 · P84

P36 = 103311831147289688284420593945175543_<36>

P84 = 404891336209507364975901542183933484748064918129084275135374317142656084838015829849_<84>

Number: n
N=41830065359477124183006535947712418300653594771241830065359477124183006535947712418300653594771241830065359477124183007
  ( 119 digits)
SNFS difficulty: 121 digits.
Divisors found:

Fri Oct 23 16:15:18 2009  prp36 factor: 103311831147289688284420593945175543
Fri Oct 23 16:15:18 2009  prp84 factor: 404891336209507364975901542183933484748064918129084275135374317142656084838015829849
Fri Oct 23 16:15:18 2009  elapsed time 00:02:51 (Msieve 1.42 - dependency 4)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.86 hours.
Scaled time: 1.58 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_7_1_118_9
n: 41830065359477124183006535947712418300653594771241830065359477124183006535947712418300653594771241830065359477124183007
m: 2000000000000000000000000
deg: 5
c5: 1
c0: 355
skew: 3.24
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
qintsize: 5000
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved  special-q in [370000, 546619)
Primes: RFBsize:59531, AFBsize:59449, largePrimes:1251581 encountered
Relations: rels:1204967, finalFF:131396
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 75390 hash collisions in 1272423 relations
Msieve: matrix is 76797 x 77022 (21.4 MB)

Total sieving time: 0.84 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 0.86 hours.
 --------- CPU info (if available) ----------

Oct 23, 2009 (2nd)

By Lionel Debroux / YAFU 1.12, Msieve / Oct 23, 2009

(64·10¹⁷²+71)/9 = 7(1)₁₇₁9_<173> = 4021 · 337153 · 158556479 · 188086429328935981_<18> · 8071301100515705712881743_<25> · 97882710111745450070186029019_<29> · C85

C85 = P36 · P49

P36 = 338146457983804408117822558114121347_<36>

P49 = 6583859148809103810072706544327361794424594066463_<49>

starting SIQS on c85: 2226308651034063875746538036419884476852225589307711032572873916862364437146965085661

==== sieve params ====
n = 87 digits, 287 bits
factor base: 55137 primes (max prime = 1449001)
single large prime cutoff: 137655095 (95 * pmax)
double large prime range from 42 to 49 bits
double large prime cutoff: 446504790620886
using 27 large prime slices of factor base
buckets hold 1024 elements
sieve interval: 7 blocks of size 65536
polynomial A has ~ 11 factors
using multiplier of 61
using small prime variation correction of 21 bits
using SSE2 for trial division and x128 sieve scanning
trial factoring cutoff at 93 bits

==== sieving in progress (1 thread):   55201 relations needed ====
====           Press ctrl-c to abort and save state           ====
55346 rels found: 21109 full + 34237 from 443418 partial, (414.95 rels/sec)
sieve time = 542.0653, relation time = 225.0556, poly_time = 425.8309
trial division touched 8721453 sieve locations out of 58844064907264
QS elapsed time = 1202.4044 seconds.

==== post processing stage (msieve-1.38) ====
begin with 464527 relations
reduce to 104232 relations in 7 passes
attempting to read 104232 relations
recovered 104232 relations
recovered 79138 polynomials
attempting to build 55346 cycles
found 55346 cycles in 4 passes
distribution of cycle lengths:
   length 1 : 21109
   length 2 : 17041
   length 3 : 9430
   length 4 : 4522
   length 5 : 1963
   length 6 : 775
   length 7 : 339
   length 9+: 167
largest cycle: 12 relations
seed1 = 3257297759, seed2 = 496421594
matrix is 55137 x 55346 (10.5 MB) with weight 2312373 (41.78/col)
sparse part has weight 2312373 (41.78/col)
filtering completed in 4 passes
matrix is 45917 x 45981 (9.0 MB) with weight 1993204 (43.35/col)
sparse part has weight 1993204 (43.35/col)
saving the first 48 matrix rows for later
matrix is 45869 x 45981 (7.8 MB) with weight 1684454 (36.63/col)
sparse part has weight 1591912 (34.62/col)
matrix includes 64 packed rows
using block size 18392 for processor cache size 4096 kB
commencing Lanczos iteration
memory use: 6.6 MB
lanczos halted after 727 iterations (dim = 45864)
recovered 14 nontrivial dependencies
Lanczos elapsed time = 17.7000 seconds.
Sqrt elapsed time = 1.4300 seconds.
SIQS elapsed time = 1222.1363 seconds.
ECM/SIQS ratio was = 0.301022

Total factoring time = 1605.5181 seconds

***factors found***

PRP49 = 6583859148809103810072706544327361794424594066463
PRP36 = 338146457983804408117822558114121347

Oct 23, 2009

By Lionel Debroux / GMP-ECM

Factorizations of 711...113 and Factorizations of 711...119 have been extended up to n=200. Composite numbers that appeared newly have passed 150 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 22, 2009 (7th)

By Jo Yeong Uk / GMP-ECM / Oct 22, 2009

(61·10¹³¹-43)/9 = 6(7)₁₃₀3_<132> = 31 · 193 · 373 · 509 · 5437 · C120

C120 = P37 · P83

P37 = 3176842301068964566003730214226708951_<37>

P83 = 34545121036016200581235088091939562853984600621026803667217884043326708540802158409_<83>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 109744401802763599807563603019940736292097143021592772647580168164876472110366275650925686730214991920095467557440218959 (120 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5415166480
Step 1 took 4446ms
Step 2 took 3744ms
********** Factor found in step 2: 3176842301068964566003730214226708951
Found probable prime factor of 37 digits: 3176842301068964566003730214226708951
Probable prime cofactor 34545121036016200581235088091939562853984600621026803667217884043326708540802158409 has 83 digits

Oct 22, 2009 (6th)

By Erik Branger / GGNFS, Msieve, YAFU / Oct 22, 2009

(62·10¹⁰⁷-17)/9 = 6(8)₁₀₆7_<108> = 3 · C108

C108 = P47 · P61

P47 = 64491293756081752461179581215688846049520648869_<47>

P61 = 3560629912281373017071203551569816106852159704383341998954041_<61>

Number: 68887_107
N=229629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629
  ( 108 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=64491293756081752461179581215688846049520648869 (pp47)
 r2=3560629912281373017071203551569816106852159704383341998954041 (pp61)
Version: Msieve-1.40
Total time: 0.79 hours.
Scaled time: 0.77 units (timescale=0.982).
Factorization parameters were as follows:
n: 229629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629629
m: 2000000000000000000000
deg: 5
c5: 775
c0: -68
skew: 0.61
type: snfs
lss: 1
rlim: 470000
alim: 470000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 470000/470000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [235000, 385001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 49917 x 50142
Total sieving time: 0.77 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,109.000,5,0,0,0,0,0,0,0,0,470000,470000,25,25,44,44,2.2,2.2,50000
total time: 0.79 hours.
 --------- CPU info (if available) ----------

(62·10¹⁰⁸+1)/9 = 6(8)₁₀₇9_<109> = 7 · 139 · 359 · 571261 · 786719 · 2979701 · C86

C86 = P35 · P51

P35 = 88487325486117617422437582413031689_<35>

P51 = 166430884397911127150765051393953307715521219894077_<51>

10/22/09 10:32:20 v1.12 @ ERIK-DATOR, starting SIQS on c86: 14727023838660376218327768453568687574256162565042157953529770729131644970005024406053
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, random seeds: 1449736531, 3653992088
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, ==== sieve params ====
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, n = 87 digits, 289 bits
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, factor base: 56327 primes (max prime = 1480903)
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, single large prime cutoff: 162899330 (110 * pmax)
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, double large prime range from 42 to 50 bits
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, double large prime cutoff: 604581336785488
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, using 0 large prime slices of factor base
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, buckets hold 1024 elements
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, polynomial A has ~ -1878638032 factors
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, using multiplier of 53
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, using small prime variation correction of 21 bits
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, trial factoring cutoff at 95 bits
10/22/09 10:32:20 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ====
10/22/09 10:47:46 v1.12 @ ERIK-DATOR, sieve time = 273.9536, relation time = 157.2822, poly_time = 456.9534
10/22/09 10:47:46 v1.12 @ ERIK-DATOR, 56755 relations found: 19831 full + 36924 from 499168 partial, using 21641994 polys (409 A polys)
10/22/09 10:47:46 v1.12 @ ERIK-DATOR, on average, sieving found 0.02 rels/poly and 560.54 rels/sec
10/22/09 10:47:46 v1.12 @ ERIK-DATOR, trial division touched 10587663 sieve locations out of 25529934938112
10/22/09 10:47:46 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ====
10/22/09 10:47:46 v1.12 @ ERIK-DATOR, begin with 518999 relations
10/22/09 10:47:47 v1.12 @ ERIK-DATOR, reduce to 112382 relations in 8 passes
10/22/09 10:47:51 v1.12 @ ERIK-DATOR, recovered 112382 relations
10/22/09 10:47:51 v1.12 @ ERIK-DATOR, recovered 87260 polynomials
10/22/09 10:47:51 v1.12 @ ERIK-DATOR, attempting to build 56755 cycles
10/22/09 10:47:51 v1.12 @ ERIK-DATOR, found 56755 cycles in 4 passes
10/22/09 10:47:51 v1.12 @ ERIK-DATOR, distribution of cycle lengths:
10/22/09 10:47:51 v1.12 @ ERIK-DATOR,    length 1 : 19831
10/22/09 10:47:51 v1.12 @ ERIK-DATOR,    length 2 : 16544
10/22/09 10:47:51 v1.12 @ ERIK-DATOR,    length 3 : 10341
10/22/09 10:47:51 v1.12 @ ERIK-DATOR,    length 4 : 5393
10/22/09 10:47:51 v1.12 @ ERIK-DATOR,    length 5 : 2628
10/22/09 10:47:51 v1.12 @ ERIK-DATOR,    length 6 : 1199
10/22/09 10:47:51 v1.12 @ ERIK-DATOR,    length 7 : 470
10/22/09 10:47:51 v1.12 @ ERIK-DATOR,    length 9+: 349
10/22/09 10:47:51 v1.12 @ ERIK-DATOR, largest cycle: 13 relations
10/22/09 10:47:51 v1.12 @ ERIK-DATOR, matrix is 56327 x 56755 (10.9 MB) with weight 2617883 (46.13/col)
10/22/09 10:47:51 v1.12 @ ERIK-DATOR, sparse part has weight 2617883 (46.13/col)
10/22/09 10:47:52 v1.12 @ ERIK-DATOR, filtering completed in 3 passes
10/22/09 10:47:52 v1.12 @ ERIK-DATOR, matrix is 48415 x 48479 (9.5 MB) with weight 2292126 (47.28/col)
10/22/09 10:47:52 v1.12 @ ERIK-DATOR, sparse part has weight 2292126 (47.28/col)
10/22/09 10:47:52 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later
10/22/09 10:47:52 v1.12 @ ERIK-DATOR, matrix is 48367 x 48479 (7.9 MB) with weight 1946755 (40.16/col)
10/22/09 10:47:52 v1.12 @ ERIK-DATOR, sparse part has weight 1768625 (36.48/col)
10/22/09 10:47:52 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows
10/22/09 10:47:52 v1.12 @ ERIK-DATOR, using block size 19391 for processor cache size 2048 kB
10/22/09 10:47:52 v1.12 @ ERIK-DATOR, commencing Lanczos iteration
10/22/09 10:47:52 v1.12 @ ERIK-DATOR, memory use: 7.2 MB
10/22/09 10:48:07 v1.12 @ ERIK-DATOR, lanczos halted after 766 iterations (dim = 48365)
10/22/09 10:48:07 v1.12 @ ERIK-DATOR, recovered 17 nontrivial dependencies
10/22/09 10:48:08 v1.12 @ ERIK-DATOR, prp51 = 166430884397911127150765051393953307715521219894077
10/22/09 10:48:09 v1.12 @ ERIK-DATOR, prp35 = 88487325486117617422437582413031689
10/22/09 10:48:09 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 20.6080 seconds.
10/22/09 10:48:09 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 2.7920 seconds.
10/22/09 10:48:09 v1.12 @ ERIK-DATOR, SIQS elapsed time = 949.2848 seconds.

(62·10¹⁰³-17)/9 = 6(8)₁₀₂7_<104> = 8301041583370987531_<19> · C85

C85 = P42 · P43

P42 = 935821881014050738831123008109811617879289_<42>

P43 = 8867953254436831317618185581870422405366893_<43>

Thu Oct 22 10:09:34 2009  Msieve v. 1.40
Thu Oct 22 10:09:34 2009  random seeds: fd34b190 bd975fae
Thu Oct 22 10:09:34 2009  factoring 8298824695311748374477858110031838988136273574343649262984615204677773844988630979077 (85 digits)
Thu Oct 22 10:09:35 2009  searching for 15-digit factors
Thu Oct 22 10:09:37 2009  commencing quadratic sieve (85-digit input)
Thu Oct 22 10:09:37 2009  using multiplier of 1
Thu Oct 22 10:09:37 2009  using 64kb Pentium 4 sieve core
Thu Oct 22 10:09:37 2009  sieve interval: 6 blocks of size 65536
Thu Oct 22 10:09:37 2009  processing polynomials in batches of 17
Thu Oct 22 10:09:37 2009  using a sieve bound of 1433021 (55000 primes)
Thu Oct 22 10:09:37 2009  using large prime bound of 114641680 (26 bits)
Thu Oct 22 10:09:37 2009  using double large prime bound of 321230343743840 (41-49 bits)
Thu Oct 22 10:09:37 2009  using trial factoring cutoff of 49 bits
Thu Oct 22 10:09:37 2009  polynomial 'A' values have 11 factors
Thu Oct 22 10:59:23 2009  55345 relations (15653 full + 39692 combined from 575487 partial), need 55096
Thu Oct 22 10:59:25 2009  begin with 591140 relations
Thu Oct 22 10:59:26 2009  reduce to 131511 relations in 10 passes
Thu Oct 22 10:59:26 2009  attempting to read 131511 relations
Thu Oct 22 10:59:28 2009  recovered 131511 relations
Thu Oct 22 10:59:28 2009  recovered 113568 polynomials
Thu Oct 22 10:59:28 2009  attempting to build 55345 cycles
Thu Oct 22 10:59:29 2009  found 55345 cycles in 5 passes
Thu Oct 22 10:59:29 2009  distribution of cycle lengths:
Thu Oct 22 10:59:29 2009     length 1 : 15653
Thu Oct 22 10:59:29 2009     length 2 : 11068
Thu Oct 22 10:59:29 2009     length 3 : 9764
Thu Oct 22 10:59:29 2009     length 4 : 7259
Thu Oct 22 10:59:29 2009     length 5 : 4848
Thu Oct 22 10:59:29 2009     length 6 : 2983
Thu Oct 22 10:59:29 2009     length 7 : 1791
Thu Oct 22 10:59:29 2009     length 9+: 1979
Thu Oct 22 10:59:29 2009  largest cycle: 19 relations
Thu Oct 22 10:59:29 2009  matrix is 55000 x 55345 (12.0 MB) with weight 2926649 (52.88/col)
Thu Oct 22 10:59:29 2009  sparse part has weight 2926649 (52.88/col)
Thu Oct 22 10:59:30 2009  filtering completed in 3 passes
Thu Oct 22 10:59:30 2009  matrix is 50419 x 50482 (11.0 MB) with weight 2681514 (53.12/col)
Thu Oct 22 10:59:30 2009  sparse part has weight 2681514 (53.12/col)
Thu Oct 22 10:59:30 2009  saving the first 48 matrix rows for later
Thu Oct 22 10:59:30 2009  matrix is 50371 x 50482 (6.5 MB) with weight 2036405 (40.34/col)
Thu Oct 22 10:59:30 2009  sparse part has weight 1390788 (27.55/col)
Thu Oct 22 10:59:30 2009  matrix includes 64 packed rows
Thu Oct 22 10:59:30 2009  using block size 20192 for processor cache size 512 kB
Thu Oct 22 10:59:31 2009  commencing Lanczos iteration
Thu Oct 22 10:59:31 2009  memory use: 6.8 MB
Thu Oct 22 10:59:52 2009  lanczos halted after 798 iterations (dim = 50368)
Thu Oct 22 10:59:52 2009  recovered 15 nontrivial dependencies
Thu Oct 22 10:59:52 2009  prp42 factor: 935821881014050738831123008109811617879289
Thu Oct 22 10:59:52 2009  prp43 factor: 8867953254436831317618185581870422405366893
Thu Oct 22 10:59:52 2009  elapsed time 00:50:18

(62·10¹¹⁰+1)/9 = 6(8)₁₀₉9_<111> = 13 · 181 · 21559 · 2174310109_<10> · C94

C94 = P35 · P59

P35 = 63432888137017016044348166423759881_<35>

P59 = 98460643496494633707032806939239407637455939456098771653683_<59>

Number: 68889_110
N=6245642984811856062235287029426084575778440342963469250312594651400868154281248395588881291723
  ( 94 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=63432888137017016044348166423759881 (pp35)
 r2=98460643496494633707032806939239407637455939456098771653683 (pp59)
Version: Msieve v. 1.41
Total time: 1.02 hours.
Scaled time: 0.80 units (timescale=0.782).
Factorization parameters were as follows:
n: 6245642984811856062235287029426084575778440342963469250312594651400868154281248395588881291723
m: 20000000000000000000000
deg: 5
c5: 31
c0: 16
skew: 0.88
type: snfs
lss: 1
rlim: 540000
alim: 540000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 540000/540000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [270000, 370001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 46726 x 46954
Total sieving time: 0.96 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,112.000,5,0,0,0,0,0,0,0,0,540000,540000,25,25,45,45,2.2,2.2,50000
total time: 1.02 hours.
 --------- CPU info (if available) ----------

(62·10¹¹²+1)/9 = 6(8)₁₁₁9_<113> = 3 · 886283 · C107

C107 = P45 · P62

P45 = 424474417621500274841350325647806085712007847_<45>

P62 = 61038518645710499741252246219722199134494898635738764960652863_<62>

Number: 68889_112
N=25909289654617050042664660117550447162997556043569562953326378778519911769675107119241780518144839699015961
  ( 107 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=424474417621500274841350325647806085712007847 (pp45)
 r2=61038518645710499741252246219722199134494898635738764960652863 (pp62)
Version: Msieve-1.40
Total time: 0.89 hours.
Scaled time: 0.92 units (timescale=1.037).
Factorization parameters were as follows:
n: 25909289654617050042664660117550447162997556043569562953326378778519911769675107119241780518144839699015961
m: 50000000000000000000000
deg: 5
c5: 248
c0: 125
skew: 0.87
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [300000, 450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 52135 x 52363
Total sieving time: 0.86 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,115.000,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000
total time: 0.89 hours.
 --------- CPU info (if available) ----------

(62·10¹¹⁸-17)/9 = 6(8)₁₁₇7_<119> = 7 · 13 · 797 · 1637 · 10495884173_<11> · C101

C101 = P46 · P56

P46 = 1107425712352658416164331896759556635993194543_<46>

P56 = 49919146890014271345218701495435856544040574826259751767_<56>

Number: 68887_118
N=55281746804711047413147085542352502587218872411016410646872878050579577112931965008102182600519007481
  ( 101 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=1107425712352658416164331896759556635993194543 (pp46)
 r2=49919146890014271345218701495435856544040574826259751767 (pp56)
Version: Msieve-1.40
Total time: 1.39 hours.
Scaled time: 1.31 units (timescale=0.944).
Factorization parameters were as follows:
n: 55281746804711047413147085542352502587218872411016410646872878050579577112931965008102182600519007481
m: 500000000000000000000000
deg: 5
c5: 496
c0: -425
skew: 0.97
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 615001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 76178 x 76404
Total sieving time: 1.35 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.39 hours.
 --------- CPU info (if available) ----------

(62·10¹²⁴-17)/9 = 6(8)₁₂₃7_<125> = 7 · 13 · 565929251 · 243301560941_<12> · C103

C103 = P44 · P59

P44 = 99814881408334166492104918462203337432729043_<44>

P59 = 55081461574459782075149704562271031348782495790432760592689_<59>

Number: 68887_124
N=5497949554852418488290940989144761344184679566894847209327534296291745092060974983110450650315423766627
  ( 103 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=99814881408334166492104918462203337432729043 (pp44)
 r2=55081461574459782075149704562271031348782495790432760592689 (pp59)
Version: Msieve-1.40
Total time: 1.66 hours.
Scaled time: 1.71 units (timescale=1.031).
Factorization parameters were as follows:
n: 5497949554852418488290940989144761344184679566894847209327534296291745092060974983110450650315423766627
m: 10000000000000000000000000
deg: 5
c5: 31
c0: -85
skew: 1.22
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 118843 x 119069
Total sieving time: 1.59 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 1.66 hours.
 --------- CPU info (if available) ----------

(62·10¹¹⁷+1)/9 = 6(8)₁₁₆9_<118> = 40464497 · C111

C111 = P41 · P70

P41 = 45130259711000452950944547303930885114601_<41>

P70 = 3772308490515012510449614847679149216069295945683508079802035124362337_<70>

Number: 68889_117
N=170245261886954603411699122044909859843034472636318422267522289697284236324224885061314091928262172365293182537
  ( 111 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=45130259711000452950944547303930885114601 (pp41)
 r2=3772308490515012510449614847679149216069295945683508079802035124362337 (pp70)
Version: Msieve v. 1.41
Total time: 1.96 hours.
Scaled time: 1.53 units (timescale=0.780).
Factorization parameters were as follows:
n: 170245261886954603411699122044909859843034472636318422267522289697284236324224885061314091928262172365293182537
m: 500000000000000000000000
deg: 5
c5: 248
c0: 125
skew: 0.87
type: snfs
lss: 1
rlim: 720000
alim: 720000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 720000/720000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [360000, 560001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 67528 x 67758
Total sieving time: 1.90 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120.000,5,0,0,0,0,0,0,0,0,720000,720000,25,25,46,46,2.2,2.2,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------

(61·10¹²⁸-43)/9 = 6(7)₁₂₇3_<129> = 23 · 67 · 9587 · C122

C122 = P58 · P64

P58 = 5536611687315353779610747923377308454801944617579961851913_<58>

P64 = 8286247372898555574310188241936816191159007996701514902479901563_<64>

Number: 67773_128
N=45877734048776289285977975243066063718922977624684531351012100041769044522408012755333751001215737389472547677739423240019
  ( 122 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=5536611687315353779610747923377308454801944617579961851913 (pp58)
 r2=8286247372898555574310188241936816191159007996701514902479901563 (pp64)
Version: Msieve-1.40
Total time: 3.17 hours.
Scaled time: 3.20 units (timescale=1.009).
Factorization parameters were as follows:
n: 45877734048776289285977975243066063718922977624684531351012100041769044522408012755333751001215737389472547677739423240019
m: 50000000000000000000000000
deg: 5
c5: 488
c0: -1075
skew: 1.17
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 1040001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 158781 x 159007
Total sieving time: 3.02 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 3.17 hours.
 --------- CPU info (if available) ----------

Oct 22, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Oct 22, 2009

(62·10¹¹¹+1)/9 = 6(8)₁₁₀9_<112> = 23 · 4639 · 315057233 · C99

C99 = P46 · P53

P46 = 3077974809623148102960387293801097224185933679_<46>

P53 = 66579795337873101825458429741248933989066545646212591_<53>

Number: n
N=204930932879838124217739423206018620661313423302611716631311830955133216392871644371769123460752289
  ( 99 digits)
SNFS difficulty: 113 digits.
Divisors found:

Fri Oct 23 00:59:50 2009  prp46 factor: 3077974809623148102960387293801097224185933679
Fri Oct 23 00:59:50 2009  prp53 factor: 66579795337873101825458429741248933989066545646212591
Fri Oct 23 00:59:50 2009  elapsed time 00:01:38 (Msieve 1.42 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.57 hours.
Scaled time: 1.04 units (timescale=1.834).
Factorization parameters were as follows:
name: KA_6_8_110_9
n: 204930932879838124217739423206018620661313423302611716631311830955133216392871644371769123460752289
m: 20000000000000000000000
deg: 5
c5: 155
c0: 8
skew: 0.55
type: snfs
lss: 1
rlim: 550000
alim: 550000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
qintsize: 2000
Factor base limits: 550000/550000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved  special-q in [275000, 399389)
Primes: RFBsize:45322, AFBsize:45075, largePrimes:1074629 encountered
Relations: rels:995016, finalFF:92748
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 53214 hash collisions in 1035831 relations
Msieve: matrix is 62559 x 62790 (16.9 MB)

Total sieving time: 0.55 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,550000,550000,25,25,45,45,2.2,2.2,50000
total time: 0.57 hours.
 --------- CPU info (if available) ----------

Oct 22, 2009 (4th)

By Sinkiti Sibata / Msieve / Oct 22, 2009

(62·10¹²³+1)/9 = 6(8)₁₂₂9_<124> = 17 · 797 · 9853043 · 138595979 · 158482889 · 76444739699_<11> · C86

C86 = P39 · P48

P39 = 140344436011805338070535887144534289733_<39>

P48 = 218975609300055754225391098819657487228955178651_<48>

Thu Oct 22 17:39:32 2009  Msieve v. 1.42
Thu Oct 22 17:39:32 2009  random seeds: b48856c4 3e37d87c
Thu Oct 22 17:39:32 2009  factoring 30732008387557760692305871105735131794858801889438045066750574222364303535014410090183 (86 digits)
Thu Oct 22 17:39:33 2009  searching for 15-digit factors
Thu Oct 22 17:39:33 2009  commencing quadratic sieve (86-digit input)
Thu Oct 22 17:39:34 2009  using multiplier of 31
Thu Oct 22 17:39:34 2009  using 32kb Intel Core sieve core
Thu Oct 22 17:39:34 2009  sieve interval: 14 blocks of size 32768
Thu Oct 22 17:39:34 2009  processing polynomials in batches of 15
Thu Oct 22 17:39:34 2009  using a sieve bound of 1451909 (55262 primes)
Thu Oct 22 17:39:34 2009  using large prime bound of 116152720 (26 bits)
Thu Oct 22 17:39:34 2009  using double large prime bound of 328891653552400 (41-49 bits)
Thu Oct 22 17:39:34 2009  using trial factoring cutoff of 49 bits
Thu Oct 22 17:39:34 2009  polynomial 'A' values have 11 factors
Thu Oct 22 18:17:35 2009  55502 relations (15906 full + 39596 combined from 580000 partial), need 55358
Thu Oct 22 18:17:36 2009  begin with 595906 relations
Thu Oct 22 18:17:36 2009  reduce to 131595 relations in 9 passes
Thu Oct 22 18:17:36 2009  attempting to read 131595 relations
Thu Oct 22 18:17:38 2009  recovered 131595 relations
Thu Oct 22 18:17:38 2009  recovered 113637 polynomials
Thu Oct 22 18:17:38 2009  attempting to build 55502 cycles
Thu Oct 22 18:17:38 2009  found 55502 cycles in 5 passes
Thu Oct 22 18:17:38 2009  distribution of cycle lengths:
Thu Oct 22 18:17:38 2009     length 1 : 15906
Thu Oct 22 18:17:38 2009     length 2 : 11109
Thu Oct 22 18:17:38 2009     length 3 : 9801
Thu Oct 22 18:17:38 2009     length 4 : 7092
Thu Oct 22 18:17:38 2009     length 5 : 4922
Thu Oct 22 18:17:38 2009     length 6 : 3058
Thu Oct 22 18:17:38 2009     length 7 : 1706
Thu Oct 22 18:17:38 2009     length 9+: 1908
Thu Oct 22 18:17:38 2009  largest cycle: 21 relations
Thu Oct 22 18:17:39 2009  matrix is 55262 x 55502 (12.7 MB) with weight 3100505 (55.86/col)
Thu Oct 22 18:17:39 2009  sparse part has weight 3100505 (55.86/col)
Thu Oct 22 18:17:39 2009  filtering completed in 3 passes
Thu Oct 22 18:17:39 2009  matrix is 50446 x 50510 (11.7 MB) with weight 2853284 (56.49/col)
Thu Oct 22 18:17:39 2009  sparse part has weight 2853284 (56.49/col)
Thu Oct 22 18:17:39 2009  saving the first 48 matrix rows for later
Thu Oct 22 18:17:40 2009  matrix is 50398 x 50510 (7.6 MB) with weight 2247840 (44.50/col)
Thu Oct 22 18:17:40 2009  sparse part has weight 1682043 (33.30/col)
Thu Oct 22 18:17:40 2009  matrix includes 64 packed rows
Thu Oct 22 18:17:40 2009  using block size 20204 for processor cache size 1024 kB
Thu Oct 22 18:17:40 2009  commencing Lanczos iteration
Thu Oct 22 18:17:40 2009  memory use: 7.8 MB
Thu Oct 22 18:17:55 2009  lanczos halted after 798 iterations (dim = 50396)
Thu Oct 22 18:17:55 2009  recovered 17 nontrivial dependencies
Thu Oct 22 18:17:56 2009  prp39 factor: 140344436011805338070535887144534289733
Thu Oct 22 18:17:56 2009  prp48 factor: 218975609300055754225391098819657487228955178651
Thu Oct 22 18:17:56 2009  elapsed time 00:38:24

(62·10¹⁰⁹-17)/9 = 6(8)₁₀₈7_<110> = 61 · 233 · 449 · 48978172804973327_<17> · C87

C87 = P33 · P54

P33 = 373226485798271546570745311604637_<33>

P54 = 590530112548685105063077860747536971066839589208013449_<54>

Thu Oct 22 18:51:43 2009  Msieve v. 1.42
Thu Oct 22 18:51:43 2009  random seeds: d2657204 ab8952dc
Thu Oct 22 18:51:43 2009  factoring 220401478664603519375383405432518926127525657644225991138432451226602722341653266763013 (87 digits)
Thu Oct 22 18:51:44 2009  searching for 15-digit factors
Thu Oct 22 18:51:44 2009  commencing quadratic sieve (87-digit input)
Thu Oct 22 18:51:44 2009  using multiplier of 5
Thu Oct 22 18:51:44 2009  using 32kb Intel Core sieve core
Thu Oct 22 18:51:44 2009  sieve interval: 19 blocks of size 32768
Thu Oct 22 18:51:44 2009  processing polynomials in batches of 11
Thu Oct 22 18:51:44 2009  using a sieve bound of 1480181 (56048 primes)
Thu Oct 22 18:51:44 2009  using large prime bound of 118414480 (26 bits)
Thu Oct 22 18:51:44 2009  using double large prime bound of 340509007839120 (41-49 bits)
Thu Oct 22 18:51:44 2009  using trial factoring cutoff of 49 bits
Thu Oct 22 18:51:44 2009  polynomial 'A' values have 11 factors
Thu Oct 22 19:34:44 2009  56304 relations (15498 full + 40806 combined from 596323 partial), need 56144
Thu Oct 22 19:34:44 2009  begin with 611821 relations
Thu Oct 22 19:34:45 2009  reduce to 135195 relations in 9 passes
Thu Oct 22 19:34:45 2009  attempting to read 135195 relations
Thu Oct 22 19:34:47 2009  recovered 135195 relations
Thu Oct 22 19:34:47 2009  recovered 115179 polynomials
Thu Oct 22 19:34:47 2009  attempting to build 56304 cycles
Thu Oct 22 19:34:47 2009  found 56304 cycles in 6 passes
Thu Oct 22 19:34:47 2009  distribution of cycle lengths:
Thu Oct 22 19:34:47 2009     length 1 : 15498
Thu Oct 22 19:34:47 2009     length 2 : 11196
Thu Oct 22 19:34:47 2009     length 3 : 9916
Thu Oct 22 19:34:47 2009     length 4 : 7345
Thu Oct 22 19:34:47 2009     length 5 : 5139
Thu Oct 22 19:34:47 2009     length 6 : 3312
Thu Oct 22 19:34:47 2009     length 7 : 1821
Thu Oct 22 19:34:47 2009     length 9+: 2077
Thu Oct 22 19:34:47 2009  largest cycle: 20 relations
Thu Oct 22 19:34:47 2009  matrix is 56048 x 56304 (13.0 MB) with weight 3169763 (56.30/col)
Thu Oct 22 19:34:47 2009  sparse part has weight 3169763 (56.30/col)
Thu Oct 22 19:34:48 2009  filtering completed in 3 passes
Thu Oct 22 19:34:48 2009  matrix is 51650 x 51714 (12.0 MB) with weight 2942276 (56.90/col)
Thu Oct 22 19:34:48 2009  sparse part has weight 2942276 (56.90/col)
Thu Oct 22 19:34:48 2009  saving the first 48 matrix rows for later
Thu Oct 22 19:34:48 2009  matrix is 51602 x 51714 (7.6 MB) with weight 2309506 (44.66/col)
Thu Oct 22 19:34:48 2009  sparse part has weight 1690525 (32.69/col)
Thu Oct 22 19:34:48 2009  matrix includes 64 packed rows
Thu Oct 22 19:34:48 2009  using block size 20685 for processor cache size 1024 kB
Thu Oct 22 19:34:49 2009  commencing Lanczos iteration
Thu Oct 22 19:34:49 2009  memory use: 7.9 MB
Thu Oct 22 19:35:05 2009  lanczos halted after 818 iterations (dim = 51597)
Thu Oct 22 19:35:05 2009  recovered 14 nontrivial dependencies
Thu Oct 22 19:35:07 2009  prp33 factor: 373226485798271546570745311604637
Thu Oct 22 19:35:07 2009  prp54 factor: 590530112548685105063077860747536971066839589208013449
Thu Oct 22 19:35:07 2009  elapsed time 00:43:24

(62·10¹¹⁰-17)/9 = 6(8)₁₀₉7_<111> = 3 · 53 · 2300021 · 517718138007541_<15> · C88

C88 = P35 · P54

P35 = 34175041639276303340196029466299407_<35>

P54 = 106467687573370376329491577608022327612581959057576959_<54>

Thu Oct 22 19:47:44 2009  Msieve v. 1.42
Thu Oct 22 19:47:44 2009  random seeds: f96bc3d0 b313e32a
Thu Oct 22 19:47:44 2009  factoring 3638537656057392856328944182463998331622023069282498652558204204437534061142225838563313 (88 digits)
Thu Oct 22 19:47:45 2009  searching for 15-digit factors
Thu Oct 22 19:47:46 2009  commencing quadratic sieve (88-digit input)
Thu Oct 22 19:47:46 2009  using multiplier of 1
Thu Oct 22 19:47:46 2009  using 32kb Intel Core sieve core
Thu Oct 22 19:47:46 2009  sieve interval: 25 blocks of size 32768
Thu Oct 22 19:47:46 2009  processing polynomials in batches of 9
Thu Oct 22 19:47:46 2009  using a sieve bound of 1517707 (57593 primes)
Thu Oct 22 19:47:46 2009  using large prime bound of 121416560 (26 bits)
Thu Oct 22 19:47:46 2009  using double large prime bound of 356205104400640 (42-49 bits)
Thu Oct 22 19:47:46 2009  using trial factoring cutoff of 49 bits
Thu Oct 22 19:47:46 2009  polynomial 'A' values have 11 factors
Thu Oct 22 20:28:46 2009  57741 relations (16316 full + 41425 combined from 604418 partial), need 57689
Thu Oct 22 20:28:47 2009  begin with 620734 relations
Thu Oct 22 20:28:47 2009  reduce to 137770 relations in 10 passes
Thu Oct 22 20:28:47 2009  attempting to read 137770 relations
Thu Oct 22 20:28:49 2009  recovered 137770 relations
Thu Oct 22 20:28:49 2009  recovered 111771 polynomials
Thu Oct 22 20:28:49 2009  attempting to build 57741 cycles
Thu Oct 22 20:28:49 2009  found 57741 cycles in 5 passes
Thu Oct 22 20:28:49 2009  distribution of cycle lengths:
Thu Oct 22 20:28:49 2009     length 1 : 16316
Thu Oct 22 20:28:49 2009     length 2 : 11459
Thu Oct 22 20:28:49 2009     length 3 : 10045
Thu Oct 22 20:28:49 2009     length 4 : 7511
Thu Oct 22 20:28:49 2009     length 5 : 5051
Thu Oct 22 20:28:49 2009     length 6 : 3272
Thu Oct 22 20:28:49 2009     length 7 : 1919
Thu Oct 22 20:28:49 2009     length 9+: 2168
Thu Oct 22 20:28:49 2009  largest cycle: 19 relations
Thu Oct 22 20:28:50 2009  matrix is 57593 x 57741 (13.4 MB) with weight 3285957 (56.91/col)
Thu Oct 22 20:28:50 2009  sparse part has weight 3285957 (56.91/col)
Thu Oct 22 20:28:50 2009  filtering completed in 3 passes
Thu Oct 22 20:28:50 2009  matrix is 52948 x 53010 (12.5 MB) with weight 3058098 (57.69/col)
Thu Oct 22 20:28:50 2009  sparse part has weight 3058098 (57.69/col)
Thu Oct 22 20:28:50 2009  saving the first 48 matrix rows for later
Thu Oct 22 20:28:50 2009  matrix is 52900 x 53010 (8.3 MB) with weight 2433607 (45.91/col)
Thu Oct 22 20:28:50 2009  sparse part has weight 1856684 (35.03/col)
Thu Oct 22 20:28:50 2009  matrix includes 64 packed rows
Thu Oct 22 20:28:50 2009  using block size 21204 for processor cache size 1024 kB
Thu Oct 22 20:28:51 2009  commencing Lanczos iteration
Thu Oct 22 20:28:51 2009  memory use: 8.4 MB
Thu Oct 22 20:29:08 2009  lanczos halted after 838 iterations (dim = 52899)
Thu Oct 22 20:29:08 2009  recovered 16 nontrivial dependencies
Thu Oct 22 20:29:08 2009  prp35 factor: 34175041639276303340196029466299407
Thu Oct 22 20:29:08 2009  prp54 factor: 106467687573370376329491577608022327612581959057576959
Thu Oct 22 20:29:08 2009  elapsed time 00:41:24

Oct 22, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.1 + yafu v1.12 / Oct 22, 2009

(61·10¹³⁴-43)/9 = 6(7)₁₃₃3_<135> = 41 · 4049 · 8804479 · 2278670221979_<13> · C111

C111 = P34 · P78

P34 = 1831503425435850397873609102464649_<34>

P78 = 111112474093513840929249072675763204026659155993419160560629525083563818952233_<78>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3439666732
Step 1 took 2376ms
Step 2 took 1740ms
********** Factor found in step 2: 1831503425435850397873609102464649
Found probable prime factor of 34 digits: 1831503425435850397873609102464649
Probable prime cofactor has 78 digits

(61·10¹³⁶-43)/9 = 6(7)₁₃₅3_<137> = 3² · 359 · 547 · 2246441856895399_<16> · C116

C116 = P29 · P41 · P48

P29 = 12762555760914007064522497751_<29>

P41 = 10349872985004151773018766049391856485769_<41>

P48 = 129239475256057751190438900176125167669174590569_<48>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3786057409
Step 1 took 2316ms
Step 2 took 1736ms
********** Factor found in step 2: 12762555760914007064522497751
Found probable prime factor of 29 digits: 12762555760914007064522497751
Composite cofactor has 88 digits
======= Welcome to YAFU (Yet Another Factoring Utility) =======
10/22/09 01:58:55 v1.12 
...
matrix is 52455 x 52519 (11.1 MB) with weight 2478722 (47.20/col)
sparse part has weight 2478722 (47.20/col)
saving the first 48 matrix rows for later
matrix is 52407 x 52519 (9.5 MB) with weight 2096421 (39.92/col)
sparse part has weight 1970874 (37.53/col)
matrix includes 64 packed rows
using block size 21007 for processor cache size 1024 kB
commencing Lanczos iteration
memory use: 7.9 MB
lanczos halted after 830 iterations (dim = 52400)
recovered 15 nontrivial dependencies
Lanczos elapsed time = 25.8200 seconds.
Sqrt elapsed time = 1.3100 seconds.
SIQS elapsed time = 396.6406 seconds.
***factors found***

PRP48 = 129239475256057751190438900176125167669174590569
PRP41 = 10349872985004151773018766049391856485769

Oct 22, 2009 (2nd)

By matsui / Msieve / Oct 22, 2009

3·10¹⁹⁸+7 = 3(0)₁₉₇7_<199> = 17 · 31 · 709 · C193

C193 = P63 · P131

P63 = 353042910133991541918917440370516843496015546212267909038130357_<63>

P131 = 22742432269025299197225941631406058277981194146870968014849567950717154661158756620175583489442241367223874181066482274509852878657_<131>

N=8029054471781888058922554416916682501746319347612560652815655585679378444129824458105731941987405089885264811598236819637996697382260607050045096522616508271264281680641682033384808493669090549
  ( 193 digits)
SNFS difficulty: 199 digits.
Divisors found:
 r1=353042910133991541918917440370516843496015546212267909038130357 (pp63)
 r2=22742432269025299197225941631406058277981194146870968014849567950717154661158756620175583489442241367223874181066482274509852878657 (pp131)
Version: Msieve v. 1.43
Total time: 1205.18 hours.
Scaled time: 2272.97 units (timescale=1.886).
Factorization parameters were as follows:
n: 8029054471781888058922554416916682501746319347612560652815655585679378444129824458105731941987405089885264811598236819637996697382260607050045096522616508271264281680641682033384808493669090549
m: 5000000000000000000000000000000000000000
deg: 5
c5: 24
c0: 175
skew: 1.49
type: snfs
lss: 1
rlim: 15000000
alim: 15000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 800000
Factor base limits: 15000000/15000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [7500000, 16300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2316723 x 2316948
Total sieving time: 1197.29 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 6.39 hours.
Time per square root: 1.33 hours.
Prototype def-par.txt line would be:
snfs,199.000,5,0,0,0,0,0,0,0,0,15000000,15000000,28,28,55,55,2.5,2.5,100000
total time: 1205.18 hours.

Oct 22, 2009

Factorizations of 677...773 have been extended up to n=150. Factorizations of 688...887 and Factorizations of 688...889 have been extended up to n=125. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 21, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve / Oct 21, 2009

(59·10¹⁴¹+31)/9 = 6(5)₁₄₀9_<142> = 7 · 17 · C140

C140 = P36 · P41 · P64

P36 = 202714043003433505522841193369798581_<36>

P41 = 86513847521584999083688598808746082189283_<41>

P64 = 3141181843994201078957348087713428893317675535697181603656810607_<64>

Number: snfs140
N=55088702147525676937441643323996265172735760971055088702147525676937441643323996265172735760971055088702147525676937441643323996265172735761
  ( 140 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=202714043003433505522841193369798581 (pp36)
 r2=86513847521584999083688598808746082189283 (pp41)
 r3=3141181843994201078957348087713428893317675535697181603656810607 (pp64)
Version: Msieve-1.40
Total time: 6.30 hours.
Scaled time: 12.41 units (timescale=1.969).
Factorization parameters were as follows:
n: 55088702147525676937441643323996265172735760971055088702147525676937441643323996265172735760971055088702147525676937441643323996265172735761
m: 20000000000000000000000000000
deg: 5
c5: 295
c0: 496
skew: 1.11
type: snfs
lss: 1
rlim: 1760000
alim: 1760000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1760000/1760000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [880000, 1980001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 247066 x 247294
Total sieving time: 6.03 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,143.000,5,0,0,0,0,0,0,0,0,1760000,1760000,26,26,48,48,2.3,2.3,100000
total time: 6.30 hours.
 --------- CPU info (if available) ----------

(59·10¹³¹+31)/9 = 6(5)₁₃₀9_<132> = C132

C132 = P60 · P72

P60 = 962401406006965270685850985472472580434859585288363395786281_<60>

P72 = 681166456598891384831603529297408001491769285992504947897110656742762639_<72>

Number: snfs132
N=655555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559
  ( 132 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=962401406006965270685850985472472580434859585288363395786281 (pp60)
 r2=681166456598891384831603529297408001491769285992504947897110656742762639 (pp72)
Version: Msieve-1.40
Total time: 2.82 hours.
Scaled time: 5.55 units (timescale=1.969).
Factorization parameters were as follows:
n: 655555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559
m: 200000000000000000000000000
deg: 5
c5: 295
c0: 496
skew: 1.11
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [600000, 1125001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 164603 x 164829
Total sieving time: 2.70 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,133.000,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000
total time: 2.82 hours.
 --------- CPU info (if available) ----------

(59·10¹⁴⁰+31)/9 = 6(5)₁₃₉9_<141> = 811 · 4052733593_<10> · C129

C129 = P47 · P82

P47 = 31794353533825285890787673170665277009742634727_<47>

P82 = 6273221073510123167356629219122283975484886020536105467461277146298668332360249979_<82>

Number: snfs129
N=199453008607023838079070199839409106867052042733553353774401098454087543645601510715530328724351254418399859063987332319806420733
  ( 129 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=31794353533825285890787673170665277009742634727 (pp47)
 r2=6273221073510123167356629219122283975484886020536105467461277146298668332360249979 (pp82)
Version: Msieve-1.40
Total time: 5.08 hours.
Scaled time: 9.97 units (timescale=1.963).
Factorization parameters were as follows:
n: 199453008607023838079070199839409106867052042733553353774401098454087543645601510715530328724351254418399859063987332319806420733
m: 10000000000000000000000000000
deg: 5
c5: 59
c0: 31
skew: 0.88
type: snfs
lss: 1
rlim: 1610000
alim: 1610000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1610000/1610000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [805000, 1705001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 234539 x 234767
Total sieving time: 4.87 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000
total time: 5.08 hours.
 --------- CPU info (if available) ----------

Oct 21, 2009 (2nd)

By Sinkiti Sibata / Msieve / Oct 21, 2009

(59·10¹⁴⁴+31)/9 = 6(5)₁₄₃9_<145> = 41 · 491 · 1759 · 1228273 · 2402256211_<10> · C122

C122 = P55 · P68

P55 = 1030195935055164467478862513328465269354231688740061333_<55>

P68 = 60903780534711599292134161407897559561055557454763874546243443709229_<68>

Number: 65559_144
N=62742827136351740608752368348775357908083902056152539473369030841599845559493036149816207568881950588591862942514478142257
  ( 122 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1030195935055164467478862513328465269354231688740061333 (pp55)
 r2=60903780534711599292134161407897559561055557454763874546243443709229 (pp68)
Version: Msieve-1.40
Total time: 8.09 hours.
Scaled time: 27.01 units (timescale=3.339).
Factorization parameters were as follows:
name: 65559_144
n: 62742827136351740608752368348775357908083902056152539473369030841599845559493036149816207568881950588591862942514478142257
m: 100000000000000000000000000000
deg: 5
c5: 59
c0: 310
skew: 1.39
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2280001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 324431 x 324679
Total sieving time: 7.84 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 8.09 hours.
 --------- CPU info (if available) ----------

(59·10¹⁴⁵+31)/9 = 6(5)₁₄₄9_<146> = 3 · 2143658599_<10> · C137

C137 = P54 · P83

P54 = 856760062815768361763837738866357554854223635115877933_<54>

P83 = 11897984890774166492465857218086872188431455311420879587059651870192417086397727159_<83>

Number: 65559_145
N=10193718282400737754721106059786272828909474988583222552525422846892352494349708645864393004425352458771748594026866239744854004082882347
  ( 137 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=856760062815768361763837738866357554854223635115877933 (pp54)
 r2=11897984890774166492465857218086872188431455311420879587059651870192417086397727159 (pp83)
Version: Msieve-1.40
Total time: 7.57 hours.
Scaled time: 25.27 units (timescale=3.339).
Factorization parameters were as follows:
name: 65559_145
n: 10193718282400737754721106059786272828909474988583222552525422846892352494349708645864393004425352458771748594026866239744854004082882347
m: 100000000000000000000000000000
deg: 5
c5: 59
c0: 31
skew: 0.88
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2180001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 335250 x 335498
Total sieving time: 7.31 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 7.57 hours.
 --------- CPU info (if available) ----------

Oct 21, 2009

By matsui / Msieve / Oct 21, 2009

8·10²³³-1 = 7(9)₂₃₃_<234> = 251 · 22619 · 1265981 · 4809859 · 14315261 · 40726433021_<11> · 2351450509731229_<16> · 7081017649253969149_<19> · 272948639013718877611_<21> · C142

C142 = P70 · P73

P70 = 1785804940045810268542281264886517345574261488360972972534774913824921_<70>

P73 = 4890589531830131453443601232937114394472385643177136672532799323334425579_<73>

N=8733638945678575210192171022888274858270746192656520260829050364149960473732896910446297879380855039388000593643582111989506447519057310054259
  ( 142 digits)
Divisors found:
 r1=1785804940045810268542281264886517345574261488360972972534774913824921 (pp70)
 r2=4890589531830131453443601232937114394472385643177136672532799323334425579 (pp73)
Version: Msieve v. 1.43
Total time: 1342.16 hours.
Scaled time: 2533.99 units (timescale=1.888).
Factorization parameters were as follows:
name: 7000
n: 8733638945678575210192171022888274858270746192656520260829050364149960473732896910446297879380855039388000593643582111989506447519057310054259
skew: 39478.21
# norm 4.84e+18
c5: 9922500
c4: -6744744256836
c3: -44821959062049922
c2: 10988881498159521937057
c1: 22740484884858987376479382
c0: -287570098211633116512417041221
# alpha -3.80
Y1: 6452082614797201
Y0: -974799316644565507313460462
# Murphy_E 1.22e-11
# M 3435918130069844254378482473890559378131699265221876409311131180564615316974237565411588830396621180889267775934771369077552493459036293694981
type: gnfs
qintsize: 800000
Factor base limits: 13600000/13600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [6800000, 21200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2568303 x 2568529
Total sieving time: 1332.71 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 8.09 hours.
Time per square root: 1.19 hours.
Prototype def-par.txt line would be:
gnfs,141,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,13600000,13600000,28,28,56,56,2.5,2.5,100000
total time: 1342.16 hours.

Oct 20, 2009 (7th)

By Ignacio Santos / GGNFS, Msieve / Oct 20, 2009

(14·10¹⁷³-11)/3 = 4(6)₁₇₂3_<174> = 1834597 · C168

C168 = P35 · P133

P35 = 55831386470652144487827908959483409_<35>

P133 = 4556041686157135365348400676745137231156165354308554677850364179698731841758069758997276163618396665365348456597581960663884011681131_<133>

Number: 46663_173
N=254370124156240671202812752155741378987683216895409000814166090245796034042717101721340799459863210648805523320198750279580020389582380580948658842605033512355392855579
  ( 168 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=55831386470652144487827908959483409 (pp35)
 r2=4556041686157135365348400676745137231156165354308554677850364179698731841758069758997276163618396665365348456597581960663884011681131 (pp133)
Version: Msieve-1.40
Total time: 82.26 hours.
Scaled time: 143.05 units (timescale=1.739).
Factorization parameters were as follows:
n: 254370124156240671202812752155741378987683216895409000814166090245796034042717101721340799459863210648805523320198750279580020389582380580948658842605033512355392855579
m: 50000000000000000000000000000000000
deg: 5
c5: 112
c0: -275
skew: 1.20
type: snfs
lss: 1
rlim: 5900000
alim: 5900000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2950000, 7050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1233796 x 1234022
Total sieving time: 79.56 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.05 hours.
Time per square root: 0.48 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5900000,5900000,28,28,52,52,2.5,2.5,100000
total time: 82.26 hours.

Oct 20, 2009 (6th)

By Sinkiti Sibata / Msieve / Oct 20, 2009

6·10¹⁸⁸-1 = 5(9)₁₈₈_<189> = 21778727 · 185311002839_<12> · C171

C171 = P68 · P103

P68 = 57117698157139964753400093009593909972789011805862001560536999047391_<68>

P103 = 2602836306674356872625815446311670047901248629915432935538570606381323277317170808071072441498712577313_<103>

Number: 59999_188
N=148668018517070905684544307890946774127347759757216531741882636657144128128110225281721236039764486753579971468028454082958518441954727658584230754908987838649991438440383
  ( 171 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=57117698157139964753400093009593909972789011805862001560536999047391 (pp68)
 r2=2602836306674356872625815446311670047901248629915432935538570606381323277317170808071072441498712577313 (pp103)
Version: Msieve-1.40
Total time: 243.25 hours.
Scaled time: 812.21 units (timescale=3.339).
Factorization parameters were as follows:
name: 59999_188
n: 148668018517070905684544307890946774127347759757216531741882636657144128128110225281721236039764486753579971468028454082958518441954727658584230754908987838649991438440383
m: 100000000000000000000000000000000000000
deg: 5
c5: 3
c0: -50
skew: 1.76
type: snfs
lss: 1
rlim: 10500000
alim: 10500000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10500000/10500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5250000, 9150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1934519 x 1934767
Total sieving time: 234.93 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 7.80 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,190.000,5,0,0,0,0,0,0,0,0,10500000,10500000,28,28,54,54,2.5,2.5,100000
total time: 243.25 hours.
 --------- CPU info (if available) ----------

(59·10¹⁵⁰+31)/9 = 6(5)₁₄₉9_<151> = 1672192031089117_<16> · 1989189259030257673_<19> · 103995178078529090828533_<24> · C95

C95 = P45 · P50

P45 = 444429722052295448763841071950487303554810699_<45>

P50 = 42641350302515484249310749133351387744656981445997_<50>

Mon Oct 19 22:33:28 2009  Msieve v. 1.42
Mon Oct 19 22:33:28 2009  random seeds: 12967db8 e38ac4e7
Mon Oct 19 22:33:28 2009  factoring 18951083462881521115582752429191411052867539550272427835447499040608071744746902067374626321903 (95 digits)
Mon Oct 19 22:33:29 2009  searching for 15-digit factors
Mon Oct 19 22:33:29 2009  commencing quadratic sieve (95-digit input)
Mon Oct 19 22:33:29 2009  using multiplier of 1
Mon Oct 19 22:33:29 2009  using 64kb Opteron sieve core
Mon Oct 19 22:33:29 2009  sieve interval: 18 blocks of size 65536
Mon Oct 19 22:33:29 2009  processing polynomials in batches of 6
Mon Oct 19 22:33:29 2009  using a sieve bound of 2124667 (78824 primes)
Mon Oct 19 22:33:29 2009  using large prime bound of 310201382 (28 bits)
Mon Oct 19 22:33:29 2009  using double large prime bound of 1927341365434108 (43-51 bits)
Mon Oct 19 22:33:29 2009  using trial factoring cutoff of 51 bits
Mon Oct 19 22:33:29 2009  polynomial 'A' values have 12 factors
Tue Oct 20 00:53:14 2009  79064 relations (19624 full + 59440 combined from 1168935 partial), need 78920
Tue Oct 20 00:53:14 2009  begin with 1188559 relations
Tue Oct 20 00:53:15 2009  reduce to 205061 relations in 12 passes
Tue Oct 20 00:53:15 2009  attempting to read 205061 relations
Tue Oct 20 00:53:16 2009  recovered 205061 relations
Tue Oct 20 00:53:16 2009  recovered 187902 polynomials
Tue Oct 20 00:53:16 2009  attempting to build 79064 cycles
Tue Oct 20 00:53:16 2009  found 79064 cycles in 6 passes
Tue Oct 20 00:53:16 2009  distribution of cycle lengths:
Tue Oct 20 00:53:16 2009     length 1 : 19624
Tue Oct 20 00:53:16 2009     length 2 : 13937
Tue Oct 20 00:53:16 2009     length 3 : 13165
Tue Oct 20 00:53:16 2009     length 4 : 10815
Tue Oct 20 00:53:16 2009     length 5 : 7949
Tue Oct 20 00:53:16 2009     length 6 : 5413
Tue Oct 20 00:53:16 2009     length 7 : 3545
Tue Oct 20 00:53:16 2009     length 9+: 4616
Tue Oct 20 00:53:16 2009  largest cycle: 21 relations
Tue Oct 20 00:53:17 2009  matrix is 78824 x 79064 (22.1 MB) with weight 5156821 (65.22/col)
Tue Oct 20 00:53:17 2009  sparse part has weight 5156821 (65.22/col)
Tue Oct 20 00:53:18 2009  filtering completed in 3 passes
Tue Oct 20 00:53:18 2009  matrix is 74759 x 74821 (21.0 MB) with weight 4910309 (65.63/col)
Tue Oct 20 00:53:18 2009  sparse part has weight 4910309 (65.63/col)
Tue Oct 20 00:53:18 2009  saving the first 48 matrix rows for later
Tue Oct 20 00:53:18 2009  matrix is 74711 x 74821 (13.8 MB) with weight 3918099 (52.37/col)
Tue Oct 20 00:53:18 2009  sparse part has weight 2879909 (38.49/col)
Tue Oct 20 00:53:18 2009  matrix includes 64 packed rows
Tue Oct 20 00:53:18 2009  using block size 21845 for processor cache size 512 kB
Tue Oct 20 00:53:18 2009  commencing Lanczos iteration
Tue Oct 20 00:53:18 2009  memory use: 12.7 MB
Tue Oct 20 00:53:52 2009  lanczos halted after 1184 iterations (dim = 74710)
Tue Oct 20 00:53:52 2009  recovered 17 nontrivial dependencies
Tue Oct 20 00:53:53 2009  prp45 factor: 444429722052295448763841071950487303554810699
Tue Oct 20 00:53:53 2009  prp50 factor: 42641350302515484249310749133351387744656981445997
Tue Oct 20 00:53:53 2009  elapsed time 02:20:25

(61·10¹¹²-43)/9 = 6(7)₁₁₁3_<113> = 3 · 19 · 277 · 433 · C106

C106 = P39 · P68

P39 = 169614191986582534837876557862778719969_<39>

P68 = 58449744446171562033124569550340500630093465656033560005869360417841_<68>

Number: 67773_112
N=9913906176059629577784776020399763476951866506555456692782983472396995449338289831356817361778572970566929
  ( 106 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=169614191986582534837876557862778719969 (pp39)
 r2=58449744446171562033124569550340500630093465656033560005869360417841 (pp68)
Version: Msieve-1.40
Total time: 0.85 hours.
Scaled time: 2.87 units (timescale=3.357).
Factorization parameters were as follows:
name: 67773_112
n: 9913906176059629577784776020399763476951866506555456692782983472396995449338289831356817361778572970566929
m: 20000000000000000000000
deg: 5
c5: 1525
c0: -344
skew: 0.74
type: snfs
lss: 1
rlim: 570000
alim: 570000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 570000/570000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [285000, 485001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 66720 x 66968
Total sieving time: 0.83 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,114.000,5,0,0,0,0,0,0,0,0,570000,570000,25,25,45,45,2.2,2.2,50000
total time: 0.85 hours.
 --------- CPU info (if available) ----------

(59·10¹²⁹+31)/9 = 6(5)₁₂₈9_<130> = 7 · 41 · 48871 · C123

C123 = P43 · P81

P43 = 1236242545703608932814642627753389991234997_<43>

P81 = 378070414900992267005464279661868960650787886552209763730065731639757888766166211_<81>

Number: 65559_129
N=467386732172422324345431020994512935216958901013138375712120129353951996039602485841489370441399950645545444396176862086367
  ( 123 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1236242545703608932814642627753389991234997 (pp43)
 r2=378070414900992267005464279661868960650787886552209763730065731639757888766166211 (pp81)
Version: Msieve-1.40
Total time: 2.45 hours.
Scaled time: 7.93 units (timescale=3.238).
Factorization parameters were as follows:
name: 65559_129
n: 467386732172422324345431020994512935216958901013138375712120129353951996039602485841489370441399950645545444396176862086367
m: 100000000000000000000000000
deg: 5
c5: 59
c0: 310
skew: 1.39
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 149376 x 149624
Total sieving time: 2.37 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.45 hours.
 --------- CPU info (if available) ----------

(59·10¹²⁶+31)/9 = 6(5)₁₂₅9_<127> = 211 · 1019 · 2347 · 2146589 · C112

C112 = P31 · P36 · P46

P31 = 1949088156959011078581266061017_<31>

P36 = 380263709629486527054620749765086821_<36>

P46 = 8165344461828363571084992097156251589533371821_<46>

Number: 65559_126
N=6051887883929230133923042308956916907181672199061927414123640902154029039892048029146863724006972034082017308697
  ( 112 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=1949088156959011078581266061017 (pp31)
 r2=380263709629486527054620749765086821 (pp36)
 r3=8165344461828363571084992097156251589533371821 (pp46)
Version: Msieve-1.40
Total time: 1.92 hours.
Scaled time: 6.38 units (timescale=3.322).
Factorization parameters were as follows:
name: 65559_126
n: 6051887883929230133923042308956916907181672199061927414123640902154029039892048029146863724006972034082017308697
m: 20000000000000000000000000
deg: 5
c5: 295
c0: 496
skew: 1.11
type: snfs
lss: 1
rlim: 990000
alim: 990000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 990000/990000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [495000, 845001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 132978 x 133225
Total sieving time: 1.82 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,128.000,5,0,0,0,0,0,0,0,0,990000,990000,26,26,47,47,2.3,2.3,50000
total time: 1.92 hours.
 --------- CPU info (if available) ----------

(59·10¹³⁹+31)/9 = 6(5)₁₃₈9_<140> = 3 · 19 · 41 · 2724256829731_<13> · 48611410979828843_<17> · C108

C108 = P37 · P72

P37 = 1466383660274322468742131090215645489_<37>

P72 = 144449785677974204985195425001317857003543007276143363103750607134733911_<72>

Number: 65559_139
N=211818805448309217908234727207176026830900904345340715812395900675577543737039589720487059640009573122477479
  ( 108 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=1466383660274322468742131090215645489 (pp37)
 r2=144449785677974204985195425001317857003543007276143363103750607134733911 (pp72)
Version: Msieve-1.40
Total time: 5.31 hours.
Scaled time: 17.72 units (timescale=3.339).
Factorization parameters were as follows:
name: 65559_139
n: 211818805448309217908234727207176026830900904345340715812395900675577543737039589720487059640009573122477479
m: 10000000000000000000000000000
deg: 5
c5: 59
c0: 310
skew: 1.39
type: snfs
lss: 1
rlim: 1610000
alim: 1610000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1610000/1610000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [805000, 1705001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 245774 x 246022
Total sieving time: 5.14 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000
total time: 5.31 hours.
 --------- CPU info (if available) ----------

Oct 20, 2009 (5th)

By Lionel Debroux / GGNFS + Msieve / Oct 20, 2009

(62·10¹¹²-71)/9 = 6(8)₁₁₁1_<113> = 43 · 283 · 1313462617_<10> · C100

C100 = P49 · P52

P49 = 3816895807268228595866518144384814798429514241609_<49>

P52 = 1129188034433739419733408412782832185204350656820233_<52>

Number: 68881_112
N=4309993074247592131456495093979585021239721431404665412061236285630073614776160187259377400441674897
  ( 100 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=3816895807268228595866518144384814798429514241609 (pp49)
 r2=1129188034433739419733408412782832185204350656820233 (pp52)
Version: Msieve v. 1.44
Total time: 4.65 hours.
Scaled time: 7.00 units (timescale=1.506).
Factorization parameters were as follows:
n: 4309993074247592131456495093979585021239721431404665412061236285630073614776160187259377400441674897
m: 20000000000000000000000
deg: 5
c5: 775
c0: -284
skew: 0.82
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [280000, 880001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 85536 x 85784
Total sieving time: 4.61 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,114.000,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000
total time: 4.65 hours.
 --------- CPU info (if available) ----------
[    0.029439] CPU0: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.101689] CPU1: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.000000] Memory: 2043420k/2096800k available (7091k kernel code, 452k absent, 52268k reserved, 3271k data, 540k init)
[    0.000999] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.57 BogoMIPS (lpj=1995288)
[    0.000999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913)
[    0.102027] Total of 2 processors activated (7980.40 BogoMIPS).

(61·10¹¹⁸+11)/9 = 6(7)₁₁₇9_<119> = 3 · 2309837 · 448500547927_<12> · C101

C101 = P47 · P55

P47 = 17632003377816731628383189280973540932700525483_<47>

P55 = 1236858729965652988254596588296867185555187756209443929_<55>

Number: 67779_118
N=21808297304636506227519999537204668039161178741858088267345270253166028218516910475914708785524142707
  ( 101 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=17632003377816731628383189280973540932700525483 (pp47)
 r2=1236858729965652988254596588296867185555187756209443929 (pp55)
Version: Msieve v. 1.44
Total time: 5.80 hours.
Scaled time: 8.46 units (timescale=1.459).
Factorization parameters were as follows:
n: 21808297304636506227519999537204668039161178741858088267345270253166028218516910475914708785524142707
m: 500000000000000000000000
deg: 5
c5: 488
c0: 275
skew: 0.89
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 1115001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 95495 x 95743
Total sieving time: 5.75 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 5.80 hours.
 --------- CPU info (if available) ----------
[    0.029439] CPU0: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.101689] CPU1: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.000000] Memory: 2043420k/2096800k available (7091k kernel code, 452k absent, 52268k reserved, 3271k data, 540k init)
[    0.000999] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.57 BogoMIPS (lpj=1995288)
[    0.000999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913)
[    0.102027] Total of 2 processors activated (7980.40 BogoMIPS).

(59·10¹³⁰+31)/9 = 6(5)₁₂₉9_<131> = 3 · 13 · 76355233 · 695075253179683703_<18> · C104

C104 = P39 · P65

P39 = 453918589660553342818948542406995277321_<39>

P65 = 69774429265765009327283464876302066657719254024336529627412341039_<65>

Number: 65559_130
N=31671910526686091534197699821958606232566539240654305812988468252560819489060433423435233682785634276519
  ( 104 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=453918589660553342818948542406995277321 (pp39)
 r2=69774429265765009327283464876302066657719254024336529627412341039 (pp65)
Version: Msieve v. 1.44
Total time: 8.26 hours.
Scaled time: 12.31 units (timescale=1.490).
Factorization parameters were as follows:
n: 31671910526686091534197699821958606232566539240654305812988468252560819489060433423435233682785634276519
m: 100000000000000000000000000
deg: 5
c5: 59
c0: 31
skew: 0.88
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 116487 x 116715
Total sieving time: 8.16 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 8.26 hours.
 --------- CPU info (if available) ----------
[    0.029439] CPU0: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.101689] CPU1: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.000000] Memory: 2043420k/2096800k available (7091k kernel code, 452k absent, 52268k reserved, 3271k data, 540k init)
[    0.000999] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.57 BogoMIPS (lpj=1995288)
[    0.000999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913)
[    0.102027] Total of 2 processors activated (7980.40 BogoMIPS).

(59·10¹⁴⁸+31)/9 = 6(5)₁₄₇9_<149> = 3 · 13 · 6151 · 33181 · 1231091243230620759491070891943314637_<37> · C103

C103 = P41 · P63

P41 = 60042495029962113831175878010034866884047_<41>

P63 = 111419376709386730266055919954390268992184409379699350676792609_<63>

Number: 65559_148
N=6689897372314829253031322880269310476024668892292054776187400625966564530383884672709397008871869608623
  ( 103 digits)
Divisors found:
 r1=60042495029962113831175878010034866884047 (pp41)
 r2=111419376709386730266055919954390268992184409379699350676792609 (pp63)
Version: Msieve v. 1.44
Total time: 13.01 hours.
Scaled time: 19.63 units (timescale=1.509).
Factorization parameters were as follows:
name: 65559_148
n: 6689897372314829253031322880269310476024668892292054776187400625966564530383884672709397008871869608623
skew: 5385.20
# norm 3.23e+14
c5: 519360
c4: -1126803032
c3: -37922374639378
c2: 42052036895894335
c1: 7654416014436206220
c0: -343397591649440870896800
# alpha -6.51
Y1: 2856422107
Y0: -26423492031371032309
# Murphy_E 2.36e-09
# M 4414740576895752756429830961025563153776401794061336229152725799050742962692043342322830049977452821193
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 2150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 201618 x 201844
Polynomial selection time: 0.56 hours.
Total sieving time: 12.20 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 13.01 hours.
 --------- CPU info (if available) ----------
[    0.029439] CPU0: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.101689] CPU1: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.000000] Memory: 2043420k/2096800k available (7091k kernel code, 452k absent, 52268k reserved, 3271k data, 540k init)
[    0.000999] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.57 BogoMIPS (lpj=1995288)
[    0.000999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913)
[    0.102027] Total of 2 processors activated (7980.40 BogoMIPS).

Oct 20, 2009 (4th)

By Serge Batalov / Msieve v. 1.44 SVN130 / Oct 20, 2009

(62·10¹¹⁶-53)/9 = 6(8)₁₁₅3_<117> = 163 · 2801 · C112

C112 = P34 · P78

P34 = 6679840150123809044106204970050911_<34>

P78 = 225882401828618911503033856318130927193899656636246403015114140502544786702431_<78>

SNFS difficulty: 118 digits.
Divisors found:
 r1=6679840150123809044106204970050911 (pp34)
 r2=225882401828618911503033856318130927193899656636246403015114140502544786702431 (pp78)
Version: Msieve v. 1.44 SVN130
Total time: 0.77 hours.
Scaled time: 1.85 units (timescale=2.400).
Factorization parameters were as follows:
n: 1508858336941208308358077393237929680874028094455505349511215076317811318238422493476012924588477140917877464641
m: 200000000000000000000000
deg: 5
c5: 155
c0: -424
skew: 1.22
type: snfs
lss: 1
rlim: 670000
alim: 670000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 670000/670000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [418750, 668751)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 68447 x 68674
Total sieving time: 0.70 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,118.000,5,0,0,0,0,0,0,0,0,670000,670000,25,25,45,45,2.2,2.2,50000
total time: 0.77 hours.

(61·10¹⁰³-43)/9 = 6(7)₁₀₂3_<104> = 3 · 7³ · 337 · C99

C99 = P38 · P61

P38 = 97989546065894474339264225075840493661_<38>

P61 = 1994629804412981161026332592472277161520353745624731661492941_<61>

SNFS difficulty: 105 digits.
Divisors found:
 r1=97989546065894474339264225075840493661 (pp38)
 r2=1994629804412981161026332592472277161520353745624731661492941 (pp61)
Version: Msieve v. 1.43 SVN74
Total time: 0.28 hours.
Scaled time: 0.67 units (timescale=2.400).
Factorization parameters were as follows:
n: 195452869103931902938746032066446285546388495580041634665264532641750591244929039394006389706747001
m: 100000000000000000000000000
deg: 4
c4: 61
c0: -430
skew: 1.63
type: snfs
lss: 1
rlim: 410000
alim: 410000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 410000/410000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [256250, 336251)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 32701 x 32929
Total sieving time: 0.25 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105.000,4,0,0,0,0,0,0,0,0,410000,410000,25,25,44,44,2.2,2.2,20000
total time: 0.28 hours.

(61·10¹⁰⁸+11)/9 = 6(7)₁₀₇9_<109> = 57855953 · 674919914887_<12> · C90

C90 = P32 · P58

P32 = 91108247087160828584254860711097_<32>

P58 = 1905150723036496927643831385952647134842981729524119029837_<58>

SNFS difficulty: 111 digits.
Divisors found:
 r1=91108247087160828584254860711097 (pp32)
 r2=1905150723036496927643831385952647134842981729524119029837 (pp58)
Version: Msieve v. 1.43 SVN74
Total time: 0.57 hours.
Scaled time: 1.37 units (timescale=2.400).
Factorization parameters were as follows:
n: 173574942812692267696268634691952789207197670714827952015840958361261434356164727580001189
m: 10000000000000000000000
deg: 5
c5: 61
c0: 1100
skew: 3
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [318750, 518751)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 53594 x 53821
Total sieving time: 0.54 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.57 hours.

(62·10¹⁰⁸-71)/9 = 6(8)₁₀₇1_<109> = 23 · 59 · 92179 · C101

C101 = P41 · P61

P41 = 50970031012402836704852021263665414998443_<41>

P61 = 1080494205493017112862343898915962169212827499405439214582789_<61>

SNFS difficulty: 111 digits.
Divisors found:
 r1=50970031012402836704852021263665414998443 (pp41)
 r2=1080494205493017112862343898915962169212827499405439214582789 (pp61)
Version: Msieve v. 1.43 SVN74
Total time: 0.68 hours.
Scaled time: 1.63 units (timescale=2.400).
Factorization parameters were as follows:
n: 55072823162700645717392882361863966596797818944233425372190155582386502037618509820239844685329597527
m: 5000000000000000000000
deg: 5
c5: 496
c0: -1775
skew: 1.29
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [312500, 562501)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 52609 x 52834
Total sieving time: 0.65 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 0.68 hours.

Oct 20, 2009 (3rd)

By Robert Backstrom / Msieve / Oct 20, 2009

(61·10¹¹⁰+11)/9 = 6(7)₁₀₉9_<111> = 7 · 1965797247224922563675203_<25> · C86

C86 = P36 · P51

P36 = 351440429148987573975248485100660149_<36>

P51 = 140151852450797442864198764926068611764798232457451_<51>

Tue Oct 20 01:11:15 2009  
Tue Oct 20 01:11:15 2009  
Tue Oct 20 01:11:15 2009  Msieve v. 1.42
Tue Oct 20 01:11:15 2009  random seeds: ddb16310 877aabd1
Tue Oct 20 01:11:15 2009  factoring 49255027171333839197078297400522298323494816812153624247751143235697657745838653820199 (86 digits)
Tue Oct 20 01:11:16 2009  searching for 15-digit factors
Tue Oct 20 01:11:17 2009  commencing quadratic sieve (86-digit input)
Tue Oct 20 01:11:17 2009  using multiplier of 55
Tue Oct 20 01:11:17 2009  using 64kb Opteron sieve core
Tue Oct 20 01:11:17 2009  sieve interval: 8 blocks of size 65536
Tue Oct 20 01:11:17 2009  processing polynomials in batches of 13
Tue Oct 20 01:11:17 2009  using a sieve bound of 1451959 (55667 primes)
Tue Oct 20 01:11:17 2009  using large prime bound of 116156720 (26 bits)
Tue Oct 20 01:11:17 2009  using double large prime bound of 328912039956560 (41-49 bits)
Tue Oct 20 01:11:17 2009  using trial factoring cutoff of 49 bits
Tue Oct 20 01:11:17 2009  polynomial 'A' values have 11 factors
Tue Oct 20 01:51:49 2009  55822 relations (16352 full + 39470 combined from 572353 partial), need 55763
Tue Oct 20 01:51:49 2009  begin with 588705 relations
Tue Oct 20 01:51:50 2009  reduce to 130643 relations in 10 passes
Tue Oct 20 01:51:50 2009  attempting to read 130643 relations
Tue Oct 20 01:51:51 2009  recovered 130643 relations
Tue Oct 20 01:51:51 2009  recovered 107436 polynomials
Tue Oct 20 01:51:52 2009  attempting to build 55822 cycles
Tue Oct 20 01:51:52 2009  found 55822 cycles in 5 passes
Tue Oct 20 01:51:52 2009  distribution of cycle lengths:
Tue Oct 20 01:51:52 2009     length 1 : 16352
Tue Oct 20 01:51:52 2009     length 2 : 11285
Tue Oct 20 01:51:52 2009     length 3 : 9947
Tue Oct 20 01:51:52 2009     length 4 : 7242
Tue Oct 20 01:51:52 2009     length 5 : 4665
Tue Oct 20 01:51:52 2009     length 6 : 2879
Tue Oct 20 01:51:52 2009     length 7 : 1643
Tue Oct 20 01:51:52 2009     length 9+: 1809
Tue Oct 20 01:51:52 2009  largest cycle: 17 relations
Tue Oct 20 01:51:52 2009  matrix is 55667 x 55822 (12.7 MB) with weight 3109913 (55.71/col)
Tue Oct 20 01:51:52 2009  sparse part has weight 3109913 (55.71/col)
Tue Oct 20 01:51:54 2009  filtering completed in 3 passes
Tue Oct 20 01:51:54 2009  matrix is 50493 x 50557 (11.7 MB) with weight 2853258 (56.44/col)
Tue Oct 20 01:51:54 2009  sparse part has weight 2853258 (56.44/col)
Tue Oct 20 01:51:54 2009  saving the first 48 matrix rows for later
Tue Oct 20 01:51:54 2009  matrix is 50445 x 50557 (7.5 MB) with weight 2226765 (44.04/col)
Tue Oct 20 01:51:54 2009  sparse part has weight 1663865 (32.91/col)
Tue Oct 20 01:51:54 2009  matrix includes 64 packed rows
Tue Oct 20 01:51:54 2009  using block size 20222 for processor cache size 1024 kB
Tue Oct 20 01:51:54 2009  commencing Lanczos iteration
Tue Oct 20 01:51:54 2009  memory use: 7.7 MB
Tue Oct 20 01:52:17 2009  lanczos halted after 799 iterations (dim = 50445)
Tue Oct 20 01:52:17 2009  recovered 19 nontrivial dependencies
Tue Oct 20 01:52:18 2009  prp36 factor: 351440429148987573975248485100660149
Tue Oct 20 01:52:18 2009  prp51 factor: 140151852450797442864198764926068611764798232457451
Tue Oct 20 01:52:18 2009  elapsed time 00:41:03

Oct 20, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM v6.2.3, YAFU v1.10 / Oct 20, 2009

(61·10¹²⁴+11)/9 = 6(7)₁₂₃9_<125> = 3 · 43 · 149791 · C118

C118 = P48 · P71

P48 = 135329388429488114701900710450078109693022954591_<48>

P71 = 25919091566712232464070995868800192058033785202911487150859363568422771_<71>

Number: 67779_124
N=3507614810371069363249630546094627132811654407869164771534010658353366557805828460925725905628911569126252748223391661
  ( 118 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=135329388429488114701900710450078109693022954591
 r2=25919091566712232464070995868800192058033785202911487150859363568422771
Version: 
Total time: 1.25 hours.
Scaled time: 2.97 units (timescale=2.380).
Factorization parameters were as follows:
n: 3507614810371069363249630546094627132811654407869164771534010658353366557805828460925725905628911569126252748223391661
m: 10000000000000000000000000
deg: 5
c5: 61
c0: 110
skew: 1.13
type: snfs
lss: 1
rlim: 800000
alim: 800000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [400000, 760001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2621857
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 117578 x 117822
Total sieving time: 1.09 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,800000,800000,26,26,46,46,2.3,2.3,40000
total time: 1.25 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(59·10¹³⁷+31)/9 = 6(5)₁₃₆9_<138> = 29 · 4643 · 15511 · C129

C129 = P36 · P39 · P54

P36 = 458432638558521664727323056207540619_<36>

P39 = 833711589045185494167470359553557417141_<39>

P54 = 821261859814952443151209166814163983713873321125972913_<54>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 313886778504384332722732947585730727116664052955402577662899770863518870526491597934334795814136562606767041549876452187557992727 (129 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=742684458
Step 1 took 4196ms
Step 2 took 5710ms
********** Factor found in step 2: 833711589045185494167470359553557417141
Found probable prime factor of 39 digits: 833711589045185494167470359553557417141
Composite cofactor 376493241342447381479258507689377998474130607563998113822613663653382400010452323341253147 has 90 digits

10/20/09 00:27:21 v1.10 @ 조영욱-PC, starting SIQS on c90: 376493241342447381479258507689377998474130607563998113822613663653382400010452323341253147
10/20/09 00:27:21 v1.10 @ 조영욱-PC, random seeds: 1541049209, 1117130648
10/20/09 00:27:22 v1.10 @ 조영욱-PC, ==== sieve params ====
10/20/09 00:27:22 v1.10 @ 조영욱-PC, n = 90 digits, 300 bits
10/20/09 00:27:22 v1.10 @ 조영욱-PC, factor base: 65244 primes (max prime = 1726447)
10/20/09 00:27:22 v1.10 @ 조영욱-PC, single large prime cutoff: 189909170 (110 * pmax)
10/20/09 00:27:22 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
10/20/09 00:27:22 v1.10 @ 조영욱-PC, double large prime cutoff: 796861205787554
10/20/09 00:27:22 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base
10/20/09 00:27:22 v1.10 @ 조영욱-PC, buckets hold 1024 elements
10/20/09 00:27:22 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536
10/20/09 00:27:22 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors
10/20/09 00:27:22 v1.10 @ 조영욱-PC, using multiplier of 3
10/20/09 00:27:22 v1.10 @ 조영욱-PC, using small prime variation correction of 19 bits
10/20/09 00:27:22 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
10/20/09 00:27:22 v1.10 @ 조영욱-PC, trial factoring cutoff at 98 bits
10/20/09 00:27:22 v1.10 @ 조영욱-PC, ==== sieving started ====
10/20/09 01:16:35 v1.10 @ 조영욱-PC, sieve time = 1379.3150, relation time = 528.0080, poly_time = 1045.8110
10/20/09 01:16:35 v1.10 @ 조영욱-PC, 65331 relations found: 19036 full + 46295 from 733853 partial, using 534260 polys (268 A polys)
10/20/09 01:16:35 v1.10 @ 조영욱-PC, on average, sieving found 1.41 rels/poly and 254.85 rels/sec
10/20/09 01:16:35 v1.10 @ 조영욱-PC, trial division touched 19389324 sieve locations out of 630238740480
10/20/09 01:16:35 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
10/20/09 01:16:36 v1.10 @ 조영욱-PC, begin with 752889 relations
10/20/09 01:16:36 v1.10 @ 조영욱-PC, reduce to 148640 relations in 9 passes
10/20/09 01:16:37 v1.10 @ 조영욱-PC, failed to read relation 75051
10/20/09 01:16:37 v1.10 @ 조영욱-PC, recovered 148639 relations
10/20/09 01:16:37 v1.10 @ 조영욱-PC, recovered 129737 polynomials
10/20/09 01:16:38 v1.10 @ 조영욱-PC, attempting to build 65330 cycles
10/20/09 01:16:38 v1.10 @ 조영욱-PC, found 65330 cycles in 5 passes
10/20/09 01:16:38 v1.10 @ 조영욱-PC, distribution of cycle lengths:
10/20/09 01:16:38 v1.10 @ 조영욱-PC,    length 1 : 19036
10/20/09 01:16:38 v1.10 @ 조영욱-PC,    length 2 : 15014
10/20/09 01:16:38 v1.10 @ 조영욱-PC,    length 3 : 12245
10/20/09 01:16:38 v1.10 @ 조영욱-PC,    length 4 : 8019
10/20/09 01:16:38 v1.10 @ 조영욱-PC,    length 5 : 5076
10/20/09 01:16:38 v1.10 @ 조영욱-PC,    length 6 : 2899
10/20/09 01:16:38 v1.10 @ 조영욱-PC,    length 7 : 1552
10/20/09 01:16:38 v1.10 @ 조영욱-PC,    length 9+: 1489
10/20/09 01:16:38 v1.10 @ 조영욱-PC, largest cycle: 16 relations
10/20/09 01:16:38 v1.10 @ 조영욱-PC, matrix is 65244 x 65330 (15.6 MB) with weight 3561192 (54.51/col)
10/20/09 01:16:38 v1.10 @ 조영욱-PC, sparse part has weight 3561192 (54.51/col)
10/20/09 01:16:38 v1.10 @ 조영욱-PC, filtering completed in 3 passes
10/20/09 01:16:38 v1.10 @ 조영욱-PC, matrix is 60204 x 60266 (14.5 MB) with weight 3330401 (55.26/col)
10/20/09 01:16:38 v1.10 @ 조영욱-PC, sparse part has weight 3330401 (55.26/col)
10/20/09 01:16:38 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
10/20/09 01:16:38 v1.10 @ 조영욱-PC, matrix is 60156 x 60266 (9.5 MB) with weight 2543062 (42.20/col)
10/20/09 01:16:38 v1.10 @ 조영욱-PC, sparse part has weight 1881855 (31.23/col)
10/20/09 01:16:38 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
10/20/09 01:16:38 v1.10 @ 조영욱-PC, using block size 24106 for processor cache size 4096 kB
10/20/09 01:16:39 v1.10 @ 조영욱-PC, commencing Lanczos iteration
10/20/09 01:16:39 v1.10 @ 조영욱-PC, memory use: 8.6 MB
10/20/09 01:16:53 v1.10 @ 조영욱-PC, lanczos halted after 953 iterations (dim = 60150)
10/20/09 01:16:53 v1.10 @ 조영욱-PC, recovered 14 nontrivial dependencies
10/20/09 01:16:54 v1.10 @ 조영욱-PC, prp36 = 458432638558521664727323056207540619
10/20/09 01:16:55 v1.10 @ 조영욱-PC, prp54 = 821261859814952443151209166814163983713873321125972913
10/20/09 01:16:55 v1.10 @ 조영욱-PC, Lanczos elapsed time = 17.7840 seconds.
10/20/09 01:16:55 v1.10 @ 조영욱-PC, Sqrt elapsed time = 1.6230 seconds.
10/20/09 01:16:55 v1.10 @ 조영욱-PC, SIQS elapsed time = 2973.6220 seconds.
10/20/09 01:16:55 v1.10 @ 조영욱-PC, 
10/20/09 01:16:55 v1.10 @ 조영욱-PC,

(59·10¹³⁸+31)/9 = 6(5)₁₃₇9_<139> = 193 · 203928801453501282368735246883167_<33> · C105

C105 = P51 · P54

P51 = 214816488267831012951485925904547340708767077033201_<51>

P54 = 775364679954002204097646833219325678871472956062921289_<54>

Number: 67779_138
N=166561117674629462667400805969917378172898099683604562150617253375526486989499027211799183699847302716089
  ( 105 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=214816488267831012951485925904547340708767077033201
 r2=775364679954002204097646833219325678871472956062921289
Version: 
Total time: 5.03 hours.
Scaled time: 12.01 units (timescale=2.388).
Factorization parameters were as follows:
n: 166561117674629462667400805969917378172898099683604562150617253375526486989499027211799183699847302716089
m: 10000000000000000000000000000
deg: 5
c5: 59
c0: 3100
skew: 2.21
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [950000, 1450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4048289
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 270753 x 271001
Total sieving time: 4.63 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,48,48,2.3,2.3,50000
total time: 5.03 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Oct 20, 2009

By Dmitry Domanov / GGNFS/msieve / Oct 20, 2009

(62·10¹¹⁸-71)/9 = 6(8)₁₁₇1_<119> = C119

C119 = P37 · P83

P37 = 3038209372850070299895662480934267163_<37>

P83 = 22674174302959870778545300248598034085760547885859190102759989856304629514396173987_<83>

Number: snfs119
N=68888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881
  ( 119 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=3038209372850070299895662480934267163 (pp37)
 r2=22674174302959870778545300248598034085760547885859190102759989856304629514396173987 (pp83)
Version: Msieve-1.40
Total time: 1.91 hours.
Scaled time: 3.75 units (timescale=1.963).
Factorization parameters were as follows:
n: 68888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881
m: 500000000000000000000000
deg: 5
c5: 496
c0: -1775
skew: 1.29
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 815001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 82546 x 82776
Total sieving time: 1.87 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.91 hours.
 --------- CPU info (if available) ----------

(61·10¹²²+11)/9 = 6(7)₁₂₁9_<123> = 7 · 29 · C121

C121 = P48 · P73

P48 = 361533924210305081649450654391335109543178661701_<48>

P73 = 9235113397381922794432779026073798516430287706951852241880434020450688293_<73>

Number: snfs121
N=3338806787082649151614668856048166392993979200875752599890530925013683634373289545703338806787082649151614668856048166393
  ( 121 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=361533924210305081649450654391335109543178661701 (pp48)
 r2=9235113397381922794432779026073798516430287706951852241880434020450688293 (pp73)
Version: Msieve-1.40
Total time: 1.57 hours.
Scaled time: 3.08 units (timescale=1.969).
Factorization parameters were as follows:
n: 3338806787082649151614668856048166392993979200875752599890530925013683634373289545703338806787082649151614668856048166393
m: 5000000000000000000000000
deg: 5
c5: 244
c0: 1375
skew: 1.41
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 740001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 125315 x 125540
Total sieving time: 1.44 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,125.000,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 1.57 hours.
 --------- CPU info (if available) ----------

(61·10¹²²-43)/9 = 6(7)₁₂₁3_<123> = C123

C123 = P47 · P77

P47 = 59544934507775516158943494685175067246137026467_<47>

P77 = 11382626975419243727594986795981518800792864977351934231028615329300433644719_<77>

Number: snfs123
N=677777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
  ( 123 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=59544934507775516158943494685175067246137026467 (pp47)
 r2=11382626975419243727594986795981518800792864977351934231028615329300433644719 (pp77)
Version: Msieve-1.40
Total time: 2.44 hours.
Scaled time: 4.78 units (timescale=1.957).
Factorization parameters were as follows:
n: 677777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773
m: 2000000000000000000000000
deg: 5
c5: 1525
c0: -344
skew: 0.74
type: snfs
lss: 1
rlim: 840000
alim: 840000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 840000/840000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [420000, 970001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 96128 x 96356
Total sieving time: 2.38 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,124.000,5,0,0,0,0,0,0,0,0,840000,840000,25,25,46,46,2.2,2.2,50000
total time: 2.44 hours.
 --------- CPU info (if available) ----------

(61·10¹⁰⁹+11)/9 = 6(7)₁₀₈9_<110> = 3 · C110

C110 = P40 · P70

P40 = 4047537538542415495109532620351832243679_<40>

P70 = 5581811750343532307079939582977515751345075804424834298521615160645967_<70>

Number: s110-1
N=22592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593
  ( 110 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=4047537538542415495109532620351832243679 (pp40)
 r2=5581811750343532307079939582977515751345075804424834298521615160645967 (pp70)
Version: Msieve-1.40
Total time: 0.84 hours.
Scaled time: 1.66 units (timescale=1.963).
Factorization parameters were as follows:
n: 22592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593
m: 10000000000000000000000
deg: 5
c5: 61
c0: 110
skew: 1.13
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [255000, 455001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 51096 x 51323
Total sieving time: 0.82 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.84 hours.
 --------- CPU info (if available) ----------

(62·10¹⁰⁹-71)/9 = 6(8)₁₀₈1_<110> = C110

C110 = P45 · P66

P45 = 449061934552096085392042792527494669801996839_<45>

P66 = 153406208784095962906433077939688161815955308844860423263872277479_<66>

Number: s110-2
N=68888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881
  ( 110 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=449061934552096085392042792527494669801996839 (pp45)
 r2=153406208784095962906433077939688161815955308844860423263872277479 (pp66)
Version: Msieve-1.40
Total time: 0.65 hours.
Scaled time: 1.27 units (timescale=1.963).
Factorization parameters were as follows:
n: 68888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881
m: 10000000000000000000000
deg: 5
c5: 31
c0: -355
skew: 1.63
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [250000, 400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 52311 x 52536
Total sieving time: 0.63 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 0.65 hours.
 --------- CPU info (if available) ----------

Oct 19, 2009 (7th)

By Markus Tervooren / Msieve / Oct 19, 2009

(4·10¹⁷¹+17)/3 = 1(3)₁₇₀9_<172> = 13 · 58573 · 31758781 · 4329375293_<10> · 3037485901254559_<16> · C133

C133 = P58 · P76

P58 = 1811998610010835822993607900189787073446791070400527729757_<58>

P76 = 2313858122637101115780520754396976599766152089544026425029700261948700504409_<76>

lpbr: 32 
lpba: 32
mfbr: 65
mfba: 65
rlambda: 2.4
alambda: 2.4

Sieve time: ~21 hours @ 0.0018secs/rel, 41718887 total relations

commencing linear algebra
read 913581 cycles
cycles contain 3080119 unique relations

read 3080119 relations
using 20 quadratic characters above 4291404732
building initial matrix
memory use: 372.8 MB
read 913581 cycles
matrix is 913322 x 913581 (273.3 MB) with weight 81825084 (89.57/col)
sparse part has weight 61599757 (67.43/col)
filtering completed in 3 passes
matrix is 908377 x 908577 (272.6 MB) with weight 81576027 (89.78/col)
sparse part has weight 61464641 (67.65/col)
read 908577 cycles
matrix is 908377 x 908577 (272.6 MB) with weight 81576027 (89.78/col)
sparse part has weight 61464641 (67.65/col)
saving the first 48 matrix rows for later
matrix is 908329 x 908577 (258.5 MB) with weight 64431455 (70.91/col)
sparse part has weight 58682398 (64.59/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (4 threads)
memory use: 274.1 MB
linear algebra completed 908252 of 908577 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 14367 iterations (dim = 908323)
recovered 35 nontrivial dependencies
BLanczosTime: 4268
elapsed time 01:11:09

commencing square root phase
reading relations for dependency 1
read 454350 cycles
cycles contain 1875691 unique relations
read 1875691 relations
multiplying 1537770 relations
multiply complete, coefficients have about 41.57 million bits
initial square root is modulo 929311
sqrtTime: 293
prp58 factor: 1811998610010835822993607900189787073446791070400527729757
prp76 factor: 2313858122637101115780520754396976599766152089544026425029700261948700504409
elapsed time 00:04:55

(61·10¹¹⁹-43)/9 = 6(7)₁₁₈3_<120> = 41 · 163 · C117

C117 = P41 · P76

P41 = 18859024783656836768732557272811082267693_<41>

P76 = 5377700769761967291695951620134659861264810742042450512996183272621691379667_<76>

N=101418192096031389761750378239978718805592963905099173691123414301627678853475651320930387217982609273945500191198231
  ( 117 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=18859024783656836768732557272811082267693 (pp41)
 r2=5377700769761967291695951620134659861264810742042450512996183272621691379667 (pp76)
Version: Msieve-1.39
Total time: 1.38 hours.
Scaled time: 2.83 units (timescale=2.056).
Factorization parameters were as follows:
n: 101418192096031389761750378239978718805592963905099173691123414301627678853475651320930387217982609273945500191198231
m: 1000000000000000000000000
deg: 5
c5: 61
c0: -430
skew: 1.48
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 28
lpba: 28
mfbr: 51
mfba: 51
rlambda: 2.3
alambda: 2.3

Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved rational special-q in [375000, 775001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 77736 x 77972
Total sieving time: 1.31 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,28,28,51,51,2.3,2.3,100000
total time: 1.38 hours.
 --------- CPU info (if available) ----------
[    0.144009] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.236014] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.330177] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.428493] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197992k/10485760k available (2226k kernel code, 189844k reserved, 1082k data, 392k init)
[    0.083761] Calibrating delay using timer specific routine.. 5402.28 BogoMIPS (lpj=10804578)
[    0.156009] Calibrating delay using timer specific routine.. 10281.27 BogoMIPS (lpj=20562558)
[    0.252015] Calibrating delay using timer specific routine.. 5333.36 BogoMIPS (lpj=10666723)
[    0.348020] Calibrating delay using timer specific routine.. 5333.36 BogoMIPS (lpj=10666724)
[    0.433291] Total of 4 processors activated (26350.29 BogoMIPS).

(62·10¹²³-53)/9 = 6(8)₁₂₂3_<124> = 942637 · 1099236740404454597537_<22> · C97

C97 = P43 · P54

P43 = 8226127289692476371319524848640942547201787_<43>

P54 = 808198493369811057446035929143293359486982523771510861_<54>

commencing square root phase
reading relations for dependency 1
read 65712 cycles
cycles contain 211206 unique relations
read 211206 relations
multiplying 171662 relations
multiply complete, coefficients have about 4.87 million bits
initial square root is modulo 405071
reading relations for dependency 2
read 65445 cycles
cycles contain 210916 unique relations
read 210916 relations
multiplying 171198 relations
multiply complete, coefficients have about 4.86 million bits
initial square root is modulo 391961
reading relations for dependency 3
read 65872 cycles
cycles contain 211966 unique relations
read 211966 relations
multiplying 172616 relations
multiply complete, coefficients have about 4.90 million bits
initial square root is modulo 435131
reading relations for dependency 4
read 65643 cycles
cycles contain 211460 unique relations
read 211460 relations
multiplying 171780 relations
multiply complete, coefficients have about 4.88 million bits
initial square root is modulo 409291
sqrtTime: 86
prp43 factor: 8226127289692476371319524848640942547201787
prp54 factor: 808198493369811057446035929143293359486982523771510861
elapsed time 00:01:27

Oct 19, 2009 (6th)

By Sinkiti Sibata / Msieve / Oct 19, 2009

(61·10¹¹¹-43)/9 = 6(7)₁₁₀3_<112> = 13 · 2909 · 8623 · 6623483621084453_<16> · C88

C88 = P36 · P53

P36 = 164701123892984704612134915020665091_<36>

P53 = 19052801221803116360701047315305558212064213085545461_<53>

Mon Oct 19 16:15:52 2009  Msieve v. 1.42
Mon Oct 19 16:15:52 2009  random seeds: 3e9a9666 ea53b05f
Mon Oct 19 16:15:52 2009  factoring 3138017774540605420592714626559217146263294135298585087177017274548906759127002736201951 (88 digits)
Mon Oct 19 16:15:53 2009  searching for 15-digit factors
Mon Oct 19 16:15:53 2009  commencing quadratic sieve (88-digit input)
Mon Oct 19 16:15:53 2009  using multiplier of 71
Mon Oct 19 16:15:53 2009  using 64kb Opteron sieve core
Mon Oct 19 16:15:53 2009  sieve interval: 13 blocks of size 65536
Mon Oct 19 16:15:53 2009  processing polynomials in batches of 8
Mon Oct 19 16:15:53 2009  using a sieve bound of 1515149 (57667 primes)
Mon Oct 19 16:15:53 2009  using large prime bound of 121211920 (26 bits)
Mon Oct 19 16:15:53 2009  using double large prime bound of 355125228672960 (42-49 bits)
Mon Oct 19 16:15:53 2009  using trial factoring cutoff of 49 bits
Mon Oct 19 16:15:53 2009  polynomial 'A' values have 11 factors
Mon Oct 19 16:53:23 2009  57972 relations (16496 full + 41476 combined from 604157 partial), need 57763
Mon Oct 19 16:53:23 2009  begin with 620653 relations
Mon Oct 19 16:53:24 2009  reduce to 137721 relations in 11 passes
Mon Oct 19 16:53:24 2009  attempting to read 137721 relations
Mon Oct 19 16:53:25 2009  recovered 137721 relations
Mon Oct 19 16:53:25 2009  recovered 114692 polynomials
Mon Oct 19 16:53:25 2009  attempting to build 57972 cycles
Mon Oct 19 16:53:25 2009  found 57972 cycles in 5 passes
Mon Oct 19 16:53:25 2009  distribution of cycle lengths:
Mon Oct 19 16:53:25 2009     length 1 : 16496
Mon Oct 19 16:53:25 2009     length 2 : 11362
Mon Oct 19 16:53:25 2009     length 3 : 10368
Mon Oct 19 16:53:25 2009     length 4 : 7452
Mon Oct 19 16:53:25 2009     length 5 : 5185
Mon Oct 19 16:53:25 2009     length 6 : 3124
Mon Oct 19 16:53:25 2009     length 7 : 1900
Mon Oct 19 16:53:25 2009     length 9+: 2085
Mon Oct 19 16:53:25 2009  largest cycle: 22 relations
Mon Oct 19 16:53:25 2009  matrix is 57667 x 57972 (14.8 MB) with weight 3412338 (58.86/col)
Mon Oct 19 16:53:25 2009  sparse part has weight 3412338 (58.86/col)
Mon Oct 19 16:53:26 2009  filtering completed in 3 passes
Mon Oct 19 16:53:26 2009  matrix is 52967 x 53031 (13.6 MB) with weight 3152165 (59.44/col)
Mon Oct 19 16:53:26 2009  sparse part has weight 3152165 (59.44/col)
Mon Oct 19 16:53:26 2009  saving the first 48 matrix rows for later
Mon Oct 19 16:53:26 2009  matrix is 52919 x 53031 (10.4 MB) with weight 2627265 (49.54/col)
Mon Oct 19 16:53:26 2009  sparse part has weight 2196751 (41.42/col)
Mon Oct 19 16:53:26 2009  matrix includes 64 packed rows
Mon Oct 19 16:53:26 2009  using block size 21212 for processor cache size 512 kB
Mon Oct 19 16:53:26 2009  commencing Lanczos iteration
Mon Oct 19 16:53:26 2009  memory use: 9.0 MB
Mon Oct 19 16:53:44 2009  lanczos halted after 839 iterations (dim = 52917)
Mon Oct 19 16:53:44 2009  recovered 16 nontrivial dependencies
Mon Oct 19 16:53:44 2009  prp36 factor: 164701123892984704612134915020665091
Mon Oct 19 16:53:44 2009  prp53 factor: 19052801221803116360701047315305558212064213085545461
Mon Oct 19 16:53:44 2009  elapsed time 00:37:52

(62·10¹⁰²-53)/9 = 6(8)₁₀₁3_<103> = 461 · 971 · 5234821 · C91

C91 = P30 · P61

P30 = 608238767329856403231492542029_<30>

P61 = 4833403936780460989909255914993332444536391473076934345986077_<61>

Mon oct 19 17:10:42 2009 Msieve v. 1.42
Mon Oct 19 17:10:42 2009  random seeds: de1ed4c7 1764d00d
Mon Oct 19 17:10:42 2009  factoring 2939863652514622780145344486414572716464648415149310198823161693782443293339686557371330233 (91 digits)
Mon Oct 19 17:10:43 2009  searching for 15-digit factors
Mon Oct 19 17:10:43 2009  commencing quadratic sieve (91-digit input)
Mon Oct 19 17:10:43 2009  using multiplier of 1
Mon Oct 19 17:10:43 2009  using 64kb Opteron sieve core
Mon Oct 19 17:10:43 2009  sieve interval: 18 blocks of size 65536
Mon Oct 19 17:10:43 2009  processing polynomials in batches of 6
Mon Oct 19 17:10:43 2009  using a sieve bound of 1685951 (63338 primes)
Mon Oct 19 17:10:43 2009  using large prime bound of 155107492 (27 bits)
Mon Oct 19 17:10:43 2009  using double large prime bound of 553527143260656 (42-49 bits)
Mon Oct 19 17:10:43 2009  using trial factoring cutoff of 49 bits
Mon Oct 19 17:10:43 2009  polynomial 'A' values have 12 factors
Mon Oct 19 18:15:38 2009  63759 relations (16500 full + 47259 combined from 732755 partial), need 63434
Mon Oct 19 18:15:38 2009  begin with 749255 relations
Mon Oct 19 18:15:38 2009  reduce to 158191 relations in 9 passes
Mon Oct 19 18:15:38 2009  attempting to read 158191 relations
Mon Oct 19 18:15:39 2009  recovered 158191 relations
Mon Oct 19 18:15:39 2009  recovered 137477 polynomials
Mon Oct 19 18:15:39 2009  attempting to build 63759 cycles
Mon Oct 19 18:15:40 2009  found 63759 cycles in 5 passes
Mon Oct 19 18:15:40 2009  distribution of cycle lengths:
Mon Oct 19 18:15:40 2009     length 1 : 16500
Mon Oct 19 18:15:40 2009     length 2 : 12001
Mon Oct 19 18:15:40 2009     length 3 : 11058
Mon Oct 19 18:15:40 2009     length 4 : 8700
Mon Oct 19 18:15:40 2009     length 5 : 6250
Mon Oct 19 18:15:40 2009     length 6 : 3970
Mon Oct 19 18:15:40 2009     length 7 : 2363
Mon Oct 19 18:15:40 2009     length 9+: 2917
Mon Oct 19 18:15:40 2009  largest cycle: 20 relations
Mon Oct 19 18:15:40 2009  matrix is 63338 x 63759 (16.4 MB) with weight 3779864 (59.28/col)
Mon Oct 19 18:15:40 2009  sparse part has weight 3779864 (59.28/col)
Mon Oct 19 18:15:41 2009  filtering completed in 4 passes
Mon Oct 19 18:15:41 2009  matrix is 59565 x 59629 (15.3 MB) with weight 3541921 (59.40/col)
Mon Oct 19 18:15:41 2009  sparse part has weight 3541921 (59.40/col)
Mon Oct 19 18:15:41 2009  saving the first 48 matrix rows for later
Mon Oct 19 18:15:41 2009  matrix is 59517 x 59629 (9.6 MB) with weight 2743720 (46.01/col)
Mon Oct 19 18:15:41 2009  sparse part has weight 1918101 (32.17/col)
Mon Oct 19 18:15:41 2009  matrix includes 64 packed rows
Mon Oct 19 18:15:41 2009  using block size 21845 for processor cache size 512 kB
Mon Oct 19 18:15:41 2009  commencing Lanczos iteration
Mon Oct 19 18:15:41 2009  memory use: 9.2 MB
Mon Oct 19 18:16:00 2009  lanczos halted after 943 iterations (dim = 59511)
Mon Oct 19 18:16:00 2009  recovered 13 nontrivial dependencies
Mon Oct 19 18:16:01 2009  prp30 factor: 608238767329856403231492542029
Mon Oct 19 18:16:01 2009  prp61 factor: 4833403936780460989909255914993332444536391473076934345986077
Mon Oct 19 18:16:01 2009  elapsed time 01:05:19

(61·10¹¹⁴+11)/9 = 6(7)₁₁₃9_<115> = 222679 · 11178637 · 18903334723259647_<17> · C87

C87 = P41 · P46

P41 = 41036055173181597710179425086539396815889_<41>

P46 = 3510065170731752561733587750619799871556698231_<46>

Mon Oct 19 18:17:44 2009  Msieve v. 1.42
Mon Oct 19 18:17:44 2009  random seeds: d73481a6 1eb8ed9a
Mon Oct 19 18:17:44 2009  factoring 144039228007611282703869034498185993003990944521551709780755994380929317069531438992359 (87 digits)
Mon Oct 19 18:17:44 2009  searching for 15-digit factors
Mon Oct 19 18:17:45 2009  commencing quadratic sieve (87-digit input)
Mon Oct 19 18:17:45 2009  using multiplier of 35
Mon Oct 19 18:17:45 2009  using 64kb Opteron sieve core
Mon Oct 19 18:17:45 2009  sieve interval: 10 blocks of size 65536
Mon Oct 19 18:17:45 2009  processing polynomials in batches of 11
Mon Oct 19 18:17:45 2009  using a sieve bound of 1471661 (56333 primes)
Mon Oct 19 18:17:45 2009  using large prime bound of 117732880 (26 bits)
Mon Oct 19 18:17:45 2009  using double large prime bound of 336989177081600 (41-49 bits)
Mon Oct 19 18:17:45 2009  using trial factoring cutoff of 49 bits
Mon Oct 19 18:17:45 2009  polynomial 'A' values have 11 factors
Mon Oct 19 18:52:29 2009  56701 relations (15919 full + 40782 combined from 592248 partial), need 56429
Mon Oct 19 18:52:29 2009  begin with 608167 relations
Mon Oct 19 18:52:29 2009  reduce to 135179 relations in 9 passes
Mon Oct 19 18:52:29 2009  attempting to read 135179 relations
Mon Oct 19 18:52:30 2009  recovered 135179 relations
Mon Oct 19 18:52:30 2009  recovered 114408 polynomials
Mon Oct 19 18:52:30 2009  attempting to build 56701 cycles
Mon Oct 19 18:52:30 2009  found 56701 cycles in 6 passes
Mon Oct 19 18:52:30 2009  distribution of cycle lengths:
Mon Oct 19 18:52:30 2009     length 1 : 15919
Mon Oct 19 18:52:30 2009     length 2 : 11227
Mon Oct 19 18:52:30 2009     length 3 : 9893
Mon Oct 19 18:52:30 2009     length 4 : 7490
Mon Oct 19 18:52:30 2009     length 5 : 5026
Mon Oct 19 18:52:30 2009     length 6 : 3180
Mon Oct 19 18:52:30 2009     length 7 : 1836
Mon Oct 19 18:52:30 2009     length 9+: 2130
Mon Oct 19 18:52:30 2009  largest cycle: 22 relations
Mon Oct 19 18:52:30 2009  matrix is 56333 x 56701 (14.3 MB) with weight 3283269 (57.90/col)
Mon Oct 19 18:52:30 2009  sparse part has weight 3283269 (57.90/col)
Mon Oct 19 18:52:31 2009  filtering completed in 3 passes
Mon Oct 19 18:52:31 2009  matrix is 51687 x 51748 (13.1 MB) with weight 3019515 (58.35/col)
Mon Oct 19 18:52:31 2009  sparse part has weight 3019515 (58.35/col)
Mon Oct 19 18:52:31 2009  saving the first 48 matrix rows for later
Mon Oct 19 18:52:31 2009  matrix is 51639 x 51748 (9.3 MB) with weight 2437777 (47.11/col)
Mon Oct 19 18:52:31 2009  sparse part has weight 1912064 (36.95/col)
Mon Oct 19 18:52:31 2009  matrix includes 64 packed rows
Mon Oct 19 18:52:31 2009  using block size 20699 for processor cache size 512 kB
Mon Oct 19 18:52:31 2009  commencing Lanczos iteration
Mon Oct 19 18:52:31 2009  memory use: 8.3 MB
Mon Oct 19 18:52:46 2009  lanczos halted after 819 iterations (dim = 51638)
Mon Oct 19 18:52:46 2009  recovered 18 nontrivial dependencies
Mon Oct 19 18:52:48 2009  prp41 factor: 41036055173181597710179425086539396815889
Mon Oct 19 18:52:48 2009  prp46 factor: 3510065170731752561733587750619799871556698231
Mon Oct 19 18:52:48 2009  elapsed time 00:35:04

(61·10¹²⁰-43)/9 = 6(7)₁₁₉3_<121> = 503 · 2719 · 85991 · 167081 · 9073215409241_<13> · C92

C92 = P39 · P54

P39 = 115735921965516571335680014573986691277_<39>

P54 = 328473751248953343156797620176244809016068048692926687_<54>

Mon Oct 19 21:04:35 2009  Msieve v. 1.42
Mon Oct 19 21:04:35 2009  random seeds: 3f195b67 1c332412
Mon Oct 19 21:04:35 2009  factoring 38016212442269365535939492811864166233423748155738998756090918118704266190664331664663409299 (92 digits)
Mon Oct 19 21:04:35 2009  searching for 15-digit factors
Mon Oct 19 21:04:36 2009  commencing quadratic sieve (92-digit input)
Mon Oct 19 21:04:36 2009  using multiplier of 11
Mon Oct 19 21:04:36 2009  using 64kb Opteron sieve core
Mon Oct 19 21:04:36 2009  sieve interval: 18 blocks of size 65536
Mon Oct 19 21:04:36 2009  processing polynomials in batches of 6
Mon Oct 19 21:04:36 2009  using a sieve bound of 1817833 (68235 primes)
Mon Oct 19 21:04:36 2009  using large prime bound of 198143797 (27 bits)
Mon Oct 19 21:04:36 2009  using double large prime bound of 860131523011962 (42-50 bits)
Mon Oct 19 21:04:36 2009  using trial factoring cutoff of 50 bits
Mon Oct 19 21:04:36 2009  polynomial 'A' values have 12 factors
Mon Oct 19 22:26:01 2009  68577 relations (17398 full + 51179 combined from 859308 partial), need 68331
Mon Oct 19 22:26:01 2009  begin with 876706 relations
Mon Oct 19 22:26:01 2009  reduce to 172614 relations in 10 passes
Mon Oct 19 22:26:01 2009  attempting to read 172614 relations
Mon Oct 19 22:26:03 2009  recovered 172614 relations
Mon Oct 19 22:26:03 2009  recovered 152321 polynomials
Mon Oct 19 22:26:03 2009  attempting to build 68577 cycles
Mon Oct 19 22:26:03 2009  found 68577 cycles in 5 passes
Mon Oct 19 22:26:03 2009  distribution of cycle lengths:
Mon Oct 19 22:26:03 2009     length 1 : 17398
Mon Oct 19 22:26:03 2009     length 2 : 12761
Mon Oct 19 22:26:03 2009     length 3 : 11901
Mon Oct 19 22:26:03 2009     length 4 : 9302
Mon Oct 19 22:26:03 2009     length 5 : 6806
Mon Oct 19 22:26:03 2009     length 6 : 4380
Mon Oct 19 22:26:03 2009     length 7 : 2524
Mon Oct 19 22:26:03 2009     length 9+: 3505
Mon Oct 19 22:26:03 2009  largest cycle: 19 relations
Mon Oct 19 22:26:03 2009  matrix is 68235 x 68577 (17.6 MB) with weight 4075157 (59.42/col)
Mon Oct 19 22:26:03 2009  sparse part has weight 4075157 (59.42/col)
Mon Oct 19 22:26:04 2009  filtering completed in 3 passes
Mon Oct 19 22:26:04 2009  matrix is 64380 x 64442 (16.6 MB) with weight 3842512 (59.63/col)
Mon Oct 19 22:26:04 2009  sparse part has weight 3842512 (59.63/col)
Mon Oct 19 22:26:04 2009  saving the first 48 matrix rows for later
Mon Oct 19 22:26:04 2009  matrix is 64332 x 64442 (9.7 MB) with weight 2887480 (44.81/col)
Mon Oct 19 22:26:04 2009  sparse part has weight 1908982 (29.62/col)
Mon Oct 19 22:26:04 2009  matrix includes 64 packed rows
Mon Oct 19 22:26:04 2009  using block size 21845 for processor cache size 512 kB
Mon Oct 19 22:26:04 2009  commencing Lanczos iteration
Mon Oct 19 22:26:04 2009  memory use: 9.7 MB
Mon Oct 19 22:26:26 2009  lanczos halted after 1019 iterations (dim = 64328)
Mon Oct 19 22:26:26 2009  recovered 15 nontrivial dependencies
Mon Oct 19 22:26:26 2009  prp39 factor: 115735921965516571335680014573986691277
Mon Oct 19 22:26:26 2009  prp54 factor: 328473751248953343156797620176244809016068048692926687
Mon Oct 19 22:26:26 2009  elapsed time 01:21:51

(62·10¹²¹-71)/9 = 6(8)₁₂₀1_<122> = 61 · 114968631523579456592837576959_<30> · C91

C91 = P35 · P57

P35 = 15339977635830331306565193967618163_<35>

P57 = 640346819253660171166999735090684748846178296261435303513_<57>

Mon Oct 19 19:42:02 2009  Msieve v. 1.42
Mon Oct 19 19:42:02 2009  random seeds: a5d802e6 78b647cf
Mon Oct 19 19:42:02 2009  factoring 9822905886526234428677805540972954060517545347969510161922102565209757680436219137596506619 (91 digits)
Mon Oct 19 19:42:03 2009  searching for 15-digit factors
Mon Oct 19 19:42:03 2009  commencing quadratic sieve (91-digit input)
Mon Oct 19 19:42:03 2009  using multiplier of 19
Mon Oct 19 19:42:03 2009  using 64kb Opteron sieve core
Mon Oct 19 19:42:03 2009  sieve interval: 18 blocks of size 65536
Mon Oct 19 19:42:03 2009  processing polynomials in batches of 6
Mon Oct 19 19:42:03 2009  using a sieve bound of 1753547 (65869 primes)
Mon Oct 19 19:42:03 2009  using large prime bound of 177108247 (27 bits)
Mon Oct 19 19:42:03 2009  using double large prime bound of 702796695147472 (42-50 bits)
Mon Oct 19 19:42:03 2009  using trial factoring cutoff of 50 bits
Mon Oct 19 19:42:03 2009  polynomial 'A' values have 12 factors
Mon Oct 19 20:49:59 2009  66216 relations (17589 full + 48627 combined from 792474 partial), need 65965
Mon Oct 19 20:49:59 2009  begin with 810063 relations
Mon Oct 19 20:50:00 2009  reduce to 163501 relations in 11 passes
Mon Oct 19 20:50:00 2009  attempting to read 163501 relations
Mon Oct 19 20:50:01 2009  recovered 163501 relations
Mon Oct 19 20:50:01 2009  recovered 141320 polynomials
Mon Oct 19 20:50:01 2009  attempting to build 66216 cycles
Mon Oct 19 20:50:01 2009  found 66216 cycles in 5 passes
Mon Oct 19 20:50:01 2009  distribution of cycle lengths:
Mon Oct 19 20:50:01 2009     length 1 : 17589
Mon Oct 19 20:50:01 2009     length 2 : 12626
Mon Oct 19 20:50:01 2009     length 3 : 11681
Mon Oct 19 20:50:01 2009     length 4 : 8758
Mon Oct 19 20:50:01 2009     length 5 : 6231
Mon Oct 19 20:50:01 2009     length 6 : 3920
Mon Oct 19 20:50:01 2009     length 7 : 2420
Mon Oct 19 20:50:01 2009     length 9+: 2991
Mon Oct 19 20:50:01 2009  largest cycle: 18 relations
Mon Oct 19 20:50:01 2009  matrix is 65869 x 66216 (17.0 MB) with weight 3932079 (59.38/col)
Mon Oct 19 20:50:01 2009  sparse part has weight 3932079 (59.38/col)
Mon Oct 19 20:50:02 2009  filtering completed in 3 passes
Mon Oct 19 20:50:02 2009  matrix is 61735 x 61799 (16.0 MB) with weight 3687676 (59.67/col)
Mon Oct 19 20:50:02 2009  sparse part has weight 3687676 (59.67/col)
Mon Oct 19 20:50:02 2009  saving the first 48 matrix rows for later
Mon Oct 19 20:50:02 2009  matrix is 61687 x 61799 (9.7 MB) with weight 2816849 (45.58/col)
Mon Oct 19 20:50:02 2009  sparse part has weight 1926080 (31.17/col)
Mon Oct 19 20:50:02 2009  matrix includes 64 packed rows
Mon Oct 19 20:50:02 2009  using block size 21845 for processor cache size 512 kB
Mon Oct 19 20:50:02 2009  commencing Lanczos iteration
Mon Oct 19 20:50:02 2009  memory use: 9.4 MB
Mon Oct 19 20:50:23 2009  lanczos halted after 977 iterations (dim = 61685)
Mon Oct 19 20:50:23 2009  recovered 17 nontrivial dependencies
Mon Oct 19 20:50:23 2009  prp35 factor: 15339977635830331306565193967618163
Mon Oct 19 20:50:23 2009  prp57 factor: 640346819253660171166999735090684748846178296261435303513
Mon Oct 19 20:50:23 2009  elapsed time 01:08:21

Oct 19, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Oct 19, 2009

(61·10¹¹⁵+11)/9 = 6(7)₁₁₄9_<116> = 3 · 11689 · C112

C112 = P53 · P60

P53 = 16395185245811434412457687799934663376577264400981837_<53>

P60 = 117888755802769552667826097972841639069866714575824487244301_<60>

Number: 67779_115
N=1932807989784634493334980972931182529950602497441405816801487945298365351406672306663751611993548857266882760937
  ( 112 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=16395185245811434412457687799934663376577264400981837
 r2=117888755802769552667826097972841639069866714575824487244301
Version: 
Total time: 0.49 hours.
Scaled time: 1.17 units (timescale=2.389).
Factorization parameters were as follows:
n: 1932807989784634493334980972931182529950602497441405816801487945298365351406672306663751611993548857266882760937
m: 100000000000000000000000
deg: 5
c5: 61
c0: 11
skew: 0.71
type: snfs
lss: 1
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [200000, 375001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 1158405
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 48565 x 48792
Total sieving time: 0.44 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,400000,400000,25,25,45,45,2.2,2.2,25000
total time: 0.49 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(62·10¹²⁰-71)/9 = 6(8)₁₁₉1_<121> = 29 · 577 · 56672831 · C109

C109 = P38 · P72

P38 = 21679127389566080283674645480303460667_<38>

P72 = 335087836893671128683748066753771626945672527368526518443982836779830241_<72>

Number: 68881_120
N=7264411902712037064371078921236694765958027268481835393958066954761270532172238326642527264043720097080630747
  ( 109 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=21679127389566080283674645480303460667
 r2=335087836893671128683748066753771626945672527368526518443982836779830241
Version: 
Total time: 0.99 hours.
Scaled time: 2.34 units (timescale=2.375).
Factorization parameters were as follows:
n: 7264411902712037064371078921236694765958027268481835393958066954761270532172238326642527264043720097080630747
m: 1000000000000000000000000
deg: 5
c5: 62
c0: -71
skew: 1.03
type: snfs
lss: 1
rlim: 540000
alim: 540000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 540000/540000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [270000, 630001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 1298818
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 83780 x 84026
Total sieving time: 0.89 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,540000,540000,25,25,46,46,2.2,2.2,30000
total time: 0.99 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Oct 19, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve / Oct 19, 2009

(59·10¹³⁵+31)/9 = 6(5)₁₃₄9_<136> = 7 · C135

C135 = P68 · P68

P68 = 15163281148863922855510327593559872326794565482235986495845009675589_<68>

P68 = 61761562508395645457663130539560263571682161366507241664417293471533_<68>

Number: snfs135
N=936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937
  ( 135 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=15163281148863922855510327593559872326794565482235986495845009675589 (pp68)
 r2=61761562508395645457663130539560263571682161366507241664417293471533 (pp68)
Version: Msieve-1.40
Total time: 3.29 hours.
Scaled time: 6.08 units (timescale=1.845).
Factorization parameters were as follows:
n: 936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937
m: 1000000000000000000000000000
deg: 5
c5: 59
c0: 31
skew: 0.88
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1265001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 185316 x 185541
Total sieving time: 3.14 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 3.29 hours.
 --------- CPU info (if available) ----------

Oct 19, 2009 (3rd)

By Robert Backstrom / Msieve / Oct 19, 2009

(61·10¹¹⁰-43)/9 = 6(7)₁₀₉3_<111> = 7789 · 6772021363007171633797_<22> · C86

C86 = P40 · P46

P40 = 4647466076771159017101224620731157755017_<40>

P46 = 2764846811338785817801461431188838166283593893_<46>

Mon Oct 19 21:52:53 2009  
Mon Oct 19 21:52:53 2009  
Mon Oct 19 21:52:53 2009  Msieve v. 1.42
Mon Oct 19 21:52:53 2009  random seeds: 53af9528 bb7b3299
Mon Oct 19 21:52:53 2009  factoring 12849531763165915780729681999759369299308766942340673904026379524101685112964411311181 (86 digits)
Mon Oct 19 21:52:54 2009  searching for 15-digit factors
Mon Oct 19 21:52:54 2009  commencing quadratic sieve (86-digit input)
Mon Oct 19 21:52:54 2009  using multiplier of 1
Mon Oct 19 21:52:54 2009  using 64kb Opteron sieve core
Mon Oct 19 21:52:54 2009  sieve interval: 6 blocks of size 65536
Mon Oct 19 21:52:54 2009  processing polynomials in batches of 17
Mon Oct 19 21:52:54 2009  using a sieve bound of 1442509 (54980 primes)
Mon Oct 19 21:52:54 2009  using large prime bound of 115400720 (26 bits)
Mon Oct 19 21:52:54 2009  using double large prime bound of 325068826146400 (41-49 bits)
Mon Oct 19 21:52:54 2009  using trial factoring cutoff of 49 bits
Mon Oct 19 21:52:54 2009  polynomial 'A' values have 11 factors
Mon Oct 19 22:40:36 2009  55214 relations (15494 full + 39720 combined from 580149 partial), need 55076
Mon Oct 19 22:40:37 2009  begin with 595643 relations
Mon Oct 19 22:40:37 2009  reduce to 131993 relations in 10 passes
Mon Oct 19 22:40:37 2009  attempting to read 131993 relations
Mon Oct 19 22:40:39 2009  recovered 131993 relations
Mon Oct 19 22:40:39 2009  recovered 114693 polynomials
Mon Oct 19 22:40:39 2009  attempting to build 55214 cycles
Mon Oct 19 22:40:39 2009  found 55214 cycles in 5 passes
Mon Oct 19 22:40:40 2009  distribution of cycle lengths:
Mon Oct 19 22:40:40 2009     length 1 : 15494
Mon Oct 19 22:40:40 2009     length 2 : 10796
Mon Oct 19 22:40:40 2009     length 3 : 9826
Mon Oct 19 22:40:40 2009     length 4 : 7278
Mon Oct 19 22:40:40 2009     length 5 : 5027
Mon Oct 19 22:40:40 2009     length 6 : 3028
Mon Oct 19 22:40:40 2009     length 7 : 1758
Mon Oct 19 22:40:40 2009     length 9+: 2007
Mon Oct 19 22:40:40 2009  largest cycle: 21 relations
Mon Oct 19 22:40:40 2009  matrix is 54980 x 55214 (11.7 MB) with weight 2856852 (51.74/col)
Mon Oct 19 22:40:40 2009  sparse part has weight 2856852 (51.74/col)
Mon Oct 19 22:40:41 2009  filtering completed in 3 passes
Mon Oct 19 22:40:41 2009  matrix is 50553 x 50617 (10.8 MB) with weight 2639886 (52.15/col)
Mon Oct 19 22:40:41 2009  sparse part has weight 2639886 (52.15/col)
Mon Oct 19 22:40:41 2009  saving the first 48 matrix rows for later
Mon Oct 19 22:40:41 2009  matrix is 50505 x 50617 (5.9 MB) with weight 1941977 (38.37/col)
Mon Oct 19 22:40:41 2009  sparse part has weight 1250286 (24.70/col)
Mon Oct 19 22:40:41 2009  matrix includes 64 packed rows
Mon Oct 19 22:40:41 2009  using block size 20246 for processor cache size 1024 kB
Mon Oct 19 22:40:42 2009  commencing Lanczos iteration
Mon Oct 19 22:40:42 2009  memory use: 7.0 MB
Mon Oct 19 22:41:03 2009  lanczos halted after 800 iterations (dim = 50502)
Mon Oct 19 22:41:03 2009  recovered 15 nontrivial dependencies
Mon Oct 19 22:41:04 2009  prp40 factor: 4647466076771159017101224620731157755017
Mon Oct 19 22:41:04 2009  prp46 factor: 2764846811338785817801461431188838166283593893
Mon Oct 19 22:41:04 2009  elapsed time 00:48:11

Oct 19, 2009 (2nd)

By Serge Batalov / GMP-ECM / Oct 19, 2009

(61·10¹¹⁷-43)/9 = 6(7)₁₁₆3_<118> = 13 · 17 · 50321 · 186071 · 80481263 · C98

C98 = P29 · C69

P29 = 54281847730996426207359531089_<29>

C69 = [749752101263345470108990615445763113552625379099289239504849511949049_<69>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2961023599
Step 1 took 2252ms
Step 2 took 1636ms
********** Factor found in step 2: 54281847730996426207359531089
Found probable prime factor of 29 digits: 54281847730996426207359531089
Composite cofactor 749752101263345470108990615445763113552625379099289239504849511949049 has 69 digits

(62·10¹¹⁷-71)/9 = 6(8)₁₁₆1_<118> = 7 · 19 · 137650277 · C108

C108 = P32 · P76

P32 = 60874828950569996693918573606471_<32>

P76 = 6181340899496695595754737044042673115580750936683073986286488159140340843071_<76>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=2871096336
Step 1 took 4636ms
Step 2 took 2768ms
********** Factor found in step 2: 60874828950569996693918573606471
Found probable prime factor of 32 digits: 60874828950569996693918573606471
Probable prime cofactor has 76 digits

Oct 19, 2009

Factorizations of 655...559 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Factorizations of 677...773, Factorizations of 677...779, Factorizations of 688...881 and Factorizations of 688...883 have been extended up to n=125. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 18, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve / Oct 18, 2009

2·10¹⁹⁵+9 = 2(0)₁₉₄9_<196> = 7 · 263 · 5309 · 376787 · 398925029 · 208929543907045046083316767984164355764039923_<45> · C130

C130 = P59 · P72

P59 = 22272790228074941650412202144206513847480230663694503321323_<59>

P72 = 292551145750263592463612261169824232947788536994442651259033585380015683_<72>

N=6515930300278598936340223067286726695961677601878157142390817149184366337340674057734940096025365308355623172051113615953328308609
  ( 130 digits)
Divisors found:
 r1=22272790228074941650412202144206513847480230663694503321323 (pp59)
 r2=292551145750263592463612261169824232947788536994442651259033585380015683 (pp72)
Version: Msieve-1.40
Total time: 114.52 hours.
Scaled time: 216.90 units (timescale=1.894).
Factorization parameters were as follows:
# Murphy_E = 7.675034e-11, selected by Jeff Gilchrist
n: 6515930300278598936340223067286726695961677601878157142390817149184366337340674057734940096025365308355623172051113615953328308609
Y0: -11564669034526998847875422
Y1: 178145966422721
c0: 594526530049952023356115970449323
c1: 20042533683248693847400228035
c2: 3094152334001331708481
c3: -77649993471691511
c4: -777885780
c5: 31500
skew: 834742.04
type: gnfs
# selected mechanically
rlim: 9700000
alim: 9700000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 9700000/9700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved algebraic special-q in [4850000, 9950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1429066 x 1429292
Total sieving time: 111.39 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.62 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
gnfs,129,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,9700000,9700000,28,28,53,53,2.5,2.5,100000
total time: 114.52 hours.
 --------- CPU info (if available) ----------

Oct 18, 2009

By Tyler Cadigan / GGNFS, Msieve / Oct 18, 2009

(16·10¹⁹³-7)/9 = 1(7)₁₉₃_<194> = 17 · 259033 · 148157323 · 877141007 · 1039070261623_<13> · C158

C158 = P54 · P105

P54 = 114914680770244681417922046941865901060341833763525707_<54>

P105 = 260171960010602604461664775697366067467941159766507302878646963259902230029113380029567278481926693891417_<105>

Number: 17777_193
N=29897577729987263351121737742387080067460264201163135704886761830414910918621330073647432413064902874620571121025724773256600087828620159733970422977746156819
  ( 158 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=114914680770244681417922046941865901060341833763525707 (pp54)
 r2=260171960010602604461664775697366067467941159766507302878646963259902230029113380029567278481926693891417 (pp105)
Version: Msieve v. 1.42
Total time: 392.12 hours.
Scaled time: 948.53 units (timescale=2.419).
Factorization parameters were as follows:
n: 29897577729987263351121737742387080067460264201163135704886761830414910918621330073647432413064902874620571121025724773256600087828620159733970422977746156819
m: 400000000000000000000000000000000000000
deg: 5
c5: 125
c0: -56
skew: 0.85
type: snfs
lss: 1
rlim: 12500000
alim: 12500000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 12500000/12500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6250000, 11450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2224158 x 2224384
Total sieving time: 379.54 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 11.84 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,195.000,5,0,0,0,0,0,0,0,0,12500000,12500000,28,28,55,55,2.5,2.5,100000
total time: 392.12 hours.
 --------- CPU info (if available) ----------

Oct 17, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve / Oct 17, 2009

(59·10¹⁴³+13)/9 = 6(5)₁₄₂7_<144> = 3 · 7 · 23 · C142

C142 = P65 · P77

P65 = 56824861300809670417610968582565253327225489040825124747375566909_<65>

P77 = 23884930784295121718305209081680340072427488597788659427641111525802353279331_<77>

Number: snfs142
N=1357257878997009431792040487692661605705083965953531170922475270301357257878997009431792040487692661605705083965953531170922475270301357257879
  ( 142 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=56824861300809670417610968582565253327225489040825124747375566909 (pp65)
 r2=23884930784295121718305209081680340072427488597788659427641111525802353279331 (pp77)
Version: Msieve-1.40
Total time: 8.41 hours.
Scaled time: 16.46 units (timescale=1.957).
Factorization parameters were as follows:
n: 1357257878997009431792040487692661605705083965953531170922475270301357257878997009431792040487692661605705083965953531170922475270301357257879
m: 50000000000000000000000000000
deg: 5
c5: 472
c0: 325
skew: 0.93
type: snfs
lss: 1
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [955000, 2455001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 287686 x 287915
Total sieving time: 8.12 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 8.41 hours.
 --------- CPU info (if available) ----------

Oct 17, 2009 (2nd)

By Sinkiti Sibata / GGNFS / Oct 17, 2009

5·10¹⁸¹-1 = 4(9)₁₈₁_<182> = 7 · 97² · 193 · 457 · 422822039 · 5656697469953_<13> · 173579002511793813594159069431_<30> · C122

C122 = P61 · P62

P61 = 1064331088086742281466450399965259429540937717843448019984241_<61>

P62 = 19478723013143054838808802263731536889575609008494945550219489_<62>

Number: 49999_181
N=20731810459118814730446116833653693666321827958599665647784054670803472164424057194952315997453223210542179715535871072849
  ( 122 digits)
Divisors found:
 r1=1064331088086742281466450399965259429540937717843448019984241 (pp61)
 r2=19478723013143054838808802263731536889575609008494945550219489 (pp62)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 140.90 hours.
Scaled time: 66.50 units (timescale=0.472).
Factorization parameters were as follows:
name: 49999_181
n: 20731810459118814730446116833653693666321827958599665647784054670803472164424057194952315997453223210542179715535871072849
skew: 101517.10
# norm 3.04e+17
c5: 29580
c4: 2156779898
c3: -6149966082058983
c2: 23385979761564979461
c1: 1440918581264063038291103
c0: -22754533970254442683757639139
# alpha -6.80
Y1: 1261519391909
Y0: -233952547110868141002320
# Murphy_E 2.33e-10
# M 2835204791081285862371599358752498154223875050445617820813767572498702847699896488863776551489942795073240664812599984655
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5320001)
Primes: RFBsize:348513, AFBsize:348097, largePrimes:7741397 encountered
Relations: rels:7907865, finalFF:796206
Max relations in full relation-set: 28
Initial matrix: 696692 x 796206 with sparse part having weight 72088621.
Pruned matrix : 615148 x 618695 with weight 51491407.
Total sieving time: 118.03 hours.
Total relation processing time: 1.24 hours.
Matrix solve time: 21.10 hours.
Time per square root: 0.53 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 140.90 hours.
 --------- CPU info (if available) ----------

Oct 17, 2009

By Ignacio Santos / GGNFS, Msieve / Oct 17, 2009

(23·10¹⁷²+13)/9 = 2(5)₁₇₁7_<173> = 3² · 7 · 109 · 33627663967_<11> · C159

C159 = P57 · P102

P57 = 262044081161281157435640211298473487606075469399350823529_<57>

P102 = 422325422840311044324580075575239212407342269048398853475771102425965377556331402375340114140038778897_<102>

Number: 25557_172
N=110667877379238850374366379526440928413416400335450304067327752353284785156750297646457827005075711428545511839998879588251140758182679780479921677512496267513
  ( 159 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=262044081161281157435640211298473487606075469399350823529 (pp57)
 r2=422325422840311044324580075575239212407342269048398853475771102425965377556331402375340114140038778897 (pp102)
Version: Msieve-1.40
Total time: 84.35 hours.
Scaled time: 146.68 units (timescale=1.739).
Factorization parameters were as follows:
n: 110667877379238850374366379526440928413416400335450304067327752353284785156750297646457827005075711428545511839998879588251140758182679780479921677512496267513
m: 20000000000000000000000000000000000
deg: 5
c5: 575
c0: 104
skew: 0.71
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 7300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1175091 x 1175339
Total sieving time: 82.08 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.85 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 84.35 hours.

Oct 16, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve / Oct 16, 2009

(59·10¹²²+31)/9 = 6(5)₁₂₁9_<123> = 199 · 223 · C119

C119 = P37 · P82

P37 = 2617252350806544967013566147544617337_<37>

P82 = 5644246393918487080312117373821903275185792933757964322841397161481678551382767991_<82>

Number: snfs122
N=14772417143014524540990953772349540427598881302376356120412726312178731224633381155904084448150067727776901447947259967
  ( 119 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=2617252350806544967013566147544617337 (pp37)
 r2=5644246393918487080312117373821903275185792933757964322841397161481678551382767991 (pp82)
Version: Msieve-1.40
Total time: 1.99 hours.
Scaled time: 3.91 units (timescale=1.963).
Factorization parameters were as follows:
n: 14772417143014524540990953772349540427598881302376356120412726312178731224633381155904084448150067727776901447947259967
m: 2000000000000000000000000
deg: 5
c5: 1475
c0: 248
skew: 0.70
type: snfs
lss: 1
rlim: 840000
alim: 840000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 840000/840000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [420000, 870001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 112892 x 113134
Total sieving time: 1.86 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,124.000,5,0,0,0,0,0,0,0,0,840000,840000,25,25,46,46,2.2,2.2,50000
total time: 1.99 hours.
 --------- CPU info (if available) ----------

(59·10¹²³+13)/9 = 6(5)₁₂₂7_<124> = 997 · 664043 · C115

C115 = P33 · P83

P33 = 981967760548551132769078879770631_<33>

P83 = 10083723101151866053703913121273268266204944970451697080119605510395613352043008357_<83>

Number: snfs115
N=9901890991629789058242256365154084293252981092378255560901687199133003716802836976489009944306161264087447376163267
  ( 115 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=981967760548551132769078879770631 (pp33)
 r2=10083723101151866053703913121273268266204944970451697080119605510395613352043008357 (pp83)
Version: Msieve-1.40
Total time: 1.73 hours.
Scaled time: 3.40 units (timescale=1.963).
Factorization parameters were as follows:
n: 9901890991629789058242256365154084293252981092378255560901687199133003716802836976489009944306161264087447376163267
m: 5000000000000000000000000
deg: 5
c5: 472
c0: 325
skew: 0.93
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 795001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 117791 x 118016
Total sieving time: 1.65 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 1.73 hours.
 --------- CPU info (if available) ----------

(59·10¹³⁸+13)/9 = 6(5)₁₃₇7_<139> = 73 · C137

C137 = P59 · P79

P59 = 37063799104643516016870773501344256457436258106731212535903_<59>

P79 = 2422906800365494708429142047443049503908526352762410639292675584284260956111203_<79>

Number: snfs137
N=89802130898021308980213089802130898021308980213089802130898021308980213089802130898021308980213089802130898021308980213089802130898021309
  ( 137 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=37063799104643516016870773501344256457436258106731212535903 (pp59)
 r2=2422906800365494708429142047443049503908526352762410639292675584284260956111203 (pp79)
Version: Msieve-1.40
Total time: 5.39 hours.
Scaled time: 10.61 units (timescale=1.969).
Factorization parameters were as follows:
n: 89802130898021308980213089802130898021308980213089802130898021308980213089802130898021308980213089802130898021308980213089802130898021309
m: 5000000000000000000000000000
deg: 5
c5: 472
c0: 325
skew: 0.93
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 1790001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 244216 x 244441
Total sieving time: 5.14 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000
total time: 5.39 hours.
 --------- CPU info (if available) ----------

2·10¹⁸⁶+9 = 2(0)₁₈₅9_<187> = 11 · 571 · 1297 · 90336178769_<11> · C169

C169 = P45 · P124

P45 = 357262445685375714446644002349895705129177657_<45>

P124 = 7606977704130228676753060368209396335418132864772317258963737679591760422481190900647054523251242045655517818742535330613289_<124>

Number: 209-5
N=2717687458851689874213860204251139251360870739438748418027921708986397314502883556437734594257957018606360831173069385218160418921517658081506947281834237272090046083873
  ( 169 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=357262445685375714446644002349895705129177657 (pp45)
 r2=7606977704130228676753060368209396335418132864772317258963737679591760422481190900647054523251242045655517818742535330613289 (pp124)
Version: Msieve-1.40
Total time: 167.46 hours.
Scaled time: 310.65 units (timescale=1.855).
Factorization parameters were as follows:
n: 2717687458851689874213860204251139251360870739438748418027921708986397314502883556437734594257957018606360831173069385218160418921517658081506947281834237272090046083873
m: 10000000000000000000000000000000000000
deg: 5
c5: 20
c0: 9
skew: 0.85
type: snfs
lss: 1
rlim: 8900000
alim: 8900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8900000/8900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4450000, 7050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1562571 x 1562799
Total sieving time: 163.98 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.13 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,186.000,5,0,0,0,0,0,0,0,0,8900000,8900000,28,28,54,54,2.5,2.5,100000
total time: 167.46 hours.
 --------- CPU info (if available) ----------

2·10¹⁸⁵+9 = 2(0)₁₈₄9_<186> = 3221 · 25309 · C178

C178 = P43 · P135

P43 = 5227693762306268399155697518001267230014289_<43>

P135 = 469303881636488913910845986301497789032248197460711815322014514424627055233095974458951755240392494538034911487605992840453516750955929_<135>

Number: 209-4
N=2453376974657192395380246995934962890035878062208538048730420963056203100555740178987834549997731239642685761332372116590509143067439321761972654439436543214413776182761079269481
  ( 178 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=5227693762306268399155697518001267230014289 (pp43)
 r2=469303881636488913910845986301497789032248197460711815322014514424627055233095974458951755240392494538034911487605992840453516750955929 (pp135)
Version: Msieve-1.40
Total time: 146.87 hours.
Scaled time: 287.43 units (timescale=1.957).
Factorization parameters were as follows:
n: 2453376974657192395380246995934962890035878062208538048730420963056203100555740178987834549997731239642685761332372116590509143067439321761972654439436543214413776182761079269481
m: 10000000000000000000000000000000000000
deg: 5
c5: 2
c0: 9
skew: 1.35
type: snfs
lss: 1
rlim: 8600000
alim: 8600000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8600000/8600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4300000, 6600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1604184 x 1604416
Total sieving time: 143.24 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.30 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,185.000,5,0,0,0,0,0,0,0,0,8600000,8600000,28,28,54,54,2.5,2.5,100000
total time: 146.87 hours.
 --------- CPU info (if available) ----------

2·10¹⁸³+9 = 2(0)₁₈₂9_<184> = 7 · 41 · 349 · 266221 · 10939063185828649_<17> · C157

C157 = P48 · P110

P48 = 344618225745749586411461042704126893948843706169_<48>

P110 = 19895826657608469488864484374369820394043609778637709304640322693139917994922066124762553757203947117837606543_<110>

Number: 209-3
N=6856464482490018001444773324050028540933716416510729022191794797020840270795309636458372328059570593686611556858681441235580276482585545763581260344523863767
  ( 157 digits)
SNFS difficulty: 183 digits.
Divisors found:
 r1=344618225745749586411461042704126893948843706169 (pp48)
 r2=19895826657608469488864484374369820394043609778637709304640322693139917994922066124762553757203947117837606543 (pp110)
Version: Msieve-1.40
Total time: 134.56 hours.
Scaled time: 258.62 units (timescale=1.922).
Factorization parameters were as follows:
n: 6856464482490018001444773324050028540933716416510729022191794797020840270795309636458372328059570593686611556858681441235580276482585545763581260344523863767
m: 2000000000000000000000000000000000000
deg: 5
c5: 125
c0: 18
skew: 0.68
type: snfs
lss: 1
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [4000000, 6100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1511833 x 1512065
Total sieving time: 131.06 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.98 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,183.000,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,53,53,2.5,2.5,100000
total time: 134.56 hours.
 --------- CPU info (if available) ----------

Oct 16, 2009 (2nd)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Oct 16, 2009

(59·10¹⁴⁹+13)/9 = 6(5)₁₄₈7_<150> = 3 · 7 · 19 · 937 · 1103 · 54493 · 962810321078392375635049_<24> · C113

C113 = P39 · P75

P39 = 147943116229641901909832786463660049913_<39>

P75 = 204807231016911815436363214460668291459094734809973992870141049693597139393_<75>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 30299819983006104728482599785278540686702021001078729957142502737791357700632490766461943016847001905472398522809 (113 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6964078966
Step 1 took 3463ms
Step 2 took 3759ms
********** Factor found in step 2: 147943116229641901909832786463660049913
Found probable prime factor of 39 digits: 147943116229641901909832786463660049913
Probable prime cofactor 204807231016911815436363214460668291459094734809973992870141049693597139393 has 75 digits

(59·10¹³⁵+13)/9 = 6(5)₁₃₄7_<136> = 53 · 13810561 · 80236733 · 54404033543_<11> · C109

C109 = P52 · P58

P52 = 1069870404942196780013630862628023931905624513873353_<52>

P58 = 1917727080979938123004390143694320794532808882295629538747_<58>

Number: 65557_135
N=2051719448696623396197945795300720223247072182095324565313553803658214982417215832376273813292701449764308691
  ( 109 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=1069870404942196780013630862628023931905624513873353
 r2=1917727080979938123004390143694320794532808882295629538747
Version: 
Total time: 1.88 hours.
Scaled time: 4.47 units (timescale=2.383).
Factorization parameters were as follows:
n: 2051719448696623396197945795300720223247072182095324565313553803658214982417215832376273813292701449764308691
m: 1000000000000000000000000000
deg: 5
c5: 59
c0: 13
skew: 0.74
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3148405
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 198946 x 199194
Total sieving time: 1.61 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,50000
total time: 1.88 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673798)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(59·10¹⁴²+13)/9 = 6(5)₁₄₁7_<143> = 523 · 31564933 · 1495279771564938081250317434363_<31> · C103

C103 = P46 · P57

P46 = 6703894625173431679040967401885793269992102259_<46>

P57 = 396144202180882171589894416421744649266280406656475887619_<57>

Number: 65557_142
N=2655708987794033222006395738022718318106965876613728083162673950146053935377047128704039001596840031321
  ( 103 digits)
Divisors found:
 r1=6703894625173431679040967401885793269992102259
 r2=396144202180882171589894416421744649266280406656475887619
Version: 
Total time: 3.81 hours.
Scaled time: 9.04 units (timescale=2.373).
Factorization parameters were as follows:
name: 65557_142
n: 2655708987794033222006395738022718318106965876613728083162673950146053935377047128704039001596840031321
skew: 3751.30
# norm 3.50e+13
c5: 78660
c4: -1283237721
c3: -3748094967622
c2: 14675610712833839
c1: 18454912549082743215
c0: -37744419676925558612862
# alpha -4.56
Y1: 84744210287
Y0: -32039745393925761293
# Murphy_E 2.48e-09
# M 2531415688351974972911924921557373481077501563677208680072258910721872535231990746324431917159123062258
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4809031
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 252586 x 252833
Polynomial selection time: 0.25 hours.
Total sieving time: 3.02 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 3.81 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673798)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(59·10¹⁵⁰+13)/9 = 6(5)₁₄₉7_<151> = 17 · 911 · 1279043 · 5013488891_<10> · C131

C131 = P51 · P81

P51 = 429592179251930619925076023414555204538013859122257_<51>

P81 = 153659931504969338803760692827314585527035777416990495872633452162987819002153371_<81>

Number: 65557_150
N=66011104838922169386588454921857859398757669838483669807968869166926747641548905738955030158002277581277821586625150229314953678347
  ( 131 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=429592179251930619925076023414555204538013859122257
 r2=153659931504969338803760692827314585527035777416990495872633452162987819002153371
Version: 
Total time: 6.36 hours.
Scaled time: 15.20 units (timescale=2.391).
Factorization parameters were as follows:
n: 66011104838922169386588454921857859398757669838483669807968869166926747641548905738955030158002277581277821586625150229314953678347
m: 1000000000000000000000000000000
deg: 5
c5: 59
c0: 13
skew: 0.74
type: snfs
lss: 1
rlim: 1800000
alim: 1800000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [900000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6668876
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 335862 x 336110
Total sieving time: 5.82 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,1800000,1800000,27,27,49,49,2.4,2.4,100000
total time: 6.36 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673798)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

Oct 16, 2009

By Serge Batalov / Msieve, GMP-ECM 6.2.3 / Oct 16, 2009

(59·10¹¹⁸+31)/9 = 6(5)₁₁₇9_<119> = 3 · 13 · 733 · 47857 · 64952802419_<11> · C99

C99 = P48 · P52

P48 = 130974788754003500820212128935309549948386590481_<48>

P52 = 5632612175418019323602106433020886254974107858338359_<52>

SNFS difficulty: 121 digits.
Divisors found:
 r1=130974788754003500820212128935309549948386590481 (pp48)
 r2=5632612175418019323602106433020886254974107858338359 (pp52)
Version: Msieve v. 1.43 SVN74
Total time: 0.97 hours.
Scaled time: 2.32 units (timescale=2.400).
Factorization parameters were as follows:
n: 737730189808603191316426643348526512468446270875955771055721823848214715493569424394356238066560679
m: 500000000000000000000000
deg: 5
c5: 472
c0: 775
skew: 1.10
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 48
mfba: 48
rlambda: 2.4
alambda: 2.4
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 48/48
Sieved rational special-q in [456250, 706251)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 112931 x 113167
Total sieving time: 0.90 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,48,48,2.4,2.4,50000
total time: 0.97 hours.

(59·10¹²¹+13)/9 = 6(5)₁₂₀7_<122> = 23 · 337 · 258733 · C113

C113 = P35 · P39 · P40

P35 = 31077092723645769101180302178920757_<35>

P39 = 958494576036167836035177225945730085227_<39>

P40 = 1097412488009198204946538922458400988361_<40>

SNFS difficulty: 123 digits.
Divisors found:
 r1=31077092723645769101180302178920757 (pp35)
 r2=958494576036167836035177225945730085227 (pp39)
 r3=1097412488009198204946538922458400988361 (pp40)
Version: Msieve v. 1.43 SVN74
Total time: 1.28 hours.
Scaled time: 3.07 units (timescale=2.400).
Factorization parameters were as follows:
n: 32688872494665826600540483901281380902958693546154519166587863352421866900860032362071309411611676918178814750879
m: 2000000000000000000000000
deg: 5
c5: 295
c0: 208
skew: 0.93
type: snfs
lss: 1
rlim: 820000
alim: 820000
lpbr: 25
lpba: 25
mfbr: 48
mfba: 48
rlambda: 2.4
alambda: 2.4
Factor base limits: 820000/820000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 48/48
Sieved rational special-q in [512500, 812501)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 133412 x 133645
Total sieving time: 1.06 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,123.000,5,0,0,0,0,0,0,0,0,820000,820000,25,25,48,48,2.4,2.4,50000
total time: 1.28 hours.

(8·10²¹⁸+7)/3 = 2(6)₂₁₇9_<219> = 307 · 89690143 · 615046225945003_<15> · 14652967475174650405061_<23> · C172

C172 = P34 · C138

P34 = 1342390712063055001925603562834767_<34>

C138 = [800522159352933722050896549761388621424585536007720393498837602232681478070960919646071118994305807360849237736779454745588953403185113129_<138>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3543900038
Step 1 took 3504ms
Step 2 took 2464ms
********** Factor found in step 2: 1342390712063055001925603562834767
Found probable prime factor of 34 digits: 1342390712063055001925603562834767
Composite cofactor has 138 digits

(8·10²¹⁵+7)/3 = 2(6)₂₁₄9_<216> = 13 · 1064519 · 7642157 · 6044612843_<10> · C192

C192 = P31 · C162

P31 = 1639123903073298608883820431719_<31>

C162 = [254492937102404188685188052615787881342045720743990894848429549297697033088006979176092744516914821078431270738413278211316625145666683242254247672880860742129183_<162>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3657846809
Step 1 took 4113ms
Step 2 took 2712ms
********** Factor found in step 2: 1639123903073298608883820431719
Found probable prime factor of 31 digits: 1639123903073298608883820431719
Composite cofactor has 162 digits

Oct 15, 2009 (5th)

By Jo Yeong Uk / GMP-ECM / Oct 15, 2009

(59·10¹³⁹+13)/9 = 6(5)₁₃₈7_<140> = 201554609984047_<15> · C126

C126 = P41 · P85

P41 = 88640247102350796577040881684578110160059_<41>

P85 = 3669321860674046149889305251133408005163302741051006855356289605523585561498123504209_<85>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 325249596428205052553125481768616288985949223457346887364028093674830338705476019372238692494311489163742306574802414950188331 (126 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1397171321
Step 1 took 4196ms
Step 2 took 4087ms
********** Factor found in step 2: 88640247102350796577040881684578110160059
Found probable prime factor of 41 digits: 88640247102350796577040881684578110160059
Probable prime cofactor 3669321860674046149889305251133408005163302741051006855356289605523585561498123504209 has 85 digits

Oct 15, 2009 (4th)

By Dmitry Domanov / YAFU v1.11/SIQS, Msieve, GGNFS, ECMNET / Oct 15, 2009

(59·10¹¹⁰+13)/9 = 6(5)₁₀₉7_<111> = 3² · 31 · 433 · 607 · 1753 · 492055353683_<12> · C89

C89 = P41 · P48

P41 = 79383400887881116058417233520726189876581_<41>

P48 = 130557893200089547416664789600785124972153290347_<48>

10/15/09 10:49:09 v1.11 @ DB-SERVER, starting SIQS on c89: 10364129574979876503127217254081877275064792906654360328149891993601289490418900988663607
10/15/09 10:49:09 v1.11 @ DB-SERVER, random seeds: 1344519226, 1972906752
10/15/09 10:49:10 v1.11 @ DB-SERVER, ==== sieve params ====
10/15/09 10:49:10 v1.11 @ DB-SERVER, n = 89 digits, 294 bits
10/15/09 10:49:10 v1.11 @ DB-SERVER, factor base: 62272 primes (max prime = 1654859)
10/15/09 10:49:10 v1.11 @ DB-SERVER, single large prime cutoff: 182034490 (110 * pmax)
10/15/09 10:49:10 v1.11 @ DB-SERVER, double large prime range from 43 to 50 bits
10/15/09 10:49:10 v1.11 @ DB-SERVER, double large prime cutoff: 738374392384870
10/15/09 10:49:10 v1.11 @ DB-SERVER, using 3159864 large prime slices of factor base
10/15/09 10:49:10 v1.11 @ DB-SERVER, buckets hold 1024 elements
10/15/09 10:49:10 v1.11 @ DB-SERVER, sieve interval: 18 blocks of size 32768
10/15/09 10:49:10 v1.11 @ DB-SERVER, polynomial A has ~ 0 factors
10/15/09 10:49:10 v1.11 @ DB-SERVER, using multiplier of 2
10/15/09 10:49:10 v1.11 @ DB-SERVER, using small prime variation correction of 20 bits
10/15/09 10:49:10 v1.11 @ DB-SERVER, using SSE2 for trial division and x128 sieve scanning
10/15/09 10:49:10 v1.11 @ DB-SERVER, trial factoring cutoff at 98 bits
10/15/09 10:49:10 v1.11 @ DB-SERVER, ==== sieving started ( 8 threads) ====
10/15/09 10:56:42 v1.11 @ DB-SERVER, sieve time = 112.7813, relation time = 53.9219, poly_time = 224.5469
10/15/09 10:56:42 v1.11 @ DB-SERVER, 63386 relations found: 19900 full + 43486 from 611150 partial, using 18049896 polys (743 A polys)
10/15/09 10:56:42 v1.11 @ DB-SERVER, on average, sieving found 0.03 rels/poly and 1390.89 rels/sec
10/15/09 10:56:42 v1.11 @ DB-SERVER, trial division touched 15764889 sieve locations out of 21292523716608
10/15/09 10:56:42 v1.11 @ DB-SERVER, ==== post processing stage (msieve-1.38) ====
10/15/09 10:56:43 v1.11 @ DB-SERVER, begin with 631050 relations
10/15/09 10:56:44 v1.11 @ DB-SERVER, reduce to 135193 relations in 10 passes
10/15/09 10:57:02 v1.11 @ DB-SERVER, failed to read relation 102445
10/15/09 10:57:04 v1.11 @ DB-SERVER, recovered 135192 relations
10/15/09 10:57:04 v1.11 @ DB-SERVER, recovered 114027 polynomials
10/15/09 10:57:05 v1.11 @ DB-SERVER, attempting to build 63385 cycles
10/15/09 10:57:05 v1.11 @ DB-SERVER, found 63385 cycles in 4 passes
10/15/09 10:57:05 v1.11 @ DB-SERVER, distribution of cycle lengths:
10/15/09 10:57:05 v1.11 @ DB-SERVER,    length 1 : 19900
10/15/09 10:57:05 v1.11 @ DB-SERVER,    length 2 : 16082
10/15/09 10:57:05 v1.11 @ DB-SERVER,    length 3 : 12004
10/15/09 10:57:05 v1.11 @ DB-SERVER,    length 4 : 7301
10/15/09 10:57:05 v1.11 @ DB-SERVER,    length 5 : 4010
10/15/09 10:57:05 v1.11 @ DB-SERVER,    length 6 : 2188
10/15/09 10:57:05 v1.11 @ DB-SERVER,    length 7 : 1060
10/15/09 10:57:05 v1.11 @ DB-SERVER,    length 9+: 840
10/15/09 10:57:05 v1.11 @ DB-SERVER, largest cycle: 14 relations
10/15/09 10:57:05 v1.11 @ DB-SERVER, matrix is 62272 x 63385 (13.4 MB) with weight 3246634 (51.22/col)
10/15/09 10:57:05 v1.11 @ DB-SERVER, sparse part has weight 3246634 (51.22/col)
10/15/09 10:57:05 v1.11 @ DB-SERVER, filtering completed in 4 passes
10/15/09 10:57:05 v1.11 @ DB-SERVER, matrix is 55816 x 55880 (11.8 MB) with weight 2866829 (51.30/col)
10/15/09 10:57:05 v1.11 @ DB-SERVER, sparse part has weight 2866829 (51.30/col)
10/15/09 10:57:06 v1.11 @ DB-SERVER, saving the first 48 matrix rows for later
10/15/09 10:57:06 v1.11 @ DB-SERVER, matrix is 55768 x 55880 (10.1 MB) with weight 2493883 (44.63/col)
10/15/09 10:57:06 v1.11 @ DB-SERVER, sparse part has weight 2314701 (41.42/col)
10/15/09 10:57:06 v1.11 @ DB-SERVER, matrix includes 64 packed rows
10/15/09 10:57:06 v1.11 @ DB-SERVER, using block size 22352 for processor cache size 4096 kB
10/15/09 10:57:06 v1.11 @ DB-SERVER, commencing Lanczos iteration
10/15/09 10:57:06 v1.11 @ DB-SERVER, memory use: 8.9 MB
10/15/09 10:57:31 v1.11 @ DB-SERVER, lanczos halted after 884 iterations (dim = 55768)
10/15/09 10:57:31 v1.11 @ DB-SERVER, recovered 18 nontrivial dependencies
10/15/09 10:57:32 v1.11 @ DB-SERVER, prp48 = 130557893200089547416664789600785124972153290347
10/15/09 10:57:34 v1.11 @ DB-SERVER, prp41 = 79383400887881116058417233520726189876581
10/15/09 10:57:34 v1.11 @ DB-SERVER, Lanczos elapsed time = 48.9380 seconds.
10/15/09 10:57:34 v1.11 @ DB-SERVER, Sqrt elapsed time = 2.5620 seconds.
10/15/09 10:57:34 v1.11 @ DB-SERVER, SIQS elapsed time = 505.2031 seconds.

(59·10¹²⁸+13)/9 = 6(5)₁₂₇7_<129> = 3² · 29 · 3163 · 6907 · 25308891017989766962105996429_<29> · C91

C91 = P45 · P47

P45 = 388037870916555061008960738628118331241660151_<45>

P47 = 11706663046031675214351099687927177731673630683_<47>

10/15/09 11:03:03 v1.11 @ DB-SERVER, starting SIQS on c91: 4542628603919644465075502386845628450173962547307743182559982213018865442956437146572013133
10/15/09 11:03:03 v1.11 @ DB-SERVER, random seeds: 1344519226, 1972906752
10/15/09 11:03:04 v1.11 @ DB-SERVER, ==== sieve params ====
10/15/09 11:03:04 v1.11 @ DB-SERVER, n = 92 digits, 305 bits
10/15/09 11:03:04 v1.11 @ DB-SERVER, factor base: 69579 primes (max prime = 1856333)
10/15/09 11:03:04 v1.11 @ DB-SERVER, single large prime cutoff: 222759960 (120 * pmax)
10/15/09 11:03:04 v1.11 @ DB-SERVER, double large prime range from 43 to 50 bits
10/15/09 11:03:04 v1.11 @ DB-SERVER, double large prime cutoff: 1061956765889454
10/15/09 11:03:04 v1.11 @ DB-SERVER, using 875902009 large prime slices of factor base
10/15/09 11:03:04 v1.11 @ DB-SERVER, buckets hold 1024 elements
10/15/09 11:03:04 v1.11 @ DB-SERVER, sieve interval: 22 blocks of size 32768
10/15/09 11:03:04 v1.11 @ DB-SERVER, polynomial A has ~ 538443777 factors
10/15/09 11:03:04 v1.11 @ DB-SERVER, using multiplier of 13
10/15/09 11:03:04 v1.11 @ DB-SERVER, using small prime variation correction of 20 bits
10/15/09 11:03:04 v1.11 @ DB-SERVER, using SSE2 for trial division and x128 sieve scanning
10/15/09 11:03:04 v1.11 @ DB-SERVER, trial factoring cutoff at 97 bits
10/15/09 11:03:04 v1.11 @ DB-SERVER, ==== sieving started ( 8 threads) ====
10/15/09 11:22:00 v1.11 @ DB-SERVER, sieve time = 226.7188, relation time = 109.3594, poly_time = 408.7031
10/15/09 11:22:00 v1.11 @ DB-SERVER, 70162 relations found: 18480 full + 51682 from 889705 partial, using 29037424 polys (855 A polys)
10/15/09 11:22:00 v1.11 @ DB-SERVER, on average, sieving found 0.03 rels/poly and 799.02 rels/sec
10/15/09 11:22:00 v1.11 @ DB-SERVER, trial division touched 35103913 sieve locations out of 41865925623808
10/15/09 11:22:00 v1.11 @ DB-SERVER, ==== post processing stage (msieve-1.38) ====
10/15/09 11:22:01 v1.11 @ DB-SERVER, begin with 908185 relations
10/15/09 11:22:02 v1.11 @ DB-SERVER, reduce to 171825 relations in 10 passes
10/15/09 11:22:21 v1.11 @ DB-SERVER, recovered 171825 relations
10/15/09 11:22:21 v1.11 @ DB-SERVER, recovered 147381 polynomials
10/15/09 11:22:21 v1.11 @ DB-SERVER, attempting to build 70162 cycles
10/15/09 11:22:21 v1.11 @ DB-SERVER, found 70162 cycles in 6 passes
10/15/09 11:22:21 v1.11 @ DB-SERVER, distribution of cycle lengths:
10/15/09 11:22:21 v1.11 @ DB-SERVER,    length 1 : 18480
10/15/09 11:22:21 v1.11 @ DB-SERVER,    length 2 : 13955
10/15/09 11:22:21 v1.11 @ DB-SERVER,    length 3 : 12442
10/15/09 11:22:21 v1.11 @ DB-SERVER,    length 4 : 9383
10/15/09 11:22:21 v1.11 @ DB-SERVER,    length 5 : 6554
10/15/09 11:22:21 v1.11 @ DB-SERVER,    length 6 : 4095
10/15/09 11:22:21 v1.11 @ DB-SERVER,    length 7 : 2377
10/15/09 11:22:21 v1.11 @ DB-SERVER,    length 9+: 2876
10/15/09 11:22:21 v1.11 @ DB-SERVER, largest cycle: 17 relations
10/15/09 11:22:22 v1.11 @ DB-SERVER, matrix is 69579 x 70162 (17.5 MB) with weight 4314262 (61.49/col)
10/15/09 11:22:22 v1.11 @ DB-SERVER, sparse part has weight 4314262 (61.49/col)
10/15/09 11:22:22 v1.11 @ DB-SERVER, filtering completed in 3 passes
10/15/09 11:22:22 v1.11 @ DB-SERVER, matrix is 65189 x 65253 (16.3 MB) with weight 4022563 (61.65/col)
10/15/09 11:22:22 v1.11 @ DB-SERVER, sparse part has weight 4022563 (61.65/col)
10/15/09 11:22:23 v1.11 @ DB-SERVER, saving the first 48 matrix rows for later
10/15/09 11:22:23 v1.11 @ DB-SERVER, matrix is 65141 x 65253 (14.0 MB) with weight 3551848 (54.43/col)
10/15/09 11:22:23 v1.11 @ DB-SERVER, sparse part has weight 3288973 (50.40/col)
10/15/09 11:22:23 v1.11 @ DB-SERVER, matrix includes 64 packed rows
10/15/09 11:22:23 v1.11 @ DB-SERVER, using block size 26101 for processor cache size 4096 kB
10/15/09 11:22:23 v1.11 @ DB-SERVER, commencing Lanczos iteration
10/15/09 11:22:24 v1.11 @ DB-SERVER, memory use: 11.9 MB
10/15/09 11:23:03 v1.11 @ DB-SERVER, lanczos halted after 1032 iterations (dim = 65138)
10/15/09 11:23:03 v1.11 @ DB-SERVER, recovered 16 nontrivial dependencies
10/15/09 11:23:05 v1.11 @ DB-SERVER, prp45 = 388037870916555061008960738628118331241660151
10/15/09 11:23:06 v1.11 @ DB-SERVER, prp47 = 11706663046031675214351099687927177731673630683
10/15/09 11:23:06 v1.11 @ DB-SERVER, Lanczos elapsed time = 63.3600 seconds.
10/15/09 11:23:06 v1.11 @ DB-SERVER, Sqrt elapsed time = 2.7500 seconds.
10/15/09 11:23:06 v1.11 @ DB-SERVER, SIQS elapsed time = 1202.7344 seconds.

(59·10¹²¹+31)/9 = 6(5)₁₂₀9_<122> = 3 · 19 · 53898503 · 27129825864773534023226576461_<29> · C84

C84 = P41 · P44

P41 = 49585585839260812980296174140738246117879_<41>

P44 = 15861910263201857558262504213501787137788891_<44>

10/15/09 11:26:17 v1.11 @ DB-SERVER, starting SIQS on c84: 786522112930647783028412494827668993729597868210456036262629440824180003640602682189
10/15/09 11:26:17 v1.11 @ DB-SERVER, random seeds: 1344519226, 1972906752
10/15/09 11:26:18 v1.11 @ DB-SERVER, ==== sieve params ====
10/15/09 11:26:18 v1.11 @ DB-SERVER, n = 85 digits, 282 bits
10/15/09 11:26:18 v1.11 @ DB-SERVER, factor base: 53604 primes (max prime = 1408241)
10/15/09 11:26:18 v1.11 @ DB-SERVER, single large prime cutoff: 133782895 (95 * pmax)
10/15/09 11:26:18 v1.11 @ DB-SERVER, double large prime range from 42 to 49 bits
10/15/09 11:26:18 v1.11 @ DB-SERVER, double large prime cutoff: 424151552894538
10/15/09 11:26:18 v1.11 @ DB-SERVER, using 3683125 large prime slices of factor base
10/15/09 11:26:18 v1.11 @ DB-SERVER, buckets hold 1024 elements
10/15/09 11:26:18 v1.11 @ DB-SERVER, sieve interval: 14 blocks of size 32768
10/15/09 11:26:18 v1.11 @ DB-SERVER, polynomial A has ~ 4456449 factors
10/15/09 11:26:18 v1.11 @ DB-SERVER, using multiplier of 5
10/15/09 11:26:18 v1.11 @ DB-SERVER, using small prime variation correction of 20 bits
10/15/09 11:26:18 v1.11 @ DB-SERVER, using SSE2 for trial division and x128 sieve scanning
10/15/09 11:26:18 v1.11 @ DB-SERVER, trial factoring cutoff at 91 bits
10/15/09 11:26:18 v1.11 @ DB-SERVER, ==== sieving started ( 8 threads) ====
10/15/09 11:29:48 v1.11 @ DB-SERVER, sieve time = 40.4219, relation time = 42.5313, poly_time = 75.6875
10/15/09 11:29:48 v1.11 @ DB-SERVER, 54303 relations found: 17846 full + 36457 from 515948 partial, using 4615496 polys (423 A polys)
10/15/09 11:29:48 v1.11 @ DB-SERVER, on average, sieving found 0.12 rels/poly and 2530.39 rels/sec
10/15/09 11:29:48 v1.11 @ DB-SERVER, trial division touched 12004008 sieve locations out of 4234736041984
10/15/09 11:29:48 v1.11 @ DB-SERVER, ==== post processing stage (msieve-1.38) ====
10/15/09 11:29:49 v1.11 @ DB-SERVER, begin with 533794 relations
10/15/09 11:29:49 v1.11 @ DB-SERVER, reduce to 114564 relations in 9 passes
10/15/09 11:29:54 v1.11 @ DB-SERVER, recovered 114564 relations
10/15/09 11:29:54 v1.11 @ DB-SERVER, recovered 83430 polynomials
10/15/09 11:29:54 v1.11 @ DB-SERVER, attempting to build 54303 cycles
10/15/09 11:29:54 v1.11 @ DB-SERVER, found 54303 cycles in 5 passes
10/15/09 11:29:54 v1.11 @ DB-SERVER, distribution of cycle lengths:
10/15/09 11:29:54 v1.11 @ DB-SERVER,    length 1 : 17846
10/15/09 11:29:54 v1.11 @ DB-SERVER,    length 2 : 13793
10/15/09 11:29:54 v1.11 @ DB-SERVER,    length 3 : 10091
10/15/09 11:29:54 v1.11 @ DB-SERVER,    length 4 : 5975
10/15/09 11:29:54 v1.11 @ DB-SERVER,    length 5 : 3378
10/15/09 11:29:54 v1.11 @ DB-SERVER,    length 6 : 1681
10/15/09 11:29:54 v1.11 @ DB-SERVER,    length 7 : 833
10/15/09 11:29:54 v1.11 @ DB-SERVER,    length 9+: 706
10/15/09 11:29:54 v1.11 @ DB-SERVER, largest cycle: 16 relations
10/15/09 11:29:54 v1.11 @ DB-SERVER, matrix is 53604 x 54303 (10.8 MB) with weight 2622699 (48.30/col)
10/15/09 11:29:54 v1.11 @ DB-SERVER, sparse part has weight 2622699 (48.30/col)
10/15/09 11:29:55 v1.11 @ DB-SERVER, filtering completed in 4 passes
10/15/09 11:29:55 v1.11 @ DB-SERVER, matrix is 46804 x 46868 (9.4 MB) with weight 2289260 (48.84/col)
10/15/09 11:29:55 v1.11 @ DB-SERVER, sparse part has weight 2289260 (48.84/col)
10/15/09 11:29:55 v1.11 @ DB-SERVER, saving the first 48 matrix rows for later
10/15/09 11:29:55 v1.11 @ DB-SERVER, matrix is 46756 x 46868 (7.7 MB) with weight 1933098 (41.25/col)
10/15/09 11:29:55 v1.11 @ DB-SERVER, sparse part has weight 1749204 (37.32/col)
10/15/09 11:29:55 v1.11 @ DB-SERVER, matrix includes 64 packed rows
10/15/09 11:29:55 v1.11 @ DB-SERVER, using block size 18747 for processor cache size 4096 kB
10/15/09 11:29:56 v1.11 @ DB-SERVER, commencing Lanczos iteration
10/15/09 11:29:56 v1.11 @ DB-SERVER, memory use: 7.1 MB
10/15/09 11:30:11 v1.11 @ DB-SERVER, lanczos halted after 741 iterations (dim = 46751)
10/15/09 11:30:12 v1.11 @ DB-SERVER, recovered 15 nontrivial dependencies
10/15/09 11:30:13 v1.11 @ DB-SERVER, prp41 = 49585585839260812980296174140738246117879
10/15/09 11:30:13 v1.11 @ DB-SERVER, prp44 = 15861910263201857558262504213501787137788891
10/15/09 11:30:13 v1.11 @ DB-SERVER, Lanczos elapsed time = 23.2190 seconds.
10/15/09 11:30:13 v1.11 @ DB-SERVER, Sqrt elapsed time = 1.5310 seconds.
10/15/09 11:30:13 v1.11 @ DB-SERVER, SIQS elapsed time = 235.7031 seconds.

(59·10¹¹⁷+31)/9 = 6(5)₁₁₆9_<118> = 7 · 149 · 21611 · 77141 · 10743395076680282999_<20> · C87

C87 = P37 · P51

P37 = 1006339068803322500630304410519443319_<37>

P51 = 348721870691372066316258363091558353915003674550923_<51>

10/15/09 11:32:39 v1.11 @ DB-SERVER, starting SIQS on c87: 350932442622908006046208304245469699700822566574232521739951595142937689076357277633437
10/15/09 11:32:39 v1.11 @ DB-SERVER, random seeds: 1344519226, 1972906752
10/15/09 11:32:39 v1.11 @ DB-SERVER, ==== sieve params ====
10/15/09 11:32:39 v1.11 @ DB-SERVER, n = 88 digits, 292 bits
10/15/09 11:32:39 v1.11 @ DB-SERVER, factor base: 59299 primes (max prime = 1563811)
10/15/09 11:32:39 v1.11 @ DB-SERVER, single large prime cutoff: 172019210 (110 * pmax)
10/15/09 11:32:39 v1.11 @ DB-SERVER, double large prime range from 43 to 50 bits
10/15/09 11:32:39 v1.11 @ DB-SERVER, double large prime cutoff: 666865896067036
10/15/09 11:32:39 v1.11 @ DB-SERVER, using 3552048 large prime slices of factor base
10/15/09 11:32:39 v1.11 @ DB-SERVER, buckets hold 1024 elements
10/15/09 11:32:39 v1.11 @ DB-SERVER, sieve interval: 18 blocks of size 32768
10/15/09 11:32:39 v1.11 @ DB-SERVER, polynomial A has ~ 0 factors
10/15/09 11:32:39 v1.11 @ DB-SERVER, using multiplier of 13
10/15/09 11:32:39 v1.11 @ DB-SERVER, using small prime variation correction of 20 bits
10/15/09 11:32:39 v1.11 @ DB-SERVER, using SSE2 for trial division and x128 sieve scanning
10/15/09 11:32:39 v1.11 @ DB-SERVER, trial factoring cutoff at 97 bits
10/15/09 11:32:39 v1.11 @ DB-SERVER, ==== sieving started ( 8 threads) ====
10/15/09 11:37:46 v1.11 @ DB-SERVER, sieve time = 82.0781, relation time = 40.9531, poly_time = 143.0938
10/15/09 11:37:46 v1.11 @ DB-SERVER, 60057 relations found: 20679 full + 39378 from 537344 partial, using 8253696 polys (503 A polys)
10/15/09 11:37:46 v1.11 @ DB-SERVER, on average, sieving found 0.07 rels/poly and 1817.76 rels/sec
10/15/09 11:37:46 v1.11 @ DB-SERVER, trial division touched 10999568 sieve locations out of 9736455979008
10/15/09 11:37:46 v1.11 @ DB-SERVER, ==== post processing stage (msieve-1.38) ====
10/15/09 11:37:47 v1.11 @ DB-SERVER, begin with 558023 relations
10/15/09 11:37:47 v1.11 @ DB-SERVER, reduce to 120144 relations in 10 passes
10/15/09 11:37:57 v1.11 @ DB-SERVER, recovered 120144 relations
10/15/09 11:37:57 v1.11 @ DB-SERVER, recovered 95960 polynomials
10/15/09 11:37:57 v1.11 @ DB-SERVER, attempting to build 60057 cycles
10/15/09 11:37:57 v1.11 @ DB-SERVER, found 60057 cycles in 5 passes
10/15/09 11:37:57 v1.11 @ DB-SERVER, distribution of cycle lengths:
10/15/09 11:37:57 v1.11 @ DB-SERVER,    length 1 : 20679
10/15/09 11:37:57 v1.11 @ DB-SERVER,    length 2 : 17162
10/15/09 11:37:57 v1.11 @ DB-SERVER,    length 3 : 11039
10/15/09 11:37:57 v1.11 @ DB-SERVER,    length 4 : 5919
10/15/09 11:37:57 v1.11 @ DB-SERVER,    length 5 : 2987
10/15/09 11:37:57 v1.11 @ DB-SERVER,    length 6 : 1259
10/15/09 11:37:57 v1.11 @ DB-SERVER,    length 7 : 615
10/15/09 11:37:57 v1.11 @ DB-SERVER,    length 9+: 397
10/15/09 11:37:57 v1.11 @ DB-SERVER, largest cycle: 15 relations
10/15/09 11:37:58 v1.11 @ DB-SERVER, matrix is 59299 x 60057 (11.6 MB) with weight 2806270 (46.73/col)
10/15/09 11:37:58 v1.11 @ DB-SERVER, sparse part has weight 2806270 (46.73/col)
10/15/09 11:37:59 v1.11 @ DB-SERVER, filtering completed in 4 passes
10/15/09 11:37:59 v1.11 @ DB-SERVER, matrix is 51616 x 51680 (10.1 MB) with weight 2451748 (47.44/col)
10/15/09 11:37:59 v1.11 @ DB-SERVER, sparse part has weight 2451748 (47.44/col)
10/15/09 11:37:59 v1.11 @ DB-SERVER, saving the first 48 matrix rows for later
10/15/09 11:37:59 v1.11 @ DB-SERVER, matrix is 51568 x 51680 (8.6 MB) with weight 2106940 (40.77/col)
10/15/09 11:37:59 v1.11 @ DB-SERVER, sparse part has weight 1933573 (37.41/col)
10/15/09 11:37:59 v1.11 @ DB-SERVER, matrix includes 64 packed rows
10/15/09 11:37:59 v1.11 @ DB-SERVER, using block size 20672 for processor cache size 4096 kB
10/15/09 11:38:00 v1.11 @ DB-SERVER, commencing Lanczos iteration
10/15/09 11:38:00 v1.11 @ DB-SERVER, memory use: 7.8 MB
10/15/09 11:38:19 v1.11 @ DB-SERVER, lanczos halted after 817 iterations (dim = 51560)
10/15/09 11:38:19 v1.11 @ DB-SERVER, recovered 12 nontrivial dependencies
10/15/09 11:38:21 v1.11 @ DB-SERVER, prp37 = 1006339068803322500630304410519443319
10/15/09 11:38:22 v1.11 @ DB-SERVER, prp51 = 348721870691372066316258363091558353915003674550923
10/15/09 11:38:22 v1.11 @ DB-SERVER, Lanczos elapsed time = 33.1250 seconds.
10/15/09 11:38:22 v1.11 @ DB-SERVER, Sqrt elapsed time = 2.7500 seconds.
10/15/09 11:38:22 v1.11 @ DB-SERVER, SIQS elapsed time = 342.8594 seconds.

(59·10¹¹¹+31)/9 = 6(5)₁₁₀9_<112> = 7² · 23 · 7099524661_<10> · 97037762429_<11> · C88

C88 = P41 · P48

P41 = 13591305598907925889100220889634951249279_<41>

P48 = 621232778672766303826611081595480582684960831967_<48>

10/15/09 11:39:04 v1.11 @ DB-SERVER, starting SIQS on c88: 8443364543000296998259060102897487391031322808944578108402658675669115095005629848901793
10/15/09 11:39:04 v1.11 @ DB-SERVER, random seeds: 1344519226, 1972906752
10/15/09 11:40:59 v1.11 @ DB-SERVER, starting SIQS on c88: 8443364543000296998259060102897487391031322808944578108402658675669115095005629848901793
10/15/09 11:40:59 v1.11 @ DB-SERVER, random seeds: 3553357154, 3455292184
10/15/09 11:40:59 v1.11 @ DB-SERVER, ==== sieve params ====
10/15/09 11:40:59 v1.11 @ DB-SERVER, n = 88 digits, 293 bits
10/15/09 11:40:59 v1.11 @ DB-SERVER, factor base: 62272 primes (max prime = 1648081)
10/15/09 11:40:59 v1.11 @ DB-SERVER, single large prime cutoff: 181288910 (110 * pmax)
10/15/09 11:40:59 v1.11 @ DB-SERVER, double large prime range from 43 to 50 bits
10/15/09 11:40:59 v1.11 @ DB-SERVER, double large prime cutoff: 732939669490134
10/15/09 11:40:59 v1.11 @ DB-SERVER, using 3420977 large prime slices of factor base
10/15/09 11:40:59 v1.11 @ DB-SERVER, buckets hold 1024 elements
10/15/09 11:40:59 v1.11 @ DB-SERVER, sieve interval: 18 blocks of size 32768
10/15/09 11:40:59 v1.11 @ DB-SERVER, polynomial A has ~ 0 factors
10/15/09 11:40:59 v1.11 @ DB-SERVER, using multiplier of 1
10/15/09 11:40:59 v1.11 @ DB-SERVER, using small prime variation correction of 19 bits
10/15/09 11:40:59 v1.11 @ DB-SERVER, using SSE2 for trial division and x128 sieve scanning
10/15/09 11:40:59 v1.11 @ DB-SERVER, trial factoring cutoff at 99 bits
10/15/09 11:40:59 v1.11 @ DB-SERVER, ==== sieving started ( 8 threads) ====
10/15/09 11:46:35 v1.11 @ DB-SERVER, sieve time = 94.3594, relation time = 34.8906, poly_time = 179.8125
10/15/09 11:46:35 v1.11 @ DB-SERVER, 63213 relations found: 20750 full + 42463 from 567952 partial, using 11344200 polys (591 A polys)
10/15/09 11:46:35 v1.11 @ DB-SERVER, on average, sieving found 0.05 rels/poly and 1748.35 rels/sec
10/15/09 11:46:35 v1.11 @ DB-SERVER, trial division touched 9909419 sieve locations out of 13382162841600
10/15/09 11:46:35 v1.11 @ DB-SERVER, ==== post processing stage (msieve-1.38) ====
10/15/09 11:46:36 v1.11 @ DB-SERVER, begin with 588782 relations
10/15/09 11:46:36 v1.11 @ DB-SERVER, reduce to 129673 relations in 9 passes
10/15/09 11:46:43 v1.11 @ DB-SERVER, failed to read relation 27450
10/15/09 11:49:23 v1.11 @ DB-SERVER, recovered 129672 relations
10/15/09 11:49:23 v1.11 @ DB-SERVER, recovered 110212 polynomials
10/15/09 11:49:24 v1.11 @ DB-SERVER, attempting to build 63208 cycles
10/15/09 11:49:24 v1.11 @ DB-SERVER, found 63208 cycles in 5 passes
10/15/09 11:49:24 v1.11 @ DB-SERVER, distribution of cycle lengths:
10/15/09 11:49:24 v1.11 @ DB-SERVER,    length 1 : 20749
10/15/09 11:49:24 v1.11 @ DB-SERVER,    length 2 : 17320
10/15/09 11:49:24 v1.11 @ DB-SERVER,    length 3 : 11955
10/15/09 11:49:24 v1.11 @ DB-SERVER,    length 4 : 6663
10/15/09 11:49:24 v1.11 @ DB-SERVER,    length 5 : 3524
10/15/09 11:49:24 v1.11 @ DB-SERVER,    length 6 : 1686
10/15/09 11:49:24 v1.11 @ DB-SERVER,    length 7 : 732
10/15/09 11:49:24 v1.11 @ DB-SERVER,    length 9+: 579
10/15/09 11:49:24 v1.11 @ DB-SERVER, largest cycle: 16 relations
10/15/09 11:49:24 v1.11 @ DB-SERVER, matrix is 62272 x 63208 (12.5 MB) with weight 3031794 (47.97/col)
10/15/09 11:49:24 v1.11 @ DB-SERVER, sparse part has weight 3031794 (47.97/col)
10/15/09 11:49:24 v1.11 @ DB-SERVER, filtering completed in 4 passes
10/15/09 11:49:24 v1.11 @ DB-SERVER, matrix is 55233 x 55297 (11.1 MB) with weight 2678208 (48.43/col)
10/15/09 11:49:24 v1.11 @ DB-SERVER, sparse part has weight 2678208 (48.43/col)
10/15/09 11:49:25 v1.11 @ DB-SERVER, saving the first 48 matrix rows for later
10/15/09 11:49:25 v1.11 @ DB-SERVER, matrix is 55185 x 55297 (9.5 MB) with weight 2346295 (42.43/col)
10/15/09 11:49:25 v1.11 @ DB-SERVER, sparse part has weight 2169291 (39.23/col)
10/15/09 11:49:25 v1.11 @ DB-SERVER, matrix includes 64 packed rows
10/15/09 11:49:25 v1.11 @ DB-SERVER, using block size 22118 for processor cache size 4096 kB
10/15/09 11:49:25 v1.11 @ DB-SERVER, commencing Lanczos iteration
10/15/09 11:49:25 v1.11 @ DB-SERVER, memory use: 8.6 MB
10/15/09 11:49:49 v1.11 @ DB-SERVER, lanczos halted after 874 iterations (dim = 55182)
10/15/09 11:49:49 v1.11 @ DB-SERVER, recovered 15 nontrivial dependencies
10/15/09 11:49:49 v1.11 @ DB-SERVER, prp48 = 621232778672766303826611081595480582684960831967
10/15/09 11:49:51 v1.11 @ DB-SERVER, prp41 = 13591305598907925889100220889634951249279
10/15/09 11:49:51 v1.11 @ DB-SERVER, Lanczos elapsed time = 193.4850 seconds.
10/15/09 11:49:51 v1.11 @ DB-SERVER, Sqrt elapsed time = 1.7970 seconds.
10/15/09 11:49:51 v1.11 @ DB-SERVER, SIQS elapsed time = 532.0000 seconds.

(59·10¹¹²+13)/9 = 6(5)₁₁₁7_<113> = C113

C113 = P55 · P59

P55 = 1188089508824001504560958518820730054517080662378037633_<55>

P59 = 55177286785777581520805192991429931927549802414792232067429_<59>

Number: snfs113
N=65555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557
  ( 113 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=1188089508824001504560958518820730054517080662378037633 (pp55)
 r2=55177286785777581520805192991429931927549802414792232067429 (pp59)
Version: Msieve-1.40
Total time: 1.03 hours.
Scaled time: 2.03 units (timescale=1.975).
Factorization parameters were as follows:
n: 65555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557
m: 20000000000000000000000
deg: 5
c5: 1475
c0: 104
skew: 0.59
type: snfs
lss: 1
rlim: 570000
alim: 570000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 570000/570000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [285000, 535001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 65504 x 65729
Total sieving time: 0.99 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,114.000,5,0,0,0,0,0,0,0,0,570000,570000,25,25,45,45,2.2,2.2,50000
total time: 1.03 hours.
 --------- CPU info (if available) ----------

(59·10¹¹⁹+13)/9 = 6(5)₁₁₈7_<120> = 3³ · 7 · C118

C118 = P37 · P38 · P44

P37 = 1736960267193906384095189045045358053_<37>

P38 = 21996508258490260973039613031960873529_<38>

P44 = 90782903336123624963421654695248978637772349_<44>

Number: snfs118
N=3468547912992357436801881246325690770135214579659024103468547912992357436801881246325690770135214579659024103468547913
  ( 118 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=1736960267193906384095189045045358053 (pp37)
 r2=21996508258490260973039613031960873529 (pp38)
 r3=90782903336123624963421654695248978637772349 (pp44)
Version: Msieve-1.40
Total time: 1.15 hours.
Scaled time: 2.27 units (timescale=1.969).
Factorization parameters were as follows:
n: 3468547912992357436801881246325690770135214579659024103468547912992357436801881246325690770135214579659024103468547913
m: 1000000000000000000000000
deg: 5
c5: 59
c0: 130
skew: 1.17
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 625001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 93874 x 94099
Total sieving time: 1.10 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 1.15 hours.
 --------- CPU info (if available) ----------

(59·10¹⁴⁸+13)/9 = 6(5)₁₄₇7_<149> = 53 · 151 · 199 · C143

C143 = P34 · P110

P34 = 3076164667088108516745389482013017_<34>

P110 = 13381168187372788462574554082701315063843264662751447519557625636265408132014611579978744571007801716168358393_<110>

C143=P34*P110
P34=3076164667088108516745389482013017

(59·10¹²³+31)/9 = 6(5)₁₂₂9_<124> = 7 · C123

C123 = P44 · P80

P44 = 67796015868967415476904212737855081432567281_<44>

P80 = 13813613152695726854162911859174511245014894719610845098773886175320964172803377_<80>

Number: snfs123
N=936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937
  ( 123 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=67796015868967415476904212737855081432567281 (pp44)
 r2=13813613152695726854162911859174511245014894719610845098773886175320964172803377 (pp80)
Version: Msieve-1.40
Total time: 1.71 hours.
Scaled time: 3.37 units (timescale=1.969).
Factorization parameters were as follows:
n: 936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937
m: 5000000000000000000000000
deg: 5
c5: 472
c0: 775
skew: 1.10
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 795001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 141708 x 141956
Total sieving time: 1.62 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 1.71 hours.
 --------- CPU info (if available) ----------

Oct 15, 2009 (3rd)

By Erik Branger / GGNFS, Msieve / Oct 15, 2009

(59·10¹⁰⁵+13)/9 = 6(5)₁₀₄7_<106> = 113 · C104

C104 = P47 · P57

P47 = 89044848505139686952915504208989039493279059687_<47>

P57 = 651511760110627643845574012013444624423762847008384690947_<57>

Number: 65557_105
N=58013765978367748279252704031465093411996066863323500491642084562438544739429695181907571288102261553589
  ( 104 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=89044848505139686952915504208989039493279059687 (pp47)
 r2=651511760110627643845574012013444624423762847008384690947 (pp57)
Version: Msieve-1.40
Total time: 0.50 hours.
Scaled time: 0.49 units (timescale=0.983).
Factorization parameters were as follows:
n: 58013765978367748279252704031465093411996066863323500491642084562438544739429695181907571288102261553589
m: 200000000000000000000000000
deg: 4
c4: 295
c0: 104
skew: 0.77
type: snfs
lss: 1
rlim: 440000
alim: 440000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 440000/440000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [220000, 300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 37846 x 38071
Total sieving time: 0.48 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107.000,4,0,0,0,0,0,0,0,0,440000,440000,25,25,44,44,2.2,2.2,20000
total time: 0.50 hours.
 --------- CPU info (if available) ----------

(59·10¹¹⁰+31)/9 = 6(5)₁₀₉9_<111> = 67 · C109

C109 = P34 · P76

P34 = 2059102914028292755130681069223181_<34>

P76 = 4751783512270892417414894843292320160601424521926456341003456625783895801217_<76>

Number: 65559_110
N=9784411276948590381426202321724709784411276948590381426202321724709784411276948590381426202321724709784411277
  ( 109 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=2059102914028292755130681069223181 (pp34)
 r2=4751783512270892417414894843292320160601424521926456341003456625783895801217 (pp76)
Version: Msieve-1.40
Total time: 0.85 hours.
Scaled time: 0.86 units (timescale=1.006).
Factorization parameters were as follows:
n: 9784411276948590381426202321724709784411276948590381426202321724709784411276948590381426202321724709784411277
m: 10000000000000000000000
deg: 5
c5: 59
c0: 31
skew: 0.88
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [255000, 405001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 46749 x 46976
Total sieving time: 0.83 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.85 hours.
 --------- CPU info (if available) ----------

(59·10¹¹¹+13)/9 = 6(5)₁₁₀7_<112> = 439 · 11927 · C106

C106 = P37 · P69

P37 = 8734694642299804010496711075496249163_<37>

P69 = 143339549665432578318932537462122730827724811404061270500557851348863_<69>

Number: 65557_111
N=1252027196492320606307114589369987766421042273594807966296786001622924337853215175070432365522676684751669
  ( 106 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=8734694642299804010496711075496249163 (pp37)
 r2=143339549665432578318932537462122730827724811404061270500557851348863 (pp69)
Version: Msieve-1.40
Total time: 1.04 hours.
Scaled time: 1.02 units (timescale=0.979).
Factorization parameters were as follows:
n: 1252027196492320606307114589369987766421042273594807966296786001622924337853215175070432365522676684751669
m: 20000000000000000000000
deg: 5
c5: 295
c0: 208
skew: 0.93
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [280000, 480001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 65478 x 65703
Total sieving time: 1.01 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,113.000,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000
total time: 1.04 hours.
 --------- CPU info (if available) ----------

(59·10¹¹⁷+13)/9 = 6(5)₁₁₆7_<118> = 77621 · 448529057554232471_<18> · C96

C96 = P42 · P54

P42 = 203428417563359135166031212662690530896047_<42>

P54 = 925610055995915867960673659959661342458083279262053241_<54>

Number: 65557_117
N=188295388971981404131261747856072315862697613453392705361511379866453078255604311299432750438327
  ( 96 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=203428417563359135166031212662690530896047 (pp42)
 r2=925610055995915867960673659959661342458083279262053241 (pp54)
Version: Msieve-1.40
Total time: 1.85 hours.
Scaled time: 1.84 units (timescale=0.997).
Factorization parameters were as follows:
n: 188295388971981404131261747856072315862697613453392705361511379866453078255604311299432750438327
m: 200000000000000000000000
deg: 5
c5: 1475
c0: 104
skew: 0.59
type: snfs
lss: 1
rlim: 690000
alim: 690000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 690000/690000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [345000, 695001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 81706 x 81931
Total sieving time: 1.79 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,119.000,5,0,0,0,0,0,0,0,0,690000,690000,25,25,45,45,2.2,2.2,50000
total time: 1.85 hours.
 --------- CPU info (if available) ----------

(59·10¹²⁶+13)/9 = 6(5)₁₂₅7_<127> = 83 · 311 · 2308817372749_<13> · 426718586346187_<15> · C96

C96 = P35 · P62

P35 = 18919908904716415662053348709684209_<35>

P62 = 13624508322953365952503185313920601420001183323669772126013967_<62>

Number: 65557_126
N=257774456341828307211875452312310580375006737357665999128945835024477312715502955571986493347103
  ( 96 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=18919908904716415662053348709684209 (pp35)
 r2=13624508322953365952503185313920601420001183323669772126013967 (pp62)
Version: Msieve-1.40
Total time: 2.74 hours.
Scaled time: 2.47 units (timescale=0.902).
Factorization parameters were as follows:
n: 257774456341828307211875452312310580375006737357665999128945835024477312715502955571986493347103 
m: 20000000000000000000000000
deg: 5
c5: 295
c0: 208
skew: 0.93
type: snfs
lss: 1
rlim: 990000
alim: 990000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 990000/990000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [495000, 945001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 151331 x 151557
Total sieving time: 2.63 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,128.000,5,0,0,0,0,0,0,0,0,990000,990000,26,26,47,47,2.3,2.3,50000
total time: 2.74 hours.
 --------- CPU info (if available) ----------

Oct 15, 2009 (2nd)

By matsui / Msieve / Oct 15, 2009

(17·10¹⁹⁶+1)/9 = 1(8)₁₉₅9_<197> = 13² · 1567 · C191

C191 = P71 · P120

P71 = 76185120133903791191690400321137479269091823110582049300522285191069163_<71>

P120 = 936225690358746416834066797014232431566481342739412821308251213266451379641923167403248207342648269437398079244571833261_<120>

N=71326466692428108166167171616094103944479478326613960603455473614032349489617174070563693066270259338837219157281991703473221317215230130649108607971697658016444526679664866302733859554830543
  ( 191 digits)
SNFS difficulty: 198 digits.
Divisors found:
 r1=76185120133903791191690400321137479269091823110582049300522285191069163 (pp71)
 r2=936225690358746416834066797014232431566481342739412821308251213266451379641923167403248207342648269437398079244571833261 (pp120)
Version: Msieve v. 1.42
Total time: 985.18 hours.
Scaled time: 2773.28 units (timescale=2.815).
Factorization parameters were as follows:
n: 71326466692428108166167171616094103944479478326613960603455473614032349489617174070563693066270259338837219157281991703473221317215230130649108607971697658016444526679664866302733859554830543
m: 2000000000000000000000000000000000000000
deg: 5
c5: 85
c0: 16
skew: 0.72
type: snfs
lss: 1
rlim: 14200000
alim: 14200000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 400000
Factor base limits: 14200000/14200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [7100000, 14300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2354821 x 2355050
Total sieving time: 977.67 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 7.12 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,198.000,5,0,0,0,0,0,0,0,0,14200000,14200000,28,28,55,55,2.5,2.5,100000
total time: 985.18 hours.

Oct 15, 2009

Factorizations of 655...557 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Factorizations of 655...559 have been extended up to n=125. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 14, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Oct 14, 2009

(13·10¹⁷³-31)/9 = 1(4)₁₇₂1_<174> = 3 · 11 · 61 · 241 · 3529 · C164

C164 = P42 · P123

P42 = 825797712453284854898455720327785686620847_<42>

P123 = 102167952869081650152765818487263698573598530904222949149986942533196188277263383377597803183509917577439764618936491835579_<123>

Number: 14441_173
N=84370061765322647928872401971571207460554744255313121875885604347392453902982301215842039579141719551627224992917852082827356743544863594372624173011525868837715413
  ( 164 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=825797712453284854898455720327785686620847 (pp42)
 r2=102167952869081650152765818487263698573598530904222949149986942533196188277263383377597803183509917577439764618936491835579 (pp123)
Version: Msieve-1.40
Total time: 66.57 hours.
Scaled time: 115.77 units (timescale=1.739).
Factorization parameters were as follows:
n: 84370061765322647928872401971571207460554744255313121875885604347392453902982301215842039579141719551627224992917852082827356743544863594372624173011525868837715413
m: 50000000000000000000000000000000000
deg: 5
c5: 104
c0: -775
skew: 1.49
type: snfs
lss: 1
rlim: 5900000
alim: 5900000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2950000, 6150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1099439 x 1099664
Total sieving time: 64.51 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.61 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5900000,5900000,28,28,52,52,2.5,2.5,100000
total time: 66.57 hours.

Oct 14, 2009

Factorizations of 266...669 have been extended up to n=225. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Oct 13, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Oct 13, 2009

(2·10¹⁸⁹+7)/9 = (2)₁₈₈3_<189> = 152681 · C184

C184 = P63 · P121

P63 = 297293579162492102984765796920071685141276210227714826259719041_<63>

P121 = 4895724391704181343633928137933080872158292132133342690122300077373183639565891040652324217278579186451361094776320686263_<121>

Number: 22223_189
N=1455467427002850532955785082768793905084602682863108194354387397398643067717805242448125321567334653442289624918766724230403404629405245067966690172465612762702773902595753382688233783
  ( 184 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=297293579162492102984765796920071685141276210227714826259719041 (pp63)
 r2=4895724391704181343633928137933080872158292132133342690122300077373183639565891040652324217278579186451361094776320686263 (pp121)
Version: Msieve-1.40
Total time: 249.40 hours.
Scaled time: 433.71 units (timescale=1.739).
Factorization parameters were as follows:
n: 1455467427002850532955785082768793905084602682863108194354387397398643067717805242448125321567334653442289624918766724230403404629405245067966690172465612762702773902595753382688233783
m: 100000000000000000000000000000000000000
deg: 5
c5: 1
c0: 35
skew: 2.04
type: snfs
lss: 1
rlim: 10300000
alim: 10300000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10300000/10300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5150000, 9150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2021483 x 2021708
Total sieving time: 242.72 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 6.21 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,190.000,5,0,0,0,0,0,0,0,0,10300000,10300000,28,28,54,54,2.5,2.5,100000
total time: 249.40 hours.

(13·10¹⁷³-7)/3 = 4(3)₁₇₂1_<174> = 17 · 47 · 137 · 13564427 · C162

C162 = P62 · P100

P62 = 36827193780046573232594260772222003028836546657202581604583859_<62>

P100 = 7924733594026371980820223389077532702295260397172538624856138458497367165468734245221852075206541109_<100>

Number: 43331_173
N=291845699722454131828950952434067433348183921452070308492393626701016645808266368050060324324481132861030766646948380844607174467577204438194077672931174721359631
  ( 162 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=36827193780046573232594260772222003028836546657202581604583859 (pp62)
 r2=7924733594026371980820223389077532702295260397172538624856138458497367165468734245221852075206541109 (pp100)
Version: Msieve-1.40
Total time: 60.95 hours.
Scaled time: 105.99 units (timescale=1.739).
Factorization parameters were as follows:
n: 291845699722454131828950952434067433348183921452070308492393626701016645808266368050060324324481132861030766646948380844607174467577204438194077672931174721359631
m: 50000000000000000000000000000000000
deg: 5
c5: 104
c0: -175
skew: 1.11
type: snfs
lss: 1
rlim: 5900000
alim: 5900000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2950000, 5850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1073147 x 1073372
Total sieving time: 58.73 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.51 hours.
Time per square root: 0.56 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5900000,5900000,28,28,52,52,2.5,2.5,100000
total time: 60.95 hours.

Oct 13, 2009 (4th)

By matsui / Msieve / Oct 13, 2009

(41·10²⁰⁵-23)/9 = 4(5)₂₀₄3_<206> = 7649 · C202

C202 = P43 · P160

P43 = 5232600658096703417078110461726312950053631_<43>

P160 = 1138201346022551538972137406175594602676219601032471693317267548973571082701802077584706733314967476041455463058018604261123628329460178633626227973006641842687_<160>

N=5955753112244156825147804360773376330965558315538705132116035502099039816388489417643555439345738731279324820964250955099432024520271349922284684998765270696242065048444967388620153687482750105315146497
  ( 202 digits)
SNFS difficulty: 206 digits.
Divisors found:
 r1=5232600658096703417078110461726312950053631 (pp43)
 r2=1138201346022551538972137406175594602676219601032471693317267548973571082701802077584706733314967476041455463058018604261123628329460178633626227973006641842687 (pp160)
Version: Msieve v. 1.42
Total time: 1681.27 hours.
Scaled time: 2891.78 units (timescale=1.720).
Factorization parameters were as follows:
n: 5955753112244156825147804360773376330965558315538705132116035502099039816388489417643555439345738731279324820964250955099432024520271349922284684998765270696242065048444967388620153687482750105315146497
m: 100000000000000000000000000000000000000000
deg: 5
c5: 41
c0: -23
skew: 0.89
type: snfs
lss: 1
rlim: 19400000
alim: 19400000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 400000

Factor base limits: 19400000/19400000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [9700000, 23300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 4011114 x 4011338
Total sieving time: 1662.59 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 17.55 hours.
Time per square root: 0.86 hours.
Prototype def-par.txt line would be:
snfs,206.000,5,0,0,0,0,0,0,0,0,19400000,19400000,29,29,56,56,2.6,2.6,100000
total time: 1681.27 hours.

Oct 13, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM v6.2.3, GGNFS, Msieve v1.39 / Oct 13, 2009

5·10¹⁸⁰-1 = 4(9)₁₈₀_<181> = 10621939 · 371220517601500959349955067754789808321_<39> · C136

C136 = P40 · P45 · P52

P40 = 1166301555538974517603112159803243199069_<40>

P45 = 455836425176168552226557086859741685930538511_<45>

P52 = 2385142595979479983692619755161942793993731666526119_<52>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 1268043725350051353132819056594165736383974526766996545360477852847986781906687610303669898118623904197788874590155678924925008343938821 (136 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2748895193
Step 1 took 4322ms
Step 2 took 2401ms
********** Factor found in step 2: 1166301555538974517603112159803243199069
Found probable prime factor of 40 digits: 1166301555538974517603112159803243199069
Composite cofactor 1087234874486692647113099056807700552174954940627876797305797217283126817336364453873278316868809 has 97 digits

Number: 49999_180
N=1087234874486692647113099056807700552174954940627876797305797217283126817336364453873278316868809
  ( 97 digits)
Divisors found:
 r1=455836425176168552226557086859741685930538511
 r2=2385142595979479983692619755161942793993731666526119
Version: 
Total time: 1.87 hours.
Scaled time: 4.47 units (timescale=2.387).
Factorization parameters were as follows:
name: 49999_180
n: 1087234874486692647113099056807700552174954940627876797305797217283126817336364453873278316868809
skew: 8632.98
# norm 2.89e+13
c5: 10920
c4: 318464128
c3: -1505481553212
c2: -20180759028973709
c1: 58577666676270824122
c0: -57414147493511642220285
# alpha -5.91
Y1: 11822671531
Y0: -2509621434827683634
# Murphy_E 5.11e-09
# M 156070940597455959127173067169783594525935570814263899470527292638724944750891421285089957590333
type: gnfs
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [500000, 850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4117386
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 143255 x 143503
Polynomial selection time: 0.11 hours.
Total sieving time: 1.52 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,96,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000
total time: 1.87 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673798)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

Oct 13, 2009 (2nd)

By Dmitry Domanov / ECMNET, GGNFS, Msieve / Oct 13, 2009

2·10¹⁹⁷+9 = 2(0)₁₉₆9_<198> = 23 · 29 · 43 · 1663 · 1270728829_<10> · 7478155481_<10> · C171

C171 = P42 · P129

P42 = 467185812127459488296885761755886497555061_<42>

P129 = 944509734505196888324435883534798002347210233678036138305231061654282177613689218732584175782493585739887365690596605198501571127_<129>

C171=P42*P129
C171=467185812127459488296885761755886497555061<42>*944509734505196888324435883534798002347210233678036138305231061654282177613689218732584175782493585739887365690596605198501571127<129>

2·10¹⁹⁶+9 = 2(0)₁₉₅9_<197> = 11 · 17 · 276401 · 1726033 · 192367662427_<12> · 16215174894011_<14> · C158

C158 = P42 · P47 · P70

P42 = 193963468016641857772145026803551171115923_<42>

P47 = 53708156977454565812877224264090874901376708881_<47>

P70 = 6898994351244504504781634659534366111507825716105635993739478162742689_<70>

C158=P40*C117
P40=193963468016641857772145026803551171115923

C117 cofactor done by gnfs:

Number: gnfs117
N=370532271603212170226704518044426969864269542358617420627750419622394581621041361936134785090231721575559523264121009
  ( 117 digits)
Divisors found:
 r1=53708156977454565812877224264090874901376708881 (pp47)
 r2=6898994351244504504781634659534366111507825716105635993739478162742689 (pp70)
Version: Msieve-1.40
Total time: 31.25 hours.
Scaled time: 58.50 units (timescale=1.872).
Factorization parameters were as follows:
name: gnfs117
n: 370532271603212170226704518044426969864269542358617420627750419622394581621041361936134785090231721575559523264121009
skew: 27131.14
# norm 5.13e+015
c5: 12840
c4: -5005419988
c3: 132835511575086
c2: 5619850704837977301
c1: 5643984592240713617760
c0: -148947437176552868590359
# alpha -4.75
Y1: 2796746329349
Y0: -31049545900540173580930
# Murphy_E 4.14e-010
# M 274660023481842263283986019784205274017274293306493453239176921056062773765217075988162189695088128426042817861964202
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved algebraic special-q in [1800000, 3300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 573142 x 573370
Polynomial selection time: 3.55 hours.
Total sieving time: 26.99 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.41 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,53,53,2.5,2.5,100000
total time: 31.25 hours.
 --------- CPU info (if available) ----------

2·10¹⁸¹+9 = 2(0)₁₈₀9_<182> = 19526445927449_<14> · C169

C169 = P52 · P117

P52 = 1261481608100983452099826583383264628723756547588583_<52>

P117 = 811943612296195715347682002355010911159697937936474250522482727122338922394138319045468538601865056237746879402333927_<117>

Number: 209-2
N=1024251933726726412159577217922272529137088964444678845265845863752286681411054066011468935166086174372679904828164827085696310014344289168171848755274554265733978755441
  ( 169 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=1261481608100983452099826583383264628723756547588583 (pp52)
 r2=811943612296195715347682002355010911159697937936474250522482727122338922394138319045468538601865056237746879402333927 (pp117)
Version: Msieve-1.40
Total time: 123.07 hours.
Scaled time: 242.33 units (timescale=1.969).
Factorization parameters were as follows:
n: 1024251933726726412159577217922272529137088964444678845265845863752286681411054066011468935166086174372679904828164827085696310014344289168171848755274554265733978755441
m: 1000000000000000000000000000000000000
deg: 5
c5: 20
c0: 9
skew: 0.85
type: snfs
lss: 1
rlim: 7400000
alim: 7400000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3700000, 5600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1270346 x 1270578
Total sieving time: 120.58 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.06 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,181.000,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,53,53,2.5,2.5,100000
total time: 123.07 hours.
 --------- CPU info (if available) ----------

2·10¹⁸⁰+9 = 2(0)₁₇₉9_<181> = 11 · 17 · 6079571 · C172

C172 = P41 · P60 · P72

P41 = 25230643818391368849433612677582025214393_<41>

P60 = 188381030611937474058452477960311181949708981007667786593139_<60>

P72 = 370126306304570492482152625078331368757963894231215299250456690859821771_<72>

Number: 209-1
N=1759200964307415945881496667699103596597795757959022961844803753598653378104728130809208685572388363453139337529090378040913995429439325843510012580688204114303635818829417
  ( 172 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=25230643818391368849433612677582025214393 (pp41)
 r2=188381030611937474058452477960311181949708981007667786593139 (pp60)
 r3=370126306304570492482152625078331368757963894231215299250456690859821771 (pp72)
Version: Msieve-1.40
Total time: 103.49 hours.
Scaled time: 199.53 units (timescale=1.928).
Factorization parameters were as follows:
n: 1759200964307415945881496667699103596597795757959022961844803753598653378104728130809208685572388363453139337529090378040913995429439325843510012580688204114303635818829417
m: 1000000000000000000000000000000000000
deg: 5
c5: 2
c0: 9
skew: 1.35
type: snfs
lss: 1
rlim: 7100000
alim: 7100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7100000/7100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3550000, 5150001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1210652 x 1210890
Total sieving time: 100.89 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.86 hours.
Time per square root: 0.58 hours.
Prototype def-par.txt line would be:
snfs,180.000,5,0,0,0,0,0,0,0,0,7100000,7100000,28,28,53,53,2.5,2.5,100000
total time: 103.49 hours.
 --------- CPU info (if available) ----------

Oct 13, 2009

By Lionel Debroux / GGNFS + Msieve / Oct 13, 2009

(2·10¹⁷⁴-11)/9 = (2)₁₇₃1_<174> = 14519 · 48049681 · 498348657919234104075045395918906731471_<39> · C123

C123 = P51 · P73

P51 = 292418693276777073349480324433832146379750349557037_<51>

P73 = 2185857505314291987785721476537254875502814208773838232705659519834440857_<73>

Number: 22221_174
N=639185595393241060368558509801103716904374062098782041091490513631206214345337531118525083250572654266352921615626524660709
  ( 123 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=292418693276777073349480324433832146379750349557037 (pp51)
 r2=2185857505314291987785721476537254875502814208773838232705659519834440857 (pp73)
Version: Msieve v. 1.43
Total time: 138.60 hours.
Scaled time: 297.29 units (timescale=2.145).
Factorization parameters were as follows:
n: 639185595393241060368558509801103716904374062098782041091490513631206214345337531118525083250572654266352921615626524660709
m: 100000000000000000000000000000000000
deg: 5
c5: 1
c0: -55
skew: 2.23
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 7000001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 684584 x 684812
Total sieving time: 137.12 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 1.14 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,52,52,2.5,2.5,100000
total time: 138.60 hours.
 --------- CPU info (if available) ----------
[    0.029439] CPU0: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.101689] CPU1: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.000000] Memory: 2043420k/2096800k available (7091k kernel code, 452k absent, 52268k reserved, 3271k data, 540k init)
[    0.000999] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.57 BogoMIPS (lpj=1995288)
[    0.000999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913)
[    0.102027] Total of 2 processors activated (7980.40 BogoMIPS).

Oct 12, 2009 (3rd)

By Dmitry Domanov / ECMNET / Oct 12, 2009

2·10²⁰⁰+9 = 2(0)₁₉₉9_<201> = 11 · 19 · 139 · 1259 · 5326345617905713_<16> · C178

C178 = P40 · C138

P40 = 1991350749169858454527790418207027923203_<40>

C138 = [515544399928007014946837975043806426611470201510365146903403741438897213435687943769990979066673545308632679985149733037848236754218334459_<138>]

C178=P40*C138
C178=1991350749169858454527790418207027923203<40>*515544399928007014946837975043806426611470201510365146903403741438897213435687943769990979066673545308632679985149733037848236754218334459<138>

Oct 12, 2009 (2nd)

By Sinkiti Sibata / Msieve / Oct 12, 2009

(7·10¹⁹¹+17)/3 = 2(3)₁₉₀9_<192> = 239 · C189

C189 = P43 · P147

P43 = 8675408230576332396338916381447764186777501_<43>

P147 = 112535349539874274622788901129843613428659566264370680778829606260498582342933455605684400377824563882400936911787444933628331607635998443024485401_<147>

Number: 23339_191
N=976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762901
  ( 189 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=8675408230576332396338916381447764186777501 (pp43)
 r2=112535349539874274622788901129843613428659566264370680778829606260498582342933455605684400377824563882400936911787444933628331607635998443024485401 (pp147)
Version: Msieve-1.40
Total time: 393.64 hours.
Scaled time: 716.83 units (timescale=1.821).
Factorization parameters were as follows:
name: 23339_191
n: 976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762901
m: 100000000000000000000000000000000000000
deg: 5
c5: 70
c0: 17
skew: 0.75
type: snfs
lss: 1
rlim: 11000000
alim: 11000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5500000, 10300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2139635 x 2139859
Total sieving time: 380.36 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 12.20 hours.
Time per square root: 0.87 hours.
Prototype def-par.txt line would be:
snfs,191.000,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,54,54,2.5,2.5,100000
total time: 393.64 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3109164k/3145344k available (2732k kernel code, 34856k reserved, 1420k data, 412k init, 2227840k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.99 BogoMIPS (lpj=2393995)
Calibrating delay using timer specific routine.. 4787.75 BogoMIPS (lpj=2393879)
Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393884)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891)
Total of 4 processors activated (19151.29 BogoMIPS).

Oct 12, 2009

By Robert Backstrom / Msieve / Oct 12, 2009

10²²⁵+3 = 1(0)₂₂₄3_<226> = 47 · C224

C224 = P50 · P85 · P89

P50 = 55596542276628893687893904461674188425734045987539_<50>

P85 = 5081699578026248101117725776351792155214522626704131970999327867748681087438765113013_<85>

P89 = 75308738556551420873071265981065825474555301071112117762996787038235739437080945584086307_<89>

Sieving ~ 170 CPU days + 147 hrs Lanczos with Msieve 1.42

Mon Oct  5 22:38:47 2009  
Mon Oct  5 22:38:47 2009  
Mon Oct  5 22:38:47 2009  Msieve v. 1.42
Mon Oct  5 22:38:47 2009  random seeds: a92c9797 c60b7a61
Mon Oct  5 22:38:47 2009  factoring 21276595744680851063829787234042553191489361702127659574468085106382978723404255319148936170212765957446808510638297872340425531914893617021276595744680851063829787234042553191489361702127659574468085106382978723404255319149 (224 digits)
Mon Oct  5 22:38:49 2009  no P-1/P+1/ECM available, skipping
Mon Oct  5 22:38:49 2009  commencing number field sieve (224-digit input)
Mon Oct  5 22:38:49 2009  R0: -20000000000000000000000000000000000000
Mon Oct  5 22:38:49 2009  R1:  1
Mon Oct  5 22:38:49 2009  A0:  24
Mon Oct  5 22:38:49 2009  A1:  0
Mon Oct  5 22:38:49 2009  A2:  0
Mon Oct  5 22:38:49 2009  A3:  0
Mon Oct  5 22:38:49 2009  A4:  0
Mon Oct  5 22:38:49 2009  A5:  0
Mon Oct  5 22:38:49 2009  A6:  125
Mon Oct  5 22:38:49 2009  skew 1.00, size 2.851665e-11, alpha 0.347772, combined = 1.390632e-12
Mon Oct  5 22:38:49 2009  
Mon Oct  5 22:38:49 2009  commencing relation filtering
Mon Oct  5 22:38:49 2009  estimated available RAM is 7924.4 MB
Mon Oct  5 22:38:49 2009  commencing duplicate removal, pass 1
Mon Oct  5 22:39:07 2009  error -11 reading relation 3251910
Mon Oct  5 22:39:54 2009  error -15 reading relation 11873790
Mon Oct  5 22:40:58 2009  error -11 reading relation 23569318
Mon Oct  5 22:41:28 2009  error -6 reading relation 28974234
Mon Oct  5 22:41:34 2009  error -11 reading relation 30144945
Mon Oct  5 22:41:58 2009  error -11 reading relation 34362278
Mon Oct  5 22:42:30 2009  error -11 reading relation 40140606
Mon Oct  5 22:42:49 2009  error -11 reading relation 43702742
Mon Oct  5 22:43:30 2009  error -6 reading relation 51057163
Mon Oct  5 22:43:34 2009  error -11 reading relation 51788557
Mon Oct  5 22:43:36 2009  error -11 reading relation 52106781
Mon Oct  5 22:43:41 2009  error -15 reading relation 52952486
Mon Oct  5 22:44:00 2009  error -11 reading relation 56495038
Mon Oct  5 22:44:01 2009  error -11 reading relation 56678613
Mon Oct  5 22:44:38 2009  error -11 reading relation 63414952
Mon Oct  5 22:44:40 2009  error -11 reading relation 63768255
Mon Oct  5 22:44:41 2009  error -11 reading relation 63804611
Mon Oct  5 22:46:05 2009  error -11 reading relation 79139720
Mon Oct  5 22:46:44 2009  found 12731978 hash collisions in 86131812 relations
Mon Oct  5 22:47:05 2009  added 1218273 free relations
Mon Oct  5 22:47:05 2009  commencing duplicate removal, pass 2
Mon Oct  5 22:48:25 2009  found 11567825 duplicates and 75782260 unique relations
Mon Oct  5 22:48:25 2009  memory use: 394.4 MB
Mon Oct  5 22:48:25 2009  reading ideals above 83951616
Mon Oct  5 22:48:25 2009  commencing singleton removal, initial pass
Mon Oct  5 22:57:02 2009  memory use: 1193.5 MB
Mon Oct  5 22:57:02 2009  reading all ideals from disk
Mon Oct  5 22:57:11 2009  memory use: 1256.8 MB
Mon Oct  5 22:57:18 2009  commencing in-memory singleton removal
Mon Oct  5 22:57:25 2009  begin with 75782260 relations and 70939492 unique ideals
Mon Oct  5 22:58:30 2009  reduce to 34052535 relations and 23016820 ideals in 17 passes
Mon Oct  5 22:58:30 2009  max relations containing the same ideal: 30
Mon Oct  5 22:58:34 2009  reading ideals above 720000
Mon Oct  5 22:58:35 2009  commencing singleton removal, initial pass
Mon Oct  5 23:03:57 2009  memory use: 596.8 MB
Mon Oct  5 23:03:58 2009  reading all ideals from disk
Mon Oct  5 23:04:09 2009  memory use: 1260.8 MB
Mon Oct  5 23:04:18 2009  keeping 32585445 ideals with weight <= 200, target excess is 178408
Mon Oct  5 23:04:26 2009  commencing in-memory singleton removal
Mon Oct  5 23:04:34 2009  begin with 34052577 relations and 32585445 unique ideals
Mon Oct  5 23:06:37 2009  reduce to 33793542 relations and 32325423 ideals in 15 passes
Mon Oct  5 23:06:37 2009  max relations containing the same ideal: 200
Mon Oct  5 23:07:13 2009  removing 3747467 relations and 3347468 ideals in 400000 cliques
Mon Oct  5 23:07:14 2009  commencing in-memory singleton removal
Mon Oct  5 23:07:22 2009  begin with 30046075 relations and 32325423 unique ideals
Mon Oct  5 23:08:41 2009  reduce to 29726997 relations and 28653594 ideals in 11 passes
Mon Oct  5 23:08:41 2009  max relations containing the same ideal: 189
Mon Oct  5 23:09:12 2009  removing 2727933 relations and 2327933 ideals in 400000 cliques
Mon Oct  5 23:09:14 2009  commencing in-memory singleton removal
Mon Oct  5 23:09:21 2009  begin with 26999064 relations and 28653594 unique ideals
Mon Oct  5 23:10:18 2009  reduce to 26809549 relations and 26133402 ideals in 9 passes
Mon Oct  5 23:10:18 2009  max relations containing the same ideal: 178
Mon Oct  5 23:10:47 2009  removing 2395260 relations and 1995260 ideals in 400000 cliques
Mon Oct  5 23:10:48 2009  commencing in-memory singleton removal
Mon Oct  5 23:10:54 2009  begin with 24414289 relations and 26133402 unique ideals
Mon Oct  5 23:11:41 2009  reduce to 24254867 relations and 23976350 ideals in 8 passes
Mon Oct  5 23:11:41 2009  max relations containing the same ideal: 170
Mon Oct  5 23:12:06 2009  removing 546494 relations and 474931 ideals in 71563 cliques
Mon Oct  5 23:12:07 2009  commencing in-memory singleton removal
Mon Oct  5 23:12:13 2009  begin with 23708373 relations and 23976350 unique ideals
Mon Oct  5 23:12:47 2009  reduce to 23699883 relations and 23492905 ideals in 6 passes
Mon Oct  5 23:12:47 2009  max relations containing the same ideal: 167
Mon Oct  5 23:12:58 2009  relations with 0 large ideals: 6457
Mon Oct  5 23:12:58 2009  relations with 1 large ideals: 1417
Mon Oct  5 23:12:58 2009  relations with 2 large ideals: 8809
Mon Oct  5 23:12:58 2009  relations with 3 large ideals: 90909
Mon Oct  5 23:12:58 2009  relations with 4 large ideals: 548714
Mon Oct  5 23:12:58 2009  relations with 5 large ideals: 1993979
Mon Oct  5 23:12:58 2009  relations with 6 large ideals: 4494587
Mon Oct  5 23:12:58 2009  relations with 7+ large ideals: 16555011
Mon Oct  5 23:12:58 2009  commencing 2-way merge
Mon Oct  5 23:13:32 2009  reduce to 14756653 relation sets and 14549675 unique ideals
Mon Oct  5 23:13:32 2009  commencing full merge
Mon Oct  5 23:19:52 2009  memory use: 1834.9 MB
Mon Oct  5 23:19:54 2009  found 7936903 cycles, need 7909875
Mon Oct  5 23:19:59 2009  weight of 7909875 cycles is about 553733050 (70.01/cycle)
Mon Oct  5 23:19:59 2009  distribution of cycle lengths:
Mon Oct  5 23:19:59 2009  1 relations: 1091511
Mon Oct  5 23:19:59 2009  2 relations: 1071229
Mon Oct  5 23:19:59 2009  3 relations: 1009555
Mon Oct  5 23:19:59 2009  4 relations: 864999
Mon Oct  5 23:19:59 2009  5 relations: 740720
Mon Oct  5 23:19:59 2009  6 relations: 619505
Mon Oct  5 23:19:59 2009  7 relations: 521785
Mon Oct  5 23:19:59 2009  8 relations: 434165
Mon Oct  5 23:19:59 2009  9 relations: 355277
Mon Oct  5 23:19:59 2009  10+ relations: 1201129
Mon Oct  5 23:19:59 2009  heaviest cycle: 24 relations
Mon Oct  5 23:20:01 2009  commencing cycle optimization
Mon Oct  5 23:20:20 2009  start with 42551860 relations
Mon Oct  5 23:21:46 2009  pruned 932820 relations
Mon Oct  5 23:21:46 2009  memory use: 1412.7 MB
Mon Oct  5 23:21:46 2009  distribution of cycle lengths:
Mon Oct  5 23:21:46 2009  1 relations: 1091511
Mon Oct  5 23:21:46 2009  2 relations: 1091986
Mon Oct  5 23:21:46 2009  3 relations: 1041031
Mon Oct  5 23:21:46 2009  4 relations: 880791
Mon Oct  5 23:21:46 2009  5 relations: 753600
Mon Oct  5 23:21:46 2009  6 relations: 623951
Mon Oct  5 23:21:46 2009  7 relations: 523485
Mon Oct  5 23:21:46 2009  8 relations: 430902
Mon Oct  5 23:21:46 2009  9 relations: 350799
Mon Oct  5 23:21:46 2009  10+ relations: 1121819
Mon Oct  5 23:21:46 2009  heaviest cycle: 23 relations
Mon Oct  5 23:22:03 2009  RelProcTime: 2594
Mon Oct  5 23:22:03 2009  
Mon Oct  5 23:22:03 2009  commencing linear algebra
Mon Oct  5 23:22:09 2009  read 7909875 cycles
Mon Oct  5 23:22:25 2009  cycles contain 23546063 unique relations
Mon Oct  5 23:24:51 2009  read 23546063 relations
Mon Oct  5 23:25:34 2009  using 20 quadratic characters above 1073739680
Mon Oct  5 23:27:32 2009  building initial matrix
Mon Oct  5 23:32:17 2009  memory use: 3001.5 MB
Mon Oct  5 23:32:22 2009  read 7909875 cycles
Mon Oct  5 23:32:28 2009  matrix is 7909697 x 7909875 (2379.0 MB) with weight 699771227 (88.47/col)
Mon Oct  5 23:32:28 2009  sparse part has weight 536644660 (67.84/col)
Mon Oct  5 23:34:17 2009  filtering completed in 2 passes
Mon Oct  5 23:34:19 2009  matrix is 7907420 x 7907598 (2378.9 MB) with weight 699711876 (88.49/col)
Mon Oct  5 23:34:19 2009  sparse part has weight 536632510 (67.86/col)
Mon Oct  5 23:34:56 2009  read 7907598 cycles
Mon Oct  5 23:35:01 2009  matrix is 7907420 x 7907598 (2378.9 MB) with weight 699711876 (88.49/col)
Mon Oct  5 23:35:01 2009  sparse part has weight 536632510 (67.86/col)
Mon Oct  5 23:35:01 2009  saving the first 48 matrix rows for later
Mon Oct  5 23:35:04 2009  matrix is 7907372 x 7907598 (2266.9 MB) with weight 556480788 (70.37/col)
Mon Oct  5 23:35:04 2009  sparse part has weight 515190655 (65.15/col)
Mon Oct  5 23:35:04 2009  matrix includes 64 packed rows
Mon Oct  5 23:35:04 2009  using block size 65536 for processor cache size 6144 kB
Mon Oct  5 23:35:35 2009  commencing Lanczos iteration (4 threads)
Mon Oct  5 23:35:35 2009  memory use: 2461.2 MB
Mon Oct 12 03:14:41 2009  lanczos halted after 125050 iterations (dim = 7907370)
Mon Oct 12 03:14:57 2009  recovered 37 nontrivial dependencies
Mon Oct 12 03:14:58 2009  BLanczosTime: 532375
Mon Oct 12 03:14:58 2009  
Mon Oct 12 03:14:58 2009  commencing square root phase
Mon Oct 12 03:14:58 2009  reading relations for dependency 1
Mon Oct 12 03:15:00 2009  read 3953999 cycles
Mon Oct 12 03:15:09 2009  cycles contain 14376401 unique relations
Mon Oct 12 03:16:52 2009  read 14376401 relations
Mon Oct 12 03:18:20 2009  multiplying 11773886 relations
Mon Oct 12 03:57:27 2009  multiply complete, coefficients have about 368.81 million bits
Mon Oct 12 03:57:30 2009  initial square root is modulo 4146367
Mon Oct 12 04:45:29 2009  reading relations for dependency 2
Mon Oct 12 04:45:32 2009  read 3952310 cycles
Mon Oct 12 04:45:41 2009  cycles contain 14373732 unique relations
Mon Oct 12 04:47:24 2009  read 14373732 relations
Mon Oct 12 04:48:52 2009  multiplying 11772002 relations
Mon Oct 12 05:27:58 2009  multiply complete, coefficients have about 368.75 million bits
Mon Oct 12 05:28:02 2009  initial square root is modulo 4136383
Mon Oct 12 06:16:19 2009  reading relations for dependency 3
Mon Oct 12 06:16:23 2009  read 3954075 cycles
Mon Oct 12 06:16:32 2009  cycles contain 14379643 unique relations
Mon Oct 12 06:18:15 2009  read 14379643 relations
Mon Oct 12 06:19:42 2009  multiplying 11773544 relations
Mon Oct 12 06:58:48 2009  multiply complete, coefficients have about 368.80 million bits
Mon Oct 12 06:58:51 2009  initial square root is modulo 4144423
Mon Oct 12 07:46:39 2009  reading relations for dependency 4
Mon Oct 12 07:46:43 2009  read 3955162 cycles
Mon Oct 12 07:46:51 2009  cycles contain 14381706 unique relations
Mon Oct 12 07:48:34 2009  read 14381706 relations
Mon Oct 12 07:50:02 2009  multiplying 11775114 relations
Mon Oct 12 08:29:07 2009  multiply complete, coefficients have about 368.85 million bits
Mon Oct 12 08:29:10 2009  initial square root is modulo 4153753
Mon Oct 12 09:17:18 2009  reading relations for dependency 5
Mon Oct 12 09:17:22 2009  read 3955387 cycles
Mon Oct 12 09:17:31 2009  cycles contain 14382445 unique relations
Mon Oct 12 09:19:14 2009  read 14382445 relations
Mon Oct 12 09:20:42 2009  multiplying 11776370 relations
Mon Oct 12 09:59:46 2009  multiply complete, coefficients have about 368.89 million bits
Mon Oct 12 09:59:49 2009  initial square root is modulo 4159699
Mon Oct 12 10:47:38 2009  sqrtTime: 27160
Mon Oct 12 10:47:38 2009  prp50 factor: 55596542276628893687893904461674188425734045987539
Mon Oct 12 10:47:38 2009  prp85 factor: 5081699578026248101117725776351792155214522626704131970999327867748681087438765113013
Mon Oct 12 10:47:38 2009  prp89 factor: 75308738556551420873071265981065825474555301071112117762996787038235739437080945584086307
Mon Oct 12 10:47:38 2009  elapsed time 156:08:51

c224 is the largest number factored by SNFS in our table so far. Congratulations!

Oct 11, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Oct 11, 2009

5·10¹⁷³-1 = 4(9)₁₇₃_<174> = 127 · 3911 · 18127 · 60115481 · 23178928080286249351_<20> · C137

C137 = P67 · P71

P67 = 2847970263141744131023830845478132413777645258337832393628729170631_<67>

P71 = 13993856238980368759578357212092380131077296745377065063456859221722961_<71>

Number: 49999_173
N=39854086435296658660320043879991005179189198819489180447210923684885908343283437049105322157599299450760049515223879981997674408379558391
  ( 137 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=2847970263141744131023830845478132413777645258337832393628729170631
 r2=13993856238980368759578357212092380131077296745377065063456859221722961
Version: 
Total time: 37.09 hours.
Scaled time: 88.50 units (timescale=2.386).
Factorization parameters were as follows:
n: 39854086435296658660320043879991005179189198819489180447210923684885908343283437049105322157599299450760049515223879981997674408379558391
m: 100000000000000000000000000000000000
deg: 5
c5: 1
c0: -20
skew: 1.82
type: snfs
lss: 1
rlim: 6400000
alim: 6400000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6400000/6400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [3200000, 5800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 15479928
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1090838 x 1091085
Total sieving time: 32.09 hours.
Total relation processing time: 2.00 hours.
Matrix solve time: 2.87 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,6400000,6400000,28,28,52,52,2.4,2.4,100000
total time: 37.09 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673798)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

Oct 10, 2009 (2nd)

By Jo Yeong Uk / GMP-ECM v6.2.3, GGNFS, Msieve v1.39 / Oct 10, 2009

5·10¹⁷⁹-1 = 4(9)₁₇₉_<180> = 100633529 · 10276894318800611063_<20> · C153

C153 = P33 · P120

P33 = 551421612914557051308292624692847_<33>

P120 = 876761814633993523106354211564896283956156882713530327635666576447814027168039294731780218758528595761801494512642521871_<120>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 483465413967370598400238048693329074423316487627052497512382988498499804040391586617159120691337958260268162836645299451358426769745806731188812854756737 (153 digits)
Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=4222987752
Step 1 took 1170ms
Step 2 took 1061ms
********** Factor found in step 2: 551421612914557051308292624692847
Found probable prime factor of 33 digits: 551421612914557051308292624692847
Probable prime cofactor 876761814633993523106354211564896283956156882713530327635666576447814027168039294731780218758528595761801494512642521871 has 120 digits

5·10¹⁷⁴-1 = 4(9)₁₇₄_<175> = 100836539 · 386045671789_<12> · 202149331951309_<15> · C141

C141 = P38 · P51 · P53

P38 = 28345499727878470190919484864294064341_<38>

P51 = 463029342608148463454164159741210468863485451451681_<51>

P53 = 48411489356292646627148450479697213943551789779252721_<53>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 635391023758808768021982182663640242957235141906592712342373275630037497448167738145615536255657952171914822743853474214435578032037202498341 (141 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=8051102569
Step 1 took 12060ms
Step 2 took 5548ms
********** Factor found in step 2: 28345499727878470190919484864294064341
Found probable prime factor of 38 digits: 28345499727878470190919484864294064341
Composite cofactor 22415940091325560592764062171757453501035854403561664187105229615762632752555588053316070194944819274001 has 104 digits

Number: 49999_174
N=22415940091325560592764062171757453501035854403561664187105229615762632752555588053316070194944819274001
  ( 104 digits)
Divisors found:
 r1=463029342608148463454164159741210468863485451451681
 r2=48411489356292646627148450479697213943551789779252721
Version: 
Total time: 4.42 hours.
Scaled time: 10.55 units (timescale=2.386).
Factorization parameters were as follows:
name: 49999_174
n: 22415940091325560592764062171757453501035854403561664187105229615762632752555588053316070194944819274001
skew: 7223.23
# norm 5.68e+14
c5: 103320
c4: -1087558846
c3: -54783974263837
c2: 45158299175990806
c1: 473317516833711936848
c0: -566285402745446146869216
# alpha -5.98
Y1: 70717608599
Y0: -46481047104932086595
# Murphy_E 2.12e-09
# M 11389210777915482262951976616597298590964859459226496768929040960719519334499979514459734483204362702854
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 5061933
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 241571 x 241818
Polynomial selection time: 0.29 hours.
Total sieving time: 3.46 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 4.42 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673798)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

Oct 10, 2009

By Dmitry Domanov / GGNFS/msieve 1.42 / Oct 10, 2009

(49·10¹⁸⁷-31)/9 = 5(4)₁₈₆1_<188> = 3 · 173 · C186

C186 = P49 · P137

P49 = 2121703601345068272130158885480734551644871829999_<49>

P137 = 49442622610066597773870255896387437835807325763621162874103458717719730334494584048229510097211957639731087242512079125873691747378918161_<137>

N=104902590451723399700278312995076000856347677156925711839006636694497966174266752301434382359237850567330336116463284093341896810104902590451723399700278312995076000856347677156925711839
  ( 186 digits)
SNFS difficulty: 189 digits.
Divisors found:
r1=2121703601345068272130158885480734551644871829999 (pp49)
r2=49442622610066597773870255896387437835807325763621162874103458717719730334494584048229510097211957639731087242512079125873691747378918161 (pp137)
Version: Msieve-1.40
Total time: 294.69 hours.
Scaled time: 568.17 units (timescale=1.928).
Factorization parameters were as follows:
n: 104902590451723399700278312995076000856347677156925711839006636694497966174266752301434382359237850567330336116463284093341896810104902590451723399700278312995076000856347677156925711839
m: 20000000000000000000000000000000000000
deg: 5
c5: 1225
c0: -248
skew: 0.73
type: snfs
lss: 1
rlim: 10100000
alim: 10100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10100000/10100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5050000, 9650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1995813 x 1996038
Total sieving time: 289.12 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 5.06 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,189.000,5,0,0,0,0,0,0,0,0,10100000,10100000,28,28,54,54,2.5,2.5,100000
total time: 294.69 hours.
 --------- CPU info (if available) ----------

Oct 9, 2009 (4th)

By Jo Yeong Uk / GMP-ECM / Oct 9, 2009

5·10¹⁸¹-1 = 4(9)₁₈₁_<182> = 7 · 97² · 193 · 457 · 422822039 · 5656697469953_<13> · C151

C151 = P30 · C122

P30 = 173579002511793813594159069431_<30>

C122 = [20731810459118814730446116833653693666321827958599665647784054670803472164424057194952315997453223210542179715535871072849_<122>]

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 3598606979757417997917427995706501314058534392261408149235484668120477312161588275805313695459204431109019053455906018698429200104947933380953449978919 (151 digits)
Using B1=50000, B2=12746592, polynomial x^2, sigma=1211348993
Step 1 took 218ms
Step 2 took 297ms
********** Factor found in step 2: 173579002511793813594159069431
Found probable prime factor of 30 digits: 173579002511793813594159069431
Composite cofactor 20731810459118814730446116833653693666321827958599665647784054670803472164424057194952315997453223210542179715535871072849 has 122 digits

Oct 9, 2009 (3rd)

By Sinkiti Sibata / Msieve / Oct 9, 2009

(28·10¹⁷²-1)/9 = 3(1)₁₇₂_<173> = 149 · 19009 · 6877246441372402649_<19> · C148

C148 = P34 · P34 · P80

P34 = 1724230517504569670736836635964441_<34>

P34 = 9768844483733605983857894729980673_<34>

P80 = 94823694499320570244033199429122419011801625776673637024727322019611784153183003_<80>

Number: 31111_172
N=1597185635087759228897797601527268513200647569431010321238582064646751736038007343385916525405877553475410220832933182429409759009145752755793865379
  ( 148 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=1724230517504569670736836635964441 (pp34)
 r2=9768844483733605983857894729980673 (pp34)
 r3=94823694499320570244033199429122419011801625776673637024727322019611784153183003 (pp80)
Version: Msieve-1.40
Total time: 79.64 hours.
Scaled time: 265.92 units (timescale=3.339).
Factorization parameters were as follows:
name: 31111_172
n: 1597185635087759228897797601527268513200647569431010321238582064646751736038007343385916525405877553475410220832933182429409759009145752755793865379
m: 50000000000000000000000000000000000
deg: 5
c5: 112
c0: -125
skew: 1.02
type: snfs
lss: 1
rlim: 5900000
alim: 5900000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2950000, 6750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1131674 x 1131922
Total sieving time: 76.63 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 2.46 hours.
Time per square root: 0.41 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5900000,5900000,28,28,52,52,2.5,2.5,100000
total time: 79.64 hours.
 --------- CPU info (if available) ----------

Oct 9, 2009 (2nd)

By Lionel Debroux / GGNFS + Msieve / Oct 9, 2009

(43·10¹⁷¹+11)/9 = 4(7)₁₇₀9_<172> = 3 · 355093 · 448570037 · 19956188840224140440597442401083283_<35> · C123

C123 = P50 · P73

P50 = 58975899398354383022435457259841236596129255822293_<50>

P73 = 8495327815107557534376716075033317622504746422419098776300330543786722167_<73>

Number: 47779_171
N=501019598579825057644595959540665425580414504347777059326970261905824979340160312991495080272365020643529680147710715868931
  ( 123 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=58975899398354383022435457259841236596129255822293 (pp50)
 r2=8495327815107557534376716075033317622504746422419098776300330543786722167 (pp73)
Version: Msieve v. 1.43
Total time: 128.20 hours.
Scaled time: 278.97 units (timescale=2.176).
Factorization parameters were as follows:
n: 501019598579825057644595959540665425580414504347777059326970261905824979340160312991495080272365020643529680147710715868931
m: 20000000000000000000000000000000000
deg: 5
c5: 215
c0: 176
skew: 0.96
type: snfs
lss: 1
rlim: 5500000
alim: 5500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2750000, 6550001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 910750 x 910975
Total sieving time: 125.56 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 2.08 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
snfs,173.000,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,52,52,2.4,2.4,100000
total time: 128.20 hours.
 --------- CPU info (if available) ----------
[    0.029439] CPU0: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.101689] CPU1: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.000000] Memory: 2043420k/2096800k available (7091k kernel code, 452k absent, 52268k reserved, 3271k data, 540k init)
[    0.000999] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.57 BogoMIPS (lpj=1995288)
[    0.000999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913)
[    0.102027] Total of 2 processors activated (7980.40 BogoMIPS).

Oct 9, 2009

By Ignacio Santos / GGNFS, Msieve / Oct 9, 2009

(4·10¹⁷⁴+11)/3 = 1(3)₁₇₃7_<175> = 23 · 47 · 22572731 · C164

C164 = P59 · P106

P59 = 18804671853396239905276877417725760828564252709047581852637_<59>

P106 = 2905782990887764523718537323099507259736355681474055210659402454039634545496153174870499580675672943930991_<106>

Number: 13337_174
N=54642295620824688198326459065548316610303351155710226746068295134663195402219582503829185601603695575758916612449293442593845354571480914637894943713551377259373267
  ( 164 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=18804671853396239905276877417725760828564252709047581852637 (pp59)
 r2=2905782990887764523718537323099507259736355681474055210659402454039634545496153174870499580675672943930991 (pp106)
Version: Msieve-1.40
Total time: 62.16 hours.
Scaled time: 108.10 units (timescale=1.739).
Factorization parameters were as follows:
n: 54642295620824688198326459065548316610303351155710226746068295134663195402219582503829185601603695575758916612449293442593845354571480914637894943713551377259373267
m: 100000000000000000000000000000000000
deg: 5
c5: 2
c0: 55
skew: 1.94
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 5900001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1109882 x 1110112
Total sieving time: 60.14 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.64 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,52,52,2.5,2.5,100000
total time: 62.16 hours.

Oct 8, 2009 (3rd)

By Wataru Sakai / Msieve / Oct 8, 2009

8·10¹⁷³+9 = 8(0)₁₇₂9_<174> = 7 · 643 · 661 · 443227 · 260680181687_<12> · C151

C151 = P46 · P52 · P53

P46 = 8189545458237210393744457523666003154315736867_<46>

P52 = 4183880356288717606362756534826033091154894241628947_<52>

P53 = 67921338602004285032869683860445350931844687971789469_<53>

Number: 80009_173
N=2327262068830754550218468227408715341596597253444007699138876048165527205915900775607263778983095431120139789820533451020131945533106053158603012224981
  ( 151 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=8189545458237210393744457523666003154315736867
 r2=4183880356288717606362756534826033091154894241628947
 r3=67921338602004285032869683860445350931844687971789469
Version: 
Total time: 100.92 hours.
Scaled time: 203.36 units (timescale=2.015).
Factorization parameters were as follows:
n: 2327262068830754550218468227408715341596597253444007699138876048165527205915900775607263778983095431120139789820533451020131945533106053158603012224981
m: 40000000000000000000000000000000000
deg: 5
c5: 125
c0: 144
skew: 1.03
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 5800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 853065 x 853313
Total sieving time: 100.92 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,52,52,2.5,2.5,100000
total time: 100.92 hours.
 --------- CPU info (if available) ----------

2·10¹⁷²-9 = 1(9)₁₇₁1_<173> = 17 · 31 · 20023 · 6637427143417951_<16> · C150

C150 = P62 · P88

P62 = 66028934282635233891831912901618375839864457254966050086431689_<62>

P88 = 4324701912262433203651625569596822613898499886371331781703808091038595706400686381022889_<88>

Number: 19991_172
N=285555458356763129168067288530927414585092843830940080941964946733783405647248783370316145632743341813305821377190485658733089506833402589555843929521
  ( 150 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=66028934282635233891831912901618375839864457254966050086431689
 r2=4324701912262433203651625569596822613898499886371331781703808091038595706400686381022889
Version: 
Total time: 69.35 hours.
Scaled time: 139.46 units (timescale=2.011).
Factorization parameters were as follows:
n: 285555458356763129168067288530927414585092843830940080941964946733783405647248783370316145632743341813305821377190485658733089506833402589555843929521
m: 20000000000000000000000000000000000
deg: 5
c5: 25
c0: -36
skew: 1.08
type: snfs
lss: 1
rlim: 5300000
alim: 5300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2650000, 4850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 674254 x 674502
Total sieving time: 69.35 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.4,2.4,100000
total time: 69.35 hours.
 --------- CPU info (if available) ----------

(44·10¹⁹⁵+1)/9 = 4(8)₁₉₄9_<196> = 139 · C194

C194 = P56 · P139

P56 = 10412466420126431250346726146039796224775804741205443513_<56>

P139 = 3377860834394406548885117292303092018330749711789663082853036841147182942536410699923182290582604658203414033362067157941568625306147377827_<139>

Number: 48889_195
N=35171862509992006394884092725819344524380495603517186250999200639488409272581934452438049560351718625099920063948840927258193445243804956035171862509992006394884092725819344524380495603517186251
  ( 194 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=10412466420126431250346726146039796224775804741205443513
 r2=3377860834394406548885117292303092018330749711789663082853036841147182942536410699923182290582604658203414033362067157941568625306147377827
Version: 
Total time: 569.46 hours.
Scaled time: 1147.46 units (timescale=2.015).
Factorization parameters were as follows:
n: 35171862509992006394884092725819344524380495603517186250999200639488409272581934452438049560351718625099920063948840927258193445243804956035171862509992006394884092725819344524380495603517186251
m: 2000000000000000000000000000000000000000
deg: 5
c5: 11
c0: 8
skew: 0.94
type: snfs
lss: 1
rlim: 13700000
alim: 13700000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 13700000/13700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6850000, 12550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1875703 x 1875951
Total sieving time: 569.46 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,13700000,13700000,28,28,55,55,2.5,2.5,100000
total time: 569.46 hours.
 --------- CPU info (if available) ----------

Oct 8, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Oct 8, 2009

(2·10¹⁷⁵+7)/9 = (2)₁₇₄3_<175> = 3³ · 440484472271_<12> · C162

C162 = P72 · P90

P72 = 978020707228890018577814164641282499503678266666331249424162522348474303_<72>

P90 = 191049131852004376166589287066630797271854337936691707239370904079629644614194662598382573_<90>

Number: 22223_175
N=186850007049362778684422153838889746512181414900901879338348429790457559971430414759426262701870399244019166893981526142656397274721585238661891239820642053521619
  ( 162 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=978020707228890018577814164641282499503678266666331249424162522348474303 (pp72)
 r2=191049131852004376166589287066630797271854337936691707239370904079629644614194662598382573 (pp90)
Version: Msieve-1.40
Total time: 57.76 hours.
Scaled time: 100.73 units (timescale=1.744).
Factorization parameters were as follows:
n: 186850007049362778684422153838889746512181414900901879338348429790457559971430414759426262701870399244019166893981526142656397274721585238661891239820642053521619
m: 100000000000000000000000000000000000
deg: 5
c5: 2
c0: 7
skew: 1.28
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 5700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1052282 x 1052515
Total sieving time: 56.07 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.45 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,52,52,2.5,2.5,100000
total time: 57.76 hours.

Oct 8, 2009

By Tyler Cadigan / GGNFS, msieve / Oct 8, 2009

10²⁰⁰+3 = 1(0)₁₉₉3_<201> = 16892897616604738393032473779_<29> · C172

C172 = P63 · P110

P63 = 142382085188774470405910710620318311201708781764203691159141491_<63>

P110 = 41575789136886395098758671741723670103749259409601292912421292205993178486578323921284022171938244838107449227_<110>

Number: 10003_200
N=5919647550678682918318585392550030687321219331802429980672060525048639901448866420111089641083403610030206379807979210510870824800479444820240779860283084327969945191577457
  ( 172 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=142382085188774470405910710620318311201708781764203691159141491 (pp63)
 r2=41575789136886395098758671741723670103749259409601292912421292205993178486578323921284022171938244838107449227 (pp110)
Version: Msieve v. 1.42
Total time: 478.11 hours.
Scaled time: 0.00 units (timescale=0.000).
Factorization parameters were as follows:
n: 5919647550678682918318585392550030687321219331802429980672060525048639901448866420111089641083403610030206379807979210510870824800479444820240779860283084327969945191577457
m: 10000000000000000000000000000000000000000
deg: 5
c5: 1
c0: 3
skew: 1.25
type: snfs
lss: 1
rlim: 15100000
alim: 15100000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 15100000/15100000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7550000, 13550001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3112395 x 3112621
Total sieving time: 452.35 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 24.85 hours.
Time per square root: 0.41 hours.
Prototype def-par.txt line would be:
snfs,200.000,5,0,0,0,0,0,0,0,0,15100000,15100000,29,29,56,56,2.6,2.6,100000
total time: 478.11 hours.
 --------- CPU info (if available) ----------

Oct 7, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Oct 7, 2009

(35·10¹⁷³-17)/9 = 3(8)₁₇₂7_<174> = 3³ · 509 · 134369 · C165

C165 = P36 · P41 · P89

P36 = 337724536741041059203277713140298669_<36>

P41 = 35379397955005834588592053197139791721891_<41>

P89 = 17625110578008454198749170325730853946484306159435410277383328749926110210790680918234559_<89>

Number: 38887_173
N=210593471317678812647952883264166395690481437610228349639995873034640934123809598449007435643491227778261219159012802941218313387354473358101928258547783837616347161
  ( 165 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=337724536741041059203277713140298669 (pp36)
 r2=35379397955005834588592053197139791721891 (pp41)
 r3=17625110578008454198749170325730853946484306159435410277383328749926110210790680918234559 (pp89)
Version: Msieve-1.40
Total time: 82.53 hours.
Scaled time: 143.52 units (timescale=1.739).
Factorization parameters were as follows:
n: 210593471317678812647952883264166395690481437610228349639995873034640934123809598449007435643491227778261219159012802941218313387354473358101928258547783837616347161
m: 50000000000000000000000000000000000
deg: 5
c5: 56
c0: -85
skew: 1.09
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 7000001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1196567 x 1196792
Total sieving time: 79.16 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.00 hours.
Time per square root: 1.21 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,52,52,2.5,2.5,100000
total time: 82.53 hours.

Oct 7, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Oct 7, 2009

(53·10¹⁷⁰-17)/9 = 5(8)₁₆₉7_<171> = 307 · 122533 · 5167733 · 294126417229_<12> · C146

C146 = P51 · P95

P51 = 193846180805187407600600338763753217911145985598911_<51>

P95 = 53131315566490633270278975197275951466009849466986055887204243258100677263931552140266771322951_<95>

Number: 58887_170
N=10299302603719411508616502097188696854986727292241823681488296293899090572336868769552116649099303398527333908486413361785907527066254281534906361
  ( 146 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=193846180805187407600600338763753217911145985598911
 r2=53131315566490633270278975197275951466009849466986055887204243258100677263931552140266771322951
Version: 
Total time: 40.30 hours.
Scaled time: 96.07 units (timescale=2.384).
Factorization parameters were as follows:
n: 10299302603719411508616502097188696854986727292241823681488296293899090572336868769552116649099303398527333908486413361785907527066254281534906361
m: 10000000000000000000000000000000000
deg: 5
c5: 53
c0: -17
skew: 0.80
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 6000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11211532
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1011596 x 1011844
Total sieving time: 36.00 hours.
Total relation processing time: 1.69 hours.
Matrix solve time: 2.35 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 40.30 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673798)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

Oct 6, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Oct 6, 2009

(13·10¹⁸⁷-7)/3 = 4(3)₁₈₆1_<188> = 277 · 2731 · C182

C182 = P61 · P122

P61 = 4621636202770150308574184509740627534498826420127262707612729_<61>

P122 = 12394381849058326533133616843178663059816232578757698684763135584464171107781199862640891030032321710302395320971040108797_<122>

Number: 43331_187
N=57282323864565198520706017860628580971428898756136368943991546891530632163319836736564320779251108523125094460755218970495637510404452863477275000539775744108402832214345168302077013
  ( 182 digits)
SNFS difficulty: 189 digits.
Divisors found:
 r1=4621636202770150308574184509740627534498826420127262707612729 (pp61)
 r2=12394381849058326533133616843178663059816232578757698684763135584464171107781199862640891030032321710302395320971040108797 (pp122)
Version: Msieve-1.40
Total time: 314.92 hours.
Scaled time: 547.65 units (timescale=1.739).
Factorization parameters were as follows:
n: 57282323864565198520706017860628580971428898756136368943991546891530632163319836736564320779251108523125094460755218970495637510404452863477275000539775744108402832214345168302077013
m: 20000000000000000000000000000000000000
deg: 5
c5: 325
c0: -56
skew: 0.70
type: snfs
lss: 1
rlim: 9900000
alim: 9900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 9900000/9900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4950000, 10050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2086172 x 2086398
Total sieving time: 307.66 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 6.69 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,189.000,5,0,0,0,0,0,0,0,0,9900000,9900000,28,28,54,54,2.5,2.5,100000
total time: 314.92 hours.

Oct 6, 2009 (2nd)

By Lionel Debroux / GGNFS + Msieve / Oct 6, 2009

(43·10²⁰³-7)/9 = 4(7)₂₀₃_<204> = 3 · 67 · 547 · 2838580823343361_<16> · 70019741574365087_<17> · 2334561165143153784276485597559959244336157_<43> · C124

C124 = P60 · P65

P60 = 375528253117018963232975349935219398139299723906573412769943_<60>

P65 = 24938648869152625653899078805207205944348712733762951036782202663_<65>

Number: 47777_203
N=9365167244931605937271157091977652941532850887100421862106964322653891953074392906416380032956187565261989128184595620958209
  ( 124 digits)
Divisors found:
 r1=375528253117018963232975349935219398139299723906573412769943 (pp60)
 r2=24938648869152625653899078805207205944348712733762951036782202663 (pp65)
Version: Msieve v. 1.43
Total time: 124.36 hours.
Scaled time: 263.27 units (timescale=2.117).
Factorization parameters were as follows:
# Murphy_E = 1.720399e-10, selected by Jeff Gilchrist
n: 9365167244931605937271157091977652941532850887100421862106964322653891953074392906416380032956187565261989128184595620958209
Y0: -791009809091308516245887
Y1: 36802700256773
c0: 14133203719709143941404877603600
c1: 178200169790415316254562260
c2: -3251458876158126409286
c3: 3149167561132455
c4: 36525171834
c5: 30240
skew: 289012.3
type: gnfs
# selected mechanically
rlim: 6700000
alim: 6700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6700000/6700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3350000, 6750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 798924 x 799149
Total sieving time: 120.74 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.58 hours.
Time per square root: 1.89 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6700000,6700000,27,27,52,52,2.5,2.5,100000
total time: 124.36 hours.
 --------- CPU info (if available) ----------
[    0.029439] CPU0: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.101689] CPU1: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.000000] Memory: 2043420k/2096800k available (7091k kernel code, 452k absent, 52268k reserved, 3271k data, 540k init)
[    0.000999] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.57 BogoMIPS (lpj=1995288)
[    0.000999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913)
[    0.102027] Total of 2 processors activated (7980.40 BogoMIPS).

Oct 6, 2009

By Sinkiti Sibata / Msieve / Oct 6, 2009

6·10¹⁷⁶-1 = 5(9)₁₇₆_<177> = 19 · 1103 · 1997 · 36996060425134747_<17> · C153

C153 = P70 · P84

P70 = 1199957761620461468118405565148809667093672061199543170259030057791043_<70>

P84 = 322940588839473726687584052243149346589728994478475409111736442256055691359527808711_<84>

Number: 59999_176
N=387515066120208673360721553568032958377932806855532462895231578125905792872581648553959939875118989601130150913793808472733556843936511913610382913175573
  ( 153 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=1199957761620461468118405565148809667093672061199543170259030057791043 (pp70)
 r2=322940588839473726687584052243149346589728994478475409111736442256055691359527808711 (pp84)
Version: Msieve-1.40
Total time: 70.81 hours.
Scaled time: 237.72 units (timescale=3.357).
Factorization parameters were as follows:
name: 59999_176
n: 387515066120208673360721553568032958377932806855532462895231578125905792872581648553959939875118989601130150913793808472733556843936511913610382913175573
m: 200000000000000000000000000000000000
deg: 5
c5: 15
c0: -8
skew: 0.88
type: snfs
lss: 1
rlim: 6400000
alim: 6400000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6400000/6400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3200000, 6400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1188531 x 1188779
Total sieving time: 67.80 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 2.75 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,177.000,5,0,0,0,0,0,0,0,0,6400000,6400000,28,28,53,53,2.5,2.5,100000
total time: 70.81 hours.
 --------- CPU info (if available) ----------

Oct 4, 2009 (2nd)

By Sinkiti Sibata / GMP-ECM 6.2.3 / Oct 4, 2009

6·10¹⁷⁹-1 = 5(9)₁₇₉_<180> = 67 · 353 · 125707 · C171

C171 = P33 · P138

P33 = 298716705932280059000729938505471_<33>

P138 = 675589309562746723090472275034259356819506679454841812592974658819494178186471751132798670903173117107700007029230329053233402544370951617_<138>

input number is
201809813115647133250553212747864288202896217227991350567295137528404617678007456453502911258079727890895528445717591847212096503608090210582105616636279664187139030796607

Run 116 out of 2350:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3490299074
Step 1 took 10244ms
Step 2 took 5970ms
********** Factor found in step 2: 298716705932280059000729938505471
Found probable prime factor of 33 digits: 298716705932280059000729938505471
Probable prime cofactor 675589309562746723090472275034259356819506679454841812592974658819494178186471751132798670903173117107700007029230329053233402544370951617 has 138 digits

6·10¹⁷⁷-1 = 5(9)₁₇₇_<178> = 7 · 20780271302226927560453_<23> · 2134599379553078846457397762501_<31> · C125

C125 = P31 · P42 · P53

P31 = 2612221635774246750954450916549_<31>

P42 = 630726357249729854245007611079998752429959_<42>

P53 = 11728287839848260529211822787806892333944451684664859_<53>

input number is
19323492290039138638815316517611068312752099363413275545931587268134829069485406364310774661002256608058736716295392500214769
Run 460 out of 7553:
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=3697522187
Step 1 took 72052ms
Step 2 took 33792ms
********** Factor found in step 2: 630726357249729854245007611079998752429959
Found probable prime factor of 42 digits: 630726357249729854245007611079998752429959
Probable prime cofactor 11728287839848260529211822787806892333944451684664859 has 53 digits

6·10¹⁸⁰-1 = 5(9)₁₈₀_<181> = 937 · 6389 · 279187417 · C166

C166 = P36 · C130

P36 = 681683799034595926517755346160165173_<36>

C130 = [5266231639949962957625555506172842343649977284297109659058979603488997179970876035150164573856074896623381506221376644219732362423_<130>]

input numer is
3589904790917281081704651844819933368931090596346351831443364502544397381852188944206243859153785535672534395186545124553864469943600705340445084551330647199178494179

Run 1018 out of 2350:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3992605710
Step 1 took 10102ms
Step 2 took 5989ms
********** Factor found in step 2: 681683799034595926517755346160165173
Found probable prime factor of 36 digits: 681683799034595926517755346160165173
Composite cofactor 5266231639949962957625555506172842343649977284297109659058979603488997179970876035150164573856074896623381506221376644219732362423 has 130 digits

Oct 4, 2009

By matsui / Msieve / Oct 4, 2009

(25·10¹⁷⁴-61)/9 = 2(7)₁₇₃1_<175> = 19 · 403409639 · C165

C165 = P44 · P121

P44 = 66522182025933914980141308358046139455527739_<44>

P121 = 5447925262173541576005437341883756530635970709270997946040684543445936204837528913808007878742336075875516134731712620029_<121>

N=362407875953992078870973210457563521793287716680851855268135599529779022325737810170065681415705662921348106771932711328587577814913912875930872703313939430576484431
  ( 165 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=66522182025933914980141308358046139455527739 (pp44)
 r2=5447925262173541576005437341883756530635970709270997946040684543445936204837528913808007878742336075875516134731712620029 (pp121)
Version: Msieve v. 1.42
Total time: 144.27 hours.
Scaled time: 429.36 units (timescale=2.976).
Factorization parameters were as follows:
n: 362407875953992078870973210457563521793287716680851855268135599529779022325737810170065681415705662921348106771932711328587577814913912875930872703313939430576484431
m: 50000000000000000000000000000000000
deg: 5
c5: 80
c0: -61
skew: 0.95
type: snfs
lss: 1
rlim: 5900000
alim: 5900000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5

Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2950000, 7050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1169139 x 1169367
Total sieving time: 142.80 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.29 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5900000,5900000,28,28,52,52,2.5,2.5,100000
total time: 144.27 hours.

Oct 3, 2009 (4th)

By Erik Branger / GGNFS, Msieve / Oct 3, 2009

6·10¹⁹⁸+7 = 6(0)₁₉₇7_<199> = 13 · 5936837 · 1592801512885567_<16> · 31002981535411234004171_<23> · 335224324447072705491257699413_<30> · C124

C124 = P61 · P63

P61 = 5578023513293801818533172337270300793467390504065490987063639_<61>

P63 = 841921861803218150630322445765550878314463032851719559505591353_<63>

Number: 60007_198
N=4696259941494445597344934071014281667903341455948176056974276671061552942678133843753512726575345913843588902774011739113567
  ( 124 digits)
Divisors found:
 r1=5578023513293801818533172337270300793467390504065490987063639 (pp61)
 r2=841921861803218150630322445765550878314463032851719559505591353 (pp63)
Version: Msieve-1.40
Total time: 105.45 hours.
Scaled time: 103.02 units (timescale=0.977).
Factorization parameters were as follows:
# Murphy_E = 1.871862e-10, selected by Jeff Gilchrist 
n: 
4696259941494445597344934071014281667903341455948176056974276671061552942678133843753512726575345913843588902774011739113567
Y0: -731385356919230950702233
Y1: 27519743625683
c0: 32127868542654071627549661608
c1: 153965668232279984138120
c2: -7127488219309338392
c3: -341107411740763
c4: -2788317394
c5: 22440
skew: 88733.3
type: gnfs
# selected mechanically
rlim: 6600000
alim: 6600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6600000/6600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3300000, 6100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 933962 x 934187
Total sieving time: 101.60 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 2.86 hours.
Time per square root: 0.75 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6600000,6600000,27,27,52,52,2.5,2.5,100000
total time: 105.45 hours.
 --------- CPU info (if available) ----------

Oct 3, 2009 (3rd)

By Sinkiti Sibata / Msieve, GMP-ECM / Oct 3, 2009

6·10¹⁷⁴-1 = 5(9)₁₇₄_<175> = 139 · 2371 · 30091 · 1665313208678010547_<19> · C147

C147 = P73 · P74

P73 = 4377830453093505504381429331801225862588053958648601821602876203502681051_<73>

P74 = 82987639321330983463201182406477468083679082354734448996697936818652462173_<74>

Number: 59999_174
N=363305814651262832969806732578323590200700059687593582374442939450804796010110135509146831467516569517986092290018743800270527413991185207861383823
  ( 147 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=4377830453093505504381429331801225862588053958648601821602876203502681051 (pp73)
 r2=82987639321330983463201182406477468083679082354734448996697936818652462173 (pp74)
Version: Msieve-1.40
Total time: 62.19 hours.
Scaled time: 207.66 units (timescale=3.339).
Factorization parameters were as follows:
name: 59999_174
n: 363305814651262832969806732578323590200700059687593582374442939450804796010110135509146831467516569517986092290018743800270527413991185207861383823
m: 100000000000000000000000000000000000
deg: 5
c5: 3
c0: -5
skew: 1.11
type: snfs
lss: 1
rlim: 5900000
alim: 5900000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2950000, 5850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1022541 x 1022789
Total sieving time: 59.77 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 2.21 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5900000,5900000,28,28,52,52,2.5,2.5,100000
total time: 62.19 hours.
 --------- CPU info (if available) ----------

6·10¹⁷⁷-1 = 5(9)₁₇₇_<178> = 7 · 20780271302226927560453_<23> · C155

C155 = P31 · C125

P31 = 2134599379553078846457397762501_<31>

C125 = [19323492290039138638815316517611068312752099363413275545931587268134829069485406364310774661002256608058736716295392500214769_<125>]

GMP-ECM6.2.3[powered by GMP 4.3.1][ECM]
input number is
41247914653116248049413346164540241593723737985855781308700472753384433598071487379042959672169128034542488669258083369424096252382458746050385502554577269

Run 28 out of 10000:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3657672614
Step 1 took 39920ms
Step 2 took 17734ms
********** Factor found in step 2: 2134599379553078846457397762501
Found probable prime factor of 31 digits: 2134599379553078846457397762501
Composite cofactor 19323492290039138638815316517611068312752099363413275545931587268134829069485406364310774661002256608058736716295392500214769 has 125 digits

Oct 3, 2009 (2nd)

By Lionel Debroux / GGNFS + Msieve, GMP-ECM 6.2.3

(55·10¹⁷²+71)/9 = 6(1)₁₇₁9_<173> = 3 · 97 · 1289 · 4415852847060229_<16> · 4051314161189975816333577239_<28> · C124

C124 = P38 · P87

P38 = 15505584418716736261260920800939868311_<38>

P87 = 587321121219860526817229192460046953047699552171738577900691895117464529118402936396041_<87>

Number: 61119_172
N=9106757225969912881333194990833285699269760699586847310985480208600176868257330699000978309517694764014428821400787481756751
  ( 124 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=15505584418716736261260920800939868311 (pp38)
 r2=587321121219860526817229192460046953047699552171738577900691895117464529118402936396041 (pp87)
Version: Msieve v. 1.43
Total time: 168.60 hours.
Scaled time: 368.73 units (timescale=2.187).
Factorization parameters were as follows:
n: 9106757225969912881333194990833285699269760699586847310985480208600176868257330699000978309517694764014428821400787481756751
m: 20000000000000000000000000000000000
deg: 5
c5: 1375
c0: 568
skew: 0.84
type: snfs
lss: 1
rlim: 5700000
alim: 5700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 10000
Factor base limits: 5700000/5700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2850000, 7430001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1067303 x 1067528
Total sieving time: 163.84 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 3.85 hours.
Time per square root: 0.75 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5700000,5700000,27,27,52,52,2.4,2.4,100000
total time: 168.60 hours.
 --------- CPU info (if available) ----------
[    0.029439] CPU0: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.101689] CPU1: Intel(R) Core(TM)2 CPU         T7200  @ 2.00GHz stepping 06
[    0.000000] Memory: 2043420k/2096800k available (7091k kernel code, 452k absent, 52268k reserved, 3271k data, 540k init)
[    0.000999] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.57 BogoMIPS (lpj=1995288)
[    0.000999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913)
[    0.102027] Total of 2 processors activated (7980.40 BogoMIPS).

(4·10¹⁷⁴+17)/3 = 1(3)₁₇₃9_<175> = 7² · 311 · 1367 · 1847 · C164

C164 = P32 · P133

P32 = 17046294381955175722850377313441_<32>

P133 = 2032904013590983323124640548830455534219890792230587335816686586190726080165488832358711164967138379379602576761258463473790718398589_<133>

$ echo 34653480265930107213911468312089814676202650490024533804881869022835266218664881461304021116792725096000602005734429619839477009825529617570745711284331483625134749 | ecm -n -c 1000 1e6
GMP-ECM 6.2.3 [powered by GMP 4.2.2] [ECM]
Input number is 34653480265930107213911468312089814676202650490024533804881869022835266218664881461304021116792725096000602005734429619839477009825529617570745711284331483625134749 (164 digits)
Run 445 out of 1000:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=811603726
Step 1 took 7293ms
Step 2 took 5490ms
********** Factor found in step 2: 17046294381955175722850377313441
Found probable prime factor of 32 digits: 17046294381955175722850377313441
Probable prime cofactor 2032904013590983323124640548830455534219890792230587335816686586190726080165488832358711164967138379379602576761258463473790718398589 has 133 digits

Oct 3, 2009

By Robert Backstrom / GGNFS, Msieve / Oct 3, 2009

(44·10²⁰⁴+1)/9 = 4(8)₂₀₃9_<205> = 3727 · C202

C202 = P65 · P138

P65 = 12642215777443416767752239365062569151194901640368783823119996813_<65>

P138 = 103759429617785294941240486367388306991041521908442118224429949294529777836170876768851200709291701192031411549441181450806379682224633939_<138>

Number: n
N=1311749098172495006409683093342873326774587842470858301284917866618966699460394120979041826908744000238499836031362728438124198789613332140834153176519691142712339385266672629162567450734877619771636407
  ( 202 digits)
SNFS difficulty: 206 digits.
Divisors found:

Sat Oct  3 03:07:12 2009  prp65 factor: 12642215777443416767752239365062569151194901640368783823119996813
Sat Oct  3 03:07:12 2009  prp138 factor: 103759429617785294941240486367388306991041521908442118224429949294529777836170876768851200709291701192031411549441181450806379682224633939
Sat Oct  3 03:07:12 2009  elapsed time 14:00:17 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 51.07 hours.
Scaled time: 102.71 units (timescale=2.011).
Factorization parameters were as follows:
name: KA_4_8_203_9
n: 1311749098172495006409683093342873326774587842470858301284917866618966699460394120979041826908744000238499836031362728438124198789613332140834153176519691142712339385266672629162567450734877619771636407
m: 100000000000000000000000000000000000000000
deg: 5
c5: 22
c0: 5
skew: 0.74
type: snfs
lss: 1
rlim: 19200000
alim: 19200000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 19200000/19200000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 21099990)
Primes: RFBsize:1222953, AFBsize:1222884, largePrimes:37218454 encountered
Relations: rels:32489696, finalFF:699411
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 8283779 hash collisions in 51853947 relations
Msieve: matrix is 2958153 x 2958401 (781.2 MB)

Total sieving time: 50.30 hours.
Total relation processing time: 0.78 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,19200000,19200000,29,29,58,58,2.6,2.6,100000
total time: 51.07 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.02 BogoMIPS (lpj=2830511)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830460)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459)
Total of 4 processors activated (22643.75 BogoMIPS).

Oct 2, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Oct 2, 2009

(64·10¹⁷³+53)/9 = 7(1)₁₇₂7_<174> = 3 · 11 · 2753 · 147028199 · C161

C161 = P51 · P53 · P58

P51 = 439231572111653323454876092277539599135182889732971_<51>

P53 = 66354886809665594141565452524880020064086534990625821_<53>

P58 = 1826628432327857002931189663671146473104422650646339516437_<58>

Number: 71117_173
N=53237380205309160401938268502777912648314709782189098631100825123672071173417036027520915538137652984326635588082815651085876674764067883749576740330280312067467
  ( 161 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=439231572111653323454876092277539599135182889732971 (pp51)
 r2=66354886809665594141565452524880020064086534990625821 (pp53)
 r3=1826628432327857002931189663671146473104422650646339516437 (pp58)
Version: Msieve-1.40
Total time: 61.30 hours.
Scaled time: 106.61 units (timescale=1.739).
Factorization parameters were as follows:
n: 53237380205309160401938268502777912648314709782189098631100825123672071173417036027520915538137652984326635588082815651085876674764067883749576740330280312067467
m: 40000000000000000000000000000000000
deg: 5
c5: 125
c0: 106
skew: 0.97
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 5900001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1057736 x 1057961
Total sieving time: 59.41 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.46 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,52,52,2.5,2.5,100000
total time: 61.30 hours.

Oct 2, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Oct 2, 2009

(52·10¹⁷⁰-43)/9 = 5(7)₁₆₉3_<171> = 3 · 53 · 1871 · 7045130639_<10> · 14036622641_<11> · C146

C146 = P69 · P77

P69 = 578927665551376438914204663528267269983143581603946449236868953675283_<69>

P77 = 33924538095586390606363467907555617985564551366711291445601666869966930931921_<77>

Number: 57773_170
N=19639853644586566926473635125864399983081674601955455224960515746857290977151949664285028054097717990517694394899376140667033181948320569213408643
  ( 146 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=578927665551376438914204663528267269983143581603946449236868953675283
 r2=33924538095586390606363467907555617985564551366711291445601666869966930931921
Version: 
Total time: 38.40 hours.
Scaled time: 91.31 units (timescale=2.378).
Factorization parameters were as follows:
n: 19639853644586566926473635125864399983081674601955455224960515746857290977151949664285028054097717990517694394899376140667033181948320569213408643
m: 10000000000000000000000000000000000
deg: 5
c5: 52
c0: -43
skew: 0.96
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 5800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10967118
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1032176 x 1032423
Total sieving time: 33.77 hours.
Total relation processing time: 1.54 hours.
Matrix solve time: 2.44 hours.
Time per square root: 0.65 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 38.40 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672363)
Calibrating delay using timer specific routine.. 5535.15 BogoMIPS (lpj=2767578)

Oct 1, 2009 (3rd)

By Wataru Sakai / Msieve / Oct 1, 2009

(22·10¹⁹⁷+23)/9 = 2(4)₁₉₆7_<198> = 7 · 113 · C195

C195 = P60 · P68 · P68

P60 = 695297672042072244900952876381872976120480443321416660609207_<60>

P68 = 15289769744936237230919203210804611301606749732361166218939120705391_<68>

P68 = 29069125530481941095166355250055849161785796071989116662232205007841_<68>

Number: 24447_197
N=309032167439247085264784379828627616238235707262255934822306503722432925972748981598539120663014468324202837477173760359601067565669335580840005618766680713583368450625087793229386149740132041017
  ( 195 digits)
SNFS difficulty: 198 digits.
Divisors found:
 r1=695297672042072244900952876381872976120480443321416660609207
 r2=15289769744936237230919203210804611301606749732361166218939120705391
 r3=29069125530481941095166355250055849161785796071989116662232205007841
Version: 
Total time: 843.82 hours.
Scaled time: 1700.29 units (timescale=2.015).
Factorization parameters were as follows:
n: 309032167439247085264784379828627616238235707262255934822306503722432925972748981598539120663014468324202837477173760359601067565669335580840005618766680713583368450625087793229386149740132041017
m: 2000000000000000000000000000000000000000
deg: 5
c5: 275
c0: 92
skew: 0.80
type: snfs
lss: 1
rlim: 14500000
alim: 14500000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 14500000/14500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [7250000, 16450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2462811 x 2463059
Total sieving time: 843.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,198,5,0,0,0,0,0,0,0,0,14500000,14500000,28,28,55,55,2.5,2.5,100000
total time: 843.82 hours.
 --------- CPU info (if available) ----------

(14·10¹⁷¹+1)/3 = 4(6)₁₇₀7_<172> = 13 · 83 · 157 · 179 · 6269917 · C158

C158 = P52 · P106

P52 = 8716281892569658959466816355313570524828127197103157_<52>

P106 = 2816045021746225571280058016558802032880013547923850367154664124292968300123708807461754097927827102820139_<106>

Number: 46667_171
N=24545442231707557443195388045005997931178690810482840774904483526903568635628800068776271020858144863975192360888664449533761102657624998421849365666000078823
  ( 158 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=8716281892569658959466816355313570524828127197103157
 r2=2816045021746225571280058016558802032880013547923850367154664124292968300123708807461754097927827102820139
Version: 
Total time: 77.95 hours.
Scaled time: 156.90 units (timescale=2.013).
Factorization parameters were as follows:
n: 24545442231707557443195388045005997931178690810482840774904483526903568635628800068776271020858144863975192360888664449533761102657624998421849365666000078823
m: 20000000000000000000000000000000000
deg: 5
c5: 35
c0: 8
skew: 0.74
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2700000, 5600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 827628 x 827876
Total sieving time: 77.95 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000
total time: 77.95 hours.
 --------- CPU info (if available) ----------

(55·10²⁰⁵+71)/9 = 6(1)₂₀₄9_<206> = 3 · 38653 · C201

C201 = P50 · P152

P50 = 26200194537354193414830555249424744078537286162689_<50>

P152 = 20114590830632865891174418642478448899424128172100897058014500078728469238559651699262525227509652933449801787184330996714251345648259452695413875227369_<152>

Number: 61119_205
N=527006192801861960788822869385826982908710070896705828017757234118189283376979028028105719358662209152468640736045594659415061453713046086212463983917687381842816091127994473142327125200382127399435241
  ( 201 digits)
SNFS difficulty: 206 digits.
Divisors found:
 r1=26200194537354193414830555249424744078537286162689
 r2=20114590830632865891174418642478448899424128172100897058014500078728469238559651699262525227509652933449801787184330996714251345648259452695413875227369
Version: 
Total time: 1461.40 hours.
Scaled time: 2941.80 units (timescale=2.013).
Factorization parameters were as follows:
n: 527006192801861960788822869385826982908710070896705828017757234118189283376979028028105719358662209152468640736045594659415061453713046086212463983917687381842816091127994473142327125200382127399435241
m: 100000000000000000000000000000000000000000
deg: 5
c5: 55
c0: 71
skew: 1.05
type: snfs
lss: 1
rlim: 19500000
alim: 19500000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 19500000/19500000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [9750000, 28250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3839828 x 3840076
Total sieving time: 1461.40 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,19500000,19500000,29,29,56,56,2.6,2.6,100000
total time: 1461.40 hours.
 --------- CPU info (if available) ----------

Oct 1, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve 1.42 / Oct 1, 2009

(35·10¹⁷¹+1)/9 = 3(8)₁₇₀9_<172> = 1315747 · C166

C166 = P41 · P126

P41 = 12878217459996999966612430708842525173647_<41>

P126 = 229507769468070544234606674705372447688355761067510543219870223637687579557401800773214413613089328397784365674061380352422621_<126>

Number: snfs166
N=2955650963968672464302703246816362787746344007540118950595280771218850500049697159779873249864061167450040842873963527098210285783580649538922671979407050815155868787
  ( 166 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=12878217459996999966612430708842525173647 (pp41)
 r2=229507769468070544234606674705372447688355761067510543219870223637687579557401800773214413613089328397784365674061380352422621 (pp126)
Version: Msieve-1.40
Total time: 78.20 hours.
Scaled time: 144.67 units (timescale=1.850).
Factorization parameters were as follows:
n: 2955650963968672464302703246816362787746344007540118950595280771218850500049697159779873249864061167450040842873963527098210285783580649538922671979407050815155868787
m: 50000000000000000000000000000000000
deg: 5
c5: 14
c0: 125
skew: 1.55
type: snfs
lss: 1
rlim: 5700000
alim: 5700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5700000/5700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2850000, 6750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1087516 x 1087746
Total sieving time: 74.03 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 3.93 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5700000,5700000,27,27,52,52,2.4,2.4,100000
total time: 78.20 hours.
 --------- CPU info (if available) ----------

Oct 1, 2009

By Ignacio Santos / GGNFS, Msieve / Oct 1, 2009

(5·10¹⁷⁴-17)/3 = 1(6)₁₇₃1_<175> = 84299 · 47682601 · C162

C162 = P80 · P83

P80 = 32158440488038156759395809693301845189137482437122786675893457460513811317417207_<80>

P83 = 12893517373837962160956529482356192177502664332718530798514584467954575263274442177_<83>

Number: 16661_174
N=414635411148054129148515657697916605888472579438489618948350222853369651192320106315500229014738785629430279620882810700768750294540964719699877769269657306339639
  ( 162 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=32158440488038156759395809693301845189137482437122786675893457460513811317417207 (pp80)
 r2=12893517373837962160956529482356192177502664332718530798514584467954575263274442177 (pp83)
Version: Msieve-1.40
Total time: 53.36 hours.
Scaled time: 93.06 units (timescale=1.744).
Factorization parameters were as follows:
n: 414635411148054129148515657697916605888472579438489618948350222853369651192320106315500229014738785629430279620882810700768750294540964719699877769269657306339639
m: 50000000000000000000000000000000000
deg: 5
c5: 16
c0: -17
skew: 1.01
type: snfs
lss: 1
rlim: 5700000
alim: 5700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5700000/5700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2850000, 5450001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 980277 x 980508
Total sieving time: 51.66 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.25 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5700000,5700000,27,27,52,52,2.4,2.4,100000
total time: 53.36 hours.

(47·10¹⁷²+61)/9 = 5(2)₁₇₁9_<173> = 29 · 1252682099_<10> · C163

C163 = P48 · P115

P48 = 155705137976349535618955127465479103372581214599_<48>

P115 = 9232377109645985396433945968057508694695399541386192131778368096665877091302329437777202702426026982598638033918501_<115>

Number: 52229_172
N=1437528551707119281313675875542368254399786406986836567956741962539411239838906542666098053887433178858381201289266668628552414894416032281242016585115461957396099
  ( 163 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=155705137976349535618955127465479103372581214599 (pp48)
 r2=9232377109645985396433945968057508694695399541386192131778368096665877091302329437777202702426026982598638033918501 (pp115)
Version: Msieve-1.40
Total time: 113.19 hours.
Scaled time: 196.84 units (timescale=1.739).
Factorization parameters were as follows:
n: 1437528551707119281313675875542368254399786406986836567956741962539411239838906542666098053887433178858381201289266668628552414894416032281242016585115461957396099
m: 20000000000000000000000000000000000
deg: 5
c5: 1175
c0: 488
skew: 0.84
type: snfs
lss: 1
rlim: 5700000
alim: 5700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5700000/5700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2850000, 9050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1275294 x 1275542
Total sieving time: 110.55 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 2.22 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5700000,5700000,27,27,52,52,2.4,2.4,100000
total time: 113.19 hours.

September 2009

Sep 30, 2009 (6th)

By Markus Tervooren / Msieve / Sep 30, 2009

5·10¹⁷¹+3 = 5(0)₁₇₀3_<172> = 2141 · 3463 · 22115239687_<11> · 2126176738288566290549353_<25> · C131

C131 = P54 · P77

P54 = 147260649364933694278877144916097788377722854278739967_<54>

P77 = 97391963406433881857367240605552004713811188886749910103549282496731302376393_<77>

N=14342003774157313216888357848440703925791970886954343965424053505716746519075757175850873535193063392798657509444707017884806399031
  ( 131 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=147260649364933694278877144916097788377722854278739967 (pp54)
 r2=97391963406433881857367240605552004713811188886749910103549282496731302376393 (pp77)
Version: Msieve-1.42
Total time: 30.58 hours.
Scaled time: 64.74 units (timescale=2.117).
Factorization parameters were as follows:
n: 14342003774157313216888357848440703925791970886954343965424053505716746519075757175850873535193063392798657509444707017884806399031
m: 10000000000000000000000000000000000
deg: 5
c5: 50
c0: 3
skew: 0.57
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5

Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [2550000, 4950001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 957853 x 958079
Total sieving time: 29.27 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 1.08 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,28,28,56,56,2.5,2.5,200000
total time: 30.58 hours.
 --------- CPU info (if available) ----------
[    0.148007] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.240015] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.335125] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.432094] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197992k/10485760k available (2226k kernel code, 189844k reserved, 1082k data, 392k init)
[    0.083917] Calibrating delay using timer specific routine.. 5503.93 BogoMIPS (lpj=11007873)
[    0.160010] Calibrating delay using timer specific routine.. 5499.97 BogoMIPS (lpj=10999957)
[    0.252015] Calibrating delay using timer specific routine.. 5500.01 BogoMIPS (lpj=11000021)
[    0.351657] Calibrating delay using timer specific routine.. 5499.99 BogoMIPS (lpj=10999983)
[    0.436823] Total of 4 processors activated (22003.91 BogoMIPS).

Sep 30, 2009 (5th)

By Sinkiti Sibata / Msieve / Sep 30, 2009

10¹⁷⁸+7 = 1(0)₁₇₇7_<179> = 9779956187_<10> · 15061360829503_<14> · 28611712108180931576351076849383_<32> · C124

C124 = P62 · P63

P62 = 14520779712977015969339895588943857520182395580183706784454421_<62>

P63 = 163404906987574736909472325954343135617120818034514302156773209_<63>

Number: 10007_178
N=2372766658386071479394164140981662985967236676580748175830928608025753371979903404338599883260199063087303313743132894406989
  ( 124 digits)
Divisors found:
 r1=14520779712977015969339895588943857520182395580183706784454421 (pp62)
 r2=163404906987574736909472325954343135617120818034514302156773209 (pp63)
Version: Msieve-1.40
Total time: 62.63 hours.
Scaled time: 209.13 units (timescale=3.339).
Factorization parameters were as follows:
name: 10007_178
# Murphy_E = 1.911810e-10, selected by Jeff Gilchrist
n: 2372766658386071479394164140981662985967236676580748175830928608025753371979903404338599883260199063087303313743132894406989
Y0: -617353060601615830149752
Y1: 20088237568453
c0: -130899536347007954275021914327
c1: 19214420838302689840482678
c2: -385427287466242970753
c3: -3461889503623372
c4: -5310923826
c5: 26460
skew: 149044.72
type: gnfs
# selected mechanically
rlim: 6500000
alim: 6500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6500000/6500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3250000, 6150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 885610 x 885858
Total sieving time: 60.70 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.50 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6500000,6500000,27,27,52,52,2.5,2.5,100000
total time: 62.63 hours.
 --------- CPU info (if available) ----------

Sep 30, 2009 (4th)

By Erik Branger / GGNFS, Msieve / Sep 30, 2009

(19·10¹⁹⁷+17)/9 = 2(1)₁₉₆3_<198> = 3 · 7 · 90017 · 189037603483_<12> · 1167987135194728007608387_<25> · 130987118004416341717932217759037_<33> · C124

C124 = P62 · P63

P62 = 15872932989461007548410407402377925558623951734243828910973433_<62>

P63 = 243273738880783002227362363624452946028222802288282346250262049_<63>

Number: 21113_197
N=3861467755350303484159223919449335539186556972805576020551599415949486879617583193229971628069176142786276497779467927144217
  ( 124 digits)
Divisors found:
 r1=15872932989461007548410407402377925558623951734243828910973433 (pp62)
 r2=243273738880783002227362363624452946028222802288282346250262049 (pp63)
Version: Msieve-1.40
Total time: 99.47 hours.
Scaled time: 98.87 units (timescale=0.994).
Factorization parameters were as follows:
# Murphy_E = 1.697274e-10, selected by Jeff Gilchrist 
n: 3861467755350303484159223919449335539186556972805576020551599415949486879617583193229971628069176142786276497779467927144217
Y0: -755771304549153749000013
Y1: 22680260791903
c0: 121490305313515955986026122165920
c1: 1176066474224985519877609868
c2: -1293811007753745607480
c3: -14927256567925211
c4: 10409629152
c5: 15660
skew: 478491.47
type: gnfs
# selected mechanically
rlim: 6600000
alim: 6600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6600000/6600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3300000, 6200001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 909121 x 909347
Total sieving time: 96.67 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 1.91 hours.
Time per square root: 0.65 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6600000,6600000,27,27,52,52,2.5,2.5,100000
total time: 99.47 hours.
 --------- CPU info (if available) ----------

Sep 30, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Sep 30, 2009

(47·10¹⁷⁰+7)/9 = 5(2)₁₆₉3_<171> = 53 · 6724829 · 67618339 · 1783969331_<10> · C146

C146 = P65 · P81

P65 = 63031244433350462277961874790503249892506486100802703001462978317_<65>

P81 = 192703884630974675279313413532569965260638475935521459497205658966223021555132643_<81>

Number: 52223_170
N=12146365655431132202943080014873332479426617499334645447393097560540169951246527581811497428728533243733416133954869342564412853855411676767901831
  ( 146 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=63031244433350462277961874790503249892506486100802703001462978317
 r2=192703884630974675279313413532569965260638475935521459497205658966223021555132643
Version: 
Total time: 37.80 hours.
Scaled time: 90.07 units (timescale=2.383).
Factorization parameters were as follows:
n: 12146365655431132202943080014873332479426617499334645447393097560540169951246527581811497428728533243733416133954869342564412853855411676767901831
m: 10000000000000000000000000000000000
deg: 5
c5: 47
c0: 7
skew: 0.68
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 5800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11056590
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1006773 x 1007021
Total sieving time: 33.71 hours.
Total relation processing time: 1.54 hours.
Matrix solve time: 2.41 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 37.80 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672363)
Calibrating delay using timer specific routine.. 5535.15 BogoMIPS (lpj=2767578)

Sep 30, 2009 (2nd)

By matsui / Msieve / Sep 30, 2009

(11·10¹⁷⁷+43)/9 = 1(2)₁₇₆7_<178> = 3² · 17 · 1607 · C172

C172 = P53 · P58 · P62

P53 = 55787633447660991296304360824773479896272139981968559_<53>

P58 = 5262473431773579047842882158186090489494636716739379529237_<58>

P62 = 16932263297944616820513923713596671722409861171887225084414439_<62>

N=4970989755693929834027690220571853623331837517325029068992366819276052166470312571316756438222572902954078448545059084732328018441468177305262606091089320099654787356875037
  ( 172 digits)
SNFS difficulty: 178 digits.
Divisors found:
 r1=55787633447660991296304360824773479896272139981968559 (pp53)
 r2=5262473431773579047842882158186090489494636716739379529237 (pp58)
 r3=16932263297944616820513923713596671722409861171887225084414439 (pp62)
Version: Msieve v. 1.42
Total time: 233.29 hours.
Scaled time: 624.52 units (timescale=2.677).
Factorization parameters were as follows:
n: 4970989755693929834027690220571853623331837517325029068992366819276052166470312571316756438222572902954078448545059084732328018441468177305262606091089320099654787356875037
m: 200000000000000000000000000000000000
deg: 5
c5: 275
c0: 344
skew: 1.05
type: snfs
lss: 1
rlim: 6700000
alim: 6700000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

Factor base limits: 6700000/6700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3350000, 8950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1521728 x 1521960
Total sieving time: 230.29 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 2.59 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,178.000,5,0,0,0,0,0,0,0,0,6700000,6700000,28,28,53,53,2.5,2.5,100000
total time: 233.29 hours.

Sep 30, 2009

By Robert Backstrom / GGNFS, Msieve / Sep 30, 2009

(49·10²⁰²-31)/9 = 5(4)₂₀₁1_<203> = 3² · 23 · C201

C201 = P62 · P139

P62 = 72555232079315990732521685350024064032570967598738850170782353_<62>

P139 = 3625054076606209123383325667965643130420860066851944590450555110710082259860226719865091185627928789968916520685882384826434539903193794471_<139>

Number: n
N=263016639828234031132581857219538378958668813741277509393451422436929683306494900697799248523886205045625335480407944176060118089103596349973161567364465915190552871712292002147074610842726784755770263
  ( 201 digits)
SNFS difficulty: 204 digits.
Divisors found:

Wed Sep 30 06:38:38 2009  prp62 factor: 72555232079315990732521685350024064032570967598738850170782353
Wed Sep 30 06:38:38 2009  prp139 factor: 3625054076606209123383325667965643130420860066851944590450555110710082259860226719865091185627928789968916520685882384826434539903193794471
Wed Sep 30 06:38:38 2009  elapsed time 14:01:14 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 39.66 hours.
Scaled time: 79.76 units (timescale=2.011).
Factorization parameters were as follows:
name: KA_5_4_201_1
n: 263016639828234031132581857219538378958668813741277509393451422436929683306494900697799248523886205045625335480407944176060118089103596349973161567364465915190552871712292002147074610842726784755770263
m: 20000000000000000000000000000000000000000
deg: 5
c5: 1225
c0: -248
skew: 0.73
type: snfs
lss: 1
rlim: 18000000
alim: 18000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 18000000/18000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 18599990)
Primes: RFBsize:1151367, AFBsize:1151002, largePrimes:37720524 encountered
Relations: rels:33609893, finalFF:756148
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 7375100 hash collisions in 48807446 relations
Msieve: matrix is 2918084 x 2918332 (782.2 MB)

Total sieving time: 38.67 hours.
Total relation processing time: 0.99 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,204,5,0,0,0,0,0,0,0,0,18000000,18000000,29,29,58,58,2.6,2.6,100000
total time: 39.66 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.09 BogoMIPS (lpj=2830549)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830455)
Total of 4 processors activated (22643.81 BogoMIPS).

Sep 29, 2009

By matsui / Msieve / Sep 29, 2009

4·10¹⁹⁶+7 = 4(0)₁₉₅7_<197> = 11 · 1067789 · C190

C190 = P54 · P137

P54 = 239682331904859805861970201199983371009733444205017707_<54>

P137 = 14208421828248700902749113805654452031722484299404367220663206740298549292027313504104977551440016026904929687743143349558675496264509019_<137>

N=3405507676482560097206811117518195414671216538439369916375204873213374893013847901002572946187274486217442175969562934590669470875204404956069376661834535066044287435404968925168140556199433
  ( 190 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=239682331904859805861970201199983371009733444205017707 (pp54)
 r2=14208421828248700902749113805654452031722484299404367220663206740298549292027313504104977551440016026904929687743143349558675496264509019 (pp137)
Version: Msieve v. 1.42
Total time: 814.38 hours.
Scaled time: 2140.18 units (timescale=2.628).
Factorization parameters were as follows:
n: 3405507676482560097206811117518195414671216538439369916375204873213374893013847901002572946187274486217442175969562934590669470875204404956069376661834535066044287435404968925168140556199433
m: 2000000000000000000000000000000000000000
deg: 5
c5: 5
c0: 28
skew: 1.41
type: snfs
lss: 1
rlim: 13500000
alim: 13500000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 13500000/13500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6750000, 12350001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2472594 x 2472824
Total sieving time: 803.27 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 10.47 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
snfs,197.000,5,0,0,0,0,0,0,0,0,13500000,13500000,28,28,55,55,2.5,2.5,100000
total time: 814.38 hours.

Sep 28, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Sep 28, 2009

(49·10¹⁷⁰+23)/9 = 5(4)₁₆₉7_<171> = 47 · 1384635630495587_<16> · 27987342719835283_<17> · C138

C138 = P57 · P81

P57 = 962128401894883341725044165527926493779232928255590121579_<57>

P81 = 310688736195671470313673402667663190506849516928902094903767311503739238397988139_<81>

Number: 54447_170
N=298922457242682389337326729911467005415371768958433454824941098921844718993540983395208066140217244944288244615587531117495645636009951481
  ( 138 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=962128401894883341725044165527926493779232928255590121579
 r2=310688736195671470313673402667663190506849516928902094903767311503739238397988139
Version: 
Total time: 40.57 hours.
Scaled time: 96.91 units (timescale=2.389).
Factorization parameters were as follows:
n: 298922457242682389337326729911467005415371768958433454824941098921844718993540983395208066140217244944288244615587531117495645636009951481
m: 10000000000000000000000000000000000
deg: 5
c5: 49
c0: 23
skew: 0.86
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 6000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11315878
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 972111 x 972359
Total sieving time: 36.23 hours.
Total relation processing time: 1.71 hours.
Matrix solve time: 2.25 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 40.57 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672363)
Calibrating delay using timer specific routine.. 5535.15 BogoMIPS (lpj=2767578)

Sep 28, 2009

By Ignacio Santos / GGNFS, Msieve / Sep 28, 2009

5·10¹⁷³+9 = 5(0)₁₇₂9_<174> = 2083 · 4217 · 10278689 · C160

C160 = P78 · P83

P78 = 226341838289515047722055879603441350450576514056429807821686474775748639597657_<78>

P83 = 24466653341794257255957958567501020770819886635243086406040717196519997052907339603_<83>

Number: 50009_173
N=5537827294174018715006923146346517706518949763642303394687652952323188747315622781370433986338555803686968324980195112714660389533930115707061390787492182110171
  ( 160 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=226341838289515047722055879603441350450576514056429807821686474775748639597657 (pp78)
 r2=24466653341794257255957958567501020770819886635243086406040717196519997052907339603 (pp83)
Version: Msieve-1.40
Total time: 57.65 hours.
Scaled time: 100.54 units (timescale=1.744).
Factorization parameters were as follows:
n: 5537827294174018715006923146346517706518949763642303394687652952323188747315622781370433986338555803686968324980195112714660389533930115707061390787492182110171
m: 50000000000000000000000000000000000
deg: 5
c5: 8
c0: 45
skew: 1.41
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 5700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1001445 x 1001678
Total sieving time: 56.14 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.29 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 57.65 hours.

(35·10¹⁷²-53)/9 = 3(8)₁₇₁3_<173> = 3 · 13² · 823 · 2957 · C164

C164 = P52 · P112

P52 = 3423371497246031422544753307472705733156021261934907_<52>

P112 = 9206877937016644470383489347435768756055010285968683328710645790936751051020760012596536946190038569116233788897_<112>

Number: 38883_172
N=31518563508206123170533606775818926341813461469744316035754497428876018488801240914806375287180907369937643817139696371770090144207390617702764486352268521993327579
  ( 164 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=3423371497246031422544753307472705733156021261934907 (pp52)
 r2=9206877937016644470383489347435768756055010285968683328710645790936751051020760012596536946190038569116233788897 (pp112)
Version: Msieve-1.40
Total time: 59.97 hours.
Scaled time: 104.29 units (timescale=1.739).
Factorization parameters were as follows:
n: 31518563508206123170533606775818926341813461469744316035754497428876018488801240914806375287180907369937643817139696371770090144207390617702764486352268521993327579
m: 20000000000000000000000000000000000
deg: 5
c5: 875
c0: -424
skew: 0.87
type: snfs
lss: 1
rlim: 5700000
alim: 5700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5700000/5700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2850000, 5850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1046216 x 1046441
Total sieving time: 58.12 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.44 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5700000,5700000,27,27,52,52,2.4,2.4,100000
total time: 59.97 hours.

Sep 27, 2009 (3rd)

By Sinkiti Sibata / Msieve / Sep 27, 2009

(37·10¹⁷⁰+17)/9 = 4(1)₁₆₉3_<171> = 7 · 19 · 349 · 73073906498809_<14> · 30445651912471563466043_<23> · C130

C130 = P64 · P66

P64 = 6128198903992383225192559986628700854438637463216120687360319601_<64>

P66 = 649623446059833056859631161403636566829760031296775263008078058147_<66>

Number: 41113_170
N=3981021690151624021971890462313322717513474933240117370947613991952532408909658873370458969162811205598079652891096332677381839347
  ( 130 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=6128198903992383225192559986628700854438637463216120687360319601 (pp64)
 r2=649623446059833056859631161403636566829760031296775263008078058147 (pp66)
Version: Msieve-1.40
Total time: 57.28 hours.
Scaled time: 191.26 units (timescale=3.339).
Factorization parameters were as follows:
name: 41113_170
n: 3981021690151624021971890462313322717513474933240117370947613991952532408909658873370458969162811205598079652891096332677381839347
m: 10000000000000000000000000000000000
deg: 5
c5: 37
c0: 17
skew: 0.86
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 945627 x 945875
Total sieving time: 55.40 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.70 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 57.28 hours.
 --------- CPU info (if available) ----------

Sep 27, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Sep 27, 2009

(56·10²⁰¹+61)/9 = 6(2)₂₀₀9_<202> = 509 · C200

C200 = P56 · P61 · P84

P56 = 12976230882709148313796352258421392734651435365133427111_<56>

P61 = 1992170746350625100689831072711659409098813349881993208178477_<61>

P84 = 472881814205812910730841366893587785212540261528760193335109318680466487590313204923_<84>

Number: n
N=12224405151713599650731281379611438550534817725387469984719493560358000436585898275485701811831477843265662519100633049552499454267627155642872735210652695917921851124208688059375682165466055446409081
  ( 200 digits)
SNFS difficulty: 203 digits.
Divisors found:

Sun Sep 27 22:33:34 2009  prp56 factor: 12976230882709148313796352258421392734651435365133427111
Sun Sep 27 22:33:34 2009  prp61 factor: 1992170746350625100689831072711659409098813349881993208178477
Sun Sep 27 22:33:34 2009  prp84 factor: 472881814205812910730841366893587785212540261528760193335109318680466487590313204923
Sun Sep 27 22:33:34 2009  elapsed time 26:37:21 (Msieve 1.39 - dependency 7)

Version: GGNFS-0.77.1-20050930-k8
Total time: 41.29 hours.
Scaled time: 83.00 units (timescale=2.010).
Factorization parameters were as follows:
name: KA_6_2_200_9
n: 12224405151713599650731281379611438550534817725387469984719493560358000436585898275485701811831477843265662519100633049552499454267627155642872735210652695917921851124208688059375682165466055446409081
m: 20000000000000000000000000000000000000000
deg: 5
c5: 35
c0: 122
skew: 1.28
type: snfs
lss: 1
rlim: 17000000
alim: 17000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 17000000/17000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 23799990)
Primes: RFBsize:1091314, AFBsize:1090698, largePrimes:33497097 encountered
Relations: rels:25939384, finalFF:334162
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 5638443 hash collisions in 42981489 relations
Msieve: matrix is 3697471 x 3697718 (1002.5 MB)

Total sieving time: 40.54 hours.
Total relation processing time: 0.75 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,203,5,0,0,0,0,0,0,0,0,17000000,17000000,29,29,58,58,2.6,2.6,100000
total time: 41.29 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.09 BogoMIPS (lpj=2830549)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830455)
Total of 4 processors activated (22643.81 BogoMIPS).

Sep 27, 2009

By Ignacio Santos / GGNFS, Msieve / Sep 27, 2009

(58·10¹⁷²-31)/9 = 6(4)₁₇₁1_<173> = 13 · 653 · 1654157 · C163

C163 = P73 · P90

P73 = 7434039565736917357902408688727950296148541622746377622861130440219054119_<73>

P90 = 617344175817281752770171093631930863567548241523686189857572426999876286631986362431351043_<90>

Number: 64441_172
N=4589361028702920399805711594247925927718250761973469099858784342783424252977537814598297905914338911400846931684460461245752456034671923153229789295463220704096117
  ( 163 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=7434039565736917357902408688727950296148541622746377622861130440219054119 (pp73)
 r2=617344175817281752770171093631930863567548241523686189857572426999876286631986362431351043 (pp90)
Version: Msieve-1.40
Total time: 92.31 hours.
Scaled time: 160.53 units (timescale=1.739).
Factorization parameters were as follows:
n: 4589361028702920399805711594247925927718250761973469099858784342783424252977537814598297905914338911400846931684460461245752456034671923153229789295463220704096117
m: 20000000000000000000000000000000000
deg: 5
c5: 725
c0: -124
skew: 0.70
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 7400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1134846 x 1135078
Total sieving time: 90.32 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.73 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 92.31 hours.

Sep 26, 2009 (5th)

By Markus Tervooren / Msieve / Sep 26, 2009

(4·10¹⁷¹+11)/3 = 1(3)₁₇₀7_<172> = 7 · 1926108869857_<13> · 448777904681194973_<18> · C141

C141 = P62 · P79

P62 = 32796263790032162260416666480613909929429271255997211512456887_<62>

P79 = 6718990513951552009093589590607436430709568483272900615696735525954611962696013_<79>

Next experiment:

rlim: 5100000
alim: 5100000
lpbr: 24
lpba: 24
mfbr: 32
mfba: 32
rlambda: 2.4
alambda: 2.4

N=220357785298278872892784664585406020968375369048489031248965332108618856387803229103228141852982521439836899650582755926946518515901949291531
  ( 141 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=32796263790032162260416666480613909929429271255997211512456887 (pp62)
 r2=6718990513951552009093589590607436430709568483272900615696735525954611962696013 (pp79)
Version: Msieve-1.39
Total time: 112.67 hours.
Scaled time: 238.86 units (timescale=2.120).
Factorization parameters were as follows:
n: 220357785298278872892784664585406020968375369048489031248965332108618856387803229103228141852982521439836899650582755926946518515901949291531
m: 10000000000000000000000000000000000
deg: 5
c5: 40
c0: 11
skew: 0.77
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 24
lpba: 24
mfbr: 32
mfba: 32
rlambda: 2.4
alambda: 2.4

Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 24/24
Max factor residue bits: 32/32
Sieved rational special-q in [2550000, 12750001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 527505 x 527730
Total sieving time: 112.13 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.41 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,24,24,32,32,2.4,2.4,200000
total time: 112.67 hours.
 --------- CPU info (if available) ----------
[    0.148007] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.240015] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.335125] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.432094] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197992k/10485760k available (2226k kernel code, 189844k reserved, 1082k data, 392k init)
[    0.083917] Calibrating delay using timer specific routine.. 5503.93 BogoMIPS (lpj=11007873)
[    0.160010] Calibrating delay using timer specific routine.. 5499.97 BogoMIPS (lpj=10999957)
[    0.252015] Calibrating delay using timer specific routine.. 5500.01 BogoMIPS (lpj=11000021)
[    0.351657] Calibrating delay using timer specific routine.. 5499.99 BogoMIPS (lpj=10999983)
[    0.436823] Total of 4 processors activated (22003.91 BogoMIPS).

Sep 26, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.1 / Sep 26, 2009

(2·10¹⁷⁴-17)/3 = (6)₁₇₃1_<174> = 223 · 161291696491_<12> · C161

C161 = P39 · P122

P39 = 708395699616853860878877455778481321243_<39>

P122 = 26164711586953036192884166397945253119833753204315227454071423665754582933911493497071983338468814151656453317768389781539_<122>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=205173984
Step 1 took 52113ms
Step 2 took 17726ms
********** Factor found in step 2: 708395699616853860878877455778481321243
Found probable prime factor of 39 digits: 708395699616853860878877455778481321243
Probable prime cofactor 26164711586953036192884166397945253119833753204315227454071423665754582933911493497071983338468814151656453317768389781539 has 122 digits

Sep 26, 2009 (3rd)

By matsui / Msieve / Sep 26, 2009

(58·10¹⁹⁸+23)/9 = 6(4)₁₉₇7_<199> = 3² · 26953 · C194

C194 = P87 · P108

P87 = 120122654799524499176412214703101874912457837887590623290818089496051374264866997231397_<87>

P108 = 221162220425611739516129953287180898210393040202298784816406964454293545788847480164075208005108893026032963_<108>

N=26566593058882105246764715716842258105444640029534722766150312867437739127965324183432248088006877999334002994696300327089725919788126839908336093052698501689955949840440125998938252367060539311
  ( 194 digits)
SNFS difficulty: 201 digits.
Divisors found:
 r1=120122654799524499176412214703101874912457837887590623290818089496051374264866997231397 (pp87)
 r2=221162220425611739516129953287180898210393040202298784816406964454293545788847480164075208005108893026032963 (pp108)
Version: Msieve v. 1.42
Total time: 1399.41 hours.
Scaled time: 3504.12 units (timescale=2.504).
Factorization parameters were as follows:
n: 26566593058882105246764715716842258105444640029534722766150312867437739127965324183432248088006877999334002994696300327089725919788126839908336093052698501689955949840440125998938252367060539311
m: 5000000000000000000000000000000000000000
deg: 5
c5: 464
c0: 575
skew: 1.04
type: snfs
lss: 1
rlim: 15800000
alim: 15800000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6

Factor base limits: 15800000/15800000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7900000, 18900001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3625589 x 3625822
Total sieving time: 1382.77 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 14.66 hours.
Time per square root: 1.72 hours.
Prototype def-par.txt line would be:
snfs,201.000,5,0,0,0,0,0,0,0,0,15800000,15800000,29,29,56,56,2.6,2.6,100000
total time: 1399.41 hours.

Sep 26, 2009 (2nd)

By Tyler Cadigan / GGNFS, Msieve / Sep 26, 2009

10¹⁹⁴+3 = 1(0)₁₉₃3_<195> = 19 · 31 · 12409 · 25729399 · 5851870639_<10> · 104158554145423_<15> · 209791664762566759429_<21> · C136

C136 = P67 · P69

P67 = 7588861276621421644017922022901115597982312020844439616721880396337_<67>

P69 = 547978823634499643594275398528213777607811823908668830812226219613837_<69>

Number: 10003_194
N=4158535275088413824378355739836501505392291656144512892575213767449847733859690592784109621148873117954270828493388445606731856649315069
  ( 136 digits)
Divisors found:
 r1=7588861276621421644017922022901115597982312020844439616721880396337 (pp67)
 r2=547978823634499643594275398528213777607811823908668830812226219613837 (pp69)
Version: Msieve v. 1.42
Total time: 339.26 hours.
Scaled time: 843.06 units (timescale=2.485).
Factorization parameters were as follows:
# Murphy_E = 3.450591e-11, selected by Jeff Gilchrist
n: 4158535275088413824378355739836501505392291656144512892575213767449847733859690592784109621148873117954270828493388445606731856649315069
Y0: -144086758106095012795679247
Y1: 1263192996076717
c0: 5480555000941595632576275173174560
c1: 244004651297638614588297790208
c2: -157910048756582916016798
c3: -234900742537823939
c4: 80808230616
c5: 66960
skew: 1322167.18
type: gnfs
# selected mechanically
rlim: 13900000
alim: 13900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6
Factor base limits: 13900000/13900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved algebraic special-q in [6950000, 11350001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1992546 x 1992771
Total sieving time: 329.61 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 8.55 hours.
Time per square root: 0.56 hours.
Prototype def-par.txt line would be:
gnfs,135,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,13900000,13900000,28,28,55,55,2.6,2.6,100000
total time: 339.26 hours.
 --------- CPU info (if available) ----------

Sep 26, 2009

By Dmitry Domanov / GGNFS/msieve 1.42 / Sep 26, 2009

(10¹⁷⁴+11)/3 = (3)₁₇₃7_<174> = 53 · 106657 · C167

C167 = P52 · P116

P52 = 1663813141164232605521375253659366783876558160712747_<52>

P116 = 35441244351012120797734685671866214672247079787653946935153849461644924094039152738627620585090548532721770420013151_<116>

Sieving ~4 cpu-days

Fri Sep 25 16:27:31 2009  Msieve v. 1.42
Fri Sep 25 16:27:31 2009  random seeds: 37744bb0 1e3de700
Fri Sep 25 16:27:31 2009  factoring 58967608090426591136236815801054612083654043411835140955875541315271319104803306761939451706207101433661765220114582317984831526300467206255661258924231517915273335797 (167 digits)
Fri Sep 25 16:27:32 2009  searching for 15-digit factors
Fri Sep 25 16:27:34 2009  commencing number field sieve (167-digit input)
Fri Sep 25 16:27:34 2009  R0: -50000000000000000000000000000000000
Fri Sep 25 16:27:34 2009  R1:  1
Fri Sep 25 16:27:34 2009  A0:  55
Fri Sep 25 16:27:34 2009  A1:  0
Fri Sep 25 16:27:34 2009  A2:  0
Fri Sep 25 16:27:34 2009  A3:  0
Fri Sep 25 16:27:34 2009  A4:  0
Fri Sep 25 16:27:34 2009  A5:  16
Fri Sep 25 16:27:34 2009  skew 1.28, size 4.220308e-012, alpha 0.346343, combined = 1.950576e-010
Fri Sep 25 16:27:34 2009  
Fri Sep 25 16:27:34 2009  commencing relation filtering
Fri Sep 25 16:27:34 2009  estimated available RAM is 4094.1 MB
Fri Sep 25 16:27:34 2009  commencing duplicate removal, pass 1
Fri Sep 25 16:29:40 2009  found 1616363 hash collisions in 12545241 relations
Fri Sep 25 16:30:13 2009  added 375841 free relations
Fri Sep 25 16:30:14 2009  commencing duplicate removal, pass 2
Fri Sep 25 16:30:40 2009  found 1316264 duplicates and 11604817 unique relations
Fri Sep 25 16:30:40 2009  memory use: 49.3 MB
Fri Sep 25 16:30:40 2009  reading ideals above 720000
Fri Sep 25 16:30:41 2009  commencing singleton removal, initial pass
Fri Sep 25 16:33:18 2009  memory use: 266.4 MB
Fri Sep 25 16:33:18 2009  reading all ideals from disk
Fri Sep 25 16:33:19 2009  memory use: 344.5 MB
Fri Sep 25 16:33:21 2009  commencing in-memory singleton removal
Fri Sep 25 16:33:23 2009  begin with 11604817 relations and 11624327 unique ideals
Fri Sep 25 16:33:42 2009  reduce to 6235504 relations and 5342672 ideals in 14 passes
Fri Sep 25 16:33:42 2009  max relations containing the same ideal: 92
Fri Sep 25 16:33:47 2009  removing 1629665 relations and 1250632 ideals in 379033 cliques
Fri Sep 25 16:33:48 2009  commencing in-memory singleton removal
Fri Sep 25 16:33:49 2009  begin with 4605839 relations and 5342672 unique ideals
Fri Sep 25 16:33:56 2009  reduce to 4338262 relations and 3805194 ideals in 8 passes
Fri Sep 25 16:33:56 2009  max relations containing the same ideal: 69
Fri Sep 25 16:34:00 2009  removing 1264439 relations and 885406 ideals in 379033 cliques
Fri Sep 25 16:34:00 2009  commencing in-memory singleton removal
Fri Sep 25 16:34:01 2009  begin with 3073823 relations and 3805194 unique ideals
Fri Sep 25 16:34:06 2009  reduce to 2828642 relations and 2653232 ideals in 11 passes
Fri Sep 25 16:34:06 2009  max relations containing the same ideal: 52
Fri Sep 25 16:34:09 2009  removing 226289 relations and 185645 ideals in 40644 cliques
Fri Sep 25 16:34:09 2009  commencing in-memory singleton removal
Fri Sep 25 16:34:10 2009  begin with 2602353 relations and 2653232 unique ideals
Fri Sep 25 16:34:12 2009  reduce to 2591305 relations and 2456371 ideals in 6 passes
Fri Sep 25 16:34:12 2009  max relations containing the same ideal: 48
Fri Sep 25 16:34:15 2009  relations with 0 large ideals: 2916
Fri Sep 25 16:34:15 2009  relations with 1 large ideals: 2398
Fri Sep 25 16:34:15 2009  relations with 2 large ideals: 29858
Fri Sep 25 16:34:15 2009  relations with 3 large ideals: 159102
Fri Sep 25 16:34:15 2009  relations with 4 large ideals: 441739
Fri Sep 25 16:34:15 2009  relations with 5 large ideals: 709449
Fri Sep 25 16:34:15 2009  relations with 6 large ideals: 703744
Fri Sep 25 16:34:15 2009  relations with 7+ large ideals: 542099
Fri Sep 25 16:34:15 2009  commencing 2-way merge
Fri Sep 25 16:34:19 2009  reduce to 1695841 relation sets and 1560907 unique ideals
Fri Sep 25 16:34:19 2009  commencing full merge
Fri Sep 25 16:34:56 2009  memory use: 167.0 MB
Fri Sep 25 16:34:56 2009  found 859064 cycles, need 841107
Fri Sep 25 16:34:56 2009  weight of 841107 cycles is about 59157155 (70.33/cycle)
Fri Sep 25 16:34:56 2009  distribution of cycle lengths:
Fri Sep 25 16:34:56 2009  1 relations: 87608
Fri Sep 25 16:34:56 2009  2 relations: 91978
Fri Sep 25 16:34:56 2009  3 relations: 94002
Fri Sep 25 16:34:56 2009  4 relations: 89624
Fri Sep 25 16:34:56 2009  5 relations: 83419
Fri Sep 25 16:34:56 2009  6 relations: 74269
Fri Sep 25 16:34:56 2009  7 relations: 64927
Fri Sep 25 16:34:56 2009  8 relations: 54915
Fri Sep 25 16:34:56 2009  9 relations: 46193
Fri Sep 25 16:34:56 2009  10+ relations: 154172
Fri Sep 25 16:34:56 2009  heaviest cycle: 20 relations
Fri Sep 25 16:34:56 2009  commencing cycle optimization
Fri Sep 25 16:34:58 2009  start with 4988233 relations
Fri Sep 25 16:35:11 2009  pruned 156130 relations
Fri Sep 25 16:35:11 2009  memory use: 125.1 MB
Fri Sep 25 16:35:11 2009  distribution of cycle lengths:
Fri Sep 25 16:35:11 2009  1 relations: 87608
Fri Sep 25 16:35:11 2009  2 relations: 94043
Fri Sep 25 16:35:11 2009  3 relations: 97631
Fri Sep 25 16:35:11 2009  4 relations: 92599
Fri Sep 25 16:35:11 2009  5 relations: 86536
Fri Sep 25 16:35:11 2009  6 relations: 76379
Fri Sep 25 16:35:11 2009  7 relations: 66348
Fri Sep 25 16:35:11 2009  8 relations: 55388
Fri Sep 25 16:35:11 2009  9 relations: 45801
Fri Sep 25 16:35:11 2009  10+ relations: 138774
Fri Sep 25 16:35:11 2009  heaviest cycle: 20 relations
Fri Sep 25 16:35:13 2009  RelProcTime: 459
Fri Sep 25 16:35:13 2009  
Fri Sep 25 16:35:13 2009  commencing linear algebra
Fri Sep 25 16:35:14 2009  read 841107 cycles
Fri Sep 25 16:35:16 2009  cycles contain 2510407 unique relations
Fri Sep 25 16:36:20 2009  read 2510407 relations
Fri Sep 25 16:36:25 2009  using 20 quadratic characters above 134215932
Fri Sep 25 16:36:41 2009  building initial matrix
Fri Sep 25 16:37:19 2009  memory use: 277.4 MB
Fri Sep 25 16:37:21 2009  read 841107 cycles
Fri Sep 25 16:37:42 2009  matrix is 840929 x 841107 (238.0 MB) with weight 74768823 (88.89/col)
Fri Sep 25 16:37:42 2009  sparse part has weight 56501333 (67.17/col)
Fri Sep 25 16:37:53 2009  filtering completed in 2 passes
Fri Sep 25 16:37:53 2009  matrix is 840412 x 840590 (238.0 MB) with weight 74749732 (88.93/col)
Fri Sep 25 16:37:53 2009  sparse part has weight 56493595 (67.21/col)
Fri Sep 25 16:37:57 2009  read 840590 cycles
Fri Sep 25 16:39:25 2009  matrix is 840412 x 840590 (238.0 MB) with weight 74749732 (88.93/col)
Fri Sep 25 16:39:25 2009  sparse part has weight 56493595 (67.21/col)
Fri Sep 25 16:39:25 2009  saving the first 48 matrix rows for later
Fri Sep 25 16:39:26 2009  matrix is 840364 x 840590 (225.3 MB) with weight 59300992 (70.55/col)
Fri Sep 25 16:39:26 2009  sparse part has weight 54009505 (64.25/col)
Fri Sep 25 16:39:26 2009  matrix includes 64 packed rows
Fri Sep 25 16:39:26 2009  using block size 65536 for processor cache size 4096 kB
Fri Sep 25 16:39:33 2009  commencing Lanczos iteration (4 threads)
Fri Sep 25 16:39:33 2009  memory use: 252.7 MB
Fri Sep 25 17:34:03 2009  lanczos halted after 13288 iterations (dim = 840361)
Fri Sep 25 17:34:05 2009  recovered 36 nontrivial dependencies
Fri Sep 25 17:34:06 2009  BLanczosTime: 3533
Fri Sep 25 17:34:06 2009  
Fri Sep 25 17:34:06 2009  commencing square root phase
Fri Sep 25 17:34:06 2009  reading relations for dependency 1
Fri Sep 25 17:34:07 2009  read 420473 cycles
Fri Sep 25 17:34:07 2009  cycles contain 1569020 unique relations
Fri Sep 25 17:34:53 2009  read 1569020 relations
Fri Sep 25 17:35:02 2009  multiplying 1254520 relations
Fri Sep 25 17:36:39 2009  multiply complete, coefficients have about 32.80 million bits
Fri Sep 25 17:36:39 2009  initial square root is modulo 2630865701
Fri Sep 25 17:39:23 2009  reading relations for dependency 2
Fri Sep 25 17:39:23 2009  read 419883 cycles
Fri Sep 25 17:39:24 2009  cycles contain 1567776 unique relations
Fri Sep 25 17:40:10 2009  read 1567776 relations
Fri Sep 25 17:40:19 2009  multiplying 1254088 relations
Fri Sep 25 17:41:56 2009  multiply complete, coefficients have about 32.79 million bits
Fri Sep 25 17:41:56 2009  initial square root is modulo 2610199171
Fri Sep 25 17:44:40 2009  reading relations for dependency 3
Fri Sep 25 17:44:40 2009  read 420742 cycles
Fri Sep 25 17:44:41 2009  cycles contain 1570664 unique relations
Fri Sep 25 17:45:38 2009  read 1570664 relations
Fri Sep 25 17:45:47 2009  multiplying 1256638 relations
Fri Sep 25 17:47:24 2009  multiply complete, coefficients have about 32.86 million bits
Fri Sep 25 17:47:25 2009  initial square root is modulo 2728664321
Fri Sep 25 17:50:08 2009  reading relations for dependency 4
Fri Sep 25 17:50:09 2009  read 420585 cycles
Fri Sep 25 17:50:10 2009  cycles contain 1568813 unique relations
Fri Sep 25 17:50:56 2009  read 1568813 relations
Fri Sep 25 17:51:05 2009  multiplying 1255100 relations
Fri Sep 25 17:52:42 2009  multiply complete, coefficients have about 32.82 million bits
Fri Sep 25 17:52:42 2009  initial square root is modulo 2658738211
Fri Sep 25 17:55:26 2009  reading relations for dependency 5
Fri Sep 25 17:55:26 2009  read 419920 cycles
Fri Sep 25 17:55:27 2009  cycles contain 1569762 unique relations
Fri Sep 25 17:56:15 2009  read 1569762 relations
Fri Sep 25 17:56:24 2009  multiplying 1255676 relations
Fri Sep 25 17:58:01 2009  multiply complete, coefficients have about 32.83 million bits
Fri Sep 25 17:58:01 2009  initial square root is modulo 2686915471
Fri Sep 25 18:00:45 2009  sqrtTime: 1599
Fri Sep 25 18:00:45 2009  prp52 factor: 1663813141164232605521375253659366783876558160712747
Fri Sep 25 18:00:45 2009  prp116 factor: 35441244351012120797734685671866214672247079787653946935153849461644924094039152738627620585090548532721770420013151
Fri Sep 25 18:00:45 2009  elapsed time 01:33:14

Sep 25, 2009 (5th)

By Sinkiti Sibata / Msieve / Sep 25, 2009

(29·10¹⁷⁰+61)/9 = 3(2)₁₆₉9_<171> = 7 · 17 · 1023943 · 50202296843_<11> · 1504744007909_<13> · C140

C140 = P66 · P75

P66 = 167947834692183450740511533147613054941648814323210418408876837823_<66>

P75 = 208435710396318151256506590232155224650182410075738412602346314976990700237_<75>

Number: 32229_170
N=35006326233588664358088072938856017419625931388340362803570219538504947562072904955252882575767520615701620286254407141842171583383056664051
  ( 140 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=167947834692183450740511533147613054941648814323210418408876837823 (pp66)
 r2=208435710396318151256506590232155224650182410075738412602346314976990700237 (pp75)
Version: Msieve-1.40
Total time: 60.58 hours.
Scaled time: 203.38 units (timescale=3.357).
Factorization parameters were as follows:
name: 32229_170
n: 35006326233588664358088072938856017419625931388340362803570219538504947562072904955252882575767520615701620286254407141842171583383056664051
m: 10000000000000000000000000000000000
deg: 5
c5: 29
c0: 61
skew: 1.16
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1003436 x 1003684
Total sieving time: 58.49 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.91 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 60.58 hours.
 --------- CPU info (if available) ----------

(2·10¹⁷¹+43)/9 = (2)₁₇₀7_<171> = 457 · 316037 · 870329 · 5794475053377775913_<19> · C138

C138 = P59 · P79

P59 = 81317872091067859211776561786730306649095464142918715845659_<59>

P79 = 3751887414744125246302985151074553352323146938504677201795126577989619237545421_<79>

Number: 22227_171
N=305095500892250044395188955647056790908387517500077469449147119054695887540930792072824496609898271372962839988185876655738738257438177439
  ( 138 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=81317872091067859211776561786730306649095464142918715845659 (pp59)
 r2=3751887414744125246302985151074553352323146938504677201795126577989619237545421 (pp79)
Version: Msieve-1.40
Total time: 84.22 hours.
Scaled time: 153.29 units (timescale=1.820).
Factorization parameters were as follows:
name: 22227_171
n: 305095500892250044395188955647056790908387517500077469449147119054695887540930792072824496609898271372962839988185876655738738257438177439
m: 10000000000000000000000000000000000
deg: 5
c5: 20
c0: 43
skew: 1.17
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5900001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 998127 x 998357
Total sieving time: 81.69 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 2.34 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 84.22 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3109164k/3145344k available (2732k kernel code, 34856k reserved, 1420k data, 412k init, 2227840k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.99 BogoMIPS (lpj=2393996)
Calibrating delay using timer specific routine.. 4787.75 BogoMIPS (lpj=2393875)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891)
Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393884)
Total of 4 processors activated (19151.29 BogoMIPS).

Sep 25, 2009 (4th)

By Erik Branger / GMP-ECM / Sep 25, 2009

4·10¹⁷¹+3 = 4(0)₁₇₀3_<172> = 439 · 36277 · 1268563 · 15218882404130261_<17> · C143

C143 = P39 · P104

P39 = 756250231338276927304375103001690458827_<39>

P104 = 17202983946086459938373724428120076924823810662429126159556894474473395321848053399384538121207658238541_<104>

Input number is 13009760588936549424115996217884317573935345630505968615454955194796197691159254066522117811387603269907811985842646853086028926492340905051407 (143 digits)
Run 277 out of 500:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3099713956
Step 1 took 46328ms
Step 2 took 21563ms
********** Factor found in step 2: 756250231338276927304375103001690458827
Found probable prime factor of 39 digits: 756250231338276927304375103001690458827
Probable prime cofactor 17202983946086459938373724428120076924823810662429126159556894474473395321848053399384538121207658238541 has 104 digits

Sep 25, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Sep 25, 2009

(46·10¹⁷²+53)/9 = 5(1)₁₇₁7_<173> = 3 · 11 · 160033 · C166

C166 = P71 · P96

P71 = 36033128261972737854237389767175430050431103081339670286348057189471141_<71>

P96 = 268590017877231787185313607856659818367106537343327607800131824893760946397809960086471717273033_<96>

Number: 51117_172
N=9678138564055843616934142013344427846436807088672641402390891558750687805320287370864439344065421187014858320151603411930969372247108713962425384444592982831971040653
  ( 166 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=36033128261972737854237389767175430050431103081339670286348057189471141 (pp71)
 r2=268590017877231787185313607856659818367106537343327607800131824893760946397809960086471717273033 (pp96)
Version: Msieve-1.40
Total time: 73.83 hours.
Scaled time: 128.39 units (timescale=1.739).
Factorization parameters were as follows:
n: 9678138564055843616934142013344427846436807088672641402390891558750687805320287370864439344065421187014858320151603411930969372247108713962425384444592982831971040653
m: 20000000000000000000000000000000000
deg: 5
c5: 575
c0: 212
skew: 0.82
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 6600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1123174 x 1123407
Total sieving time: 71.46 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.66 hours.
Time per square root: 0.61 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 73.83 hours.

Sep 25, 2009 (2nd)

By Markus Tervooren / Msieve / Sep 25, 2009

(38·10¹⁷⁰+61)/9 = 4(2)₁₆₉9_<171> = 3² · 11 · 13 · 47 · 2111 · 108275039 · 861487663 · C146

C146 = P63 · P84

P63 = 112571824006096729158420064343072159842458593951521181965941557_<63>

P84 = 314897588409925172578173765266062287127679189995340781348626644393883516585549040599_<84>

Another experiment, this time it was a really bad choice:

rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 47
mfba: 47
rlambda: 2.6
alambda: 2.6

~65 Hours sieve time, 10M rels.

Msieve v. 1.42
Thu Sep 24 17:26:59 2009
random seeds: 9382ecfa 81315f41
factoring 35448595902426381689814754249814433581331280418318339807608728957850624199532445178670719626970890252637535566455445691961293138457991395054272643 (146 digits)
searching for 15-digit factors
commencing number field sieve (146-digit input)
R0: -10000000000000000000000000000000000
R1:  1
A0:  61
A1:  0
A2:  0
A3:  0
A4:  0
A5:  38
skew 1.10, size 6.368856e-12, alpha 0.160832, combined = 2.502776e-10

commencing relation filtering
estimated available RAM is 8010.2 MB
commencing duplicate removal, pass 1
found 1023559 hash collisions in 9955173 relations
added 220533 free relations
commencing duplicate removal, pass 2
found 844550 duplicates and 9331156 unique relations
memory use: 49.3 MB
reading ideals above 100000
commencing singleton removal, initial pass
memory use: 266.4 MB
reading all ideals from disk
memory use: 332.7 MB
keeping 12217529 ideals with weight <= 200, target excess is 53180
commencing in-memory singleton removal
begin with 9331156 relations and 12217529 unique ideals
reduce to 2115084 relations and 2019675 ideals in 13 passes
max relations containing the same ideal: 74
removing 120615 relations and 103755 ideals in 16860 cliques
commencing in-memory singleton removal
begin with 1994469 relations and 2019675 unique ideals
reduce to 1991343 relations and 1912754 ideals in 6 passes
max relations containing the same ideal: 71
removing 91079 relations and 74219 ideals in 16860 cliques
commencing in-memory singleton removal
begin with 1900264 relations and 1912754 unique ideals
reduce to 1898231 relations and 1836483 ideals in 5 passes
max relations containing the same ideal: 69
relations with 0 large ideals: 1229
relations with 1 large ideals: 460
relations with 2 large ideals: 6558
relations with 3 large ideals: 46287
relations with 4 large ideals: 173673
relations with 5 large ideals: 381617
relations with 6 large ideals: 540247
relations with 7+ large ideals: 748160
commencing 2-way merge
reduce to 1231937 relation sets and 1170189 unique ideals
commencing full merge
memory use: 156.4 MB
found 664544 cycles, need 656389
weight of 656389 cycles is about 46150723 (70.31/cycle)
distribution of cycle lengths:
1 relations: 49537
2 relations: 73714
3 relations: 83423
4 relations: 78374
5 relations: 71572
6 relations: 61363
7 relations: 51337
8 relations: 42368
9 relations: 34711
10+ relations: 109990
heaviest cycle: 20 relations
commencing cycle optimization
start with 3854757 relations
pruned 112168 relations
memory use: 119.1 MB
distribution of cycle lengths:
1 relations: 49537
2 relations: 75523
3 relations: 86761
4 relations: 80833
5 relations: 73657
6 relations: 62299
7 relations: 51926
8 relations: 42154
9 relations: 34237
10+ relations: 99462
heaviest cycle: 20 relations
RelProcTime: 251

commencing linear algebra
read 656389 cycles
cycles contain 1863372 unique relations
read 1863372 relations
using 20 quadratic characters above 536545832
building initial matrix
memory use: 241.4 MB
read 656389 cycles
matrix is 656212 x 656389 (196.5 MB) with weight 59521673 (90.68/col)
sparse part has weight 44280835 (67.46/col)
filtering completed in 2 passes
matrix is 656066 x 656243 (196.4 MB) with weight 59515687 (90.69/col)
sparse part has weight 44278419 (67.47/col)
read 656243 cycles
matrix is 656066 x 656243 (196.4 MB) with weight 59515687 (90.69/col)
sparse part has weight 44278419 (67.47/col)
saving the first 48 matrix rows for later
matrix is 656018 x 656243 (186.1 MB) with weight 46692234 (71.15/col)
sparse part has weight 42211934 (64.32/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (4 threads)
memory use: 196.3 MB
linear algebra completed 655925 of 656243 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 10376 iterations (dim = 656018)
recovered 39 nontrivial dependencies
BLanczosTime: 2244

commencing square root phase
reading relations for dependency 1
read 327915 cycles
cycles contain 1156352 unique relations
read 1156352 relations
multiplying 930682 relations
multiply complete, coefficients have about 25.51 million bits
initial square root is modulo 21184151
reading relations for dependency 2
read 328610 cycles
cycles contain 1158712 unique relations
read 1158712 relations
multiplying 933210 relations
multiply complete, coefficients have about 25.58 million bits
initial square root is modulo 22136071
sqrtTime: 331
prp63 factor: 112571824006096729158420064343072159842458593951521181965941557
prp84 factor: 314897588409925172578173765266062287127679189995340781348626644393883516585549040599
elapsed time 00:47:07

Sep 25, 2009

By Wataru Sakai / GMP-ECM 6.2.1 / Sep 25, 2009

(26·10¹⁷³-71)/9 = 2(8)₁₇₂1_<174> = 3659 · 2994692089_<10> · 1180877675714413_<16> · C146

C146 = P33 · P113

P33 = 713468875576511513283306519138119_<33>

P113 = 31292215261332474324598857424033910552657776703198753648313833959464824814897277997193127602654614246649390049073_<113>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=927773744
Step 1 took 47554ms
Step 2 took 15738ms
********** Factor found in step 2: 713468875576511513283306519138119
Found probable prime factor of 33 digits: 713468875576511513283306519138119
Probable prime cofactor 31292215261332474324598857424033910552657776703198753648313833959464824814897277997193127602654614246649390049073 has 113 digits

Sep 24, 2009 (6th)

By Ignacio Santos / GGNFS, Msieve / Sep 24, 2009

(23·10¹⁷²+31)/9 = 2(5)₁₇₁9_<173> = 379 · 31891 · C166

C166 = P39 · P128

P39 = 174631780230614695944104960370984977291_<39>

P128 = 12107506134278770155177928819140151041059023958173485072036790346524085153258724473425765312615846580779575809523040588323053941_<128>

Number: 25559_172
N=2114355350382189494207682149805919185606211556825492536091195492459147046437246425018096813408167907319825599513279075481759773545555408561894457245946806073653053831
  ( 166 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=174631780230614695944104960370984977291 (pp39)
 r2=12107506134278770155177928819140151041059023958173485072036790346524085153258724473425765312615846580779575809523040588323053941 (pp128)
Version: Msieve-1.40
Total time: 91.32 hours.
Scaled time: 158.81 units (timescale=1.739).
Factorization parameters were as follows:
n: 2114355350382189494207682149805919185606211556825492536091195492459147046437246425018096813408167907319825599513279075481759773545555408561894457245946806073653053831
m: 20000000000000000000000000000000000
deg: 5
c5: 575
c0: 248
skew: 0.85
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 7800001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1172139 x 1172368
Total sieving time: 89.23 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.83 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 91.32 hours.

Sep 24, 2009 (5th)

By Erik Branger / GGNFS, Msieve / Sep 24, 2009

(38·10¹⁷²-11)/9 = 4(2)₁₇₁1_<173> = 59 · 67699 · C167

C167 = P46 · P60 · P61

P46 = 5140420555539630577906068364265885081730496753_<46>

P60 = 373113006277293158634413308769938788385364188269480018332333_<60>

P61 = 5511474241224288959853093152333391854645304737723708263721969_<61>

Number: 42221_172
N=10570774828615054079666755767171340493030396068294883113518243446557737057484068242808138573066127512641881704739954905630937698106404251076042287438895705647761920781
  ( 167 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=5140420555539630577906068364265885081730496753 (pp46)
 r2=373113006277293158634413308769938788385364188269480018332333 (pp60)
 r3=5511474241224288959853093152333391854645304737723708263721969 (pp61)
Version: Msieve-1.40
Total time: 144.64 hours.
Scaled time: 140.44 units (timescale=0.971).
Factorization parameters were as follows:
n: 10570774828615054079666755767171340493030396068294883113518243446557737057484068242808138573066127512641881704739954905630937698106404251076042287438895705647761920781
m: 20000000000000000000000000000000000
deg: 5
c5: 475
c0: -44
skew: 0.62
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 7300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1149676 x 1149901
Total sieving time: 139.33 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 4.04 hours.
Time per square root: 1.04 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 144.64 hours.
 --------- CPU info (if available) ----------

Sep 24, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Sep 24, 2009

(79·10¹⁷⁰-7)/9 = 8(7)₁₇₀_<171> = 1765641831386057_<16> · 519984567881869875839623965217_<30> · C126

C126 = P59 · P68

P59 = 15483071709542096611001643849713935813843215215290261622477_<59>

P68 = 61749634635882785264612312275923906912881470874063040973717176318829_<68>

Number: 87777_170
N=956074021105397536437342755056849754612201290610974264349641650804121960025424871623231611685371025112062981295261387784719433
  ( 126 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=15483071709542096611001643849713935813843215215290261622477
 r2=61749634635882785264612312275923906912881470874063040973717176318829
Version: 
Total time: 38.52 hours.
Scaled time: 91.67 units (timescale=2.380).
Factorization parameters were as follows:
n: 956074021105397536437342755056849754612201290610974264349641650804121960025424871623231611685371025112062981295261387784719433
m: 10000000000000000000000000000000000
deg: 5
c5: 79
c0: -7
skew: 0.62
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 5900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11273123
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 973375 x 973623
Total sieving time: 34.70 hours.
Total relation processing time: 1.63 hours.
Matrix solve time: 2.06 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 38.52 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672363)
Calibrating delay using timer specific routine.. 5535.15 BogoMIPS (lpj=2767578)

Sep 24, 2009 (3rd)

By Lionel Debroux / GMP-ECM 6.2.3 / Sep 24, 2009

(55·10¹⁷²+71)/9 = 6(1)₁₇₁9_<173> = 3 · 97 · 1289 · 4415852847060229_<16> · C152

C152 = P28 · C124

P28 = 4051314161189975816333577239_<28>

C124 = [9106757225969912881333194990833285699269760699586847310985480208600176868257330699000978309517694764014428821400787481756751_<124>]

GMP-ECM 6.2.3 [powered by GMP 4.2.2] [ECM]
Input number is 36894334512091048654236822948499683065906696676088162506229580105617891866969334928288193930352386232758819724487918773536877070945133685323995868190489 (152 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=937539043
Step 1 took 6087ms
Step 2 took 4888ms
Run 2 out of 820:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3259751403
Step 1 took 6043ms
Step 2 took 4888ms
Run 3 out of 820:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2439804481
Step 1 took 6045ms
Step 2 took 4879ms
Run 4 out of 820:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=806004781
Step 1 took 6057ms
Step 2 took 4933ms
Run 5 out of 820:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3046784091
Step 1 took 6096ms
Step 2 took 4901ms
Run 6 out of 820:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3621452165
Step 1 took 6024ms
Step 2 took 4950ms
Run 7 out of 820:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1549145450
Step 1 took 6084ms
Step 2 took 4925ms
Run 8 out of 820:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1183815268
Step 1 took 6092ms
Step 2 took 4937ms
Run 9 out of 820:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2498803284
Step 1 took 6157ms
Step 2 took 4941ms
Run 10 out of 820:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=440176220
Step 1 took 6072ms
Step 2 took 4917ms
********** Factor found in step 2: 4051314161189975816333577239
Found probable prime factor of 28 digits: 4051314161189975816333577239
Composite cofactor 9106757225969912881333194990833285699269760699586847310985480208600176868257330699000978309517694764014428821400787481756751 has 124 digits

3·10¹⁷³+7 = 3(0)₁₇₂7_<174> = 283 · 1913 · 12781 · 123368533577_<12> · C153

C153 = P36 · P118

P36 = 273075549184718167710054152780236687_<36>

P118 = 1286968141075529714067699681620509401294955843542948675197022676011814934805266689072732719905213815274493968019250807_<118>

GMP-ECM 6.2.3 [powered by GMP 4.2.2] [ECM]
Input number is 351439531907436124055536444128806791254168353017680566366500535357910840702470719997506193679475389903251705103144679714049115729736189648524865875756409 (153 digits)
Run 228 out of 900:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4028931106
Step 1 took 6076ms
********** Factor found in step 1: 273075549184718167710054152780236687
Found probable prime factor of 36 digits: 273075549184718167710054152780236687
Probable prime cofactor 1286968141075529714067699681620509401294955843542948675197022676011814934805266689072732719905213815274493968019250807 has 118 digits

Sep 24, 2009 (2nd)

By Markus Tervooren / Msieve / Sep 24, 2009

(37·10¹⁷⁰+53)/9 = 4(1)₁₆₉7_<171> = 3² · 401 · 529066550015453_<15> · 224095050481431878583827_<24> · C129

C129 = P52 · P78

P52 = 2060454176204106527686604895224268091652282863420069_<52>

P78 = 466301490140428261860982955098960860463183987146647186020739663643778439019367_<78>

Msieve v. 1.42
Wed Sep 23 23:30:02 2009
random seeds: 9265f727 ad073a50
factoring 960792852730043416587536301900355013291868929009077724099208649994807360505992935335860729053144258511065251226798984308147476323 (129 digits)
searching for 15-digit factors
commencing number field sieve (129-digit input)
R0: -10000000000000000000000000000000000
R1:  1
A0:  53
A1:  0
A2:  0
A3:  0
A4:  0
A5:  37
skew 1.07, size 5.920174e-12, alpha 0.452227, combined = 2.402113e-10

commencing square root phase
reading relations for dependency 1
read 352479 cycles
cycles contain 1297241 unique relations
read 1297241 relations
multiplying 1044346 relations
multiply complete, coefficients have about 28.31 million bits
initial square root is modulo 134631661
reading relations for dependency 2
read 352550 cycles
cycles contain 1297471 unique relations
read 1297471 relations
multiplying 1044696 relations
multiply complete, coefficients have about 28.32 million bits
initial square root is modulo 135591101
sqrtTime: 385
prp52 factor: 2060454176204106527686604895224268091652282863420069
prp78 factor: 466301490140428261860982955098960860463183987146647186020739663643778439019367
elapsed time 00:06:26

this was another experiment:
lpbr: 32
lpba: 32
mfbr: 50
mfba: 50
rlambda: 2.7
alambda: 2.7

Sieve time:  ~ 26 hours

Sep 24, 2009

By Jo Yeong Uk / GMP-ECM v6.2.3 / Sep 24, 2009

(55·10¹⁷⁰+53)/9 = 6(1)₁₆₉7_<171> = 19 · 14543 · 1536751818053759_<16> · 39450159861961322302501_<23> · C128

C128 = P45 · P84

P45 = 138076070934145108899829431997603725655307579_<45>

P84 = 264205376804078662541102594999473809307029747928977642336676775472227007205794914041_<84>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 36480440348782502181098190984609803333422429452696004192197999151018411873622928140737009346361855906541450334801422615720816739 (128 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=8183252458
Step 1 took 50063ms
Step 2 took 16700ms
********** Factor found in step 2: 138076070934145108899829431997603725655307579
Found probable prime factor of 45 digits: 138076070934145108899829431997603725655307579
Probable prime cofactor 264205376804078662541102594999473809307029747928977642336676775472227007205794914041 has 84 digits

Sep 23, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM v6.2.3, YAFU v1.10 / Sep 23, 2009

(44·10¹⁷⁰-17)/9 = 4(8)₁₆₉7_<171> = 523 · 26393 · 5248786129_<10> · 67204076825777480647940943101_<29> · C126

C126 = P58 · P68

P58 = 6818697425968909012852708610079174806710449887951263213393_<58>

P68 = 14725288230184419653350401245759339451836336800397026644804321531889_<68>

Number: 48887_170
N=100407284951808774048499368281072908226415208673026207174570944509767601913362756510328274963943649362315407074660910461389377
  ( 126 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=6818697425968909012852708610079174806710449887951263213393
 r2=14725288230184419653350401245759339451836336800397026644804321531889
Version: 
Total time: 31.40 hours.
Scaled time: 74.92 units (timescale=2.386).
Factorization parameters were as follows:
n: 100407284951808774048499368281072908226415208673026207174570944509767601913362756510328274963943649362315407074660910461389377
m: 10000000000000000000000000000000000
deg: 5
c5: 44
c0: -17
skew: 0.83
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 5300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10984366
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 901958 x 902206
Total sieving time: 28.01 hours.
Total relation processing time: 1.28 hours.
Matrix solve time: 1.90 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 31.40 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672363)
Calibrating delay using timer specific routine.. 5535.15 BogoMIPS (lpj=2767578)

(53·10¹⁷⁰-71)/9 = 5(8)₁₆₉1_<171> = 7 · 59 · 1427 · 568218567627765334438930578061_<30> · C136

C136 = P43 · P45 · P49

P43 = 2263601622974746710068103777175357428919279_<43>

P45 = 129968124481852563001973196053531945137907861_<45>

P49 = 5977327695821253697952452498480093874447527049209_<49>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 1758506242568529843518862184298300192461949248965270914514846025080664578579799593627607383834257179355214779859822982674375843959144771 (136 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=5649517295
Step 1 took 47877ms
Step 2 took 18142ms
********** Factor found in step 2: 2263601622974746710068103777175357428919279
Found probable prime factor of 43 digits: 2263601622974746710068103777175357428919279
Composite cofactor 776862070039321652585092816078249433530009012184886494488579907901648422652529493601054931949 has 93 digits

09/23/09 21:37:37 v1.10 @ 조영욱-PC, starting SIQS on c93: 776862070039321652585092816078249433530009012184886494488579907901648422652529493601054931949
09/23/09 21:37:37 v1.10 @ 조영욱-PC, random seeds: 2381196637, 590092736
09/23/09 21:37:38 v1.10 @ 조영욱-PC, ==== sieve params ====
09/23/09 21:37:38 v1.10 @ 조영욱-PC, n = 93 digits, 311 bits
09/23/09 21:37:38 v1.10 @ 조영욱-PC, factor base: 77164 primes (max prime = 2082163)
09/23/09 21:37:38 v1.10 @ 조영욱-PC, single large prime cutoff: 249859560 (120 * pmax)
09/23/09 21:37:38 v1.10 @ 조영욱-PC, double large prime range from 43 to 51 bits
09/23/09 21:37:38 v1.10 @ 조영욱-PC, double large prime cutoff: 1305728091160594
09/23/09 21:37:38 v1.10 @ 조영욱-PC, using 16 large prime slices of factor base
09/23/09 21:37:38 v1.10 @ 조영욱-PC, buckets hold 1024 elements
09/23/09 21:37:38 v1.10 @ 조영욱-PC, sieve interval: 11 blocks of size 65536
09/23/09 21:37:38 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors
09/23/09 21:37:38 v1.10 @ 조영욱-PC, using multiplier of 5
09/23/09 21:37:38 v1.10 @ 조영욱-PC, using small prime variation correction of 21 bits
09/23/09 21:37:38 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
09/23/09 21:37:38 v1.10 @ 조영욱-PC, trial factoring cutoff at 98 bits
09/23/09 21:37:38 v1.10 @ 조영욱-PC, ==== sieving started ====
09/23/09 22:51:21 v1.10 @ 조영욱-PC, sieve time = 2008.9570, relation time = 942.9800, poly_time = 1470.2500
09/23/09 22:51:21 v1.10 @ 조영욱-PC, 77251 relations found: 21724 full + 55527 from 955480 partial, using 610736 polys (298 A polys)
09/23/09 22:51:21 v1.10 @ 조영욱-PC, on average, sieving found 1.60 rels/poly and 220.91 rels/sec
09/23/09 22:51:21 v1.10 @ 조영욱-PC, trial division touched 36666660 sieve locations out of 880554278912
09/23/09 22:51:21 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
09/23/09 22:51:21 v1.10 @ 조영욱-PC, begin with 977204 relations
09/23/09 22:51:22 v1.10 @ 조영욱-PC, reduce to 183482 relations in 10 passes
09/23/09 22:51:23 v1.10 @ 조영욱-PC, recovered 183482 relations
09/23/09 22:51:23 v1.10 @ 조영욱-PC, recovered 158359 polynomials
09/23/09 22:51:24 v1.10 @ 조영욱-PC, attempting to build 77251 cycles
09/23/09 22:51:24 v1.10 @ 조영욱-PC, found 77251 cycles in 5 passes
09/23/09 22:51:24 v1.10 @ 조영욱-PC, distribution of cycle lengths:
09/23/09 22:51:24 v1.10 @ 조영욱-PC,    length 1 : 21724
09/23/09 22:51:24 v1.10 @ 조영욱-PC,    length 2 : 15983
09/23/09 22:51:24 v1.10 @ 조영욱-PC,    length 3 : 14131
09/23/09 22:51:24 v1.10 @ 조영욱-PC,    length 4 : 10108
09/23/09 22:51:24 v1.10 @ 조영욱-PC,    length 5 : 6699
09/23/09 22:51:24 v1.10 @ 조영욱-PC,    length 6 : 3793
09/23/09 22:51:24 v1.10 @ 조영욱-PC,    length 7 : 2214
09/23/09 22:51:24 v1.10 @ 조영욱-PC,    length 9+: 2599
09/23/09 22:51:24 v1.10 @ 조영욱-PC, largest cycle: 19 relations
09/23/09 22:51:24 v1.10 @ 조영욱-PC, matrix is 77164 x 77251 (20.1 MB) with weight 4645464 (60.13/col)
09/23/09 22:51:24 v1.10 @ 조영욱-PC, sparse part has weight 4645464 (60.13/col)
09/23/09 22:51:24 v1.10 @ 조영욱-PC, filtering completed in 3 passes
09/23/09 22:51:24 v1.10 @ 조영욱-PC, matrix is 71727 x 71791 (18.9 MB) with weight 4374381 (60.93/col)
09/23/09 22:51:24 v1.10 @ 조영욱-PC, sparse part has weight 4374381 (60.93/col)
09/23/09 22:51:25 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
09/23/09 22:51:25 v1.10 @ 조영욱-PC, matrix is 71679 x 71791 (13.6 MB) with weight 3579075 (49.85/col)
09/23/09 22:51:25 v1.10 @ 조영욱-PC, sparse part has weight 2838426 (39.54/col)
09/23/09 22:51:25 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
09/23/09 22:51:25 v1.10 @ 조영욱-PC, using block size 28716 for processor cache size 4096 kB
09/23/09 22:51:25 v1.10 @ 조영욱-PC, commencing Lanczos iteration
09/23/09 22:51:25 v1.10 @ 조영욱-PC, memory use: 11.5 MB
09/23/09 22:51:49 v1.10 @ 조영욱-PC, lanczos halted after 1135 iterations (dim = 71677)
09/23/09 22:51:50 v1.10 @ 조영욱-PC, recovered 16 nontrivial dependencies
09/23/09 22:51:51 v1.10 @ 조영욱-PC, prp45 = 129968124481852563001973196053531945137907861
09/23/09 22:51:52 v1.10 @ 조영욱-PC, prp49 = 5977327695821253697952452498480093874447527049209
09/23/09 22:51:52 v1.10 @ 조영욱-PC, Lanczos elapsed time = 28.7970 seconds.
09/23/09 22:51:52 v1.10 @ 조영욱-PC, Sqrt elapsed time = 2.0130 seconds.
09/23/09 22:51:52 v1.10 @ 조영욱-PC, SIQS elapsed time = 4454.3950 seconds.
09/23/09 22:51:52 v1.10 @ 조영욱-PC, 
09/23/09 22:51:52 v1.10 @ 조영욱-PC,

Sep 23, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Sep 23, 2009

(19·10¹⁷²+71)/9 = 2(1)₁₇₁9_<173> = 7² · 8513 · C167

C167 = P45 · P123

P45 = 110527258301512944407034947393828659078821691_<45>

P123 = 457891920936034296955040759482830030956478893226740620438124139533279660951936241323594087842050389692669698370301114641357_<123>

Number: 21119_172
N=50609538619473005538015354934017148109880233858686980802736537662952725629975550265526939856956134581950560873552600491232163800169035858989039838496971285479617274687
  ( 167 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=110527258301512944407034947393828659078821691 (pp45)
 r2=457891920936034296955040759482830030956478893226740620438124139533279660951936241323594087842050389692669698370301114641357 (pp123)
Version: Msieve-1.40
Total time: 79.89 hours.
Scaled time: 138.92 units (timescale=1.739).
Factorization parameters were as follows:
n: 50609538619473005538015354934017148109880233858686980802736537662952725629975550265526939856956134581950560873552600491232163800169035858989039838496971285479617274687
m: 20000000000000000000000000000000000
deg: 5
c5: 475
c0: 568
skew: 1.04
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 7000001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1106971 x 1107201
Total sieving time: 78.02 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.61 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 79.89 hours.

Sep 23, 2009

By Markus Tervooren / Msieve / Sep 23, 2009

(34·10¹⁷⁰-43)/9 = 3(7)₁₆₉3_<171> = 1039 · 4993 · 48383 · 444279782318951143_<18> · C142

C142 = P62 · P81

P62 = 10046624647981434329731923157230013497017529691223640585456559_<62>

P81 = 337201713860184384671484513359560681560564747081840826807931543797600519507180469_<81>

this was an experiment, some parameters way off:

rlim: 6100000
alim: 6100000
lpbr: 32
lpba: 32
mfbr: 60
mfba: 60
rlambda: 2.7
alambda: 2.7

gnfs-lasieve4I13e, r-side only. >100M relations needed, but not as slow as I expected!

N=3387739049809311289031891114415217162097560958715790029603763531389843477916648874856656639848448031799156492074641358386383526373413172746171
  ( 142 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=10046624647981434329731923157230013497017529691223640585456559 (pp62)
 r2=337201713860184384671484513359560681560564747081840826807931543797600519507180469 (pp81)
Version: Msieve-1.39
Total time: 42.85 hours.
Scaled time: 90.89 units (timescale=2.121).
Factorization parameters were as follows:
n: 3387739049809311289031891114415217162097560958715790029603763531389843477916648874856656639848448031799156492074641358386383526373413172746171
m: 10000000000000000000000000000000000
deg: 5
c5: 34
c0: -43
skew: 1.05
type: snfs
lss: 1
rlim: 6100000
alim: 6100000
lpbr: 32
lpba: 32
mfbr: 60
mfba: 60
rlambda: 2.7
alambda: 2.7

Factor base limits: 6100000/6100000
Large primes per side: 3
Large prime bits: 32/32
Max factor residue bits: 60/60
Sieved rational special-q in [3050000, 5050001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1234878 x 1235103
Total sieving time: 38.84 hours.
Total relation processing time: 1.19 hours.
Matrix solve time: 2.49 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6100000,6100000,32,32,60,60,2.7,2.7,200000
total time: 42.85 hours.
 --------- CPU info (if available) ----------
[    0.148007] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.240015] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.335125] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.432094] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197992k/10485760k available (2226k kernel code, 189844k reserved, 1082k data, 392k init)
[    0.083917] Calibrating delay using timer specific routine.. 5503.93 BogoMIPS (lpj=11007873)
[    0.160010] Calibrating delay using timer specific routine.. 5499.97 BogoMIPS (lpj=10999957)
[    0.252015] Calibrating delay using timer specific routine.. 5500.01 BogoMIPS (lpj=11000021)
[    0.351657] Calibrating delay using timer specific routine.. 5499.99 BogoMIPS (lpj=10999983)
[    0.436823] Total of 4 processors activated (22003.91 BogoMIPS).

Sep 22, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Sep 22, 2009

(38·10¹⁸⁶+43)/9 = 4(2)₁₈₅7_<187> = 3 · 17 · C185

C185 = P73 · P113

P73 = 1891585429967514596086920515141982806978394946772213980599659632904031163_<73>

P113 = 43766815768604711815967463936726026448836428954307420888133000133113089530668709178784976770389471795428755770579_<113>

Number: 42227_186
N=82788671023965141612200435729847494553376906318082788671023965141612200435729847494553376906318082788671023965141612200435729847494553376906318082788671023965141612200435729847494553377
  ( 185 digits)
SNFS difficulty: 188 digits.
Divisors found:
 r1=1891585429967514596086920515141982806978394946772213980599659632904031163 (pp73)
 r2=43766815768604711815967463936726026448836428954307420888133000133113089530668709178784976770389471795428755770579 (pp113)
Version: Msieve-1.40
Total time: 292.57 hours.
Scaled time: 508.79 units (timescale=1.739).
Factorization parameters were as follows:
n: 82788671023965141612200435729847494553376906318082788671023965141612200435729847494553376906318082788671023965141612200435729847494553376906318082788671023965141612200435729847494553377
m: 20000000000000000000000000000000000000
deg: 5
c5: 95
c0: 344
skew: 1.29
type: snfs
lss: 1
rlim: 9700000
alim: 9700000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 9700000/9700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4850000, 9550001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1953083 x 1953306
Total sieving time: 285.69 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 5.81 hours.
Time per square root: 0.84 hours.
Prototype def-par.txt line would be:
snfs,188.000,5,0,0,0,0,0,0,0,0,9700000,9700000,28,28,54,54,2.5,2.5,100000
total time: 292.57 hours.

Sep 22, 2009 (2nd)

By Markus Tervooren / Msieve / Sep 22, 2009

(31·10¹⁷⁰+41)/9 = 3(4)₁₆₉9_<171> = 853 · 2803 · 17789517266374707409659285068323_<32> · C133

C133 = P65 · P69

P65 = 27780788152852831461500887890696440817757461017360421126755061577_<65>

P69 = 291499845878488279711112644141316213438152182705016277066973021038941_<69>

N=8098095464939533472257174858096288112060750390776624907535616984326680395854794231308671432066690891950563756090331388949682969869957
  ( 133 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=27780788152852831461500887890696440817757461017360421126755061577 (pp65)
 r2=291499845878488279711112644141316213438152182705016277066973021038941 (pp69)
Version: Msieve-1.39
Total time: 38.71 hours.
Scaled time: 82.30 units (timescale=2.126).
Factorization parameters were as follows:
n: 8098095464939533472257174858096288112060750390776624907535616984326680395854794231308671432066690891950563756090331388949682969869957
m: 10000000000000000000000000000000000
deg: 5
c5: 31
c0: 41
skew: 1.06
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 26
lpba: 26
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4

Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5900001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 810989 x 811214
Total sieving time: 37.62 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.85 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,26,26,52,52,2.4,2.4,200000
total time: 38.71 hours.
 --------- CPU info (if available) ----------
[    0.148007] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.240015] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.335125] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.432094] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197992k/10485760k available (2226k kernel code, 189844k reserved, 1082k data, 392k init)
[    0.083917] Calibrating delay using timer specific routine.. 5503.93 BogoMIPS (lpj=11007873)
[    0.160010] Calibrating delay using timer specific routine.. 5499.97 BogoMIPS (lpj=10999957)
[    0.252015] Calibrating delay using timer specific routine.. 5500.01 BogoMIPS (lpj=11000021)
[    0.351657] Calibrating delay using timer specific routine.. 5499.99 BogoMIPS (lpj=10999983)
[    0.436823] Total of 4 processors activated (22003.91 BogoMIPS).

Sep 22, 2009

By Sinkiti Sibata / Msieve / Sep 22, 2009

(59·10¹⁷⁹-23)/9 = 6(5)₁₇₈3_<180> = 19 · 2015473 · C173

C173 = P36 · P137

P36 = 265950273339045083658501704336465111_<36>

P137 = 64369253958059454454071720059779934517007813788573707868537817779248209579620751914898588371608462553066047076092102225842982124009465229_<137>

Number: 65553_179
N=17119020684776321555537049604042419389643485165322575462188242649049720405335583248502057400175008038613361297572790097713135891427433647887214135095297221351110699326125419
  ( 173 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=265950273339045083658501704336465111 (pp36)
 r2=64369253958059454454071720059779934517007813788573707868537817779248209579620751914898588371608462553066047076092102225842982124009465229 (pp137)
Version: Msieve-1.40
Total time: 235.94 hours.
Scaled time: 429.64 units (timescale=1.821).
Factorization parameters were as follows:
name: 65553_179
n: 17119020684776321555537049604042419389643485165322575462188242649049720405335583248502057400175008038613361297572790097713135891427433647887214135095297221351110699326125419
m: 1000000000000000000000000000000000000
deg: 5
c5: 59
c0: -230
skew: 1.31
type: snfs
lss: 1
rlim: 7500000
alim: 7500000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7500000/7500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3750000, 6850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1536395 x 1536620
Total sieving time: 229.72 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 5.89 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,181.000,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,53,53,2.5,2.5,100000
total time: 235.94 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3109164k/3145344k available (2732k kernel code, 34856k reserved, 1420k data, 412k init, 2227840k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.99 BogoMIPS (lpj=2393996)
Calibrating delay using timer specific routine.. 4787.75 BogoMIPS (lpj=2393875)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891)
Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393884)
Total of 4 processors activated (19151.29 BogoMIPS).

Sep 21, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Sep 21, 2009

(22·10¹⁷⁰-31)/9 = 2(4)₁₆₉1_<171> = 643 · 797 · 10837 · 344349949 · 51523958402942910120527119_<26> · C127

C127 = P62 · P66

P62 = 24512183185152555874872601627711724616592509609277977297743897_<62>

P66 = 101207003405412029690244968621692294006581722262048299972092070569_<66>

Number: 24441_170
N=2480804607093818215117690482806396339262667371876217980622632068551160814692874825909881008959568445704096870937243247013067393
  ( 127 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=24512183185152555874872601627711724616592509609277977297743897
 r2=101207003405412029690244968621692294006581722262048299972092070569
Version: 
Total time: 37.73 hours.
Scaled time: 89.92 units (timescale=2.383).
Factorization parameters were as follows:
n: 2480804607093818215117690482806396339262667371876217980622632068551160814692874825909881008959568445704096870937243247013067393
m: 10000000000000000000000000000000000
deg: 5
c5: 22
c0: -31
skew: 1.07
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 5800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11218005
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 959758 x 960006
Total sieving time: 33.86 hours.
Total relation processing time: 1.58 hours.
Matrix solve time: 2.17 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 37.73 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672363)
Calibrating delay using timer specific routine.. 5535.15 BogoMIPS (lpj=2767578)

Sep 21, 2009 (2nd)

By Markus Tervooren / Msieve / Sep 21, 2009

(53·10¹⁷⁸+1)/9 = 5(8)₁₇₇9_<179> = 29 · 83 · 56671 · 397302042061058419_<18> · 764648480363550491427385880911_<30> · C124

C124 = P57 · P67

P57 = 561805943477853761856674267872978066478843702421886731769_<57>

P67 = 2529457794411425253963747749161488771720116899521120577840536881597_<67>

Msieve v. 1.42
Sun Sep 20 17:41:27 2009
random seeds: ca005200 5206fa9f
factoring 1421064422676721817294303535151760278742043022221943758499295816466638534361724872580455743508352819227160020715265251355093 (124 digits)
no P-1/P+1/ECM available, skipping
commencing number field sieve (124-digit input)
R0: -563417788087954445078359
R1:  93114086034739
A0:  9062705301363742144378237740
A1: -138345562111090607522292
A2: -102636921381222766097
A3:  2505116646396433
A4:  60558688503
A5:  25020
skew 42407.21, size 7.642535e-12, alpha -6.074372, combined = 1.859517e-10

commencing square root phase
reading relations for dependency 1
read 347688 cycles
cycles contain 1268747 unique relations
read 1268747 relations
multiplying 1013154 relations
multiply complete, coefficients have about 49.40 million bits
initial square root is modulo 12361093
reading relations for dependency 2
read 347667 cycles
cycles contain 1268260 unique relations
read 1268260 relations
multiplying 1012028 relations
multiply complete, coefficients have about 49.34 million bits
initial square root is modulo 12139177
sqrtTime: 643
prp57 factor: 561805943477853761856674267872978066478843702421886731769
prp67 factor: 2529457794411425253963747749161488771720116899521120577840536881597
elapsed time 00:10:44
-> Computing time scale for this machine...
sumName = g124-nn.txt
-> Factorization summary written to g124-nn.txt.
debian:/mnt/ewww/worker/nfs/nn# cat g124-nn.txt
Number: nn
N=1421064422676721817294303535151760278742043022221943758499295816466638534361724872580455743508352819227160020715265251355093
  ( 124 digits)
Divisors found:
 r1=561805943477853761856674267872978066478843702421886731769 (pp57)
 r2=2529457794411425253963747749161488771720116899521120577840536881597 (pp67)
Version: Msieve-1.39
Total time: 46.33 hours.
Scaled time: 98.54 units (timescale=2.127).
Factorization parameters were as follows:
name: nn
n: 1421064422676721817294303535151760278742043022221943758499295816466638534361724872580455743508352819227160020715265251355093
skew: 42407.21
# norm 9.89e+16
c5: 25020
c4: 60558688503
c3: 2505116646396433
c2: -102636921381222766097
c1: -138345562111090607522292
c0: 9062705301363742144378237740
# alpha -6.07
Y1: 93114086034739
Y0: -563417788087954445078359
# Murphy_E 1.87e-10
# M 161784788761033858021168675376476101605306824352832905557000717915689308176872004727381341087251505583966762495087450514790
type: gnfs
rlim: 6000000
alim: 6000000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 260000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [3000000, 7420001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 695948 x 696173
Total sieving time: 45.50 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.59 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6000000,6000000,26,26,50,50,2.4,2.4,60000
total time: 46.33 hours.
 --------- CPU info (if available) ----------
[    0.148007] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.240015] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.335125] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.432094] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197992k/10485760k available (2226k kernel code, 189844k reserved, 1082k data, 392k init)
[    0.083917] Calibrating delay using timer specific routine.. 5503.93 BogoMIPS (lpj=11007873)
[    0.160010] Calibrating delay using timer specific routine.. 5499.97 BogoMIPS (lpj=10999957)
[    0.252015] Calibrating delay using timer specific routine.. 5500.01 BogoMIPS (lpj=11000021)
[    0.351657] Calibrating delay using timer specific routine.. 5499.99 BogoMIPS (lpj=10999983)
[    0.436823] Total of 4 processors activated (22003.91 BogoMIPS).

(10¹⁷¹+71)/9 = (1)₁₇₀9_<171> = 7 · 211 · 8893 · 1020013 · 8458713931_<10> · 10347507427_<11> · 45794704847_<11> · C127

C127 = P58 · P70

P58 = 1147968296263409095588135283290648861826345355194536694219_<58>

P70 = 1802344282551482866164093574575264853010705594176792033320430112532863_<70>

N=2069034095320722195548923215079703378937455489202419208172765615328926241741952336155268048786153404925113396948730329019618997
  ( 127 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=1147968296263409095588135283290648861826345355194536694219 (pp58)
 r2=1802344282551482866164093574575264853010705594176792033320430112532863 (pp70)
Version: Msieve-1.39
Total time: 24.46 hours.
Scaled time: 52.05 units (timescale=2.128).
Factorization parameters were as follows:
n: 2069034095320722195548923215079703378937455489202419208172765615328926241741952336155268048786153404925113396948730329019618997
m: 10000000000000000000000000000000000
deg: 5
c5: 10
c0: 71
skew: 1.48
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 30
lpba: 30
mfbr: 59
mfba: 59
rlambda: 2.4
alambda: 2.4

Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 30/30
Max factor residue bits: 59/59
Sieved rational special-q in [2500000, 4500001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 999891 x 1000139
Total sieving time: 23.06 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.16 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,30,30,59,59,2.4,2.4,200000
total time: 24.46 hours.
 --------- CPU info (if available) ----------
[    0.148007] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.240015] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.335125] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.432094] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197992k/10485760k available (2226k kernel code, 189844k reserved, 1082k data, 392k init)
[    0.083917] Calibrating delay using timer specific routine.. 5503.93 BogoMIPS (lpj=11007873)
[    0.160010] Calibrating delay using timer specific routine.. 5499.97 BogoMIPS (lpj=10999957)
[    0.252015] Calibrating delay using timer specific routine.. 5500.01 BogoMIPS (lpj=11000021)
[    0.351657] Calibrating delay using timer specific routine.. 5499.99 BogoMIPS (lpj=10999983)
[    0.436823] Total of 4 processors activated (22003.91 BogoMIPS).

Sep 21, 2009

By matsui / Msieve / Sep 21, 2009

(23·10¹⁹⁸+31)/9 = 2(5)₁₉₇9_<199> = 3 · 17 · 613 · C194

C194 = P88 · P107

P88 = 1773544851690857091455303578767620287335292839195633314214919261703524198142442232843039_<88>

P107 = 46090614675202519151121521301857710646255963027179329623754599707153708440227623256930972490373887356299687_<107>

N=81743772368472493220598009006031268769969470478058905273184133178375573539185476619504064087117536882434684948839060728514715656064854798181734176360411846449654721413669691186244300148915828793
  ( 194 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=1773544851690857091455303578767620287335292839195633314214919261703524198142442232843039 (pp88)
 r2=46090614675202519151121521301857710646255963027179329623754599707153708440227623256930972490373887356299687 (pp107)
Version: Msieve v. 1.42
Total time: 1259.43 hours.
Scaled time: 2168.73 units (timescale=1.722).
Factorization parameters were as follows:
n: 81743772368472493220598009006031268769969470478058905273184133178375573539185476619504064087117536882434684948839060728514715656064854798181734176360411846449654721413669691186244300148915828793
m: 5000000000000000000000000000000000000000
deg: 5
c5: 184
c0: 775
skew: 1.33
type: snfs
lss: 1
rlim: 15500000
alim: 15500000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6

Factor base limits: 15500000/15500000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7750000, 17950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3488309 x 3488539
Total sieving time: 1245.21 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 13.11 hours.
Time per square root: 0.84 hours.
Prototype def-par.txt line would be:
snfs,200.000,5,0,0,0,0,0,0,0,0,15500000,15500000,29,29,56,56,2.6,2.6,100000
total time: 1259.43 hours.

Sep 19, 2009

By Jo Yeong Uk / GMP-ECM / Sep 19, 2009

(29·10¹⁷⁰+43)/9 = 3(2)₁₆₉7_<171> = 3 · 1954336561162450967604444406439339_<34> · C137

C137 = P51 · P86

P51 = 903942870607759014353719475842760274151489835510297_<51>

P86 = 60798643985188028202680269739785039692943127907673564694636146843446912085467238806923_<86>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 54958500773030027645652315828411893842541871854764460247889669905548548420516193561916002544292592741336996889228227378146037689161386131 (137 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3500915563
Step 1 took 45093ms
Step 2 took 18232ms
********** Factor found in step 2: 903942870607759014353719475842760274151489835510297
Found probable prime factor of 51 digits: 903942870607759014353719475842760274151489835510297
Probable prime cofactor 60798643985188028202680269739785039692943127907673564694636146843446912085467238806923 has 86 digits

Sep 18, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Sep 18, 2009

(34·10¹⁷²+11)/9 = 3(7)₁₇₁9_<173> = 3 · 7⁵ · 22906207 · C161

C161 = P62 · P100

P62 = 13399547216048116206746496990163592721856158829124504594553373_<62>

P100 = 2441077953299866038839432759567807758029461670857114077392486299910968603071411404050302508894875309_<100>

Number: 37779_172
N=32709339293295653405389161183476271106949633991618747095363256042686944231211075637390850182455576410290605734321924801278797776521913329995119050282353380367257
  ( 161 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=13399547216048116206746496990163592721856158829124504594553373 (pp62)
 r2=2441077953299866038839432759567807758029461670857114077392486299910968603071411404050302508894875309 (pp100)
Version: Msieve-1.40
Total time: 85.38 hours.
Scaled time: 148.47 units (timescale=1.739).
Factorization parameters were as follows:
n: 32709339293295653405389161183476271106949633991618747095363256042686944231211075637390850182455576410290605734321924801278797776521913329995119050282353380367257
m: 20000000000000000000000000000000000
deg: 5
c5: 425
c0: 44
skew: 0.64
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 7300001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1195146 x 1195392
Total sieving time: 82.40 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.91 hours.
Time per square root: 0.97 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 85.38 hours.

Sep 18, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Sep 18, 2009

(32·10¹⁷⁰-23)/9 = 3(5)₁₆₉3_<171> = 149 · 33503 · 51263 · 667559 · 833873 · 4272601 · 2796767434453_<13> · C129

C129 = P46 · P84

P46 = 1645559899404926371376615695449343668738907841_<46>

P84 = 126935041708511926851398719627088041819405074396017925333247593624781393774875551543_<84>

Number: 35553_170
N=208879214464819019629450168438377319652848948698329271863993602063397043954681950453722916336345741936562797730018813558322348663
  ( 129 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=1645559899404926371376615695449343668738907841
 r2=126935041708511926851398719627088041819405074396017925333247593624781393774875551543
Version: 
Total time: 25.64 hours.
Scaled time: 61.20 units (timescale=2.387).
Factorization parameters were as follows:
n: 208879214464819019629450168438377319652848948698329271863993602063397043954681950453722916336345741936562797730018813558322348663
m: 20000000000000000000000000000000000
deg: 5
c5: 1
c0: -23
skew: 1.87
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2700000, 4600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10732993
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 828076 x 828324
Total sieving time: 22.74 hours.
Total relation processing time: 1.02 hours.
Matrix solve time: 1.47 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000
total time: 25.64 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672363)
Calibrating delay using timer specific routine.. 5535.15 BogoMIPS (lpj=2767578)

Sep 17, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.1 / Sep 17, 2009

(53·10¹⁷²-17)/9 = 5(8)₁₇₁7_<173> = 3 · 23 · 139 · 1447 · 3673 · 29181318710990417_<17> · C146

C146 = P36 · P111

P36 = 208315392186507557875574457526219127_<36>

P111 = 190043812887773452615147548555234527720338584588002284271867096892313001181562043797469305967347210061472949433_<111>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2640349756
Step 1 took 47357ms
Step 2 took 15663ms
********** Factor found in step 2: 208315392186507557875574457526219127
Found probable prime factor of 36 digits: 208315392186507557875574457526219127
Probable prime cofactor 190043812887773452615147548555234527720338584588002284271867096892313001181562043797469305967347210061472949433 has 111 digits

Sep 17, 2009 (3rd)

By Tyler Cadigan / GGNFS, Msieve / Sep 17, 2009

(8·10¹⁹⁸+7)/3 = 2(6)₁₉₇9_<199> = 36527 · 223908898999444076156054297_<27> · C168

C168 = P70 · P99

P70 = 2320931133956130818830015669886269704250399712699520140790309803080087_<70>

P99 = 140482141451250686133341198476651965065015485607240103507079549953316466653678246806832754878676573_<99>

Number: 26669_198
N=326049375859036824171261381255444031591741388878737437254646291435738645613348668941532143029811314115047415862021325774539435314337582793850998673813206148313689701851
  ( 168 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=2320931133956130818830015669886269704250399712699520140790309803080087 (pp70)
 r2=140482141451250686133341198476651965065015485607240103507079549953316466653678246806832754878676573 (pp99)
Version: Msieve v. 1.42
Total time: 690.72 hours.
Scaled time: 0.00 units (timescale=0.000).
Factorization parameters were as follows:
n: 326049375859036824171261381255444031591741388878737437254646291435738645613348668941532143029811314115047415862021325774539435314337582793850998673813206148313689701851
m: 4000000000000000000000000000000000000000
deg: 5
c5: 125
c0: 112
skew: 0.98
type: snfs
lss: 1
rlim: 15100000
alim: 15100000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 15100000/15100000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7550000, 16250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3134307 x 3134554
Total sieving time: 664.13 hours.
Total relation processing time: 0.66 hours.
Matrix solve time: 25.39 hours.
Time per square root: 0.54 hours.
Prototype def-par.txt line would be:
snfs,200.000,5,0,0,0,0,0,0,0,0,15100000,15100000,29,29,56,56,2.6,2.6,100000
total time: 690.72 hours.
 --------- CPU info (if available) ----------

Sep 17, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Sep 17, 2009

5·10¹⁷²-1 = 4(9)₁₇₂_<173> = 10889 · 2882359 · C163

C163 = P47 · P116

P47 = 23331915524945545696221472599200406173115587461_<47>

P116 = 68278432084467642690581024494631409446426792252293530420303471343294308319297030303253720850691295975733917647872509_<116>

Number: 49999_172
N=1593066609570530649370271023806535039809721860723856941429268203635476830520142259302322810459745823053514922077193405530808546778438857687622783273098732367009649
  ( 163 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=23331915524945545696221472599200406173115587461 (pp47)
 r2=68278432084467642690581024494631409446426792252293530420303471343294308319297030303253720850691295975733917647872509 (pp116)
Version: Msieve-1.40
Total time: 56.01 hours.
Scaled time: 97.40 units (timescale=1.739).
Factorization parameters were as follows:
n: 1593066609570530649370271023806535039809721860723856941429268203635476830520142259302322810459745823053514922077193405530808546778438857687622783273098732367009649
m: 50000000000000000000000000000000000
deg: 5
c5: 4
c0: -25
skew: 1.44
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 5600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1013275 x 1013505
Total sieving time: 54.26 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.33 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
snfs,174.000,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 56.01 hours.

Sep 17, 2009

By Erik Branger / GGNFS, Msieve / Sep 17, 2009

(59·10¹⁷⁶-23)/9 = 6(5)₁₇₅3_<177> = 10607 · 170707 · 1907561 · 7383695113_<10> · 13356533207_<11> · 94204984191876091349_<20> · C122

C122 = P54 · P68

P54 = 403844630858790500575868682495392203682876092519852009_<54>

P68 = 50586131707898714276738487374243579850913014442871160843064241211167_<68>

Number: 65553_176
N=20428937686150513716188331842654470818745885047506256942173091368357721595601970731854222314405131366557147229049758184503
  ( 122 digits)
Divisors found:
 r1=403844630858790500575868682495392203682876092519852009 (pp54)
 r2=50586131707898714276738487374243579850913014442871160843064241211167 (pp68)
Version: Msieve-1.40
Total time: 78.97 hours.
Scaled time: 82.21 units (timescale=1.041).
Factorization parameters were as follows:
name: 65553_176
n: 20428937686150513716188331842654470818745885047506256942173091368357721595601970731854222314405131366557147229049758184503
skew: 158770.76
# norm 3.94e+016
c5: 20760
c4: -474624674
c3: -1380158940384592
c2: 5554901797311219178
c1: 16747120367105975305015272
c0: 124551652241894432233486857885
# alpha -5.72
Y1: 24618278168627
Y0: -250382448565819244511008
# Murphy_E 2.24e-010
# M 18715881824280198266006146453563496886158383900731234471211620004399319029508825653052462610260773931023761550378367199990
type: gnfs
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved algebraic special-q in [2350000, 4750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 810844 x 811069
Polynomial selection time: 6.85 hours.
Total sieving time: 69.05 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.98 hours.
Time per square root: 0.89 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4700000,4700000,27,27,53,53,2.5,2.5,100000
total time: 78.97 hours.
 --------- CPU info (if available) ----------

Sep 16, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Sep 16, 2009

(28·10¹⁷⁰+71)/9 = 3(1)₁₆₉9_<171> = 11 · 29 · 331 · 19859450154315389409262513980231995152171_<41> · C126

C126 = P49 · P77

P49 = 2420617356194089718965053622654500415943294600059_<49>

P77 = 61291956131286495071168227013284416712975208459016724382733705642630335199739_<77>

Number: 31119_170
N=148364372806478843118018056613754483141353836691388837731243793211133214062412958758919222671776635993740297014703909886184601
  ( 126 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=2420617356194089718965053622654500415943294600059
 r2=61291956131286495071168227013284416712975208459016724382733705642630335199739
Version: 
Total time: 30.43 hours.
Scaled time: 72.76 units (timescale=2.391).
Factorization parameters were as follows:
n: 148364372806478843118018056613754483141353836691388837731243793211133214062412958758919222671776635993740297014703909886184601
m: 10000000000000000000000000000000000
deg: 5
c5: 28
c0: 71
skew: 1.20
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 5200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10954934
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 878849 x 879097
Total sieving time: 26.96 hours.
Total relation processing time: 1.25 hours.
Matrix solve time: 1.83 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 30.43 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672363)
Calibrating delay using timer specific routine.. 5535.15 BogoMIPS (lpj=2767578)

Sep 16, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Sep 16, 2009

(29·10¹⁷¹+7)/9 = 3(2)₁₇₀3_<172> = 11 · 1479791 · C165

C165 = P40 · P125

P40 = 9589733359425817076200622132279045714657_<40>

P125 = 20642195637875465109091115889554275724787712865926398073936739639918145829101307921345461505744380337731802369225974101445539_<125>

Number: 32223_171
N=197953152120328431037173014925278589539285813286668812888393896793055863492161591014739871571680928542809713866978034688204570302785523718750100043133991847019565123
  ( 165 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=9589733359425817076200622132279045714657 (pp40)
 r2=20642195637875465109091115889554275724787712865926398073936739639918145829101307921345461505744380337731802369225974101445539 (pp125)
Version: Msieve-1.40
Total time: 55.68 hours.
Scaled time: 96.82 units (timescale=1.739).
Factorization parameters were as follows:
n: 197953152120328431037173014925278589539285813286668812888393896793055863492161591014739871571680928542809713866978034688204570302785523718750100043133991847019565123
m: 20000000000000000000000000000000000
deg: 5
c5: 145
c0: 112
skew: 0.95
type: snfs
lss: 1
rlim: 5500000
alim: 5500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2750000, 5550001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1008999 x 1009224
Total sieving time: 54.12 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.32 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,173.000,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,52,52,2.4,2.4,100000
total time: 55.68 hours.

Sep 16, 2009 (2nd)

By matsui / Msieve / Sep 16, 2009

(5·10¹⁹²-23)/9 = (5)₁₉₁3_<192> = 163 · 1279 · C187

C187 = P60 · P128

P60 = 145799094413327602537748495764843958560973257709379649763033_<60>

P128 = 18277404337185425598239891100735103652779933589824068526521803540526698706975024559967802397321441019434259076595377171175687133_<128>

N=2664829000587861277529682197823047892839764365160452018954395715381339694813123536675775052190675976513263120418825844364392981266785091667452791221840085743537922915024465795054397154389
  ( 187 digits)
SNFS difficulty: 193 digits.
Divisors found:
 r1=145799094413327602537748495764843958560973257709379649763033 (pp60)
 r2=18277404337185425598239891100735103652779933589824068526521803540526698706975024559967802397321441019434259076595377171175687133 (pp128)
Version: Msieve v. 1.42
Total time: 792.35 hours.
Scaled time: 1412.76 units (timescale=1.783).
Factorization parameters were as follows:
n: 2664829000587861277529682197823047892839764365160452018954395715381339694813123536675775052190675976513263120418825844364392981266785091667452791221840085743537922915024465795054397154389
m: 200000000000000000000000000000000000000
deg: 5
c5: 125
c0: -184
skew: 1.08
type: snfs
lss: 1
rlim: 11800000
alim: 11800000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

Factor base limits: 11800000/11800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [5900000, 12200001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2317522 x 2317749
Total sieving time: 786.22 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 5.22 hours.
Time per square root: 0.74 hours.
Prototype def-par.txt line would be:
snfs,193.000,5,0,0,0,0,0,0,0,0,11800000,11800000,28,28,55,55,2.5,2.5,100000
total time: 792.35 hours.

Sep 16, 2009

By Dmitry Domanov / GMP-ECM 6.2.3 / Sep 16, 2009

(16·10²⁰¹-7)/9 = 1(7)₂₀₁_<202> = 22907 · 116828141 · 3234480311_<10> · 124391079730784249328107521_<27> · C154

C154 = P48 · P106

P48 = 444230759317260795175403240257992335842297058029_<48>

P106 = 3716716325424141693210925501479496473096886450257293112197934420640713023480015000833716684844466642631629_<106>

Run 250 out of 800:
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=315076985
Step 1 took 758047ms
Step 2 took 166062ms
********** Factor found in step 2: 444230759317260795175403240257992335842297058029
Found probable prime factor of 48 digits: 444230759317260795175403240257992335842297058029
Probable prime cofactor 3716716325424141693210925501479496473096886450257293112197934420640713023480015000833716684844466642631629 has 106 digits

Sep 15, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Sep 15, 2009

(59·10¹⁸⁴-41)/9 = 6(5)₁₈₃1_<185> = 4457 · C182

C182 = P82 · P100

P82 = 3925650796614450304608790541101120065188901574343160408611576754300302438605223543_<82>

P100 = 3746754205773394619342272537105245022521421337297176218292005706321173734203160089060992570783164401_<100>

Number: 65551_184
N=14708448632612868646074838581008650562161892653254555879640016952110288435170642933712262857427766559469498666267793483409368533891755789893550719218208560815695659761174681524692743
  ( 182 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=3925650796614450304608790541101120065188901574343160408611576754300302438605223543 (pp82)
 r2=3746754205773394619342272537105245022521421337297176218292005706321173734203160089060992570783164401 (pp100)
Version: Msieve-1.40
Total time: 302.32 hours.
Scaled time: 525.74 units (timescale=1.739).
Factorization parameters were as follows:
n: 14708448632612868646074838581008650562161892653254555879640016952110288435170642933712262857427766559469498666267793483409368533891755789893550719218208560815695659761174681524692743
m: 10000000000000000000000000000000000000
deg: 5
c5: 59
c0: -410
skew: 1.47
type: snfs
lss: 1
rlim: 9100000
alim: 9100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 9100000/9100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4550000, 9550001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2015554 x 2015780
Total sieving time: 295.54 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 6.26 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,186.000,5,0,0,0,0,0,0,0,0,9100000,9100000,28,28,54,54,2.5,2.5,100000
total time: 302.32 hours.

(4·10¹⁷³+17)/3 = 1(3)₁₇₂9_<174> = 71 · 103 · 1193 · C167

C167 = P52 · P115

P52 = 3055312741028287927419953994566699688539650674426697_<52>

P115 = 5002038710496443223237430195243628039136222337015568712568093688915681320808688259006916876185102925314392005660443_<115>

Number: 13339_173
N=15282792603296490723134751400734804309762796922213680414723029758615550157418494861180090632309114959343759942172969347646738401802727649899647452719529005727876046771
  ( 167 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=3055312741028287927419953994566699688539650674426697 (pp52)
 r2=5002038710496443223237430195243628039136222337015568712568093688915681320808688259006916876185102925314392005660443 (pp115)
Version: Msieve-1.40
Total time: 64.00 hours.
Scaled time: 111.30 units (timescale=1.739).
Factorization parameters were as follows:
n: 15282792603296490723134751400734804309762796922213680414723029758615550157418494861180090632309114959343759942172969347646738401802727649899647452719529005727876046771
m: 20000000000000000000000000000000000
deg: 5
c5: 125
c0: 17
skew: 0.67
type: snfs
lss: 1
rlim: 5500000
alim: 5500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2750000, 6050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1011480 x 1011706
Total sieving time: 62.32 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.33 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,173.000,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,52,52,2.4,2.4,100000
total time: 64.00 hours.

Sep 15, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Sep 15, 2009

(17·10¹⁷²-53)/9 = 1(8)₁₇₁3_<173> = 462931566953_<12> · C161

C161 = P34 · P127

P34 = 4243054134278387643902015996987107_<34>

P127 = 9616367306177254454400989800479749240068989346224909729607233753965222432813638290499093357045250756981484447816404226835696073_<127>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2577178989
Step 1 took 52114ms
Step 2 took 17800ms
********** Factor found in step 2: 4243054134278387643902015996987107
Found probable prime factor of 34 digits: 4243054134278387643902015996987107
Probable prime cofactor 9616367306177254454400989800479749240068989346224909729607233753965222432813638290499093357045250756981484447816404226835696073 has 127 digits

Sep 15, 2009

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Sep 15, 2009

(28·10¹⁷⁰-1)/9 = 3(1)₁₇₀_<171> = 19 · 194022611 · 5328187985291_<13> · 523160083277781738962657179_<27> · C122

C122 = P46 · P77

P46 = 2034416473796509875496633128017420031802765447_<46>

P77 = 14881803754980492436345625472473603610295959695851442433011508052049006779313_<77>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 30275786718939073262198283789978155876672082056701271284678851780538889561037058996711978385933115010226062811804230797911 (122 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=5560633114
Step 1 took 36482ms
Step 2 took 16064ms
********** Factor found in step 2: 2034416473796509875496633128017420031802765447
Found probable prime factor of 46 digits: 2034416473796509875496633128017420031802765447
Probable prime cofactor 14881803754980492436345625472473603610295959695851442433011508052049006779313 has 77 digits

(25·10¹⁷⁰-7)/9 = 2(7)₁₇₀_<171> = 19 · 70404865994208751_<17> · 73366186660775416995914888233_<29> · C124

C124 = P55 · P69

P55 = 2876888773808448545612389450797680965722057990005266781_<55>

P69 = 983834854012949827795189415448811266443835744019552456282786436621921_<69>

Number: 27777_170
N=2830383446791329213045810558076746303928335194452563864665352732692769492808311351008681355733769971965505177430248037706301
  ( 124 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=2876888773808448545612389450797680965722057990005266781
 r2=983834854012949827795189415448811266443835744019552456282786436621921
Version: 
Total time: 28.60 hours.
Scaled time: 68.21 units (timescale=2.385).
Factorization parameters were as follows:
n: 2830383446791329213045810558076746303928335194452563864665352732692769492808311351008681355733769971965505177430248037706301
m: 10000000000000000000000000000000000
deg: 5
c5: 25
c0: -7
skew: 0.78
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 5000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10897777
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 858756 x 859004
Total sieving time: 25.55 hours.
Total relation processing time: 1.16 hours.
Matrix solve time: 1.69 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,52,52,2.4,2.4,100000
total time: 28.60 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672363)
Calibrating delay using timer specific routine.. 5535.15 BogoMIPS (lpj=2767578)

Sep 14, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Sep 14, 2009

(37·10¹⁷²+17)/9 = 4(1)₁₇₁3_<173> = 1019 · 500107 · 1606379 · 113767669 · 55172481563_<11> · C139

C139 = P38 · P102

P38 = 22736814924784767224815309943955870851_<38>

P102 = 351886879859479926106674281094605843954692625172311480161859483512498327727310770210259206169473031847_<102>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3910885405
Step 1 took 42500ms
Step 2 took 14634ms
********** Factor found in step 2: 22736814924784767224815309943955870851
Found probable prime factor of 38 digits: 22736814924784767224815309943955870851
Probable prime cofactor 351886879859479926106674281094605843954692625172311480161859483512498327727310770210259206169473031847 has 102 digits

Sep 14, 2009

By Erik Branger / GGNFS, Msieve / Sep 14, 2009

(55·10¹⁷⁵-1)/9 = 6(1)₁₇₅_<176> = 559821770843_<12> · 493891397250154369_<18> · 246041480448468935505424191257093_<33> · C114

C114 = P51 · P64

P51 = 391017902359935460396295293287515147769285653999791_<51>

P64 = 2297385954982518572904767806255584155891087077691780714089840591_<64>

Number: 61111_175
N=898319037028441530467871708720637399015885456002350928697575599818325407407797676281432751591884328633936737316481
  ( 114 digits)
Divisors found:
 r1=391017902359935460396295293287515147769285653999791 (pp51)
 r2=2297385954982518572904767806255584155891087077691780714089840591 (pp64)
Version: Msieve-1.40
Total time: 33.95 hours.
Scaled time: 28.38 units (timescale=0.836).
Factorization parameters were as follows:
name: 61111_175
n: 898319037028441530467871708720637399015885456002350928697575599818325407407797676281432751591884328633936737316481
skew: 27326.58
# norm 1.34e+016
c5: 39960
c4: -13065988698
c3: -531998152742487
c2: 10936317674746143358
c1: 41491178267049779716272
c0: -290167518519014402796604480
# alpha -6.57
Y1: 207470951633
Y0: -7419280982151022683621
# Murphy_E 6.05e-010
# M 421724283038624203547494160550808401767561659534889227030843559691311517724997876398849781291780144316139807082033
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2850001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 487262 x 487489
Polynomial selection time: 2.40 hours.
Total sieving time: 30.65 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.65 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 33.95 hours.
 --------- CPU info (if available) ----------

Sep 13, 2009 (3rd)

By matsui / Msieve / Sep 13, 2009

9·10¹⁷⁵+1 = 9(0)₁₇₄1_<176> = 7 · 13 · 93455747615903_<14> · 781769166175247748256859_<24> · C137

C137 = P67 · P70

P67 = 1628016159426033701278393782246899502990135743608549066928747844161_<67>

P70 = 8314915735262452439319787506005991721407656494214518451363732004308663_<70>

N=13536817181273073003693400687887924526607703152525801239445965870724371117220030478103125284496228788782993959108776273823788324466266743
  ( 137 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=1628016159426033701278393782246899502990135743608549066928747844161 (pp67)
 r2=8314915735262452439319787506005991721407656494214518451363732004308663 (pp70)
Version: Msieve v. 1.42
Total time: 107.83 hours.
Scaled time: 194.42 units (timescale=1.803).
Factorization parameters were as follows:
n: 13536817181273073003693400687887924526607703152525801239445965870724371117220030478103125284496228788782993959108776273823788324466266743
m: 100000000000000000000000000000000000
deg: 5
c5: 9
c0: 1
skew: 0.64
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 5800001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1032129 x 1032362
Total sieving time: 105.76 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.70 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,52,52,2.5,2.5,100000
total time: 107.83 hours.

Sep 13, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve 1.42 / Sep 13, 2009

(59·10¹⁹⁰-23)/9 = 6(5)₁₈₉3_<191> = 3² · C190

C190 = P69 · P122

P69 = 595930134278907987018097882864219937198080120308454580288752400192693_<69>

P122 = 12222826466222811769941835851841951524169028228224503246579993591785109785182270777425388414418679194209613457906566723669_<122>

Sieving ~ 12 cpu-days

Sun Sep 13 07:57:55 2009  Msieve v. 1.42
Sun Sep 13 07:57:55 2009  random seeds: 8c162888 c6fe34f8
Sun Sep 13 07:57:55 2009  factoring 7283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617 (190 digits)
Sun Sep 13 07:57:57 2009  searching for 15-digit factors
Sun Sep 13 07:57:58 2009  commencing number field sieve (190-digit input)
Sun Sep 13 07:57:58 2009  R0: -100000000000000000000000000000000000000
Sun Sep 13 07:57:58 2009  R1:  1
Sun Sep 13 07:57:58 2009  A0: -23
Sun Sep 13 07:57:58 2009  A1:  0
Sun Sep 13 07:57:58 2009  A2:  0
Sun Sep 13 07:57:58 2009  A3:  0
Sun Sep 13 07:57:58 2009  A4:  0
Sun Sep 13 07:57:58 2009  A5:  59
Sun Sep 13 07:57:58 2009  skew 0.83, size 2.553821e-013, alpha 0.725916, combined = 3.581467e-011
Sun Sep 13 07:57:58 2009  
Sun Sep 13 07:57:58 2009  commencing relation filtering
Sun Sep 13 07:57:58 2009  estimated available RAM is 4096.0 MB
Sun Sep 13 07:57:58 2009  commencing duplicate removal, pass 1
Sun Sep 13 08:00:18 2009  error -11 reading relation 17862868
Sun Sep 13 08:01:03 2009  found 4163747 hash collisions in 23615959 relations
Sun Sep 13 08:01:54 2009  added 717815 free relations
Sun Sep 13 08:01:54 2009  commencing duplicate removal, pass 2
Sun Sep 13 08:02:38 2009  found 3990250 duplicates and 20343523 unique relations
Sun Sep 13 08:02:38 2009  memory use: 106.6 MB
Sun Sep 13 08:02:38 2009  reading ideals above 17891328
Sun Sep 13 08:02:43 2009  commencing singleton removal, initial pass
Sun Sep 13 08:05:59 2009  memory use: 298.4 MB
Sun Sep 13 08:05:59 2009  reading all ideals from disk
Sun Sep 13 08:05:59 2009  memory use: 344.9 MB
Sun Sep 13 08:06:01 2009  commencing in-memory singleton removal
Sun Sep 13 08:06:03 2009  begin with 20343523 relations and 19743339 unique ideals
Sun Sep 13 08:06:21 2009  reduce to 9359078 relations and 6668121 ideals in 16 passes
Sun Sep 13 08:06:21 2009  max relations containing the same ideal: 28
Sun Sep 13 08:06:23 2009  reading ideals above 100000
Sun Sep 13 08:06:23 2009  commencing singleton removal, initial pass
Sun Sep 13 08:08:26 2009  memory use: 149.2 MB
Sun Sep 13 08:08:26 2009  reading all ideals from disk
Sun Sep 13 08:08:27 2009  memory use: 366.9 MB
Sun Sep 13 08:08:29 2009  keeping 8915335 ideals with weight <= 200, target excess is 49957
Sun Sep 13 08:08:31 2009  commencing in-memory singleton removal
Sun Sep 13 08:08:32 2009  begin with 9361029 relations and 8915335 unique ideals
Sun Sep 13 08:08:56 2009  reduce to 9326998 relations and 8872064 ideals in 12 passes
Sun Sep 13 08:08:56 2009  max relations containing the same ideal: 200
Sun Sep 13 08:09:05 2009  removing 1450945 relations and 1252453 ideals in 198492 cliques
Sun Sep 13 08:09:06 2009  commencing in-memory singleton removal
Sun Sep 13 08:09:07 2009  begin with 7876053 relations and 8872064 unique ideals
Sun Sep 13 08:09:24 2009  reduce to 7710435 relations and 7449485 ideals in 10 passes
Sun Sep 13 08:09:24 2009  max relations containing the same ideal: 184
Sun Sep 13 08:09:31 2009  removing 1087103 relations and 888611 ideals in 198492 cliques
Sun Sep 13 08:09:32 2009  commencing in-memory singleton removal
Sun Sep 13 08:09:33 2009  begin with 6623332 relations and 7449485 unique ideals
Sun Sep 13 08:09:45 2009  reduce to 6509266 relations and 6443963 ideals in 9 passes
Sun Sep 13 08:09:45 2009  max relations containing the same ideal: 163
Sun Sep 13 08:09:53 2009  relations with 0 large ideals: 1039
Sun Sep 13 08:09:53 2009  relations with 1 large ideals: 94
Sun Sep 13 08:09:53 2009  relations with 2 large ideals: 1531
Sun Sep 13 08:09:53 2009  relations with 3 large ideals: 18363
Sun Sep 13 08:09:53 2009  relations with 4 large ideals: 124425
Sun Sep 13 08:09:53 2009  relations with 5 large ideals: 496441
Sun Sep 13 08:09:53 2009  relations with 6 large ideals: 1286558
Sun Sep 13 08:09:53 2009  relations with 7+ large ideals: 4580815
Sun Sep 13 08:09:53 2009  commencing 2-way merge
Sun Sep 13 08:10:03 2009  reduce to 4032036 relation sets and 3966734 unique ideals
Sun Sep 13 08:10:03 2009  ignored 1 oversize relation sets
Sun Sep 13 08:10:03 2009  commencing full merge
Sun Sep 13 08:11:55 2009  memory use: 432.4 MB
Sun Sep 13 08:11:56 2009  found 2083563 cycles, need 2070934
Sun Sep 13 08:11:56 2009  weight of 2070934 cycles is about 145206036 (70.12/cycle)
Sun Sep 13 08:11:56 2009  distribution of cycle lengths:
Sun Sep 13 08:11:56 2009  1 relations: 265751
Sun Sep 13 08:11:56 2009  2 relations: 255767
Sun Sep 13 08:11:56 2009  3 relations: 245138
Sun Sep 13 08:11:56 2009  4 relations: 217974
Sun Sep 13 08:11:56 2009  5 relations: 196631
Sun Sep 13 08:11:56 2009  6 relations: 167146
Sun Sep 13 08:11:56 2009  7 relations: 143957
Sun Sep 13 08:11:56 2009  8 relations: 121627
Sun Sep 13 08:11:56 2009  9 relations: 99995
Sun Sep 13 08:11:56 2009  10+ relations: 356948
Sun Sep 13 08:11:56 2009  heaviest cycle: 24 relations
Sun Sep 13 08:11:57 2009  commencing cycle optimization
Sun Sep 13 08:12:02 2009  start with 11830058 relations
Sun Sep 13 08:12:31 2009  pruned 283532 relations
Sun Sep 13 08:12:31 2009  memory use: 308.4 MB
Sun Sep 13 08:12:31 2009  distribution of cycle lengths:
Sun Sep 13 08:12:31 2009  1 relations: 265751
Sun Sep 13 08:12:31 2009  2 relations: 261074
Sun Sep 13 08:12:31 2009  3 relations: 253204
Sun Sep 13 08:12:31 2009  4 relations: 222854
Sun Sep 13 08:12:31 2009  5 relations: 200968
Sun Sep 13 08:12:31 2009  6 relations: 169433
Sun Sep 13 08:12:31 2009  7 relations: 145141
Sun Sep 13 08:12:31 2009  8 relations: 120987
Sun Sep 13 08:12:31 2009  9 relations: 98774
Sun Sep 13 08:12:31 2009  10+ relations: 332748
Sun Sep 13 08:12:31 2009  heaviest cycle: 24 relations
Sun Sep 13 08:12:39 2009  RelProcTime: 881
Sun Sep 13 08:12:39 2009  
Sun Sep 13 08:12:39 2009  commencing linear algebra
Sun Sep 13 08:12:40 2009  read 2070934 cycles
Sun Sep 13 08:12:45 2009  cycles contain 6402908 unique relations
Sun Sep 13 08:18:40 2009  read 6402908 relations
Sun Sep 13 08:18:51 2009  using 20 quadratic characters above 268435292
Sun Sep 13 08:19:24 2009  building initial matrix
Sun Sep 13 08:20:47 2009  memory use: 706.9 MB
Sun Sep 13 08:20:52 2009  read 2070934 cycles
Sun Sep 13 08:24:47 2009  matrix is 2070756 x 2070934 (589.3 MB) with weight 184162812 (88.93/col)
Sun Sep 13 08:24:47 2009  sparse part has weight 139977590 (67.59/col)
Sun Sep 13 08:25:23 2009  filtering completed in 2 passes
Sun Sep 13 08:25:24 2009  matrix is 2069505 x 2069683 (589.2 MB) with weight 184122195 (88.96/col)
Sun Sep 13 08:25:24 2009  sparse part has weight 139964532 (67.63/col)
Sun Sep 13 08:25:36 2009  read 2069683 cycles
Sun Sep 13 08:35:19 2009  matrix is 2069505 x 2069683 (589.2 MB) with weight 184122195 (88.96/col)
Sun Sep 13 08:35:19 2009  sparse part has weight 139964532 (67.63/col)
Sun Sep 13 08:35:19 2009  saving the first 48 matrix rows for later
Sun Sep 13 08:35:20 2009  matrix is 2069457 x 2069683 (558.5 MB) with weight 146281012 (70.68/col)
Sun Sep 13 08:35:20 2009  sparse part has weight 133994588 (64.74/col)
Sun Sep 13 08:35:20 2009  matrix includes 64 packed rows
Sun Sep 13 08:35:20 2009  using block size 65536 for processor cache size 6144 kB
Sun Sep 13 08:35:35 2009  commencing Lanczos iteration (8 threads)
Sun Sep 13 08:35:35 2009  memory use: 694.2 MB
Sun Sep 13 13:42:19 2009  lanczos halted after 32726 iterations (dim = 2069455)
Sun Sep 13 13:42:24 2009  recovered 34 nontrivial dependencies
Sun Sep 13 13:42:28 2009  BLanczosTime: 19789
Sun Sep 13 13:42:28 2009  
Sun Sep 13 13:42:28 2009  commencing square root phase
Sun Sep 13 13:42:28 2009  reading relations for dependency 1
Sun Sep 13 13:42:29 2009  read 1035770 cycles
Sun Sep 13 13:42:31 2009  cycles contain 3948645 unique relations
Sun Sep 13 13:46:04 2009  read 3948645 relations
Sun Sep 13 13:46:27 2009  multiplying 3203982 relations
Sun Sep 13 13:52:07 2009  multiply complete, coefficients have about 90.91 million bits
Sun Sep 13 13:52:08 2009  initial square root is modulo 3350881
Sun Sep 13 13:59:12 2009  sqrtTime: 1004
Sun Sep 13 13:59:12 2009  prp69 factor: 595930134278907987018097882864219937198080120308454580288752400192693
Sun Sep 13 13:59:12 2009  prp122 factor: 12222826466222811769941835851841951524169028228224503246579993591785109785182270777425388414418679194209613457906566723669
Sun Sep 13 13:59:12 2009  elapsed time 06:01:17

Sep 13, 2009

By Erik Branger / GMP-ECM / Sep 13, 2009

(55·10¹⁷⁵-1)/9 = 6(1)₁₇₅_<176> = 559821770843_<12> · 493891397250154369_<18> · C147

C147 = P33 · C114

P33 = 246041480448468935505424191257093_<33>

C114 = [898319037028441530467871708720637399015885456002350928697575599818325407407797676281432751591884328633936737316481_<114>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 221023745785520738530183158323401649838072496227609848123552585054296532467811331267623414997472764179348057363824316443974920322581617998777049733 (147 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=712893148
Step 1 took 66098ms
Step 2 took 16302ms
********** Factor found in step 2: 246041480448468935505424191257093
Found probable prime factor of 33 digits: 246041480448468935505424191257093
Composite cofactor 898319037028441530467871708720637399015885456002350928697575599818325407407797676281432751591884328633936737316481 has 114 digits

Sep 12, 2009

By Dmitry Domanov / GGNFS/msieve 1.42 / Sep 12, 2009

(59·10¹⁶⁹-23)/9 = 6(5)₁₆₈3_<170> = 3 · 7 · 89 · C167

C167 = P41 · P127

P41 = 28430964259781917943980748374208784514853_<41>

P127 = 1233697291939774133711286527411120375881469802995317171773279409219618101136753281894577979510992906387685595566502805933883329_<127>

N=35075203614529457226086439569585637001367338445990131383389810356102490933951608108911479697996551929136198799120147434754176327210035075203614529457226086439569585637
  ( 167 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=28430964259781917943980748374208784514853 (pp41)
 r2=1233697291939774133711286527411120375881469802995317171773279409219618101136753281894577979510992906387685595566502805933883329 (pp127)
Version: Msieve-1.40
Total time: 71.59 hours.
Scaled time: 131.66 units (timescale=1.839).
Factorization parameters were as follows:
n: 35075203614529457226086439569585637001367338445990131383389810356102490933951608108911479697996551929136198799120147434754176327210035075203614529457226086439569585637
m: 10000000000000000000000000000000000
deg: 5
c5: 59
c0: -230
skew: 1.31
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 6250001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1065258 x 1065492
Total sieving time: 67.56 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 3.78 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 71.59 hours.
 --------- CPU info (if available) ----------

Sep 11, 2009 (3rd)

By Sinkiti Sibata / Msieve / Sep 11, 2009

(59·10¹⁶⁵-23)/9 = 6(5)₁₆₄3_<166> = 1741 · 38960227999134538231_<20> · C143

C143 = P28 · P116

P28 = 2064990475929912749997390361_<28>

P116 = 46802730236683154984816134421376388063144540153731467205541612475533926974676458033603066779475822373135228517421563_<116>

Number: 65553_165
N=96647192186267666218374132506936329952557529182361162213091431954136502206263711389409088399037651233385794443350281121504327314015274509754243
  ( 143 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=2064990475929912749997390361 (pp28)
 r2=46802730236683154984816134421376388063144540153731467205541612475533926974676458033603066779475822373135228517421563 (pp116)
Version: Msieve-1.40
Total time: 51.38 hours.
Scaled time: 93.56 units (timescale=1.821).
Factorization parameters were as follows:
name: 65553_165
n: 96647192186267666218374132506936329952557529182361162213091431954136502206263711389409088399037651233385794443350281121504327314015274509754243
m: 1000000000000000000000000000000000
deg: 5
c5: 59
c0: -23
skew: 0.83
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4200001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 816412 x 816637
Total sieving time: 49.26 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.54 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 51.38 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3109164k/3145344k available (2732k kernel code, 34856k reserved, 1420k data, 412k init, 2227840k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.99 BogoMIPS (lpj=2393997)
Calibrating delay using timer specific routine.. 4787.75 BogoMIPS (lpj=2393879)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393890)
Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393888)
Total of 4 processors activated (19151.30 BogoMIPS).

Sep 11, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Sep 11, 2009

(29·10¹⁷¹-11)/9 = 3(2)₁₇₀1_<172> = 77378189879_<11> · C161

C161 = P58 · P104

P58 = 1373059027510165266686030191368009754437222748912948998947_<58>

P104 = 30328275365755465480725921312582058358200443978085503922256042894999692403183763300297990866427565037417_<104>

Number: 32221_171
N=41642512279764701242995617662091759439388865446300500712469273427447764117297156736480630877206853227818477826739783384151735931075439602326578252912586748599899
  ( 161 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=1373059027510165266686030191368009754437222748912948998947 (pp58)
 r2=30328275365755465480725921312582058358200443978085503922256042894999692403183763300297990866427565037417 (pp104)
Version: Msieve-1.40
Total time: 72.57 hours.
Scaled time: 126.57 units (timescale=1.744).
Factorization parameters were as follows:
n: 41642512279764701242995617662091759439388865446300500712469273427447764117297156736480630877206853227818477826739783384151735931075439602326578252912586748599899
m: 20000000000000000000000000000000000
deg: 5
c5: 145
c0: -176
skew: 1.04
type: snfs
lss: 1
rlim: 5500000
alim: 5500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2750000, 6550001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1050536 x 1050764
Total sieving time: 70.90 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.44 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,173.000,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,52,52,2.4,2.4,100000
total time: 72.57 hours.

Sep 11, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Sep 11, 2009

(19·10¹⁷⁰+71)/9 = 2(1)₁₆₉9_<171> = 3² · 73 · 1143526333241_<13> · 26806091100941_<14> · C143

C143 = P46 · P97

P46 = 1472916625511933818304086346266260652139237503_<46>

P97 = 7116851409399948800992630964973514929835328139534602203013552485803304887760559036954951326947469_<97>

Number: 21119_170
N=10482528762203222779447796871500280565529891335012482902432438626124840006434825907390863943724652265498027597009542119289264411940490195729907
  ( 143 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=1472916625511933818304086346266260652139237503
 r2=7116851409399948800992630964973514929835328139534602203013552485803304887760559036954951326947469
Version: 
Total time: 41.40 hours.
Scaled time: 98.74 units (timescale=2.385).
Factorization parameters were as follows:
n: 10482528762203222779447796871500280565529891335012482902432438626124840006434825907390863943724652265498027597009542119289264411940490195729907
m: 10000000000000000000000000000000000
deg: 5
c5: 19
c0: 71
skew: 1.30
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 6100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11129718
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1061046 x 1061293
Total sieving time: 36.83 hours.
Total relation processing time: 1.69 hours.
Matrix solve time: 2.61 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 41.40 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672387)
Calibrating delay using timer specific routine.. 5344.57 BogoMIPS (lpj=2672286)
Calibrating delay using timer specific routine.. 5237.81 BogoMIPS (lpj=2618908)

Sep 10, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Sep 10, 2009

(52·10¹⁷¹-7)/9 = 5(7)₁₇₁_<172> = 1952178017533_<13> · C160

C160 = P50 · P110

P50 = 39592814745574705902699945898782321093833965047403_<50>

P110 = 74752382368221238007239043624856816631832755356506250342177409326733359592982167470607142927525246902943388623_<110>

Number: 57777_171
N=2959657226895348486983068529357280561791280143455803222127889917932424116381080897985883660911699420346378168816946684119097523441838243885561586972205645896069
  ( 160 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=39592814745574705902699945898782321093833965047403 (pp50)
 r2=74752382368221238007239043624856816631832755356506250342177409326733359592982167470607142927525246902943388623 (pp110)
Version: Msieve-1.40
Total time: 63.82 hours.
Scaled time: 111.30 units (timescale=1.744).
Factorization parameters were as follows:
n: 2959657226895348486983068529357280561791280143455803222127889917932424116381080897985883660911699420346378168816946684119097523441838243885561586972205645896069
m: 20000000000000000000000000000000000
deg: 5
c5: 65
c0: -28
skew: 0.84
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2700000, 6000001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1032105 x 1032337
Total sieving time: 62.09 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.38 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,173.000,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000
total time: 63.82 hours.

Sep 10, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Sep 10, 2009

(19·10¹⁷⁰-7)/3 = 6(3)₁₆₉1_<171> = 23 · 1693 · 1199754677923870469881793579521_<31> · C137

C137 = P68 · P69

P68 = 19363256165470831739734671261834093462756927660295485797238711171749_<68>

P69 = 700126811195158293901619994127610847780854332564369683876988029909301_<69>

Number: 63331_170
N=13556734793486081777091329350501324438959824086504966141450657440300019933595539917931323461796454538355073091348758169494393299903537449
  ( 137 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=19363256165470831739734671261834093462756927660295485797238711171749
 r2=700126811195158293901619994127610847780854332564369683876988029909301
Version: 
Total time: 27.91 hours.
Scaled time: 66.52 units (timescale=2.383).
Factorization parameters were as follows:
n: 13556734793486081777091329350501324438959824086504966141450657440300019933595539917931323461796454538355073091348758169494393299903537449
m: 10000000000000000000000000000000000
deg: 5
c5: 19
c0: -7
skew: 0.82
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 4900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10788670
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 868645 x 868893
Total sieving time: 24.93 hours.
Total relation processing time: 1.13 hours.
Matrix solve time: 1.61 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 27.91 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672387)
Calibrating delay using timer specific routine.. 5344.57 BogoMIPS (lpj=2672286)
Calibrating delay using timer specific routine.. 5237.81 BogoMIPS (lpj=2618908)

Sep 9, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve 1.42 / Sep 9, 2009

(4·10¹⁷²-31)/9 = (4)₁₇₁1_<172> = 41 · 4556732659_<10> · C161

C161 = P57 · P105

P57 = 154672668131208332773994942553144120407006879014809000343_<57>

P105 = 153803599121423245988030142267402289768022067254300628720236883515007414392873119738585516383755757888173_<105>

Number: 44441_172
N=23789213044293303229550735607486601307766306706298497379290758255801377010322518700127858457364260309316537501324589084283252677872502791566794880261178912643339
  ( 161 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=154672668131208332773994942553144120407006879014809000343 (pp57)
 r2=153803599121423245988030142267402289768022067254300628720236883515007414392873119738585516383755757888173 (pp105)
Version: Msieve-1.40
Total time: 63.16 hours.
Scaled time: 109.84 units (timescale=1.739).
Factorization parameters were as follows:
n: 23789213044293303229550735607486601307766306706298497379290758255801377010322518700127858457364260309316537501324589084283252677872502791566794880261178912643339
m: 20000000000000000000000000000000000
deg: 5
c5: 25
c0: -62
skew: 1.20
type: snfs
lss: 1
rlim: 5300000
alim: 5300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2650000, 5950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 998422 x 998655
Total sieving time: 61.66 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.28 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,172.000,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.4,2.4,100000
total time: 63.16 hours.

Sep 9, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve 1.42 / Sep 9, 2009

(59·10¹⁶⁶-23)/9 = 6(5)₁₆₅3_<167> = 3 · 337 · C164

C164 = P77 · P88

P77 = 13762016883863372331245726248307835934280238168059759413862859606014645511587_<77>

P88 = 4711685133710953668512566356995788489413041337701567967488467192158358794694291911725929_<88>

N=64842290361578195406088581162765139026266622705791845257720628640509946147928343774041103417958017364545554456533685020331904604901637542587097483239916474337839323
  ( 164 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=13762016883863372331245726248307835934280238168059759413862859606014645511587 (pp77)
 r2=4711685133710953668512566356995788489413041337701567967488467192158358794694291911725929 (pp88)
Version: Msieve-1.40
Total time: 58.57 hours.
Scaled time: 106.78 units (timescale=1.823).
Factorization parameters were as follows:
n: 64842290361578195406088581162765139026266622705791845257720628640509946147928343774041103417958017364545554456533685020331904604901637542587097483239916474337839323
m: 2000000000000000000000000000000000
deg: 5
c5: 295
c0: -368
skew: 1.05
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2300000, 5400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 945033 x 945257
Total sieving time: 55.42 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 2.67 hours.
Time per square root: 0.37 hours.
Prototype def-par.txt line would be:
snfs,168.000,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000
total time: 58.57 hours.
 --------- CPU info (if available) ----------

Sep 9, 2009 (3rd)

By Erik Branger / GGNFS, Msieve / Sep 9, 2009

(10¹⁸⁷+17)/9 = (1)₁₈₆3_<187> = 3³ · 311 · 1231 · 283233089 · 2951213879_<10> · 130396245425519_<15> · 47490956088523379331353_<23> · C125

C125 = P49 · P76

P49 = 2743641069602876421817939887754517698871698068469_<49>

P76 = 7568804996257901058444820569101293068078524183161107631106691480771145301383_<76>

Number: 11113_187
N=2076608423554862273326948827588460567685888236599784909184558742554793600727192235715606019606276692599332219017

8505974392627
  ( 125 digits)
Divisors found:
 r1=2743641069602876421817939887754517698871698068469 (pp49)
 r2=7568804996257901058444820569101293068078524183161107631106691480771145301383 (pp76)
Version: Msieve-1.40
Total time: 93.26 hours.
Scaled time: 97.64 units (timescale=1.047).
Factorization parameters were as follows:
n: 

207660842355486227332694882758846056768588823659978490918455874255479360072719223571560601960627669259933221901785

05974392627
Y0: -1235968266724011336173423
Y1:  25826703503071
c0: -6752457784721708041933315518400
c1:  65470140297054341898845356
c2:  1163854576425161625392
c3:  447583726895349
c4: -11493947732
c5:  7200
skew: 315435.66
type: gnfs
rlim: 6900000
alim: 6900000
lbpr: 27
lbpa: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5Factor base limits: 6900000/6900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3450000, 7050001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 997410 x 997635
Total sieving time: 90.31 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.34 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
gnfs,124,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6900000,6900000,27,27,52,52,2.5,2.5,100000
total time: 93.26 hours.
 --------- CPU info (if available) ----------

Sep 9, 2009 (2nd)

By Sinkiti Sibata / Msieve / Sep 9, 2009

(59·10¹⁵⁸-23)/9 = 6(5)₁₅₇3_<159> = 12487 · 2207698132336061_<16> · C140

C140 = P48 · P93

P48 = 138950783711105562238509825389437166829461858261_<48>

P93 = 171139673698799815993773112254601075308395029276065689096470124575931764320838076484006014039_<93>

Number: 65553_158
N=23779991784511114479490852640978328737126836338072236250440978127472921436941578643368685604269870370029495705310629134612847124288594126179
  ( 140 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=138950783711105562238509825389437166829461858261 (pp48)
 r2=171139673698799815993773112254601075308395029276065689096470124575931764320838076484006014039 (pp93)
Version: Msieve-1.40
Total time: 39.17 hours.
Scaled time: 71.37 units (timescale=1.822).
Factorization parameters were as follows:
name: 65553_158
n: 23779991784511114479490852640978328737126836338072236250440978127472921436941578643368685604269870370029495705310629134612847124288594126179
m: 50000000000000000000000000000000
deg: 5
c5: 472
c0: -575
skew: 1.04
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3400001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 705731 x 705958
Total sieving time: 37.90 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 1.13 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 39.17 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3109164k/3145344k available (2732k kernel code, 34856k reserved, 1420k data, 412k init, 2227840k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.99 BogoMIPS (lpj=2393997)
Calibrating delay using timer specific routine.. 4787.75 BogoMIPS (lpj=2393879)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393890)
Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393888)
Total of 4 processors activated (19151.30 BogoMIPS).

Sep 9, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Sep 9, 2009

(7·10¹⁷⁰-61)/9 = (7)₁₆₉1_<170> = 16033 · 27179 · 19782504017_<11> · 34433491170137_<14> · C138

C138 = P51 · P88

P51 = 102997828312150381163336333220697978781017456072607_<51>

P88 = 2543998649635394006349204860850381213757448610270145010190730784237897849483369671738151_<88>

Number: 77771_170
N=262026336141488722740887471511504618353946493011121522733691596871647376350077584500144346575937690543468618961950015644602813919747929657
  ( 138 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=102997828312150381163336333220697978781017456072607
 r2=2543998649635394006349204860850381213757448610270145010190730784237897849483369671738151
Version: 
Total time: 31.20 hours.
Scaled time: 74.57 units (timescale=2.390).
Factorization parameters were as follows:
n: 262026336141488722740887471511504618353946493011121522733691596871647376350077584500144346575937690543468618961950015644602813919747929657
m: 10000000000000000000000000000000000
deg: 5
c5: 7
c0: -61
skew: 1.54
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 5100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10872906
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 911180 x 911428
Total sieving time: 27.40 hours.
Total relation processing time: 1.24 hours.
Matrix solve time: 1.88 hours.
Time per square root: 0.68 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 31.20 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672387)
Calibrating delay using timer specific routine.. 5344.57 BogoMIPS (lpj=2672286)
Calibrating delay using timer specific routine.. 5237.81 BogoMIPS (lpj=2618908)

(16·10¹⁷⁰-61)/9 = 1(7)₁₆₉1_<171> = 3 · 199 · 18773 · 38669 · 36501139 · 21671373617_<11> · C141

C141 = P64 · P78

P64 = 2083352443623955517456574595370861273778187700398395438300935987_<64>

P78 = 248914913845551113972421378475204343559532544725717959578969110953994879400519_<78>

Number: 17771_170
N=518577494014575271846975043011137983452218308820037588072919544803916121046830631947861998124248547425682307209664821092279905057663153577253
  ( 141 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=2083352443623955517456574595370861273778187700398395438300935987
 r2=248914913845551113972421378475204343559532544725717959578969110953994879400519
Version: 
Total time: 25.77 hours.
Scaled time: 61.55 units (timescale=2.388).
Factorization parameters were as follows:
n: 518577494014575271846975043011137983452218308820037588072919544803916121046830631947861998124248547425682307209664821092279905057663153577253
m: 20000000000000000000000000000000000
deg: 5
c5: 1
c0: -122
skew: 2.61
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 4700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10618324
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 860509 x 860757
Total sieving time: 23.02 hours.
Total relation processing time: 1.02 hours.
Matrix solve time: 1.65 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 25.77 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672387)
Calibrating delay using timer specific routine.. 5344.57 BogoMIPS (lpj=2672286)
Calibrating delay using timer specific routine.. 5237.81 BogoMIPS (lpj=2618908)

Sep 8, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Sep 8, 2009

5·10¹⁷⁰-3 = 4(9)₁₆₉7_<171> = 7 · 5651 · 227097137 · 15754689472675987541294126496349_<32> · C127

C127 = P61 · P67

P61 = 1282193342543925932322422945370800329162612510700818603591681_<61>

P67 = 2755317386704286894836646040390450824249315418803775935856090488957_<67>

Number: 49997_170
N=3532849609827764557824712935521280431199925581138817459746251706817133265070845561065976460386265718854344947085699143667566717
  ( 127 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=1282193342543925932322422945370800329162612510700818603591681
 r2=2755317386704286894836646040390450824249315418803775935856090488957
Version: 
Total time: 27.21 hours.
Scaled time: 65.04 units (timescale=2.390).
Factorization parameters were as follows:
n: 3532849609827764557824712935521280431199925581138817459746251706817133265070845561065976460386265718854344947085699143667566717
m: 10000000000000000000000000000000000
deg: 5
c5: 5
c0: -3
skew: 0.90
type: snfs
lss: 1
rlim: 5200000
alim: 5200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2600000, 4700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10670849
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 881121 x 881369
Total sieving time: 24.19 hours.
Total relation processing time: 1.10 hours.
Matrix solve time: 1.75 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5200000,5200000,27,27,52,52,2.4,2.4,100000
total time: 27.21 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672387)
Calibrating delay using timer specific routine.. 5344.57 BogoMIPS (lpj=2672286)
Calibrating delay using timer specific routine.. 5237.81 BogoMIPS (lpj=2618908)

6·10¹⁷⁰+7 = 6(0)₁₆₉7_<171> = 7949 · 460073 · 2163987266008573_<16> · C146

C146 = P53 · P94

P53 = 54259207804217377507164325108667689661711419580711023_<53>

P94 = 1397281332661513419734474128891275205904136412680671506450765242423612261405435404496170098729_<94>

Number: 60007_170
N=75815378189834846567408712131031443528261571612454128600975701196926299880446137951213378979847518018044496146504128402875774881726424065928589767
  ( 146 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=54259207804217377507164325108667689661711419580711023
 r2=1397281332661513419734474128891275205904136412680671506450765242423612261405435404496170098729
Version: 
Total time: 35.86 hours.
Scaled time: 85.45 units (timescale=2.383).
Factorization parameters were as follows:
n: 75815378189834846567408712131031443528261571612454128600975701196926299880446137951213378979847518018044496146504128402875774881726424065928589767
m: 10000000000000000000000000000000000
deg: 5
c5: 6
c0: 7
skew: 1.03
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2700000, 5500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11028490
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 993787 x 994035
Total sieving time: 32.00 hours.
Total relation processing time: 1.50 hours.
Matrix solve time: 2.25 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000
total time: 35.86 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672387)
Calibrating delay using timer specific routine.. 5344.57 BogoMIPS (lpj=2672286)
Calibrating delay using timer specific routine.. 5237.81 BogoMIPS (lpj=2618908)

Sep 8, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Sep 8, 2009

(53·10¹⁷¹-71)/9 = 5(8)₁₇₀1_<172> = 1129399 · C166

C166 = P61 · P106

P61 = 1012782147434752932667684249508918320121901242771161953907631_<61>

P106 = 5148372050856343302191719932929532293542830496633217654226873938020652977210113515374231410045450654341849_<106>

Number: 58881_171
N=5214179301459350405736935209690188223018515944222448301166274176698304929337540487364420270328633980452336941053506235518969725392787570104886659974808627322043749719
  ( 166 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=1012782147434752932667684249508918320121901242771161953907631 (pp61)
 r2=5148372050856343302191719932929532293542830496633217654226873938020652977210113515374231410045450654341849 (pp106)
Version: Msieve-1.40
Total time: 103.07 hours.
Scaled time: 179.23 units (timescale=1.739).
Factorization parameters were as follows:
n: 5214179301459350405736935209690188223018515944222448301166274176698304929337540487364420270328633980452336941053506235518969725392787570104886659974808627322043749719
m: 10000000000000000000000000000000000
deg: 5
c5: 530
c0: -71
skew: 0.67
type: snfs
lss: 1
rlim: 5300000
alim: 5300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2650000, 7550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1151007 x 1151255
Total sieving time: 100.84 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.74 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,172.000,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.4,2.4,100000
total time: 103.07 hours.

Sep 8, 2009

By Wataru Sakai / GMP-ECM 6.2.1 / Sep 8, 2009

(32·10¹⁷²+31)/9 = 3(5)₁₇₁9_<173> = 3 · 181 · 301183 · 34599996752173866857_<20> · C145

C145 = P36 · P37 · P73

P36 = 380180911264424017571063306253381757_<36>

P37 = 8546276063952874782271324462814821241_<37>

P73 = 1933899502523280503850307241008143800862805194330635461115742340415465779_<73>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3539868959
Step 1 took 47496ms
Step 2 took 15500ms
********** Factor found in step 2: 380180911264424017571063306253381757
Found probable prime factor of 36 digits: 380180911264424017571063306253381757
Composite cofactor 16527639028505084337691953712714662144081862856051421639105985515388478037245990081581868705420160179637811739 has 110 digits
--------------
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=118001667
Step 1 took 30447ms
Step 2 took 13004ms
********** Factor found in step 2: 8546276063952874782271324462814821241
Found probable prime factor of 37 digits: 8546276063952874782271324462814821241
Probable prime cofactor 1933899502523280503850307241008143800862805194330635461115742340415465779 has 73 digits

Sep 7, 2009 (3rd)

By Sinkiti Sibata / Msieve / Sep 7, 2009

(59·10¹⁷⁷-41)/9 = 6(5)₁₇₆1_<178> = 47 · C177

C177 = P53 · P124

P53 = 39687847630220780350691478307685779181822692767363689_<53>

P124 = 3514423526740805777583860968498743829622846093892057431067432159680018844965167259451240360217848717877904331681750827177897_<124>

Number: 65551_177
N=139479905437352245862884160756501182033096926713947990543735224586288416075650118203309692671394799054373522458628841607565011820330969267139479905437352245862884160756501182033
  ( 177 digits)
SNFS difficulty: 179 digits.
Divisors found:
 r1=39687847630220780350691478307685779181822692767363689 (pp53)
 r2=3514423526740805777583860968498743829622846093892057431067432159680018844965167259451240360217848717877904331681750827177897 (pp124)
Version: Msieve-1.40
Total time: 141.35 hours.
Scaled time: 471.97 units (timescale=3.339).
Factorization parameters were as follows:
name: 65551_177
n: 139479905437352245862884160756501182033096926713947990543735224586288416075650118203309692671394799054373522458628841607565011820330969267139479905437352245862884160756501182033
m: 200000000000000000000000000000000000
deg: 5
c5: 1475
c0: -328
skew: 0.74
type: snfs
lss: 1
rlim: 6900000
alim: 6900000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6900000/6900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3450000, 9950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1535526 x 1535774
Total sieving time: 135.54 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 5.32 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
snfs,179.000,5,0,0,0,0,0,0,0,0,6900000,6900000,28,28,53,53,2.5,2.5,100000
total time: 141.35 hours.
 --------- CPU info (if available) ----------

(59·10¹⁵⁴-23)/9 = 6(5)₁₅₃3_<155> = 3² · 149 · 193 · C150

C150 = P36 · P52 · P63

P36 = 288769991604994884130111881413557783_<36>

P52 = 1875491618469598154603619066440565706645821058259017_<52>

P63 = 467688000648417307991081251498306258138477804436279588786510971_<63>

Number: 65553_154
N=253293132707999812820668032732341712184301235083073707872307633525192148599782683078344424567373182782764218008970011381018556083178030298151775820981
  ( 150 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=288769991604994884130111881413557783 (pp36)
 r2=1875491618469598154603619066440565706645821058259017 (pp52)
 r3=467688000648417307991081251498306258138477804436279588786510971 (pp63)
Version: Msieve-1.40
Total time: 29.11 hours.
Scaled time: 52.97 units (timescale=1.820).
Factorization parameters were as follows:
name: 65553_154
n: 253293132707999812820668032732341712184301235083073707872307633525192148599782683078344424567373182782764218008970011381018556083178030298151775820981
m: 10000000000000000000000000000000
deg: 5
c5: 59
c0: -230
skew: 1.31
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1450000, 2750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 514980 x 515210
Total sieving time: 28.24 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.59 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000
total time: 29.11 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3109164k/3145344k available (2732k kernel code, 34856k reserved, 1420k data, 412k init, 2227840k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.99 BogoMIPS (lpj=2393997)
Calibrating delay using timer specific routine.. 4787.75 BogoMIPS (lpj=2393879)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393890)
Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393888)
Total of 4 processors activated (19151.30 BogoMIPS).

Sep 7, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Sep 7, 2009

(59·10¹⁴¹-23)/9 = 6(5)₁₄₀3_<142> = 11166371 · C135

C135 = P68 · P68

P68 = 11269772850015485143716117717785059488909143582753326718169637309397_<68>

P68 = 52093349964758237235431796266725582935721900063340311411451502216319_<68>

Number: n
N=587080221099187511820586612746034997006239140321914394171173029765494586876573916051647894876102142366177476599654046561372137425449643
  ( 135 digits)
SNFS difficulty: 143 digits.
Divisors found:

Mon Sep 07 05:05:39 2009  prp68 factor: 11269772850015485143716117717785059488909143582753326718169637309397
Mon Sep 07 05:05:39 2009  prp68 factor: 52093349964758237235431796266725582935721900063340311411451502216319
Mon Sep 07 05:05:39 2009  elapsed time 00:28:28 (Msieve 1.42 - dependency 4)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.76 hours.
Scaled time: 14.18 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_6_5_140_3
n: 587080221099187511820586612746034997006239140321914394171173029765494586876573916051647894876102142366177476599654046561372137425449643
m: 20000000000000000000000000000
deg: 5
c5: 295
c0: -368
skew: 1.05
type: snfs
lss: 1
rlim: 1760000
alim: 1760000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 10000
Factor base limits: 1760000/1760000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [880000, 1861261)
Primes: RFBsize:132292, AFBsize:132276, largePrimes:9375668 encountered
Relations: rels:8453983, finalFF:287077
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1043937 hash collisions in 9489724 relations
Msieve: matrix is 326807 x 327033 (87.3 MB)

Total sieving time: 7.45 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1760000,1760000,28,28,56,56,2.4,2.4,100000
total time: 7.76 hours.
 --------- CPU info (if available) ----------

Sep 7, 2009

By Dmitry Domanov / msieve 1.42 / Sep 7, 2009

(59·10¹⁶¹-23)/9 = 6(5)₁₆₀3_<162> = 19 · 39209 · 180021081371137571_<18> · 340082579942596827767_<21> · 6000615750606979819104103_<25> · C94

C94 = P38 · P56

P38 = 50470778712824982105703199363588480917_<38>

P56 = 47459871643003397735547411318564745587048731951584716349_<56>

Sun Sep 06 18:55:07 2009  Msieve v. 1.42
Sun Sep 06 18:55:07 2009  random seeds: c648a480 f38ba1b4
Sun Sep 06 18:55:07 2009  factoring 2395336679433101895019383795965100530165054971110873423475461569832676195124708259167244412033 (94 digits)
Sun Sep 06 18:55:08 2009  searching for 15-digit factors
Sun Sep 06 18:55:08 2009  commencing quadratic sieve (94-digit input)
Sun Sep 06 18:55:08 2009  using multiplier of 7
Sun Sep 06 18:55:08 2009  using 32kb Intel Core sieve core
Sun Sep 06 18:55:08 2009  sieve interval: 36 blocks of size 32768
Sun Sep 06 18:55:08 2009  processing polynomials in batches of 6
Sun Sep 06 18:55:08 2009  using a sieve bound of 2025307 (75271 primes)
Sun Sep 06 18:55:08 2009  using large prime bound of 271391138 (28 bits)
Sun Sep 06 18:55:08 2009  using double large prime bound of 1515207662043732 (42-51 bits)
Sun Sep 06 18:55:08 2009  using trial factoring cutoff of 51 bits
Sun Sep 06 18:55:08 2009  polynomial 'A' values have 12 factors
Sun Sep 06 20:53:33 2009  75497 relations (19243 full + 56254 combined from 1061192 partial), need 75367
Sun Sep 06 20:53:34 2009  begin with 1080435 relations
Sun Sep 06 20:53:34 2009  reduce to 193426 relations in 10 passes
Sun Sep 06 20:53:34 2009  attempting to read 193426 relations
Sun Sep 06 20:53:36 2009  recovered 193426 relations
Sun Sep 06 20:53:36 2009  recovered 174118 polynomials
Sun Sep 06 20:53:36 2009  attempting to build 75497 cycles
Sun Sep 06 20:53:36 2009  found 75497 cycles in 6 passes
Sun Sep 06 20:53:36 2009  distribution of cycle lengths:
Sun Sep 06 20:53:36 2009     length 1 : 19243
Sun Sep 06 20:53:36 2009     length 2 : 13536
Sun Sep 06 20:53:36 2009     length 3 : 12791
Sun Sep 06 20:53:36 2009     length 4 : 10134
Sun Sep 06 20:53:36 2009     length 5 : 7578
Sun Sep 06 20:53:36 2009     length 6 : 4890
Sun Sep 06 20:53:36 2009     length 7 : 3169
Sun Sep 06 20:53:36 2009     length 9+: 4156
Sun Sep 06 20:53:36 2009  largest cycle: 21 relations
Sun Sep 06 20:53:37 2009  matrix is 75271 x 75497 (19.8 MB) with weight 4877005 (64.60/col)
Sun Sep 06 20:53:37 2009  sparse part has weight 4877005 (64.60/col)
Sun Sep 06 20:53:37 2009  filtering completed in 3 passes
Sun Sep 06 20:53:37 2009  matrix is 71038 x 71101 (18.7 MB) with weight 4622979 (65.02/col)
Sun Sep 06 20:53:37 2009  sparse part has weight 4622979 (65.02/col)
Sun Sep 06 20:53:37 2009  saving the first 48 matrix rows for later
Sun Sep 06 20:53:37 2009  matrix is 70990 x 71101 (11.8 MB) with weight 3654990 (51.41/col)
Sun Sep 06 20:53:37 2009  sparse part has weight 2663763 (37.46/col)
Sun Sep 06 20:53:37 2009  matrix includes 64 packed rows
Sun Sep 06 20:53:37 2009  using block size 28440 for processor cache size 6144 kB
Sun Sep 06 20:53:38 2009  commencing Lanczos iteration
Sun Sep 06 20:53:38 2009  memory use: 11.8 MB
Sun Sep 06 20:54:03 2009  lanczos halted after 1124 iterations (dim = 70985)
Sun Sep 06 20:54:03 2009  recovered 16 nontrivial dependencies
Sun Sep 06 20:54:03 2009  prp38 factor: 50470778712824982105703199363588480917
Sun Sep 06 20:54:03 2009  prp56 factor: 47459871643003397735547411318564745587048731951584716349
Sun Sep 06 20:54:03 2009  elapsed time 01:58:56

Sep 6, 2009 (6th)

By Dmitry Domanov / GGNFS/msieve 1.42 / Sep 6, 2009

(59·10¹³⁵-23)/9 = 6(5)₁₃₄3_<136> = 17² · C134

C134 = P64 · P70

P64 = 4033384965435623345569638585775206175700568128455161178295943361_<64>

P70 = 5623956907561519679072678462943544587725062461900245913207560067776257_<70>

Number: snfs134
N=22683583237216455209534794309880815071126489811610918877354863514033064206074586697424067666282199154171472510572856593617839292579777
  ( 134 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=4033384965435623345569638585775206175700568128455161178295943361 (pp64)
 r2=5623956907561519679072678462943544587725062461900245913207560067776257 (pp70)
Version: Msieve-1.40
Total time: 3.25 hours.
Scaled time: 5.95 units (timescale=1.834).
Factorization parameters were as follows:
n: 22683583237216455209534794309880815071126489811610918877354863514033064206074586697424067666282199154171472510572856593617839292579777
m: 1000000000000000000000000000
deg: 5
c5: 59
c0: -23
skew: 0.83
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1265001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 192581 x 192805
Total sieving time: 3.09 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 3.25 hours.
 --------- CPU info (if available) ----------

(59·10¹⁶⁷-23)/9 = 6(5)₁₆₆3_<168> = 17 · 234187 · 7987796963_<10> · 10020240696915019_<17> · 46087452381739399_<17> · 2023426230947608269258352112759_<31> · C89

C89 = P44 · P45

P44 = 56774832039193096194261868776283784454786901_<44>

P45 = 388567694701708852377210234670993803512837191_<45>

Sun Sep 06 18:03:13 2009  
Sun Sep 06 18:03:13 2009  
Sun Sep 06 18:03:13 2009  Msieve v. 1.42
Sun Sep 06 18:03:13 2009  random seeds: b2e0af38 b093f247
Sun Sep 06 18:03:13 2009  factoring 22060865602545981243055564636242542421973027626548743656887041186534561695216883812435091 (89 digits)
Sun Sep 06 18:03:13 2009  searching for 15-digit factors
Sun Sep 06 18:03:14 2009  commencing quadratic sieve (89-digit input)
Sun Sep 06 18:03:14 2009  using multiplier of 1
Sun Sep 06 18:03:14 2009  using 32kb Intel Core sieve core
Sun Sep 06 18:03:14 2009  sieve interval: 30 blocks of size 32768
Sun Sep 06 18:03:14 2009  processing polynomials in batches of 7
Sun Sep 06 18:03:14 2009  using a sieve bound of 1545259 (58667 primes)
Sun Sep 06 18:03:14 2009  using large prime bound of 123620720 (26 bits)
Sun Sep 06 18:03:14 2009  using double large prime bound of 367929134797280 (42-49 bits)
Sun Sep 06 18:03:14 2009  using trial factoring cutoff of 49 bits
Sun Sep 06 18:03:14 2009  polynomial 'A' values have 11 factors
Sun Sep 06 18:53:21 2009  58771 relations (15246 full + 43525 combined from 629283 partial), need 58763
Sun Sep 06 18:53:21 2009  begin with 644529 relations
Sun Sep 06 18:53:22 2009  reduce to 144345 relations in 10 passes
Sun Sep 06 18:53:22 2009  attempting to read 144345 relations
Sun Sep 06 18:53:23 2009  recovered 144345 relations
Sun Sep 06 18:53:23 2009  recovered 125300 polynomials
Sun Sep 06 18:53:23 2009  attempting to build 58771 cycles
Sun Sep 06 18:53:23 2009  found 58771 cycles in 5 passes
Sun Sep 06 18:53:23 2009  distribution of cycle lengths:
Sun Sep 06 18:53:23 2009     length 1 : 15246
Sun Sep 06 18:53:23 2009     length 2 : 11254
Sun Sep 06 18:53:23 2009     length 3 : 10180
Sun Sep 06 18:53:23 2009     length 4 : 7937
Sun Sep 06 18:53:23 2009     length 5 : 5742
Sun Sep 06 18:53:23 2009     length 6 : 3762
Sun Sep 06 18:53:23 2009     length 7 : 2086
Sun Sep 06 18:53:23 2009     length 9+: 2564
Sun Sep 06 18:53:23 2009  largest cycle: 19 relations
Sun Sep 06 18:53:23 2009  matrix is 58667 x 58771 (14.5 MB) with weight 3563385 (60.63/col)
Sun Sep 06 18:53:23 2009  sparse part has weight 3563385 (60.63/col)
Sun Sep 06 18:53:24 2009  filtering completed in 3 passes
Sun Sep 06 18:53:24 2009  matrix is 55220 x 55284 (13.8 MB) with weight 3387006 (61.27/col)
Sun Sep 06 18:53:24 2009  sparse part has weight 3387006 (61.27/col)
Sun Sep 06 18:53:24 2009  saving the first 48 matrix rows for later
Sun Sep 06 18:53:24 2009  matrix is 55172 x 55284 (9.9 MB) with weight 2793695 (50.53/col)
Sun Sep 06 18:53:24 2009  sparse part has weight 2261581 (40.91/col)
Sun Sep 06 18:53:24 2009  matrix includes 64 packed rows
Sun Sep 06 18:53:24 2009  using block size 22113 for processor cache size 6144 kB
Sun Sep 06 18:53:24 2009  commencing Lanczos iteration
Sun Sep 06 18:53:24 2009  memory use: 9.4 MB
Sun Sep 06 18:53:39 2009  lanczos halted after 873 iterations (dim = 55172)
Sun Sep 06 18:53:39 2009  recovered 18 nontrivial dependencies
Sun Sep 06 18:53:40 2009  prp44 factor: 56774832039193096194261868776283784454786901
Sun Sep 06 18:53:40 2009  prp45 factor: 388567694701708852377210234670993803512837191
Sun Sep 06 18:53:40 2009  elapsed time 00:50:27

Sep 6, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Sep 6, 2009

(43·10¹⁶⁹+11)/9 = 4(7)₁₆₈9_<170> = 7³ · 2909 · 18427 · 135902677 · 3463763110428983_<16> · C136

C136 = P56 · P80

P56 = 81252320210182399363922268950875546607594968965365595353_<56>

P80 = 67939368147411435522154683506427206182683553203992873652333118479925931746389377_<80>

Number: 47779_169
N=5520231295590940539197249599138046209630756826318725972965406383812669404715544425978782964608321656158441984145263113551359935759765081
  ( 136 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=81252320210182399363922268950875546607594968965365595353
 r2=67939368147411435522154683506427206182683553203992873652333118479925931746389377
Version: 
Total time: 39.07 hours.
Scaled time: 92.44 units (timescale=2.366).
Factorization parameters were as follows:
n: 5520231295590940539197249599138046209630756826318725972965406383812669404715544425978782964608321656158441984145263113551359935759765081
m: 10000000000000000000000000000000000
deg: 5
c5: 43
c0: 110
skew: 1.21
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3100000, 6000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11015701
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1045458 x 1045706
Total sieving time: 35.38 hours.
Total relation processing time: 1.00 hours.
Matrix solve time: 2.56 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,27,27,52,52,2.4,2.4,100000
total time: 39.07 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

(59·10¹⁵¹-23)/9 = 6(5)₁₅₀3_<152> = 3 · 7 · 17 · 6818551739_<10> · 3398061299561541566987807_<25> · C115

C115 = P38 · P78

P38 = 13740345644921944219850244595159735469_<38>

P78 = 576793395614788307245751528168087790216527747222217724082610560048684629879117_<78>

Number: 65553_151
N=7925340621455396556581145145490049625685767373956068033649201654737271721423010028135320022942647034809447167300873
  ( 115 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=13740345644921944219850244595159735469
 r2=576793395614788307245751528168087790216527747222217724082610560048684629879117
Version: 
Total time: 10.65 hours.
Scaled time: 25.38 units (timescale=2.384).
Factorization parameters were as follows:
n: 7925340621455396556581145145490049625685767373956068033649201654737271721423010028135320022942647034809447167300873
m: 1000000000000000000000000000000
deg: 5
c5: 590
c0: -23
skew: 0.52
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1100000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8204986
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 419280 x 419528
Total sieving time: 9.78 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000
total time: 10.65 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

(59·10¹⁵⁶-23)/9 = 6(5)₁₅₅3_<157> = 3181 · 438937215039323846231549903527101748549_<39> · C115

C115 = P34 · P82

P34 = 3545667648843745074148059792301669_<34>

P82 = 1324175061514614755674758049165946651544932139925601108255858176964575458176417773_<82>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 4695084677018045603842074288842484708119800217816928379866927797835782641849930394785264137027431830668104989163137 (115 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3686906529
Step 1 took 3448ms
********** Factor found in step 1: 3545667648843745074148059792301669
Found probable prime factor of 34 digits: 3545667648843745074148059792301669
Probable prime cofactor 1324175061514614755674758049165946651544932139925601108255858176964575458176417773 has 82 digits

(59·10¹⁷²-23)/9 = 6(5)₁₇₁3_<173> = 3³ · 2243 · 1558388347_<10> · 9692197913461901_<16> · 27647054178045035024590372529_<29> · C115

C115 = P38 · P78

P38 = 14936440304226310362691079505554837839_<38>

P78 = 173549164616500844104280220544007979602810463123114581040836784586235411904689_<78>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 2592206737142709885718286033118701376329525131139133587872249673847964893917667097442560727671516946385417518727071 (115 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4356979258
Step 1 took 3432ms
********** Factor found in step 1: 14936440304226310362691079505554837839
Found probable prime factor of 38 digits: 14936440304226310362691079505554837839
Probable prime cofactor 173549164616500844104280220544007979602810463123114581040836784586235411904689 has 78 digits

(59·10¹⁶⁰-23)/9 = 6(5)₁₅₉3_<161> = 3 · 647 · 653209 · C152

C152 = P50 · P50 · P52

P50 = 77920359733043141718152669423045508379211105199251_<50>

P50 = 98172545308143954510401342127697808960301693255503_<50>

P52 = 6759130118453366726339492334933329085640787085108329_<52>

Number: 65553_160
N=51704912432402122505900093785358538558673042519303994659725248170064099055802914178971454527685216191262821502327487738146934275424390435545339674419237
  ( 152 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=77920359733043141718152669423045508379211105199251
 r2=98172545308143954510401342127697808960301693255503
 r3=6759130118453366726339492334933329085640787085108329
Version: 
Total time: 17.56 hours.
Scaled time: 41.96 units (timescale=2.389).
Factorization parameters were as follows:
n: 51704912432402122505900093785358538558673042519303994659725248170064099055802914178971454527685216191262821502327487738146934275424390435545339674419237
m: 100000000000000000000000000000000
deg: 5
c5: 59
c0: -23
skew: 0.83
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9702530
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 599904 x 600152
Total sieving time: 15.85 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 0.77 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 17.56 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

(59·10¹⁶⁸-23)/9 = 6(5)₁₆₇3_<169> = 3037 · 70949 · 3479122711429_<13> · 626993149292111216903692304785352393_<36> · C113

C113 = P51 · P63

P51 = 110048503437674618577003803131929796931304105206341_<51>

P63 = 126736511344598905102072768628781352839776284565818193000471953_<63>

Number: 65553_168
N=13947163404384980904449611579937234571143384609283321436478575782877294124024028675585055821628876528177448253973
  ( 113 digits)
Divisors found:
 r1=110048503437674618577003803131929796931304105206341
 r2=126736511344598905102072768628781352839776284565818193000471953
Version: 
Total time: 12.39 hours.
Scaled time: 29.60 units (timescale=2.389).
Factorization parameters were as follows:
name: 65553_168
n: 13947163404384980904449611579937234571143384609283321436478575782877294124024028675585055821628876528177448253973
skew: 30341.71
# norm 2.74e+15
c5: 11520
c4: 3547307216
c3: 31970109244044
c2: -1494195806439033348
c1: -18910051566890323672779
c0: 197314988295368160487900042
# alpha -5.67
Y1: 1335513367129
Y0: -4136166820263797078415
# Murphy_E 7.24e-10
# M 10761249407017046921767924501253986810419556514280555902620125284141451123916896917737311249044919496952507380243
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1200000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8481116
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 411853 x 412101
Polynomial selection time: 1.01 hours.
Total sieving time: 10.25 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000
total time: 12.39 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

(59·10¹⁶⁴-23)/9 = 6(5)₁₆₃3_<165> = 29 · 773 · 58035983 · 29850219915001_<14> · 75817706828629901061159433_<26> · C114

C114 = P47 · P67

P47 = 27815983394117839176196626068399018951259031327_<47>

P67 = 8004276222190184739443821823422506202968291528399513054947594684353_<67>

Number: 65553_164
N=222646814478374450338234698285148075726867288214094116966184385653080985735321919403590210157704609540249103726431
  ( 114 digits)
Divisors found:
 r1=27815983394117839176196626068399018951259031327
 r2=8004276222190184739443821823422506202968291528399513054947594684353
Version: 
Total time: 14.58 hours.
Scaled time: 34.66 units (timescale=2.377).
Factorization parameters were as follows:
name: 65553_164
n: 222646814478374450338234698285148075726867288214094116966184385653080985735321919403590210157704609540249103726431
skew: 14589.88
# norm 4.00e+15
c5: 39480
c4: 8823160412
c3: -211860480826100
c2: -1714619343608612451
c1: 3854389669948840000634
c0: 19650474694996136084335000
# alpha -5.63
Y1: 2045091898741
Y0: -5626532258234618459367
# Murphy_E 6.59e-10
# M 67252567476305861782973305505120502252366792284866018311366103807602776466695151389546156372623498063127017024007
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1400000, 2450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9485177
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 463525 x 463773
Polynomial selection time: 1.15 hours.
Total sieving time: 12.23 hours.
Total relation processing time: 0.70 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000
total time: 14.58 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

Sep 6, 2009 (4th)

By Sinkiti Sibata / Msieve / Sep 6, 2009

(59·10¹³⁴-23)/9 = 6(5)₁₃₃3_<135> = 22453618057915517777_<20> · 32779549948892930549_<20> · C96

C96 = P39 · P58

P39 = 109549546925366048058099112355570359543_<39>

P58 = 8130356687467199190018185491945775555626225108447828911227_<58>

Sat Sep 05 21:27:27 2009  Msieve v. 1.42
Sat Sep 05 21:27:27 2009  random seeds: 5b72e100 56d12c6c
Sat Sep 05 21:27:27 2009  factoring 890676891453651598342319703158395378192271201476401819686147034391191837296864223046734619289261 (96 digits)
Sat Sep 05 21:27:28 2009  searching for 15-digit factors
Sat Sep 05 21:27:28 2009  commencing quadratic sieve (96-digit input)
Sat Sep 05 21:27:29 2009  using multiplier of 5
Sat Sep 05 21:27:29 2009  using 32kb Intel Core sieve core
Sat Sep 05 21:27:29 2009  sieve interval: 36 blocks of size 32768
Sat Sep 05 21:27:29 2009  processing polynomials in batches of 6
Sat Sep 05 21:27:29 2009  using a sieve bound of 2297153 (84706 primes)
Sat Sep 05 21:27:29 2009  using large prime bound of 344572950 (28 bits)
Sat Sep 05 21:27:29 2009  using double large prime bound of 2328660176259750 (43-52 bits)
Sat Sep 05 21:27:29 2009  using trial factoring cutoff of 52 bits
Sat Sep 05 21:27:29 2009  polynomial 'A' values have 12 factors
Sun Sep 06 03:34:37 2009  84927 relations (19358 full + 65569 combined from 1298983 partial), need 84802
Sun Sep 06 03:34:38 2009  begin with 1318341 relations
Sun Sep 06 03:34:40 2009  reduce to 227125 relations in 11 passes
Sun Sep 06 03:34:40 2009  attempting to read 227125 relations
Sun Sep 06 03:34:44 2009  recovered 227125 relations
Sun Sep 06 03:34:44 2009  recovered 215678 polynomials
Sun Sep 06 03:34:44 2009  attempting to build 84927 cycles
Sun Sep 06 03:34:44 2009  found 84927 cycles in 6 passes
Sun Sep 06 03:34:44 2009  distribution of cycle lengths:
Sun Sep 06 03:34:44 2009     length 1 : 19358
Sun Sep 06 03:34:44 2009     length 2 : 14177
Sun Sep 06 03:34:44 2009     length 3 : 14202
Sun Sep 06 03:34:44 2009     length 4 : 11758
Sun Sep 06 03:34:44 2009     length 5 : 8957
Sun Sep 06 03:34:44 2009     length 6 : 6366
Sun Sep 06 03:34:44 2009     length 7 : 4119
Sun Sep 06 03:34:44 2009     length 9+: 5990
Sun Sep 06 03:34:44 2009  largest cycle: 21 relations
Sun Sep 06 03:34:44 2009  matrix is 84706 x 84927 (24.2 MB) with weight 5994457 (70.58/col)
Sun Sep 06 03:34:44 2009  sparse part has weight 5994457 (70.58/col)
Sun Sep 06 03:34:46 2009  filtering completed in 3 passes
Sun Sep 06 03:34:46 2009  matrix is 81590 x 81654 (23.3 MB) with weight 5787567 (70.88/col)
Sun Sep 06 03:34:46 2009  sparse part has weight 5787567 (70.88/col)
Sun Sep 06 03:34:46 2009  saving the first 48 matrix rows for later
Sun Sep 06 03:34:46 2009  matrix is 81542 x 81654 (17.3 MB) with weight 4878019 (59.74/col)
Sun Sep 06 03:34:46 2009  sparse part has weight 4046406 (49.56/col)
Sun Sep 06 03:34:46 2009  matrix includes 64 packed rows
Sun Sep 06 03:34:46 2009  using block size 32661 for processor cache size 1024 kB
Sun Sep 06 03:34:47 2009  commencing Lanczos iteration
Sun Sep 06 03:34:47 2009  memory use: 15.8 MB
Sun Sep 06 03:35:41 2009  lanczos halted after 1291 iterations (dim = 81541)
Sun Sep 06 03:35:41 2009  recovered 17 nontrivial dependencies
Sun Sep 06 03:35:42 2009  prp39 factor: 109549546925366048058099112355570359543
Sun Sep 06 03:35:42 2009  prp58 factor: 8130356687467199190018185491945775555626225108447828911227
Sun Sep 06 03:35:42 2009  elapsed time 06:08:15

(59·10¹⁴⁴-23)/9 = 6(5)₁₄₃3_<145> = 163 · 3697 · 6737 · 35257 · 415536401498401_<15> · C117

C117 = P56 · P61

P56 = 22668087948353567565904107786791717805911245941992313013_<56>

P61 = 4862242115508238125345457419625722788001039034862505270628919_<61>

Number: 65553_144
N=110217731900529447653474164119681216660909871112734753012110542294173220474143695570691679432969528601793942017822947
  ( 117 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=22668087948353567565904107786791717805911245941992313013 (pp56)
 r2=4862242115508238125345457419625722788001039034862505270628919 (pp61)
Version: Msieve-1.40
Total time: 12.40 hours.
Scaled time: 22.59 units (timescale=1.822).
Factorization parameters were as follows:
name: 65553_144
n: 110217731900529447653474164119681216660909871112734753012110542294173220474143695570691679432969528601793942017822947
m: 100000000000000000000000000000
deg: 5
c5: 59
c0: -230
skew: 1.31
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2580001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 352117 x 352343
Total sieving time: 12.03 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 12.40 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3109164k/3145344k available (2732k kernel code, 34856k reserved, 1420k data, 412k init, 2227840k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.99 BogoMIPS (lpj=2393997)
Calibrating delay using timer specific routine.. 4787.75 BogoMIPS (lpj=2393879)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393890)
Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393888)
Total of 4 processors activated (19151.30 BogoMIPS).

Sep 6, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve / Sep 6, 2009

(59·10¹⁸⁵-23)/9 = 6(5)₁₈₄3_<186> = 1048633 · 2362619143_<10> · 1036894629011489_<16> · 4697396739519487642802809_<25> · C131

C131 = P39 · P39 · P54

P39 = 537864844057359624847291754331147978083_<39>

P39 = 776657403616698039772996030898887190021_<39>

P54 = 130046225239590461392743611635298754997217503927033609_<54>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1118099787
Step 1 took 38152ms
Step 2 took 13868ms
********** Factor found in step 2: 537864844057359624847291754331147978083
Found probable prime factor of 39 digits: 537864844057359624847291754331147978083
Composite cofactor 101001363644732632713992975105108019771451144136143646007278262873787714212299043412036415789 has 93 digits
--------------------
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2072657346
Step 1 took 23630ms
Step 2 took 10801ms
********** Factor found in step 2: 776657403616698039772996030898887190021
Found probable prime factor of 39 digits: 776657403616698039772996030898887190021
Probable prime cofactor 130046225239590461392743611635298754997217503927033609 has 54 digits

(29·10¹⁹¹+43)/9 = 3(2)₁₉₀7_<192> = 3 · 17 · 83 · C188

C188 = P38 · C150

P38 = 89772704053724486006486540198851407887_<38>

C150 = [847935685840806277833661045834924473041673739231006872680426030083019421217724220292086043060147725435599367453149401122050672500972766551928528604437_<150>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3208370085
Step 1 took 70078ms
Step 2 took 21614ms
********** Factor found in step 2: 89772704053724486006486540198851407887
Found probable prime factor of 38 digits: 89772704053724486006486540198851407887
Composite cofactor 847935685840806277833661045834924473041673739231006872680426030083019421217724220292086043060147725435599367453149401122050672500972766551928528604437 has 150 digits

(23·10¹⁹⁹-41)/9 = 2(5)₁₉₈1_<200> = 3 · 7 · 431 · C196

C196 = P39 · P40 · P58 · P60

P39 = 822166237785966937833596339772273380167_<39>

P40 = 8016571463986106513104624218307848381307_<40>

P58 = 2765643382267819668781591954418791280834022267016280940169_<58>

P60 = 154897452662266545680968239519414846256501968007596611529641_<60>

Number: 25551_199
N=2823506303784726058507961060165236499343227881510944155955756883831129770804944818865932555027682637891454596791023705176837427417473821186118169876870572926257381013761524202359469180814888471501
  ( 196 digits)
SNFS difficulty: 201 digits.
Divisors found:
 r1=822166237785966937833596339772273380167
 r2=8016571463986106513104624218307848381307
 r3=2765643382267819668781591954418791280834022267016280940169
 r4=154897452662266545680968239519414846256501968007596611529641
Version: 
Total time: 904.98 hours.
Scaled time: 1816.29 units (timescale=2.007).
Factorization parameters were as follows:
n: 2823506303784726058507961060165236499343227881510944155955756883831129770804944818865932555027682637891454596791023705176837427417473821186118169876870572926257381013761524202359469180814888471501
m: 10000000000000000000000000000000000000000
deg: 5
c5: 23
c0: -410
skew: 1.78
type: snfs
lss: 1
rlim: 15900000
alim: 15900000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 15900000/15900000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7950000, 17150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3310669 x 3310916
Total sieving time: 904.98 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,201,5,0,0,0,0,0,0,0,0,15900000,15900000,29,29,56,56,2.6,2.6,100000
total time: 904.98 hours.
 --------- CPU info (if available) ----------

Sep 6, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Sep 6, 2009

(53·10¹⁶⁹-71)/9 = 5(8)₁₆₈1_<170> = 3² · 55619 · 268408781245025917238865818507107_<33> · C132

C132 = P62 · P71

P62 = 23558974883254664303215516645325268137706557468101857830919331_<62>

P71 = 18604352743858630351683027420410354047658125089089380509126300180803083_<71>

Number: 58881_169
N=438299479011775469486372343095698175154784520161586980563186912608598242291187115880197057529976739290204068936254644363207769097473
  ( 132 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=23558974883254664303215516645325268137706557468101857830919331 (pp62)
 r2=18604352743858630351683027420410354047658125089089380509126300180803083 (pp71)
Version: Msieve-1.40
Total time: 143.39 hours.
Scaled time: 139.52 units (timescale=0.973).
Factorization parameters were as follows:
n: 438299479011775469486372343095698175154784520161586980563186912608598242291187115880197057529976739290204068936254644363207769097473
m: 10000000000000000000000000000000000
deg: 5
c5: 53
c0: -710
skew: 1.68
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 1000
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 6750000)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1058580 x 1058805
Total sieving time: 139.51 hours.
Total relation processing time: 0.66 hours.
Matrix solve time: 2.90 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 143.39 hours.
 --------- CPU info (if available) ----------

Sep 6, 2009

By Dmitry Domanov / GGNFS/msieve 1.42

(59·10¹¹⁷-23)/9 = 6(5)₁₁₆3_<118> = 433 · C116

C116 = P32 · P84

P32 = 97184768442645505553580695132117_<32>

P84 = 155784197566923435384179951190141128237442649031951845773179362399075390459437211373_<84>

N=15139851167564793430844239158326918142160636386964331537079804978188350012830382345393892738003592507056710289966641
  ( 116 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=97184768442645505553580695132117 (pp32)
 r2=155784197566923435384179951190141128237442649031951845773179362399075390459437211373 (pp84)
Version: Msieve-1.40
Total time: 1.50 hours.
Scaled time: 2.75 units (timescale=1.839).
Factorization parameters were as follows:
n: 15139851167564793430844239158326918142160636386964331537079804978188350012830382345393892738003592507056710289966641
m: 200000000000000000000000
deg: 5
c5: 1475
c0: -184
skew: 0.66
type: snfs
lss: 1
rlim: 690000
alim: 690000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 690000/690000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [345000, 695001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 81222 x 81447
Total sieving time: 1.44 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,119.000,5,0,0,0,0,0,0,0,0,690000,690000,25,25,45,45,2.2,2.2,50000
total time: 1.50 hours.
 --------- CPU info (if available) ----------

Sep 5, 2009 (5th)

By Dmitry Domanov / ECMNET / Sep 5, 2009

(59·10¹⁵⁶-23)/9 = 6(5)₁₅₅3_<157> = 3181 · C154

C154 = P39 · C115

P39 = 438937215039323846231549903527101748549_<39>

C115 = [4695084677018045603842074288842484708119800217816928379866927797835782641849930394785264137027431830668104989163137_<115>]

C154=P39*C115
C154=438937215039323846231549903527101748549<39>*4695084677018045603842074288842484708119800217816928379866927797835782641849930394785264137027431830668104989163137<115>

(59·10¹⁹⁵-23)/9 = 6(5)₁₉₄3_<196> = 466619 · C191

C191 = P38 · P153

P38 = 15020558240790961519556181394535596901_<38>

P153 = 935321699295305091769020291865845968537538790564424714932276783460783187423104867410069646498110493649355467142860211527355440858568679417266056052216087_<153>

C191=P38*P153
C191=15020558240790961519556181394535596901<38>*935321699295305091769020291865845968537538790564424714932276783460783187423104867410069646498110493649355467142860211527355440858568679417266056052216087<153>

Sep 5, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Sep 5, 2009

(31·10¹⁶⁹+23)/9 = 3(4)₁₆₈7_<170> = 37 · 1049 · 184039 · 4093623094878874617067367543_<28> · C133

C133 = P56 · P77

P56 = 71089222420470519987060723122743432410918632642974202029_<56>

P77 = 16569922963272521761078068102437369922025373749414100129260936324165493837143_<77>

Number: 34447_169
N=1177942939026142270485845048200505220851691100165908162124674755917755546818795317147407818367893046192630450490921217649737706163147
  ( 133 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=71089222420470519987060723122743432410918632642974202029
 r2=16569922963272521761078068102437369922025373749414100129260936324165493837143
Version: 
Total time: 48.87 hours.
Scaled time: 114.70 units (timescale=2.347).
Factorization parameters were as follows:
n: 1177942939026142270485845048200505220851691100165908162124674755917755546818795317147407818367893046192630450490921217649737706163147
m: 10000000000000000000000000000000000
deg: 5
c5: 31
c0: 230
skew: 1.49
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3100000, 6800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11393121
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1104162 x 1104410
Total sieving time: 44.18 hours.
Total relation processing time: 1.68 hours.
Matrix solve time: 2.88 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,27,27,52,52,2.4,2.4,100000
total time: 48.87 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673785)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

(59·10¹²⁶-23)/9 = 6(5)₁₂₅3_<127> = 75503 · C122

C122 = P60 · P63

P60 = 564188894543914208956794527643148388913774124253997606584441_<60>

P63 = 153893671499699811407798392541980060364509504361334033629409511_<63>

Number: 65553_126
N=86825100400719912527390375952684735117221243600327875124903057567984789419699290830239269374138187297929294936036390018351
  ( 122 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=564188894543914208956794527643148388913774124253997606584441
 r2=153893671499699811407798392541980060364509504361334033629409511
Version: 
Total time: 1.57 hours.
Scaled time: 3.74 units (timescale=2.384).
Factorization parameters were as follows:
n: 86825100400719912527390375952684735117221243600327875124903057567984789419699290830239269374138187297929294936036390018351
m: 10000000000000000000000000
deg: 5
c5: 590
c0: -23
skew: 0.52
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [450000, 900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2850657
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 135750 x 135997
Total sieving time: 1.38 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,900000,900000,26,26,47,47,2.3,2.3,50000
total time: 1.57 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

(59·10¹³⁸-23)/9 = 6(5)₁₃₇3_<139> = 255913187 · 370691351 · 2710218850040774104583_<22> · C101

C101 = P36 · P65

P36 = 314501601214746905872981699611119539_<36>

P65 = 81073171272865284477958404680830239933166102622820941120013499337_<65>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 25497642180873552505796492657762440287368611158736844024891567239903511874853673955958426951604245643 (101 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5471242219
Step 1 took 3495ms
Step 2 took 3650ms
********** Factor found in step 2: 314501601214746905872981699611119539
Found probable prime factor of 36 digits: 314501601214746905872981699611119539
Probable prime cofactor 81073171272865284477958404680830239933166102622820941120013499337 has 65 digits

(59·10¹³¹-23)/9 = 6(5)₁₃₀3_<132> = 505717870849_<12> · 31193260277616139170827_<23> · C98

C98 = P46 · P53

P46 = 2213940512772066993915618104377958245498637731_<46>

P53 = 18770441375137419556441967816076411508423217279309281_<53>

Number: 65553_131
N=41556640603029760970119631553974196119945973651913576045110048478128044376147075110846618125081411
  ( 98 digits)
Divisors found:
 r1=2213940512772066993915618104377958245498637731
 r2=18770441375137419556441967816076411508423217279309281
Version: 
Total time: 1.89 hours.
Scaled time: 4.46 units (timescale=2.360).
Factorization parameters were as follows:
name: 65553_131
n: 41556640603029760970119631553974196119945973651913576045110048478128044376147075110846618125081411
skew: 2479.09
# norm 3.90e+13
c5: 167700
c4: -1099413860
c3: -4150612370357
c2: -3464623607138653
c1: 11184030524249065405
c0: 388113312493516493000
# alpha -5.68
Y1: 9825158849
Y0: -3011780600774398341
# Murphy_E 4.26e-09
# M 1878336600636826816372762955980462052612739052524793761595897644192885404135275630993910786474838
type: gnfs
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [500000, 850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3964484
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 160389 x 160637
Polynomial selection time: 0.13 hours.
Total sieving time: 1.52 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000
total time: 1.89 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

(59·10¹³⁶-23)/9 = 6(5)₁₃₅3_<137> = 3² · 29 · 283 · C132

C132 = P41 · P92

P41 = 26705301404713169736168719314021674245521_<41>

P92 = 33234188241310821888516958762778464633803409872337761429587661457861788148008353259184887911_<92>

Number: 65553_136
N=887529013925179799839643062907755649723888219481412284304124603056409238124034436125740296976233778150840820919209286862915878796631
  ( 132 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=26705301404713169736168719314021674245521
 r2=33234188241310821888516958762778464633803409872337761429587661457861788148008353259184887911
Version: 
Total time: 3.36 hours.
Scaled time: 7.86 units (timescale=2.341).
Factorization parameters were as follows:
n: 887529013925179799839643062907755649723888219481412284304124603056409238124034436125740296976233778150840820919209286862915878796631
m: 1000000000000000000000000000
deg: 5
c5: 590
c0: -23
skew: 0.52
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3853685
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 245199 x 245447
Total sieving time: 2.80 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,50000
total time: 3.36 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673799)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378)
Calibrating delay using timer specific routine.. 5237.88 BogoMIPS (lpj=2618943)

Sep 5, 2009 (3rd)

By Sinkiti Sibata / Msieve / Sep 5, 2009

(59·10¹²⁹-23)/9 = 6(5)₁₂₈3_<130> = 75653 · 9309641963847287_<16> · C109

C109 = P34 · P76

P34 = 4614725795883954275429109017216659_<34>

P76 = 2016993358196965486133176761640833276461425032272165651768369914842420187897_<76>

Number: 65553_129
N=9307871280198141222073809578401823180095105964710473041921070433376439862681920643349744303784280882738576123
  ( 109 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=4614725795883954275429109017216659 (pp34)
 r2=2016993358196965486133176761640833276461425032272165651768369914842420187897 (pp76)
Version: Msieve-1.40
Total time: 3.79 hours.
Scaled time: 6.90 units (timescale=1.822).
Factorization parameters were as follows:
name: 65553_129
n: 9307871280198141222073809578401823180095105964710473041921070433376439862681920643349744303784280882738576123
m: 100000000000000000000000000
deg: 5
c5: 59
c0: -230
skew: 1.31
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 167065 x 167290
Total sieving time: 3.65 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 3.79 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
Memory: 3109164k/3145344k available (2732k kernel code, 34856k reserved, 1420k data, 412k init, 2227840k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.99 BogoMIPS (lpj=2393997)
Calibrating delay using timer specific routine.. 4787.75 BogoMIPS (lpj=2393879)
Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393890)
Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393888)
Total of 4 processors activated (19151.30 BogoMIPS).

(59·10¹²⁵-23)/9 = 6(5)₁₂₄3_<126> = 19 · 89 · 331711 · 723334286072127760440979_<24> · C94

C94 = P41 · P53

P41 = 42222680564788862551510597914520769117009_<41>

P53 = 38266713798433521128707810484637485291912398620879023_<53>

Sat Sep 05 18:47:56 2009  Msieve v. 1.42
Sat Sep 05 18:47:56 2009  random seeds: 9a9a5890 65e26772
Sat Sep 05 18:47:56 2009  factoring 1615723232975456823692132683727246708644840647352559264005507007327656423428932420159120602207 (94 digits)
Sat Sep 05 18:47:57 2009  searching for 15-digit factors
Sat Sep 05 18:47:57 2009  commencing quadratic sieve (94-digit input)
Sat Sep 05 18:47:57 2009  using multiplier of 7
Sat Sep 05 18:47:57 2009  using 32kb Intel Core sieve core
Sat Sep 05 18:47:57 2009  sieve interval: 36 blocks of size 32768
Sat Sep 05 18:47:57 2009  processing polynomials in batches of 6
Sat Sep 05 18:47:57 2009  using a sieve bound of 1991597 (74030 primes)
Sat Sep 05 18:47:57 2009  using large prime bound of 256916013 (27 bits)
Sat Sep 05 18:47:57 2009  using double large prime bound of 1372853067158631 (42-51 bits)
Sat Sep 05 18:47:57 2009  using trial factoring cutoff of 51 bits
Sat Sep 05 18:47:57 2009  polynomial 'A' values have 12 factors
Sat Sep 05 21:11:00 2009  74187 relations (18938 full + 55249 combined from 1020687 partial), need 74126
Sat Sep 05 21:11:02 2009  begin with 1039625 relations
Sat Sep 05 21:11:03 2009  reduce to 189177 relations in 11 passes
Sat Sep 05 21:11:03 2009  attempting to read 189177 relations
Sat Sep 05 21:11:06 2009  recovered 189177 relations
Sat Sep 05 21:11:06 2009  recovered 169082 polynomials
Sat Sep 05 21:11:06 2009  attempting to build 74187 cycles
Sat Sep 05 21:11:06 2009  found 74187 cycles in 5 passes
Sat Sep 05 21:11:06 2009  distribution of cycle lengths:
Sat Sep 05 21:11:06 2009     length 1 : 18938
Sat Sep 05 21:11:06 2009     length 2 : 13425
Sat Sep 05 21:11:06 2009     length 3 : 12855
Sat Sep 05 21:11:06 2009     length 4 : 9836
Sat Sep 05 21:11:06 2009     length 5 : 7375
Sat Sep 05 21:11:06 2009     length 6 : 4857
Sat Sep 05 21:11:06 2009     length 7 : 2939
Sat Sep 05 21:11:06 2009     length 9+: 3962
Sat Sep 05 21:11:06 2009  largest cycle: 20 relations
Sat Sep 05 21:11:06 2009  matrix is 74030 x 74187 (19.0 MB) with weight 4672524 (62.98/col)
Sat Sep 05 21:11:06 2009  sparse part has weight 4672524 (62.98/col)
Sat Sep 05 21:11:07 2009  filtering completed in 3 passes
Sat Sep 05 21:11:07 2009  matrix is 69864 x 69928 (18.0 MB) with weight 4441598 (63.52/col)
Sat Sep 05 21:11:07 2009  sparse part has weight 4441598 (63.52/col)
Sat Sep 05 21:11:07 2009  saving the first 48 matrix rows for later
Sat Sep 05 21:11:08 2009  matrix is 69816 x 69928 (11.1 MB) with weight 3460622 (49.49/col)
Sat Sep 05 21:11:08 2009  sparse part has weight 2491797 (35.63/col)
Sat Sep 05 21:11:08 2009  matrix includes 64 packed rows
Sat Sep 05 21:11:08 2009  using block size 27971 for processor cache size 1024 kB
Sat Sep 05 21:11:08 2009  commencing Lanczos iteration
Sat Sep 05 21:11:08 2009  memory use: 11.4 MB
Sat Sep 05 21:11:40 2009  lanczos halted after 1106 iterations (dim = 69816)
Sat Sep 05 21:11:40 2009  recovered 18 nontrivial dependencies
Sat Sep 05 21:11:42 2009  prp41 factor: 42222680564788862551510597914520769117009
Sat Sep 05 21:11:42 2009  prp53 factor: 38266713798433521128707810484637485291912398620879023
Sat Sep 05 21:11:42 2009  elapsed time 02:23:46

Sep 5, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3 / Sep 5, 2009

(59·10¹⁴⁸-23)/9 = 6(5)₁₄₇3_<149> = 3 · 67 · 313 · 16672259 · 19427300411_<11> · 93935018478585253673833_<23> · C104

C104 = P33 · P71

P33 = 685951288658961228928569473938697_<33>

P71 = 49927681780334666208187600144807819546142020708870361608063723439122369_<71>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=2715254249
Step 1 took 4448ms
Step 2 took 2821ms
********** Factor found in step 2: 685951288658961228928569473938697
Found probable prime factor of 33 digits: 685951288658961228928569473938697
Probable prime cofactor 49927681780334666208187600144807819546142020708870361608063723439122369 has 71 digits

(59·10¹⁴²-23)/9 = 6(5)₁₄₁3_<143> = 3 · 43 · 61 · 109 · 1530962800903_<13> · 46434594023085269_<17> · C109

C109 = P28 · P81

P28 = 5122432882476929452340127769_<28>

P81 = 209884753199464087080383859154803953570616666555689425626499446356382804153212171_<81>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=2627240755
Step 1 took 4221ms
Step 2 took 2816ms
********** Factor found in step 2: 5122432882476929452340127769
Found probable prime factor of 28 digits: 5122432882476929452340127769
Probable prime cofactor has 81 digits

(59·10¹²¹-23)/9 = 6(5)₁₂₀3_<122> = 3 · 7 · 43 · 83 · 62659 · 252001 · 3890318671781_<13> · C95

C95 = P38 · P57

P38 = 16254745280724313259542306996318654639_<38>

P57 = 875976771301044758722134852221364087178881271056936925037_<57>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=2732121548
Step 1 took 3696ms
Step 2 took 2568ms
********** Factor found in step 2: 16254745280724313259542306996318654639
Found probable prime factor of 38 digits: 16254745280724313259542306996318654639
Probable prime cofactor 875976771301044758722134852221364087178881271056936925037 has 57 digits

(59·10¹⁹⁴-23)/9 = 6(5)₁₉₃3_<195> = 167 · 228285157736039_<15> · C179

C179 = P29 · C150

P29 = 35873687474441774208125952619_<29>

C150 = [479335213207741245003527583887158873557699863891692498384699765863943251282055477987014761294737828507118107156662030571583407504914367032971015241299_<150>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=918327226
Step 1 took 8236ms
Step 2 took 4457ms
********** Factor found in step 2: 35873687474441774208125952619
Found probable prime factor of 29 digits: 35873687474441774208125952619
Composite cofactor has 150 digits

(59·10¹⁴⁰-23)/9 = 6(5)₁₃₉3_<141> = 1483 · 172801 · 197759 · 886399667667622120942040383_<27> · C101

C101 = P31 · P70

P31 = 5689289916654150275926497293389_<31>

P70 = 2565063923866998207044226037098494558613110402926733815660812190741327_<70>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=1172970948
Step 1 took 4696ms
Step 2 took 2820ms
********** Factor found in step 2: 5689289916654150275926497293389
Found probable prime factor of 31 digits: 5689289916654150275926497293389
Probable prime cofactor 2565063923866998207044226037098494558613110402926733815660812190741327 has 70 digits

(59·10¹⁷²-23)/9 = 6(5)₁₇₁3_<173> = 3³ · 2243 · 1558388347_<10> · 9692197913461901_<16> · C143

C143 = P29 · C115

P29 = 27647054178045035024590372529_<29>

C115 = [2592206737142709885718286033118701376329525131139133587872249673847964893917667097442560727671516946385417518727071_<115>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=3507598991
Step 1 took 6024ms
Step 2 took 3584ms
********** Factor found in step 2: 27647054178045035024590372529
Found probable prime factor of 29 digits: 27647054178045035024590372529
Composite cofactor has 115 digits

(59·10¹⁹¹-23)/9 = 6(5)₁₉₀3_<192> = 47 · 77528047081_<11> · C180

C180 = P28 · C152

P28 = 2455742348484227844082877051_<28>

C152 = [73260520584241407194752819396743407478406879886808326799427220021755832921946863859759750649538346315894856165489947703114639788915596931404635410219029_<152>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=383201064
Step 1 took 8308ms
Step 2 took 4301ms
********** Factor found in step 2: 2455742348484227844082877051
Found probable prime factor of 28 digits: 2455742348484227844082877051
Composite cofactor has 152 digits

(59·10¹²³-23)/9 = 6(5)₁₂₂3_<124> = 16423871 · C117

C117 = P38 · P80

P38 = 33690683433359402920174483777695242957_<38>

P80 = 11847430126160377731229441236227256582416556719472932180179868318471140022894299_<80>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=188559141
Step 1 took 5252ms
Step 2 took 3056ms
********** Factor found in step 2: 33690683433359402920174483777695242957
Found probable prime factor of 38 digits: 33690683433359402920174483777695242957
Probable prime cofactor 11847430126160377731229441236227256582416556719472932180179868318471140022894299 has 80 digits

(59·10¹⁶⁸-23)/9 = 6(5)₁₆₇3_<169> = 3037 · 70949 · 3479122711429_<13> · C148

C148 = P36 · C113

P36 = 626993149292111216903692304785352393_<36>

C113 = [13947163404384980904449611579937234571143384609283321436478575782877294124024028675585055821628876528177448253973_<113>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=565118240
Step 1 took 8960ms
Step 2 took 5169ms
********** Factor found in step 2: 626993149292111216903692304785352393
Found probable prime factor of 36 digits: 626993149292111216903692304785352393
Composite cofactor has 113 digits

Sep 5, 2009

Factorizations of 655...553 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Sep 4, 2009

By Dmitry Domanov / GGNFS/msieve 1.42 / Sep 4, 2009

(16·10²³²-7)/9 = 1(7)₂₃₂_<233> = 19 · 104953 · 1986217 · 34068054807426322294331_<23> · 13848896772790568546388233869_<29> · 56772616833085221976414195028964401_<35> · C135

C135 = P54 · P81

P54 = 991707038199261642635694918632181570921619177195911067_<54>

P81 = 168973070893309583226946762274636602940726732619466985073885282922429123577148191_<81>

Sieving ~14.5 cpu-days

Thu Sep 03 23:17:11 2009  Msieve v. 1.42
Thu Sep 03 23:17:11 2009  random seeds: c59a8090 61a115f0
Thu Sep 03 23:17:11 2009  factoring 167571783671037912466408452319759362185008616848696629101669918550562953076710717850252795352341060164798120833972449628332765915929797 (135 digits)
Thu Sep 03 23:17:13 2009  searching for 15-digit factors
Thu Sep 03 23:17:14 2009  commencing number field sieve (135-digit input)
Thu Sep 03 23:17:14 2009  R0: -88241649868393719374997646
Thu Sep 03 23:17:14 2009  R1:  726831347675741
Thu Sep 03 23:17:14 2009  A0: -170933990638688721822011537328945
Thu Sep 03 23:17:14 2009  A1:  3795778977486688813543737737
Thu Sep 03 23:17:14 2009  A2: -29194701397701178266901
Thu Sep 03 23:17:14 2009  A3:  19617994558279607
Thu Sep 03 23:17:14 2009  A4:  96670755294
Thu Sep 03 23:17:14 2009  A5:  31320
Thu Sep 03 23:17:14 2009  skew 568986.10, size 6.136336e-013, alpha -6.764677, combined = 4.549516e-011
Thu Sep 03 23:17:14 2009  
Thu Sep 03 23:17:14 2009  commencing relation filtering
Thu Sep 03 23:17:14 2009  estimated available RAM is 4094.1 MB
Thu Sep 03 23:17:14 2009  commencing duplicate removal, pass 1
Thu Sep 03 23:21:44 2009  error -15 reading relation 18121325
Thu Sep 03 23:22:30 2009  found 3394543 hash collisions in 21168001 relations
Thu Sep 03 23:24:05 2009  added 120075 free relations
Thu Sep 03 23:24:05 2009  commencing duplicate removal, pass 2
Thu Sep 03 23:25:11 2009  found 3004998 duplicates and 18283077 unique relations
Thu Sep 03 23:25:11 2009  memory use: 106.6 MB
Thu Sep 03 23:25:11 2009  reading ideals above 17235968
Thu Sep 03 23:25:24 2009  commencing singleton removal, initial pass
Thu Sep 03 23:30:40 2009  memory use: 298.4 MB
Thu Sep 03 23:30:40 2009  reading all ideals from disk
Thu Sep 03 23:30:41 2009  memory use: 296.1 MB
Thu Sep 03 23:30:43 2009  commencing in-memory singleton removal
Thu Sep 03 23:30:45 2009  begin with 18283077 relations and 17750433 unique ideals
Thu Sep 03 23:31:03 2009  reduce to 7274205 relations and 4928931 ideals in 19 passes
Thu Sep 03 23:31:03 2009  max relations containing the same ideal: 25
Thu Sep 03 23:31:05 2009  reading ideals above 100000
Thu Sep 03 23:31:05 2009  commencing singleton removal, initial pass
Thu Sep 03 23:33:56 2009  memory use: 149.2 MB
Thu Sep 03 23:33:56 2009  reading all ideals from disk
Thu Sep 03 23:33:57 2009  memory use: 277.9 MB
Thu Sep 03 23:33:59 2009  keeping 7146032 ideals with weight <= 200, target excess is 40579
Thu Sep 03 23:34:01 2009  commencing in-memory singleton removal
Thu Sep 03 23:34:03 2009  begin with 7284313 relations and 7146032 unique ideals
Thu Sep 03 23:34:31 2009  reduce to 7162150 relations and 6975502 ideals in 16 passes
Thu Sep 03 23:34:31 2009  max relations containing the same ideal: 200
Thu Sep 03 23:34:40 2009  removing 731699 relations and 661911 ideals in 69788 cliques
Thu Sep 03 23:34:41 2009  commencing in-memory singleton removal
Thu Sep 03 23:34:42 2009  begin with 6430451 relations and 6975502 unique ideals
Thu Sep 03 23:34:58 2009  reduce to 6377992 relations and 6260433 ideals in 10 passes
Thu Sep 03 23:34:58 2009  max relations containing the same ideal: 191
Thu Sep 03 23:35:06 2009  removing 531862 relations and 462074 ideals in 69788 cliques
Thu Sep 03 23:35:06 2009  commencing in-memory singleton removal
Thu Sep 03 23:35:08 2009  begin with 5846130 relations and 6260433 unique ideals
Thu Sep 03 23:35:20 2009  reduce to 5814049 relations and 5765944 ideals in 8 passes
Thu Sep 03 23:35:20 2009  max relations containing the same ideal: 178
Thu Sep 03 23:35:29 2009  relations with 0 large ideals: 126
Thu Sep 03 23:35:29 2009  relations with 1 large ideals: 107
Thu Sep 03 23:35:29 2009  relations with 2 large ideals: 1356
Thu Sep 03 23:35:29 2009  relations with 3 large ideals: 17628
Thu Sep 03 23:35:29 2009  relations with 4 large ideals: 124254
Thu Sep 03 23:35:29 2009  relations with 5 large ideals: 498727
Thu Sep 03 23:35:29 2009  relations with 6 large ideals: 1196711
Thu Sep 03 23:35:29 2009  relations with 7+ large ideals: 3975140
Thu Sep 03 23:35:29 2009  commencing 2-way merge
Thu Sep 03 23:35:40 2009  reduce to 3432549 relation sets and 3384445 unique ideals
Thu Sep 03 23:35:40 2009  ignored 1 oversize relation sets
Thu Sep 03 23:35:40 2009  commencing full merge
Thu Sep 03 23:37:25 2009  memory use: 348.3 MB
Thu Sep 03 23:37:26 2009  found 1791693 cycles, need 1786645
Thu Sep 03 23:37:26 2009  weight of 1786645 cycles is about 125238188 (70.10/cycle)
Thu Sep 03 23:37:26 2009  distribution of cycle lengths:
Thu Sep 03 23:37:26 2009  1 relations: 240311
Thu Sep 03 23:37:26 2009  2 relations: 234300
Thu Sep 03 23:37:26 2009  3 relations: 219512
Thu Sep 03 23:37:26 2009  4 relations: 187773
Thu Sep 03 23:37:26 2009  5 relations: 163477
Thu Sep 03 23:37:26 2009  6 relations: 134470
Thu Sep 03 23:37:26 2009  7 relations: 116196
Thu Sep 03 23:37:26 2009  8 relations: 95886
Thu Sep 03 23:37:26 2009  9 relations: 78945
Thu Sep 03 23:37:26 2009  10+ relations: 315775
Thu Sep 03 23:37:26 2009  heaviest cycle: 26 relations
Thu Sep 03 23:37:28 2009  commencing cycle optimization
Thu Sep 03 23:37:33 2009  start with 10207707 relations
Thu Sep 03 23:38:04 2009  pruned 213384 relations
Thu Sep 03 23:38:04 2009  memory use: 272.2 MB
Thu Sep 03 23:38:04 2009  distribution of cycle lengths:
Thu Sep 03 23:38:04 2009  1 relations: 240311
Thu Sep 03 23:38:04 2009  2 relations: 239131
Thu Sep 03 23:38:04 2009  3 relations: 226170
Thu Sep 03 23:38:04 2009  4 relations: 191236
Thu Sep 03 23:38:04 2009  5 relations: 165968
Thu Sep 03 23:38:04 2009  6 relations: 135445
Thu Sep 03 23:38:04 2009  7 relations: 116170
Thu Sep 03 23:38:04 2009  8 relations: 94947
Thu Sep 03 23:38:04 2009  9 relations: 77934
Thu Sep 03 23:38:04 2009  10+ relations: 299333
Thu Sep 03 23:38:04 2009  heaviest cycle: 26 relations
Thu Sep 03 23:38:12 2009  RelProcTime: 1258
Thu Sep 03 23:38:12 2009  
Thu Sep 03 23:38:12 2009  commencing linear algebra
Thu Sep 03 23:38:13 2009  read 1786645 cycles
Thu Sep 03 23:38:19 2009  cycles contain 5751378 unique relations
Thu Sep 03 23:42:39 2009  read 5751378 relations
Thu Sep 03 23:42:51 2009  using 20 quadratic characters above 268434582
Thu Sep 03 23:43:40 2009  building initial matrix
Thu Sep 03 23:45:27 2009  memory use: 662.0 MB
Thu Sep 03 23:45:33 2009  read 1786645 cycles
Thu Sep 03 23:47:26 2009  matrix is 1786468 x 1786645 (509.3 MB) with weight 167615762 (93.82/col)
Thu Sep 03 23:47:26 2009  sparse part has weight 120993610 (67.72/col)
Thu Sep 03 23:47:56 2009  filtering completed in 2 passes
Thu Sep 03 23:47:57 2009  matrix is 1785630 x 1785807 (509.2 MB) with weight 167585845 (93.84/col)
Thu Sep 03 23:47:57 2009  sparse part has weight 120987158 (67.75/col)
Thu Sep 03 23:48:16 2009  read 1785807 cycles
Thu Sep 03 23:53:35 2009  matrix is 1785630 x 1785807 (509.2 MB) with weight 167585845 (93.84/col)
Thu Sep 03 23:53:35 2009  sparse part has weight 120987158 (67.75/col)
Thu Sep 03 23:53:36 2009  saving the first 48 matrix rows for later
Thu Sep 03 23:53:37 2009  matrix is 1785582 x 1785807 (490.6 MB) with weight 133642017 (74.84/col)
Thu Sep 03 23:53:37 2009  sparse part has weight 117896943 (66.02/col)
Thu Sep 03 23:53:37 2009  matrix includes 64 packed rows
Thu Sep 03 23:53:37 2009  using block size 65536 for processor cache size 4096 kB
Thu Sep 03 23:53:57 2009  commencing Lanczos iteration (4 threads)
Thu Sep 03 23:53:57 2009  memory use: 546.0 MB
Fri Sep 04 05:07:20 2009  lanczos halted after 28239 iterations (dim = 1785582)
Fri Sep 04 05:07:25 2009  recovered 30 nontrivial dependencies
Fri Sep 04 05:07:35 2009  BLanczosTime: 19763
Fri Sep 04 05:07:35 2009  
Fri Sep 04 05:07:35 2009  commencing square root phase
Fri Sep 04 05:07:35 2009  reading relations for dependency 1
Fri Sep 04 05:07:36 2009  read 893981 cycles
Fri Sep 04 05:07:39 2009  cycles contain 3510263 unique relations
Fri Sep 04 05:11:33 2009  read 3510263 relations
Fri Sep 04 05:12:04 2009  multiplying 2876640 relations
Fri Sep 04 05:22:21 2009  multiply complete, coefficients have about 138.34 million bits
Fri Sep 04 05:22:29 2009  initial square root is modulo 92221
Fri Sep 04 05:38:01 2009  reading relations for dependency 2
Fri Sep 04 05:38:02 2009  read 893689 cycles
Fri Sep 04 05:38:05 2009  cycles contain 3510081 unique relations
Fri Sep 04 05:42:07 2009  read 3510081 relations
Fri Sep 04 05:42:38 2009  multiplying 2877082 relations
Fri Sep 04 05:52:54 2009  multiply complete, coefficients have about 138.36 million bits
Fri Sep 04 05:53:02 2009  initial square root is modulo 92431
Fri Sep 04 06:08:37 2009  sqrtTime: 3662
Fri Sep 04 06:08:37 2009  prp54 factor: 991707038199261642635694918632181570921619177195911067
Fri Sep 04 06:08:37 2009  prp81 factor: 168973070893309583226946762274636602940726732619466985073885282922429123577148191
Fri Sep 04 06:08:37 2009  elapsed time 06:51:26

Sep 3, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Sep 3, 2009

(46·10¹⁶⁹+71)/9 = 5(1)₁₆₈9_<170> = 31 · 646102036844022206006504343271_<30> · C139

C139 = P55 · P84

P55 = 7869899312705939875327158792352250969639308808703596351_<55>

P84 = 324252506725723163935370179632867223784323136137681244398680972982897152912578221369_<84>

Number: 51119_169
N=2551834579823946874729908717308735635277974678882990847240512167590000681701754074603221507742987070694414782032556889668754576709298624519
  ( 139 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=7869899312705939875327158792352250969639308808703596351
 r2=324252506725723163935370179632867223784323136137681244398680972982897152912578221369
Version: 
Total time: 44.46 hours.
Scaled time: 105.85 units (timescale=2.381).
Factorization parameters were as follows:
n: 2551834579823946874729908717308735635277974678882990847240512167590000681701754074603221507742987070694414782032556889668754576709298624519
m: 10000000000000000000000000000000000
deg: 5
c5: 23
c0: 355
skew: 1.73
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 6400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11235283
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1086131 x 1086379
Total sieving time: 40.21 hours.
Total relation processing time: 1.45 hours.
Matrix solve time: 2.67 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 44.46 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673801)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672349)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Sep 2, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Sep 2, 2009

(19·10¹⁹¹+17)/9 = 2(1)₁₉₀3_<192> = 3 · 7 · 1627 · C187

C187 = P37 · P151

P37 = 5159821878045688607762327346221433523_<37>

P151 = 1197483489481970933197735726304293294387797401694296550112736151012667802612072712189611721185927094362433494974127049810061666990228118386344080983493_<151>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2833440132
Step 1 took 69753ms
Step 2 took 21721ms
********** Factor found in step 2: 5159821878045688607762327346221433523
Found probable prime factor of 37 digits: 5159821878045688607762327346221433523
Probable prime cofactor 1197483489481970933197735726304293294387797401694296550112736151012667802612072712189611721185927094362433494974127049810061666990228118386344080983493 has 151 digits

Sep 2, 2009

By Robert Backstrom / GGNFS, Msieve / Sep 2, 2009

(59·10¹⁵³-41)/9 = 6(5)₁₅₂1_<154> = 71 · 31547078069965587199548803369110194703_<38> · C115

C115 = P41 · P74

P41 = 73342284603167236937378850206607287487629_<41>

P74 = 39905943091587869748534627021584733575920194395623184525750449074965747363_<74>

Number: n
N=2926793035581032985985372497805728366509485826817219355709884856091272013245694366598974490036970962573306601872327
  ( 115 digits)
SNFS difficulty: 156 digits.
Divisors found:

Wed Sep 02 18:33:10 2009  prp41 factor: 73342284603167236937378850206607287487629
Wed Sep 02 18:33:10 2009  prp74 factor: 39905943091587869748534627021584733575920194395623184525750449074965747363
Wed Sep 02 18:33:10 2009  elapsed time 01:15:38 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 22.88 hours.
Scaled time: 41.85 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_6_5_152_1
n: 2926793035581032985985372497805728366509485826817219355709884856091272013245694366598974490036970962573306601872327
m: 5000000000000000000000000000000
deg: 5
c5: 472
c0: -1025
skew: 1.17
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 26
lpba: 26
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 20000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 56/56
Sieved  special-q in [1400000, 2727419)
Primes: RFBsize:203362, AFBsize:203613, largePrimes:5498081 encountered
Relations: rels:5530934, finalFF:406243
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 528977 hash collisions in 6054896 relations
Msieve: matrix is 523627 x 523875 (139.9 MB)

Total sieving time: 22.74 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,26,26,56,56,2.4,2.4,100000
total time: 22.88 hours.
 --------- CPU info (if available) ----------

Sep 1, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve 1.42 / Sep 1, 2009

(59·10¹⁵⁶-41)/9 = 6(5)₁₅₅1_<157> = 375149 · C152

C152 = P69 · P84

P69 = 122402430418751797731067365839873473441811272250720725639712914399843_<69>

P84 = 142763000744037084102025742155044287189683532814771668495075908139458734730887232393_<84>

N=17474538264944210315249555658033356227940246556849559923005407332967848922842805273519469745502601781040481396873123893587762610470921035523366863714299
  ( 152 digits)
SNFS difficulty: 157 digits.
Divisors found:
r1=122402430418751797731067365839873473441811272250720725639712914399843 (pp69)
r2=142763000744037084102025742155044287189683532814771668495075908139458734730887232393 (pp84)
Version: Msieve-1.40
Total time: 23.63 hours.
Scaled time: 43.71 units (timescale=1.850).
Factorization parameters were as follows:
n: 17474538264944210315249555658033356227940246556849559923005407332967848922842805273519469745502601781040481396873123893587762610470921035523366863714299
m: 10000000000000000000000000000000
deg: 5
c5: 590
c0: -41
skew: 0.59
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2800001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 580838 x 581063
Total sieving time: 22.42 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.05 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,157.000,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 23.63 hours.
 --------- CPU info (if available) ----------

Sep 1, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve / Sep 1, 2009

(52·10¹⁹¹+11)/9 = 5(7)₁₉₀9_<192> = 3 · 65309 · C187

C187 = P35 · C152

P35 = 30801606174199913457588213935842219_<35>

C152 = [95739946791903685132248909040386648829197591890573936370776635152212693642358749880570399774978728195176825298861308146931074602792034098577412749483983_<152>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3691768300
Step 1 took 69848ms
Step 2 took 22050ms
********** Factor found in step 2: 30801606174199913457588213935842219
Found probable prime factor of 35 digits: 30801606174199913457588213935842219
Composite cofactor 95739946791903685132248909040386648829197591890573936370776635152212693642358749880570399774978728195176825298861308146931074602792034098577412749483983 has 152 digits

(59·10¹⁴⁴-41)/9 = 6(5)₁₄₃1_<145> = 103 · 362969 · 2614458695951705504047_<22> · 15499856740693157390708362031_<29> · C88

C88 = P39 · P50

P39 = 138047683300448222085519702666913652443_<39>

P50 = 31344702379181432031160906155447922850088032738243_<50>

Fri Aug 28 16:00:29 2009  Msieve v. 1.42
Fri Aug 28 16:00:29 2009  random seeds: e5f7fef0 7bd40aad
Fri Aug 28 16:00:29 2009  factoring 4327063547188044230148567591766663446607409468377257772873755338116673621132197696477649 (88 digits)
Fri Aug 28 16:00:30 2009  searching for 15-digit factors
Fri Aug 28 16:00:31 2009  commencing quadratic sieve (88-digit input)
Fri Aug 28 16:00:31 2009  using multiplier of 5
Fri Aug 28 16:00:31 2009  using 64kb Pentium 3 sieve core
Fri Aug 28 16:00:31 2009  sieve interval: 14 blocks of size 65536
Fri Aug 28 16:00:31 2009  processing polynomials in batches of 8
Fri Aug 28 16:00:31 2009  using a sieve bound of 1527497 (57966 primes)
Fri Aug 28 16:00:31 2009  using large prime bound of 122199760 (26 bits)
Fri Aug 28 16:00:31 2009  using double large prime bound of 360351695070240 (42-49 bits)
Fri Aug 28 16:00:31 2009  using trial factoring cutoff of 49 bits
Fri Aug 28 16:00:31 2009  polynomial 'A' values have 11 factors
Fri Aug 28 17:52:14 2009  58122 relations (15513 full + 42609 combined from 620007 partial), need 58062
Fri Aug 28 17:52:15 2009  begin with 635520 relations
Fri Aug 28 17:52:15 2009  reduce to 141666 relations in 9 passes
Fri Aug 28 17:52:15 2009  attempting to read 141666 relations
Fri Aug 28 17:52:19 2009  recovered 141666 relations
Fri Aug 28 17:52:19 2009  recovered 121281 polynomials
Fri Aug 28 17:52:20 2009  attempting to build 58122 cycles
Fri Aug 28 17:52:20 2009  found 58122 cycles in 5 passes
Fri Aug 28 17:52:20 2009  distribution of cycle lengths:
Fri Aug 28 17:52:20 2009     length 1 : 15513
Fri Aug 28 17:52:20 2009     length 2 : 11293
Fri Aug 28 17:52:20 2009     length 3 : 10112
Fri Aug 28 17:52:20 2009     length 4 : 7777
Fri Aug 28 17:52:20 2009     length 5 : 5525
Fri Aug 28 17:52:20 2009     length 6 : 3418
Fri Aug 28 17:52:20 2009     length 7 : 2054
Fri Aug 28 17:52:20 2009     length 9+: 2430
Fri Aug 28 17:52:20 2009  largest cycle: 19 relations
Fri Aug 28 17:52:20 2009  matrix is 57966 x 58122 (14.0 MB) with weight 3441484 (59.21/col)
Fri Aug 28 17:52:20 2009  sparse part has weight 3441484 (59.21/col)
Fri Aug 28 17:52:21 2009  filtering completed in 3 passes
Fri Aug 28 17:52:21 2009  matrix is 54094 x 54158 (13.2 MB) with weight 3241096 (59.85/col)
Fri Aug 28 17:52:21 2009  sparse part has weight 3241096 (59.85/col)
Fri Aug 28 17:52:21 2009  saving the first 48 matrix rows for later
Fri Aug 28 17:52:21 2009  matrix is 54046 x 54158 (9.3 MB) with weight 2653683 (49.00/col)
Fri Aug 28 17:52:21 2009  sparse part has weight 2108341 (38.93/col)
Fri Aug 28 17:52:21 2009  matrix includes 64 packed rows
Fri Aug 28 17:52:21 2009  using block size 21663 for processor cache size 1024 kB
Fri Aug 28 17:52:22 2009  commencing Lanczos iteration
Fri Aug 28 17:52:22 2009  memory use: 9.0 MB
Fri Aug 28 17:52:53 2009  lanczos halted after 856 iterations (dim = 54042)
Fri Aug 28 17:52:54 2009  recovered 15 nontrivial dependencies
Fri Aug 28 17:52:54 2009  prp39 factor: 138047683300448222085519702666913652443
Fri Aug 28 17:52:54 2009  prp50 factor: 31344702379181432031160906155447922850088032738243
Fri Aug 28 17:52:54 2009  elapsed time 01:52:25

(59·10¹²¹-41)/9 = 6(5)₁₂₀1_<122> = 61 · 127 · 373 · 21051403 · 2300728836789203473636063_<25> · C84

C84 = P42 · P43

P42 = 365889507198266340309586761903526109721049_<42>

P43 = 1280178939027176122266235863939883244142661_<43>

Fri Aug 28 15:13:48 2009  Msieve v. 1.42
Fri Aug 28 15:13:48 2009  random seeds: 94be0cd0 f187796d
Fri Aug 28 15:13:48 2009  factoring 468404041126252924160492585690317091352005873396330654608841861863525407541870571389 (84 digits)
Fri Aug 28 15:13:49 2009  searching for 15-digit factors
Fri Aug 28 15:13:50 2009  commencing quadratic sieve (84-digit input)
Fri Aug 28 15:13:50 2009  using multiplier of 19
Fri Aug 28 15:13:50 2009  using 64kb Pentium 3 sieve core
Fri Aug 28 15:13:50 2009  sieve interval: 6 blocks of size 65536
Fri Aug 28 15:13:50 2009  processing polynomials in batches of 17
Fri Aug 28 15:13:50 2009  using a sieve bound of 1399273 (53529 primes)
Fri Aug 28 15:13:50 2009  using large prime bound of 120337478 (26 bits)
Fri Aug 28 15:13:50 2009  using double large prime bound of 350527068529426 (41-49 bits)
Fri Aug 28 15:13:50 2009  using trial factoring cutoff of 49 bits
Fri Aug 28 15:13:50 2009  polynomial 'A' values have 11 factors
Fri Aug 28 15:56:37 2009  53850 relations (16360 full + 37490 combined from 568032 partial), need 53625
Fri Aug 28 15:56:37 2009  begin with 584392 relations
Fri Aug 28 15:56:38 2009  reduce to 124395 relations in 11 passes
Fri Aug 28 15:56:38 2009  attempting to read 124395 relations
Fri Aug 28 15:56:40 2009  recovered 124395 relations
Fri Aug 28 15:56:40 2009  recovered 99407 polynomials
Fri Aug 28 15:56:40 2009  attempting to build 53850 cycles
Fri Aug 28 15:56:40 2009  found 53850 cycles in 5 passes
Fri Aug 28 15:56:40 2009  distribution of cycle lengths:
Fri Aug 28 15:56:40 2009     length 1 : 16360
Fri Aug 28 15:56:40 2009     length 2 : 11103
Fri Aug 28 15:56:40 2009     length 3 : 9605
Fri Aug 28 15:56:40 2009     length 4 : 6627
Fri Aug 28 15:56:40 2009     length 5 : 4469
Fri Aug 28 15:56:40 2009     length 6 : 2687
Fri Aug 28 15:56:40 2009     length 7 : 1450
Fri Aug 28 15:56:40 2009     length 9+: 1549
Fri Aug 28 15:56:40 2009  largest cycle: 20 relations
Fri Aug 28 15:56:40 2009  matrix is 53529 x 53850 (11.4 MB) with weight 2778426 (51.60/col)
Fri Aug 28 15:56:40 2009  sparse part has weight 2778426 (51.60/col)
Fri Aug 28 15:56:41 2009  filtering completed in 3 passes
Fri Aug 28 15:56:41 2009  matrix is 47789 x 47851 (10.2 MB) with weight 2489072 (52.02/col)
Fri Aug 28 15:56:41 2009  sparse part has weight 2489072 (52.02/col)
Fri Aug 28 15:56:41 2009  saving the first 48 matrix rows for later
Fri Aug 28 15:56:41 2009  matrix is 47741 x 47851 (5.7 MB) with weight 1833801 (38.32/col)
Fri Aug 28 15:56:41 2009  sparse part has weight 1197884 (25.03/col)
Fri Aug 28 15:56:41 2009  matrix includes 64 packed rows
Fri Aug 28 15:56:41 2009  using block size 19140 for processor cache size 1024 kB
Fri Aug 28 15:56:42 2009  commencing Lanczos iteration
Fri Aug 28 15:56:42 2009  memory use: 6.5 MB
Fri Aug 28 15:57:00 2009  lanczos halted after 756 iterations (dim = 47737)
Fri Aug 28 15:57:00 2009  recovered 16 nontrivial dependencies
Fri Aug 28 15:57:00 2009  prp42 factor: 365889507198266340309586761903526109721049
Fri Aug 28 15:57:00 2009  prp43 factor: 1280178939027176122266235863939883244142661
Fri Aug 28 15:57:00 2009  elapsed time 00:43:12

(44·10¹⁸⁶-71)/9 = 4(8)₁₈₅1_<187> = 3³ · 17 · 41 · C183

C183 = P49 · P134

P49 = 2781358159338341230540981818870343356361601462647_<49>

P134 = 93402114377596838227799236814397000522231663886462612272154867872283444096094978505488882758006792303268745560227245467020075767533917_<134>

Number: 48881_186
N=259784732923581959131138152340129065778675215946059242727503527758589132732285928523773255161745517237307449327216583712678085386518353200961203511817253248785211163658477543381098299
  ( 183 digits)
SNFS difficulty: 188 digits.
Divisors found:
 r1=2781358159338341230540981818870343356361601462647
 r2=93402114377596838227799236814397000522231663886462612272154867872283444096094978505488882758006792303268745560227245467020075767533917
Version: 
Total time: 366.82 hours.
Scaled time: 737.67 units (timescale=2.011).
Factorization parameters were as follows:
n: 259784732923581959131138152340129065778675215946059242727503527758589132732285928523773255161745517237307449327216583712678085386518353200961203511817253248785211163658477543381098299
m: 20000000000000000000000000000000000000
deg: 5
c5: 55
c0: -284
skew: 1.39
type: snfs
lss: 1
rlim: 9600000
alim: 9600000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 9600000/9600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4800000, 8400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1661836 x 1662084
Total sieving time: 366.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,188,5,0,0,0,0,0,0,0,0,9600000,9600000,28,28,54,54,2.5,2.5,100000
total time: 366.82 hours.
 --------- CPU info (if available) ----------

Sep 1, 2009

By Sinkiti Sibata / Msieve / Sep 1, 2009

(59·10¹⁶²-41)/9 = 6(5)₁₆₁1_<163> = 43 · 739 · 2161 · 80614627 · C148

C148 = P45 · P103

P45 = 121239891454093519261731817652882419678157587_<45>

P103 = 9767478267692126100157672302286065670936776448217885428023920416603215607907947844277447345437813925767_<103>

Number: 65551_162
N=1184208004955210770830172663043312929709173836438995308375769074655838736378823569880462727262595960362475989456294661603514048867308740826145844229
  ( 148 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=121239891454093519261731817652882419678157587 (pp45)
 r2=9767478267692126100157672302286065670936776448217885428023920416603215607907947844277447345437813925767 (pp103)
Version: Msieve-1.40
Total time: 58.87 hours.
Scaled time: 122.74 units (timescale=2.085).
Factorization parameters were as follows:
name: 65551_162
n: 1184208004955210770830172663043312929709173836438995308375769074655838736378823569880462727262595960362475989456294661603514048867308740826145844229
m: 200000000000000000000000000000000
deg: 5
c5: 1475
c0: -328
skew: 0.74
type: snfs
lss: 1
rlim: 3900000
alim: 3900000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3900000/3900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1950000, 4250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 740219 x 740467
Total sieving time: 56.25 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.05 hours.
Time per square root: 0.37 hours.
Prototype def-par.txt line would be:
snfs,164.000,5,0,0,0,0,0,0,0,0,3900000,3900000,27,27,51,51,2.4,2.4,100000
total time: 58.87 hours.
 --------- CPU info (if available) ----------

August 2009

Aug 31, 2009 (5th)

By Erik Branger / GGNFS, Msieve / Aug 31, 2009

(59·10¹⁵⁴-41)/9 = 6(5)₁₅₃1_<155> = 3797 · 159093639765504071562915217735497341_<36> · C117

C117 = P55 · P62

P55 = 2589791619531563881290259667937807775007827680200185973_<55>

P62 = 41903593307858982204461105941512747941924740493989831900396931_<62>

Number: 65551_154
N=108521574776952115645717588039054192051980803534687113921049522702179053232133262478345190473870479199937478718448863
  ( 117 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=2589791619531563881290259667937807775007827680200185973 (pp55)
 r2=41903593307858982204461105941512747941924740493989831900396931 (pp62)
Version: Msieve v. 1.42
Total time: 46.92 hours.
Scaled time: 18.02 units (timescale=0.384).
Factorization parameters were as follows:
n: 108521574776952115645717588039054192051980803534687113921049522702179053232133262478345190473870479199937478718448863 
m: 10000000000000000000000000000000 
deg: 5 
c5: 59 
c0: -410 
skew: 1.47 
type: snfs 
lss: 1 
rlim: 2900000 
alim: 2900000 
lpbr: 27 
lpba: 27 
mfbr: 50 
mfba: 50 
rlambda: 2.4 
alambda: 2.4 
qintsize: 100000
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1450000, 2950001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 551770 x 551994
Total sieving time: 45.21 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.05 hours.
Time per square root: 0.55 hours.
Prototype def-par.txt line would be:
snfs ,156.000,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,
total time: 46.92 hours.
 --------- CPU info (if available) ----------

Aug 31, 2009 (4th)

By Sinkiti Sibata / Msieve / Aug 31, 2009

(59·10¹⁶⁷-41)/9 = 6(5)₁₆₆1_<168> = 3² · 13 · 31 · 6389 · 132096631 · C153

C153 = P47 · P106

P47 = 29066651586528410702821561866512390233285664069_<47>

P106 = 7367876067116486925377923809061947616100280902108981773894021319523839837975817484936114364116391604057203_<106>

Number: 65551_167
N=214159486575596141707211680720002581157646854390477143895630202872280827983759826601254749071627804247303991319745959188294916234845748005710716517739007
  ( 153 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=29066651586528410702821561866512390233285664069 (pp47)
 r2=7367876067116486925377923809061947616100280902108981773894021319523839837975817484936114364116391604057203 (pp106)
Version: Msieve-1.40
Total time: 61.17 hours.
Scaled time: 203.20 units (timescale=3.322).
Factorization parameters were as follows:
name: 65551_167
n: 214159486575596141707211680720002581157646854390477143895630202872280827983759826601254749071627804247303991319745959188294916234845748005710716517739007
m: 2000000000000000000000000000000000
deg: 5
c5: 1475
c0: -328
skew: 0.74
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 5550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 935564 x 935811
Total sieving time: 59.13 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.66 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,169.000,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000
total time: 61.17 hours.
 --------- CPU info (if available) ----------

Aug 31, 2009 (3rd)

By Markus Tervooren / gnfs-lasieve4I14e, gnfs-lasieve4I15e, msieve 1.42 / Aug 31, 2009

8·10²³⁰-1 = 7(9)₂₃₀_<231> = 171847177 · C223

C223 = P70 · P74 · P80

P70 = 7194989070351007241001770794481202899232920377811344337193524816903113_<70>

P74 = 28405869825449471447004672858393144480378760112284964510299428948566224457_<74>

P80 = 22777672993897316831397692267111749997397458530603944165484429112280289213344407_<80>

Sieving took ~191 CPU-days  @ 2.66Ghz Core 2 + 120 CPU-days @2.00 Ghz P4

Sat Aug 22 14:08:04 2009  commencing relation filtering
Sat Aug 22 14:08:04 2009  estimated available RAM is 8010.2 MB
Sat Aug 22 14:08:04 2009  commencing duplicate removal, pass 1
-- some errors snipped
Sat Aug 22 14:19:35 2009  found 17364933 hash collisions in 92302860 relations
Sat Aug 22 14:19:55 2009  added 419490 free relations
Sat Aug 22 14:19:55 2009  commencing duplicate removal, pass 2
Sat Aug 22 14:24:57 2009  found 17849103 duplicates and 74873247 unique relations
Sat Aug 22 14:24:57 2009  memory use: 426.4 MB
Sat Aug 22 14:24:57 2009  reading ideals above 53280768
Sat Aug 22 14:24:57 2009  commencing singleton removal, initial pass
Sat Aug 22 14:38:55 2009  memory use: 1193.5 MB
Sat Aug 22 14:38:55 2009  reading all ideals from disk
Sat Aug 22 14:39:25 2009  memory use: 1323.7 MB
Sat Aug 22 14:39:34 2009  commencing in-memory singleton removal
Sat Aug 22 14:39:42 2009  begin with 74873247 relations and 74233171 unique ideals
Sat Aug 22 14:41:11 2009  reduce to 32087832 relations and 25064968 ideals in 19 passes
Sat Aug 22 14:41:11 2009  max relations containing the same ideal: 21
Sat Aug 22 14:41:16 2009  reading ideals above 720000
Sat Aug 22 14:41:16 2009  commencing singleton removal, initial pass
Sat Aug 22 14:48:39 2009  memory use: 596.8 MB
Sat Aug 22 14:48:39 2009  reading all ideals from disk
Sat Aug 22 14:49:00 2009  memory use: 1198.3 MB
Sat Aug 22 14:49:10 2009  keeping 31255991 ideals with weight <= 200, target excess is 177317
Sat Aug 22 14:49:19 2009  commencing in-memory singleton removal
Sat Aug 22 14:49:28 2009  begin with 32087840 relations and 31255991 unique ideals
Sat Aug 22 14:51:30 2009  reduce to 32043145 relations and 31211249 ideals in 14 passes
Sat Aug 22 14:51:30 2009  max relations containing the same ideal: 200
Sat Aug 22 14:52:11 2009  removing 3404380 relations and 3091276 ideals in 313104 cliques
Sat Aug 22 14:52:12 2009  commencing in-memory singleton removal
Sat Aug 22 14:52:21 2009  begin with 28638765 relations and 31211249 unique ideals
Sat Aug 22 14:54:01 2009  reduce to 28324631 relations and 27801343 ideals in 13 passes
Sat Aug 22 14:54:01 2009  max relations containing the same ideal: 192
Sat Aug 22 14:54:36 2009  removing 2504006 relations and 2190902 ideals in 313104 cliques
Sat Aug 22 14:54:38 2009  commencing in-memory singleton removal
Sat Aug 22 14:54:45 2009  begin with 25820625 relations and 27801343 unique ideals
Sat Aug 22 14:56:01 2009  reduce to 25626526 relations and 25413937 ideals in 11 passes
Sat Aug 22 14:56:01 2009  max relations containing the same ideal: 182
Sat Aug 22 14:56:43 2009  relations with 0 large ideals: 6650
Sat Aug 22 14:56:43 2009  relations with 1 large ideals: 776
Sat Aug 22 14:56:43 2009  relations with 2 large ideals: 9374
Sat Aug 22 14:56:43 2009  relations with 3 large ideals: 93183
Sat Aug 22 14:56:43 2009  relations with 4 large ideals: 547174
Sat Aug 22 14:56:43 2009  relations with 5 large ideals: 1991731
Sat Aug 22 14:56:43 2009  relations with 6 large ideals: 4560537
Sat Aug 22 14:56:43 2009  relations with 7+ large ideals: 18417101
Sat Aug 22 14:56:43 2009  commencing 2-way merge
Sat Aug 22 14:57:27 2009  reduce to 15063412 relation sets and 14850827 unique ideals
Sat Aug 22 14:57:27 2009  ignored 4 oversize relation sets
Sat Aug 22 14:57:27 2009  commencing full merge
Sat Aug 22 15:04:59 2009  memory use: 1764.4 MB
Sat Aug 22 15:05:01 2009  found 7950941 cycles, need 7925027
Sat Aug 22 15:05:06 2009  weight of 7925027 cycles is about 554942333 (70.02/cycle)
Sat Aug 22 15:05:06 2009  distribution of cycle lengths:
Sat Aug 22 15:05:06 2009  1 relations: 1169843
Sat Aug 22 15:05:06 2009  2 relations: 1106346
Sat Aug 22 15:05:06 2009  3 relations: 1021429
Sat Aug 22 15:05:06 2009  4 relations: 874258
Sat Aug 22 15:05:06 2009  5 relations: 743662
Sat Aug 22 15:05:06 2009  6 relations: 615047
Sat Aug 22 15:05:06 2009  7 relations: 500678
Sat Aug 22 15:05:06 2009  8 relations: 404363
Sat Aug 22 15:05:06 2009  9 relations: 328390
Sat Aug 22 15:05:06 2009  10+ relations: 1161011
Sat Aug 22 15:05:06 2009  heaviest cycle: 26 relations
Sat Aug 22 15:05:09 2009  commencing cycle optimization
Sat Aug 22 15:05:30 2009  start with 42060266 relations
Sat Aug 22 15:06:59 2009  pruned 704586 relations
Sat Aug 22 15:06:59 2009  memory use: 1471.4 MB
Sat Aug 22 15:06:59 2009  distribution of cycle lengths:
Sat Aug 22 15:06:59 2009  1 relations: 1169843
Sat Aug 22 15:06:59 2009  2 relations: 1125822
Sat Aug 22 15:06:59 2009  3 relations: 1048997
Sat Aug 22 15:06:59 2009  4 relations: 885549
Sat Aug 22 15:06:59 2009  5 relations: 751949
Sat Aug 22 15:06:59 2009  6 relations: 615186
Sat Aug 22 15:06:59 2009  7 relations: 497737
Sat Aug 22 15:06:59 2009  8 relations: 399716
Sat Aug 22 15:06:59 2009  9 relations: 322988
Sat Aug 22 15:06:59 2009  10+ relations: 1107240
Sat Aug 22 15:06:59 2009  heaviest cycle: 26 relations
Sat Aug 22 15:07:18 2009  RelProcTime: 3554
Sat Aug 22 15:07:18 2009  elapsed time 00:59:16

Sat Aug 22 15:45:07 2009  commencing linear algebra
Sat Aug 22 15:45:08 2009  read 7925027 cycles
Sat Aug 22 15:45:25 2009  cycles contain 25287775 unique relations
Sat Aug 22 15:50:50 2009  read 25287775 relations
Sat Aug 22 15:51:38 2009  using 20 quadratic characters above 1073741312
Sat Aug 22 15:54:07 2009  building initial matrix
Sat Aug 22 15:59:14 2009  memory use: 3135.0 MB
Sat Aug 22 15:59:21 2009  read 7925027 cycles
Sat Aug 22 15:59:29 2009  matrix is 7924849 x 7925027 (2395.5 MB) with weight 696021674 (87.83/col)
Sat Aug 22 15:59:29 2009  sparse part has weight 540796398 (68.24/col)
Sat Aug 22 16:01:56 2009  filtering completed in 2 passes
Sat Aug 22 16:01:58 2009  matrix is 7915028 x 7915206 (2394.8 MB) with weight 695762853 (87.90/col)
Sat Aug 22 16:01:58 2009  sparse part has weight 540725492 (68.31/col)
Sat Aug 22 16:03:01 2009  read 7915206 cycles
Sat Aug 22 16:03:05 2009  matrix is 7915028 x 7915206 (2394.8 MB) with weight 695762853 (87.90/col)
Sat Aug 22 16:03:05 2009  sparse part has weight 540725492 (68.31/col)
Sat Aug 22 16:03:05 2009  saving the first 48 matrix rows for later
Sat Aug 22 16:03:09 2009  matrix is 7914980 x 7915206 (2286.5 MB) with weight 561446210 (70.93/col)
Sat Aug 22 16:03:09 2009  sparse part has weight 520247528 (65.73/col)
Sat Aug 22 16:03:09 2009  matrix includes 64 packed rows
Sat Aug 22 16:03:09 2009  using block size 65536 for processor cache size 4096 kB
Sat Aug 22 16:03:42 2009  commencing Lanczos iteration (4 threads)
Sat Aug 22 16:03:42 2009  memory use: 2480.9 MB
Sun Aug 30 13:18:16 2009  lanczos halted after 125170 iterations (dim = 7914978)
Sun Aug 30 13:18:31 2009  recovered 38 nontrivial dependencies
Sun Aug 30 13:18:31 2009  BLanczosTime: 682404
Sun Aug 30 13:18:31 2009  elapsed time 189:33:27


Sun Aug 30 15:39:04 2009  commencing square root phase
Sun Aug 30 15:39:04 2009  reading relations for dependency 5
Sun Aug 30 15:39:16 2009  read 3957653 cycles
Sun Aug 30 15:39:31 2009  cycles contain 15233059 unique relations
Sun Aug 30 15:44:24 2009  read 15233059 relations
Sun Aug 30 15:47:18 2009  multiplying 12643428 relations
Sun Aug 30 16:39:02 2009  sqrtTime: 11943
Sun Aug 30 16:39:02 2009  prp70 factor: 7194989070351007241001770794481202899232920377811344337193524816903113
Sun Aug 30 16:39:02 2009  prp74 factor: 28405869825449471447004672858393144480378760112284964510299428948566224457
Sun Aug 30 16:39:02 2009  prp80 factor: 22777672993897316831397692267111749997397458530603944165484429112280289213344407
Sun Aug 30 16:39:02 2009  elapsed time 03:19:06

c223 is the largest number factored by SNFS in our tables so far. Congratulations!!!

Aug 31, 2009 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS / Aug 31, 2009

(59·10¹⁷⁰-41)/9 = 6(5)₁₆₉1_<171> = 3 · 7 · 214170980453_<12> · 3324849806533_<13> · C146

C146 = P36 · P46 · P65

P36 = 804107783923129451039657356402486843_<36>

P46 = 2776050591687826340964640438188313241988097739_<46>

P65 = 19638843448420433381809909722623979282848939454441955452939170147_<65>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 43838688281452999209382287472067018505906351758921389540363873721972984740431326457383916438597688638236307286955968711139765929965483119754642619 (146 digits)
Using B1=3242000, B2=5707206970, polynomial Dickson(6), sigma=2430415712
Step 1 took 38250ms
Step 2 took 14281ms
********** Factor found in step 2: 804107783923129451039657356402486843
Found probable prime factor of 36 digits: 804107783923129451039657356402486843
Composite cofactor 54518422975052135935953956558967048083415118898869480584619417866224478054192616489161192182019931353786997633 has 110 digits

Number: n
N=54518422975052135935953956558967048083415118898869480584619417866224478054192616489161192182019931353786997633
  ( 110 digits)
Divisors found:
 r1=2776050591687826340964640438188313241988097739 (pp46)
 r2=19638843448420433381809909722623979282848939454441955452939170147 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 16.34 hours.
Scaled time: 29.87 units (timescale=1.828).
Factorization parameters were as follows:
name: KA_6_5_169_1
n: 54518422975052135935953956558967048083415118898869480584619417866224478054192616489161192182019931353786997633
Y0: -1907280307381663206726
Y1:  332678452343
c0:  899049179931483930219743873
c1: -50751007675298549806423
c2: -1403077213923752919
c3:  75397464258793
c4:  482168956
c5:  2160
skew: 32525.21
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 20000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1600000, 2160001)
Primes: RFBsize:230209, AFBsize:230958, largePrimes:16207647 encountered
Relations: rels:14256599, finalFF:544460
Max relations in full relation-set: 48
Initial matrix: 461242 x 544460 with sparse part having weight 61863544.
Pruned matrix : 397836 x 400206 with weight 37670194.
Total sieving time: 13.78 hours.
Total relation processing time: 0.51 hours.
Matrix solve time: 1.82 hours.
Total square root time: 0.22 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000
total time: 16.34 hours.
 --------- CPU info (if available) ----------

Jo Yeong Uk also found P36.

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 43838688281452999209382287472067018505906351758921389540363873721972984740431326457383916438597688638236307286955968711139765929965483119754642619 (146 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5417305544
Step 1 took 4727ms
Step 2 took 4493ms
********** Factor found in step 2: 804107783923129451039657356402486843
Found probable prime factor of 36 digits: 804107783923129451039657356402486843
Composite cofactor 54518422975052135935953956558967048083415118898869480584619417866224478054192616489161192182019931353786997633 has 110 digits

Aug 31, 2009

By Dmitry Domanov / GGNFS/msieve 1.42 / Aug 31, 2009

(16·10²⁰²-7)/9 = 1(7)₂₀₂_<203> = 23663522088959665379_<20> · 41175088192813174267_<20> · 1085821989830191408574448787_<28> · C137

C137 = P46 · P92

P46 = 1081532647714971214037755172969779401345844853_<46>

P92 = 15536932645254557221822951817675878742208962257314811273026340883379604360838433963316815599_<92>

Sieving ~ 18.5 cpu-days

Sun Aug 30 11:15:50 2009  Msieve v. 1.42
Sun Aug 30 11:15:50 2009  random seeds: bee3af00 d09e99d0
Sun Aug 30 11:15:50 2009  factoring 16803699901191332856731624940085075709418965141403433009136434244527057083294180228918835965492442107538029009528292583619187682264261947 (137 digits)
Sun Aug 30 11:15:52 2009  searching for 15-digit factors
Sun Aug 30 11:15:53 2009  commencing number field sieve (137-digit input)
Sun Aug 30 11:15:53 2009  R0: -291093131217969603025891500
Sun Aug 30 11:15:53 2009  R1:  926622307161661
Sun Aug 30 11:15:53 2009  A0: -30036619351616900804396764665813653
Sun Aug 30 11:15:53 2009  A1:  42857501262580016590013505029
Sun Aug 30 11:15:53 2009  A2:  97333981214042173293399
Sun Aug 30 11:15:53 2009  A3: -72897361794663101
Sun Aug 30 11:15:53 2009  A4: -63509433778
Sun Aug 30 11:15:53 2009  A5:  8040
Sun Aug 30 11:15:53 2009  skew 1401827.32, size 3.338525e-013, alpha -6.680700, combined = 3.197034e-011
Sun Aug 30 11:15:53 2009  
Sun Aug 30 11:15:53 2009  commencing relation filtering
Sun Aug 30 11:15:53 2009  estimated available RAM is 4094.1 MB
Sun Aug 30 11:15:53 2009  commencing duplicate removal, pass 1
Sun Aug 30 11:18:03 2009  error -6 reading relation 8603340
Sun Aug 30 11:21:44 2009  found 3672019 hash collisions in 23132690 relations
Sun Aug 30 11:23:26 2009  added 121221 free relations
Sun Aug 30 11:23:26 2009  commencing duplicate removal, pass 2
Sun Aug 30 11:24:44 2009  found 3326171 duplicates and 19927739 unique relations
Sun Aug 30 11:24:44 2009  memory use: 106.6 MB
Sun Aug 30 11:24:44 2009  reading ideals above 19595264
Sun Aug 30 11:24:59 2009  commencing singleton removal, initial pass
Sun Aug 30 11:30:51 2009  memory use: 298.4 MB
Sun Aug 30 11:30:51 2009  reading all ideals from disk
Sun Aug 30 11:30:51 2009  memory use: 326.5 MB
Sun Aug 30 11:30:53 2009  commencing in-memory singleton removal
Sun Aug 30 11:30:56 2009  begin with 19927739 relations and 19184707 unique ideals
Sun Aug 30 11:31:18 2009  reduce to 8405921 relations and 5821694 ideals in 19 passes
Sun Aug 30 11:31:18 2009  max relations containing the same ideal: 28
Sun Aug 30 11:31:20 2009  reading ideals above 100000
Sun Aug 30 11:31:20 2009  commencing singleton removal, initial pass
Sun Aug 30 11:34:58 2009  memory use: 149.2 MB
Sun Aug 30 11:34:58 2009  reading all ideals from disk
Sun Aug 30 11:34:59 2009  memory use: 326.5 MB
Sun Aug 30 11:35:01 2009  keeping 8264605 ideals with weight <= 200, target excess is 44720
Sun Aug 30 11:35:04 2009  commencing in-memory singleton removal
Sun Aug 30 11:35:06 2009  begin with 8407054 relations and 8264605 unique ideals
Sun Aug 30 11:35:35 2009  reduce to 8284360 relations and 8136440 ideals in 13 passes
Sun Aug 30 11:35:35 2009  max relations containing the same ideal: 200
Sun Aug 30 11:35:45 2009  removing 604136 relations and 556114 ideals in 48022 cliques
Sun Aug 30 11:35:46 2009  commencing in-memory singleton removal
Sun Aug 30 11:35:48 2009  begin with 7680224 relations and 8136440 unique ideals
Sun Aug 30 11:36:08 2009  reduce to 7647797 relations and 7547616 ideals in 10 passes
Sun Aug 30 11:36:08 2009  max relations containing the same ideal: 195
Sun Aug 30 11:36:18 2009  removing 436373 relations and 388351 ideals in 48022 cliques
Sun Aug 30 11:36:18 2009  commencing in-memory singleton removal
Sun Aug 30 11:36:20 2009  begin with 7211424 relations and 7547616 unique ideals
Sun Aug 30 11:36:36 2009  reduce to 7192976 relations and 7140672 ideals in 8 passes
Sun Aug 30 11:36:36 2009  max relations containing the same ideal: 186
Sun Aug 30 11:36:48 2009  relations with 0 large ideals: 129
Sun Aug 30 11:36:48 2009  relations with 1 large ideals: 111
Sun Aug 30 11:36:48 2009  relations with 2 large ideals: 1351
Sun Aug 30 11:36:48 2009  relations with 3 large ideals: 17575
Sun Aug 30 11:36:48 2009  relations with 4 large ideals: 127018
Sun Aug 30 11:36:48 2009  relations with 5 large ideals: 533702
Sun Aug 30 11:36:48 2009  relations with 6 large ideals: 1356073
Sun Aug 30 11:36:48 2009  relations with 7+ large ideals: 5157017
Sun Aug 30 11:36:48 2009  commencing 2-way merge
Sun Aug 30 11:37:02 2009  reduce to 4228031 relation sets and 4175727 unique ideals
Sun Aug 30 11:37:02 2009  commencing full merge
Sun Aug 30 11:39:22 2009  memory use: 438.0 MB
Sun Aug 30 11:39:23 2009  found 2185706 cycles, need 2181927
Sun Aug 30 11:39:24 2009  weight of 2181927 cycles is about 153056632 (70.15/cycle)
Sun Aug 30 11:39:24 2009  distribution of cycle lengths:
Sun Aug 30 11:39:24 2009  1 relations: 318590
Sun Aug 30 11:39:24 2009  2 relations: 287686
Sun Aug 30 11:39:24 2009  3 relations: 265305
Sun Aug 30 11:39:24 2009  4 relations: 224441
Sun Aug 30 11:39:24 2009  5 relations: 193393
Sun Aug 30 11:39:24 2009  6 relations: 158988
Sun Aug 30 11:39:24 2009  7 relations: 134476
Sun Aug 30 11:39:24 2009  8 relations: 111474
Sun Aug 30 11:39:24 2009  9 relations: 91852
Sun Aug 30 11:39:24 2009  10+ relations: 395722
Sun Aug 30 11:39:24 2009  heaviest cycle: 28 relations
Sun Aug 30 11:39:25 2009  commencing cycle optimization
Sun Aug 30 11:39:32 2009  start with 12568120 relations
Sun Aug 30 11:40:11 2009  pruned 267617 relations
Sun Aug 30 11:40:11 2009  memory use: 335.1 MB
Sun Aug 30 11:40:11 2009  distribution of cycle lengths:
Sun Aug 30 11:40:11 2009  1 relations: 318590
Sun Aug 30 11:40:11 2009  2 relations: 293890
Sun Aug 30 11:40:11 2009  3 relations: 273827
Sun Aug 30 11:40:11 2009  4 relations: 228287
Sun Aug 30 11:40:11 2009  5 relations: 196248
Sun Aug 30 11:40:11 2009  6 relations: 159693
Sun Aug 30 11:40:11 2009  7 relations: 134312
Sun Aug 30 11:40:11 2009  8 relations: 110397
Sun Aug 30 11:40:11 2009  9 relations: 90366
Sun Aug 30 11:40:11 2009  10+ relations: 376317
Sun Aug 30 11:40:11 2009  heaviest cycle: 28 relations
Sun Aug 30 11:40:24 2009  RelProcTime: 1471
Sun Aug 30 11:40:24 2009  
Sun Aug 30 11:40:24 2009  commencing linear algebra
Sun Aug 30 11:40:26 2009  read 2181927 cycles
Sun Aug 30 11:40:33 2009  cycles contain 7124612 unique relations
Sun Aug 30 11:47:52 2009  read 7124612 relations
Sun Aug 30 11:48:08 2009  using 20 quadratic characters above 268435034
Sun Aug 30 11:49:08 2009  building initial matrix
Sun Aug 30 11:51:23 2009  memory use: 814.7 MB
Sun Aug 30 11:51:31 2009  read 2181927 cycles
Sun Aug 30 11:55:11 2009  matrix is 2181750 x 2181927 (629.4 MB) with weight 206833828 (94.79/col)
Sun Aug 30 11:55:11 2009  sparse part has weight 147540980 (67.62/col)
Sun Aug 30 11:55:51 2009  filtering completed in 2 passes
Sun Aug 30 11:55:52 2009  matrix is 2180999 x 2181176 (629.4 MB) with weight 206805813 (94.81/col)
Sun Aug 30 11:55:52 2009  sparse part has weight 147535633 (67.64/col)
Sun Aug 30 11:56:09 2009  read 2181176 cycles
Sun Aug 30 12:02:33 2009  matrix is 2180999 x 2181176 (629.4 MB) with weight 206805813 (94.81/col)
Sun Aug 30 12:02:33 2009  sparse part has weight 147535633 (67.64/col)
Sun Aug 30 12:02:33 2009  saving the first 48 matrix rows for later
Sun Aug 30 12:02:35 2009  matrix is 2180951 x 2181176 (604.3 MB) with weight 164620917 (75.47/col)
Sun Aug 30 12:02:35 2009  sparse part has weight 145323930 (66.63/col)
Sun Aug 30 12:02:35 2009  matrix includes 64 packed rows
Sun Aug 30 12:02:35 2009  using block size 65536 for processor cache size 4096 kB
Sun Aug 30 12:02:59 2009  commencing Lanczos iteration (4 threads)
Sun Aug 30 12:02:59 2009  memory use: 673.2 MB
Sun Aug 30 20:35:43 2009  lanczos halted after 34495 iterations (dim = 2180951)
Sun Aug 30 20:35:49 2009  recovered 28 nontrivial dependencies
Sun Aug 30 20:35:52 2009  BLanczosTime: 32128
Sun Aug 30 20:35:52 2009  
Sun Aug 30 20:35:52 2009  commencing square root phase
Sun Aug 30 20:35:52 2009  reading relations for dependency 1
Sun Aug 30 20:35:54 2009  read 1092247 cycles
Sun Aug 30 20:35:57 2009  cycles contain 4349405 unique relations
Sun Aug 30 20:41:33 2009  read 4349405 relations
Sun Aug 30 20:42:16 2009  multiplying 3565232 relations
Sun Aug 30 21:00:27 2009  multiply complete, coefficients have about 168.77 million bits
Sun Aug 30 21:00:37 2009  initial square root is modulo 1139683
Sun Aug 30 21:22:39 2009  reading relations for dependency 2
Sun Aug 30 21:22:40 2009  read 1091237 cycles
Sun Aug 30 21:22:44 2009  cycles contain 4347764 unique relations
Sun Aug 30 21:29:18 2009  read 4347764 relations
Sun Aug 30 21:29:59 2009  multiplying 3563378 relations
Sun Aug 30 21:48:03 2009  multiply complete, coefficients have about 168.68 million bits
Sun Aug 30 21:48:13 2009  initial square root is modulo 1131341
Sun Aug 30 22:10:07 2009  reading relations for dependency 3
Sun Aug 30 22:10:08 2009  read 1090577 cycles
Sun Aug 30 22:10:12 2009  cycles contain 4345517 unique relations
Sun Aug 30 22:15:38 2009  read 4345517 relations
Sun Aug 30 22:16:19 2009  multiplying 3563306 relations
Sun Aug 30 22:34:24 2009  multiply complete, coefficients have about 168.68 million bits
Sun Aug 30 22:34:35 2009  initial square root is modulo 1131191
Sun Aug 30 22:56:32 2009  reading relations for dependency 4
Sun Aug 30 22:56:33 2009  read 1090876 cycles
Sun Aug 30 22:56:37 2009  cycles contain 4348230 unique relations
Sun Aug 30 23:02:54 2009  read 4348230 relations
Sun Aug 30 23:03:36 2009  multiplying 3564124 relations
Sun Aug 30 23:21:43 2009  multiply complete, coefficients have about 168.72 million bits
Sun Aug 30 23:21:53 2009  initial square root is modulo 1135019
Sun Aug 30 23:43:48 2009  sqrtTime: 11276
Sun Aug 30 23:43:48 2009  prp46 factor: 1081532647714971214037755172969779401345844853
Sun Aug 30 23:43:48 2009  prp92 factor: 15536932645254557221822951817675878742208962257314811273026340883379604360838433963316815599
Sun Aug 30 23:43:48 2009  elapsed time 12:27:58

Aug 30, 2009 (2nd)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Aug 30, 2009

(43·10¹⁷⁰-61)/9 = 4(7)₁₆₉1_<171> = 3⁴ · 2297 · 86142190922609442826319581_<26> · C140

C140 = P35 · P105

P35 = 61205871025572349031057520850672879_<35>

P105 = 487047071018647562838374099050351413427398683541739940812874899307923729937987987488512016099910123356097_<105>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 29810140212150119020193034504540165336135631922025659778353692043960704366721925412459175875355132428078825083113940577992345976016177193263 (140 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2242790170
Step 1 took 13962ms
Step 2 took 10124ms
********** Factor found in step 2: 61205871025572349031057520850672879
Found probable prime factor of 35 digits: 61205871025572349031057520850672879
Probable prime cofactor 487047071018647562838374099050351413427398683541739940812874899307923729937987987488512016099910123356097 has 105 digits

(59·10¹⁶⁵-41)/9 = 6(5)₁₆₄1_<166> = 15853671262377575120216579_<26> · C141

C141 = P46 · P95

P46 = 6340161287912131268161125425786578533212741867_<46>

P95 = 65219782716166814592146317374475128145739944922584322010120403135302390427100230848435276962207_<95>

Number: 65551_165
N=413503941583081550029323061610568526119686926032409887198149321241700574934648467048889309789763186916268930747752107818183593351933005620469
  ( 141 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=6340161287912131268161125425786578533212741867
 r2=65219782716166814592146317374475128145739944922584322010120403135302390427100230848435276962207
Version: 
Total time: 25.78 hours.
Scaled time: 61.36 units (timescale=2.380).
Factorization parameters were as follows:
n: 413503941583081550029323061610568526119686926032409887198149321241700574934648467048889309789763186916268930747752107818183593351933005620469
m: 1000000000000000000000000000000000
deg: 5
c5: 59
c0: -41
skew: 0.93
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2300000, 4400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10023616
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 759607 x 759855
Total sieving time: 23.19 hours.
Total relation processing time: 1.02 hours.
Matrix solve time: 1.18 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,51,51,2.4,2.4,100000
total time: 25.78 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

Aug 30, 2009

By Sinkiti Sibata / Msieve / Aug 30, 2009

(59·10¹⁵¹-41)/9 = 6(5)₁₅₀1_<152> = 786086982781_<12> · 435721903752358018180169_<24> · C117

C117 = P49 · P68

P49 = 4559565812653039995170667321098441921755424461139_<49>

P68 = 41976479907500678916377186105933586601154615587003436570164974072481_<68>

Number: 65551_151
N=191394522721757338189978481862379468868860410055039494993662461032118366979363583455183244670769264779036865753815859
  ( 117 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=4559565812653039995170667321098441921755424461139 (pp49)
 r2=41976479907500678916377186105933586601154615587003436570164974072481 (pp68)
Version: Msieve-1.40
Total time: 22.57 hours.
Scaled time: 47.06 units (timescale=2.085).
Factorization parameters were as follows:
name: 65551_151
n: 191394522721757338189978481862379468868860410055039494993662461032118366979363583455183244670769264779036865753815859
m: 1000000000000000000000000000000
deg: 5
c5: 590
c0: -41
skew: 0.59
type: snfs
lss: 1
rlim: 2500000
alim: 2500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1250000, 2150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 467967 x 468215
Total sieving time: 21.24 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.76 hours.
Time per square root: 0.43 hours.
Prototype def-par.txt line would be:
snfs,152.000,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000
total time: 22.57 hours.
 --------- CPU info (if available) ----------

Aug 29, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 29, 2009

(44·10¹⁶⁹-53)/9 = 4(8)₁₆₈3_<170> = 17 · 43 · 1630423 · 21750516732549499949_<20> · C142

C142 = P48 · P94

P48 = 489641797116893462699294028241035350517514338379_<48>

P94 = 3851628881325874837178721243483272939017889163594114474066555739511475683749623855910191557521_<94>

Number: 48883_169
N=1885918487279731334844061215429615053174211390022725930251012918160514773580971772193004553379869884756817593843749606903596980083631836398459
  ( 142 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=489641797116893462699294028241035350517514338379
 r2=3851628881325874837178721243483272939017889163594114474066555739511475683749623855910191557521
Version: 
Total time: 33.52 hours.
Scaled time: 78.24 units (timescale=2.334).
Factorization parameters were as follows:
n: 1885918487279731334844061215429615053174211390022725930251012918160514773580971772193004553379869884756817593843749606903596980083631836398459
m: 10000000000000000000000000000000000
deg: 5
c5: 22
c0: -265
skew: 1.64
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 5500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11061459
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 921196 x 921444
Total sieving time: 30.41 hours.
Total relation processing time: 0.79 hours.
Matrix solve time: 1.88 hours.
Time per square root: 0.45 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 33.52 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672349)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

(59·10¹⁵⁹-41)/9 = 6(5)₁₅₈1_<160> = 1451 · 6917 · 37094443609_<11> · 2598169745728791720663187707556303091_<37> · C106

C106 = P48 · P58

P48 = 820889968246951339790540386495386854270140538021_<48>

P58 = 8255872609163889121125670485890992574796509420461607010047_<58>

Number: 65551_159
N=6777163003987420249369446581356217664161110220076196504409799447202003922532945122069823146006361732496987
  ( 106 digits)
Divisors found:
 r1=820889968246951339790540386495386854270140538021
 r2=8255872609163889121125670485890992574796509420461607010047
Version: 
Total time: 5.41 hours.
Scaled time: 12.69 units (timescale=2.348).
Factorization parameters were as follows:
name: 65551_159
n: 6777163003987420249369446581356217664161110220076196504409799447202003922532945122069823146006361732496987
skew: 12582.78
# norm 1.29e+15
c5: 262440
c4: -4659048357
c3: -146542938404236
c2: 790340887867501438
c1: 8313308791385384666564
c0: -14544187091187097192015545
# alpha -7.04
Y1: 86304481709
Y0: -120893981641063169426
# Murphy_E 1.67e-09
# M 233941627322368526897049390385975758084765376780110111644521819338376892631029209741812043543819236488285
type: gnfs
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 1850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7132778
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 299772 x 300020
Polynomial selection time: 0.38 hours.
Total sieving time: 4.16 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000
total time: 5.41 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672349)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

(59·10¹⁴⁹-41)/9 = 6(5)₁₄₈1_<150> = 3² · 13 · 19851087923_<11> · 26776182667895359173751_<23> · C116

C116 = P54 · P62

P54 = 652082745253715773516074932609579615606989934537126869_<54>

P62 = 16165455891393350287819085890362832406948198797702538297578619_<62>

Number: 65551_149
N=10541214855937628876152464065866311686150262293869601020055860706093425225533958519391800940530932095752139904813911
  ( 116 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=652082745253715773516074932609579615606989934537126869
 r2=16165455891393350287819085890362832406948198797702538297578619
Version: 
Total time: 10.94 hours.
Scaled time: 26.12 units (timescale=2.387).
Factorization parameters were as follows:
n: 10541214855937628876152464065866311686150262293869601020055860706093425225533958519391800940530932095752139904813911
m: 1000000000000000000000000000000
deg: 5
c5: 59
c0: -410
skew: 1.47
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7377549
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 392381 x 392629
Total sieving time: 10.17 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 0.31 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000
total time: 10.94 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

Aug 29, 2009 (4th)

By Erik Branger / GGNFS, Msieve / Aug 29, 2009

(59·10¹⁴⁵-41)/9 = 6(5)₁₄₄1_<146> = 211 · 844447 · 37668119627_<11> · C127

C127 = P42 · P42 · P44

P42 = 549690954084227334046373836255244354233007_<42>

P42 = 721044887110064073265612393855556722934303_<42>

P44 = 24643354074993241023553893354420056835203009_<44>

Number: 65551_145
N=9767439025466310689382920239378941208099550425943607238692087452651281025110190773764650914274716357618807670061234159412815089
  ( 127 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=549690954084227334046373836255244354233007 (pp42)
 r2=721044887110064073265612393855556722934303 (pp42)
 r3=24643354074993241023553893354420056835203009 (pp44)
Version: Msieve v. 1.41
Total time: 14.27 hours.
Scaled time: 11.19 units (timescale=0.784).
Factorization parameters were as follows:
n: 9767439025466310689382920239378941208099550425943607238692087452651281025110190773764650914274716357618807670061234159412815089
m: 100000000000000000000000000000
deg: 5
c5: 59
c0: -41
skew: 0.93
type: snfs
lss: 1
rlim: 1960000
alim: 1960000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1960000/1960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [980000, 2180001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 318356 x 318596
Total sieving time: 13.32 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000
total time: 14.27 hours.
 --------- CPU info (if available) ----------

(49·10¹⁷¹-13)/9 = 5(4)₁₇₀3_<172> = 1309907 · 1509331 · 186135721123313863044793461731766127889_<39> · C122

C122 = P41 · P81

P41 = 78118283689308132829443292403611291227803_<41>

P81 = 189385269551937878693181478095539023949471844401877418236197269245497479472145737_<81>

Number: 54443_171
N=14794452213434372946420738528169896579615815849117777730825714913852145946553387018597884831622546553977005766909682325811
  ( 122 digits)
Divisors found:
 r1=78118283689308132829443292403611291227803 (pp41)
 r2=189385269551937878693181478095539023949471844401877418236197269245497479472145737 (pp81)
Version: Msieve v. 1.42
Total time: 94.54 hours.
Scaled time: 84.14 units (timescale=0.890).
Factorization parameters were as follows:
name: 54443_171
n: 14794452213434372946420738528169896579615815849117777730825714913852145946553387018597884831622546553977005766909682325811
skew: 100801.55
# norm 2.51e+016
c5: 15540
c4: -3524203548
c3: -420650336721402
c2: 65567099398070687185
c1: 4319439315112807051384690
c0: -690078891322799688013927425
# alpha -5.18
Y1: 25679226421157
Y0: -248731969491594434266556
# Murphy_E 2.31e-010
# M 413839379239698306525414216049804652849438324257727581695754799129246235176693693402226716314260713159272150579379954349
type: gnfs
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved algebraic special-q in [2350000, 4750001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : submatrix x not
Polynomial selection time: 6.85 hours.
Total sieving time: 82.76 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 4.47 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4700000,4700000,27,27,53,53,2.5,2.5,100000
total time: 94.54 hours.
 --------- CPU info (if available) ----------

Aug 29, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Aug 29, 2009

(59·10¹³⁶-41)/9 = 6(5)₁₃₅1_<137> = 311 · C135

C135 = P38 · P44 · P54

P38 = 26179380007226157021127248101170405337_<38>

P44 = 14297798976196798020082250427539153295127879_<44>

P54 = 563145436761579883955917094967740928748812991722141367_<54>

Number: n
N=210789567702750982493747767059664165773490532332976062879599857091818506609503394069310468024294390853876384423008217220435869953554841
  ( 135 digits)
SNFS difficulty: 137 digits.
Divisors found:

Sat Aug 29 01:44:27 2009  prp38 factor: 26179380007226157021127248101170405337
Sat Aug 29 01:44:27 2009  prp44 factor: 14297798976196798020082250427539153295127879
Sat Aug 29 01:44:27 2009  prp54 factor: 563145436761579883955917094967740928748812991722141367
Sat Aug 29 01:44:27 2009  elapsed time 00:16:47 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.02 hours.
Scaled time: 7.32 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_5_135_1
n: 210789567702750982493747767059664165773490532332976062879599857091818506609503394069310468024294390853876384423008217220435869953554841
m: 1000000000000000000000000000
deg: 5
c5: 590
c0: -41
skew: 0.59
type: snfs
lss: 1
rlim: 1380000
alim: 1380000
lpbr: 26
lpba: 26
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 50000
Factor base limits: 1380000/1380000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 56/56
Sieved  special-q in [690000, 1461797)
Primes: RFBsize:105690, AFBsize:105947, largePrimes:3177187 encountered
Relations: rels:3014745, finalFF:214239
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 323499 hash collisions in 3418073 relations
Msieve: matrix is 225284 x 225532 (60.0 MB)

Total sieving time: 3.96 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1380000,1380000,26,26,56,56,2.3,2.3,75000
total time: 4.02 hours.
 --------- CPU info (if available) ----------

(59·10¹⁵⁸-41)/9 = 6(5)₁₅₇1_<159> = 3³ · 7 · 449 · 1478429 · 8960605669_<10> · 972619078189867_<15> · C123

C123 = P48 · P76

P48 = 217923913046764811356626710395989581702567843659_<48>

P76 = 2751159983487564578438662871520344645588319823419937844950095840125164584947_<76>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 599543549019282937413245056494763681133772472976550903769136303031395960534601089463284130350567362781324328315687520801073 (123 digits)
Using B1=2958000, B2=4281751120, polynomial Dickson(6), sigma=962280220
Step 1 took 25656ms
Step 2 took 10953ms
********** Factor found in step 2: 217923913046764811356626710395989581702567843659
Found probable prime factor of 48 digits: 217923913046764811356626710395989581702567843659
Probable prime cofactor 2751159983487564578438662871520344645588319823419937844950095840125164584947 has 76 digits

Aug 29, 2009 (2nd)

By Sinkiti Sibata / Msieve / Aug 29, 2009

(59·10¹⁴⁸-41)/9 = 6(5)₁₄₇1_<149> = 26728403302199_<14> · 533273908107113_<15> · C121

C121 = P47 · P74

P47 = 90745693245729358517082419197212783245968267481_<47>

P74 = 50682745018821389408300370756291566831716285785457828913075299356070158233_<74>

Number: 65551_148
N=4599240832329483446438911438293912091197844869217679103966516381860976339020948840206178483537950205688304180256538321073
  ( 121 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=90745693245729358517082419197212783245968267481 (pp47)
 r2=50682745018821389408300370756291566831716285785457828913075299356070158233 (pp74)
Version: Msieve-1.40
Total time: 21.67 hours.
Scaled time: 43.75 units (timescale=2.019).
Factorization parameters were as follows:
name: 65551_148
n: 4599240832329483446438911438293912091197844869217679103966516381860976339020948840206178483537950205688304180256538321073
m: 500000000000000000000000000000
deg: 5
c5: 472
c0: -1025
skew: 1.17
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4

*1 These parameters were not fully adjusted. The approximate expressions which were 
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 2050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 437631 x 437879
Total sieving time: 20.54 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.67 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 21.67 hours.
 --------- CPU info (if available) ----------

Aug 29, 2009

By Dmitry Domanov / ECMNET / Aug 29, 2009

(59·10¹⁵³-41)/9 = 6(5)₁₅₂1_<154> = 71 · C152

C152 = P38 · C115

P38 = 31547078069965587199548803369110194703_<38>

C115 = [2926793035581032985985372497805728366509485826817219355709884856091272013245694366598974490036970962573306601872327_<115>]

C152=P38*C115
C152=31547078069965587199548803369110194703<38>*2926793035581032985985372497805728366509485826817219355709884856091272013245694366598974490036970962573306601872327<115>

(59·10¹⁵⁴-41)/9 = 6(5)₁₅₃1_<155> = 3797 · C152

C152 = P36 · C117

P36 = 159093639765504071562915217735497341_<36>

C117 = [108521574776952115645717588039054192051980803534687113921049522702179053232133262478345190473870479199937478718448863_<117>]

C152=P36*C117
C152=159093639765504071562915217735497341<36>*108521574776952115645717588039054192051980803534687113921049522702179053232133262478345190473870479199937478718448863<117>

Aug 28, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, YAFU 1.10, GMP-ECM / Aug 28, 2009

(59·10¹¹⁰-41)/9 = 6(5)₁₀₉1_<111> = 3 · 7² · 103 · 16665469 · C100

C100 = P36 · P65

P36 = 100569868188240422212672513519393283_<36>

P65 = 25832683422264164337538558517870859590637727898173160332304112293_<65>

Number: 65551_110
N=2597989566725650502849872479791838917651440564302408490731586236718833328085585735067306147261927919
  ( 100 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=100569868188240422212672513519393283
 r2=25832683422264164337538558517870859590637727898173160332304112293
Version: 
Total time: 0.38 hours.
Scaled time: 0.91 units (timescale=2.388).
Factorization parameters were as follows:
n: 2597989566725650502849872479791838917651440564302408490731586236718833328085585735067306147261927919
m: 10000000000000000000000
deg: 5
c5: 59
c0: -41
skew: 0.93
type: snfs
lss: 1
rlim: 320000
alim: 320000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 320000/320000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [160000, 300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 1042212
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 40915 x 41147
Total sieving time: 0.34 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,320000,320000,25,25,44,44,2.2,2.2,20000
total time: 0.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673788)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)

(59·10¹³⁰-41)/9 = 6(5)₁₂₉1_<131> = 863 · 12380033 · 578081849930021_<15> · 1286027650661759_<16> · C91

C91 = P46 · P46

P46 = 1874536995577468817771844750195374139545485531_<46>

P46 = 4402944871230901384323087592619302612598638441_<46>

08/27/09 23:30:17 v1.10 @ 조영욱-PC, starting SIQS on c91: 8253483050610399201614656565498306273254000866702463502996230748570396254465732878865897171
08/27/09 23:30:17 v1.10 @ 조영욱-PC, random seeds: 131344719, 45773372
08/27/09 23:30:18 v1.10 @ 조영욱-PC, ==== sieve params ====
08/27/09 23:30:18 v1.10 @ 조영욱-PC, n = 91 digits, 307 bits
08/27/09 23:30:18 v1.10 @ 조영욱-PC, factor base: 70662 primes (max prime = 1893187)
08/27/09 23:30:18 v1.10 @ 조영욱-PC, single large prime cutoff: 227182440 (120 * pmax)
08/27/09 23:30:18 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
08/27/09 23:30:18 v1.10 @ 조영욱-PC, double large prime cutoff: 1100207414487985
08/27/09 23:30:18 v1.10 @ 조영욱-PC, using 16 large prime slices of factor base
08/27/09 23:30:18 v1.10 @ 조영욱-PC, buckets hold 1024 elements
08/27/09 23:30:18 v1.10 @ 조영욱-PC, sieve interval: 11 blocks of size 65536
08/27/09 23:30:18 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors
08/27/09 23:30:18 v1.10 @ 조영욱-PC, using multiplier of 19
08/27/09 23:30:18 v1.10 @ 조영욱-PC, using small prime variation correction of 22 bits
08/27/09 23:30:18 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
08/27/09 23:30:18 v1.10 @ 조영욱-PC, trial factoring cutoff at 97 bits
08/27/09 23:30:18 v1.10 @ 조영욱-PC, ==== sieving started ====
08/28/09 00:26:05 v1.10 @ 조영욱-PC, sieve time = 1542.6450, relation time = 702.4350, poly_time = 1100.0520
08/28/09 00:26:05 v1.10 @ 조영욱-PC, 70735 relations found: 20355 full + 50380 from 853952 partial, using 471953 polys (230 A polys)
08/28/09 00:26:05 v1.10 @ 조영욱-PC, on average, sieving found 1.85 rels/poly and 261.20 rels/sec
08/28/09 00:26:05 v1.10 @ 조영욱-PC, trial division touched 26612272 sieve locations out of 680458059776
08/28/09 00:26:05 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
08/28/09 00:26:05 v1.10 @ 조영욱-PC, begin with 874307 relations
08/28/09 00:26:06 v1.10 @ 조영욱-PC, reduce to 163723 relations in 9 passes
08/28/09 00:26:07 v1.10 @ 조영욱-PC, recovered 163723 relations
08/28/09 00:26:07 v1.10 @ 조영욱-PC, recovered 138447 polynomials
08/28/09 00:26:07 v1.10 @ 조영욱-PC, attempting to build 70735 cycles
08/28/09 00:26:07 v1.10 @ 조영욱-PC, found 70735 cycles in 4 passes
08/28/09 00:26:07 v1.10 @ 조영욱-PC, distribution of cycle lengths:
08/28/09 00:26:07 v1.10 @ 조영욱-PC,    length 1 : 20355
08/28/09 00:26:07 v1.10 @ 조영욱-PC,    length 2 : 15712
08/28/09 00:26:07 v1.10 @ 조영욱-PC,    length 3 : 13220
08/28/09 00:26:07 v1.10 @ 조영욱-PC,    length 4 : 8823
08/28/09 00:26:07 v1.10 @ 조영욱-PC,    length 5 : 5767
08/28/09 00:26:07 v1.10 @ 조영욱-PC,    length 6 : 3219
08/28/09 00:26:07 v1.10 @ 조영욱-PC,    length 7 : 1799
08/28/09 00:26:07 v1.10 @ 조영욱-PC,    length 9+: 1840
08/28/09 00:26:07 v1.10 @ 조영욱-PC, largest cycle: 19 relations
08/28/09 00:26:08 v1.10 @ 조영욱-PC, matrix is 70662 x 70735 (17.6 MB) with weight 4054145 (57.31/col)
08/28/09 00:26:08 v1.10 @ 조영욱-PC, sparse part has weight 4054145 (57.31/col)
08/28/09 00:26:08 v1.10 @ 조영욱-PC, filtering completed in 3 passes
08/28/09 00:26:08 v1.10 @ 조영욱-PC, matrix is 65082 x 65146 (16.4 MB) with weight 3786317 (58.12/col)
08/28/09 00:26:08 v1.10 @ 조영욱-PC, sparse part has weight 3786317 (58.12/col)
08/28/09 00:26:08 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
08/28/09 00:26:08 v1.10 @ 조영욱-PC, matrix is 65034 x 65146 (11.3 MB) with weight 3022515 (46.40/col)
08/28/09 00:26:08 v1.10 @ 조영욱-PC, sparse part has weight 2318790 (35.59/col)
08/28/09 00:26:08 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
08/28/09 00:26:08 v1.10 @ 조영욱-PC, using block size 26058 for processor cache size 4096 kB
08/28/09 00:26:09 v1.10 @ 조영욱-PC, commencing Lanczos iteration
08/28/09 00:26:09 v1.10 @ 조영욱-PC, memory use: 9.9 MB
08/28/09 00:26:30 v1.10 @ 조영욱-PC, lanczos halted after 1030 iterations (dim = 65030)
08/28/09 00:26:30 v1.10 @ 조영욱-PC, recovered 15 nontrivial dependencies
08/28/09 00:26:31 v1.10 @ 조영욱-PC, prp46 = 4402944871230901384323087592619302612598638441
08/28/09 00:26:33 v1.10 @ 조영욱-PC, prp46 = 1874536995577468817771844750195374139545485531
08/28/09 00:26:33 v1.10 @ 조영욱-PC, Lanczos elapsed time = 25.0990 seconds.
08/28/09 00:26:33 v1.10 @ 조영욱-PC, Sqrt elapsed time = 3.2240 seconds.
08/28/09 00:26:33 v1.10 @ 조영욱-PC, SIQS elapsed time = 3375.6350 seconds.
08/28/09 00:26:33 v1.10 @ 조영욱-PC, 
08/28/09 00:26:33 v1.10 @ 조영욱-PC,

(59·10¹²⁸-41)/9 = 6(5)₁₂₇1_<129> = 3 · 7 · 11273 · 807217798013115349249_<21> · C103

C103 = P35 · P69

P35 = 15687391337389820067594699621928049_<35>

P69 = 218680088493350538687823046086955801253237178180069851711522664388347_<69>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 3430520125890226509593731402569423321015647527360602456706265755347841481793027317214936054879428045003 (103 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6225541169
Step 1 took 3463ms
Step 2 took 3682ms
********** Factor found in step 2: 15687391337389820067594699621928049
Found probable prime factor of 35 digits: 15687391337389820067594699621928049
Probable prime cofactor 218680088493350538687823046086955801253237178180069851711522664388347 has 69 digits

(59·10¹³²-41)/9 = 6(5)₁₃₁1_<133> = 19 · 83 · 2161 · 2602723 · C120

C120 = P35 · P86

P35 = 64762468536958753275997370026592189_<35>

P86 = 11412261060476583010801648653588374466659404427949117412495467433944876668021019371489_<86>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 739086197864674243080103063204723838549459620630445797290182833000541981305222698078503131350548820404722187029296699421 (120 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3807268069
Step 1 took 4180ms
Step 2 took 4041ms
********** Factor found in step 2: 64762468536958753275997370026592189
Found probable prime factor of 35 digits: 64762468536958753275997370026592189
Probable prime cofactor 11412261060476583010801648653588374466659404427949117412495467433944876668021019371489 has 86 digits

(59·10¹⁶¹-41)/9 = 6(5)₁₆₀1_<162> = 3 · 13² · 29 · 4703 · 8394739 · 3133872767_<10> · 143369462659_<12> · 6687547849938316622715871634891_<31> · C96

C96 = P39 · P58

P39 = 356847838604780119196330765207415979007_<39>

P58 = 1053254630446441697498609349401656856796194164343781800341_<58>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 375851638375289155490915074834142837946749360995064073843851662872671638502051544695517521441387 (96 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5608720449
Step 1 took 2980ms
Step 2 took 3260ms
********** Factor found in step 2: 356847838604780119196330765207415979007
Found probable prime factor of 39 digits: 356847838604780119196330765207415979007
Probable prime cofactor 1053254630446441697498609349401656856796194164343781800341 has 58 digits

(38·10¹⁶⁹-11)/9 = 4(2)₁₆₈1_<170> = 17² · 83 · 211 · 2339 · 244251602108399660808017_<24> · C137

C137 = P50 · P88

P50 = 12643456665765147374218786433570546868392699029511_<50>

P88 = 1154912892544551407467844162921108648037743984077350799609066744377902172336659747050721_<88>

Number: 42221_169
N=14602091109620515869366332015142728586054934512934342589581239347419963235977351626438610141371466520699267476440359057526064881192827431
  ( 137 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=12643456665765147374218786433570546868392699029511
 r2=1154912892544551407467844162921108648037743984077350799609066744377902172336659747050721
Version: 
Total time: 39.39 hours.
Scaled time: 94.03 units (timescale=2.387).
Factorization parameters were as follows:
n: 14602091109620515869366332015142728586054934512934342589581239347419963235977351626438610141371466520699267476440359057526064881192827431
m: 10000000000000000000000000000000000
deg: 5
c5: 19
c0: -55
skew: 1.24
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 5900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11130436
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1006398 x 1006645
Total sieving time: 35.52 hours.
Total relation processing time: 1.32 hours.
Matrix solve time: 2.29 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,52,52,2.4,2.4,100000
total time: 39.39 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673788)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)

(59·10¹⁵⁹-41)/9 = 6(5)₁₅₈1_<160> = 1451 · 6917 · 37094443609_<11> · C143

C143 = P37 · C106

P37 = 2598169745728791720663187707556303091_<37>

C106 = [6777163003987420249369446581356217664161110220076196504409799447202003922532945122069823146006361732496987_<106>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 17608219878832569939402941493323999511486423867559456103886959410813000481338848062703009217991518592534765451863274229281547530390998016286817 (143 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6442492946
Step 1 took 4048ms
Step 2 took 2450ms
********** Factor found in step 2: 2598169745728791720663187707556303091
Found probable prime factor of 37 digits: 2598169745728791720663187707556303091
Composite cofactor 6777163003987420249369446581356217664161110220076196504409799447202003922532945122069823146006361732496987 has 106 digits

Aug 28, 2009 (3rd)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve / Aug 28, 2009

(59·10¹¹⁸-41)/9 = 6(5)₁₁₇1_<119> = 71 · C117

C117 = P48 · P70

P48 = 342040803041321313688302451689958483852221604999_<48>

P70 = 2699437247460560632206497429854420932366137288553121858772250208311119_<70>

Number: n
N=923317683881064162754303599374021909233176838810641627543035993740219092331768388106416275430359937402190923317683881
  ( 117 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=342040803041321313688302451689958483852221604999 (pp48)
 r2=2699437247460560632206497429854420932366137288553121858772250208311119 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.60 hours.
Scaled time: 2.91 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_5_117_1
n: 923317683881064162754303599374021909233176838810641627543035993740219092331768388106416275430359937402190923317683881
m: 500000000000000000000000
deg: 5
c5: 472
c0: -1025
skew: 1.17
type: snfs
lss: 1
rlim: 740000
alim: 740000
mfbr: 56
mfba: 56
rlambda: 2.2
alambda: 2.2
qintsize: 50000
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 56/56
Sieved rational special-q in [370000, 720001)
Primes: RFBsize:59531, AFBsize:59694, largePrimes:1359196 encountered
Relations: rels:1337738, finalFF:155412
Max relations in full relation-set: 48
Initial matrix: 119292 x 155412 with sparse part having weight 7787649.
Pruned matrix : 106776 x 107436 with weight 4030051.
Total sieving time: 1.49 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Total square root time: 0.05 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,56,56,2.2,2.2,50000
total time: 1.60 hours.
 --------- CPU info (if available) ----------

(59·10¹¹⁹-41)/9 = 6(5)₁₁₈1_<120> = 3 · 13 · 547 · 556399 · 31606445333_<11> · C100

C100 = P34 · P67

P34 = 1238586755744250042256057931648171_<34>

P67 = 1410811987959398448543925216694404844029838755220880952470146831371_<67>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 1747413043131727277788190198313073799579267718733141705256364062479384714596122432332591695237572441 (100 digits)
Using B1=726000, B2=696728352, polynomial Dickson(3), sigma=672678217
Step 1 took 5031ms
Step 2 took 2625ms
********** Factor found in step 2: 1238586755744250042256057931648171
Found probable prime factor of 34 digits: 1238586755744250042256057931648171
Probable prime cofactor 1410811987959398448543925216694404844029838755220880952470146831371 has 67 digits

(16·10²²¹-61)/9 = 1(7)₂₂₀1_<222> = 3 · 11 · C220

C220 = P74 · P147

P74 = 40547480142119922688518914038786161136818885750756170028782710211441154919_<74>

P147 = 132861656712651410768724637841254958549779105856049539596201523367987125563433527252580925341831118918802493988686721629211532202122209163723587773_<147>

Number: n
N=5387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387
  ( 220 digits)
SNFS difficulty: 222 digits.
Divisors found:

Fri Aug 28 17:17:55 2009  prp74 factor: 40547480142119922688518914038786161136818885750756170028782710211441154919
Fri Aug 28 17:17:55 2009  prp147 factor: 132861656712651410768724637841254958549779105856049539596201523367987125563433527252580925341831118918802493988686721629211532202122209163723587773
Fri Aug 28 17:17:55 2009  elapsed time 67:04:23 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 174.43 hours.
Scaled time: 351.30 units (timescale=2.014).
Factorization parameters were as follows:
name: KA_1_7_220_1
n: 5387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387
m: 10000000000000000000000000000000000000
deg: 6
c6: 8
c0: -305
skew: 1.83
type: snfs
lss: 1
rlim: 36000000
alim: 36000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 36000000/36000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [18000000, 54149990)
Primes: RFBsize:2204262, AFBsize:2201981, largePrimes:38297939 encountered
Relations: rels:36171342, finalFF:1790359
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 9529631 hash collisions in 52517034 relations
Msieve: matrix is 5639739 x 5639987 (1521.0 MB)

Total sieving time: 172.55 hours.
Total relation processing time: 1.88 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,222,6,0,0,0,0,0,0,0,0,36000000,36000000,29,29,58,58,2.6,2.6,100000
total time: 174.43 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3352028k/3407296k available (3120k kernel code, 53984k reserved, 1898k data, 424k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.41 BogoMIPS (lpj=2830706)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830451)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Total of 4 processors activated (22644.14 BogoMIPS).

c220 is the third largest number factored by SNFS in our tables so far. Congratulations!

Aug 28, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3, yafu, Msieve / Aug 28, 2009

(59·10¹⁴²-41)/9 = 6(5)₁₄₁1_<143> = 131 · 1402671779_<10> · 3596836632895354892741_<22> · C110

C110 = P31 · P39 · P42

P31 = 1279201868994144050132194828067_<31>

P39 = 137662433006997570220530848318162243587_<39>

P42 = 563257402843915535764008602767320453683491_<42>

Input number is 99188525553478613740693018714173592981572951837275851680687204631968974415083826327584353647304252763642664539 (110 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3055685713
Step 1 took 2305ms
Step 2 took 1920ms
********** Factor found in step 2: 1279201868994144050132194828067
Found probable prime factor of 31 digits: 1279201868994144050132194828067
Composite cofactor has 80 digits

starting SIQS on c80: 77539384484695965128406068996129563971417687858859427676654726298502214942522217
==== sieve params ====
n = 80 digits, 266 bits
...
Lanczos elapsed time = 4.8700 seconds.
Sqrt elapsed time = 0.5300 seconds.
SIQS elapsed time = 379.4000 seconds.
***factors found***
PRP39 = 137662433006997570220530848318162243587
PRP42 = 563257402843915535764008602767320453683491

(59·10¹⁴⁷-41)/9 = 6(5)₁₄₆1_<148> = 3863 · 28901 · 8004709 · 77945136156599114050070531_<26> · C107

C107 = P33 · P75

P33 = 266941962748313436907550064124241_<33>

P75 = 352549827314674485749210699129788765635093418756045159371124172879548044443_<75>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1124467645
Step 1 took 6828ms
Step 2 took 4264ms
********** Factor found in step 2: 266941962748313436907550064124241
Found probable prime factor of 33 digits: 266941962748313436907550064124241
Probable prime cofactor has 75 digits

(59·10¹⁸⁵-41)/9 = 6(5)₁₈₄1_<186> = 3³ · 13 · C184

C184 = P31 · P153

P31 = 3314037138425310906358457868773_<31>

P153 = 563566299183015474614878269645043450470219877270863059769326842164610494746548875667368937571772996793911384692710424597648306758405487025010001461232237_<153>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=3092775926
Step 1 took 8885ms
Step 2 took 4720ms
********** Factor found in step 2: 3314037138425310906358457868773
Found probable prime factor of 31 digits: 3314037138425310906358457868773
Probable prime cofactor has 153 digits

(59·10¹⁷⁶-41)/9 = 6(5)₁₇₅1_<177> = 3² · 7 · 241 · 47977 · 93149814203_<11> · C157

C157 = P38 · P120

P38 = 38625847807622427747634970352985604971_<38>

P120 = 250125980536769192609880404461832864559611828012339046983407808013266788748920882215142885060832727293121873895915028897_<120>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=1022211378
Step 1 took 7720ms
Step 2 took 4092ms
********** Factor found in step 2: 38625847807622427747634970352985604971
Found probable prime factor of 38 digits: 38625847807622427747634970352985604971
Probable prime cofactor has 120 digits

(59·10¹⁴⁰-41)/9 = 6(5)₁₃₉1_<141> = 3² · 7 · 2319241 · C133

C133 = P34 · P36 · P64

P34 = 1121072026810203394520355219374897_<34>

P36 = 665636968570409833311374016398251961_<36>

P64 = 6012458927193535206829524119375218118645993092105672468842645041_<64>

SNFS difficulty: 141 digits.
Divisors found:
 r1=1121072026810203394520355219374897 (pp34)
 r2=665636968570409833311374016398251961 (pp36)
 r3=6012458927193535206829524119375218118645993092105672468842645041 (pp64)
Version: Msieve v. 1.43
Total time: 2.99 hours.
Scaled time: 7.17 units (timescale=2.400).
Factorization parameters were as follows:
n: 4486659100532058682304100237524721368070693704956523410204305520201252181384187214255470781348572114315447299528442166629976061308697
m: 10000000000000000000000000000
deg: 5
c5: 59
c0: -41
skew: 0.93
type: snfs
lss: 1
rlim: 1610000
alim: 1610000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1610000/1610000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [805000, 1605001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 251292 x 251517
Total sieving time: 2.84 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000
total time: 2.99 hours.

Aug 28, 2009

By Erik Branger / GGNFS, Msieve / Aug 28, 2009

(59·10¹¹¹-41)/9 = 6(5)₁₁₀1_<112> = C112

C112 = P34 · P79

P34 = 2453439594373098072663247600625437_<34>

P79 = 2671985717761528403081198923694369774910242295609051984693196496700468164596523_<79>

Number: 65551_111
N=6555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551
  ( 112 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=2453439594373098072663247600625437 (pp34)
 r2=2671985717761528403081198923694369774910242295609051984693196496700468164596523 (pp79)
Version: Msieve v. 1.41
Total time: 1.74 hours.
Scaled time: 1.37 units (timescale=0.788).
Factorization parameters were as follows:
n: 6555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551
m: 10000000000000000000000
deg: 5
c5: 590
c0: -41
skew: 0.59
type: snfs
lss: 1
rlim: 530000
alim: 530000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 530000/530000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [265000, 465001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 53595 x 53823
Total sieving time: 1.69 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,112.000,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000
total time: 1.74 hours.
 --------- CPU info (if available) ----------

Aug 27, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.3 / Aug 27, 2009

4·10²⁴³+9 = 4(0)₂₄₂9_<244> = 211 · 761 · C239

C239 = P42 · P198

P42 = 127566948277192337869764297638109721127023_<42>

P198 = 195278627055004260165165796713698923970426519764143364350420080659555185314378363696270057757429282480559027603944657848259735353558435498871600913917817557530384015450970490735110900823076695659173_<198>

Run 578 out of 1000:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3161935447
Step 1 took 57743ms
Step 2 took 20450ms
********** Factor found in step 2: 127566948277192337869764297638109721127023
Found probable prime factor of 42 digits: 127566948277192337869764297638109721127023
Probable prime cofactor has 198 digits

4·10²⁰⁴+9 = 4(0)₂₀₃9_<205> = 13³ · 3163073222102835073_<19> · C183

C183 = P33 · C151

P33 = 104371341092297168434106963028253_<33>

C151 = [5514922642801281170779376780759437194775023248270464884245911662908683979158794827643748726590188350303750194354785166138207825960686703194983314150313_<151>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3928819928
Step 1 took 12684ms
Step 2 took 6453ms
********** Factor found in step 2: 104371341092297168434106963028253
Found probable prime factor of 33 digits: 104371341092297168434106963028253
Composite cofactor has 151 digits

Aug 27, 2009 (2nd)

Factorizations of 655...551 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Aug 27, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 27, 2009

(34·10¹⁶⁹+11)/9 = 3(7)₁₆₈9_<170> = 3³ · 13 · 6316473139_<10> · 407799232266689_<15> · 75988493960251357_<17> · C126

C126 = P53 · P74

P53 = 18996040647697883281745471417581144798771086079754053_<53>

P74 = 28946583100012908073644120379111826298817121794389208345765758626662639919_<74>

Number: 37779_169
N=549870469179809804400773189900652481997984884146536985427414341642160967172160491609374388356461473305517418822641431219841707
  ( 126 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=18996040647697883281745471417581144798771086079754053
 r2=28946583100012908073644120379111826298817121794389208345765758626662639919
Version: 
Total time: 35.34 hours.
Scaled time: 84.18 units (timescale=2.382).
Factorization parameters were as follows:
n: 549870469179809804400773189900652481997984884146536985427414341642160967172160491609374388356461473305517418822641431219841707
m: 10000000000000000000000000000000000
deg: 5
c5: 17
c0: 55
skew: 1.26
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 5600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11191619
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 933173 x 933421
Total sieving time: 32.04 hours.
Total relation processing time: 1.13 hours.
Matrix solve time: 1.94 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,52,52,2.4,2.4,100000
total time: 35.34 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672386)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672380)

Aug 26, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Aug 26, 2009

(37·10¹⁸⁷+71)/9 = 4(1)₁₈₆9_<188> = 7 · 131² · 347 · 449 · 787 · 3793 · 54751 · 98240367022528967_<17> · 11521275019116676381_<20> · C131

C131 = P39 · P92

P39 = 469202909278931356117976919565489527769_<39>

P92 = 25307073155146640842672255497156160022227569263192069413856806792430390779517568555111001253_<92>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3909651050
Step 1 took 38287ms
Step 2 took 14195ms
********** Factor found in step 2: 469202909278931356117976919565489527769
Found probable prime factor of 39 digits: 469202909278931356117976919565489527769
Probable prime cofactor 25307073155146640842672255497156160022227569263192069413856806792430390779517568555111001253 has 92 digits

(7·10²⁰⁵-43)/9 = (7)₂₀₄3_<205> = 3⁴ · 17 · C202

C202 = P62 · P69 · P72

P62 = 62604108974342978505062826478040576438184094528258457506805873_<62>

P69 = 662021298149734281561229659528509403900190047328271154405447199062439_<69>

P72 = 136284601949026682390730569825694949184102512515689530468924678839170267_<72>

Number: 77773_205
N=5648349874929395626563382554667957718066650528524166868393447914145081901073186476236585169047042685386911966432663600419591704994755103687565561203905430484951182118938110223513273622206084079722423949
  ( 202 digits)
SNFS difficulty: 205 digits.
Divisors found:
 r1=62604108974342978505062826478040576438184094528258457506805873
 r2=662021298149734281561229659528509403900190047328271154405447199062439
 r3=136284601949026682390730569825694949184102512515689530468924678839170267
Version: 
Total time: 1118.63 hours.
Scaled time: 2254.03 units (timescale=2.015).
Factorization parameters were as follows:
n: 5648349874929395626563382554667957718066650528524166868393447914145081901073186476236585169047042685386911966432663600419591704994755103687565561203905430484951182118938110223513273622206084079722423949
m: 100000000000000000000000000000000000000000
deg: 5
c5: 7
c0: -43
skew: 1.44
type: snfs
lss: 1
rlim: 18900000
alim: 18900000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 18900000/18900000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [9450000, 21450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3577131 x 3577378
Total sieving time: 1118.63 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,205,5,0,0,0,0,0,0,0,0,18900000,18900000,29,29,56,56,2.6,2.6,100000
total time: 1118.63 hours.
 --------- CPU info (if available) ----------

Aug 26, 2009

By Erik Branger / GGNFS, Msieve / Aug 26, 2009

(34·10¹⁶²+11)/9 = 3(7)₁₆₁9_<163> = 47 · 459443 · 67124546794083294248340603185287579_<35> · C121

C121 = P60 · P62

P60 = 106851167940478740045730236724328448611032403830368245522011_<60>

P62 = 24391935925025616413012597364043838783569401954353983491549671_<62>

Number: 37779_162
N=2606306841918308784669025209898688038053573715705451307168694698444179234703434235423308619590868129220762915004730308381
  ( 121 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=106851167940478740045730236724328448611032403830368245522011 (pp60)
 r2=24391935925025616413012597364043838783569401954353983491549671 (pp62)
Version: Msieve v. 1.42
Total time: 59.21 hours.
Scaled time: 23.39 units (timescale=0.395).
Factorization parameters were as follows:
n: 2606306841918308784669025209898688038053573715705451307168694698444179234703434235423308619590868129220762915004730308381
m: 200000000000000000000000000000000
deg: 5
c5: 425
c0: 44
skew: 0.64
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 4100001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 728523 x 728749
Total sieving time: 56.59 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 2.13 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,164.000,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 59.21 hours.
 --------- CPU info (if available) ----------

Aug 25, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 25, 2009

(32·10¹⁶⁹-23)/9 = 3(5)₁₆₈3_<170> = 3² · 11 · 1823 · 2846155130424323406378163_<25> · C140

C140 = P49 · P92

P49 = 3054037465657598396665128463543860241767984014899_<49>

P92 = 22664841036145811481509986875433404714496667158274671465882815159605493593530416205438845997_<92>

Number: 35559_169
N=69219273677563090593398149236428754097982185713146430612942470417139285929049376313365862167983876981615989343694701114817723025993414509303
  ( 140 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=3054037465657598396665128463543860241767984014899
 r2=22664841036145811481509986875433404714496667158274671465882815159605493593530416205438845997
Version: 
Total time: 26.26 hours.
Scaled time: 62.73 units (timescale=2.389).
Factorization parameters were as follows:
n: 69219273677563090593398149236428754097982185713146430612942470417139285929049376313365862167983876981615989343694701114817723025993414509303
m: 20000000000000000000000000000000000
deg: 5
c5: 1
c0: -230
skew: 2.97
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 4800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10687531
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 861414 x 861662
Total sieving time: 23.85 hours.
Total relation processing time: 0.67 hours.
Matrix solve time: 1.66 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 26.26 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.62 BogoMIPS (lpj=2673813)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672386)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

Aug 25, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Aug 25, 2009

8·10¹⁹⁸+3 = 8(0)₁₉₇3_<199> = 11 · 53 · C197

C197 = P43 · P155

P43 = 1350678383321052486001773788083398163612589_<43>

P155 = 10159433288577617053454552915986316337776945515442442225397613087026136705762770406500515286186663991881893416281217389552885939501195077102302205387682969_<155>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=184675988
Step 1 took 75436ms
Step 2 took 22771ms
********** Factor found in step 2: 1350678383321052486001773788083398163612589
Found probable prime factor of 43 digits: 1350678383321052486001773788083398163612589
Probable prime cofactor 10159433288577617053454552915986316337776945515442442225397613087026136705762770406500515286186663991881893416281217389552885939501195077102302205387682969 has 155 digits

Aug 25, 2009

By Dmitry Domanov / ECMNET, GMP-ECM, GGNFS/msieve 1.42 / Aug 25, 2009

(16·10²⁴⁴-7)/9 = 1(7)₂₄₄_<245> = 357131 · 5718499 · 50074501 · 49725910634419_<14> · C211

C211 = P50 · P162

P50 = 18626347316752091887613730912259192759279958920129_<50>

P162 = 187689856289552606645258672395266771629129914562572777562468039096119103199366120307762823572047220965155854278003711101806936593196982626950879534048742843552783_<162>

C211=P50*P162
C211=18626347316752091887613730912259192759279958920129<50>*187689856289552606645258672395266771629129914562572777562468039096119103199366120307762823572047220965155854278003711101806936593196982626950879534048742843552783<162>
Method=ECM  B1=11000000  Sigma=1786901496

(2·10²⁰⁵+1)/3 = (6)₂₀₄7_<205> = 7 · C204

C204 = P50 · P155

P50 = 48640687651801423804337056354992853346324870893769_<50>

P155 = 19579923688551731244546269150496163178660313660002447546455753332835083003773596869975317881941326532491200104594142764296885809934157623594946146289883349_<155>

sieving ~43 cpu-days

Mon Aug 24 23:16:31 2009  Msieve v. 1.42
Mon Aug 24 23:16:31 2009  random seeds: ddd8b5c8 ded37060
Mon Aug 24 23:16:31 2009  factoring 952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952381 (204 digits)
Mon Aug 24 23:16:33 2009  searching for 15-digit factors
Mon Aug 24 23:16:35 2009  commencing number field sieve (204-digit input)
Mon Aug 24 23:16:35 2009  R0: -100000000000000000000000000000000000000000
Mon Aug 24 23:16:35 2009  R1:  1
Mon Aug 24 23:16:35 2009  A0:  1
Mon Aug 24 23:16:35 2009  A1:  0
Mon Aug 24 23:16:35 2009  A2:  0
Mon Aug 24 23:16:35 2009  A3:  0
Mon Aug 24 23:16:35 2009  A4:  0
Mon Aug 24 23:16:35 2009  A5:  2
Mon Aug 24 23:16:35 2009  skew 0.87, size 5.998329e-014, alpha 1.449076, combined = 1.362059e-011
Mon Aug 24 23:16:35 2009  
Mon Aug 24 23:16:35 2009  commencing relation filtering
Mon Aug 24 23:16:35 2009  estimated available RAM is 4094.1 MB
Mon Aug 24 23:16:35 2009  commencing duplicate removal, pass 1
Mon Aug 24 23:22:00 2009  error -11 reading relation 30239153
Mon Aug 24 23:24:55 2009  found 4896193 hash collisions in 46646507 relations
Mon Aug 24 23:26:17 2009  added 731191 free relations
Mon Aug 24 23:26:17 2009  commencing duplicate removal, pass 2
Mon Aug 24 23:29:41 2009  found 3615445 duplicates and 43762252 unique relations
Mon Aug 24 23:29:41 2009  memory use: 197.2 MB
Mon Aug 24 23:29:41 2009  reading ideals above 26935296
Mon Aug 24 23:29:41 2009  commencing singleton removal, initial pass
Mon Aug 24 23:43:52 2009  memory use: 596.8 MB
Mon Aug 24 23:43:52 2009  reading all ideals from disk
Mon Aug 24 23:43:53 2009  memory use: 754.2 MB
Mon Aug 24 23:43:59 2009  commencing in-memory singleton removal
Mon Aug 24 23:44:05 2009  begin with 43762252 relations and 38545902 unique ideals
Mon Aug 24 23:44:57 2009  reduce to 24714676 relations and 17302634 ideals in 13 passes
Mon Aug 24 23:44:57 2009  max relations containing the same ideal: 60
Mon Aug 24 23:45:03 2009  reading ideals above 720000
Mon Aug 24 23:45:04 2009  commencing singleton removal, initial pass
Tue Aug 25 00:02:10 2009  memory use: 532.8 MB
Tue Aug 25 00:02:10 2009  reading all ideals from disk
Tue Aug 25 00:02:12 2009  memory use: 850.5 MB
Tue Aug 25 00:02:19 2009  keeping 20528578 ideals with weight <= 200, target excess is 132773
Tue Aug 25 00:02:26 2009  commencing in-memory singleton removal
Tue Aug 25 00:02:33 2009  begin with 24714716 relations and 20528578 unique ideals
Tue Aug 25 00:03:33 2009  reduce to 24711529 relations and 20525237 ideals in 8 passes
Tue Aug 25 00:03:33 2009  max relations containing the same ideal: 200
Tue Aug 25 00:04:04 2009  removing 2497614 relations and 2097614 ideals in 400000 cliques
Tue Aug 25 00:04:06 2009  commencing in-memory singleton removal
Tue Aug 25 00:04:13 2009  begin with 22213915 relations and 20525237 unique ideals
Tue Aug 25 00:05:13 2009  reduce to 22061876 relations and 18272637 ideals in 9 passes
Tue Aug 25 00:05:13 2009  max relations containing the same ideal: 192
Tue Aug 25 00:05:41 2009  removing 1868490 relations and 1468490 ideals in 400000 cliques
Tue Aug 25 00:05:43 2009  commencing in-memory singleton removal
Tue Aug 25 00:05:49 2009  begin with 20193386 relations and 18272637 unique ideals
Tue Aug 25 00:06:32 2009  reduce to 20096884 relations and 16706033 ideals in 7 passes
Tue Aug 25 00:06:32 2009  max relations containing the same ideal: 183
Tue Aug 25 00:06:58 2009  removing 1673961 relations and 1273961 ideals in 400000 cliques
Tue Aug 25 00:06:59 2009  commencing in-memory singleton removal
Tue Aug 25 00:07:05 2009  begin with 18422923 relations and 16706033 unique ideals
Tue Aug 25 00:07:49 2009  reduce to 18338178 relations and 15345854 ideals in 8 passes
Tue Aug 25 00:07:49 2009  max relations containing the same ideal: 172
Tue Aug 25 00:08:12 2009  removing 1558416 relations and 1158416 ideals in 400000 cliques
Tue Aug 25 00:08:13 2009  commencing in-memory singleton removal
Tue Aug 25 00:08:19 2009  begin with 16779762 relations and 15345854 unique ideals
Tue Aug 25 00:08:48 2009  reduce to 16693317 relations and 14099363 ideals in 6 passes
Tue Aug 25 00:08:48 2009  max relations containing the same ideal: 164
Tue Aug 25 00:09:10 2009  removing 1492815 relations and 1092815 ideals in 400000 cliques
Tue Aug 25 00:09:11 2009  commencing in-memory singleton removal
Tue Aug 25 00:09:16 2009  begin with 15200502 relations and 14099363 unique ideals
Tue Aug 25 00:09:47 2009  reduce to 15116492 relations and 12920846 ideals in 7 passes
Tue Aug 25 00:09:47 2009  max relations containing the same ideal: 153
Tue Aug 25 00:10:06 2009  removing 1440970 relations and 1040970 ideals in 400000 cliques
Tue Aug 25 00:10:07 2009  commencing in-memory singleton removal
Tue Aug 25 00:10:12 2009  begin with 13675522 relations and 12920846 unique ideals
Tue Aug 25 00:10:36 2009  reduce to 13585042 relations and 11787407 ideals in 6 passes
Tue Aug 25 00:10:36 2009  max relations containing the same ideal: 143
Tue Aug 25 00:10:53 2009  removing 1414062 relations and 1014062 ideals in 400000 cliques
Tue Aug 25 00:10:54 2009  commencing in-memory singleton removal
Tue Aug 25 00:10:58 2009  begin with 12170980 relations and 11787407 unique ideals
Tue Aug 25 00:11:23 2009  reduce to 12073653 relations and 10673537 ideals in 7 passes
Tue Aug 25 00:11:23 2009  max relations containing the same ideal: 129
Tue Aug 25 00:11:39 2009  removing 1385748 relations and 985748 ideals in 400000 cliques
Tue Aug 25 00:11:40 2009  commencing in-memory singleton removal
Tue Aug 25 00:11:43 2009  begin with 10687905 relations and 10673537 unique ideals
Tue Aug 25 00:12:02 2009  reduce to 10581657 relations and 9578472 ideals in 6 passes
Tue Aug 25 00:12:02 2009  max relations containing the same ideal: 118
Tue Aug 25 00:12:16 2009  removing 1370298 relations and 970298 ideals in 400000 cliques
Tue Aug 25 00:12:17 2009  commencing in-memory singleton removal
Tue Aug 25 00:12:19 2009  begin with 9211359 relations and 9578472 unique ideals
Tue Aug 25 00:12:38 2009  reduce to 9094789 relations and 8487968 ideals in 7 passes
Tue Aug 25 00:12:38 2009  max relations containing the same ideal: 106
Tue Aug 25 00:12:50 2009  removing 1358293 relations and 958293 ideals in 400000 cliques
Tue Aug 25 00:12:51 2009  commencing in-memory singleton removal
Tue Aug 25 00:12:54 2009  begin with 7736496 relations and 8487968 unique ideals
Tue Aug 25 00:13:09 2009  reduce to 7598810 relations and 7386845 ideals in 7 passes
Tue Aug 25 00:13:09 2009  max relations containing the same ideal: 92
Tue Aug 25 00:13:20 2009  removing 293684 relations and 235736 ideals in 57948 cliques
Tue Aug 25 00:13:20 2009  commencing in-memory singleton removal
Tue Aug 25 00:13:22 2009  begin with 7305126 relations and 7386845 unique ideals
Tue Aug 25 00:13:33 2009  reduce to 7298052 relations and 7143994 ideals in 5 passes
Tue Aug 25 00:13:33 2009  max relations containing the same ideal: 89
Tue Aug 25 00:13:37 2009  relations with 0 large ideals: 2925
Tue Aug 25 00:13:37 2009  relations with 1 large ideals: 486
Tue Aug 25 00:13:37 2009  relations with 2 large ideals: 9057
Tue Aug 25 00:13:37 2009  relations with 3 large ideals: 78455
Tue Aug 25 00:13:37 2009  relations with 4 large ideals: 369097
Tue Aug 25 00:13:37 2009  relations with 5 large ideals: 1033882
Tue Aug 25 00:13:37 2009  relations with 6 large ideals: 1870884
Tue Aug 25 00:13:37 2009  relations with 7+ large ideals: 3933266
Tue Aug 25 00:13:37 2009  commencing 2-way merge
Tue Aug 25 00:13:51 2009  reduce to 4877616 relation sets and 4723558 unique ideals
Tue Aug 25 00:13:51 2009  commencing full merge
Tue Aug 25 00:16:24 2009  memory use: 535.7 MB
Tue Aug 25 00:16:25 2009  found 2596663 cycles, need 2575758
Tue Aug 25 00:16:26 2009  weight of 2575758 cycles is about 180583247 (70.11/cycle)
Tue Aug 25 00:16:26 2009  distribution of cycle lengths:
Tue Aug 25 00:16:26 2009  1 relations: 279212
Tue Aug 25 00:16:26 2009  2 relations: 299234
Tue Aug 25 00:16:26 2009  3 relations: 313601
Tue Aug 25 00:16:26 2009  4 relations: 299542
Tue Aug 25 00:16:26 2009  5 relations: 280947
Tue Aug 25 00:16:26 2009  6 relations: 247235
Tue Aug 25 00:16:26 2009  7 relations: 208707
Tue Aug 25 00:16:26 2009  8 relations: 169480
Tue Aug 25 00:16:26 2009  9 relations: 134175
Tue Aug 25 00:16:26 2009  10+ relations: 343625
Tue Aug 25 00:16:26 2009  heaviest cycle: 20 relations
Tue Aug 25 00:16:28 2009  commencing cycle optimization
Tue Aug 25 00:16:35 2009  start with 14016520 relations
Tue Aug 25 00:17:18 2009  pruned 414403 relations
Tue Aug 25 00:17:18 2009  memory use: 357.6 MB
Tue Aug 25 00:17:18 2009  distribution of cycle lengths:
Tue Aug 25 00:17:18 2009  1 relations: 279212
Tue Aug 25 00:17:18 2009  2 relations: 305935
Tue Aug 25 00:17:18 2009  3 relations: 325203
Tue Aug 25 00:17:18 2009  4 relations: 308910
Tue Aug 25 00:17:18 2009  5 relations: 290433
Tue Aug 25 00:17:18 2009  6 relations: 253052
Tue Aug 25 00:17:18 2009  7 relations: 211890
Tue Aug 25 00:17:18 2009  8 relations: 169290
Tue Aug 25 00:17:18 2009  9 relations: 131652
Tue Aug 25 00:17:18 2009  10+ relations: 300181
Tue Aug 25 00:17:18 2009  heaviest cycle: 20 relations
Tue Aug 25 00:17:33 2009  RelProcTime: 3658
Tue Aug 25 00:17:33 2009  
Tue Aug 25 00:17:33 2009  commencing linear algebra
Tue Aug 25 00:17:35 2009  read 2575758 cycles
Tue Aug 25 00:17:42 2009  cycles contain 7222300 unique relations
Tue Aug 25 00:27:08 2009  read 7222300 relations
Tue Aug 25 00:27:26 2009  using 20 quadratic characters above 536866442
Tue Aug 25 00:28:29 2009  building initial matrix
Tue Aug 25 00:30:54 2009  memory use: 846.8 MB
Tue Aug 25 00:31:01 2009  read 2575758 cycles
Tue Aug 25 00:33:17 2009  matrix is 2575581 x 2575758 (730.1 MB) with weight 226524143 (87.94/col)
Tue Aug 25 00:33:17 2009  sparse part has weight 173363652 (67.31/col)
Tue Aug 25 00:34:04 2009  filtering completed in 2 passes
Tue Aug 25 00:34:05 2009  matrix is 2575290 x 2575467 (730.1 MB) with weight 226516174 (87.95/col)
Tue Aug 25 00:34:05 2009  sparse part has weight 173361396 (67.31/col)
Tue Aug 25 00:34:30 2009  read 2575467 cycles
Tue Aug 25 00:41:23 2009  matrix is 2575290 x 2575467 (730.1 MB) with weight 226516174 (87.95/col)
Tue Aug 25 00:41:23 2009  sparse part has weight 173361396 (67.31/col)
Tue Aug 25 00:41:24 2009  saving the first 48 matrix rows for later
Tue Aug 25 00:41:26 2009  matrix is 2575242 x 2575467 (690.6 MB) with weight 178986811 (69.50/col)
Tue Aug 25 00:41:26 2009  sparse part has weight 165592916 (64.30/col)
Tue Aug 25 00:41:26 2009  matrix includes 64 packed rows
Tue Aug 25 00:41:26 2009  using block size 65536 for processor cache size 4096 kB
Tue Aug 25 00:41:52 2009  commencing Lanczos iteration (4 threads)
Tue Aug 25 00:41:52 2009  memory use: 786.1 MB
Tue Aug 25 14:23:24 2009  lanczos halted after 40727 iterations (dim = 2575240)
Tue Aug 25 14:23:33 2009  recovered 35 nontrivial dependencies
Tue Aug 25 14:23:38 2009  BLanczosTime: 50765
Tue Aug 25 14:23:38 2009  
Tue Aug 25 14:23:38 2009  commencing square root phase
Tue Aug 25 14:23:38 2009  reading relations for dependency 1
Tue Aug 25 14:23:42 2009  read 1285922 cycles
Tue Aug 25 14:23:46 2009  cycles contain 4488674 unique relations
Tue Aug 25 14:32:25 2009  read 4488674 relations
Tue Aug 25 14:33:06 2009  multiplying 3608038 relations
Tue Aug 25 14:41:39 2009  multiply complete, coefficients have about 90.10 million bits
Tue Aug 25 14:41:41 2009  initial square root is modulo 2935241
Tue Aug 25 14:52:21 2009  sqrtTime: 1723
Tue Aug 25 14:52:21 2009  prp50 factor: 48640687651801423804337056354992853346324870893769
Tue Aug 25 14:52:21 2009  prp155 factor: 19579923688551731244546269150496163178660313660002447546455753332835083003773596869975317881941326532491200104594142764296885809934157623594946146289883349
Tue Aug 25 14:52:21 2009  elapsed time 15:35:50

Aug 24, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve v. 1.42 / Aug 24, 2009

(16·10²⁰⁰+17)/3 = 5(3)₁₉₉9_<201> = 7 · 11 · 53 · 1867 · 2162879 · 6576017627_<10> · 49830784277_<11> · 16059890440978574700941544301_<29> · C139

C139 = P43 · P48 · P49

P43 = 5465589490197817703795797688544120931163749_<43>

P48 = 298131801644473477455962103738371299534531237091_<48>

P49 = 3774044422137398794264282715509644849768141470003_<49>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1866420656
Step 1 took 42771ms
Step 2 took 14797ms
********** Factor found in step 2: 5465589490197817703795797688544120931163749
Found probable prime factor of 43 digits: 5465589490197817703795797688544120931163749
Composite cofactor 1125162663058098504797405482943005184164299914993771206716128207364181036419506148377602857481273 has 97 digits
-------------------------------
Sun Aug 23 13:25:48 2009  Msieve v. 1.42
Sun Aug 23 13:25:48 2009  random seeds: 5c7374a8 5ef10529
Sun Aug 23 13:25:48 2009  factoring 1125162663058098504797405482943005184164299914993771206716128207364181036419506148377602857481273 (97 digits)
Sun Aug 23 13:25:49 2009  searching for 15-digit factors
Sun Aug 23 13:25:50 2009  commencing quadratic sieve (97-digit input)
Sun Aug 23 13:25:50 2009  using multiplier of 1
Sun Aug 23 13:25:50 2009  using 64kb Pentium 3 sieve core
Sun Aug 23 13:25:50 2009  sieve interval: 18 blocks of size 65536
Sun Aug 23 13:25:50 2009  processing polynomials in batches of 6
Sun Aug 23 13:25:50 2009  using a sieve bound of 2334881 (85864 primes)
Sun Aug 23 13:25:50 2009  using large prime bound of 350232150 (28 bits)
Sun Aug 23 13:25:50 2009  using double large prime bound of 2397953724173250 (43-52 bits)
Sun Aug 23 13:25:50 2009  using trial factoring cutoff of 52 bits
Sun Aug 23 13:25:50 2009  polynomial 'A' values have 12 factors
Sun Aug 23 22:43:02 2009  86190 relations (20613 full + 65577 combined from 1302314 partial), need 85960
Sun Aug 23 22:43:09 2009  begin with 1322927 relations
Sun Aug 23 22:43:11 2009  reduce to 227316 relations in 13 passes
Sun Aug 23 22:43:11 2009  attempting to read 227316 relations
Sun Aug 23 22:43:23 2009  recovered 227316 relations
Sun Aug 23 22:43:23 2009  recovered 213982 polynomials
Sun Aug 23 22:43:24 2009  attempting to build 86190 cycles
Sun Aug 23 22:43:24 2009  found 86190 cycles in 6 passes
Sun Aug 23 22:43:24 2009  distribution of cycle lengths:
Sun Aug 23 22:43:24 2009     length 1 : 20613
Sun Aug 23 22:43:24 2009     length 2 : 14554
Sun Aug 23 22:43:24 2009     length 3 : 14469
Sun Aug 23 22:43:24 2009     length 4 : 11952
Sun Aug 23 22:43:24 2009     length 5 : 8905
Sun Aug 23 22:43:24 2009     length 6 : 6215
Sun Aug 23 22:43:24 2009     length 7 : 3905
Sun Aug 23 22:43:24 2009     length 9+: 5577
Sun Aug 23 22:43:24 2009  largest cycle: 19 relations
Sun Aug 23 22:43:24 2009  matrix is 85864 x 86190 (23.8 MB) with weight 5890275 (68.34/col)
Sun Aug 23 22:43:24 2009  sparse part has weight 5890275 (68.34/col)
Sun Aug 23 22:43:27 2009  filtering completed in 3 passes
Sun Aug 23 22:43:27 2009  matrix is 82166 x 82230 (22.8 MB) with weight 5637674 (68.56/col)
Sun Aug 23 22:43:27 2009  sparse part has weight 5637674 (68.56/col)
Sun Aug 23 22:43:27 2009  saving the first 48 matrix rows for later
Sun Aug 23 22:43:27 2009  matrix is 82118 x 82230 (16.2 MB) with weight 4678949 (56.90/col)
Sun Aug 23 22:43:27 2009  sparse part has weight 3758275 (45.70/col)
Sun Aug 23 22:43:27 2009  matrix includes 64 packed rows
Sun Aug 23 22:43:27 2009  using block size 32892 for processor cache size 1024 kB
Sun Aug 23 22:43:28 2009  commencing Lanczos iteration
Sun Aug 23 22:43:28 2009  memory use: 15.2 MB
Sun Aug 23 22:44:47 2009  lanczos halted after 1300 iterations (dim = 82116)
Sun Aug 23 22:44:48 2009  recovered 15 nontrivial dependencies
Sun Aug 23 22:44:48 2009  prp48 factor: 298131801644473477455962103738371299534531237091
Sun Aug 23 22:44:48 2009  prp49 factor: 3774044422137398794264282715509644849768141470003
Sun Aug 23 22:44:48 2009  elapsed time 09:19:00

Aug 24, 2009

By Dmitry Domanov / ECMNET / Aug 24, 2009

(16·10²⁰⁸-7)/9 = 1(7)₂₀₈_<209> = 613 · 155312749 · 122870845801218751_<18> · C181

C181 = P44 · P137

P44 = 33196494245589085028001912695928770935280171_<44>

P137 = 45779265693588795907442339030823949447819912433245685072037175910245588951267538385400947054816041565951371323741983261114872494043160301_<137>

C181=P44*P137
C181=33196494245589085028001912695928770935280171<44>*45779265693588795907442339030823949447819912433245685072037175910245588951267538385400947054816041565951371323741983261114872494043160301<137>

Aug 23, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 23, 2009

(32·10¹⁶⁹+13)/9 = 3(5)₁₆₈7_<170> = 31 · 37² · 197 · 647 · 6581 · 5064601914373430809_<19> · C138

C138 = P64 · P74

P64 = 2662996647046263982196858217327530760359601577131613151314289971_<64>

P74 = 74056638451825662200473333254579946422969866696922537212821981772723385623_<74>

Number: 35557_169
N=197212579888729164471309556399936640756410330307724816872021002362065422823075007141756856489734111483154757167846859583742889531474486933
  ( 138 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=2662996647046263982196858217327530760359601577131613151314289971
 r2=74056638451825662200473333254579946422969866696922537212821981772723385623
Version: 
Total time: 30.05 hours.
Scaled time: 71.60 units (timescale=2.383).
Factorization parameters were as follows:
n: 197212579888729164471309556399936640756410330307724816872021002362065422823075007141756856489734111483154757167846859583742889531474486933
m: 20000000000000000000000000000000000
deg: 5
c5: 1
c0: 130
skew: 2.65
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 5100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11119594
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 850829 x 851077
Total sieving time: 27.63 hours.
Total relation processing time: 0.71 hours.
Matrix solve time: 1.48 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 30.05 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673801)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672380)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)

Aug 23, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Aug 23, 2009

(28·10¹⁹⁵+53)/9 = 3(1)₁₉₄7_<196> = 3 · 59 · 395953 · 42767503850028819725441309_<26> · 352426542677057137608275426464363_<33> · C130

C130 = P38 · P92

P38 = 83818878880914915377013698879274119363_<38>

P92 = 35137774993989565829855092330752915371536012111459064937383666423536942780985993383926108817_<92>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3984559737
Step 1 took 38183ms
Step 2 took 14303ms
********** Factor found in step 2: 83818878880914915377013698879274119363
Found probable prime factor of 38 digits: 83818878880914915377013698879274119363
Probable prime cofactor 35137774993989565829855092330752915371536012111459064937383666423536942780985993383926108817 has 92 digits

Aug 23, 2009

By Justin Card / gmp-ecm 6.2 / Aug 23, 2009

(64·10²⁰³+53)/9 = 7(1)₂₀₂7_<204> = 3³ · 11² · 2069 · 7103 · 24324049 · 336174101 · 3482198767_<10> · C168

C168 = P37 · P132

P37 = 3980843238588010489892024931548862143_<37>

P132 = 130664397334782295209650590742356899679167397610942074331579761558024231657405938067573861191185006433921905590657151181446661170297_<132>

Run 52 out of 4480:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=194726714
Step 1 took 63016ms
Step 2 took 25201ms
********** Factor found in step 2: 3980843238588010489892024931548862143
Found probable prime factor of 37 digits: 3980843238588010489892024931548862143
Probable prime cofactor 130664397334782295209650590742356899679167397610942074331579761558024231657405938067573861191185006433921905590657151181446661170297 has 132 digits

Aug 22, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve v. 1.42 / Aug 22, 2009

(13·10¹⁷²+23)/9 = 1(4)₁₇₁7_<173> = 149371 · 167722932457097_<15> · 44064556377957406403542099_<26> · C128

C128 = P36 · P41 · P52

P36 = 149913770606299879910229935179747037_<36>

P41 = 50877483285356724843669322116346571593229_<41>

P52 = 1715479597622848701658232150207211689815887239314303_<52>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=789472094
Step 1 took 38413ms
Step 2 took 14089ms
********** Factor found in step 2: 149913770606299879910229935179747037
Found probable prime factor of 36 digits: 149913770606299879910229935179747037
Composite cofactor 87279284554426964743980580315959098898746362920358811195503822260589842067230516396197654387 has 92 digits
-------------------------------
Tue Aug 18 20:18:26 2009  Msieve v. 1.42
Tue Aug 18 20:18:26 2009  random seeds: 6d03c3f8 644abe73
Tue Aug 18 20:18:26 2009  factoring 87279284554426964743980580315959098898746362920358811195503822260589842067230516396197654387 (92 digits)
Tue Aug 18 20:18:27 2009  searching for 15-digit factors
Tue Aug 18 20:18:28 2009  commencing quadratic sieve (92-digit input)
Tue Aug 18 20:18:28 2009  using multiplier of 3
Tue Aug 18 20:18:28 2009  using 64kb Pentium 3 sieve core
Tue Aug 18 20:18:28 2009  sieve interval: 18 blocks of size 65536
Tue Aug 18 20:18:28 2009  processing polynomials in batches of 6
Tue Aug 18 20:18:28 2009  using a sieve bound of 1855349 (69378 primes)
Tue Aug 18 20:18:28 2009  using large prime bound of 209654437 (27 bits)
Tue Aug 18 20:18:28 2009  using double large prime bound of 952154221467417 (42-50 bits)
Tue Aug 18 20:18:28 2009  using trial factoring cutoff of 50 bits
Tue Aug 18 20:18:28 2009  polynomial 'A' values have 12 factors
Tue Aug 18 23:33:35 2009  69929 relations (17625 full + 52304 combined from 894203 partial), need 69474
Tue Aug 18 23:33:39 2009  begin with 911828 relations
Tue Aug 18 23:33:40 2009  reduce to 177278 relations in 11 passes
Tue Aug 18 23:33:40 2009  attempting to read 177278 relations
Tue Aug 18 23:33:47 2009  recovered 177278 relations
Tue Aug 18 23:33:47 2009  recovered 158770 polynomials
Tue Aug 18 23:33:47 2009  attempting to build 69929 cycles
Tue Aug 18 23:33:47 2009  found 69929 cycles in 5 passes
Tue Aug 18 23:33:47 2009  distribution of cycle lengths:
Tue Aug 18 23:33:47 2009     length 1 : 17625
Tue Aug 18 23:33:47 2009     length 2 : 12725
Tue Aug 18 23:33:47 2009     length 3 : 11937
Tue Aug 18 23:33:47 2009     length 4 : 9581
Tue Aug 18 23:33:47 2009     length 5 : 7001
Tue Aug 18 23:33:47 2009     length 6 : 4657
Tue Aug 18 23:33:47 2009     length 7 : 2783
Tue Aug 18 23:33:47 2009     length 9+: 3620
Tue Aug 18 23:33:47 2009  largest cycle: 19 relations
Tue Aug 18 23:33:47 2009  matrix is 69378 x 69929 (17.2 MB) with weight 4231188 (60.51/col)
Tue Aug 18 23:33:47 2009  sparse part has weight 4231188 (60.51/col)
Tue Aug 18 23:33:49 2009  filtering completed in 3 passes
Tue Aug 18 23:33:49 2009  matrix is 65612 x 65676 (16.1 MB) with weight 3968846 (60.43/col)
Tue Aug 18 23:33:49 2009  sparse part has weight 3968846 (60.43/col)
Tue Aug 18 23:33:49 2009  saving the first 48 matrix rows for later
Tue Aug 18 23:33:49 2009  matrix is 65564 x 65676 (9.3 MB) with weight 2999864 (45.68/col)
Tue Aug 18 23:33:49 2009  sparse part has weight 2045539 (31.15/col)
Tue Aug 18 23:33:49 2009  matrix includes 64 packed rows
Tue Aug 18 23:33:49 2009  using block size 26270 for processor cache size 1024 kB
Tue Aug 18 23:33:50 2009  commencing Lanczos iteration
Tue Aug 18 23:33:50 2009  memory use: 10.1 MB
Tue Aug 18 23:34:24 2009  lanczos halted after 1038 iterations (dim = 65562)
Tue Aug 18 23:34:24 2009  recovered 16 nontrivial dependencies
Tue Aug 18 23:34:25 2009  prp41 factor: 50877483285356724843669322116346571593229
Tue Aug 18 23:34:25 2009  prp52 factor: 1715479597622848701658232150207211689815887239314303
Tue Aug 18 23:34:25 2009  elapsed time 03:15:59

Aug 22, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 22, 2009

7·10¹⁶⁹+9 = 7(0)₁₆₈9_<170> = 19 · 197 · 1218731 · 76893204345311_<14> · 5094367215912347_<16> · C131

C131 = P62 · P70

P62 = 14895146820296515742340476222921748580100430093472165449145387_<62>

P70 = 2629949201635387234251242596490670534870085851462962353425228926560387_<70>

Number: 70009_169
N=39173479488280698301566650872036774199426866136397189452808421112916404369440174985140115774837583709302975448240597911414597984769
  ( 131 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=14895146820296515742340476222921748580100430093472165449145387
 r2=2629949201635387234251242596490670534870085851462962353425228926560387
Version: 
Total time: 34.98 hours.
Scaled time: 83.07 units (timescale=2.375).
Factorization parameters were as follows:
n: 39173479488280698301566650872036774199426866136397189452808421112916404369440174985140115774837583709302975448240597911414597984769
m: 10000000000000000000000000000000000
deg: 5
c5: 7
c0: 90
skew: 1.67
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 5600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11269680
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 925303 x 925551
Total sieving time: 32.31 hours.
Total relation processing time: 0.81 hours.
Matrix solve time: 1.77 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 34.98 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673788)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

Aug 22, 2009

Factorizations of Phi_n(10) is available. It is the origin of Factorizations of 11...11 (Repunit) and Factorizations of 100...001.

Aug 21, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Aug 21, 2009

(52·10¹⁹⁹+11)/9 = 5(7)₁₉₈9_<200> = 4547 · 15254923091918551452759372589_<29> · 1731348293684325255443601154609_<31> · C138

C138 = P37 · P102

P37 = 1786826983403462415473402018217405391_<37>

P102 = 269251983922852962675309422494691188138974240910425994172961541962117182925129658737872261636387448427_<102>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1647347969
Step 1 took 42593ms
Step 2 took 14619ms
********** Factor found in step 2: 1786826983403462415473402018217405391
Found probable prime factor of 37 digits: 1786826983403462415473402018217405391
Probable prime cofactor 269251983922852962675309422494691188138974240910425994172961541962117182925129658737872261636387448427 has 102 digits

(46·10¹⁷¹+53)/9 = 5(1)₁₇₀7_<172> = 7 · 43 · 1373 · 8081 · 21174365965009_<14> · C149

C149 = P33 · P117

P33 = 605173586951071077503844970287679_<33>

P117 = 119432576933846853692398300562496450873677590281019524438614039543969108708295893722582025789172845080826012999716619_<117>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=43475544
Step 1 took 47342ms
Step 2 took 16749ms
********** Factor found in step 2: 605173586951071077503844970287679
Found probable prime factor of 33 digits: 605173586951071077503844970287679
Probable prime cofactor 119432576933846853692398300562496450873677590281019524438614039543969108708295893722582025789172845080826012999716619 has 117 digits

Aug 21, 2009

By Serge Batalov and Bruce Dodson / Aug 20, 2009

c175 from 10²⁴¹+1 was splitted into p62 and p114.

Aug 20, 2009

By Dmitry Domanov / ECMNET / Aug 20, 2009

(53·10¹⁹⁶-71)/9 = 5(8)₁₉₅1_<197> = 3² · 4973 · 74797 · 122655881 · C180

C180 = P39 · P142

P39 = 112054989341662601618892514165224888241_<39>

P142 = 1279878186755975199770625717338893764280326490898655144840134732459923961450639607812280526526379705342401644682052605125245400793894469473609_<142>

C180=P39*P142
C180=112054989341662601618892514165224888241<39>*1279878186755975199770625717338893764280326490898655144840134732459923961450639607812280526526379705342401644682052605125245400793894469473609<142>

(53·10²⁰²-71)/9 = 5(8)₂₀₁1_<203> = 3 · 19 · 857 · 1259 · 1004317 · 71365367 · C182

C182 = P42 · C140

P42 = 779769064987480193874703347294131196204883_<42>

C140 = [17132771907515894174556863898939580232543643866401830701290571585218041096109532000936311816177590847856617333605840706370680024403860034243_<140>]

C182=P42*C140
C182=779769064987480193874703347294131196204883<42>*17132771907515894174556863898939580232543643866401830701290571585218041096109532000936311816177590847856617333605840706370680024403860034243<140>

(53·10¹⁹⁰-71)/9 = 5(8)₁₈₉1_<191> = 3 · 61 · 173 · 39203873 · 211360399 · C171

C171 = P36 · C136

P36 = 168914326803248671710673803592753171_<36>

C136 = [1328975843267167003533199181021679263944069843997313562305346088568990122619806818358213686861743331804899354370025982954624757057766927_<136>]

C171=P36*C136
C171=168914326803248671710673803592753171<36>*1328975843267167003533199181021679263944069843997313562305346088568990122619806818358213686861743331804899354370025982954624757057766927<136>

Aug 18, 2009 (3rd)

By Wataru Sakai / Msieve / Aug 18, 2009

(19·10¹⁸⁵-7)/3 = 6(3)₁₈₄1_<186> = 307 · 2129 · C180

C180 = P44 · P47 · P90

P44 = 92441972095372479843278989499675612962293661_<44>

P47 = 46224877490952496513455145253411202856771657321_<47>

P90 = 226763597697597739551036386348904373582419249675420678746058970902269764864275707817984317_<90>

Number: 63331_185
N=968987800443592415171492990903244528151390573992673432241488079665077016680359994267672170007379607090746727498700791357036814906500327160881044507649648690922981279665689008975377
  ( 180 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=92441972095372479843278989499675612962293661
 r2=46224877490952496513455145253411202856771657321
 r3=226763597697597739551036386348904373582419249675420678746058970902269764864275707817984317
Version: 
Total time: 214.40 hours.
Scaled time: 429.87 units (timescale=2.005).
Factorization parameters were as follows:
n: 968987800443592415171492990903244528151390573992673432241488079665077016680359994267672170007379607090746727498700791357036814906500327160881044507649648690922981279665689008975377
m: 10000000000000000000000000000000000000
deg: 5
c5: 19
c0: -7
skew: 0.82
type: snfs
lss: 1
rlim: 8900000
alim: 8900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8900000/8900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4450000, 6650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1532242 x 1532490
Total sieving time: 214.40 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,8900000,8900000,28,28,54,54,2.5,2.5,100000
total time: 214.40 hours.
 --------- CPU info (if available) ----------

(4·10²⁰⁰-31)/9 = (4)₁₉₉1_<200> = 221047 · C195

C195 = P46 · P52 · P98

P46 = 6099950637964487344624524200296949847675258491_<46>

P52 = 2617574360209393093008226658654893652993339169215851_<52>

P98 = 12592370931196073272289411784959848587864333346912734305442667923493511107809613626421022457004183_<98>

Number: 44441_200
N=201063323385725408824568731737795330605909351605968162628058487310139673664172978798375207283719952971288660078826875933373646529672171277802659364046761297119818158330329949940259060039016337903
  ( 195 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=6099950637964487344624524200296949847675258491
 r2=2617574360209393093008226658654893652993339169215851
 r3=12592370931196073272289411784959848587864333346912734305442667923493511107809613626421022457004183
Version: 
Total time: 732.85 hours.
Scaled time: 1472.29 units (timescale=2.009).
Factorization parameters were as follows:
n: 201063323385725408824568731737795330605909351605968162628058487310139673664172978798375207283719952971288660078826875933373646529672171277802659364046761297119818158330329949940259060039016337903
m: 10000000000000000000000000000000000000000
deg: 5
c5: 4
c0: -31
skew: 1.51
type: snfs
lss: 1
rlim: 15400000
alim: 15400000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 15400000/15400000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7700000, 15500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2968446 x 2968694
Total sieving time: 732.85 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15400000,15400000,29,29,56,56,2.6,2.6,100000
total time: 732.85 hours.
 --------- CPU info (if available) ----------

Aug 18, 2009 (2nd)

By Dmitry Domanov / ECMNET / Aug 18, 2009

(53·10¹⁹³-71)/9 = 5(8)₁₉₂1_<194> = 3 · 17 · 2131 · 122614102349_<12> · 157528172059_<12> · C167

C167 = P33 · P134

P33 = 386318917324635401637343670457937_<33>

P134 = 72616464843759242682094782381797010874803934727294295921255817042629723671550851219691527308314086340987245476998440916635306218917703_<134>

C167=P33*P134
C167=386318917324635401637343670457937<33>*72616464843759242682094782381797010874803934727294295921255817042629723671550851219691527308314086340987245476998440916635306218917703<134>

Aug 18, 2009

By Robert Backstrom / GGNFS, Msieve / Aug 18, 2009

10²¹²+3 = 1(0)₂₁₁3_<213> = 19 · 313 · C209

C209 = P53 · P156

P53 = 72100344457846728686995566050906079023204339527194013_<53>

P156 = 233219425899999887904779450574060410914770791909686397507236849819912243596530554293769515201797100091341545546091157355719851915551928373643299913434059373_<156>

Number: n
N=16815200941651252732470153018328569026399865478392466789978140238775853371447788801076172860265680174878089793173028417689591390617117874558600975281654615772658483268875063057003531192197746763073818732133849
  ( 209 digits)
SNFS difficulty: 213 digits.
Divisors found:

Tue Aug 18 04:27:28 2009  prp53 factor: 72100344457846728686995566050906079023204339527194013
Tue Aug 18 04:27:28 2009  prp156 factor: 233219425899999887904779450574060410914770791909686397507236849819912243596530554293769515201797100091341545546091157355719851915551928373643299913434059373
Tue Aug 18 04:27:28 2009  elapsed time 30:40:57 (Msieve 1.39 - dependency 9)

...
Msieve: warning: no irreducible prime found, switching to small primes
Msieve: Newton iteration failed several times (see at end, below)
...

Version: GGNFS-0.77.1-20050930-k8
Total time: 65.90 hours.
Scaled time: 132.86 units (timescale=2.016).
Factorization parameters were as follows:
name: KA_1_0_211_3
n: 16815200941651252732470153018328569026399865478392466789978140238775853371447788801076172860265680174878089793173028417689591390617117874558600975281654615772658483268875063057003531192197746763073818732133849
m: 200000000000000000000000000000000000
deg: 6
c6: 25
c0: 48
skew: 1.11
type: snfs
lss: 1
rlim: 25000000
alim: 25000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 25000000/25000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [12500000, 27749990)
Primes: RFBsize:1565927, AFBsize:1566435, largePrimes:40192350 encountered
Relations: rels:39845888, finalFF:1905146
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 9102934 hash collisions in 52197256 relations
Msieve: matrix is 3731532 x 3731780 (996.2 MB)

Total sieving time: 64.23 hours.
Total relation processing time: 1.67 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,213,6,0,0,0,0,0,0,0,0,25000000,25000000,29,29,58,58,2.6,2.6,100000
total time: 65.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3352028k/3407296k available (3120k kernel code, 53984k reserved, 1898k data, 424k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.97 BogoMIPS (lpj=2830989)
Calibrating delay using timer specific routine.. 5660.88 BogoMIPS (lpj=2830443)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Total of 4 processors activated (22644.69 BogoMIPS).

...
Msieve: warning: no irreducible prime found, switching to small primes
Msieve: Newton iteration failed several times:
...
Tue Aug 18 02:20:00 2009  reading relations for dependency 7
Tue Aug 18 02:20:10 2009  read 1866396 cycles
Tue Aug 18 02:20:17 2009  cycles contain 6394091 unique relations
Tue Aug 18 02:21:41 2009  read 6394091 relations
Tue Aug 18 02:22:18 2009  multiplying 5186178 relations
Tue Aug 18 02:32:05 2009  multiply complete, coefficients have about 148.72 million bits
Tue Aug 18 02:32:07 2009  warning: no irreducible prime found, switching to small primes
Tue Aug 18 02:56:28 2009  initial square root is modulo 53
Tue Aug 18 03:18:43 2009  Newton iteration failed to converge
Tue Aug 18 03:18:43 2009  algebraic square root failed
Tue Aug 18 03:18:43 2009  reading relations for dependency 8
Tue Aug 18 03:18:53 2009  read 1865384 cycles
Tue Aug 18 03:19:00 2009  cycles contain 6392057 unique relations
Tue Aug 18 03:20:24 2009  read 6392057 relations
Tue Aug 18 03:21:01 2009  multiplying 5184576 relations
Tue Aug 18 03:30:49 2009  multiply complete, coefficients have about 148.68 million bits
Tue Aug 18 03:30:50 2009  warning: no irreducible prime found, switching to small primes
Tue Aug 18 03:30:50 2009  initial square root is modulo 53
Tue Aug 18 03:53:06 2009  Newton iteration failed to converge
Tue Aug 18 03:53:06 2009  algebraic square root failed
Tue Aug 18 03:53:06 2009  reading relations for dependency 9
Tue Aug 18 03:53:16 2009  read 1866216 cycles
Tue Aug 18 03:53:23 2009  cycles contain 6390913 unique relations
Tue Aug 18 03:54:47 2009  read 6390913 relations
Tue Aug 18 03:55:25 2009  multiplying 5183958 relations
Tue Aug 18 04:05:12 2009  multiply complete, coefficients have about 148.66 million bits
Tue Aug 18 04:05:13 2009  warning: no irreducible prime found, switching to small primes
Tue Aug 18 04:05:13 2009  initial square root is modulo 53
Tue Aug 18 04:27:28 2009  prp53 factor: 72100344457846728686995566050906079023204339527194013
Tue Aug 18 04:27:28 2009  prp156 factor: 233219425899999887904779450574060410914770791909686397507236849819912243596530554293769515201797100091341545546091157355719851915551928373643299913434059373
Tue Aug 18 04:27:28 2009  elapsed time 30:40:57

Aug 17, 2009 (5th)

By Wataru Sakai / GMP-ECM 6.2.1 / Aug 17, 2009

9·10¹⁹⁵-7 = 8(9)₁₉₄3_<196> = 17 · 439 · 119183 · 1271399 · 242885213 · 461827684596426570878380861037770727_<36> · C137

C137 = P47 · P90

P47 = 90273726781308008410859820613528673953162767949_<47>

P90 = 785941965246821725517634354985618196758423193048763238517231673375963788322474444838897417_<90>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1202030130
Step 1 took 156685ms
Step 2 took 47668ms
********** Factor found in step 2: 90273726781308008410859820613528673953162767949
Found probable prime factor of 47 digits: 90273726781308008410859820613528673953162767949
Probable prime cofactor 785941965246821725517634354985618196758423193048763238517231673375963788322474444838897417 has 90 digits

Aug 17, 2009 (4th)

By Sinkiti Sibata / Msieve / Aug 17, 2009

(58·10¹⁸⁰+41)/9 = 6(4)₁₇₉9_<181> = 11 · 1627 · C177

C177 = P34 · P144

P34 = 1280000823649561544625004925310473_<34>

P144 = 281316364893573382047531009276426345002478941203207649965104069424638937150544933870763338855019543891400117696494924919567782620672341626777329_<144>

Number: 64449_180
N=360085178769874528940294152340864080261744674774791554140048301080876372824744060146641584871455799544305997901572578892800158934147870841171394336729309071042322425235762666617
  ( 177 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=1280000823649561544625004925310473 (pp34)
 r2=281316364893573382047531009276426345002478941203207649965104069424638937150544933870763338855019543891400117696494924919567782620672341626777329 (pp144)
Version: Msieve-1.40
Total time: 139.70 hours.
Scaled time: 468.96 units (timescale=3.357).
Factorization parameters were as follows:
name: 64449_180
n: 360085178769874528940294152340864080261744674774791554140048301080876372824744060146641584871455799544305997901572578892800158934147870841171394336729309071042322425235762666617
m: 1000000000000000000000000000000000000
deg: 5
c5: 58
c0: 41
skew: 0.93
type: snfs
lss: 1
rlim: 7500000
alim: 7500000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7500000/7500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3750000, 6050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1433571 x 1433819
Total sieving time: 134.91 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 4.50 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,181.000,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,53,53,2.5,2.5,100000
total time: 139.70 hours.
 --------- CPU info (if available) ----------

Aug 17, 2009 (3rd)

By Justin Card / ggnfs, msieve / Aug 17, 2009

(8·10¹⁹⁷+7)/3 = 2(6)₁₉₆9_<198> = 13 · 29 · 73 · 113786895756473091763216512239_<30> · C164

C164 = P70 · P95

P70 = 2325412411440405653690878974819812220657268033511965719935728303192037_<70>

P95 = 36619489557764519846267534525547256193377038956838686278299696905702216244880052542768324514023_<95>

Number: 26669_197
N=85155415518237946102479936799298669533177788063631844025863034765370542187259018971925248551625065434263578805689864621162022682754722142419580647352642227668434851
  ( 164 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=2325412411440405653690878974819812220657268033511965719935728303192037 (pp70)
 r2=36619489557764519846267534525547256193377038956838686278299696905702216244880052542768324514023 (pp95)
Version: Msieve-1.40
Total time: 342.90 hours.
Scaled time: 684.42 units (timescale=1.996).
Factorization parameters were as follows:
n: 85155415518237946102479936799298669533177788063631844025863034765370542187259018971925248551625065434263578805689864621162022682754722142419580647352642227668434851
m: 2000000000000000000000000000000000000000
deg: 5
c5: 25
c0: 7
skew: 0.78
type: snfs
lss: 1
rlim: 13900000
alim: 13900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

Factor base limits: 13900000/13900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6950000, 12650001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2445649 x 2445874
Total sieving time: 297.25 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 43.74 hours.
Time per square root: 1.50 hours.
Prototype def-par.txt line would be:
snfs,197.000,5,0,0,0,0,0,0,0,0,13900000,13900000,28,28,55,55,2.5,2.5,100000
total time: 342.90 hours.
 --------- CPU info (if available) ----------
[    0.138978] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.231791] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init)
[    0.084027] Calibrating delay using timer specific routine.. 4004.64 BogoMIPS (lpj=8009297)
[    0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000305)
[    0.231806] Total of 2 processors activated (8004.80 BogoMIPS).

Aug 17, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Aug 17, 2009

(5·10²⁰⁰+13)/9 = (5)₁₉₉7_<200> = 3 · 19 · C198

C198 = P89 · P110

P89 = 52593328804790143359951630636697845044104157190753524779891824241888335192056207024750447_<89>

P110 = 18531986690048427358425949212844400767279971081177871933577024616257238836726538482785916221117286551415305283_<110>

Number: 55557_200
N=974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711501
  ( 198 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=52593328804790143359951630636697845044104157190753524779891824241888335192056207024750447 (pp89)
 r2=18531986690048427358425949212844400767279971081177871933577024616257238836726538482785916221117286551415305283 (pp110)
Version: Msieve-1.40
Total time: 509.70 hours.
Scaled time: 888.93 units (timescale=1.744).
Factorization parameters were as follows:
n: 974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711501
m: 10000000000000000000000000000000000000000
deg: 5
c5: 5
c0: 13
skew: 1.21
type: snfs
lss: 1
rlim: 15500000
alim: 15500000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 15500000/15500000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7750000, 15350001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3174393 x 3174619
Total sieving time: 490.48 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 18.45 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,200.000,5,0,0,0,0,0,0,0,0,15500000,15500000,29,29,56,56,2.6,2.6,100000
total time: 509.70 hours.

Aug 17, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Aug 17, 2009

(61·10¹⁷¹-7)/9 = 6(7)₁₇₁_<172> = 3 · 2803 · 3690984696370158400897064979949717_<34> · C135

C135 = P35 · P101

P35 = 18349916058226002381325132005750817_<35>

P101 = 11900539403604735254297165860871207760195905493929857397119064848185233384993512653727172540270521877_<101>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 218373899103757824771934513730446408208901986048652105451130131357315856486078756863651890930918440628821417715447161662433665809123509 (135 digits)
Using B1=50000, B2=12746592, polynomial x^2, sigma=5473602807
Step 1 took 202ms
Step 2 took 234ms
********** Factor found in step 2: 18349916058226002381325132005750817
Found probable prime factor of 35 digits: 18349916058226002381325132005750817
Probable prime cofactor 11900539403604735254297165860871207760195905493929857397119064848185233384993512653727172540270521877 has 101 digits

Aug 16, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Aug 16, 2009

(25·10¹⁶⁹+11)/9 = 2(7)₁₆₈9_<170> = 29 · 467052151217671807_<18> · 25562040522225893199206593_<26> · C125

C125 = P51 · P75

P51 = 726341733161813647858156175202119648900783529862783_<51>

P75 = 110458109920047163481828000865195622785385713219451478383234067978685288847_<75>

Number: 27779_169
N=80230335001105177866805283220394479113117091317066824102441316262293178583056975568401818887106425370321835996839030630281201
  ( 125 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=726341733161813647858156175202119648900783529862783
 r2=110458109920047163481828000865195622785385713219451478383234067978685288847
Version: 
Total time: 34.73 hours.
Scaled time: 82.09 units (timescale=2.364).
Factorization parameters were as follows:
n: 80230335001105177866805283220394479113117091317066824102441316262293178583056975568401818887106425370321835996839030630281201
m: 10000000000000000000000000000000000
deg: 5
c5: 5
c0: 22
skew: 1.34
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 5500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11038674
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 973380 x 973628
Total sieving time: 31.10 hours.
Total relation processing time: 1.44 hours.
Matrix solve time: 1.98 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 34.73 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673791)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672381)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Aug 16, 2009

By Dmitry Domanov / ECMNET / Aug 16, 2009

(23·10²⁰⁵+31)/9 = 2(5)₂₀₄9_<206> = 40545719773789_<14> · C192

C192 = P34 · C159

P34 = 4202462726885897525922861991796773_<34>

C159 = [149981068011369458327294192549304395213719767345838336061005720263500366352537864270906566505780532829539650383016948492667426233305737362820224459405598540247_<159>]

C192=P34*C159
C192=4202462726885897525922861991796773<34>*149981068011369458327294192549304395213719767345838336061005720263500366352537864270906566505780532829539650383016948492667426233305737362820224459405598540247<159>

Aug 15, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 15, 2009

(58·10¹⁶⁸+41)/9 = 6(4)₁₆₇9_<169> = 11² · 17 · 336340635039131954550293537507006243_<36> · C130

C130 = P61 · P70

P61 = 6468180746247313164919651472070638965886398620871300817741023_<61>

P70 = 1440090234293645015127160651757741514630147400069989660127682788576013_<70>

Number: 64449_168
N=9314763926316936870617423027014862687838866087875593973448170193850377580272582112388416930433089994630940974221974276541583881299
  ( 130 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=6468180746247313164919651472070638965886398620871300817741023
 r2=1440090234293645015127160651757741514630147400069989660127682788576013
Version: 
Total time: 39.52 hours.
Scaled time: 94.28 units (timescale=2.386).
Factorization parameters were as follows:
n: 9314763926316936870617423027014862687838866087875593973448170193850377580272582112388416930433089994630940974221974276541583881299
m: 10000000000000000000000000000000000
deg: 5
c5: 29
c0: 2050
skew: 2.34
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3100000, 6100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11320930
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 971090 x 971338
Total sieving time: 36.11 hours.
Total relation processing time: 1.20 hours.
Matrix solve time: 1.97 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,27,27,52,52,2.4,2.4,100000
total time: 39.52 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673791)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672381)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)

Aug 15, 2009

By Serge Batalov / GMP-ECM 6.2.3 / Aug 15, 2009

(73·10²⁴⁹-1)/9 = 8(1)₂₄₉_<250> = 17 · 5443 · 15809 · C241

C241 = P38 · C204

P38 = 32607769874736976738779806206337465479_<38>

C204 = [170046461128108574995927236581628482215136764041055238483652624154293003769490480684917928338533050156473440999584084450662282572700445782394777642120172552258120330384289238781876693262128523142851830971_<204>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3778736387
Step 1 took 5244ms
Step 2 took 2780ms
********** Factor found in step 2: 32607769874736976738779806206337465479
Found probable prime factor of 38 digits: 32607769874736976738779806206337465479
Composite cofactor has 204 digits

Aug 14, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3 / Aug 14, 2009

(73·10²¹⁶-1)/9 = 8(1)₂₁₆_<217> = 71 · 28808051 · C208

C208 = P34 · P175

P34 = 3620576061701876499733072865659927_<34>

P175 = 1095293345497329293397673211340210417659625724719865891699257885248592552342275988711289537372777550314530400518083640878622741178698608241670961162797540046118753399114398333_<175>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2394144579
Step 1 took 12049ms
********** Factor found in step 1: 3620576061701876499733072865659927
Found probable prime factor of 34 digits: 3620576061701876499733072865659927
Probable prime cofactor has 175 digits

(73·10²⁴²-1)/9 = 8(1)₂₄₂_<243> = 6661 · 5768443348883_<13> · 2433133368010550753_<19> · C208

C208 = P33 · C176

P33 = 146337898716429751088899432223507_<33>

C176 = [59287011032147246415404357711918292857582091957106148141677454653007379683860195517172477070080575255441763542889691583392291227603304875315501329180227976487363263981212546307_<176>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=380702607
Step 1 took 11965ms
Step 2 took 5392ms
********** Factor found in step 2: 146337898716429751088899432223507
Found probable prime factor of 33 digits: 146337898716429751088899432223507
Composite cofactor has 176 digits

Aug 14, 2009

By Dmitry Domanov / ECMNET / Aug 14, 2009

(23·10¹⁹⁴+31)/9 = 2(5)₁₉₃9_<195> = 7 · 19 · 37 · 1801 · C188

C188 = P39 · P45 · P104

P39 = 829120576370272477495488439345330306211_<39>

P45 = 373665017540682988557616909862451034443569869_<45>

P104 = 93071800242908434411113725305788079538407132412622804537132101554811430232078431135405103826930054200481_<104>

C188=P39*P45*P104
C188=829120576370272477495488439345330306211<39>*373665017540682988557616909862451034443569869<45>*93071800242908434411113725305788079538407132412622804537132101554811430232078431135405103826930054200481<104>

Aug 13, 2009 (6th)

By Andreas Tete / Msieve v. 1.42, GGNFS / Aug 13, 2009

(58·10¹⁶³+41)/9 = 6(4)₁₆₂9_<164> = 3 · 53 · 337 · 41203 · 158613152738522987_<18> · 1748203055833034139767_<22> · C117

C117 = P41 · P76

P41 = 35354718772917701681492033166427827343819_<41>

P76 = 2977495823399103642870676144152784725505450903763932457717703309648252436651_<76>

Thu Aug 13 14:51:14 2009  
Thu Aug 13 14:51:14 2009  
Thu Aug 13 14:51:14 2009  Msieve v. 1.42
Thu Aug 13 14:51:14 2009  random seeds: 6239ca34 0a4dea92
Thu Aug 13 14:51:14 2009  factoring 105268527483812339334342341086979371310318838050297559395543654117627237975927554198893362237003523082233591893910169 (117 digits)
Thu Aug 13 14:51:15 2009  searching for 15-digit factors
Thu Aug 13 14:51:16 2009  commencing number field sieve (117-digit input)
Thu Aug 13 14:51:16 2009  R0: -29317831392317037372404
Thu Aug 13 14:51:16 2009  R1:  1913949221161
Thu Aug 13 14:51:16 2009  A0: -728982585579479297678902795
Thu Aug 13 14:51:16 2009  A1:  1550972593082845957057335
Thu Aug 13 14:51:16 2009  A2: -9804057744669819423
Thu Aug 13 14:51:16 2009  A3: -515744502109505
Thu Aug 13 14:51:16 2009  A4:  525317832
Thu Aug 13 14:51:16 2009  A5:  4860
Thu Aug 13 14:51:16 2009  skew 119821.42, size 4.205158e-011, alpha -6.397800, combined = 4.770932e-010
Thu Aug 13 14:51:16 2009  
Thu Aug 13 14:51:16 2009  commencing relation filtering
Thu Aug 13 14:51:16 2009  estimated available RAM is 3069.5 MB
Thu Aug 13 14:51:16 2009  commencing duplicate removal, pass 1
Thu Aug 13 14:51:23 2009  error -11 reading relation 454382
Thu Aug 13 14:53:02 2009  found 1086882 hash collisions in 9055892 relations
Thu Aug 13 14:53:29 2009  added 59696 free relations
Thu Aug 13 14:53:29 2009  commencing duplicate removal, pass 2
Thu Aug 13 14:54:05 2009  found 703872 duplicates and 8411715 unique relations
Thu Aug 13 14:54:05 2009  memory use: 41.3 MB
Thu Aug 13 14:54:05 2009  reading ideals above 100000
Thu Aug 13 14:54:05 2009  commencing singleton removal, initial pass
Thu Aug 13 14:56:27 2009  memory use: 149.2 MB
Thu Aug 13 14:56:27 2009  reading all ideals from disk
Thu Aug 13 14:56:43 2009  memory use: 289.6 MB
Thu Aug 13 14:56:45 2009  keeping 8758426 ideals with weight <= 200, target excess is 44355
Thu Aug 13 14:56:47 2009  commencing in-memory singleton removal
Thu Aug 13 14:56:49 2009  begin with 8411715 relations and 8758426 unique ideals
Thu Aug 13 14:57:02 2009  reduce to 3547796 relations and 3091338 ideals in 13 passes
Thu Aug 13 14:57:02 2009  max relations containing the same ideal: 115
Thu Aug 13 14:57:07 2009  removing 928378 relations and 725875 ideals in 202503 cliques
Thu Aug 13 14:57:07 2009  commencing in-memory singleton removal
Thu Aug 13 14:57:08 2009  begin with 2619418 relations and 3091338 unique ideals
Thu Aug 13 14:57:13 2009  reduce to 2479610 relations and 2216512 ideals in 8 passes
Thu Aug 13 14:57:13 2009  max relations containing the same ideal: 89
Thu Aug 13 14:57:16 2009  removing 715041 relations and 512538 ideals in 202503 cliques
Thu Aug 13 14:57:16 2009  commencing in-memory singleton removal
Thu Aug 13 14:57:16 2009  begin with 1764569 relations and 2216512 unique ideals
Thu Aug 13 14:57:19 2009  reduce to 1631712 relations and 1560558 ideals in 8 passes
Thu Aug 13 14:57:19 2009  max relations containing the same ideal: 68
Thu Aug 13 14:57:21 2009  removing 118317 relations and 98615 ideals in 19702 cliques
Thu Aug 13 14:57:21 2009  commencing in-memory singleton removal
Thu Aug 13 14:57:22 2009  begin with 1513395 relations and 1560558 unique ideals
Thu Aug 13 14:57:24 2009  reduce to 1507858 relations and 1456319 ideals in 6 passes
Thu Aug 13 14:57:24 2009  max relations containing the same ideal: 67
Thu Aug 13 14:57:24 2009  relations with 0 large ideals: 175
Thu Aug 13 14:57:24 2009  relations with 1 large ideals: 1081
Thu Aug 13 14:57:24 2009  relations with 2 large ideals: 9840
Thu Aug 13 14:57:24 2009  relations with 3 large ideals: 54246
Thu Aug 13 14:57:24 2009  relations with 4 large ideals: 176982
Thu Aug 13 14:57:24 2009  relations with 5 large ideals: 349708
Thu Aug 13 14:57:24 2009  relations with 6 large ideals: 426938
Thu Aug 13 14:57:24 2009  relations with 7+ large ideals: 488888
Thu Aug 13 14:57:24 2009  commencing 2-way merge
Thu Aug 13 14:57:27 2009  reduce to 954045 relation sets and 902506 unique ideals
Thu Aug 13 14:57:27 2009  commencing full merge
Thu Aug 13 14:57:53 2009  memory use: 95.9 MB
Thu Aug 13 14:57:53 2009  found 477338 cycles, need 470706
Thu Aug 13 14:57:53 2009  weight of 470706 cycles is about 33244760 (70.63/cycle)
Thu Aug 13 14:57:53 2009  distribution of cycle lengths:
Thu Aug 13 14:57:53 2009  1 relations: 46902
Thu Aug 13 14:57:53 2009  2 relations: 48364
Thu Aug 13 14:57:53 2009  3 relations: 51540
Thu Aug 13 14:57:53 2009  4 relations: 50100
Thu Aug 13 14:57:53 2009  5 relations: 46810
Thu Aug 13 14:57:53 2009  6 relations: 42132
Thu Aug 13 14:57:53 2009  7 relations: 36419
Thu Aug 13 14:57:53 2009  8 relations: 30854
Thu Aug 13 14:57:53 2009  9 relations: 26007
Thu Aug 13 14:57:53 2009  10+ relations: 91578
Thu Aug 13 14:57:53 2009  heaviest cycle: 21 relations
Thu Aug 13 14:57:53 2009  commencing cycle optimization
Thu Aug 13 14:57:55 2009  start with 2871862 relations
Thu Aug 13 14:58:05 2009  pruned 81938 relations
Thu Aug 13 14:58:05 2009  memory use: 72.8 MB
Thu Aug 13 14:58:05 2009  distribution of cycle lengths:
Thu Aug 13 14:58:05 2009  1 relations: 46902
Thu Aug 13 14:58:05 2009  2 relations: 49463
Thu Aug 13 14:58:05 2009  3 relations: 53366
Thu Aug 13 14:58:05 2009  4 relations: 51651
Thu Aug 13 14:58:05 2009  5 relations: 48234
Thu Aug 13 14:58:05 2009  6 relations: 43133
Thu Aug 13 14:58:05 2009  7 relations: 37001
Thu Aug 13 14:58:05 2009  8 relations: 31076
Thu Aug 13 14:58:05 2009  9 relations: 26045
Thu Aug 13 14:58:05 2009  10+ relations: 83835
Thu Aug 13 14:58:05 2009  heaviest cycle: 21 relations
Thu Aug 13 14:58:05 2009  RelProcTime: 409
Thu Aug 13 14:58:05 2009  
Thu Aug 13 14:58:05 2009  commencing linear algebra
Thu Aug 13 14:58:06 2009  read 470706 cycles
Thu Aug 13 14:58:07 2009  cycles contain 1474652 unique relations
Thu Aug 13 14:58:43 2009  read 1474652 relations
Thu Aug 13 14:58:47 2009  using 20 quadratic characters above 134213298
Thu Aug 13 14:58:58 2009  building initial matrix
Thu Aug 13 14:59:26 2009  memory use: 167.9 MB
Thu Aug 13 14:59:28 2009  read 470706 cycles
Thu Aug 13 14:59:28 2009  matrix is 470527 x 470706 (135.6 MB) with weight 45098600 (95.81/col)
Thu Aug 13 14:59:28 2009  sparse part has weight 31768393 (67.49/col)
Thu Aug 13 14:59:36 2009  filtering completed in 2 passes
Thu Aug 13 14:59:36 2009  matrix is 470306 x 470485 (135.5 MB) with weight 45089323 (95.84/col)
Thu Aug 13 14:59:36 2009  sparse part has weight 31765638 (67.52/col)
Thu Aug 13 14:59:38 2009  read 470485 cycles
Thu Aug 13 14:59:39 2009  matrix is 470306 x 470485 (135.5 MB) with weight 45089323 (95.84/col)
Thu Aug 13 14:59:39 2009  sparse part has weight 31765638 (67.52/col)
Thu Aug 13 14:59:39 2009  saving the first 48 matrix rows for later
Thu Aug 13 14:59:40 2009  matrix is 470258 x 470485 (129.3 MB) with weight 35913518 (76.33/col)
Thu Aug 13 14:59:40 2009  sparse part has weight 31066595 (66.03/col)
Thu Aug 13 14:59:40 2009  matrix includes 64 packed rows
Thu Aug 13 14:59:40 2009  using block size 65536 for processor cache size 3072 kB
Thu Aug 13 14:59:44 2009  commencing Lanczos iteration
Thu Aug 13 14:59:44 2009  memory use: 130.2 MB
Thu Aug 13 15:39:12 2009  lanczos halted after 7439 iterations (dim = 470256)
Thu Aug 13 15:39:14 2009  recovered 29 nontrivial dependencies
Thu Aug 13 15:39:14 2009  BLanczosTime: 2469
Thu Aug 13 15:39:14 2009  
Thu Aug 13 15:39:14 2009  commencing square root phase
Thu Aug 13 15:39:14 2009  reading relations for dependency 1
Thu Aug 13 15:39:14 2009  read 235617 cycles
Thu Aug 13 15:39:15 2009  cycles contain 924126 unique relations
Thu Aug 13 15:39:48 2009  read 924126 relations
Thu Aug 13 15:39:53 2009  multiplying 737592 relations
Thu Aug 13 15:41:37 2009  multiply complete, coefficients have about 31.47 million bits
Thu Aug 13 15:41:38 2009  initial square root is modulo 1088586883
Thu Aug 13 15:44:50 2009  sqrtTime: 336
Thu Aug 13 15:44:50 2009  prp41 factor: 35354718772917701681492033166427827343819
Thu Aug 13 15:44:50 2009  prp76 factor: 2977495823399103642870676144152784725505450903763932457717703309648252436651
Thu Aug 13 15:44:50 2009  elapsed time 00:53:36
Thu Aug 13 15:44:50 2009  total time ~ 41,11 hours

Aug 13, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 13, 2009

(58·10¹⁶¹+41)/9 = 6(4)₁₆₀9_<162> = 13 · 229 · C159

C159 = P40 · P119

P40 = 3654704663721431785734998256008161717483_<40>

P119 = 59231722451106549788320435782143534486295223609948241326485620953755925134115062706023714637202558162648631578274012739_<119>

Number: 64449_161
N=216474452282312544321277945732094203709924233941701190609487552718993767028701526518120404583286679356548352181539954465718657858395849662225208076736461015937
  ( 159 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=3654704663721431785734998256008161717483
 r2=59231722451106549788320435782143534486295223609948241326485620953755925134115062706023714637202558162648631578274012739
Version: 
Total time: 18.03 hours.
Scaled time: 42.94 units (timescale=2.381).
Factorization parameters were as follows:
n: 216474452282312544321277945732094203709924233941701190609487552718993767028701526518120404583286679356548352181539954465718657858395849662225208076736461015937
m: 100000000000000000000000000000000
deg: 5
c5: 580
c0: 41
skew: 0.59
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 3500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9614060
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 672370 x 672618
Total sieving time: 16.52 hours.
Total relation processing time: 0.51 hours.
Matrix solve time: 0.92 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 18.03 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673798)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672387)

Aug 13, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.1 / Aug 13, 2009

(49·10¹⁷¹-13)/9 = 5(4)₁₇₀3_<172> = 1309907 · 1509331 · C160

C160 = P39 · C122

P39 = 186135721123313863044793461731766127889_<39>

C122 = [14794452213434372946420738528169896579615815849117777730825714913852145946553387018597884831622546553977005766909682325811_<122>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2313565796
Step 1 took 52141ms
Step 2 took 17706ms
********** Factor found in step 2: 186135721123313863044793461731766127889
Found probable prime factor of 39 digits: 186135721123313863044793461731766127889
Composite cofactor 14794452213434372946420738528169896579615815849117777730825714913852145946553387018597884831622546553977005766909682325811 has 122 digits

Aug 13, 2009 (3rd)

By Dmitry Domanov / ECMNET / Aug 13, 2009

(16·10²¹⁰-7)/9 = 1(7)₂₁₀_<211> = 2306753 · 707999891526611_<15> · 34982088008588268790615606126668383363_<38> · C152

C152 = P43 · P110

P43 = 1742276401997614863682400832116335307416429_<43>

P110 = 17859956858070459648332660652295189478614882396823687035320140864284662019894144474128047165289895725299940797_<110>

C152=P43*P110
C152=1742276401997614863682400832116335307416429<43>*17859956858070459648332660652295189478614882396823687035320140864284662019894144474128047165289895725299940797<110>

Aug 13, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Aug 13, 2009

(25·10²¹⁵-1)/3 = 8(3)₂₁₅_<216> = 468653 · C211

C211 = P47 · P165

P47 = 10837959565633376609020155979327155879453500933_<47>

P165 = 164066466998120886009170753099955422048842327500144372228690573743783715684021657284565055073307989853343982097643796221647012749477812858299698290812380055168396917_<165>

Number: n
N=1778145735401956956070553977747573008885749868950659300875772337600171840003869245120234658336409525455578718867335391714836634638705680606617973923848419477381630616540027127391339292255321812371484516973823561
  ( 211 digits)
SNFS difficulty: 216 digits.
Divisors found:

Thu Aug 13 17:10:17 2009  prp47 factor: 10837959565633376609020155979327155879453500933
Thu Aug 13 17:10:17 2009  prp165 factor: 164066466998120886009170753099955422048842327500144372228690573743783715684021657284565055073307989853343982097643796221647012749477812858299698290812380055168396917
Thu Aug 13 17:10:17 2009  elapsed time 69:23:21 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 148.72 hours.
Scaled time: 299.67 units (timescale=2.015).
Factorization parameters were as follows:
name: KA_8_3_215
n: 1778145735401956956070553977747573008885749868950659300875772337600171840003869245120234658336409525455578718867335391714836634638705680606617973923848419477381630616540027127391339292255321812371484516973823561
m: 1000000000000000000000000000000000000
deg: 6
c6: 5
c0: -2
skew: 0.86
type: snfs
lss: 1
rlim: 29000000
alim: 29000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 29000000/29000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [14500000, 41549990)
Primes: RFBsize:1799676, AFBsize:1800322, largePrimes:38147337 encountered
Relations: rels:34668211, finalFF:912109
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 9105302 hash collisions in 49974295 relations
Msieve: matrix is 5732590 x 5732838 (1550.1 MB)

Total sieving time: 147.03 hours.
Total relation processing time: 1.69 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,216,6,0,0,0,0,0,0,0,0,29000000,29000000,29,29,58,58,2.6,2.6,100000
total time: 148.72 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3352028k/3407296k available (3120k kernel code, 53984k reserved, 1898k data, 424k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5662.12 BogoMIPS (lpj=2831063)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830445)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459)
Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830460)
Total of 4 processors activated (22644.85 BogoMIPS).

Aug 13, 2009

By Serge Batalov, Bruce Dodson / Msieve / Aug 12, 2009

c253 from 10³⁹³+1 was splitted into p119 and p134. Congratulations!

Aug 12, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Aug 12, 2009

(58·10¹⁵²+41)/9 = 6(4)₁₅₁9_<153> = 11 · 17 · 16007 · C147

C147 = P68 · P80

P68 = 11070022447903046623645328650347018977427326705944677000437857521689_<68>

P80 = 19448469542909211426583031757749301794789777521107886109243313377103525520008349_<80>

Number: n
N=215294994417363674931136225643408162820625750446894872679180279899083069754724435213485959666858464810831238754316525438718302869648420675728581461
  ( 147 digits)
SNFS difficulty: 154 digits.
Divisors found:

Wed Aug 12 12:03:18 2009  prp68 factor: 11070022447903046623645328650347018977427326705944677000437857521689
Wed Aug 12 12:03:18 2009  prp80 factor: 19448469542909211426583031757749301794789777521107886109243313377103525520008349
Wed Aug 12 12:03:18 2009  elapsed time 01:52:28 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.90 hours.
Scaled time: 18.76 units (timescale=0.943).
Factorization parameters were as follows:
name: KA_6_4_151_9
n: 215294994417363674931136225643408162820625750446894872679180279899083069754724435213485959666858464810831238754316525438718302869648420675728581461
m: 2000000000000000000000000000000
deg: 5
c5: 725
c0: 164
skew: 0.74
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [1300000, 2050001)
Primes: RFBsize:189880, AFBsize:189046, largePrimes:27535725 encountered
Relations: rels:24932402, finalFF:456925
Max relations in full relation-set: 28
Initial matrix: 378993 x 456925 with sparse part having weight 73195773.
Pruned matrix : 

Msieve: found 2077426 hash collisions in 26024074 relations
Msieve: matrix is 475387 x 475634 (127.1 MB)

Total sieving time: 19.20 hours.
Total relation processing time: 0.70 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,29,29,58,58,2.6,2.6,100000
total time: 19.90 hours.
 --------- CPU info (if available) ----------

Aug 12, 2009

By Dmitry Domanov / ECMNET / Aug 12, 2009

(58·10¹⁶⁸+41)/9 = 6(4)₁₆₇9_<169> = 11² · 17 · C166

C166 = P36 · C130

P36 = 336340635039131954550293537507006243_<36>

C130 = [9314763926316936870617423027014862687838866087875593973448170193850377580272582112388416930433089994630940974221974276541583881299_<130>]

C166=P36*C130
C166=336340635039131954550293537507006243<36>*9314763926316936870617423027014862687838866087875593973448170193850377580272582112388416930433089994630940974221974276541583881299<130>

(16·10²³⁰-7)/9 = 1(7)₂₃₀_<231> = 3² · 140681 · 1402277 · C219

C219 = P43 · P176

P43 = 3944281709221934348316789231845083597207091_<43>

P176 = 25386204870744998992688276663987897077304779888008176579483498199145614420279845835462036189475927778331120836559408570910727745551926370892296621414363814700980634305953356159_<176>

C219=P43*P176
C219=3944281709221934348316789231845083597207091<43>*25386204870744998992688276663987897077304779888008176579483498199145614420279845835462036189475927778331120836559408570910727745551926370892296621414363814700980634305953356159<176>

Aug 11, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Aug 11, 2009

(58·10¹⁴⁸+41)/9 = 6(4)₁₄₇9_<149> = 3² · 7² · 11 · 7655322337515029619053_<22> · C124

C124 = P50 · P74

P50 = 37355104026158289925635199403391287893388509054633_<50>

P74 = 46455889216811801389017392632315875552686098951001099958910251693636540751_<74>

Number: 64449_148
N=1735364574321690008200642197598958580298118964657785245246879331636960268082291614275971412554302452221654247232075389849383
  ( 124 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=37355104026158289925635199403391287893388509054633
 r2=46455889216811801389017392632315875552686098951001099958910251693636540751
Version: 
Total time: 7.25 hours.
Scaled time: 17.32 units (timescale=2.388).
Factorization parameters were as follows:
n: 1735364574321690008200642197598958580298118964657785245246879331636960268082291614275971412554302452221654247232075389849383
m: 1000000000000000000000000000000
deg: 5
c5: 29
c0: 2050
skew: 2.34
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 1700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6663329
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 391208 x 391456
Total sieving time: 6.67 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.31 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000
total time: 7.25 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673788)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672383)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

(58·10¹⁷⁵+41)/9 = 6(4)₁₇₄9_<176> = 3² · 113 · 180799 · 18369017 · 20724731513_<11> · 194278867157_<12> · 4211528010489493_<16> · C124

C124 = P40 · P84

P40 = 2202184715456389693063837224368295327739_<40>

P84 = 510945617062227781245498909898705264220997982507792737736799211040862361156935490637_<84>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 1125196628323871537050544410903193876581153579714044972724099733552508728126037056929993269101100025133827011425034680879743 (124 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2028390863
Step 1 took 3343ms
Step 2 took 2092ms
********** Factor found in step 2: 2202184715456389693063837224368295327739
Found probable prime factor of 40 digits: 2202184715456389693063837224368295327739
Probable prime cofactor 510945617062227781245498909898705264220997982507792737736799211040862361156935490637 has 84 digits

Aug 11, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.1 / Aug 11, 2009

(4·10¹⁷²+11)/3 = 1(3)₁₇₁7_<173> = 89 · 44298394983828534317971_<23> · C148

C148 = P36 · P113

P36 = 147668611851868658810324482778075801_<36>

P113 = 22901954443464829237690488724952674774172113307515222316314785504936376877185871170914885048443823739100628195923_<113>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1532346831
Step 1 took 46999ms
Step 2 took 16538ms
********** Factor found in step 2: 147668611851868658810324482778075801
Found probable prime factor of 36 digits: 147668611851868658810324482778075801
Probable prime cofactor 22901954443464829237690488724952674774172113307515222316314785504936376877185871170914885048443823739100628195923 has 113 digits

Aug 11, 2009 (3rd)

By Robert Backstrom / GGNFS / Aug 11, 2009

(58·10¹⁸⁹+41)/9 = 6(4)₁₈₈9_<190> = 53 · 71 · 1009 · 12964271 · 39384977 · 1248374028769795019_<19> · 41054055524932111007_<20> · 261420106563786798596455219_<27> · C105

C105 = P43 · P62

P43 = 3339319253796127630188959796136480948753637_<43>

P62 = 74299122286499570025192389670970928627261334898949097017828959_<62>

Number: n
N=248108489591460980312417272537903441658361226851702740557431060424235449229527746069508933855398695173883
  ( 105 digits)
Divisors found:
 r1=3339319253796127630188959796136480948753637 (pp43)
 r2=74299122286499570025192389670970928627261334898949097017828959 (pp62)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.55 hours.
Scaled time: 15.64 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_6_4_188_9
n: 248108489591460980312417272537903441658361226851702740557431060424235449229527746069508933855398695173883
Y0: -136270219024381679450
Y1:  45562200853
c0: -684169272975852034269820119
c1:  45234606651522858406119
c2:  188909143076621294
c3: -34709869262836
c4:  106646558
c5:  5280
skew: 46076.58
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1250000, 1950001)
Primes: RFBsize:183072, AFBsize:183774, largePrimes:14525770 encountered
Relations: rels:12546494, finalFF:474415
Max relations in full relation-set: 48
Initial matrix: 366932 x 474415 with sparse part having weight 52901740.
Pruned matrix : 288929 x 290827 with weight 26572457.
Total sieving time: 7.25 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 0.76 hours.
Total square root time: 0.15 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000
total time: 8.55 hours.
 --------- CPU info (if available) ----------

Aug 11, 2009 (2nd)

By Sinkiti Sibata / Msieve / Aug 11, 2009

(58·10¹⁶⁶+41)/9 = 6(4)₁₆₅9_<167> = 3³ · 7 · 11 · 215443 · 4093637 · C152

C152 = P72 · P80

P72 = 706604938908288596762603928693621117476374747431908877267657716973583417_<72>

P80 = 49740782017038381446898408076325283314020354933960390731754594066785632705466473_<80>

Number: 64449_166
N=35147082238399905566036355276072819135190316906897480108713199435188564513655611555102672917103076788399563036475073085609589123129960373650671362278241
  ( 152 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=706604938908288596762603928693621117476374747431908877267657716973583417 (pp72)
 r2=49740782017038381446898408076325283314020354933960390731754594066785632705466473 (pp80)
Version: Msieve-1.40
Total time: 43.05 hours.
Scaled time: 143.74 units (timescale=3.339).
Factorization parameters were as follows:
name: 64449_166
n: 35147082238399905566036355276072819135190316906897480108713199435188564513655611555102672917103076788399563036475073085609589123129960373650671362278241
m: 2000000000000000000000000000000000
deg: 5
c5: 145
c0: 328
skew: 1.18
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 4450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 842623 x 842871
Total sieving time: 41.52 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.36 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,168.000,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000
total time: 43.05 hours.
 --------- CPU info (if available) ----------

Aug 11, 2009

By Serge Batalov / PFGW / Aug 10, 2009

(64·10⁸³⁴⁶¹-1)/9 = 7(1)₈₃₄₆₁_<83462>

Aug 10, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 10, 2009

(58·10¹⁴⁶+41)/9 = 6(4)₁₄₅9_<147> = 11² · 139 · 30586547 · 8854610330194782473_<19> · C117

C117 = P46 · P72

P46 = 1044143941895224076008252929168616516373419781_<46>

P72 = 135495551116589058893468838756066885759317128660887029717156341753187261_<72>

Number: 64449_146
N=141476858852141129982085096165096307405123624215597661573103210099884666813868205468677251665186249925639019054609841
  ( 117 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=1044143941895224076008252929168616516373419781
 r2=135495551116589058893468838756066885759317128660887029717156341753187261
Version: 
Total time: 6.16 hours.
Scaled time: 14.51 units (timescale=2.355).
Factorization parameters were as follows:
n: 141476858852141129982085096165096307405123624215597661573103210099884666813868205468677251665186249925639019054609841
m: 100000000000000000000000000000
deg: 5
c5: 580
c0: 41
skew: 0.59
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1500000, 2700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6811242
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 372186 x 372434
Total sieving time: 5.31 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,49,49,2.3,2.3,75000
total time: 6.16 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Aug 10, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Aug 10, 2009

(58·10¹⁷⁰+41)/9 = 6(4)₁₆₉9_<171> = 11 · 8442103296703_<13> · 6243174303238469933530387_<25> · C133

C133 = P52 · P81

P52 = 1268227929841860533189429196657056691419100472647721_<52>

P81 = 876474658081602209257265498268798224770709796472774664205322953842768425268663639_<81>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1249571775
Step 1 took 37981ms
Step 2 took 13962ms
********** Factor found in step 2: 1268227929841860533189429196657056691419100472647721
Found probable prime factor of 52 digits: 1268227929841860533189429196657056691419100472647721
Probable prime cofactor 876474658081602209257265498268798224770709796472774664205322953842768425268663639 has 81 digits

Aug 10, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 10, 2009

(58·10¹⁴²+41)/9 = 6(4)₁₄₁9_<143> = 3 · 7 · 11 · 13229 · 126653 · 15815032747_<11> · C122

C122 = P57 · P65

P57 = 522074508523921921621312471446082179548893172922272368021_<57>

P65 = 20166402113362492556571937451567880430507687069249483258274948441_<65>

Number: 64449_142
N=10528364472029503674546930418450190626108381180174211115822246930224941166469042970442458502269726972756776294182752205261
  ( 122 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=522074508523921921621312471446082179548893172922272368021
 r2=20166402113362492556571937451567880430507687069249483258274948441
Version: 
Total time: 4.72 hours.
Scaled time: 11.29 units (timescale=2.390).
Factorization parameters were as follows:
n: 10528364472029503674546930418450190626108381180174211115822246930224941166469042970442458502269726972756776294182752205261
m: 20000000000000000000000000000
deg: 5
c5: 725
c0: 164
skew: 0.74
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 2200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4703864
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 321444 x 321692
Total sieving time: 4.07 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,2400000,2400000,26,26,49,49,2.3,2.3,50000
total time: 4.72 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Aug 9, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Aug 9, 2009

(58·10¹⁴¹+41)/9 = 6(4)₁₄₀9_<142> = 13417 · 11465492388766613_<17> · 85492832353215785749_<20> · C102

C102 = P48 · P55

P48 = 297188596750020055603166795930122343745013718293_<48>

P55 = 1648828582186947758223219615219991321258882551942718717_<55>

Number: 64449_141
N=490013052621464118683651322907303005438915081644290634464703535904536125332452737523019513099576390081
  ( 102 digits)
Divisors found:
 r1=297188596750020055603166795930122343745013718293
 r2=1648828582186947758223219615219991321258882551942718717
Version: 
Total time: 3.55 hours.
Scaled time: 8.48 units (timescale=2.391).
Factorization parameters were as follows:
name: 64449_141
n: 490013052621464118683651322907303005438915081644290634464703535904536125332452737523019513099576390081
skew: 2999.04
# norm 2.87e+14
c5: 285840
c4: -580998390
c3: -39809786971105
c2: 13101624497222693
c1: 51794700540962006453
c0: -6871927561416625019595
# alpha -6.32
Y1: 42203408671
Y0: -17652952443475187786
# Murphy_E 2.92e-09
# M 43468290854972797452314451564270390388087360027321479264612436286247719101896379620470713861572886086
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4920370
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 221588 x 221836
Polynomial selection time: 0.22 hours.
Total sieving time: 2.86 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 3.55 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

(58·10²⁰⁰+41)/9 = 6(4)₁₉₉9_<201> = 11 · 17 · 107 · 2377 · 932774347987103381_<18> · 13826677866082240683703_<23> · 21474065269491482871681097_<26> · 9617476601959055323120190872597_<31> · C97

C97 = P48 · P50

P48 = 105112228249013874195504102675707517143167052699_<48>

P50 = 48395817392296351722664742435602568363350373923061_<50>

Number: 64449_200
N=5086992204036649549554802325517951171974055226822069754918148594115667379490630513181229558391639
  ( 97 digits)
Divisors found:
 r1=105112228249013874195504102675707517143167052699
 r2=48395817392296351722664742435602568363350373923061
Version: 
Total time: 1.81 hours.
Scaled time: 4.32 units (timescale=2.386).
Factorization parameters were as follows:
name: 64449_200
n: 5086992204036649549554802325517951171974055226822069754918148594115667379490630513181229558391639
skew: 4251.50
# norm 3.00e+13
c5: 88920
c4: -552671486
c3: -4344467514261
c2: 3144978948596562
c1: 41332925549711484436
c0: 1886464308075611431704
# alpha -5.85
Y1: 3492390701
Y0: -2246431410188375885
# Murphy_E 4.64e-09
# M 1588946694778192353638204469934463977067134430662642725994726068441844085253881674329972420828066
type: gnfs
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [500000, 850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3998077
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 145180 x 145428
Polynomial selection time: 0.11 hours.
Total sieving time: 1.49 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
gnfs,96,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000
total time: 1.81 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

(58·10¹⁴⁹+41)/9 = 6(4)₁₄₈9_<150> = 13 · 421 · 673 · 100732103 · 10121236004206718958491_<23> · C114

C114 = P34 · P81

P34 = 1696102823243283336102096639983899_<34>

P81 = 101179223498410154287697137052894881945104457224269718891386984074813463313174703_<81>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 171610366629216617736141540111186208266328445401431653663190700487849543363369209052931064897099041336492494106997 (114 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=8045793004
Step 1 took 2679ms
Step 2 took 1931ms
********** Factor found in step 2: 1696102823243283336102096639983899
Found probable prime factor of 34 digits: 1696102823243283336102096639983899
Probable prime cofactor 101179223498410154287697137052894881945104457224269718891386984074813463313174703 has 81 digits

(58·10¹³⁹+41)/9 = 6(4)₁₃₈9_<140> = 3³ · 31 · 354401 · 54080105661919_<14> · C118

C118 = P48 · P71

P48 = 240281321672102092031822941423701958764184969789_<48>

P71 = 16718893984341374478344248259057953266891108617477674510284921115332047_<71>

Number: 64449_139
N=4017237943453302397946339277421751791024513472930215399935475761833309366097049405279496394556016946350294521398528083
  ( 118 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=240281321672102092031822941423701958764184969789
 r2=16718893984341374478344248259057953266891108617477674510284921115332047
Version: 
Total time: 2.70 hours.
Scaled time: 6.45 units (timescale=2.387).
Factorization parameters were as follows:
n: 4017237943453302397946339277421751791024513472930215399935475761833309366097049405279496394556016946350294521398528083
m: 10000000000000000000000000000
deg: 5
c5: 29
c0: 205
skew: 1.48
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [950000, 1550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4087260
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 225814 x 226062
Total sieving time: 2.35 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,48,48,2.3,2.3,50000
total time: 2.70 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

(58·10¹⁵⁴+41)/9 = 6(4)₁₅₃9_<155> = 3 · 7 · 11 · 31 · 71 · 5855357 · C143

C143 = P38 · P106

P38 = 19602950039461147737333838041523754911_<38>

P106 = 1104278583638193529919243527908672991914078598007534915906542790083954395182929626640133526640510031759077_<106>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 21647117904706426189450950955016520273027057886377657995652670021137134050778094557363598017537468435215087853257755032275763510326739547577147 (143 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=127652953
Step 1 took 4052ms
Step 2 took 2504ms
********** Factor found in step 2: 19602950039461147737333838041523754911
Found probable prime factor of 38 digits: 19602950039461147737333838041523754911
Probable prime cofactor 1104278583638193529919243527908672991914078598007534915906542790083954395182929626640133526640510031759077 has 106 digits

(58·10¹⁵⁹+41)/9 = 6(4)₁₅₈9_<160> = 47 · C159

C159 = P32 · P127

P32 = 21092604873221414521443936704579_<32>

P127 = 6500659357516210823212559424126325115688797215821254650858989687046391572429678404166908697240963504783993737251101929522190373_<127>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 137115839243498817966903073286052009456264775413711583924349881796690307328605200945626477541371158392434988179669030732860520094562647754137115839243498817967 (159 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1988145448
Step 1 took 4787ms
Step 2 took 2705ms
********** Factor found in step 2: 21092604873221414521443936704579
Found probable prime factor of 32 digits: 21092604873221414521443936704579
Probable prime cofactor 6500659357516210823212559424126325115688797215821254650858989687046391572429678404166908697240963504783993737251101929522190373 has 127 digits

(58·10¹⁴⁰+41)/9 = 6(4)₁₃₉9_<141> = 11 · 19 · 127 · 2801 · 517961019025123_<15> · C119

C119 = P44 · P75

P44 = 28571814345470798457850196642434401668480249_<44>

P75 = 585716518304778674109618639218066670643040948267599228491642409925313514109_<75>

Number: 64449_140
N=16734983620079684836530558211268541781736781482763673605856165874596688227525266870848902799120670143654113023649333141
  ( 119 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=28571814345470798457850196642434401668480249
 r2=585716518304778674109618639218066670643040948267599228491642409925313514109
Version: 
Total time: 3.15 hours.
Scaled time: 7.52 units (timescale=2.385).
Factorization parameters were as follows:
n: 16734983620079684836530558211268541781736781482763673605856165874596688227525266870848902799120670143654113023649333141
m: 10000000000000000000000000000
deg: 5
c5: 58
c0: 41
skew: 0.93
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [950000, 1650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3952668
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 274683 x 274930
Total sieving time: 2.65 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,48,48,2.3,2.3,50000
total time: 3.15 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

(43·10²⁰⁰+11)/9 = 4(7)₁₉₉9_<201> = C201

C201 = P91 · P111

P91 = 2174373058099133778955027754091881176658176439236542612023908234704073354923429801680431157_<91>

P111 = 219731281160859097400420474569740172057755221825684698747872340583961067609816288201669884937774558773451626247_<111>

Number: 47779_200
N=477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
  ( 201 digits)
SNFS difficulty: 201 digits.
Divisors found:
 r1=2174373058099133778955027754091881176658176439236542612023908234704073354923429801680431157
 r2=219731281160859097400420474569740172057755221825684698747872340583961067609816288201669884937774558773451626247
Version: 
Total time: 448.74 hours.
Scaled time: 1069.34 units (timescale=2.383).
Factorization parameters were as follows:
n: 477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
m: 10000000000000000000000000000000000000000
deg: 5
c5: 43
c0: 11
skew: 0.76
type: snfs
lss: 1
rlim: 20000000
alim: 20000000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [10000000, 19500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 39359230
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3461402 x 3461650
Total sieving time: 402.68 hours.
Total relation processing time: 11.76 hours.
Matrix solve time: 33.25 hours.
Time per square root: 1.06 hours.
Prototype def-par.txt line would be:
snfs,201,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,56,56,2.6,2.6,100000
total time: 448.74 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Aug 9, 2009 (4th)

By Wataru Sakai / Msieve / Aug 9, 2009

(55·10¹⁸²+71)/9 = 6(1)₁₈₁9_<183> = 81629 · C178

C178 = P87 · P92

P87 = 268968386937796209285255055537985514655500461536626239747662232571641324962733344449049_<87>

P92 = 27833925818601073393361973681889386756037781086677916726445315318676185387360456995972477139_<92>

Number: 61119_182
N=7486446129575409610691189541843108590220523479536820383823287203213454913218477637985410958251492865416838514634641011296366623517513519841124001410174216407295337577467702790811
  ( 178 digits)
SNFS difficulty: 184 digits.
Divisors found:
 r1=268968386937796209285255055537985514655500461536626239747662232571641324962733344449049
 r2=27833925818601073393361973681889386756037781086677916726445315318676185387360456995972477139
Version: 
Total time: 310.69 hours.
Scaled time: 624.49 units (timescale=2.010).
Factorization parameters were as follows:
n: 7486446129575409610691189541843108590220523479536820383823287203213454913218477637985410958251492865416838514634641011296366623517513519841124001410174216407295337577467702790811
m: 2000000000000000000000000000000000000
deg: 5
c5: 1375
c0: 568
skew: 0.84
type: snfs
lss: 1
rlim: 8400000
alim: 8400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4200000, 7800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1285146 x 1285394
Total sieving time: 310.69 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,184,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,54,54,2.5,2.5,100000
total time: 310.69 hours.
 --------- CPU info (if available) ----------

(4·10¹⁹⁹-7)/3 = 1(3)₁₉₈1_<200> = 11 · 313 · C196

C196 = P80 · P117

P80 = 14245284449048868649167658171982103265194892503790476016535809966373146771405253_<80>

P117 = 271850783034045904709166657548054817831235558520384314653175768959548794237356697623685222130093654997355896460223789_<117>

Number: 13331_199
N=3872591732016652144447671604221124987898150837447962048601026236808984412818278632975118598121793009971923709942879271952754380869396843837738406428502275147642559783134863007067479910930390163617
  ( 196 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=14245284449048868649167658171982103265194892503790476016535809966373146771405253
 r2=271850783034045904709166657548054817831235558520384314653175768959548794237356697623685222130093654997355896460223789
Version: 
Total time: 513.72 hours.
Scaled time: 1035.14 units (timescale=2.015).
Factorization parameters were as follows:
n: 3872591732016652144447671604221124987898150837447962048601026236808984412818278632975118598121793009971923709942879271952754380869396843837738406428502275147642559783134863007067479910930390163617
m: 10000000000000000000000000000000000000000
deg: 5
c5: 2
c0: -35
skew: 1.77
type: snfs
lss: 1
rlim: 15300000
alim: 15300000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 15300000/15300000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7650000, 12650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2913154 x 2913400
Total sieving time: 513.72 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15300000,15300000,29,29,56,56,2.6,2.6,100000
total time: 513.72 hours.
 --------- CPU info (if available) ----------

(37·10¹⁹³-1)/9 = 4(1)₁₉₃_<194> = 541 · C191

C191 = P95 · P97

P95 = 16982086357914803637623741673240335869987959520338455554555164416476118201559316006982399568593_<95>

P97 = 4474771923497334638554968073323091298281184099854318393507188833675114725959431699712597968081347_<97>

Number: 41111_193
N=75990963236804271924419798726637913329225713698911480796878209077839392072294105565824604641610186896693366194290408708153624974327377284863421647155473403162867118504826453070445676730334771
  ( 191 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=16982086357914803637623741673240335869987959520338455554555164416476118201559316006982399568593
 r2=4474771923497334638554968073323091298281184099854318393507188833675114725959431699712597968081347
Version: 
Total time: 650.69 hours.
Scaled time: 1307.89 units (timescale=2.010).
Factorization parameters were as follows:
n: 75990963236804271924419798726637913329225713698911480796878209077839392072294105565824604641610186896693366194290408708153624974327377284863421647155473403162867118504826453070445676730334771
m: 1000000000000000000000000000000000000000
deg: 5
c5: 37
c0: -100
skew: 1.22
type: snfs
lss: 1
rlim: 13200000
alim: 13200000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 13200000/13200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6600000, 13700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2320654 x 2320902
Total sieving time: 650.69 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,13200000,13200000,28,28,55,55,2.5,2.5,100000
total time: 650.69 hours.
 --------- CPU info (if available) ----------

Aug 9, 2009 (3rd)

By matsui / Msieve / Aug 9, 2009

9·10¹⁹⁶+7 = 9(0)₁₉₅7_<197> = 379 · 84347 · C190

C190 = P70 · P121

P70 = 2793581839990665879086071955488871732154051874807346381894557450536389_<70>

P121 = 1007795141038902862381302247759455291325233747340278362348189347943401583915173253582538601189245685674010445568232328851_<121>

N=2815358204437110888169498828388683223496303888263062566049476542013136899326513138510337041233079345271557408923240290854030465241384276593552961095221889797933295592935240223410560590059039
  ( 190 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=2793581839990665879086071955488871732154051874807346381894557450536389 (pp70)
 r2=1007795141038902862381302247759455291325233747340278362348189347943401583915173253582538601189245685674010445568232328851 (pp121)
Version: Msieve v. 1.42
Total time: 502.44 hours.
Scaled time: 1121.95 units (timescale=2.233).
Factorization parameters were as follows:
n: 2815358204437110888169498828388683223496303888263062566049476542013136899326513138510337041233079345271557408923240290854030465241384276593552961095221889797933295592935240223410560590059039
m: 1000000000000000000000000000000000000000
deg: 5
c5: 90
c0: 7
skew: 0.60
type: snfs
lss: 1
rlim: 13400000
alim: 13400000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 300000

Factor base limits: 13400000/13400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6700000, 14800001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2655010 x 2655235
Total sieving time: 488.23 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 13.50 hours.
Time per square root: 0.51 hours.
Prototype def-par.txt line would be:
snfs,196.000,5,0,0,0,0,0,0,0,0,13400000,13400000,28,28,55,55,2.5,2.5,100000
total time: 502.44 hours.

Aug 9, 2009 (2nd)

By Sinkiti Sibata / Msieve / Aug 9, 2009

(58·10¹⁴⁷+41)/9 = 6(4)₁₄₆9_<148> = 107 · 691 · 1870639 · 15308009 · C130

C130 = P57 · P74

P57 = 104226810757989487023155307155618642769595857629037983413_<57>

P74 = 29203541189843452413587717044503298257109696168892743916901538636843884779_<74>

Number: 64449_147
N=3043791961056964650204073474298058150487255812058742155043591009507435709246375658619967190325348574728898111100942827283085170727
  ( 130 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=104226810757989487023155307155618642769595857629037983413 (pp57)
 r2=29203541189843452413587717044503298257109696168892743916901538636843884779 (pp74)
Version: Msieve-1.40
Total time: 10.41 hours.
Scaled time: 34.93 units (timescale=3.357).
Factorization parameters were as follows:
name: 64449_147
n: 3043791961056964650204073474298058150487255812058742155043591009507435709246375658619967190325348574728898111100942827283085170727
m: 200000000000000000000000000000
deg: 5
c5: 725
c0: 164
skew: 0.74
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 2700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 368768 x 369016
Total sieving time: 10.10 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,149.000,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000
total time: 10.41 hours.
 --------- CPU info (if available) ----------

Aug 9, 2009

Many small prime numbers up to 215 digits in the primesize.txt were proved by Robert Backstrom.

Aug 8, 2009 (5th)

By Jo Yeong Uk / YAFU 1.10, Msieve, GGNFS, GMP-ECM / Aug 8, 2009

(58·10¹²⁰+41)/9 = 6(4)₁₁₉9_<121> = 11 · 17 · 1432943 · 13858699 · 96751818844475480137_<20> · C86

C86 = P40 · P46

P40 = 4171154534180201577214509051813439982857_<40>

P46 = 4300085410829145193862369954805882431917303879_<46>

08/08/09 14:59:52 v1.10 @ 조영욱-PC, starting SIQS on c86: 17936320758742123847911845494663667844121370803322423565926859018744477965975419602303
08/08/09 14:59:52 v1.10 @ 조영욱-PC, random seeds: 3513321531, 909715568
08/08/09 14:59:52 v1.10 @ 조영욱-PC, ==== sieve params ====
08/08/09 14:59:52 v1.10 @ 조영욱-PC, n = 86 digits, 287 bits
08/08/09 14:59:52 v1.10 @ 조영욱-PC, factor base: 56921 primes (max prime = 1493971)
08/08/09 14:59:52 v1.10 @ 조영욱-PC, single large prime cutoff: 164336810 (110 * pmax)
08/08/09 14:59:52 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
08/08/09 14:59:52 v1.10 @ 조영욱-PC, double large prime cutoff: 614218275674814
08/08/09 14:59:52 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base
08/08/09 14:59:52 v1.10 @ 조영욱-PC, buckets hold 1024 elements
08/08/09 14:59:52 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536
08/08/09 14:59:52 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors
08/08/09 14:59:52 v1.10 @ 조영욱-PC, using multiplier of 13
08/08/09 14:59:52 v1.10 @ 조영욱-PC, using small prime variation correction of 24 bits
08/08/09 14:59:52 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
08/08/09 14:59:52 v1.10 @ 조영욱-PC, trial factoring cutoff at 91 bits
08/08/09 14:59:52 v1.10 @ 조영욱-PC, ==== sieving started ====
08/08/09 15:17:13 v1.10 @ 조영욱-PC, sieve time = 453.0300, relation time = 269.1360, poly_time = 318.0120
08/08/09 15:17:13 v1.10 @ 조영욱-PC, 57094 relations found: 20657 full + 36437 from 472011 partial, using 168286 polys (164 A polys)
08/08/09 15:17:13 v1.10 @ 조영욱-PC, on average, sieving found 2.93 rels/poly and 473.28 rels/sec
08/08/09 15:17:13 v1.10 @ 조영욱-PC, trial division touched 15023845 sieve locations out of 198518243328
08/08/09 15:17:13 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
08/08/09 15:17:13 v1.10 @ 조영욱-PC, begin with 492668 relations
08/08/09 15:17:13 v1.10 @ 조영욱-PC, reduce to 111147 relations in 8 passes
08/08/09 15:17:14 v1.10 @ 조영욱-PC, recovered 111147 relations
08/08/09 15:17:14 v1.10 @ 조영욱-PC, recovered 81457 polynomials
08/08/09 15:17:14 v1.10 @ 조영욱-PC, attempting to build 57094 cycles
08/08/09 15:17:14 v1.10 @ 조영욱-PC, found 57094 cycles in 4 passes
08/08/09 15:17:14 v1.10 @ 조영욱-PC, distribution of cycle lengths:
08/08/09 15:17:14 v1.10 @ 조영욱-PC,    length 1 : 20657
08/08/09 15:17:14 v1.10 @ 조영욱-PC,    length 2 : 16661
08/08/09 15:17:14 v1.10 @ 조영욱-PC,    length 3 : 10075
08/08/09 15:17:14 v1.10 @ 조영욱-PC,    length 4 : 5301
08/08/09 15:17:14 v1.10 @ 조영욱-PC,    length 5 : 2549
08/08/09 15:17:14 v1.10 @ 조영욱-PC,    length 6 : 1083
08/08/09 15:17:14 v1.10 @ 조영욱-PC,    length 7 : 461
08/08/09 15:17:14 v1.10 @ 조영욱-PC,    length 9+: 307
08/08/09 15:17:14 v1.10 @ 조영욱-PC, largest cycle: 14 relations
08/08/09 15:17:14 v1.10 @ 조영욱-PC, matrix is 56921 x 57094 (11.8 MB) with weight 2647073 (46.36/col)
08/08/09 15:17:14 v1.10 @ 조영욱-PC, sparse part has weight 2647073 (46.36/col)
08/08/09 15:17:14 v1.10 @ 조영욱-PC, filtering completed in 3 passes
08/08/09 15:17:14 v1.10 @ 조영욱-PC, matrix is 48448 x 48508 (10.3 MB) with weight 2307516 (47.57/col)
08/08/09 15:17:14 v1.10 @ 조영욱-PC, sparse part has weight 2307516 (47.57/col)
08/08/09 15:17:14 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
08/08/09 15:17:15 v1.10 @ 조영욱-PC, matrix is 48400 x 48508 (7.3 MB) with weight 1823058 (37.58/col)
08/08/09 15:17:15 v1.10 @ 조영욱-PC, sparse part has weight 1420269 (29.28/col)
08/08/09 15:17:15 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
08/08/09 15:17:15 v1.10 @ 조영욱-PC, using block size 19403 for processor cache size 4096 kB
08/08/09 15:17:15 v1.10 @ 조영욱-PC, commencing Lanczos iteration
08/08/09 15:17:15 v1.10 @ 조영욱-PC, memory use: 6.5 MB
08/08/09 15:17:24 v1.10 @ 조영욱-PC, lanczos halted after 766 iterations (dim = 48398)
08/08/09 15:17:24 v1.10 @ 조영욱-PC, recovered 17 nontrivial dependencies
08/08/09 15:17:25 v1.10 @ 조영욱-PC, prp40 = 4171154534180201577214509051813439982857
08/08/09 15:17:26 v1.10 @ 조영욱-PC, prp46 = 4300085410829145193862369954805882431917303879
08/08/09 15:17:26 v1.10 @ 조영욱-PC, Lanczos elapsed time = 10.8730 seconds.
08/08/09 15:17:26 v1.10 @ 조영욱-PC, Sqrt elapsed time = 2.5110 seconds.
08/08/09 15:17:26 v1.10 @ 조영욱-PC, SIQS elapsed time = 1054.3570 seconds.
08/08/09 15:17:26 v1.10 @ 조영욱-PC, 
08/08/09 15:17:26 v1.10 @ 조영욱-PC,

(58·10¹²⁴+41)/9 = 6(4)₁₂₃9_<125> = 3 · 7 · 11² · 31 · 53 · 3336601 · 4436867425279643_<16> · C97

C97 = P48 · P49

P48 = 267492333084733470268984029104710701455232281551_<48>

P49 = 3898083961532116929988497717471694102623444454411_<49>

Number: 64449_124
N=1042707573430406393491906031296711719332378538641660681551632980630039511373360505714837935871461
  ( 97 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=267492333084733470268984029104710701455232281551
 r2=3898083961532116929988497717471694102623444454411
Version: 
Total time: 0.79 hours.
Scaled time: 1.89 units (timescale=2.388).
Factorization parameters were as follows:
n: 1042707573430406393491906031296711719332378538641660681551632980630039511373360505714837935871461
m: 10000000000000000000000000
deg: 5
c5: 29
c0: 205
skew: 1.48
type: snfs
lss: 1
rlim: 800000
alim: 800000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [400000, 600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2446613
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 95442 x 95690
Total sieving time: 0.70 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,800000,800000,26,26,46,46,2.3,2.3,40000
total time: 0.79 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

(58·10¹³⁵+41)/9 = 6(4)₁₃₄9_<136> = 1439 · 53697084205907_<14> · C119

C119 = P52 · P68

P52 = 1128787256771068110891967257486158744224357811724497_<52>

P68 = 73885954557658207227978625191186478807384791934220624008771044803029_<68>

Number: 64449_135
N=83401523959050804924972610883019020772103327350516411471050111549524066031956548155738313342090261880249108256179101413
  ( 119 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=1128787256771068110891967257486158744224357811724497
 r2=73885954557658207227978625191186478807384791934220624008771044803029
Version: 
Total time: 2.26 hours.
Scaled time: 5.40 units (timescale=2.388).
Factorization parameters were as follows:
n: 83401523959050804924972610883019020772103327350516411471050111549524066031956548155738313342090261880249108256179101413
m: 1000000000000000000000000000
deg: 5
c5: 58
c0: 41
skew: 0.93
type: snfs
lss: 1
rlim: 1400000
alim: 1400000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [700000, 1250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3548779
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 194905 x 195153
Total sieving time: 1.95 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,26,26,48,48,2.3,2.3,50000
total time: 2.26 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

(58·10¹³⁸+41)/9 = 6(4)₁₃₇9_<139> = 11 · 1907 · 33947487199_<11> · C124

C124 = P36 · P89

P36 = 619682416402246260242658300172564813_<36>

P89 = 14603780594971380709213275235955179207952396770027290460063940971518463105065496294225451_<89>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 9049706047700098778472617130075705484325248766095900478012943598748454740374814077391893881246699892749334477158507931655663 (124 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3967165505
Step 1 took 4212ms
Step 2 took 4149ms
********** Factor found in step 2: 619682416402246260242658300172564813
Found probable prime factor of 36 digits: 619682416402246260242658300172564813
Probable prime cofactor 14603780594971380709213275235955179207952396770027290460063940971518463105065496294225451 has 89 digits

(58·10¹³⁷+41)/9 = 6(4)₁₃₆9_<138> = 13² · 53 · 89 · 2371780942173151_<16> · C117

C117 = P35 · P83

P35 = 14884551379367473034365581346771321_<35>

P83 = 22899319608705534678406447304938033748166187889155106711843604195847753505863147003_<83>

Number: 64449_137
N=340846099268334589063925286498769963997410140964630221918445886354506313410431118519162224524675570357048474447500963
  ( 117 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=14884551379367473034365581346771321
 r2=22899319608705534678406447304938033748166187889155106711843604195847753505863147003
Version: 
Total time: 3.14 hours.
Scaled time: 7.51 units (timescale=2.389).
Factorization parameters were as follows:
n: 340846099268334589063925286498769963997410140964630221918445886354506313410431118519162224524675570357048474447500963
m: 2000000000000000000000000000
deg: 5
c5: 725
c0: 164
skew: 0.74
type: snfs
lss: 1
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [900000, 1600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3960377
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 243100 x 243348
Total sieving time: 2.71 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,50000
total time: 3.14 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

(58·10¹⁴⁴+41)/9 = 6(4)₁₄₃9_<145> = 11 · 199 · 6581 · 10586419 · 178413835756643_<15> · 13295261417971829_<17> · C101

C101 = P46 · P55

P46 = 3550330562770319439823346494483581255745491313_<46>

P55 = 5017698363791318288256268260704825461570233445854479429_<55>

Number: 64449_144
N=17814487855730942101864005469134517687896385849816384316995836597205299202233380008914073671456700277
  ( 101 digits)
Divisors found:
 r1=3550330562770319439823346494483581255745491313
 r2=5017698363791318288256268260704825461570233445854479429
Version: 
Total time: 2.62 hours.
Scaled time: 6.24 units (timescale=2.384).
Factorization parameters were as follows:
name: 64449_144
n: 17814487855730942101864005469134517687896385849816384316995836597205299202233380008914073671456700277
skew: 1770.95
# norm 5.81e+13
c5: 602640
c4: 1871645292
c3: 8704689514020
c2: -3695448870658363
c1: -15197534558257118770
c0: 5588911043113068396936
# alpha -5.76
Y1: 62518557167
Y0: -7836839010963824795
# Murphy_E 3.24e-09
# M 16121912846489293313346083522004164419855127380897457966767740960635640065692258082666037901042514449
type: gnfs
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [600000, 1100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4181672
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 208491 x 208739
Polynomial selection time: 0.19 hours.
Total sieving time: 2.06 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,26,26,49,49,2.5,2.5,50000
total time: 2.62 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Aug 8, 2009 (4th)

By Sinkiti Sibata / Msieve / Aug 8, 2009

(58·10¹¹⁷+41)/9 = 6(4)₁₁₆9_<118> = 6981103 · 20052849473375479961204639_<26> · C86

C86 = P37 · P50

P37 = 2158588796290758972254217158621260613_<37>

P50 = 21326295670555186762106081990279592452723366079869_<50>

at Aug 08 15:22:45 2009  Msieve v. 1.42
Sat Aug 08 15:22:45 2009  random seeds: ac5f2114 ee093235
Sat Aug 08 15:22:45 2009  factoring 46034702900844545055529893009178313512466417637783840356525323468254990122504821899697 (86 digits)
Sat Aug 08 15:22:47 2009  searching for 15-digit factors
Sat Aug 08 15:22:47 2009  commencing quadratic sieve (86-digit input)
Sat Aug 08 15:22:48 2009  using multiplier of 1
Sat Aug 08 15:22:48 2009  using 32kb Intel Core sieve core
Sat Aug 08 15:22:48 2009  sieve interval: 16 blocks of size 32768
Sat Aug 08 15:22:48 2009  processing polynomials in batches of 13
Sat Aug 08 15:22:48 2009  using a sieve bound of 1459427 (55667 primes)
Sat Aug 08 15:22:48 2009  using large prime bound of 116754160 (26 bits)
Sat Aug 08 15:22:48 2009  using double large prime bound of 331963366994880 (41-49 bits)
Sat Aug 08 15:22:48 2009  using trial factoring cutoff of 49 bits
Sat Aug 08 15:22:48 2009  polynomial 'A' values have 11 factors
Sat Aug 08 15:56:44 2009  56109 relations (16197 full + 39912 combined from 581509 partial), need 55763
Sat Aug 08 15:56:46 2009  begin with 597706 relations
Sat Aug 08 15:56:46 2009  reduce to 132368 relations in 10 passes
Sat Aug 08 15:56:46 2009  attempting to read 132368 relations
Sat Aug 08 15:56:48 2009  recovered 132368 relations
Sat Aug 08 15:56:48 2009  recovered 108695 polynomials
Sat Aug 08 15:56:48 2009  attempting to build 56109 cycles
Sat Aug 08 15:56:48 2009  found 56109 cycles in 6 passes
Sat Aug 08 15:56:48 2009  distribution of cycle lengths:
Sat Aug 08 15:56:48 2009     length 1 : 16197
Sat Aug 08 15:56:48 2009     length 2 : 11144
Sat Aug 08 15:56:48 2009     length 3 : 10111
Sat Aug 08 15:56:48 2009     length 4 : 7157
Sat Aug 08 15:56:48 2009     length 5 : 4913
Sat Aug 08 15:56:48 2009     length 6 : 2935
Sat Aug 08 15:56:48 2009     length 7 : 1722
Sat Aug 08 15:56:48 2009     length 9+: 1930
Sat Aug 08 15:56:48 2009  largest cycle: 18 relations
Sat Aug 08 15:56:48 2009  matrix is 55667 x 56109 (12.0 MB) with weight 2917724 (52.00/col)
Sat Aug 08 15:56:48 2009  sparse part has weight 2917724 (52.00/col)
Sat Aug 08 15:56:49 2009  filtering completed in 3 passes
Sat Aug 08 15:56:49 2009  matrix is 50596 x 50660 (10.9 MB) with weight 2647779 (52.27/col)
Sat Aug 08 15:56:49 2009  sparse part has weight 2647779 (52.27/col)
Sat Aug 08 15:56:49 2009  saving the first 48 matrix rows for later
Sat Aug 08 15:56:49 2009  matrix is 50548 x 50660 (6.1 MB) with weight 1968508 (38.86/col)
Sat Aug 08 15:56:49 2009  sparse part has weight 1285742 (25.38/col)
Sat Aug 08 15:56:49 2009  matrix includes 64 packed rows
Sat Aug 08 15:56:49 2009  using block size 20264 for processor cache size 1024 kB
Sat Aug 08 15:56:50 2009  commencing Lanczos iteration
Sat Aug 08 15:56:50 2009  memory use: 7.0 MB
Sat Aug 08 15:57:03 2009  lanczos halted after 801 iterations (dim = 50546)
Sat Aug 08 15:57:04 2009  recovered 16 nontrivial dependencies
Sat Aug 08 15:57:04 2009  prp37 factor: 2158588796290758972254217158621260613
Sat Aug 08 15:57:04 2009  prp50 factor: 21326295670555186762106081990279592452723366079869
Sat Aug 08 15:57:04 2009  elapsed time 00:34:19

(58·10¹²⁸+41)/9 = 6(4)₁₂₇9_<129> = 11 · C128

C128 = P32 · P45 · P52

P32 = 39898048673574179603199844885073_<32>

P45 = 649715236944848403995371739583303968875535713_<45>

P52 = 2260050228906597591554901754728515026209895212840691_<52>

Number: 64449_128
N=58585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585859
  ( 128 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=39898048673574179603199844885073 (pp32)
 r2=649715236944848403995371739583303968875535713 (pp45)
 r3=2260050228906597591554901754728515026209895212840691 (pp52)
Version: Msieve-1.40
Total time: 2.46 hours.
Scaled time: 8.09 units (timescale=3.287).
Factorization parameters were as follows:
name: 64449_128
n: 58585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585859
m: 50000000000000000000000000
deg: 5
c5: 464
c0: 1025
skew: 1.17
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 985001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 147934 x 148182
Total sieving time: 2.37 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 2.46 hours.
 --------- CPU info (if available) ----------

Aug 8, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Aug 8, 2009

(14·10¹⁷¹+13)/9 = 1(5)₁₇₀7_<172> = 3 · 9761352401_<10> · 291815750197_<12> · 5862396613066093442304343_<25> · C125

C125 = P33 · P92

P33 = 335286451551713195473353730926391_<33>

P92 = 92609246362301408513269952814555626164032637076591129306358448623522057405639132520561888379_<92>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3294866312
Step 1 took 34035ms
Step 2 took 13670ms
********** Factor found in step 2: 335286451551713195473353730926391
Found probable prime factor of 33 digits: 335286451551713195473353730926391
Probable prime cofactor 92609246362301408513269952814555626164032637076591129306358448623522057405639132520561888379 has 92 digits

Aug 8, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve / Aug 8, 2009

(58·10²⁰⁰+41)/9 = 6(4)₁₉₉9_<201> = 11 · 17 · 107 · 2377 · 932774347987103381_<18> · 13826677866082240683703_<23> · 21474065269491482871681097_<26> · C128

C128 = P31 · C97

P31 = 9617476601959055323120190872597_<31>

C97 = [5086992204036649549554802325517951171974055226822069754918148594115667379490630513181229558391639_<97>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1094701982
Step 1 took 2496ms
Step 2 took 2004ms
********** Factor found in step 2: 9617476601959055323120190872597
Found probable prime factor of 31 digits: 9617476601959055323120190872597
Composite cofactor has 97 digits

(58·10¹⁹²+41)/9 = 6(4)₁₉₁9_<193> = 11 · 139 · 24107297 · 440052311 · 10402068055283_<14> · C161

C161 = P30 · P131

P30 = 389330198417547379466454031507_<30>

P131 = 98104152943332266788674463871533087097832143310616650750836727883467574943205234124279264185234168457469978071068936557397216769703_<131>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=131367667
Step 1 took 3576ms
Step 2 took 2408ms
********** Factor found in step 2: 389330198417547379466454031507
Found probable prime factor of 30 digits: 389330198417547379466454031507
Probable prime cofactor 9810415294333226678867446387153308709783214331061665075083672788346757494320523412427926418523416845746997807106
8936557397216769703 has 131 digits

(58·10²⁰³+41)/9 = 6(4)₂₀₂9_<204> = 13 · 4562672679804431624287_<22> · C182

C182 = P35 · P147

P35 = 51152262708347907152704942961133901_<35>

P147 = 212401690156098939939913557892512052200649177854946363470388068645251151818923654748302693711054147745443858651608553980275034876545681804713872679_<147>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2588790684
Step 1 took 4076ms
Step 2 took 2652ms
********** Factor found in step 2: 51152262708347907152704942961133901
Found probable prime factor of 35 digits: 51152262708347907152704942961133901
Probable prime cofactor has 147 digits

(58·10¹⁰⁴+41)/9 = 6(4)₁₀₃9_<105> = 11 · 17 · 19 · 109 · 842887 · C94

C94 = P36 · P58

P36 = 550869718097003447204551975703287171_<36>

P58 = 3583814511051657908982940011891001026899175054919974150481_<58>

SNFS difficulty: 105 digits.
Divisors found:
 r1=550869718097003447204551975703287171 (pp36)
 r2=3583814511051657908982940011891001026899175054919974150481 (pp58)
Version: Msieve v. 1.43
Total time: 0.32 hours.
Scaled time: 0.76 units (timescale=2.400).
Factorization parameters were as follows:
n: 1974214889414977037467608582187196548946406411233375487631192692026183614045274001659910779251
m: 100000000000000000000000000
deg: 4
c4: 58
c0: 41
skew: 0.92
type: snfs
lss: 1
rlim: 410000
alim: 410000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 410000/410000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [205000, 305001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 38641 x 38889
Total sieving time: 0.30 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105.000,4,0,0,0,0,0,0,0,0,410000,410000,25,25,44,44,2.2,2.2,20000
total time: 0.32 hours.

(58·10¹⁷⁹+41)/9 = 6(4)₁₇₈9_<180> = 13 · 257 · 8101 · 115998234137_<12> · 26557839579002128971173217971_<29> · C133

C133 = P32 · P102

P32 = 12168445837390283378749132344323_<32>

P102 = 635171702715363223405943616590905150867918196427406156053354992650488343086622847098876838786815913809_<102>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4122123285
Step 1 took 2544ms
Step 2 took 1992ms
********** Factor found in step 2: 12168445837390283378749132344323
Found probable prime factor of 32 digits: 12168445837390283378749132344323
Probable prime cofactor has 102 digits

(58·10¹¹²+41)/9 = 6(4)₁₁₁9_<113> = 3⁵ · 7 · 11 · 181 · 19411741 · C99

C99 = P45 · P55

P45 = 108154283898859034137377190207499452312048313_<45>

P55 = 9063620148804105342986892378964642781241934655305454783_<55>

SNFS difficulty: 114 digits.
Divisors found:
 r1=108154283898859034137377190207499452312048313 (pp45)
 r2=9063620148804105342986892378964642781241934655305454783 (pp55)
Version: Msieve v. 1.43
Total time: 0.57 hours.
Scaled time: 1.36 units (timescale=2.400).
Factorization parameters were as follows:
n: 980269346725178173569345476627308050099291195661372298815557195739472378690464284127582580732931079
m: 20000000000000000000000
deg: 5
c5: 725
c0: 164
skew: 0.74
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [280000, 480001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 52644 x 52877
Total sieving time: 0.54 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,114.000,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000
total time: 0.57 hours.

(58·10¹⁹⁷+41)/9 = 6(4)₁₉₆9_<198> = 13 · 933299923 · 8436592305409_<13> · 111772795484434550519_<21> · C155

C155 = P34 · C122

P34 = 5087832120754440156018956894208167_<34>

C122 = [11070951636149765536840257253607829444595086747622399008620240727882623901740891490497776510088174513384413377746808577543_<122>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=3097237382
Step 1 took 7492ms
********** Factor found in step 1: 5087832120754440156018956894208167
Found probable prime factor of 34 digits: 5087832120754440156018956894208167
Composite cofactor has 122 digits

Aug 8, 2009

Factorizations of 644...449 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Aug 7, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Aug 7, 2009

(52·10¹⁷¹-43)/9 = 5(7)₁₇₀3_<172> = 19 · 30158387489_<11> · 570722929894025945844003120791_<30> · C131

C131 = P37 · P94

P37 = 5740582896936804596177972515586571449_<37>

P94 = 3077639887964649309299233949920934152559049053053399717566063157179476351969374735826702962817_<94>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1753045546
Step 1 took 38331ms
Step 2 took 13954ms
********** Factor found in step 2: 5740582896936804596177972515586571449
Found probable prime factor of 37 digits: 5740582896936804596177972515586571449
Probable prime cofactor 3077639887964649309299233949920934152559049053053399717566063157179476351969374735826702962817 has 94 digits

Aug 7, 2009

By Justin Card / ggnfs, msieve / Aug 7, 2009

(8·10¹⁸⁷+7)/3 = 2(6)₁₈₆9_<188> = 109 · 334385738359_<12> · 1156043727761581055051_<22> · C153

C153 = P50 · P104

P50 = 50479019016684754981287962531941919871490137032437_<50>

P104 = 12537453051487436307735149209875880318604212209305100871443655159262572184508170463967147425732527050177_<104>

Number: 26669_187
N=632878331006826607892921413052373101493750270973351039252297873320440059704872140878402857753484859895707714576386291447104887955102355026445584175591349
  ( 153 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=50479019016684754981287962531941919871490137032437 (pp50)
 r2=12537453051487436307735149209875880318604212209305100871443655159262572184508170463967147425732527050177 (pp104)
Version: Msieve-1.40
Total time: 154.81 hours.
Scaled time: 313.18 units (timescale=2.023).
Factorization parameters were as follows:
n: 632878331006826607892921413052373101493750270973351039252297873320440059704872140878402857753484859895707714576386291447104887955102355026445584175591349
m: 20000000000000000000000000000000000000
deg: 5
c5: 25
c0: 7
skew: 0.78
type: snfs
lss: 1
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5

Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4750000, 7550001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1798825 x 1799050
Total sieving time: 137.64 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 16.50 hours.
Time per square root: 0.37 hours.
Prototype def-par.txt line would be:
snfs,187.000,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,54,54,2.5,2.5,100000
total time: 154.81 hours.
 --------- CPU info (if available) ----------
[    0.138978] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.231791] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init)
[    0.084027] Calibrating delay using timer specific routine.. 4004.64 BogoMIPS (lpj=8009297)
[    0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000305)
[    0.231806] Total of 2 processors activated (8004.80 BogoMIPS).

Aug 4, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Aug 4, 2009

4·10²¹³+9 = 4(0)₂₁₂9_<214> = 89 · 211 · C210

C210 = P40 · P57 · P114

P40 = 4912330291777329830182920462792184153201_<40>

P57 = 209197765948292508715840081366263723462559353816430654219_<57>

P114 = 207273092529491319737806399512561945738725389466995842008096844701461670330893312911176031446241487096666609893809_<114>

Number: n
N=213003887320943607220831780179988284786197348101602854252090100644336759145854411843016135044464561478246978007348634112572554449118696416209595825123808509505298471697108472229618190531977208584056659034027371
  ( 210 digits)
SNFS difficulty: 213 digits.
Divisors found:

Tue Aug  4 04:37:56 2009  prp40 factor: 4912330291777329830182920462792184153201
Tue Aug  4 04:37:56 2009  prp57 factor: 209197765948292508715840081366263723462559353816430654219
Tue Aug  4 04:37:56 2009  prp114 factor: 207273092529491319737806399512561945738725389466995842008096844701461670330893312911176031446241487096666609893809
Tue Aug  4 04:37:56 2009  elapsed time 44:31:12 (Msieve 1.39 - dependency 7)

Version: GGNFS-0.77.1-20050930-k8
Total time: 120.93 hours.
Scaled time: 184.54 units (timescale=1.526).
Factorization parameters were as follows:
name: KA_4_0_212_9
n: 213003887320943607220831780179988284786197348101602854252090100644336759145854411843016135044464561478246978007348634112572554449118696416209595825123808509505298471697108472229618190531977208584056659034027371
m: 200000000000000000000000000000000000
deg: 6
c6: 125
c0: 18
skew: 0.72
type: snfs
lss: 1
rlim: 26000000
alim: 26000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 26000000/26000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [13000000, 37049990)
Primes: RFBsize:1624527, AFBsize:1624093, largePrimes:39831436 encountered
Relations: rels:39025275, finalFF:1913417
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 7571502 hash collisions in 47357091 relations
Msieve: matrix is 4518042 x 4518290 (1229.8 MB)

Total sieving time: 119.25 hours.
Total relation processing time: 1.68 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,213,6,0,0,0,0,0,0,0,0,26000000,26000000,29,29,58,58,2.6,2.6,100000
total time: 120.93 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3352036k/3407296k available (3118k kernel code, 53976k reserved, 1895k data, 424k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830492)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830448)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830455)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Total of 4 processors activated (22643.70 BogoMIPS).

(53·10¹⁸⁵-71)/9 = 5(8)₁₈₄1_<186> = 23 · 233 · C183

C183 = P45 · P138

P45 = 215325522097885785506678338135721202120862759_<45>

P138 = 510333519255213660531524689794452061284434462061881762456420580789577174717938354675826912683331869019878654674813170859867374521644491401_<138>

Number: n
N=109887831477680330078165495220916008376355456034500632373369824386805166801434761875142543177624349484771205241442225954261781841554187141050361800501751985237710186394642449876635359
  ( 183 digits)
SNFS difficulty: 186 digits.
Divisors found:

Tue Aug 04 22:42:53 2009  prp45 factor: 215325522097885785506678338135721202120862759
Tue Aug 04 22:42:53 2009  prp138 factor: 510333519255213660531524689794452061284434462061881762456420580789577174717938354675826912683331869019878654674813170859867374521644491401
Tue Aug 04 22:42:53 2009  elapsed time 03:07:10 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 125.56 hours.
Scaled time: 333.98 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_8_184_1
n: 109887831477680330078165495220916008376355456034500632373369824386805166801434761875142543177624349484771205241442225954261781841554187141050361800501751985237710186394642449876635359
m: 10000000000000000000000000000000000000
deg: 5
c5: 53
c0: -71
skew: 1.06
type: snfs
lss: 1
rlim: 9200000
alim: 9200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 9200000/9200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4600000, 6800333)
Primes: RFBsize:614917, AFBsize:614931, largePrimes:21290734 encountered
Relations: rels:21649629, finalFF:1102807
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2166378 hash collisions in 23132561 relations
Msieve: matrix is 1494834 x 1495082 (404.5 MB)

Total sieving time: 124.87 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,9200000,9200000,28,28,56,56,2.5,2.5,100000
total time: 125.56 hours.
 --------- CPU info (if available) ----------

Aug 4, 2009

By Jo Yeong Uk / GMP-ECM / Aug 4, 2009

(8·10¹⁷³-71)/9 = (8)₁₇₂1_<173> = 3² · 13 · 17 · 43 · 73819349 · 689479898902332034363_<21> · C140

C140 = P41 · P99

P41 = 33715138294680734832618454572413769091987_<41>

P99 = 605658021115666294214978686237465472994827629075929272382467836621789553075490427237044226574344187_<99>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 20419843941197353791040696092597137963865400866495972289330486942965055929496647996235911574909705507595684650681311127191200053805001729569 (140 digits)
Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=5942098668
Step 1 took 996ms
Step 2 took 562ms
********** Factor found in step 2: 33715138294680734832618454572413769091987
Found probable prime factor of 41 digits: 33715138294680734832618454572413769091987
Probable prime cofactor 605658021115666294214978686237465472994827629075929272382467836621789553075490427237044226574344187 has 99 digits

Aug 3, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 3, 2009

(49·10¹⁶⁸-13)/9 = 5(4)₁₆₇3_<169> = 23 · 1447 · 11261 · 12853 · 2308951277_<10> · 5036853781320968279371_<22> · C125

C125 = P46 · P80

P46 = 4436645900924865896891648618121442838385371837_<46>

P80 = 21905181562068919290990994467028446773934788898829226150669261394310130185658329_<80>

Number: 54443_168
N=97185533986368021681783378062396574919435537754075193262983788450856674826360508129284134177950827777893612589454003301080373
  ( 125 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=4436645900924865896891648618121442838385371837
 r2=21905181562068919290990994467028446773934788898829226150669261394310130185658329
Version: 
Total time: 46.73 hours.
Scaled time: 111.36 units (timescale=2.383).
Factorization parameters were as follows:
n: 97185533986368021681783378062396574919435537754075193262983788450856674826360508129284134177950827777893612589454003301080373
m: 10000000000000000000000000000000000
deg: 5
c5: 49
c0: -1300
skew: 1.93
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3100000, 6600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11417062
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1034547 x 1034795
Total sieving time: 42.04 hours.
Total relation processing time: 2.01 hours.
Matrix solve time: 2.54 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,27,27,52,52,2.4,2.4,100000
total time: 46.73 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Aug 3, 2009 (2nd)

By Justin Card / ggnfs, msieve 1.42 / Aug 3, 2009

(56·10¹⁷⁰-11)/9 = 6(2)₁₆₉1_<171> = 3 · 761 · 4228649 · 10979083 · 1343420723_<10> · 12114269027672661198796230498491836711_<38> · C108

C108 = P49 · P60

P49 = 1944800934677037047463766918371467712069304130887_<49>

P60 = 185475900387806551829482684307834368733260784549539663636751_<60>

Number: 62221_170
N=360713704434271200183541622591615185634374495249172894015298812631314181864019058110537097267991345727428137
  ( 108 digits)
Divisors found:
 r1=1944800934677037047463766918371467712069304130887 (pp49)
 r2=185475900387806551829482684307834368733260784549539663636751 (pp60)
Version: Msieve-1.40
Total time: 8.69 hours.
Scaled time: 17.57 units (timescale=2.021).
Factorization parameters were as follows:
n: 360713704434271200183541622591615185634374495249172894015298812631314181864019058110537097267991345727428137
skew: 33882.38
Y0: -844453122631185029679
Y1:  158724253097
c0:  3030270268952056684732360
c1:  1682226644659762561296
c2: -88344194390410036
c3:  2546804784059
c4:  57899656
c5:  840
type: gnfs

Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2600001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 328483 x 328708
Total sieving time: 8.15 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 8.69 hours.
 --------- CPU info (if available) ----------
[    0.138978] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.231791] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init)
[    0.084027] Calibrating delay using timer specific routine.. 4004.64 BogoMIPS (lpj=8009297)
[    0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000305)
[    0.231806] Total of 2 processors activated (8004.80 BogoMIPS).

Aug 3, 2009

By Serge Batalov / PFGW 3.2 / Aug 2, 2009

(4·10¹⁰³⁷⁰³-1)/3 = 1(3)₁₀₃₇₀₃_<103704> is PRP.

This is the largest unprovable near-repdigit PRP in our tables so far. Congratulations!

Aug 2, 2009 (2nd)

By Justin Card / ggnfs, msieve / Aug 2, 2009

(8·10¹⁸²+7)/3 = 2(6)₁₈₁9_<183> = 146833703 · 769436999 · 22087156719475884876001_<23> · C144

C144 = P49 · P95

P49 = 1313874628553225970702945084785841581827031259121_<49>

P95 = 81334757462238608757273597406493936479682614546275200441982222523538919383871427624411039249037_<95>

Number: 26669_182
N=106863674249165476277135950768201346179664064572388256062379170668048285931254966336140306142687056863527571470316756489216772473680220396716477
  ( 144 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=1313874628553225970702945084785841581827031259121 (pp49)
 r2=81334757462238608757273597406493936479682614546275200441982222523538919383871427624411039249037 (pp95)
Version: Msieve-1.40
Total time: 108.67 hours.
Scaled time: 219.84 units (timescale=2.023).
Factorization parameters were as follows:
n: 106863674249165476277135950768201346179664064572388256062379170668048285931254966336140306142687056863527571470316756489216772473680220396716477
m: 2000000000000000000000000000000000000
deg: 5
c5: 25
c0: 7
skew: 0.78
type: snfs
lss: 1
rlim: 7800000
alim: 7800000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

Factor base limits: 7800000/7800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3900000, 6000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1285649 x 1285897
Total sieving time: 100.57 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 7.27 hours.
Time per square root: 0.46 hours.
Prototype def-par.txt line would be:
snfs,182.000,5,0,0,0,0,0,0,0,0,7800000,7800000,28,28,53,53,2.5,2.5,100000
total time: 108.67 hours.
 --------- CPU info (if available) ----------
[    0.138978] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.231791] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init)
[    0.084027] Calibrating delay using timer specific routine.. 4004.64 BogoMIPS (lpj=8009297)
[    0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000305)
[    0.231806] Total of 2 processors activated (8004.80 BogoMIPS).

Aug 2, 2009

By Robert Backstrom / GGNFS, Msieve / Aug 2, 2009

(13·10¹⁸⁴+41)/9 = 1(4)₁₈₃9_<185> = 163 · 1579 · C179

C179 = P71 · P108

P71 = 92587192841326317904370509461876612279913187413506323373335331228760777_<71>

P108 = 606150114546001300708435303470338784608990441248267320938295610733948093243853858789867890785546836431405881_<108>

Number: n
N=56121737546262659229241324766565949733054796832834497427681744850722653712042818295513757812253792858120362131987102361300521975329747586009800582198271191460171050421927539929537
  ( 179 digits)
SNFS difficulty: 185 digits.
Divisors found:

Sun Aug 02 08:53:24 2009  prp71 factor: 92587192841326317904370509461876612279913187413506323373335331228760777
Sun Aug 02 08:53:24 2009  prp108 factor: 606150114546001300708435303470338784608990441248267320938295610733948093243853858789867890785546836431405881
Sun Aug 02 08:53:24 2009  elapsed time 03:35:50 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 147.60 hours.
Scaled time: 384.64 units (timescale=2.606).
Factorization parameters were as follows:
name: KA_1_4_183_9
n: 56121737546262659229241324766565949733054796832834497427681744850722653712042818295513757812253792858120362131987102361300521975329747586009800582198271191460171050421927539929537
m: 5000000000000000000000000000000000000
deg: 5
c5: 208
c0: 205
skew: 1.00
type: snfs
lss: 1
rlim: 8800000
alim: 8800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8800000/8800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4400000, 7035647)
Primes: RFBsize:590006, AFBsize:590266, largePrimes:21302773 encountered
Relations: rels:21438521, finalFF:1122149
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2374612 hash collisions in 23329475 relations
Msieve: matrix is 1562449 x 1562697 (420.7 MB)

Total sieving time: 146.75 hours.
Total relation processing time: 0.84 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,8800000,8800000,28,28,56,56,2.5,2.5,100000
total time: 147.60 hours.
 --------- CPU info (if available) ----------

Aug 1, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 1, 2009

(29·10¹⁶⁸-11)/9 = 3(2)₁₆₇1_<169> = 47 · 1354711 · 33098700893973541_<17> · 80197477465388443_<17> · C128

C128 = P46 · P83

P46 = 1100732423272300277487241527837358243053560351_<46>

P83 = 17320385646653016613128923249554916759743959254925800399695761532181811650257807901_<83>

Number: 32221_168
N=19065110064851142634598305011711690781910600659166456675477203921277050640697856822512892845451487883248668975816575374668133251
  ( 128 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=1100732423272300277487241527837358243053560351
 r2=17320385646653016613128923249554916759743959254925800399695761532181811650257807901
Version: 
Total time: 45.11 hours.
Scaled time: 107.72 units (timescale=2.388).
Factorization parameters were as follows:
n: 19065110064851142634598305011711690781910600659166456675477203921277050640697856822512892845451487883248668975816575374668133251
m: 10000000000000000000000000000000000
deg: 5
c5: 29
c0: -1100
skew: 2.07
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 6400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11391845
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1021901 x 1022149
Total sieving time: 40.54 hours.
Total relation processing time: 1.96 hours.
Matrix solve time: 2.48 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000
total time: 45.11 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Aug 1, 2009

By Wataru Sakai / GMP-ECM 6.2.1 / Aug 1, 2009

(56·10¹⁷⁰-11)/9 = 6(2)₁₆₉1_<171> = 3 · 761 · 4228649 · 10979083 · 1343420723_<10> · C145

C145 = P38 · C108

P38 = 12114269027672661198796230498491836711_<38>

C108 = [360713704434271200183541622591615185634374495249172894015298812631314181864019058110537097267991345727428137_<108>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2365907108
Step 1 took 47029ms
Step 2 took 15502ms
********** Factor found in step 2: 12114269027672661198796230498491836711
Found probable prime factor of 38 digits: 12114269027672661198796230498491836711
Composite cofactor 360713704434271200183541622591615185634374495249172894015298812631314181864019058110537097267991345727428137 has 108 digits

July 2009

Jul 31, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Jul 31, 2009

(28·10¹⁷¹+53)/9 = 3(1)₁₇₀7_<172> = 3² · 23 · 70791068989559_<14> · 7208176534331825153_<19> · C137

C137 = P38 · P99

P38 = 57051566739178370843228849594143099081_<38>

P99 = 516266227940538332202888300931167534392439128247533459514322573271390395942085268059433207374745613_<99>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1536419490
Step 1 took 42867ms
Step 2 took 14840ms
********** Factor found in step 2: 57051566739178370843228849594143099081
Found probable prime factor of 38 digits: 57051566739178370843228849594143099081
Probable prime cofactor 516266227940538332202888300931167534392439128247533459514322573271390395942085268059433207374745613 has 99 digits

Jul 31, 2009

By Justin Card / ggnfs, msieve / Jul 31, 2009

(8·10¹⁸⁴+7)/3 = 2(6)₁₈₃9_<185> = 23 · 3331 · 9974131 · 44534953 · 560165357 · 10490142307214064479640205122143_<32> · C126

C126 = P52 · P74

P52 = 1840576491455917515487089567659492600807511867287417_<52>

P74 = 72450051758129853557618859992660448536058606321454023390500476783160491073_<74>

Number: 26669_184
N=133349862070778274177903595909790086247733391434306851920325896211332328606192378743990711854039144978397117642580702153728441
  ( 126 digits)
Divisors found:
 r1=1840576491455917515487089567659492600807511867287417 (pp52)
 r2=72450051758129853557618859992660448536058606321454023390500476783160491073 (pp74)
Version: Msieve-1.40
Total time: 62.14 hours.
Scaled time: 124.59 units (timescale=2.005).
Factorization parameters were as follows:
# Murphy_E = 1.553772e-10, selected by Jeff Gilchrist
n: 133349862070778274177903595909790086247733391434306851920325896211332328606192378743990711854039144978397117642580702153728441
Y0: -1383792360506376182622027
Y1: 36174105794699
c0: -25094862387985409537622023408320
c1: 497422368223576071131877836
c2: -3851721490457031123500
c3: 1380029445101797
c4: 29089581582
c5: 26280
skew: 376543.69
type: gnfs
# selected mechanically
rlim: 7200000
alim: 7200000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

Factor base limits: 7200000/7200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved algebraic special-q in [3600000, 6800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 971988 x 972236
Total sieving time: 57.96 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 3.70 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,125,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,7200000,7200000,27,27,53,53,2.5,2.5,100000
total time: 62.14 hours.
 --------- CPU info (if available) ----------
[    0.138880] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.231790] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init)
[    0.084029] Calibrating delay using timer specific routine.. 4004.53 BogoMIPS (lpj=8009076)
[    0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000316)
[    0.231806] Total of 2 processors activated (8004.69 BogoMIPS).

Jul 30, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Jul 30, 2009

(28·10¹⁷²+71)/9 = 3(1)₁₇₁9_<173> = 3 · 11² · 19 · 199 · 2063 · 1071859429_<10> · 987784778531_<12> · 3787644855281754211_<19> · C124

C124 = P39 · P41 · P46

P39 = 145981945043538922447045171242551767513_<39>

P41 = 12106747692684234696061311650272036055929_<41>

P46 = 1550268564261924241434791929036957421411556307_<46>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1284649349
Step 1 took 34253ms
Step 2 took 4413ms
********** Factor found in step 2: 145981945043538922447045171242551767513
Found probable prime factor of 39 digits: 145981945043538922447045171242551767513
Composite cofactor 18768710363418952533350681677121336057034379650028828291507491066449182303657984694203 has 86 digits
-----------------
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3517402920
Step 1 took 20558ms
Step 2 took 10567ms
********** Factor found in step 2: 12106747692684234696061311650272036055929
Found probable prime factor of 41 digits: 12106747692684234696061311650272036055929
Probable prime cofactor 1550268564261924241434791929036957421411556307 has 46 digits

Jul 30, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jul 30, 2009

(55·10¹⁸⁴+53)/9 = 6(1)₁₈₃7_<185> = 7 · 3701 · C181

C181 = P63 · P118

P63 = 299186033889093434494711100919736508233251687550293980333909521_<63>

P118 = 7884274535829624751955048946137314807144323255787431031881040268248974228611948641297326772368968198018694299874423311_<118>

Number: n
N=2358864828467638518975995333736484776744166098394685263099205276995063539240788632844833871583398738221759026946814031385768754047597603393334276879264720388740923731466827927244031
  ( 181 digits)
SNFS difficulty: 186 digits.
Divisors found:

Thu Jul 30 08:47:27 2009  prp63 factor: 299186033889093434494711100919736508233251687550293980333909521
Thu Jul 30 08:47:27 2009  prp118 factor: 7884274535829624751955048946137314807144323255787431031881040268248974228611948641297326772368968198018694299874423311
Thu Jul 30 08:47:27 2009  elapsed time 02:59:55 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 197.17 hours.
Scaled time: 513.83 units (timescale=2.606).
Factorization parameters were as follows:
name: KA_6_1_183_7
n: 2358864828467638518975995333736484776744166098394685263099205276995063539240788632844833871583398738221759026946814031385768754047597603393334276879264720388740923731466827927244031
m: 10000000000000000000000000000000000000
deg: 5
c5: 11
c0: 106
skew: 1.57
type: snfs
lss: 1
rlim: 8800000
alim: 8800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8800000/8800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4400000, 7801231)
Primes: RFBsize:590006, AFBsize:590541, largePrimes:21231701 encountered
Relations: rels:21472492, finalFF:1016701
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2220134 hash collisions in 23704512 relations
Msieve: matrix is 1468917 x 1469164 (396.3 MB)

Total sieving time: 196.53 hours.
Total relation processing time: 0.65 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,8800000,8800000,28,28,56,56,2.5,2.5,100000
total time: 197.17 hours.
 --------- CPU info (if available) ----------

Jul 30, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jul 30, 2009

(38·10¹⁶⁸+7)/9 = 4(2)₁₆₇3_<169> = 41 · 3109 · 352271 · 78050827122051106417692700691_<29> · C130

C130 = P62 · P68

P62 = 44517847976265306807164707134605905018604880543571240978940213_<62>

P68 = 27061255665644746692439217262915386433661197680520042446537611351019_<68>

Number: 42223_168
N=1204708865770021054615557951951723014686056920324982297118240921405162844773742860832148665618930386587825784814043462037757627047
  ( 130 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=44517847976265306807164707134605905018604880543571240978940213
 r2=27061255665644746692439217262915386433661197680520042446537611351019
Version: 
Total time: 39.74 hours.
Scaled time: 95.03 units (timescale=2.391).
Factorization parameters were as follows:
n: 1204708865770021054615557951951723014686056920324982297118240921405162844773742860832148665618930386587825784814043462037757627047
m: 10000000000000000000000000000000000
deg: 5
c5: 19
c0: 350
skew: 1.79
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 6000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11347850
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 962055 x 962303
Total sieving time: 35.98 hours.
Total relation processing time: 1.72 hours.
Matrix solve time: 1.93 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,52,52,2.4,2.4,100000
total time: 39.74 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 29, 2009 (3rd)

By Justin Card / GGNFS, Msieve / Jul 29, 2009

(25·10¹⁹³-61)/9 = 2(7)₁₉₂1_<194> = 3 · 7 · 73883 · 26925317 · 19159973142181_<14> · 284017799510891_<15> · 80485311297327121853982640517_<29> · C124

C124 = P54 · P71

P54 = 128613570680091058920064785055072809139946797083167593_<54>

P71 = 11803993992833193782465781270323656372348977417985328398765195618890491_<71>

Number: 27771_193
N=1518153815704622240936737904859078621016147552740776785285576396386699185397561525934124104891750356941221401004594467058163
  ( 124 digits)
Divisors found:
 r1=128613570680091058920064785055072809139946797083167593 (pp54)
 r2=11803993992833193782465781270323656372348977417985328398765195618890491 (pp71)
Version: Msieve-1.40
Total time: 58.22 hours.
Scaled time: 117.89 units (timescale=2.025).
Factorization parameters were as follows:
# Murphy_E = 1.861264e-10, selected by Jeff Gilchrist
n: 1518153815704622240936737904859078621016147552740776785285576396386699185397561525934124104891750356941221401004594467058163
Y0: -609424693195493084629365
Y1: 14285840635807
c0: 449801078557326487786247371904
c1: 56040688801503068267930764
c2: 249106677690281349198
c3: -2249875713199399
c4: -3915672212
c5: 18060
skew: 221678.63
type: gnfs
# selected mechanically
rlim: 6400000
alim: 6400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5

Factor base limits: 6400000/6400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3200000, 6300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 884389 x 884637
Total sieving time: 54.32 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.21 hours.
Time per square root: 0.48 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6400000,6400000,27,27,52,52,2.5,2.5,100000
total time: 58.22 hours.
 --------- CPU info (if available) ----------
[    0.138880] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.231790] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01
[    0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init)
[    0.084029] Calibrating delay using timer specific routine.. 4004.53 BogoMIPS (lpj=8009076)
[    0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000316)
[    0.231806] Total of 2 processors activated (8004.69 BogoMIPS).

Jul 29, 2009 (2nd)

By matsui / Msieve / Jul 29, 2009

9·10¹⁸⁸-7 = 8(9)₁₈₇3_<189> = 6689591 · C183

C183 = P61 · P122

P61 = 2889983980206166400633343347830421444067318005274107662508507_<61>

P122 = 46552982294567003262611165131940242875979617104663519183548141215584144647077930746442394215984131576858766423362881560989_<122>

N=134537373062119941263972640479814087288744558523832025007208960906578593519394533985710038177221895927568666006636280155244169636080890446067629545662806590118887686855594011651833423
  ( 183 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=2889983980206166400633343347830421444067318005274107662508507 (pp61)
 r2=46552982294567003262611165131940242875979617104663519183548141215584144647077930746442394215984131576858766423362881560989 (pp122)
Version: Msieve v. 1.42
Total time: 288.28 hours.
Scaled time: 646.03 units (timescale=2.241).
Factorization parameters were as follows:
n: 134537373062119941263972640479814087288744558523832025007208960906578593519394533985710038177221895927568666006636280155244169636080890446067629545662806590118887686855594011651833423
m: 50000000000000000000000000000000000000
deg: 5
c5: 72
c0: -175
skew: 1.19
type: snfs
lss: 1
rlim: 10400000
alim: 10400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 100000

Factor base limits: 10400000/10400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5200000, 9700001)
Primes: , , 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2068834 x 2069058
Total sieving time: 279.68 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 7.81 hours.
Time per square root: 0.62 hours.
Prototype def-par.txt line would be:
snfs,190.000,5,0,0,0,0,0,0,0,0,10400000,10400000,28,28,54,54,2.5,2.5,100000
total time: 288.28 hours.

Jul 29, 2009

By Andreas Tete / GMP-ECM / Jul 29, 2009

(31·10¹⁷⁸-13)/9 = 3(4)₁₇₇3_<179> = 3 · 1353967 · C172

C172 = P37 · P135

P37 = 9537440536427082503420258687477304493_<37>

P135 = 889115142825712264336270323676477942025280940056505408267252597985808653661232222615018940714817662000729558352000823164963884428325251_<135>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2445707087
Step 1 took 18922ms
Step 2 took 7161ms
********** Factor found in step 2: 9537440536427082503420258687477304493
Found probable prime factor of 37 digits: 9537440536427082503420258687477304493
Probable prime cofactor 889115142825712264336270323676477942025280940056505408267252597985808653661232222615018940714817662000729558352000823164963884428325251

Jul 28, 2009

By Jo Yeong Uk / GGNFS / Msieve v1.39 / Jul 28, 2009

(34·10¹⁶⁸+11)/9 = 3(7)₁₆₇9_<169> = 112010779 · 1237487765219969_<16> · 216088201207134256529_<21> · C126

C126 = P56 · P70

P56 = 21007045637904397929220783078171057473056938111949250991_<56>

P70 = 6003985612856955994763940375687682631208042011489199930435766202839511_<70>

Number: 37779_168
N=126125999778607480690246033713828018537651058546696590725316441020016541300976869122526673281587490530406309722393433830705401
  ( 126 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=21007045637904397929220783078171057473056938111949250991
 r2=6003985612856955994763940375687682631208042011489199930435766202839511
Version: 
Total time: 32.90 hours.
Scaled time: 78.31 units (timescale=2.380).
Factorization parameters were as follows:
n: 126125999778607480690246033713828018537651058546696590725316441020016541300976869122526673281587490530406309722393433830705401
m: 10000000000000000000000000000000000
deg: 5
c5: 17
c0: 550
skew: 2.00
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2900000, 5400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10879636
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 958587 x 958835
Total sieving time: 29.47 hours.
Total relation processing time: 1.34 hours.
Matrix solve time: 1.97 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,52,52,2.4,2.4,100000
total time: 32.90 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 27, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jul 27, 2009

(31·10¹⁸³-13)/9 = 3(4)₁₈₂3_<184> = 11 · 6271 · C179

C179 = P90 · P90

P90 = 100207618408818769953369343053477573985594867867454028216858231374779324945945217331537721_<90>

P90 = 498297786397843298786484049159684239369074605709847311257469554644236411505194367194905543_<90>

Number: n
N=49933234433314165414308932089190421194886192494229489923956516206556072606144365034494200496432995237013734860968157093177026202062081507146090147206396608405857329473977536487503
  ( 179 digits)
SNFS difficulty: 185 digits.
Divisors found:

Mon Jul 27 21:53:00 2009  prp90 factor: 100207618408818769953369343053477573985594867867454028216858231374779324945945217331537721
Mon Jul 27 21:53:00 2009  prp90 factor: 498297786397843298786484049159684239369074605709847311257469554644236411505194367194905543
Mon Jul 27 21:53:00 2009  elapsed time 03:09:48 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 179.90 hours.
Scaled time: 474.76 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_3_4_182_3
n: 49933234433314165414308932089190421194886192494229489923956516206556072606144365034494200496432995237013734860968157093177026202062081507146090147206396608405857329473977536487503
m: 5000000000000000000000000000000000000
deg: 5
c5: 248
c0: -325
skew: 1.06
type: snfs
lss: 1
rlim: 8800000
alim: 8800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8800000/8800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4400000, 7600193)
Primes: RFBsize:590006, AFBsize:590071, largePrimes:20924935 encountered
Relations: rels:20804592, finalFF:1225824
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1977048 hash collisions in 22136093 relations
Msieve: matrix is 1499067 x 1499315 (407.0 MB)

Total sieving time: 179.24 hours.
Total relation processing time: 0.66 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,8800000,8800000,28,28,56,56,2.5,2.5,100000
total time: 179.90 hours.
 --------- CPU info (if available) ----------

Two P90s are the second largest nice split so far in our tables. Congratulations!

(2·10²⁰⁹+1)/3 = (6)₂₀₈7_<209> = 409 · C207

C207 = P88 · P119

P88 = 2052187685408499669360164389950216452837367795140694640921654294506879070840299204220861_<88>

P119 = 79427035920269184206421164842740391735969944599658873023811379866142644488461289389623308760621268628589866983939306783_<119>

Number: n
N=162999185004074979625101874490627546862265688671556642216788916055419722901385493072534637326813365933170334148329258353708231458842705786471067644661776691116544417277913610431947840260798696006519967400163
  ( 207 digits)
SNFS difficulty: 210 digits.
Divisors found:

Mon Jul 27 22:21:24 2009  prp88 factor: 2052187685408499669360164389950216452837367795140694640921654294506879070840299204220861
Mon Jul 27 22:21:24 2009  prp119 factor: 79427035920269184206421164842740391735969944599658873023811379866142644488461289389623308760621268628589866983939306783
Mon Jul 27 22:21:24 2009  elapsed time 20:52:07 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20050930-k8
Total time: 48.98 hours.
Scaled time: 98.64 units (timescale=2.014).
Factorization parameters were as follows:
name: KA_6_208_7
n: 162999185004074979625101874490627546862265688671556642216788916055419722901385493072534637326813365933170334148329258353708231458842705786471067644661776691116544417277913610431947840260798696006519967400163
m: 1000000000000000000000000000000000000000000
deg: 5
c5: 1
c0: 5
skew: 1.38
type: snfs
lss: 1
rlim: 22000000
alim: 22000000
rlim: 25000000
alim: 25000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 25000000/25000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [12500000, 23001929)
Primes: RFBsize:1565927, AFBsize:1565758, largePrimes:40927685 encountered
Relations: rels:42499863, finalFF:3067740
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 6259415 hash collisions in 46321697 relations
Msieve: matrix is 3453945 x 3454193 (931.6 MB)

Total sieving time: 47.74 hours.
Total relation processing time: 1.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,210,5,0,0,0,0,0,0,0,0,25000000,25000000,29,29,58,58,2.6,2.6,100000
total time: 48.98 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3352036k/3407296k available (3118k kernel code, 53976k reserved, 1895k data, 424k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.51 BogoMIPS (lpj=2830757)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830448)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830455)
Total of 4 processors activated (22644.23 BogoMIPS).

Jul 27, 2009 (3rd)

By Justin Card / cado-nfs for sieving, msieve 1.43 for postprocessing / Jul 27, 2009

(10¹⁸⁸+17)/9 = (1)₁₈₇3_<188> = 13 · 31 · 80423813 · 11725919509_<11> · C167

C167 = P69 · P99

P69 = 101101428297969763167582651911552568964064074821357008687845402353373_<69>

P99 = 289176891454586933473472026592329087156730099564830191435580236364586283574771523426365696790224631_<99>

sieve over 6 days, 

Sat Jul 25 19:12:35 2009
Sat Jul 25 19:12:35 2009
Sat Jul 25 19:12:35 2009  Msieve v. 1.43
Sat Jul 25 19:12:35 2009  random seeds: d9fcc312 d1ea6900
Sat Jul 25 19:12:35 2009  factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits)
Sat Jul 25 19:12:39 2009
Sat Jul 25 19:12:39 2009
Sat Jul 25 19:12:39 2009  Msieve v. 1.43
Sat Jul 25 19:12:39 2009  random seeds: ed3f30ae 2d551ca1
Sat Jul 25 19:12:39 2009  factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits)
Sat Jul 25 19:12:41 2009  searching for 15-digit factors
Sat Jul 25 19:12:41 2009  commencing number field sieve (167-digit input)
Sat Jul 25 19:12:41 2009  R0: -20000000000000000000000000000000000000
Sat Jul 25 19:12:41 2009  R1:  1
Sat Jul 25 19:12:41 2009  A0:  68
Sat Jul 25 19:12:41 2009  A1:  0
Sat Jul 25 19:12:41 2009  A2:  0
Sat Jul 25 19:12:41 2009  A3:  0
Sat Jul 25 19:12:41 2009  A4:  0
Sat Jul 25 19:12:41 2009  A5:  125
Sat Jul 25 19:12:41 2009  skew 1.00, size 4.008652e-13, alpha 0.098689, combined = 4.774392e-11
Sat Jul 25 19:12:41 2009
Sat Jul 25 19:12:41 2009  commencing relation filtering
Sat Jul 25 19:12:41 2009  estimated available RAM is 972.2 MB
Sat Jul 25 19:12:41 2009  commencing duplicate removal, pass 1
Sat Jul 25 19:15:39 2009  found 151952 hash collisions in 18139084 relations
Sat Jul 25 19:17:00 2009  added 675602 free relations
Sat Jul 25 19:17:00 2009  commencing duplicate removal, pass 2
Sat Jul 25 19:17:23 2009  found 0 duplicates and 18814686 unique relations
Sat Jul 25 19:17:23 2009  memory use: 132.2 MB
Sat Jul 25 19:17:23 2009  reading ideals above 10551296
Sat Jul 25 19:17:30 2009  commencing singleton removal, initial pass
Sat Jul 25 19:21:37 2009  memory use: 298.4 MB
Sat Jul 25 19:21:37 2009  reading all ideals from disk
Sat Jul 25 19:21:41 2009  memory use: 369.4 MB
Sat Jul 25 19:21:44 2009  commencing in-memory singleton removal
Sat Jul 25 19:21:47 2009  begin with 18814686 relations and 19739995 unique ideals
Sat Jul 25 19:22:13 2009  reduce to 7464939 relations and 5902802 ideals in 19 passes
Sat Jul 25 19:22:13 2009  max relations containing the same ideal: 30
Sat Jul 25 19:22:14 2009  reading ideals above 100000
Sat Jul 25 19:22:14 2009  commencing singleton removal, initial pass
Sat Jul 25 19:24:22 2009  memory use: 149.2 MB
Sat Jul 25 19:24:22 2009  reading all ideals from disk
Sat Jul 25 19:24:27 2009  memory use: 287.9 MB
Sat Jul 25 19:24:29 2009  keeping 7293870 ideals with weight <= 200, target excess is 40024
Sat Jul 25 19:24:31 2009  commencing in-memory singleton removal
Sat Jul 25 19:24:34 2009  begin with 7470460 relations and 7293870 unique ideals
Sat Jul 25 19:24:51 2009  reduce to 7462644 relations and 7259412 ideals in 8 passes
Sat Jul 25 19:24:51 2009  max relations containing the same ideal: 200
Sat Jul 25 19:25:02 2009  removing 783390 relations and 704988 ideals in 78402 cliques
Sat Jul 25 19:25:02 2009  commencing in-memory singleton removal
Sat Jul 25 19:25:04 2009  begin with 6679254 relations and 7259412 unique ideals
Sat Jul 25 19:25:26 2009  reduce to 6620572 relations and 6494876 ideals in 11 passes
Sat Jul 25 19:25:26 2009  max relations containing the same ideal: 190
Sat Jul 25 19:25:35 2009  removing 562841 relations and 484439 ideals in 78402 cliques
Sat Jul 25 19:25:36 2009  commencing in-memory singleton removal
Sat Jul 25 19:25:38 2009  begin with 6057731 relations and 6494876 unique ideals
Sat Jul 25 19:25:52 2009  reduce to 6024322 relations and 5976634 ideals in 8 passes
Sat Jul 25 19:25:52 2009  max relations containing the same ideal: 180
Sat Jul 25 19:26:03 2009  relations with 0 large ideals: 704
Sat Jul 25 19:26:03 2009  relations with 1 large ideals: 76
Sat Jul 25 19:26:03 2009  relations with 2 large ideals: 1129
Sat Jul 25 19:26:03 2009  relations with 3 large ideals: 14195
Sat Jul 25 19:26:03 2009  relations with 4 large ideals: 101657
Sat Jul 25 19:26:03 2009  relations with 5 large ideals: 427840
Sat Jul 25 19:26:03 2009  relations with 6 large ideals: 1150165
Sat Jul 25 19:26:03 2009  relations with 7+ large ideals: 4328556
Sat Jul 25 19:26:03 2009  commencing 2-way merge
Sat Jul 25 19:26:15 2009  reduce to 3653878 relation sets and 3606190 unique ideals
Sat Jul 25 19:26:15 2009  commencing full merge
Sat Jul 25 19:28:47 2009  memory use: 449.3 MB
Sat Jul 25 19:28:48 2009  found 1907384 cycles, need 1902390
Sat Jul 25 19:28:51 2009  weight of 1902390 cycles is about 133337095 (70.09/cycle)
Sat Jul 25 19:28:51 2009  distribution of cycle lengths:
Sat Jul 25 19:28:51 2009  1 relations: 218410
Sat Jul 25 19:28:51 2009  2 relations: 247296
Sat Jul 25 19:28:51 2009  3 relations: 242476
Sat Jul 25 19:28:51 2009  4 relations: 209739
Sat Jul 25 19:28:51 2009  5 relations: 179661
Sat Jul 25 19:28:51 2009  6 relations: 147072
Sat Jul 25 19:28:51 2009  7 relations: 124095
Sat Jul 25 19:28:51 2009  8 relations: 103425
Sat Jul 25 19:28:51 2009  9 relations: 85413
Sat Jul 25 19:28:51 2009  10+ relations: 344803
Sat Jul 25 19:28:51 2009  heaviest cycle: 27 relations
Sat Jul 25 19:28:51 2009  commencing cycle optimization
Sat Jul 25 19:28:57 2009  start with 11102912 relations
Sat Jul 25 19:29:48 2009  pruned 252249 relations
Sat Jul 25 19:29:48 2009  memory use: 362.4 MB
Sat Jul 25 19:29:48 2009  distribution of cycle lengths:
Sat Jul 25 19:29:48 2009  1 relations: 218410
Sat Jul 25 19:29:48 2009  2 relations: 252454
Sat Jul 25 19:29:48 2009  3 relations: 250838
Sat Jul 25 19:29:48 2009  4 relations: 213542
Sat Jul 25 19:29:48 2009  5 relations: 182810
Sat Jul 25 19:29:48 2009  6 relations: 147901
Sat Jul 25 19:29:48 2009  7 relations: 123902
Sat Jul 25 19:29:48 2009  8 relations: 102741
Sat Jul 25 19:29:48 2009  9 relations: 84252
Sat Jul 25 19:29:48 2009  10+ relations: 325540
Sat Jul 25 19:29:48 2009  heaviest cycle: 27 relations
Sat Jul 25 19:29:54 2009  RelProcTime: 1033
Sat Jul 25 19:29:54 2009  elapsed time 00:17:15
Sat Jul 25 19:30:08 2009
Sat Jul 25 19:30:08 2009
Sat Jul 25 19:30:08 2009  Msieve v. 1.43
Sat Jul 25 19:30:08 2009  random seeds: f59dc650 7a49ec57
Sat Jul 25 19:30:08 2009  factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits)
Sat Jul 25 19:30:10 2009  searching for 15-digit factors
Sat Jul 25 19:30:10 2009  commencing number field sieve (167-digit input)
Sat Jul 25 19:30:10 2009  R0: -20000000000000000000000000000000000000
Sat Jul 25 19:30:10 2009  R1:  1
Sat Jul 25 19:30:10 2009  A0:  68
Sat Jul 25 19:30:10 2009  A1:  0
Sat Jul 25 19:30:10 2009  A2:  0
Sat Jul 25 19:30:10 2009  A3:  0
Sat Jul 25 19:30:10 2009  A4:  0
Sat Jul 25 19:30:10 2009  A5:  125
Sat Jul 25 19:30:10 2009  skew 1.00, size 4.008652e-13, alpha 0.098689, combined = 4.774392e-11
Sat Jul 25 19:30:10 2009
Sat Jul 25 19:30:10 2009  commencing linear algebra
Sat Jul 25 19:30:11 2009  read 1902390 cycles
Sat Jul 25 19:30:16 2009  cycles contain 5965208 unique relations
Sat Jul 25 19:32:01 2009  read 5965208 relations
Sat Jul 25 19:33:00 2009  using 20 quadratic characters above 268434500
Sat Jul 25 19:33:58 2009  building initial matrix
Sat Jul 25 19:36:15 2009  memory use: 732.8 MB
Sat Jul 25 19:36:20 2009  read 1902390 cycles
Sat Jul 25 19:36:28 2009  matrix is 1902213 x 1902390 (570.9 MB) with weight 169455496 (89.08/col)
Sat Jul 25 19:36:28 2009  sparse part has weight 128720555 (67.66/col)
Sat Jul 25 19:37:31 2009  filtering completed in 2 passes
Sat Jul 25 19:37:32 2009  matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col)
Sat Jul 25 19:37:32 2009  sparse part has weight 128715828 (67.68/col)
Sat Jul 25 19:38:00 2009  read 1901778 cycles
Sat Jul 25 19:38:09 2009  matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col)
Sat Jul 25 19:38:09 2009  sparse part has weight 128715828 (67.68/col)
Sat Jul 25 19:38:09 2009  saving the first 48 matrix rows for later
Sat Jul 25 19:38:11 2009  matrix is 1901554 x 1901778 (541.8 MB) with weight 134697483 (70.83/col)
Sat Jul 25 19:38:11 2009  sparse part has weight 123006791 (64.68/col)
Sat Jul 25 19:38:11 2009  matrix includes 64 packed rows
Sat Jul 25 19:38:11 2009  using block size 10922 for processor cache size 256 kB
Sat Jul 25 19:38:23 2009  commencing Lanczos iteration
Sat Jul 25 19:38:23 2009  memory use: 538.2 MB
Sat Jul 25 19:39:31 2009  lanczos halted after 23 iterations (dim = 1460)
Sat Jul 25 19:39:31 2009  BLanczosTime: 561
Sat Jul 25 19:39:31 2009  elapsed time 00:09:23
Sat Jul 25 19:40:06 2009
Sat Jul 25 19:40:06 2009
Sat Jul 25 19:40:06 2009  Msieve v. 1.43
Sat Jul 25 19:40:06 2009  random seeds: eb58ec47 f7b10534
Sat Jul 25 19:40:06 2009  factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits)
Sat Jul 25 19:40:08 2009  searching for 15-digit factors
Sat Jul 25 19:40:08 2009  commencing number field sieve (167-digit input)
Sat Jul 25 19:40:08 2009  R0: -20000000000000000000000000000000000000
Sat Jul 25 19:40:08 2009  R1:  1
Sat Jul 25 19:40:08 2009  A0:  68
Sat Jul 25 19:40:08 2009  A1:  0
Sat Jul 25 19:40:08 2009  A2:  0
Sat Jul 25 19:40:08 2009  A3:  0
Sat Jul 25 19:40:08 2009  A4:  0
Sat Jul 25 19:40:08 2009  A5:  125
Sat Jul 25 19:40:08 2009  skew 1.00, size 4.008652e-13, alpha 0.098689, combined = 4.774392e-11
Sat Jul 25 19:40:08 2009
Sat Jul 25 19:40:08 2009  commencing linear algebra
Sat Jul 25 19:40:09 2009  read 1901778 cycles
Sat Jul 25 19:40:14 2009  cycles contain 5965168 unique relations
Sat Jul 25 19:41:38 2009  read 5965168 relations
Sat Jul 25 19:42:42 2009  using 20 quadratic characters above 268434500
Sat Jul 25 19:43:41 2009  building initial matrix
Sat Jul 25 19:46:58 2009  memory use: 732.8 MB
Sat Jul 25 19:47:03 2009  read 1901778 cycles
Sat Jul 25 19:47:11 2009  matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col)
Sat Jul 25 19:47:11 2009  sparse part has weight 128715828 (67.68/col)
Sat Jul 25 19:47:41 2009  filtering completed in 1 passes
Sat Jul 25 19:47:42 2009  matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col)
Sat Jul 25 19:47:42 2009  sparse part has weight 128715828 (67.68/col)
Sat Jul 25 19:48:09 2009  read 1901778 cycles
Sat Jul 25 19:48:17 2009  matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col)
Sat Jul 25 19:48:17 2009  sparse part has weight 128715828 (67.68/col)
Sat Jul 25 19:48:18 2009  saving the first 48 matrix rows for later
Sat Jul 25 19:48:19 2009  matrix is 1901554 x 1901778 (541.8 MB) with weight 134697483 (70.83/col)
Sat Jul 25 19:48:19 2009  sparse part has weight 123006791 (64.68/col)
Sat Jul 25 19:48:19 2009  matrix includes 64 packed rows
Sat Jul 25 19:48:19 2009  using block size 10922 for processor cache size 256 kB
Sat Jul 25 19:48:31 2009  commencing Lanczos iteration (2 threads)
Sat Jul 25 19:48:31 2009  memory use: 552.7 MB
Sun Jul 26 15:44:14 2009
Sun Jul 26 15:44:14 2009
Sun Jul 26 15:44:14 2009  Msieve v. 1.43
Sun Jul 26 15:44:14 2009  random seeds: eccd68a9 d80b29f0
Sun Jul 26 15:44:14 2009  factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits)
Sun Jul 26 15:44:17 2009  searching for 15-digit factors
Sun Jul 26 15:44:18 2009  commencing number field sieve (167-digit input)
Sun Jul 26 15:44:19 2009  R0: -20000000000000000000000000000000000000
Sun Jul 26 15:44:19 2009  R1:  1
Sun Jul 26 15:44:19 2009  A0:  68
Sun Jul 26 15:44:19 2009  A1:  0
Sun Jul 26 15:44:19 2009  A2:  0
Sun Jul 26 15:44:19 2009  A3:  0
Sun Jul 26 15:44:19 2009  A4:  0
Sun Jul 26 15:44:19 2009  A5:  125
Sun Jul 26 15:44:19 2009  skew 1.00, size 4.008652e-13, alpha 0.098689, combined = 4.774392e-11
Sun Jul 26 15:44:19 2009
Sun Jul 26 15:44:19 2009  commencing linear algebra
Sun Jul 26 15:44:20 2009  read 1901778 cycles
Sun Jul 26 15:45:51 2009  matrix is 1901602 x 1901778 (570.8 MB) with weight 169437007 (89.09/col)
Sun Jul 26 15:45:51 2009  sparse part has weight 128715828 (67.68/col)
Sun Jul 26 15:45:56 2009  saving the first 48 matrix rows for later
Sun Jul 26 15:47:30 2009  matrix is 1901554 x 1901778 (541.8 MB) with weight 134697483 (70.83/col)
Sun Jul 26 15:47:30 2009  sparse part has weight 123006791 (64.68/col)
Sun Jul 26 15:47:30 2009  matrix includes 64 packed rows
Sun Jul 26 15:47:30 2009  using block size 10922 for processor cache size 256 kB
Sun Jul 26 15:51:08 2009  commencing Lanczos iteration
Sun Jul 26 15:51:08 2009  memory use: 538.2 MB
Sun Jul 26 15:51:15 2009  restarting at iteration 23725 (dim = 1500119)
Sun Jul 26 16:14:59 2009  lanczos halted after 23730 iterations (dim = 1500436)
Sun Jul 26 16:17:00 2009  BLanczosTime: 1961
Sun Jul 26 16:17:00 2009  elapsed time 00:32:46
Sun Jul 26 17:40:20 2009  lanczos halted after 30075 iterations (dim = 1901553)
Sun Jul 26 17:40:29 2009  recovered 38 nontrivial dependencies
Sun Jul 26 17:40:29 2009  BLanczosTime: 79221
Sun Jul 26 17:40:29 2009  elapsed time 22:00:23
Sun Jul 26 17:40:40 2009
Sun Jul 26 17:40:40 2009
Sun Jul 26 17:40:40 2009  Msieve v. 1.43
Sun Jul 26 17:40:40 2009  random seeds: 40f05cc9 dbd37a0e
Sun Jul 26 17:40:40 2009  factoring 29236196756825705984570046178024533820243975892239644578877837946904172992070299514980635998415019069671574087205586916757001765454390541489468221491344352348710530363 (167 digits)
Sun Jul 26 17:40:42 2009  searching for 15-digit factors
Sun Jul 26 17:40:43 2009  commencing number field sieve (167-digit input)
Sun Jul 26 17:40:43 2009  R0: -20000000000000000000000000000000000000
Sun Jul 26 17:40:43 2009  R1:  1
Sun Jul 26 17:40:43 2009  A0:  68
Sun Jul 26 17:40:43 2009  A1:  0
Sun Jul 26 17:40:43 2009  A2:  0
Sun Jul 26 17:40:43 2009  A3:  0
Sun Jul 26 17:40:43 2009  A4:  0
Sun Jul 26 17:40:43 2009  A5:  125
Sun Jul 26 17:40:43 2009  skew 1.00, size 4.008652e-13, alpha 0.098689, combined = 4.774392e-11
Sun Jul 26 17:40:43 2009
Sun Jul 26 17:40:43 2009  commencing square root phase
Sun Jul 26 17:40:43 2009  reading relations for dependency 1
Sun Jul 26 17:40:44 2009  read 952156 cycles
Sun Jul 26 17:40:47 2009  cycles contain 3664144 unique relations
Sun Jul 26 17:41:31 2009  read 3664144 relations
Sun Jul 26 17:42:00 2009  multiplying 2983448 relations
Sun Jul 26 17:50:53 2009  multiply complete, coefficients have about 87.65 million bits
Sun Jul 26 17:50:55 2009  initial square root is modulo 1956611
Sun Jul 26 18:03:12 2009  sqrtTime: 1349
Sun Jul 26 18:03:12 2009  prp69 factor: 101101428297969763167582651911552568964064074821357008687845402353373
Sun Jul 26 18:03:12 2009  prp99 factor: 289176891454586933473472026592329087156730099564830191435580236364586283574771523426365696790224631
Sun Jul 26 18:03:12 2009  elapsed time 00:22:32

Jul 27, 2009 (2nd)

By Jo Yeong Uk / Msieve / Jul 27, 2009

(13·10¹⁶⁸-1)/3 = 4(3)₁₆₈_<169> = 20947 · 771585846463_<12> · 39603215950776900109_<20> · C133

C133 = P46 · P88

P46 = 1938224840403052580372387224495153919668245331_<46>

P88 = 3492861805147986371594013038659339678087070803636098353203209518029135382931515883660607_<88>

Number: 43333_168
N=6769951514832874024854036768853409897637506303253507175204255793012536446458911961588877677283372873422176238901148203977372816375917
  ( 133 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=1938224840403052580372387224495153919668245331
 r2=3492861805147986371594013038659339678087070803636098353203209518029135382931515883660607
Version: 
Total time: 34.46 hours.
Scaled time: 82.46 units (timescale=2.393).
Factorization parameters were as follows:
n: 6769951514832874024854036768853409897637506303253507175204255793012536446458911961588877677283372873422176238901148203977372816375917
m: 10000000000000000000000000000000000
deg: 5
c5: 13
c0: -100
skew: 1.50
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2700000, 5400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11025872
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 947012 x 947259
Total sieving time: 30.92 hours.
Total relation processing time: 1.46 hours.
Matrix solve time: 1.87 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000
total time: 34.46 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 27, 2009

By Andreas Tete / Sys`s Databaseworkers / Jul 27, 2009

(58·10²⁰²+23)/9 = 6(4)₂₀₁7_<203> = 122203 · 287922001189726263337_<21> · C178

C178 = P39 · C139

P39 = 900888654245586171146217023177567172781_<39>

C139 = [2033094880569783215278126749021287699566111873184365711870097919375967568012016979486944089877439038338587424781953667086152516217685482617_<139>]

Syd`s Databaseworkers hit this p39 factor
p39 = 900888654245586171146217023177567172781

Jul 26, 2009 (2nd)

By Wataru Sakai / GMP-ECM / Jul 26, 2009

(17·10¹⁷¹+7)/3 = 5(6)₁₇₀9_<172> = 283 · 2808665746949_<13> · C157

C157 = P30 · P128

P30 = 310692117837628822353435398753_<30>

P128 = 22946208622966530086181294683282074760948833484150202522041144943775782218378532782991915144433011255535400598496135511752228619_<128>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1603423327
Step 1 took 52394ms
Step 2 took 17646ms
********** Factor found in step 2: 310692117837628822353435398753
Found probable prime factor of 30 digits: 310692117837628822353435398753
Probable prime cofactor 22946208622966530086181294683282074760948833484150202522041144943775782218378532782991915144433011255535400598496135511752228619 has 128 digits

Jul 26, 2009

By Andreas Tete / Syd`s Databaseworkers with ECM / Jul 26, 2009

(47·10¹⁶⁹+43)/9 = 5(2)₁₆₈7_<170> = 3 · 8572033 · 2460206087289861850132545179847589_<34> · C129

C129 = P34 · P96

P34 = 5947600359084872453635233580884281_<34>

P96 = 138783230265768766152371928057610712541819675642385676028172380581542216339866361236637806555397_<96>

Syd`s Database workers hit this p34 with B1=1e6
p34 = 5947600359084872453635233580884281

Jul 25, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jul 25, 2009

(47·10¹⁸²+43)/9 = 5(2)₁₈₁7_<183> = 31 · 401 · C179

C179 = P39 · P140

P39 = 724670646436597737957829265930693298467_<39>

P140 = 57970708996105002215788203509108410471504630076942583716286001043883185692786443798047081444061638563025160902815892854666009628608598216351_<140>

Number: n
N=42009671162595303855057696261139266529017956899865032758605278917401835912012084484130176351236603830924480912414304739942259047721198795126878145138944752813307233707845082633917
  ( 179 digits)
SNFS difficulty: 184 digits.
Divisors found:

Sat Jul 25 18:54:33 2009  prp39 factor: 724670646436597737957829265930693298467
Sat Jul 25 18:54:33 2009  prp140 factor: 57970708996105002215788203509108410471504630076942583716286001043883185692786443798047081444061638563025160902815892854666009628608598216351
Sat Jul 25 18:54:33 2009  elapsed time 03:09:32 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 216.75 hours.
Scaled time: 576.57 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_2_181_7
n: 42009671162595303855057696261139266529017956899865032758605278917401835912012084484130176351236603830924480912414304739942259047721198795126878145138944752813307233707845082633917
m: 2000000000000000000000000000000000000
deg: 5
c5: 1175
c0: 344
skew: 0.78
type: snfs
lss: 1
rlim: 8400000
alim: 8400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4200000, 7800409)
Primes: RFBsize:564877, AFBsize:565056, largePrimes:21409291 encountered
Relations: rels:21835602, finalFF:971958
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2386706 hash collisions in 23549779 relations
Msieve: matrix is 1431432 x 1431680 (384.4 MB)

Total sieving time: 216.03 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,184,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,56,56,2.5,2.5,100000
total time: 216.75 hours.
 --------- CPU info (if available) ----------

Jul 25, 2009

By Jo Yeong Uk / GMP-ECM 6.2.3, YAFU 1.10, Msieve / Jul 25, 2009

(34·10¹⁷⁰-61)/9 = 3(7)₁₆₉1_<171> = 7 · 1549 · 1104921407_<10> · 10187536427529899_<17> · 391353153935485813_<18> · C124

C124 = P40 · P41 · P44

P40 = 6725886983982318771880439066030047436221_<40>

P41 = 13026818417600827639174618332243277437991_<41>

P44 = 90267127858585686761229484150679606606868203_<44>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 7908926676514675413083853032827063880118980193445471625562601469958414706043143581401715516956542424923236530406833110566233 (124 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=7372562557
Step 1 took 4180ms
********** Factor found in step 1: 90267127858585686761229484150679606606868203
Found probable prime factor of 44 digits: 90267127858585686761229484150679606606868203
Composite cofactor 87616908437642552977838315920860564586991837524724010046764766223080042854872011 has 80 digits

07/25/09 02:40:39 v1.10 @ 조영욱-PC, starting SIQS on c80: 87616908437642552977838315920860564586991837524724010046764766223080042854872011
07/25/09 02:40:39 v1.10 @ 조영욱-PC, random seeds: 4212545165, 4213289736
07/25/09 02:40:39 v1.10 @ 조영욱-PC, ==== sieve params ====
07/25/09 02:40:39 v1.10 @ 조영욱-PC, n = 80 digits, 266 bits
07/25/09 02:40:39 v1.10 @ 조영욱-PC, factor base: 43638 primes (max prime = 1122259)
07/25/09 02:40:39 v1.10 @ 조영욱-PC, single large prime cutoff: 106614605 (95 * pmax)
07/25/09 02:40:39 v1.10 @ 조영욱-PC, using 13 large prime slices of factor base
07/25/09 02:40:39 v1.10 @ 조영욱-PC, buckets hold 1024 elements
07/25/09 02:40:39 v1.10 @ 조영욱-PC, sieve interval: 7 blocks of size 65536
07/25/09 02:40:39 v1.10 @ 조영욱-PC, polynomial A has ~ 10 factors
07/25/09 02:40:39 v1.10 @ 조영욱-PC, using multiplier of 1
07/25/09 02:40:39 v1.10 @ 조영욱-PC, using small prime variation correction of 18 bits
07/25/09 02:40:39 v1.10 @ 조영욱-PC, using SSE2 for trial division and x64 sieve scanning
07/25/09 02:40:39 v1.10 @ 조영욱-PC, trial factoring cutoff at 95 bits
07/25/09 02:40:39 v1.10 @ 조영욱-PC, ==== sieving started ====
07/25/09 02:48:32 v1.10 @ 조영욱-PC, sieve time = 244.3230, relation time = 65.8900, poly_time = 162.9600
07/25/09 02:48:32 v1.10 @ 조영욱-PC, 43837 relations found: 21442 full + 22395 from 239791 partial, using 121730 polys (238 A polys)
07/25/09 02:48:32 v1.10 @ 조영욱-PC, on average, sieving found 2.15 rels/poly and 551.53 rels/sec
07/25/09 02:48:32 v1.10 @ 조영욱-PC, trial division touched 3557500 sieve locations out of 111687761920
07/25/09 02:48:32 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
07/25/09 02:48:33 v1.10 @ 조영욱-PC, begin with 261233 relations
07/25/09 02:48:33 v1.10 @ 조영욱-PC, reduce to 63321 relations in 2 passes
07/25/09 02:48:33 v1.10 @ 조영욱-PC, recovered 63321 relations
07/25/09 02:48:33 v1.10 @ 조영욱-PC, recovered 49420 polynomials
07/25/09 02:48:33 v1.10 @ 조영욱-PC, attempting to build 43837 cycles
07/25/09 02:48:33 v1.10 @ 조영욱-PC, found 43837 cycles in 1 passes
07/25/09 02:48:33 v1.10 @ 조영욱-PC, distribution of cycle lengths:
07/25/09 02:48:33 v1.10 @ 조영욱-PC,    length 1 : 21442
07/25/09 02:48:33 v1.10 @ 조영욱-PC,    length 2 : 22395
07/25/09 02:48:33 v1.10 @ 조영욱-PC, largest cycle: 2 relations
07/25/09 02:48:33 v1.10 @ 조영욱-PC, matrix is 43638 x 43837 (6.5 MB) with weight 1357350 (30.96/col)
07/25/09 02:48:33 v1.10 @ 조영욱-PC, sparse part has weight 1357350 (30.96/col)
07/25/09 02:48:33 v1.10 @ 조영욱-PC, filtering completed in 3 passes
07/25/09 02:48:33 v1.10 @ 조영욱-PC, matrix is 32275 x 32339 (5.2 MB) with weight 1109999 (34.32/col)
07/25/09 02:48:33 v1.10 @ 조영욱-PC, sparse part has weight 1109999 (34.32/col)
07/25/09 02:48:33 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
07/25/09 02:48:33 v1.10 @ 조영욱-PC, matrix is 32227 x 32339 (3.8 MB) with weight 864751 (26.74/col)
07/25/09 02:48:33 v1.10 @ 조영욱-PC, sparse part has weight 669894 (20.71/col)
07/25/09 02:48:33 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
07/25/09 02:48:33 v1.10 @ 조영욱-PC, using block size 12935 for processor cache size 4096 kB
07/25/09 02:48:33 v1.10 @ 조영욱-PC, commencing Lanczos iteration
07/25/09 02:48:33 v1.10 @ 조영욱-PC, memory use: 3.7 MB
07/25/09 02:48:37 v1.10 @ 조영욱-PC, lanczos halted after 511 iterations (dim = 32221)
07/25/09 02:48:37 v1.10 @ 조영욱-PC, recovered 14 nontrivial dependencies
07/25/09 02:48:37 v1.10 @ 조영욱-PC, prp41 = 13026818417600827639174618332243277437991
07/25/09 02:48:38 v1.10 @ 조영욱-PC, prp40 = 6725886983982318771880439066030047436221
07/25/09 02:48:38 v1.10 @ 조영욱-PC, Lanczos elapsed time = 4.1810 seconds.
07/25/09 02:48:38 v1.10 @ 조영욱-PC, Sqrt elapsed time = 1.0450 seconds.
07/25/09 02:48:38 v1.10 @ 조영욱-PC, SIQS elapsed time = 478.8780 seconds.
07/25/09 02:48:38 v1.10 @ 조영욱-PC, 
07/25/09 02:48:38 v1.10 @ 조영욱-PC,

(37·10¹⁶⁹+53)/9 = 4(1)₁₆₈7_<170> = 19 · 291511918341504324969778930777933_<33> · C136

C136 = P40 · P97

P40 = 6256622275585770775151492306219379972061_<40>

P97 = 1186340513227261878040769445245614823177468731961871849452046522629392283910274236941531315901911_<97>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 7422484481487542405434963871001284300917097043855519001904556196162796366335291956314614258679614931018465138599301201369883800196508571 (136 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3546435855
Step 1 took 4851ms
Step 2 took 4259ms
********** Factor found in step 2: 6256622275585770775151492306219379972061
Found probable prime factor of 40 digits: 6256622275585770775151492306219379972061
Probable prime cofactor 1186340513227261878040769445245614823177468731961871849452046522629392283910274236941531315901911 has 97 digits

Jul 24, 2009 (3rd)

By Wataru Sakai / Msieve / Jul 24, 2009

(22·10¹⁹¹-1)/3 = 7(3)₁₉₁_<192> = 1297 · C189

C189 = P80 · P110

P80 = 31599751978617979691934192792502734631798298443748846506515340551417632686335601_<80>

P110 = 17892778104022385586692910064435301213675071970966671817147805915015452599464091933241233683195001902978482389_<110>

Number: 73333_191
N=565407350295553842199948599331791313287072731945515291698792084297095862246209200719609354921613980981752762785916216910819840657928553071189925469031097404266255461320997172963248522230789
  ( 189 digits)
SNFS difficulty: 193 digits.
Divisors found:
 r1=31599751978617979691934192792502734631798298443748846506515340551417632686335601
 r2=17892778104022385586692910064435301213675071970966671817147805915015452599464091933241233683195001902978482389
Version: 
Total time: 483.64 hours.
Scaled time: 971.64 units (timescale=2.009).
Factorization parameters were as follows:
n: 565407350295553842199948599331791313287072731945515291698792084297095862246209200719609354921613980981752762785916216910819840657928553071189925469031097404266255461320997172963248522230789
m: 200000000000000000000000000000000000000
deg: 5
c5: 55
c0: -8
skew: 0.68
type: snfs
lss: 1
rlim: 11600000
alim: 11600000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 11600000/11600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [5800000, 10800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1830862 x 1831110
Total sieving time: 483.64 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,193,5,0,0,0,0,0,0,0,0,11600000,11600000,28,28,55,55,2.5,2.5,100000
total time: 483.64 hours.
 --------- CPU info (if available) ----------

(67·10²⁰⁰+23)/9 = 7(4)₁₉₉7_<201> = 3⁴ · 1153 · C196

C196 = P69 · P128

P69 = 196592506741212520044538167570720429219402274779774438764525711972609_<69>

P128 = 40546279211618582655414497439811038556876425327404273148537996988167822927209105501508855259371162388034501678989737104551746031_<128>

Number: 74447_200
N=7971094669241211273269350427167394177769687711546309085739235750478563109060041378309342717810161837016098042085000422349045907556716718002895767824616881826736955065630662302789764162672196464879
  ( 196 digits)
SNFS difficulty: 201 digits.
Divisors found:
 r1=196592506741212520044538167570720429219402274779774438764525711972609
 r2=40546279211618582655414497439811038556876425327404273148537996988167822927209105501508855259371162388034501678989737104551746031
Version: 
Total time: 699.71 hours.
Scaled time: 1405.71 units (timescale=2.009).
Factorization parameters were as follows:
n: 7971094669241211273269350427167394177769687711546309085739235750478563109060041378309342717810161837016098042085000422349045907556716718002895767824616881826736955065630662302789764162672196464879
m: 10000000000000000000000000000000000000000
deg: 5
c5: 67
c0: 23
skew: 0.81
type: snfs
lss: 1
rlim: 16200000
alim: 16200000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 16200000/16200000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [8100000, 15200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2869202 x 2869450
Total sieving time: 699.71 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,201,5,0,0,0,0,0,0,0,0,16200000,16200000,29,29,56,56,2.6,2.6,100000
total time: 699.71 hours.
 --------- CPU info (if available) ----------

Jul 24, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jul 24, 2009

2·10²¹²-1 = 1(9)₂₁₂_<213> = 23 · C211

C211 = P46 · P61 · P106

P46 = 2659264777745734405392508581327747941839503713_<46>

P61 = 2624192453344997234656310661787467697906712795425020425430953_<61>

P106 = 1246077046444953259325719448796658447093073224853980853958734916369485280891634235590281319558742952446417_<106>

Number: n
N=8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913
  ( 211 digits)
SNFS difficulty: 213 digits.
Divisors found:

Fri Jul 24 20:24:31 2009  prp46 factor: 2659264777745734405392508581327747941839503713
Fri Jul 24 20:24:31 2009  prp61 factor: 2624192453344997234656310661787467697906712795425020425430953
Fri Jul 24 20:24:31 2009  prp106 factor: 1246077046444953259325719448796658447093073224853980853958734916369485280891634235590281319558742952446417
Fri Jul 24 20:24:31 2009  elapsed time 39:56:00 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20050930-k8
Total time: 95.16 hours.
Scaled time: 191.65 units (timescale=2.014).
Factorization parameters were as follows:
name: KA_1_9_212
n: 8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913
m: 200000000000000000000000000000000000
deg: 6
c6: 25
c0: -8
skew: 0.83
type: snfs
lss: 1
rlim: 25000000
alim: 25000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 25000000/25000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [12500000, 30599990)
Primes: RFBsize:1565927, AFBsize:1563644, largePrimes:38836401 encountered
Relations: rels:36263602, finalFF:1107921
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 8322646 hash collisions in 48064285 relations
Msieve: matrix is 4525782 x 4526029 (1218.8 MB)

Total sieving time: 94.03 hours.
Total relation processing time: 1.13 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,213,6,0,0,0,0,0,0,0,0,25000000,25000000,29,29,58,58,2.6,2.6,100000
total time: 95.16 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3352056k/3407296k available (3119k kernel code, 53956k reserved, 1894k data, 424k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.68 BogoMIPS (lpj=2830844)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22644.41 BogoMIPS).

Jul 24, 2009

By Andreas Tete / Syd`s Databaseworkers / Jul 24, 2009

(58·10¹⁹⁴+23)/9 = 6(4)₁₉₃7_<195> = 257 · 403464209177_<12> · 3543970882437511879731257595620290877_<37> · C145

C145 = P36 · P109

P36 = 277910928745730887156179766492458017_<36>

P109 = 6310322790083620064791690811822998614035354857083272254295215385444318070690134698155017866341817570459038947_<109>

Syd`s Databaseworkers hit this p36 factor
p36 = 277910928745730887156179766492458017

Jul 23, 2009 (3rd)

By Andreas Tete / GGNFS, Msieve v 1.42, Syd`s Database workers / Jul 23, 2009

5·10¹⁹³-3 = 4(9)₁₉₂7_<194> = 139 · 124367 · 416128249 · 5670353807_<10> · 630601422409414751_<18> · 1628951248743679743054506189_<28> · C124

C124 = P44 · P80

P44 = 14620629278240550652432989762103729163476871_<44>

P80 = 81617556881746859330571187100259479960634045948609207766222314981106404568681507_<80>

Thu Jul 23 13:49:00 2009  Msieve v. 1.42
Thu Jul 23 13:49:00 2009  random seeds: 7f123710 3ac4bbe3
Thu Jul 23 13:49:00 2009  factoring 1193300041763731671870987439029906012365042862204137739005604691718275603021397760465734919821660412096935234987760359924597 (124 digits)
Thu Jul 23 13:49:02 2009  searching for 15-digit factors
Thu Jul 23 13:49:03 2009  commencing number field sieve (124-digit input)
Thu Jul 23 13:49:03 2009  R0: -543336852106466897936255
Thu Jul 23 13:49:03 2009  R1:  18897792025541
Thu Jul 23 13:49:03 2009  A0: -56096130083591137671762443568
Thu Jul 23 13:49:03 2009  A1:  18511784021721927080713518
Thu Jul 23 13:49:03 2009  A2: -165566443634317392579
Thu Jul 23 13:49:03 2009  A3: -3652011178397938
Thu Jul 23 13:49:03 2009  A4:  5511588632
Thu Jul 23 13:49:03 2009  A5:  25200
Thu Jul 23 13:49:03 2009  skew 149034.11, size 7.586280e-012, alpha -6.213274, combined = 1.859200e-010
Thu Jul 23 13:49:03 2009  
Thu Jul 23 13:49:03 2009  commencing relation filtering
Thu Jul 23 13:49:03 2009  estimated available RAM is 3069.5 MB
Thu Jul 23 13:49:03 2009  commencing duplicate removal, pass 1
Thu Jul 23 13:49:03 2009  error -15 reading relation 27880
Thu Jul 23 13:50:52 2009  found 1488308 hash collisions in 9178490 relations
Thu Jul 23 13:51:22 2009  added 59182 free relations
Thu Jul 23 13:51:22 2009  commencing duplicate removal, pass 2
Thu Jul 23 13:51:47 2009  found 1228693 duplicates and 8008978 unique relations
Thu Jul 23 13:51:47 2009  memory use: 41.3 MB
Thu Jul 23 13:51:47 2009  reading ideals above 100000
Thu Jul 23 13:51:47 2009  commencing singleton removal, initial pass
Thu Jul 23 13:53:56 2009  memory use: 149.2 MB
Thu Jul 23 13:53:56 2009  reading all ideals from disk
Thu Jul 23 13:54:03 2009  memory use: 287.9 MB
Thu Jul 23 13:54:05 2009  keeping 8633531 ideals with weight <= 200, target excess is 43827
Thu Jul 23 13:54:07 2009  commencing in-memory singleton removal
Thu Jul 23 13:54:09 2009  begin with 8008978 relations and 8633531 unique ideals
Thu Jul 23 13:54:21 2009  reduce to 3184608 relations and 3001298 ideals in 15 passes
Thu Jul 23 13:54:21 2009  max relations containing the same ideal: 106
Thu Jul 23 13:54:24 2009  removing 456604 relations and 390369 ideals in 66235 cliques
Thu Jul 23 13:54:24 2009  commencing in-memory singleton removal
Thu Jul 23 13:54:25 2009  begin with 2728004 relations and 3001298 unique ideals
Thu Jul 23 13:54:30 2009  reduce to 2687707 relations and 2569635 ideals in 9 passes
Thu Jul 23 13:54:30 2009  max relations containing the same ideal: 98
Thu Jul 23 13:54:33 2009  removing 347400 relations and 281165 ideals in 66235 cliques
Thu Jul 23 13:54:33 2009  commencing in-memory singleton removal
Thu Jul 23 13:54:33 2009  begin with 2340307 relations and 2569635 unique ideals
Thu Jul 23 13:54:37 2009  reduce to 2310136 relations and 2257591 ideals in 8 passes
Thu Jul 23 13:54:37 2009  max relations containing the same ideal: 85
Thu Jul 23 13:54:40 2009  relations with 0 large ideals: 159
Thu Jul 23 13:54:40 2009  relations with 1 large ideals: 448
Thu Jul 23 13:54:40 2009  relations with 2 large ideals: 5181
Thu Jul 23 13:54:40 2009  relations with 3 large ideals: 37785
Thu Jul 23 13:54:40 2009  relations with 4 large ideals: 157995
Thu Jul 23 13:54:40 2009  relations with 5 large ideals: 402047
Thu Jul 23 13:54:40 2009  relations with 6 large ideals: 632608
Thu Jul 23 13:54:40 2009  relations with 7+ large ideals: 1073913
Thu Jul 23 13:54:40 2009  commencing 2-way merge
Thu Jul 23 13:54:43 2009  reduce to 1431580 relation sets and 1379035 unique ideals
Thu Jul 23 13:54:43 2009  commencing full merge
Thu Jul 23 13:55:20 2009  memory use: 151.7 MB
Thu Jul 23 13:55:20 2009  found 735016 cycles, need 727235
Thu Jul 23 13:55:20 2009  weight of 727235 cycles is about 51191425 (70.39/cycle)
Thu Jul 23 13:55:20 2009  distribution of cycle lengths:
Thu Jul 23 13:55:20 2009  1 relations: 83344
Thu Jul 23 13:55:20 2009  2 relations: 84619
Thu Jul 23 13:55:20 2009  3 relations: 84693
Thu Jul 23 13:55:20 2009  4 relations: 78225
Thu Jul 23 13:55:20 2009  5 relations: 70392
Thu Jul 23 13:55:20 2009  6 relations: 61090
Thu Jul 23 13:55:20 2009  7 relations: 52459
Thu Jul 23 13:55:20 2009  8 relations: 44423
Thu Jul 23 13:55:20 2009  9 relations: 36816
Thu Jul 23 13:55:20 2009  10+ relations: 131174
Thu Jul 23 13:55:20 2009  heaviest cycle: 22 relations
Thu Jul 23 13:55:20 2009  commencing cycle optimization
Thu Jul 23 13:55:22 2009  start with 4253137 relations
Thu Jul 23 13:55:34 2009  pruned 113256 relations
Thu Jul 23 13:55:34 2009  memory use: 109.9 MB
Thu Jul 23 13:55:34 2009  distribution of cycle lengths:
Thu Jul 23 13:55:34 2009  1 relations: 83344
Thu Jul 23 13:55:34 2009  2 relations: 86599
Thu Jul 23 13:55:34 2009  3 relations: 87818
Thu Jul 23 13:55:34 2009  4 relations: 80345
Thu Jul 23 13:55:34 2009  5 relations: 72065
Thu Jul 23 13:55:34 2009  6 relations: 62062
Thu Jul 23 13:55:34 2009  7 relations: 52824
Thu Jul 23 13:55:34 2009  8 relations: 44435
Thu Jul 23 13:55:34 2009  9 relations: 36553
Thu Jul 23 13:55:34 2009  10+ relations: 121190
Thu Jul 23 13:55:34 2009  heaviest cycle: 21 relations
Thu Jul 23 13:55:35 2009  RelProcTime: 392
Thu Jul 23 13:55:35 2009  
Thu Jul 23 13:55:35 2009  commencing linear algebra
Thu Jul 23 13:55:36 2009  read 727235 cycles
Thu Jul 23 13:55:38 2009  cycles contain 2259892 unique relations
Thu Jul 23 13:56:23 2009  read 2259892 relations
Thu Jul 23 13:56:27 2009  using 20 quadratic characters above 134214264
Thu Jul 23 13:56:42 2009  building initial matrix
Thu Jul 23 13:57:21 2009  memory use: 265.6 MB
Thu Jul 23 13:57:22 2009  read 727235 cycles
Thu Jul 23 13:57:23 2009  matrix is 727058 x 727235 (209.7 MB) with weight 69362639 (95.38/col)
Thu Jul 23 13:57:23 2009  sparse part has weight 49161753 (67.60/col)
Thu Jul 23 13:57:35 2009  filtering completed in 2 passes
Thu Jul 23 13:57:35 2009  matrix is 726657 x 726834 (209.7 MB) with weight 69345359 (95.41/col)
Thu Jul 23 13:57:35 2009  sparse part has weight 49156190 (67.63/col)
Thu Jul 23 13:57:38 2009  read 726834 cycles
Thu Jul 23 13:57:40 2009  matrix is 726657 x 726834 (209.7 MB) with weight 69345359 (95.41/col)
Thu Jul 23 13:57:40 2009  sparse part has weight 49156190 (67.63/col)
Thu Jul 23 13:57:40 2009  saving the first 48 matrix rows for later
Thu Jul 23 13:57:40 2009  matrix is 726609 x 726834 (200.2 MB) with weight 54862726 (75.48/col)
Thu Jul 23 13:57:40 2009  sparse part has weight 48114957 (66.20/col)
Thu Jul 23 13:57:40 2009  matrix includes 64 packed rows
Thu Jul 23 13:57:40 2009  using block size 65536 for processor cache size 3072 kB
Thu Jul 23 13:57:47 2009  commencing Lanczos iteration
Thu Jul 23 13:57:47 2009  memory use: 202.6 MB
Thu Jul 23 15:23:28 2009  lanczos halted after 11492 iterations (dim = 726608)
Thu Jul 23 15:23:31 2009  recovered 31 nontrivial dependencies
Thu Jul 23 15:23:31 2009  BLanczosTime: 5276
Thu Jul 23 15:23:31 2009  
Thu Jul 23 15:23:31 2009  commencing square root phase
Thu Jul 23 15:23:31 2009  reading relations for dependency 1
Thu Jul 23 15:23:32 2009  read 363673 cycles
Thu Jul 23 15:23:32 2009  cycles contain 1398991 unique relations
Thu Jul 23 15:23:58 2009  read 1398991 relations
Thu Jul 23 15:24:07 2009  multiplying 1130618 relations
Thu Jul 23 15:27:48 2009  multiply complete, coefficients have about 51.58 million bits
Thu Jul 23 15:27:51 2009  initial square root is modulo 25424593
Thu Jul 23 15:33:23 2009  sqrtTime: 592
Thu Jul 23 15:33:23 2009  prp44 factor: 14620629278240550652432989762103729163476871
Thu Jul 23 15:33:23 2009  prp80 factor: 81617556881746859330571187100259479960634045948609207766222314981106404568681507
Thu Jul 23 15:33:23 2009  elapsed time 01:44:23
Thu Jul 23 15:33:23 2009  total time ~ 125 hours

(58·10¹⁹⁴+23)/9 = 6(4)₁₉₃7_<195> = 257 · 403464209177_<12> · C181

C181 = P37 · C145

P37 = 3543970882437511879731257595620290877_<37>

C145 = [1753707667277490662296596455138203925886352047609268924626142234554596780596769030414778657310009459856568838766914928341099729251362501565388099_<145>]

Syd`s Database workers hit this p37 factor
p37 = 3543970882437511879731257595620290877

Jul 23, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve 1.42 / Jul 23, 2009

(56·10²⁰³+43)/9 = 6(2)₂₀₂7_<204> = 3 · C204

C204 = P60 · P144

P60 = 591752848190830505194723691088958573025065122850764427487837_<60>

P144 = 350496677863934757609414005722989412369536157605989693540146711579200859237238102599130471318852834601704462309602498012951936078401332556541157_<144>

Sieving time ~ 40 cpu-days

Thu Jul 16 01:25:58 2009  Msieve v. 1.42
Thu Jul 16 01:25:58 2009  random seeds: c56a6980 fe74d888
Thu Jul 16 01:25:58 2009  factoring 207407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407409 (204 digits)
Thu Jul 16 01:26:05 2009  
Thu Jul 16 01:26:05 2009  
Thu Jul 16 01:26:05 2009  Msieve v. 1.42
Thu Jul 16 01:26:05 2009  random seeds: f71ce5d8 4f84c420
Thu Jul 16 01:26:05 2009  factoring 207407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407409 (204 digits)
Thu Jul 16 01:26:07 2009  searching for 15-digit factors
Thu Jul 16 01:26:10 2009  commencing number field sieve (204-digit input)
Thu Jul 16 01:26:10 2009  R0: -100000000000000000000000000000000000000000
Thu Jul 16 01:26:10 2009  R1:  1
Thu Jul 16 01:26:10 2009  A0:  1075
Thu Jul 16 01:26:10 2009  A1:  0
Thu Jul 16 01:26:10 2009  A2:  0
Thu Jul 16 01:26:10 2009  A3:  0
Thu Jul 16 01:26:10 2009  A4:  0
Thu Jul 16 01:26:10 2009  A5:  14
Thu Jul 16 01:26:10 2009  skew 2.38, size 3.186562e-014, alpha -0.612885, combined = 9.720684e-012
Thu Jul 16 01:26:10 2009  
Thu Jul 16 01:26:10 2009  commencing relation filtering
Thu Jul 16 01:26:10 2009  commencing duplicate removal, pass 1
Thu Jul 16 01:29:27 2009  error -11 reading relation 24287251
Thu Jul 16 01:31:01 2009  error -11 reading relation 34401760
Thu Jul 16 01:31:07 2009  error -9 reading relation 35087611
Thu Jul 16 01:31:12 2009  error -15 reading relation 35782753
Thu Jul 16 01:31:18 2009  error -9 reading relation 36477916
Thu Jul 16 01:31:24 2009  error -15 reading relation 37169656
Thu Jul 16 01:31:29 2009  error -9 reading relation 37870362
Thu Jul 16 01:31:35 2009  error -9 reading relation 38571298
Thu Jul 16 01:31:41 2009  found 5319528 hash collisions in 39277598 relations
Thu Jul 16 01:32:30 2009  added 840 free relations
Thu Jul 16 01:32:30 2009  commencing duplicate removal, pass 2
Thu Jul 16 01:33:43 2009  found 3699116 duplicates and 35579322 unique relations
Thu Jul 16 01:33:43 2009  memory use: 165.2 MB
Thu Jul 16 01:33:43 2009  reading rational ideals above 21168128
Thu Jul 16 01:33:43 2009  reading algebraic ideals above 21168128
Thu Jul 16 01:33:43 2009  commencing singleton removal, pass 1
Thu Jul 16 01:39:13 2009  relations with 0 large ideals: 581552
Thu Jul 16 01:39:13 2009  relations with 1 large ideals: 3668835
Thu Jul 16 01:39:13 2009  relations with 2 large ideals: 10320596
Thu Jul 16 01:39:13 2009  relations with 3 large ideals: 13424743
Thu Jul 16 01:39:13 2009  relations with 4 large ideals: 6899607
Thu Jul 16 01:39:13 2009  relations with 5 large ideals: 20129
Thu Jul 16 01:39:13 2009  relations with 6 large ideals: 663860
Thu Jul 16 01:39:13 2009  relations with 7+ large ideals: 0
Thu Jul 16 01:39:13 2009  35579322 relations and about 31817912 large ideals
Thu Jul 16 01:39:13 2009  commencing singleton removal, pass 2
Thu Jul 16 01:44:30 2009  found 11545324 singletons
Thu Jul 16 01:44:30 2009  current dataset: 24033998 relations and about 18608908 large ideals
Thu Jul 16 01:44:30 2009  commencing singleton removal, pass 3
Thu Jul 16 01:48:14 2009  found 2658569 singletons
Thu Jul 16 01:48:14 2009  current dataset: 21375429 relations and about 15826556 large ideals
Thu Jul 16 01:48:14 2009  commencing singleton removal, pass 4
Thu Jul 16 01:51:35 2009  found 701176 singletons
Thu Jul 16 01:51:35 2009  current dataset: 20674253 relations and about 15115803 large ideals
Thu Jul 16 01:51:35 2009  commencing singleton removal, pass 5
Thu Jul 16 01:54:54 2009  found 185715 singletons
Thu Jul 16 01:54:54 2009  current dataset: 20488538 relations and about 14929365 large ideals
Thu Jul 16 01:54:54 2009  commencing singleton removal, final pass
Thu Jul 16 01:58:25 2009  memory use: 351.4 MB
Thu Jul 16 01:58:25 2009  commencing in-memory singleton removal
Thu Jul 16 01:58:27 2009  begin with 20488538 relations and 18081880 unique ideals
Thu Jul 16 01:59:05 2009  reduce to 13835158 relations and 11057496 ideals in 23 passes
Thu Jul 16 01:59:05 2009  max relations containing the same ideal: 40
Thu Jul 16 01:59:10 2009  reading rational ideals above 720000
Thu Jul 16 01:59:10 2009  reading algebraic ideals above 720000
Thu Jul 16 01:59:10 2009  commencing singleton removal, final pass
Thu Jul 16 02:02:23 2009  keeping 12338074 ideals with weight <= 20, new excess is 1437415
Thu Jul 16 02:02:42 2009  memory use: 360.9 MB
Thu Jul 16 02:02:42 2009  commencing in-memory singleton removal
Thu Jul 16 02:02:44 2009  begin with 13866106 relations and 12338074 unique ideals
Thu Jul 16 02:03:09 2009  reduce to 13835805 relations and 12287758 ideals in 12 passes
Thu Jul 16 02:03:09 2009  max relations containing the same ideal: 20
Thu Jul 16 02:03:11 2009  filtering wants 358062 more relations
Thu Jul 16 02:03:11 2009  elapsed time 00:37:06
Thu Jul 16 20:16:09 2009  
Thu Jul 16 20:16:09 2009  
Thu Jul 16 20:16:09 2009  Msieve v. 1.42
Thu Jul 16 20:16:09 2009  random seeds: 641e9e94 e8e91ac0
Thu Jul 16 20:16:09 2009  factoring 207407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407409 (204 digits)
Thu Jul 16 20:16:11 2009  searching for 15-digit factors
Thu Jul 16 20:16:14 2009  commencing number field sieve (204-digit input)
Thu Jul 16 20:16:14 2009  R0: -100000000000000000000000000000000000000000
Thu Jul 16 20:16:14 2009  R1:  1
Thu Jul 16 20:16:14 2009  A0:  1075
Thu Jul 16 20:16:14 2009  A1:  0
Thu Jul 16 20:16:14 2009  A2:  0
Thu Jul 16 20:16:14 2009  A3:  0
Thu Jul 16 20:16:14 2009  A4:  0
Thu Jul 16 20:16:14 2009  A5:  14
Thu Jul 16 20:16:14 2009  skew 2.38, size 3.186562e-014, alpha -0.612885, combined = 9.720684e-012
Thu Jul 16 20:16:14 2009  
Thu Jul 16 20:16:14 2009  commencing relation filtering
Thu Jul 16 20:16:14 2009  commencing duplicate removal, pass 1
Thu Jul 16 20:19:38 2009  error -11 reading relation 24287251
Thu Jul 16 20:22:02 2009  error -11 reading relation 34401760
Thu Jul 16 20:22:08 2009  error -9 reading relation 35087611
Thu Jul 16 20:22:14 2009  error -15 reading relation 35782753
Thu Jul 16 20:22:26 2009  error -9 reading relation 36477916
Thu Jul 16 20:22:37 2009  error -15 reading relation 37169656
Thu Jul 16 20:22:43 2009  error -9 reading relation 37870362
Thu Jul 16 20:22:54 2009  error -9 reading relation 38571298
Thu Jul 16 20:23:04 2009  error -11 reading relation 39277606
Thu Jul 16 20:23:47 2009  found 6511908 hash collisions in 44449153 relations
Thu Jul 16 20:24:38 2009  added 390 free relations
Thu Jul 16 20:24:38 2009  commencing duplicate removal, pass 2
Thu Jul 16 20:26:09 2009  found 4542027 duplicates and 39907516 unique relations
Thu Jul 16 20:26:09 2009  memory use: 165.2 MB
Thu Jul 16 20:26:09 2009  reading rational ideals above 22740992
Thu Jul 16 20:26:09 2009  reading algebraic ideals above 22740992
Thu Jul 16 20:26:09 2009  commencing singleton removal, pass 1
Thu Jul 16 20:33:34 2009  relations with 0 large ideals: 716732
Thu Jul 16 20:33:34 2009  relations with 1 large ideals: 4434970
Thu Jul 16 20:33:34 2009  relations with 2 large ideals: 11968351
Thu Jul 16 20:33:34 2009  relations with 3 large ideals: 14857882
Thu Jul 16 20:33:34 2009  relations with 4 large ideals: 7237102
Thu Jul 16 20:33:34 2009  relations with 5 large ideals: 32882
Thu Jul 16 20:33:34 2009  relations with 6 large ideals: 659597
Thu Jul 16 20:33:34 2009  relations with 7+ large ideals: 0
Thu Jul 16 20:33:34 2009  39907516 relations and about 32967969 large ideals
Thu Jul 16 20:33:34 2009  commencing singleton removal, pass 2
Thu Jul 16 20:39:52 2009  found 11282742 singletons
Thu Jul 16 20:39:52 2009  current dataset: 28624774 relations and about 20371358 large ideals
Thu Jul 16 20:39:52 2009  commencing singleton removal, pass 3
Thu Jul 16 20:44:48 2009  found 2206322 singletons
Thu Jul 16 20:44:48 2009  current dataset: 26418452 relations and about 18093846 large ideals
Thu Jul 16 20:44:48 2009  commencing singleton removal, pass 4
Thu Jul 16 20:49:32 2009  found 472986 singletons
Thu Jul 16 20:49:32 2009  current dataset: 25945466 relations and about 17617214 large ideals
Thu Jul 16 20:49:32 2009  commencing singleton removal, final pass
Thu Jul 16 20:55:53 2009  memory use: 532.8 MB
Thu Jul 16 20:55:53 2009  commencing in-memory singleton removal
Thu Jul 16 20:55:56 2009  begin with 25945466 relations and 21393353 unique ideals
Thu Jul 16 20:56:37 2009  reduce to 19717751 relations and 14872914 ideals in 14 passes
Thu Jul 16 20:56:37 2009  max relations containing the same ideal: 48
Thu Jul 16 20:56:43 2009  reading rational ideals above 720000
Thu Jul 16 20:56:43 2009  reading algebraic ideals above 720000
Thu Jul 16 20:56:43 2009  commencing singleton removal, final pass
Thu Jul 16 21:03:01 2009  keeping 15815981 ideals with weight <= 20, new excess is 1924615
Thu Jul 16 21:03:40 2009  memory use: 499.5 MB
Thu Jul 16 21:03:40 2009  commencing in-memory singleton removal
Thu Jul 16 21:03:43 2009  begin with 19718141 relations and 15815981 unique ideals
Thu Jul 16 21:04:11 2009  reduce to 19714577 relations and 15810571 ideals in 9 passes
Thu Jul 16 21:04:11 2009  max relations containing the same ideal: 20
Thu Jul 16 21:04:26 2009  removing 2731961 relations and 2331961 ideals in 400000 cliques
Thu Jul 16 21:04:27 2009  commencing in-memory singleton removal
Thu Jul 16 21:04:29 2009  begin with 16982616 relations and 15810571 unique ideals
Thu Jul 16 21:04:52 2009  reduce to 16727703 relations and 13217278 ideals in 9 passes
Thu Jul 16 21:04:52 2009  max relations containing the same ideal: 20
Thu Jul 16 21:05:05 2009  removing 2046788 relations and 1646788 ideals in 400000 cliques
Thu Jul 16 21:05:06 2009  commencing in-memory singleton removal
Thu Jul 16 21:05:08 2009  begin with 14680915 relations and 13217278 unique ideals
Thu Jul 16 21:05:28 2009  reduce to 14507203 relations and 11392654 ideals in 9 passes
Thu Jul 16 21:05:28 2009  max relations containing the same ideal: 20
Thu Jul 16 21:05:40 2009  removing 1838879 relations and 1438879 ideals in 400000 cliques
Thu Jul 16 21:05:41 2009  commencing in-memory singleton removal
Thu Jul 16 21:05:42 2009  begin with 12668324 relations and 11392654 unique ideals
Thu Jul 16 21:05:58 2009  reduce to 12506345 relations and 9787669 ideals in 8 passes
Thu Jul 16 21:05:58 2009  max relations containing the same ideal: 20
Thu Jul 16 21:06:08 2009  removing 1726132 relations and 1326132 ideals in 400000 cliques
Thu Jul 16 21:06:09 2009  commencing in-memory singleton removal
Thu Jul 16 21:06:10 2009  begin with 10780213 relations and 9787669 unique ideals
Thu Jul 16 21:06:25 2009  reduce to 10606310 relations and 8282583 ideals in 9 passes
Thu Jul 16 21:06:25 2009  max relations containing the same ideal: 20
Thu Jul 16 21:06:34 2009  removing 526329 relations and 435156 ideals in 91173 cliques
Thu Jul 16 21:06:34 2009  commencing in-memory singleton removal
Thu Jul 16 21:06:36 2009  begin with 10079981 relations and 8282583 unique ideals
Thu Jul 16 21:06:45 2009  reduce to 10062987 relations and 7830297 ideals in 6 passes
Thu Jul 16 21:06:45 2009  max relations containing the same ideal: 19
Thu Jul 16 21:06:56 2009  relations with 0 large ideals: 271062
Thu Jul 16 21:06:56 2009  relations with 1 large ideals: 1391142
Thu Jul 16 21:06:56 2009  relations with 2 large ideals: 3031669
Thu Jul 16 21:06:56 2009  relations with 3 large ideals: 3193544
Thu Jul 16 21:06:56 2009  relations with 4 large ideals: 1672318
Thu Jul 16 21:06:56 2009  relations with 5 large ideals: 419717
Thu Jul 16 21:06:56 2009  relations with 6 large ideals: 81329
Thu Jul 16 21:06:56 2009  relations with 7+ large ideals: 2206
Thu Jul 16 21:06:56 2009  commencing 2-way merge
Thu Jul 16 21:07:06 2009  reduce to 6429038 relation sets and 4196348 unique ideals
Thu Jul 16 21:07:06 2009  commencing full merge
Thu Jul 16 21:08:12 2009  memory use: 301.3 MB
Thu Jul 16 21:08:13 2009  found 3209621 cycles, need 2904548
Thu Jul 16 21:08:14 2009  weight of 2904548 cycles is about 203674766 (70.12/cycle)
Thu Jul 16 21:08:14 2009  distribution of cycle lengths:
Thu Jul 16 21:08:14 2009  1 relations: 405554
Thu Jul 16 21:08:14 2009  2 relations: 321261
Thu Jul 16 21:08:14 2009  3 relations: 317273
Thu Jul 16 21:08:14 2009  4 relations: 298681
Thu Jul 16 21:08:14 2009  5 relations: 283233
Thu Jul 16 21:08:14 2009  6 relations: 258043
Thu Jul 16 21:08:14 2009  7 relations: 231041
Thu Jul 16 21:08:14 2009  8 relations: 201003
Thu Jul 16 21:08:14 2009  9 relations: 173146
Thu Jul 16 21:08:14 2009  10+ relations: 415313
Thu Jul 16 21:08:14 2009  heaviest cycle: 16 relations
Thu Jul 16 21:08:15 2009  commencing cycle optimization
Thu Jul 16 21:08:21 2009  start with 15578527 relations
Thu Jul 16 21:08:55 2009  pruned 464052 relations
Thu Jul 16 21:08:55 2009  memory use: 415.4 MB
Thu Jul 16 21:08:55 2009  distribution of cycle lengths:
Thu Jul 16 21:08:55 2009  1 relations: 405554
Thu Jul 16 21:08:55 2009  2 relations: 330438
Thu Jul 16 21:08:55 2009  3 relations: 331927
Thu Jul 16 21:08:55 2009  4 relations: 309381
Thu Jul 16 21:08:55 2009  5 relations: 294647
Thu Jul 16 21:08:55 2009  6 relations: 266318
Thu Jul 16 21:08:55 2009  7 relations: 236587
Thu Jul 16 21:08:55 2009  8 relations: 202715
Thu Jul 16 21:08:55 2009  9 relations: 171618
Thu Jul 16 21:08:55 2009  10+ relations: 355363
Thu Jul 16 21:08:55 2009  heaviest cycle: 16 relations
Thu Jul 16 21:09:03 2009  RelProcTime: 2681
Thu Jul 16 21:09:03 2009  
Thu Jul 16 21:09:03 2009  commencing linear algebra
Thu Jul 16 21:09:08 2009  read 2904548 cycles
Thu Jul 16 21:09:15 2009  cycles contain 8808029 unique relations
Thu Jul 16 21:12:59 2009  read 8808029 relations
Thu Jul 16 21:13:19 2009  using 20 quadratic characters above 536869788
Thu Jul 16 21:14:06 2009  building initial matrix
Thu Jul 16 21:18:40 2009  memory use: 1022.6 MB
Thu Jul 16 21:18:52 2009  read 2904548 cycles
Thu Jul 16 21:20:09 2009  matrix is 2903959 x 2904548 (820.7 MB) with weight 259265005 (89.26/col)
Thu Jul 16 21:20:09 2009  sparse part has weight 194797795 (67.07/col)
Thu Jul 16 21:21:56 2009  filtering completed in 3 passes
Thu Jul 16 21:21:57 2009  matrix is 2888026 x 2888226 (818.2 MB) with weight 258365301 (89.45/col)
Thu Jul 16 21:21:57 2009  sparse part has weight 194268239 (67.26/col)
Thu Jul 16 21:22:23 2009  read 2888226 cycles
Thu Jul 16 21:40:33 2009  matrix is 2888026 x 2888226 (818.2 MB) with weight 258365301 (89.45/col)
Thu Jul 16 21:40:33 2009  sparse part has weight 194268239 (67.26/col)
Thu Jul 16 21:40:33 2009  saving the first 48 matrix rows for later
Thu Jul 16 21:40:35 2009  matrix is 2887978 x 2888226 (778.5 MB) with weight 204903337 (70.94/col)
Thu Jul 16 21:40:35 2009  sparse part has weight 186738649 (64.66/col)
Thu Jul 16 21:40:35 2009  matrix includes 64 packed rows
Thu Jul 16 21:40:35 2009  using block size 65536 for processor cache size 6144 kB
Thu Jul 16 21:41:03 2009  commencing Lanczos iteration (4 threads)
Thu Jul 16 21:41:03 2009  memory use: 859.7 MB
Fri Jul 17 16:38:12 2009  lanczos halted after 45672 iterations (dim = 2887977)
Fri Jul 17 16:38:34 2009  recovered 37 nontrivial dependencies
Fri Jul 17 16:38:42 2009  BLanczosTime: 70179
Fri Jul 17 16:38:42 2009  
Fri Jul 17 16:38:42 2009  commencing square root phase
Fri Jul 17 16:38:42 2009  reading relations for dependency 1
Fri Jul 17 16:39:10 2009  read 1444749 cycles
Fri Jul 17 16:39:13 2009  cycles contain 5349769 unique relations
Fri Jul 17 16:45:39 2009  read 5349769 relations
Fri Jul 17 16:46:16 2009  multiplying 4394854 relations
Fri Jul 17 16:52:56 2009  multiply complete, coefficients have about 124.55 million bits
Fri Jul 17 16:52:57 2009  initial square root is modulo 870936721
Fri Jul 17 17:05:43 2009  reading relations for dependency 2
Fri Jul 17 17:05:44 2009  read 1443452 cycles
Fri Jul 17 17:05:48 2009  cycles contain 5351642 unique relations
Fri Jul 17 17:11:20 2009  read 5351642 relations
Fri Jul 17 17:11:57 2009  multiplying 4399136 relations
Fri Jul 17 17:18:46 2009  multiply complete, coefficients have about 124.68 million bits
Fri Jul 17 17:18:47 2009  initial square root is modulo 889146281
Fri Jul 17 17:31:55 2009  reading relations for dependency 3
Fri Jul 17 17:31:56 2009  read 1442841 cycles
Fri Jul 17 17:32:00 2009  cycles contain 5342987 unique relations
Fri Jul 17 17:36:56 2009  read 5342987 relations
Fri Jul 17 17:37:31 2009  multiplying 4391770 relations
Fri Jul 17 17:44:00 2009  multiply complete, coefficients have about 124.47 million bits
Fri Jul 17 17:44:01 2009  initial square root is modulo 858842561
Fri Jul 17 17:57:08 2009  sqrtTime: 4706
Fri Jul 17 17:57:08 2009  prp60 factor: 591752848190830505194723691088958573025065122850764427487837
Fri Jul 17 17:57:08 2009  prp144 factor: 350496677863934757609414005722989412369536157605989693540146711579200859237238102599130471318852834601704462309602498012951936078401332556541157
Fri Jul 17 17:57:08 2009  elapsed time 21:40:59

Jul 23, 2009

By Robert Backstrom / GGNFS, Msieve / Jul 23, 2009

(43·10¹⁸²-61)/9 = 4(7)₁₈₁1_<183> = 3 · 2089 · C179

C179 = P88 · P92

P88 = 2548035129424789240102727461554777927306120058219282754067737790435073236169501864294189_<88>

P92 = 29919948397719090871041566799694898064009331023404415989596038975250131952057312120806299317_<92>

Number: n
N=76237079587965179157137031718171019272024537701895289257663599453929755509458716734925447227984327074800985763168625782316543446270588443877098735882843111182029324681311277768913
  ( 179 digits)
SNFS difficulty: 184 digits.
Divisors found:

Thu Jul 23 08:02:02 2009  prp88 factor: 2548035129424789240102727461554777927306120058219282754067737790435073236169501864294189
Thu Jul 23 08:02:02 2009  prp92 factor: 29919948397719090871041566799694898064009331023404415989596038975250131952057312120806299317
Thu Jul 23 08:02:02 2009  elapsed time 03:04:57 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 225.40 hours.
Scaled time: 571.17 units (timescale=2.534).
Factorization parameters were as follows:
name: KA_4_7_181_1
n: 76237079587965179157137031718171019272024537701895289257663599453929755509458716734925447227984327074800985763168625782316543446270588443877098735882843111182029324681311277768913
m: 2000000000000000000000000000000000000
deg: 5
c5: 1075
c0: -488
skew: 0.85
type: snfs
lss: 1
rlim: 8400000
alim: 8400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4200000, 8000023)
Primes: RFBsize:564877, AFBsize:563787, largePrimes:21426695 encountered
Relations: rels:21796035, finalFF:1216407
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2437177 hash collisions in 23571532 relations
Msieve: matrix is 1477220 x 1477468 (396.0 MB)

Total sieving time: 224.66 hours.
Total relation processing time: 0.74 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,184,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,56,56,2.5,2.5,100000
total time: 225.40 hours.
 --------- CPU info (if available) ----------

Jul 22, 2009 (2nd)

By Dmitry Domanov / GGNFS/msieve 1.42 / Jul 22, 2009

2·10¹⁹³+9 = 2(0)₁₉₂9_<194> = 41 · 200183 · 5328527 · 1518763338461_<13> · 711262813661921_<15> · 8504621858298220990261_<22> · C131

C131 = P56 · P76

P56 = 13056246011809721884007205309537122134790655929126011321_<56>

P76 = 3812573573319637471194915345352510153300362083742249817651638622768023693649_<76>

Wed Jul 22 14:19:03 2009  Msieve v. 1.42
Wed Jul 22 14:19:03 2009  random seeds: a5bf0718 1df83478
Wed Jul 22 14:19:03 2009  factoring 49777898511385657017959200641343160463020017114075893159149402568741104300447500577409539628482154712527537552631680837117009800329 (131 digits)
Wed Jul 22 14:19:04 2009  searching for 15-digit factors
Wed Jul 22 14:19:06 2009  commencing number field sieve (131-digit input)
Wed Jul 22 14:19:06 2009  R0: -17132883862694021714256889
Wed Jul 22 14:19:06 2009  R1:  279017036996591
Wed Jul 22 14:19:06 2009  A0:  2507317928392803584490096701088
Wed Jul 22 14:19:06 2009  A1:  179085986367648223641880884
Wed Jul 22 14:19:06 2009  A2:  1315353739759960626176
Wed Jul 22 14:19:06 2009  A3: -4013501703489901
Wed Jul 22 14:19:06 2009  A4: -16033052242
Wed Jul 22 14:19:06 2009  A5:  33720
Wed Jul 22 14:19:06 2009  skew 253679.99, size 1.756545e-012, alpha -6.062530, combined = 8.425983e-011
Wed Jul 22 14:19:06 2009  
Wed Jul 22 14:19:06 2009  commencing relation filtering
Wed Jul 22 14:19:06 2009  estimated available RAM is 3232.4 MB
Wed Jul 22 14:19:06 2009  commencing duplicate removal, pass 1
Wed Jul 22 14:22:45 2009  found 3646224 hash collisions in 24883919 relations
Wed Jul 22 14:23:33 2009  added 120024 free relations
Wed Jul 22 14:23:33 2009  commencing duplicate removal, pass 2
Wed Jul 22 14:24:31 2009  found 3092029 duplicates and 21911914 unique relations
Wed Jul 22 14:24:31 2009  memory use: 106.6 MB
Wed Jul 22 14:24:31 2009  reading ideals above 11993088
Wed Jul 22 14:24:35 2009  commencing singleton removal, initial pass
Wed Jul 22 14:28:26 2009  memory use: 298.4 MB
Wed Jul 22 14:28:26 2009  reading all ideals from disk
Wed Jul 22 14:28:26 2009  memory use: 370.8 MB
Wed Jul 22 14:28:26 2009  commencing in-memory singleton removal
Wed Jul 22 14:28:29 2009  begin with 21911914 relations and 19550344 unique ideals
Wed Jul 22 14:28:57 2009  reduce to 11773877 relations and 8107541 ideals in 16 passes
Wed Jul 22 14:28:57 2009  max relations containing the same ideal: 44
Wed Jul 22 14:28:59 2009  reading ideals above 720000
Wed Jul 22 14:28:59 2009  commencing singleton removal, initial pass
Wed Jul 22 14:31:26 2009  memory use: 149.2 MB
Wed Jul 22 14:31:26 2009  reading all ideals from disk
Wed Jul 22 14:31:26 2009  memory use: 354.5 MB
Wed Jul 22 14:31:26 2009  commencing in-memory singleton removal
Wed Jul 22 14:31:29 2009  begin with 11774472 relations and 9569468 unique ideals
Wed Jul 22 14:31:47 2009  reduce to 11771578 relations and 9563831 ideals in 7 passes
Wed Jul 22 14:31:47 2009  max relations containing the same ideal: 191
Wed Jul 22 14:31:59 2009  removing 2015830 relations and 1615830 ideals in 400000 cliques
Wed Jul 22 14:32:00 2009  commencing in-memory singleton removal
Wed Jul 22 14:32:03 2009  begin with 9755748 relations and 9563831 unique ideals
Wed Jul 22 14:32:20 2009  reduce to 9572181 relations and 7757315 ideals in 8 passes
Wed Jul 22 14:32:20 2009  max relations containing the same ideal: 154
Wed Jul 22 14:32:30 2009  removing 1521692 relations and 1121692 ideals in 400000 cliques
Wed Jul 22 14:32:30 2009  commencing in-memory singleton removal
Wed Jul 22 14:32:32 2009  begin with 8050489 relations and 7757315 unique ideals
Wed Jul 22 14:32:44 2009  reduce to 7907442 relations and 6487093 ideals in 7 passes
Wed Jul 22 14:32:44 2009  max relations containing the same ideal: 131
Wed Jul 22 14:32:53 2009  removing 1369689 relations and 969689 ideals in 400000 cliques
Wed Jul 22 14:32:53 2009  commencing in-memory singleton removal
Wed Jul 22 14:32:55 2009  begin with 6537753 relations and 6487093 unique ideals
Wed Jul 22 14:33:04 2009  reduce to 6397323 relations and 5370834 ideals in 7 passes
Wed Jul 22 14:33:04 2009  max relations containing the same ideal: 111
Wed Jul 22 14:33:11 2009  removing 1286700 relations and 886700 ideals in 400000 cliques
Wed Jul 22 14:33:12 2009  commencing in-memory singleton removal
Wed Jul 22 14:33:13 2009  begin with 5110623 relations and 5370834 unique ideals
Wed Jul 22 14:33:20 2009  reduce to 4952018 relations and 4316640 ideals in 7 passes
Wed Jul 22 14:33:20 2009  max relations containing the same ideal: 89
Wed Jul 22 14:33:25 2009  removing 1214883 relations and 814883 ideals in 400000 cliques
Wed Jul 22 14:33:26 2009  commencing in-memory singleton removal
Wed Jul 22 14:33:26 2009  begin with 3737135 relations and 4316640 unique ideals
Wed Jul 22 14:33:32 2009  reduce to 3544361 relations and 3295202 ideals in 8 passes
Wed Jul 22 14:33:32 2009  max relations containing the same ideal: 72
Wed Jul 22 14:33:36 2009  removing 466668 relations and 352093 ideals in 114575 cliques
Wed Jul 22 14:33:36 2009  commencing in-memory singleton removal
Wed Jul 22 14:33:37 2009  begin with 3077693 relations and 3295202 unique ideals
Wed Jul 22 14:33:40 2009  reduce to 3041291 relations and 2905657 ideals in 6 passes
Wed Jul 22 14:33:40 2009  max relations containing the same ideal: 68
Wed Jul 22 14:33:44 2009  relations with 0 large ideals: 471
Wed Jul 22 14:33:44 2009  relations with 1 large ideals: 2091
Wed Jul 22 14:33:44 2009  relations with 2 large ideals: 28692
Wed Jul 22 14:33:44 2009  relations with 3 large ideals: 163521
Wed Jul 22 14:33:44 2009  relations with 4 large ideals: 481707
Wed Jul 22 14:33:44 2009  relations with 5 large ideals: 813905
Wed Jul 22 14:33:44 2009  relations with 6 large ideals: 827216
Wed Jul 22 14:33:44 2009  relations with 7+ large ideals: 723688
Wed Jul 22 14:33:44 2009  commencing 2-way merge
Wed Jul 22 14:33:48 2009  reduce to 2028230 relation sets and 1892596 unique ideals
Wed Jul 22 14:33:48 2009  commencing full merge
Wed Jul 22 14:34:37 2009  memory use: 196.2 MB
Wed Jul 22 14:34:38 2009  found 1047881 cycles, need 1028796
Wed Jul 22 14:34:38 2009  weight of 1028796 cycles is about 72288141 (70.26/cycle)
Wed Jul 22 14:34:38 2009  distribution of cycle lengths:
Wed Jul 22 14:34:38 2009  1 relations: 83203
Wed Jul 22 14:34:38 2009  2 relations: 111470
Wed Jul 22 14:34:38 2009  3 relations: 123757
Wed Jul 22 14:34:38 2009  4 relations: 122068
Wed Jul 22 14:34:38 2009  5 relations: 113877
Wed Jul 22 14:34:38 2009  6 relations: 101487
Wed Jul 22 14:34:38 2009  7 relations: 86569
Wed Jul 22 14:34:38 2009  8 relations: 71513
Wed Jul 22 14:34:38 2009  9 relations: 57361
Wed Jul 22 14:34:38 2009  10+ relations: 157491
Wed Jul 22 14:34:38 2009  heaviest cycle: 18 relations
Wed Jul 22 14:34:39 2009  commencing cycle optimization
Wed Jul 22 14:34:41 2009  start with 5912490 relations
Wed Jul 22 14:34:56 2009  pruned 179772 relations
Wed Jul 22 14:34:56 2009  memory use: 149.2 MB
Wed Jul 22 14:34:56 2009  distribution of cycle lengths:
Wed Jul 22 14:34:56 2009  1 relations: 83203
Wed Jul 22 14:34:56 2009  2 relations: 114003
Wed Jul 22 14:34:56 2009  3 relations: 128763
Wed Jul 22 14:34:56 2009  4 relations: 125973
Wed Jul 22 14:34:56 2009  5 relations: 117959
Wed Jul 22 14:34:56 2009  6 relations: 104371
Wed Jul 22 14:34:56 2009  7 relations: 88089
Wed Jul 22 14:34:56 2009  8 relations: 71735
Wed Jul 22 14:34:56 2009  9 relations: 56564
Wed Jul 22 14:34:56 2009  10+ relations: 138136
Wed Jul 22 14:34:56 2009  heaviest cycle: 18 relations
Wed Jul 22 14:35:00 2009  RelProcTime: 954
Wed Jul 22 14:35:00 2009  
Wed Jul 22 14:35:00 2009  commencing linear algebra
Wed Jul 22 14:35:00 2009  read 1028796 cycles
Wed Jul 22 14:35:02 2009  cycles contain 2962793 unique relations
Wed Jul 22 14:36:51 2009  read 2962793 relations
Wed Jul 22 14:36:57 2009  using 20 quadratic characters above 268433820
Wed Jul 22 14:37:12 2009  building initial matrix
Wed Jul 22 14:37:56 2009  memory use: 347.5 MB
Wed Jul 22 14:37:58 2009  read 1028796 cycles
Wed Jul 22 14:38:49 2009  matrix is 1028619 x 1028796 (291.5 MB) with weight 97512281 (94.78/col)
Wed Jul 22 14:38:49 2009  sparse part has weight 69225192 (67.29/col)
Wed Jul 22 14:39:04 2009  filtering completed in 2 passes
Wed Jul 22 14:39:04 2009  matrix is 1028282 x 1028459 (291.5 MB) with weight 97497904 (94.80/col)
Wed Jul 22 14:39:04 2009  sparse part has weight 69220272 (67.30/col)
Wed Jul 22 14:39:09 2009  read 1028459 cycles
Wed Jul 22 14:42:03 2009  matrix is 1028282 x 1028459 (291.5 MB) with weight 97497904 (94.80/col)
Wed Jul 22 14:42:03 2009  sparse part has weight 69220272 (67.30/col)
Wed Jul 22 14:42:04 2009  saving the first 48 matrix rows for later
Wed Jul 22 14:42:04 2009  matrix is 1028234 x 1028459 (282.0 MB) with weight 77197089 (75.06/col)
Wed Jul 22 14:42:04 2009  sparse part has weight 67760950 (65.89/col)
Wed Jul 22 14:42:04 2009  matrix includes 64 packed rows
Wed Jul 22 14:42:04 2009  using block size 65536 for processor cache size 6144 kB
Wed Jul 22 14:42:12 2009  commencing Lanczos iteration (4 threads)
Wed Jul 22 14:42:12 2009  memory use: 312.2 MB
Wed Jul 22 16:23:16 2009  lanczos halted after 16260 iterations (dim = 1028232)
Wed Jul 22 16:23:19 2009  recovered 28 nontrivial dependencies
Wed Jul 22 16:23:20 2009  BLanczosTime: 6500
Wed Jul 22 16:23:20 2009  
Wed Jul 22 16:23:20 2009  commencing square root phase
Wed Jul 22 16:23:20 2009  reading relations for dependency 1
Wed Jul 22 16:23:20 2009  read 514616 cycles
Wed Jul 22 16:23:22 2009  cycles contain 1855521 unique relations
Wed Jul 22 16:25:56 2009  read 1855521 relations
Wed Jul 22 16:26:07 2009  multiplying 1482034 relations
Wed Jul 22 16:29:41 2009  multiply complete, coefficients have about 68.61 million bits
Wed Jul 22 16:29:44 2009  initial square root is modulo 84317
Wed Jul 22 16:37:05 2009  reading relations for dependency 2
Wed Jul 22 16:37:06 2009  read 513871 cycles
Wed Jul 22 16:37:07 2009  cycles contain 1853804 unique relations
Wed Jul 22 16:40:23 2009  read 1853804 relations
Wed Jul 22 16:40:36 2009  multiplying 1480638 relations
Wed Jul 22 16:44:27 2009  multiply complete, coefficients have about 68.54 million bits
Wed Jul 22 16:44:29 2009  initial square root is modulo 83207
Wed Jul 22 16:52:48 2009  sqrtTime: 1768
Wed Jul 22 16:52:48 2009  prp56 factor: 13056246011809721884007205309537122134790655929126011321
Wed Jul 22 16:52:48 2009  prp76 factor: 3812573573319637471194915345352510153300362083742249817651638622768023693649
Wed Jul 22 16:52:48 2009  elapsed time 02:33:45

Jul 22, 2009

By Sinkiti Sibata / Msieve / Jul 22, 2009

(4·10¹⁷⁰-13)/9 = (4)₁₆₉3_<170> = 43 · 49843993 · 2475812821_<10> · 125520143958780691_<18> · C134

C134 = P66 · P69

P66 = 134952326025103652801521248618834398257383508096149729562130206993_<66>

P69 = 494452513887969866030765721406804005551992171945654486556735975996359_<69>

Number: 44443_170
N=66727516858141401074243180482446319845168157241778593460594338756127146244380514569050496334811780938019385938969552861994164084338487
  ( 134 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=134952326025103652801521248618834398257383508096149729562130206993 (pp66)
 r2=494452513887969866030765721406804005551992171945654486556735975996359 (pp69)
Version: Msieve-1.40
Total time: 62.21 hours.
Scaled time: 159.50 units (timescale=2.564).
Factorization parameters were as follows:
name: 44443_170
n: 66727516858141401074243180482446319845168157241778593460594338756127146244380514569050496334811780938019385938969552861994164084338487
m: 10000000000000000000000000000000000
deg: 5
c5: 4
c0: -13
skew: 1.27
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 4950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 959702 x 959950
Total sieving time: 59.84 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 2.12 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 62.21 hours.
 --------- CPU info (if available) ----------

Jul 21, 2009

By Jo Yeong Uk / GMP-ECM / Jul 21, 2009

(43·10¹⁶⁸-61)/9 = 4(7)₁₆₇1_<169> = 22697 · 847871 · 280048951928996363825795273_<27> · C132

C132 = P38 · P95

P38 = 16901046374539237625557269338688649493_<38>

P95 = 52454187242637751875089575327021264362767456784230240263930131709150203218780655157553340044497_<95>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 886530651126585105903250758298570538352456873152422573299364523119106894143736122032708526032962960174606258358367676475085456490021 (132 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2321597130
Step 1 took 9853ms
Step 2 took 5141ms
********** Factor found in step 2: 16901046374539237625557269338688649493
Found probable prime factor of 38 digits: 16901046374539237625557269338688649493
Probable prime cofactor 52454187242637751875089575327021264362767456784230240263930131709150203218780655157553340044497 has 95 digits

(14·10¹⁷⁰-11)/3 = 4(6)₁₆₉3_<171> = 17 · 11317 · 526732469 · 441078895079741_<15> · C143

C143 = P35 · P108

P35 = 35579941592008772423172650690055857_<35>

P108 = 293437047888738978141986455944132593215288834033455785264598594536814464364859742626924248414572744526052939_<108>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 10440473024812813910784256169406112481945315164487396088488010879249685174451988965209380312566607654421939858109611857042610749685869649013723 (143 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=7299964278
Step 1 took 12030ms
Step 2 took 5520ms
********** Factor found in step 2: 35579941592008772423172650690055857
Found probable prime factor of 35 digits: 35579941592008772423172650690055857
Probable prime cofactor 293437047888738978141986455944132593215288834033455785264598594536814464364859742626924248414572744526052939 has 108 digits

Jul 20, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Jul 20, 2009

(43·10¹⁸²+11)/9 = 4(7)₁₈₁9_<183> = 97 · 353 · C179

C179 = P50 · P129

P50 = 14420577088818323505616863399192301373953570591687_<50>

P129 = 967602241982232345120213379837347731892522485447083941533704978769489168236118988664746004583450464381451226448194873652427696437_<129>

Number: n
N=13953382721818223117834694599391892111146805811097157728389292887993276416511719218999964305300013953382721818223117834694599391892111146805811097157728389292887993276416511719219
  ( 179 digits)
SNFS difficulty: 184 digits.
Divisors found:

Mon Jul 20 15:34:20 2009  prp50 factor: 14420577088818323505616863399192301373953570591687
Mon Jul 20 15:34:20 2009  prp129 factor: 967602241982232345120213379837347731892522485447083941533704978769489168236118988664746004583450464381451226448194873652427696437
Mon Jul 20 15:34:20 2009  elapsed time 02:54:11 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 193.09 hours.
Scaled time: 501.06 units (timescale=2.595).
Factorization parameters were as follows:
name: KA_4_7_181_9
n: 13953382721818223117834694599391892111146805811097157728389292887993276416511719218999964305300013953382721818223117834694599391892111146805811097157728389292887993276416511719219
m: 2000000000000000000000000000000000000
deg: 5
c5: 1075
c0: 88
skew: 0.61
type: snfs
lss: 1
rlim: 8400000
alim: 8400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4200000, 7800571)
Primes: RFBsize:564877, AFBsize:565987, largePrimes:20079391 encountered
Relations: rels:20295618, finalFF:975193
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2163898 hash collisions in 21874822 relations
Msieve: matrix is 1411695 x 1411943 (380.5 MB)

Total sieving time: 192.43 hours.
Total relation processing time: 0.66 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,184,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,56,56,2.4,2.4,100000
total time: 193.09 hours.
 --------- CPU info (if available) ----------

Jul 20, 2009 (2nd)

By JPascoa / ggnfs, Msieve / Jul 20, 2009

(58·10¹⁶³+23)/9 = 6(4)₁₆₂7_<164> = 89 · 1361722388871787_<16> · 4310597647035065104719854951_<28> · C120

C120 = P52 · P68

P52 = 1394721122046343598898954744537561461564601370683041_<52>

P68 = 88446781495499968050670791016168541995795404733544043226877321557619_<68>

Number: 64447_163
N=123358594328791495556126661691507931865080054364763831788218995633927970659697113723897937644655278724450733932067639379
  ( 120 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=1394721122046343598898954744537561461564601370683041 (pp52)
 r2=88446781495499968050670791016168541995795404733544043226877321557619 (pp68)
Version: Msieve-1.40
Total time: 122.50 hours.
Scaled time: 109.52 units (timescale=0.894).
Factorization parameters were as follows:
n: 123358594328791495556126661691507931865080054364763831788218995633927970659697113723897937644655278724450733932067639379
m: 500000000000000000000000000000000
deg: 5
c5: 464
c0: 575
skew: 1.04
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 783565 x 783813
Total sieving time: 116.92 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 4.71 hours.
Time per square root: 0.65 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 122.50 hours.
 --------- CPU info (if available) ----------

Jul 20, 2009

Msieve version 1.42 now available

Jul 19, 2009 (2nd)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Jul 19, 2009

(52·10¹⁶⁹+11)/9 = 5(7)₁₆₈9_<170> = 4898850088247_<13> · 439584041643524138030023_<24> · C134

C134 = P37 · P97

P37 = 8664505744431290401102450208330703623_<37>

P97 = 3096570505500625044991977990181851031592172948921210009806769010994433962313317765726822407471733_<97>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 26830252932946670433282633304656708361984848210275832396303656863160017951525807757982726879368734099148688994835598198398948373188659 (134 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3033120199
Step 1 took 4243ms
Step 2 took 4227ms
********** Factor found in step 2: 8664505744431290401102450208330703623
Found probable prime factor of 37 digits: 8664505744431290401102450208330703623
Probable prime cofactor 3096570505500625044991977990181851031592172948921210009806769010994433962313317765726822407471733 has 97 digits

(58·10¹⁶⁷+23)/9 = 6(4)₁₆₆7_<168> = 383 · 81817 · 116411 · 2539015319297239760208862106037195769_<37> · C119

C119 = P45 · P75

P45 = 374955885683995304806408659651797737916881109_<45>

P75 = 185568237447150266710225357815093455211539272721334490104275510776087852567_<75>

Number: 64447_167
N=69579902826814172117370151834844693730354578571165992862664790776297462544881688493563687017875009631281121822059456803
  ( 119 digits)
Divisors found:
 r1=374955885683995304806408659651797737916881109
 r2=185568237447150266710225357815093455211539272721334490104275510776087852567
Version: 
Total time: 26.73 hours.
Scaled time: 63.92 units (timescale=2.391).
Factorization parameters were as follows:
name: 64447_167
n: 69579902826814172117370151834844693730354578571165992862664790776297462544881688493563687017875009631281121822059456803
skew: 47349.17
# norm 2.24e+16
c5: 97680
c4: -13680015272
c3: -938576535914888
c2: 23575289591187172209
c1: 621356567553877682728762
c0: -9041730036885776114944853304
# alpha -5.82
Y1: 8824749378397
Y0: -58957282053378243449603
# Murphy_E 3.17e-10
# M 47344066638380041334839352664793755654023650330881408512311320265554362175946657539853017303858866715609793853414241683
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2000000, 4000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9815119
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 649556 x 649804
Polynomial selection time: 2.28 hours.
Total sieving time: 22.39 hours.
Total relation processing time: 0.92 hours.
Matrix solve time: 0.86 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,52,52,2.4,2.4,100000
total time: 26.73 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794)
Calibrating delay using timer specific routine.. 5556.53 BogoMIPS (lpj=2778268)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 19, 2009

By Andreas Tete / Msieve v.1.42, GGNFS / Jul 19, 2009

(58·10¹⁷⁶+23)/9 = 6(4)₁₇₅7_<177> = 8929 · 495108312917_<12> · 11709965533731842879_<20> · 584523038568799821949_<21> · C122

C122 = P59 · P63

P59 = 45945311893089576120617083406295313405032488551893964974131_<59>

P63 = 463536555085071903813929644352373972274237777973789300237822779_<63>

Sat Jul 18 19:00:08 2009  Msieve v. 1.42
Sat Jul 18 19:00:08 2009  random seeds: 9b67fae0 8958af49
Sat Jul 18 19:00:08 2009  factoring 21297331597231925575431021475147344519208861186265435531663300064057696819420851677903908845421164785867653061776497530049 (122 digits)
Sat Jul 18 19:00:09 2009  searching for 15-digit factors
Sat Jul 18 19:00:11 2009  commencing number field sieve (122-digit input)
Sat Jul 18 19:00:11 2009  R0: -267740348395822115091009
Sat Jul 18 19:00:11 2009  R1:  9996088625369
Sat Jul 18 19:00:11 2009  A0: -12649253990942022464562560360
Sat Jul 18 19:00:11 2009  A1: -29032392364374356043724
Sat Jul 18 19:00:11 2009  A2:  71278176830714457495
Sat Jul 18 19:00:11 2009  A3:  1599979649307247
Sat Jul 18 19:00:11 2009  A4: -14210029177
Sat Jul 18 19:00:11 2009  A5:  15480
Sat Jul 18 19:00:11 2009  skew 70537.14, size 1.157191e-011, alpha -5.675436, combined = 2.303915e-010
Sat Jul 18 19:00:12 2009  
Sat Jul 18 19:00:12 2009  commencing relation filtering
Sat Jul 18 19:00:12 2009  estimated available RAM is 3069.5 MB
Sat Jul 18 19:00:13 2009  commencing duplicate removal, pass 1
Sat Jul 18 19:01:46 2009  found 1157953 hash collisions in 8680732 relations
Sat Jul 18 19:02:09 2009  added 58990 free relations
Sat Jul 18 19:02:09 2009  commencing duplicate removal, pass 2
Sat Jul 18 19:02:23 2009  found 1051971 duplicates and 7687750 unique relations
Sat Jul 18 19:02:23 2009  memory use: 49.3 MB
Sat Jul 18 19:02:24 2009  reading ideals above 100000
Sat Jul 18 19:02:24 2009  commencing singleton removal, initial pass
Sat Jul 18 19:04:18 2009  memory use: 149.2 MB
Sat Jul 18 19:04:18 2009  reading all ideals from disk
Sat Jul 18 19:04:24 2009  memory use: 274.8 MB
Sat Jul 18 19:04:26 2009  keeping 8454285 ideals with weight <= 200, target excess is 42010
Sat Jul 18 19:04:28 2009  commencing in-memory singleton removal
Sat Jul 18 19:04:30 2009  begin with 7687750 relations and 8454285 unique ideals
Sat Jul 18 19:04:42 2009  reduce to 2823891 relations and 2738944 ideals in 17 passes
Sat Jul 18 19:04:42 2009  max relations containing the same ideal: 99
Sat Jul 18 19:04:44 2009  removing 194198 relations and 176090 ideals in 18108 cliques
Sat Jul 18 19:04:44 2009  commencing in-memory singleton removal
Sat Jul 18 19:04:45 2009  begin with 2629693 relations and 2738944 unique ideals
Sat Jul 18 19:04:50 2009  reduce to 2620563 relations and 2553639 ideals in 9 passes
Sat Jul 18 19:04:50 2009  max relations containing the same ideal: 92
Sat Jul 18 19:04:52 2009  removing 143450 relations and 125342 ideals in 18108 cliques
Sat Jul 18 19:04:52 2009  commencing in-memory singleton removal
Sat Jul 18 19:04:53 2009  begin with 2477113 relations and 2553639 unique ideals
Sat Jul 18 19:04:56 2009  reduce to 2471536 relations and 2422684 ideals in 7 passes
Sat Jul 18 19:04:56 2009  max relations containing the same ideal: 90
Sat Jul 18 19:04:59 2009  relations with 0 large ideals: 128
Sat Jul 18 19:04:59 2009  relations with 1 large ideals: 447
Sat Jul 18 19:04:59 2009  relations with 2 large ideals: 5310
Sat Jul 18 19:04:59 2009  relations with 3 large ideals: 38239
Sat Jul 18 19:04:59 2009  relations with 4 large ideals: 163031
Sat Jul 18 19:04:59 2009  relations with 5 large ideals: 422649
Sat Jul 18 19:04:59 2009  relations with 6 large ideals: 675623
Sat Jul 18 19:04:59 2009  relations with 7+ large ideals: 1166109
Sat Jul 18 19:04:59 2009  commencing 2-way merge
Sat Jul 18 19:05:02 2009  reduce to 1466516 relation sets and 1417664 unique ideals
Sat Jul 18 19:05:02 2009  commencing full merge
Sat Jul 18 19:05:39 2009  memory use: 153.5 MB
Sat Jul 18 19:05:40 2009  found 749622 cycles, need 743864
Sat Jul 18 19:05:40 2009  weight of 743864 cycles is about 52090418 (70.03/cycle)
Sat Jul 18 19:05:40 2009  distribution of cycle lengths:
Sat Jul 18 19:05:40 2009  1 relations: 94279
Sat Jul 18 19:05:40 2009  2 relations: 90634
Sat Jul 18 19:05:40 2009  3 relations: 87859
Sat Jul 18 19:05:40 2009  4 relations: 78025
Sat Jul 18 19:05:40 2009  5 relations: 69180
Sat Jul 18 19:05:40 2009  6 relations: 57697
Sat Jul 18 19:05:40 2009  7 relations: 49517
Sat Jul 18 19:05:40 2009  8 relations: 41441
Sat Jul 18 19:05:40 2009  9 relations: 34605
Sat Jul 18 19:05:40 2009  10+ relations: 140627
Sat Jul 18 19:05:40 2009  heaviest cycle: 24 relations
Sat Jul 18 19:05:40 2009  commencing cycle optimization
Sat Jul 18 19:05:42 2009  start with 4383951 relations
Sat Jul 18 19:05:54 2009  pruned 102411 relations
Sat Jul 18 19:05:54 2009  memory use: 115.6 MB
Sat Jul 18 19:05:54 2009  distribution of cycle lengths:
Sat Jul 18 19:05:54 2009  1 relations: 94279
Sat Jul 18 19:05:54 2009  2 relations: 92647
Sat Jul 18 19:05:54 2009  3 relations: 90891
Sat Jul 18 19:05:54 2009  4 relations: 79701
Sat Jul 18 19:05:54 2009  5 relations: 70495
Sat Jul 18 19:05:54 2009  6 relations: 58154
Sat Jul 18 19:05:54 2009  7 relations: 49857
Sat Jul 18 19:05:54 2009  8 relations: 41116
Sat Jul 18 19:05:54 2009  9 relations: 34380
Sat Jul 18 19:05:54 2009  10+ relations: 132344
Sat Jul 18 19:05:54 2009  heaviest cycle: 24 relations
Sat Jul 18 19:05:55 2009  RelProcTime: 343
Sat Jul 18 19:05:55 2009  
Sat Jul 18 19:05:55 2009  commencing linear algebra
Sat Jul 18 19:05:55 2009  read 743864 cycles
Sat Jul 18 19:05:57 2009  cycles contain 2425496 unique relations
Sat Jul 18 19:06:36 2009  read 2425496 relations
Sat Jul 18 19:06:41 2009  using 20 quadratic characters above 134216420
Sat Jul 18 19:06:56 2009  building initial matrix
Sat Jul 18 19:07:34 2009  memory use: 284.7 MB
Sat Jul 18 19:07:35 2009  read 743864 cycles
Sat Jul 18 19:07:36 2009  matrix is 743687 x 743864 (213.6 MB) with weight 71084008 (95.56/col)
Sat Jul 18 19:07:36 2009  sparse part has weight 50032887 (67.26/col)
Sat Jul 18 19:07:46 2009  filtering completed in 2 passes
Sat Jul 18 19:07:46 2009  matrix is 743088 x 743265 (213.5 MB) with weight 71058320 (95.60/col)
Sat Jul 18 19:07:46 2009  sparse part has weight 50025604 (67.31/col)
Sat Jul 18 19:07:49 2009  read 743265 cycles
Sat Jul 18 19:07:51 2009  matrix is 743088 x 743265 (213.5 MB) with weight 71058320 (95.60/col)
Sat Jul 18 19:07:51 2009  sparse part has weight 50025604 (67.31/col)
Sat Jul 18 19:07:51 2009  saving the first 48 matrix rows for later
Sat Jul 18 19:07:51 2009  matrix is 743040 x 743265 (203.9 MB) with weight 56099385 (75.48/col)
Sat Jul 18 19:07:51 2009  sparse part has weight 48981570 (65.90/col)
Sat Jul 18 19:07:51 2009  matrix includes 64 packed rows
Sat Jul 18 19:07:51 2009  using block size 65536 for processor cache size 3072 kB
Sat Jul 18 19:07:57 2009  commencing Lanczos iteration
Sat Jul 18 19:07:57 2009  memory use: 207.0 MB
Sat Jul 18 20:29:59 2009  lanczos halted after 11749 iterations (dim = 743039)
Sat Jul 18 20:30:01 2009  recovered 33 nontrivial dependencies
Sat Jul 18 20:30:02 2009  BLanczosTime: 5047
Sat Jul 18 20:30:02 2009  
Sat Jul 18 20:30:02 2009  commencing square root phase
Sat Jul 18 20:30:02 2009  reading relations for dependency 1
Sat Jul 18 20:30:02 2009  read 371133 cycles
Sat Jul 18 20:30:03 2009  cycles contain 1485520 unique relations
Sat Jul 18 20:30:39 2009  read 1485520 relations
Sat Jul 18 20:30:48 2009  multiplying 1210228 relations
Sat Jul 18 20:34:22 2009  multiply complete, coefficients have about 55.54 million bits
Sat Jul 18 20:34:24 2009  initial square root is modulo 94007273
Sat Jul 18 20:40:15 2009  reading relations for dependency 2
Sat Jul 18 20:40:15 2009  read 371938 cycles
Sat Jul 18 20:40:16 2009  cycles contain 1488775 unique relations
Sat Jul 18 20:40:51 2009  read 1488775 relations
Sat Jul 18 20:40:59 2009  multiplying 1213308 relations
Sat Jul 18 20:44:33 2009  multiply complete, coefficients have about 55.67 million bits
Sat Jul 18 20:44:36 2009  initial square root is modulo 98413577
Sat Jul 18 20:50:27 2009  reading relations for dependency 3
Sat Jul 18 20:50:28 2009  read 371787 cycles
Sat Jul 18 20:50:28 2009  cycles contain 1488232 unique relations
Sat Jul 18 20:51:02 2009  read 1488232 relations
Sat Jul 18 20:51:10 2009  multiplying 1212158 relations
Sat Jul 18 20:54:44 2009  multiply complete, coefficients have about 55.62 million bits
Sat Jul 18 20:54:47 2009  initial square root is modulo 96742643
Sat Jul 18 21:00:38 2009  reading relations for dependency 4
Sat Jul 18 21:00:38 2009  read 372619 cycles
Sat Jul 18 21:00:39 2009  cycles contain 1490002 unique relations
Sat Jul 18 21:01:12 2009  read 1490002 relations
Sat Jul 18 21:01:22 2009  multiplying 1214630 relations
Sat Jul 18 21:04:56 2009  multiply complete, coefficients have about 55.74 million bits
Sat Jul 18 21:04:58 2009  initial square root is modulo 100489853
Sat Jul 18 21:10:49 2009  reading relations for dependency 5
Sat Jul 18 21:10:49 2009  read 371616 cycles
Sat Jul 18 21:10:50 2009  cycles contain 1487843 unique relations
Sat Jul 18 21:11:23 2009  read 1487843 relations
Sat Jul 18 21:11:32 2009  multiplying 1212846 relations
Sat Jul 18 21:15:06 2009  multiply complete, coefficients have about 55.66 million bits
Sat Jul 18 21:15:09 2009  initial square root is modulo 97915031
Sat Jul 18 21:21:01 2009  reading relations for dependency 6
Sat Jul 18 21:21:01 2009  read 371752 cycles
Sat Jul 18 21:21:02 2009  cycles contain 1489453 unique relations
Sat Jul 18 21:21:37 2009  read 1489453 relations
Sat Jul 18 21:21:46 2009  multiplying 1214234 relations
Sat Jul 18 21:25:21 2009  multiply complete, coefficients have about 55.72 million bits
Sat Jul 18 21:25:23 2009  initial square root is modulo 99859171
Sat Jul 18 21:31:15 2009  sqrtTime: 3673
Sat Jul 18 21:31:15 2009  prp59 factor: 45945311893089576120617083406295313405032488551893964974131
Sat Jul 18 21:31:15 2009  prp63 factor: 463536555085071903813929644352373972274237777973789300237822779
Sat Jul 18 21:31:15 2009  elapsed time 02:31:07

Jul 18, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jul 18, 2009

(58·10¹⁶¹+23)/9 = 6(4)₁₆₀7_<162> = 41119327973436033475483754806134272837_<38> · C125

C125 = P50 · P75

P50 = 26871790039300526486196912904597959855554874021199_<50>

P75 = 583234060233196823479456446336892759281171709697223343472935319966425238269_<75>

Number: 64447_161
N=15672543210355221701053940350577676484197328922241828151784149179051334607839580596202241048609582134533477776622521732064531
  ( 125 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=26871790039300526486196912904597959855554874021199
 r2=583234060233196823479456446336892759281171709697223343472935319966425238269
Version: 
Total time: 20.09 hours.
Scaled time: 47.97 units (timescale=2.388).
Factorization parameters were as follows:
n: 15672543210355221701053940350577676484197328922241828151784149179051334607839580596202241048609582134533477776622521732064531
m: 100000000000000000000000000000000
deg: 5
c5: 580
c0: 23
skew: 0.52
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 3700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9704756
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 695279 x 695527
Total sieving time: 18.21 hours.
Total relation processing time: 0.80 hours.
Matrix solve time: 1.01 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 20.09 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794)
Calibrating delay using timer specific routine.. 5556.53 BogoMIPS (lpj=2778268)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

(58·10¹⁶²+23)/9 = 6(4)₁₆₁7_<163> = 3² · 24247 · 1079831 · 2020506749_<10> · C143

C143 = P42 · P101

P42 = 149341881640836290021255337570732276202949_<42>

P101 = 90633185966835800545817749240634207154524406954605664798680122666388901649995696515931063037625341319_<101>

Number: 64447_162
N=13535330531391096719446805778580505859562186778278308618604894946818978050168809172701900039808903911493436257192219298250447501692737439349731
  ( 143 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=149341881640836290021255337570732276202949
 r2=90633185966835800545817749240634207154524406954605664798680122666388901649995696515931063037625341319
Version: 
Total time: 26.23 hours.
Scaled time: 62.57 units (timescale=2.385).
Factorization parameters were as follows:
n: 13535330531391096719446805778580505859562186778278308618604894946818978050168809172701900039808903911493436257192219298250447501692737439349731
m: 200000000000000000000000000000000
deg: 5
c5: 725
c0: 92
skew: 0.66
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 4400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9867056
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 798231 x 798479
Total sieving time: 23.63 hours.
Total relation processing time: 1.06 hours.
Matrix solve time: 1.34 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 26.23 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794)
Calibrating delay using timer specific routine.. 5556.53 BogoMIPS (lpj=2778268)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 18, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Jul 18, 2009

(58·10¹⁶⁴+23)/9 = 6(4)₁₆₃7_<165> = 17 · 71 · 109 · 1811 · C157

C157 = P50 · P108

P50 = 11500057744747399273355108662919213155050608195831_<50>

P108 = 235197794368519156880312362442167554274367596081043998198046134333506670922483690675068444570466640194016809_<108>

Number: n
N=2704788216675194980499542551060655021724236388702534810044917685756135276824583595510670303940880582146643295076682884124461339036642305529913813504377723279
  ( 157 digits)
SNFS difficulty: 166 digits.
Divisors found:

Sat Jul 18 06:33:52 2009  prp50 factor: 11500057744747399273355108662919213155050608195831
Sat Jul 18 06:33:52 2009  prp108 factor: 235197794368519156880312362442167554274367596081043998198046134333506670922483690675068444570466640194016809
Sat Jul 18 06:33:52 2009  elapsed time 00:48:58 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 33.45 hours.
Scaled time: 88.29 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_6_4_163_7
n: 2704788216675194980499542551060655021724236388702534810044917685756135276824583595510670303940880582146643295076682884124461339036642305529913813504377723279
m: 1000000000000000000000000000000000
deg: 5
c5: 29
c0: 115
skew: 1.32
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 20000
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2100000, 3879990)
Primes: RFBsize:296314, AFBsize:296441, largePrimes:15128491 encountered
Relations: rels:14197589, finalFF:565554
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1497712 hash collisions in 16067174 relations
Msieve: matrix is 728489 x 728737 (194.4 MB)

Total sieving time: 33.16 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,56,56,2.4,2.4,100000
total time: 33.45 hours.
 --------- CPU info (if available) ----------

2·10²²⁰-1 = 1(9)₂₂₀_<221> = 7 · 8524543 · C213

C213 = P49 · P165

P49 = 1083123216870509849562557573497140850225905243919_<49>

P165 = 309444654420209152261395329908853882478560572701303797798488365664928863916804072609327933421236573012248026757692102667702446776183075707594247676208587347163650521_<165>

Number: n
N=335166689539000171957270067984038222677408379210810144644368954106144709793491904157543359551021428027620617651543649570757886124469412277333476159031968885939943391351636931487956932957327699896304453756976431799
  ( 213 digits)
SNFS difficulty: 221 digits.
Divisors found:

Sat Jul 18 23:40:02 2009  prp49 factor: 1083123216870509849562557573497140850225905243919
Sat Jul 18 23:40:02 2009  prp165 factor: 309444654420209152261395329908853882478560572701303797798488365664928863916804072609327933421236573012248026757692102667702446776183075707594247676208587347163650521
Sat Jul 18 23:40:02 2009  elapsed time 66:40:35 (Msieve 1.39 - dependency 5)

Version: GGNFS-0.77.1-20050930-k8
Total time: 235.94 hours.
Scaled time: 475.41 units (timescale=2.015).
Factorization parameters were as follows:
name: KA_1_9_220
n: 335166689539000171957270067984038222677408379210810144644368954106144709793491904157543359551021428027620617651543649570757886124469412277333476159031968885939943391351636931487956932957327699896304453756976431799
m: 5000000000000000000000000000000000000
deg: 6
c6: 32
c0: -25
skew: 0.96
type: snfs
lss: 1
rlim: 35000000
alim: 35000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 35000000/35000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [17500000, 57299990)
Primes: RFBsize:2146775, AFBsize:2145196, largePrimes:38632996 encountered
Relations: rels:36859864, finalFF:1918519
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 8934321 hash collisions in 51196493 relations
Msieve: matrix is 5501339 x 5501587 (1489.6 MB)

Total sieving time: 233.50 hours.
Total relation processing time: 2.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,221,6,0,0,0,0,0,0,0,0,35000000,35000000,29,29,58,58,2.6,2.6,100000
total time: 235.94 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3352056k/3407296k available (3119k kernel code, 53956k reserved, 1894k data, 424k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.68 BogoMIPS (lpj=2830844)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22644.41 BogoMIPS).

Jul 18, 2009 (2nd)

By JPascoa / ggnfs, Msieve / Jul 18, 2009

(56·10¹⁷⁵+61)/9 = 6(2)₁₇₄9_<176> = 3 · 31 · 2711 · C171

C171 = P48 · P53 · P70

P48 = 388515540492427348907583886855452752043478553029_<48>

P53 = 70798724686624585386544472933176159270934345581903249_<53>

P70 = 8972205695485573426892548531463913519652897767969898815437666920730963_<70>

Number: 62229_175
N=246793121699417436022188464448789766194366330014406548479203492827795251612198102601596134514590982267473503893822547812862064239368174352289248589863765789801891228575823
  ( 171 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=388515540492427348907583886855452752043478553029 (pp48)
 r2=70798724686624585386544472933176159270934345581903249 (pp53)
 r3=8972205695485573426892548531463913519652897767969898815437666920730963 (pp70)
Version: Msieve-1.40
Total time: 190.37 hours.
Scaled time: 170.00 units (timescale=0.893).
Factorization parameters were as follows:
n: 246793121699417436022188464448789766194366330014406548479203492827795251612198102601596134514590982267473503893822547812862064239368174352289248589863765789801891228575823
m: 100000000000000000000000000000000000
deg: 5
c5: 56
c0: 61
skew: 1.02
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3100000, 6400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1186087 x 1186335
Total sieving time: 175.31 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 12.30 hours.
Time per square root: 2.33 hours.
Prototype def-par.txt line would be:
snfs,176.000,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,53,53,2.5,2.5,100000
total time: 190.37 hours.
 --------- CPU info (if available) ----------

Jul 18, 2009

By Andreas Tete / Syd`s Database workers / Jul 18, 2009

(58·10¹⁶⁹+23)/9 = 6(4)₁₆₈7_<170> = 19 · 595027205653663_<15> · C154

C154 = P44 · P111

P44 = 25375530110051932248409455637683310452044129_<44>

P111 = 224636299692188654900752577911302035085906908095641797207881999549460700135118306963468485330593067442061655419_<111>

Syd`s Database Workers found this p44 factor
25375530110051932248409455637683310452044129

Jul 17, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Jul 17, 2009

(58·10¹⁵⁸+23)/9 = 6(4)₁₅₇7_<159> = 507258946185199073_<18> · C142

C142 = P52 · P90

P52 = 1278645878079139367561302863672131908561906870215169_<52>

P90 = 993586051553808199193408457585820294273094326234517367149202785954627596743988796894988031_<90>

Number: 64447_158
N=1270444709336204120838955092427862236338311988888771908849602795998904887144640225487688999309661201835162015891793735455328916625770649642239
  ( 142 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=1278645878079139367561302863672131908561906870215169
 r2=993586051553808199193408457585820294273094326234517367149202785954627596743988796894988031
Version: 
Total time: 19.20 hours.
Scaled time: 45.85 units (timescale=2.388).
Factorization parameters were as follows:
n: 1270444709336204120838955092427862236338311988888771908849602795998904887144640225487688999309661201835162015891793735455328916625770649642239
m: 100000000000000000000000000000000
deg: 5
c5: 29
c0: 1150
skew: 2.09
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9559208
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 662774 x 663022
Total sieving time: 17.47 hours.
Total relation processing time: 0.77 hours.
Matrix solve time: 0.88 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 19.20 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794)
Calibrating delay using timer specific routine.. 5556.53 BogoMIPS (lpj=2778268)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

(58·10¹⁶⁷+23)/9 = 6(4)₁₆₆7_<168> = 383 · 81817 · 116411 · C156

C156 = P37 · C119

P37 = 2539015319297239760208862106037195769_<37>

C119 = [69579902826814172117370151834844693730354578571165992862664790776297462544881688493563687017875009631281121822059456803_<119>]

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 176664439192494500603903652629064270381455362741433055190135752367595572210582780887956047748456308226710844007728629140020317113769890466444789777509866507 (156 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4052174073
Step 1 took 5585ms
Step 2 took 4930ms
********** Factor found in step 2: 2539015319297239760208862106037195769
Found probable prime factor of 37 digits: 2539015319297239760208862106037195769
Composite cofactor 69579902826814172117370151834844693730354578571165992862664790776297462544881688493563687017875009631281121822059456803 has 119 digits

Jul 17, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Jul 17, 2009

(25·10¹⁸²-7)/9 = 2(7)₁₈₂_<183> = 17117 · C179

C179 = P56 · P124

P56 = 11668612365029158264973585406781904053320654630592190117_<56>

P124 = 1390755018908550004808948472357508980894052680062194565556521981244963879863839918251881991075491489862525029001916349179393_<124>

Number: n
N=16228181210362667393689184890914165903942149779621299163274976793700869181385627024465605992742757362725815141542196516783185007757070618553355014183430377856971302084347594658981
  ( 179 digits)
SNFS difficulty: 184 digits.
Divisors found:

Fri Jul 17 20:32:46 2009  prp56 factor: 11668612365029158264973585406781904053320654630592190117
Fri Jul 17 20:32:46 2009  prp124 factor: 1390755018908550004808948472357508980894052680062194565556521981244963879863839918251881991075491489862525029001916349179393
Fri Jul 17 20:32:46 2009  elapsed time 02:17:34 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 144.30 hours.
Scaled time: 368.54 units (timescale=2.554).
Factorization parameters were as follows:
name: KA_2_7_182
n: 16228181210362667393689184890914165903942149779621299163274976793700869181385627024465605992742757362725815141542196516783185007757070618553355014183430377856971302084347594658981
m: 5000000000000000000000000000000000000
deg: 5
c5: 4
c0: -35
skew: 1.54
type: snfs
lss: 1
rlim: 8200000
alim: 8200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8200000/8200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4100000, 6500519)
Primes: RFBsize:552319, AFBsize:551943, largePrimes:21016285 encountered
Relations: rels:21228277, finalFF:1081466
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1872658 hash collisions in 22409992 relations
Msieve: matrix is 1283524 x 1283772 (345.3 MB)

Total sieving time: 143.77 hours.
Total relation processing time: 0.52 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,184,5,0,0,0,0,0,0,0,0,8200000,8200000,28,28,56,56,2.5,2.5,100000
total time: 144.30 hours.
 --------- CPU info (if available) ----------

Jul 17, 2009 (2nd)

By Andreas Tete / Syd`s Databaseworkers / Jul 17, 2009

(58·10²⁰⁵+23)/9 = 6(4)₂₀₄7_<206> = 19 · 4673817737_<10> · 5386475191_<10> · C186

C186 = P44 · C142

P44 = 37279635067379744491429662807584297718778261_<44>

C142 = [3613963770556477654016730027656282688127304025375501313679954016553439847689009024896441883490154237053247753961776552755718531951417094099999_<142>]

Syd`s Databaseworkers found this factor with ecm and a B1 with 3000000
p44 = 37279635067379744491429662807584297718778261

(58·10²⁰¹+23)/9 = 6(4)₂₀₀7_<202> = 3 · 7 · 59 · 1077279209_<10> · 1781627747_<10> · C181

C181 = P32 · P149

P32 = 30297092310814121029529794339259_<32>

P149 = 89447453611115384235878445655526795835222280743403456616133385462314670368342358184437926433531052514215730265019173286277064719302589369837790759489_<149>

Syd`s Databaseworkers found this p32 factor
30297092310814121029529794339259

Jul 17, 2009

By Jo Yeong Uk / GMP-ECM / Jul 17, 2009

(58·10¹⁶⁶+23)/9 = 6(4)₁₆₅7_<167> = 67 · 269 · 24659821 · 359583120536779_<15> · 37955506286865983_<17> · C125

C125 = P38 · P87

P38 = 34290262392024774518344843759406959751_<38>

P87 = 309830085865730714982413828543955085580794667849260732917353228988602413576841495364287_<87>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 10624154941279472588706800909070323594739495600215523842393261989133431103918712360142396758107111721514498237754750891812537 (125 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5400989727
Step 1 took 4399ms
Step 2 took 4274ms
********** Factor found in step 2: 34290262392024774518344843759406959751
Found probable prime factor of 38 digits: 34290262392024774518344843759406959751
Probable prime cofactor 309830085865730714982413828543955085580794667849260732917353228988602413576841495364287 has 87 digits

Jul 16, 2009 (2nd)

By Jo Yeong Uk / GGNFS/Msieve v1.39 / Jul 16, 2009

(58·10¹⁵³+23)/9 = 6(4)₁₅₂7_<154> = 3³ · 7² · 13386589 · 92319833 · 394377397 · C127

C127 = P45 · P83

P45 = 814705712881851172222015572110575961300237593_<45>

P83 = 12267269943728648564005575671767203078380537568076048469810797003362184815778995757_<83>

Number: 64447_153
N=9994214904619554942976947840573200293185186344913231726692244414931835344290389939721451670688386247341373699755831583038892901
  ( 127 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=814705712881851172222015572110575961300237593
 r2=12267269943728648564005575671767203078380537568076048469810797003362184815778995757
Version: 
Total time: 12.80 hours.
Scaled time: 30.18 units (timescale=2.358).
Factorization parameters were as follows:
n: 9994214904619554942976947840573200293185186344913231726692244414931835344290389939721451670688386247341373699755831583038892901
m: 10000000000000000000000000000000
deg: 5
c5: 29
c0: 1150
skew: 2.09
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8451961
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 479129 x 479377
Total sieving time: 11.73 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 0.46 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 12.80 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794)
Calibrating delay using timer specific routine.. 5556.53 BogoMIPS (lpj=2778268)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)

Jul 16, 2009

By Robert Backstrom / GGNFS, Msieve / Jul 16, 2009

(14·10¹⁸³+1)/3 = 4(6)₁₈₂7_<184> = 13 · 223 · 647 · C178

C178 = P76 · P103

P76 = 2382309436848608429515710782337046103074905774875135063353620428270919969829_<76>

P103 = 1044374150200446498197582320576516819989106942296904804562163907478690398558019374206562021089536289091_<103>

Number: n
N=2488022393623269691497663302682674602747238783861762632356126995060742401002033247443245987752887483274713748580716511351868744734056174925034996700704590170285584096134341835439
  ( 178 digits)
SNFS difficulty: 185 digits.
Divisors found:

Thu Jul 16 02:37:54 2009  prp76 factor: 2382309436848608429515710782337046103074905774875135063353620428270919969829
Thu Jul 16 02:37:54 2009  prp103 factor: 1044374150200446498197582320576516819989106942296904804562163907478690398558019374206562021089536289091
Thu Jul 16 02:37:54 2009  elapsed time 02:45:14 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 193.61 hours.
Scaled time: 494.47 units (timescale=2.554).
Factorization parameters were as follows:
name: KA_4_6_182_7
n: 2488022393623269691497663302682674602747238783861762632356126995060742401002033247443245987752887483274713748580716511351868744734056174925034996700704590170285584096134341835439
m: 10000000000000000000000000000000000000
deg: 5
c5: 7
c0: 50
skew: 1.48
type: snfs
lss: 1
rlim: 8800000
alim: 8800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8800000/8800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4400000, 7649990)
Primes: RFBsize:590006, AFBsize:591015, largePrimes:20956756 encountered
Relations: rels:20817925, finalFF:1183054
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2257684 hash collisions in 23732928 relations
Msieve: matrix is 1367636 x 1367884 (364.2 MB)

Total sieving time: 193.00 hours.
Total relation processing time: 0.61 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,8800000,8800000,28,28,56,56,2.5,2.5,100000
total time: 193.61 hours.
 --------- CPU info (if available) ----------

Jul 15, 2009 (2nd)

By JPascoa / ggnfs, Msieve / Jul 15, 2009

(58·10¹⁵⁶+23)/9 = 6(4)₁₅₅7_<157> = 3 · 307 · 763897 · C148

C148 = P42 · P107

P42 = 120066543180694111133541404474922697213321_<42>

P107 = 76290250756513641445476454090142648409983943145226476005174220199825080683439408569647411791219214819389111_<107>

Number: 64447_156
N=9159906686722926709303097964633626498847435078929596419140294453156929171877364472475281345479703778592573903540222016425335256213162613039271547631
  ( 148 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=120066543180694111133541404474922697213321 (pp42)
 r2=76290250756513641445476454090142648409983943145226476005174220199825080683439408569647411791219214819389111 (pp107)
Version: Msieve-1.40
Total time: 59.23 hours.
Scaled time: 52.66 units (timescale=0.889).
Factorization parameters were as follows:
n: 9159906686722926709303097964633626498847435078929596419140294453156929171877364472475281345479703778592573903540222016425335256213162613039271547631
m: 20000000000000000000000000000000
deg: 5
c5: 145
c0: 184
skew: 1.05
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1550000, 2750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 604903 x 605151
Total sieving time: 56.56 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.34 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,158.000,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000
total time: 59.23 hours.
 --------- CPU info (if available) ----------

Jul 15, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jul 15, 2009

(58·10¹⁴⁵+23)/9 = 6(4)₁₄₄7_<146> = 318103 · 23255597 · 24166991 · 24837440522145492041_<20> · C107

C107 = P42 · P65

P42 = 155862830136335532804447504661369172098147_<42>

P65 = 93114699926353630931013362844178771981034759538690356442350389481_<65>

Number: 64447_145
N=14513120657817110724068948596869268773609716183566522071117683501229380132163791152524290662673843408391707
  ( 107 digits)
Divisors found:
 r1=155862830136335532804447504661369172098147
 r2=93114699926353630931013362844178771981034759538690356442350389481
Version: 
Total time: 6.15 hours.
Scaled time: 14.67 units (timescale=2.385).
Factorization parameters were as follows:
name: 64447_145
n: 14513120657817110724068948596869268773609716183566522071117683501229380132163791152524290662673843408391707
skew: 39366.66
# norm 1.35e+15
c5: 10260
c4: -1732448568
c3: -40955835229705
c2: 2591026688417304464
c1: 35043786271468244640188
c0: -384519196336207960118558544
# alpha -6.76
Y1: 94483556057
Y0: -269232718404910182205
# Murphy_E 1.52e-09
# M 1883062411933760718032814856662790779215812496228563671416845431180490880688470056173105140057998316018953
type: gnfs
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 2000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7242468
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 327166 x 327414
Polynomial selection time: 0.43 hours.
Total sieving time: 4.66 hours.
Total relation processing time: 0.66 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000
total time: 6.15 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356)
Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹⁴⁷+23)/9 = 6(4)₁₄₆7_<148> = 3 · 7 · 19448841488893_<14> · 805559364860507_<15> · C119

C119 = P51 · P69

P51 = 117743176838317603744085092073414896474908231317839_<51>

P69 = 166356261680136035603069369279866858793166950948301687007455754691363_<69>

Number: 64447_147
N=19587314737165695603470071257269254262295902571320784295305733164689395113045338701101302069147682911255882924201124557
  ( 119 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=117743176838317603744085092073414896474908231317839
 r2=166356261680136035603069369279866858793166950948301687007455754691363
Version: 
Total time: 8.55 hours.
Scaled time: 20.40 units (timescale=2.387).
Factorization parameters were as follows:
n: 19587314737165695603470071257269254262295902571320784295305733164689395113045338701101302069147682911255882924201124557
m: 200000000000000000000000000000
deg: 5
c5: 725
c0: 92
skew: 0.66
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1500000, 3225001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6995787
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 442563 x 442811
Total sieving time: 7.39 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,49,49,2.3,2.3,75000
total time: 8.55 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356)
Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

Jul 14, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM, YAFU 1.10 / Jul 14, 2009

(58·10¹²⁸+23)/9 = 6(4)₁₂₇7_<129> = 131 · 41813 · 21245655914760583_<17> · C106

C106 = P36 · P70

P36 = 760985107913167809574082276999951959_<36>

P70 = 7277070100650168876742315488211887360553220961176794222662356452710017_<70>

Number: 64447_128
N=5537741975834955696163581925148970165169810424088982787295926273785929205033292036428911457802364358073303
  ( 106 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=760985107913167809574082276999951959
 r2=7277070100650168876742315488211887360553220961176794222662356452710017
Version: 
Total time: 1.72 hours.
Scaled time: 4.09 units (timescale=2.378).
Factorization parameters were as follows:
n: 5537741975834955696163581925148970165169810424088982787295926273785929205033292036428911457802364358073303
m: 100000000000000000000000000
deg: 5
c5: 29
c0: 1150
skew: 2.09
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 1000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2901625
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 158539 x 158787
Total sieving time: 1.53 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 1.72 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356)
Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹⁷¹+23)/9 = 6(4)₁₇₀7_<172> = 3² · 7 · 163 · 229 · 43607 · 355636003 · 1269791928287_<13> · 111929378928377_<15> · 29987432328229516862586197167_<29> · C98

C98 = P31 · P32 · P36

P31 = 5256085350367721968365243508879_<31>

P32 = 14889514327152662463708208717849_<32>

P36 = 529786685826043275442599790114501549_<36>

Number: 64447_171
N=41461401722079143647924150625301340578093020537184821796736112311143710226687952818709906878188779
  ( 98 digits)
Divisors found:
 r1=5256085350367721968365243508879
 r2=14889514327152662463708208717849
 r3=529786685826043275442599790114501549
Version: 
Total time: 2.08 hours.
Scaled time: 4.95 units (timescale=2.384).
Factorization parameters were as follows:
name: 64447_171
n: 41461401722079143647924150625301340578093020537184821796736112311143710226687952818709906878188779
skew: 7857.64
# norm 2.45e+13
c5: 11880
c4: 788898
c3: -613633019573
c2: -6822373166044091
c1: -68762375014291434697
c0: 108707619335330199856823
# alpha -5.99
Y1: 2407654091
Y0: -5111701737676163862
# Murphy_E 4.55e-09
# M 6269349845825020629740171875377268828302419233862240622567814041128462207806673633291997154454334
type: gnfs
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [500000, 900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4333827
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 144083 x 144331
Polynomial selection time: 0.13 hours.
Total sieving time: 1.71 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000
total time: 2.08 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356)
Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹²⁹+23)/9 = 6(4)₁₂₈7_<130> = 3 · 7 · 71 · 421 · 1390317957013_<13> · C112

C112 = P53 · P59

P53 = 75763157022055757160940379455506947440975308080533513_<53>

P59 = 97466091234717045166053084915874283627086578275412208937333_<59>

Number: 64447_129
N=7384338774541879783190749762116627536820641207265619697558830813010085523088627253291340919120199082377423340829
  ( 112 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=75763157022055757160940379455506947440975308080533513
 r2=97466091234717045166053084915874283627086578275412208937333
Version: 
Total time: 1.47 hours.
Scaled time: 3.50 units (timescale=2.386).
Factorization parameters were as follows:
n: 7384338774541879783190749762116627536820641207265619697558830813010085523088627253291340919120199082377423340829
m: 100000000000000000000000000
deg: 5
c5: 29
c0: 115
skew: 1.32
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2805388
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 147296 x 147539
Total sieving time: 1.27 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 1.47 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356)
Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹³⁶+23)/9 = 6(4)₁₃₅7_<137> = 317 · 463 · 4231 · C129

C129 = P40 · P89

P40 = 6119790257462840180408171750175750836047_<40>

P89 = 16957650012616993070182468852439375057528923539892416047822926309148813178064338505119101_<89>

Number: 64447_136
N=103777261336678083054677475123544185985045862327150201617863921750804117975272515639465440328049771189487645987027446190059033747
  ( 129 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=6119790257462840180408171750175750836047
 r2=16957650012616993070182468852439375057528923539892416047822926309148813178064338505119101
Version: 
Total time: 2.64 hours.
Scaled time: 6.30 units (timescale=2.389).
Factorization parameters were as follows:
n: 103777261336678083054677475123544185985045862327150201617863921750804117975272515639465440328049771189487645987027446190059033747
m: 1000000000000000000000000000
deg: 5
c5: 580
c0: 23
skew: 0.52
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3620190
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 246289 x 246537
Total sieving time: 2.28 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,50000
total time: 2.64 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356)
Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹⁴¹+23)/9 = 6(4)₁₄₀7_<142> = 3 · 7 · 436439 · 103617691367_<12> · 2579254893476128243_<19> · C106

C106 = P50 · P56

P50 = 76186258682820596721818032631403693765457390966091_<50>

P56 = 34533278839482980957953122866654334570356354654042530003_<56>

Number: 64447_141
N=2630961314830825037808404552418118055910889450264586094583925505760367689427304261765390068171674023128273
  ( 106 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=76186258682820596721818032631403693765457390966091
 r2=34533278839482980957953122866654334570356354654042530003
Version: 
Total time: 4.22 hours.
Scaled time: 10.08 units (timescale=2.387).
Factorization parameters were as follows:
n: 2630961314830825037808404552418118055910889450264586094583925505760367689427304261765390068171674023128273
m: 10000000000000000000000000000
deg: 5
c5: 580
c0: 23
skew: 0.52
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [1100000, 2050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4380215
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 298553 x 298801
Total sieving time: 3.66 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,48,48,2.3,2.3,50000
total time: 4.22 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356)
Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹⁴⁸+23)/9 = 6(4)₁₄₇7_<149> = 17 · 15737 · 1600057148951_<13> · 281957788581047651_<18> · C114

C114 = P30 · P84

P30 = 957229269729820319274362209397_<30>

P84 = 557800703761628951235813012289882908409521924268072584602236892834526943369023125519_<84>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 533943160316523918951469911012731137258971520498099742586223078317083887622231588054788137903703903967979292302043 (114 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6037326045
Step 1 took 3463ms
Step 2 took 3806ms
********** Factor found in step 2: 957229269729820319274362209397
Found probable prime factor of 30 digits: 957229269729820319274362209397
Probable prime cofactor 557800703761628951235813012289882908409521924268072584602236892834526943369023125519 has 84 digits

(58·10¹⁴⁹+23)/9 = 6(4)₁₄₈7_<150> = 51307 · 814665077 · 125452973878408950737_<21> · C117

C117 = P36 · P38 · P44

P36 = 239805938435749179530628678236164969_<36>

P38 = 41430417338281880250147847818250316533_<38>

P44 = 12369996045565239429686508194506888049892077_<44>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 122899128267307932285652056221776691270027659426723777828073895284388924281020552605381106797530820720034481264684729 (117 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5739799736
Step 1 took 4602ms
Step 2 took 3994ms
********** Factor found in step 2: 239805938435749179530628678236164969
Found probable prime factor of 36 digits: 239805938435749179530628678236164969
Composite cofactor 512494098640664391257456959015229005123844681619807604130051122581206101738809041 has 81 digits

07/14/09 22:52:48 v1.10 @ 조영욱-PC, starting SIQS on c81: 512494098640664391257456959015229005123844681619807604130051122581206101738809041
07/14/09 22:52:48 v1.10 @ 조영욱-PC, random seeds: 703900670, 2446589440
07/14/09 22:52:48 v1.10 @ 조영욱-PC, ==== sieve params ====
07/14/09 22:52:48 v1.10 @ 조영욱-PC, n = 81 digits, 274 bits
07/14/09 22:52:48 v1.10 @ 조영욱-PC, factor base: 45938 primes (max prime = 1188269)
07/14/09 22:52:48 v1.10 @ 조영욱-PC, single large prime cutoff: 112885555 (95 * pmax)
07/14/09 22:52:48 v1.10 @ 조영욱-PC, using 14 large prime slices of factor base
07/14/09 22:52:48 v1.10 @ 조영욱-PC, buckets hold 1024 elements
07/14/09 22:52:48 v1.10 @ 조영욱-PC, sieve interval: 7 blocks of size 65536
07/14/09 22:52:48 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors
07/14/09 22:52:48 v1.10 @ 조영욱-PC, using multiplier of 41
07/14/09 22:52:48 v1.10 @ 조영욱-PC, using small prime variation correction of 21 bits
07/14/09 22:52:48 v1.10 @ 조영욱-PC, using SSE2 for trial division and x64 sieve scanning
07/14/09 22:52:48 v1.10 @ 조영욱-PC, trial factoring cutoff at 95 bits
07/14/09 22:52:48 v1.10 @ 조영욱-PC, ==== sieving started ====
07/14/09 23:01:04 v1.10 @ 조영욱-PC, sieve time = 249.9540, relation time = 70.0050, poly_time = 175.6000
07/14/09 23:01:04 v1.10 @ 조영욱-PC, 46066 relations found: 23464 full + 22602 from 247296 partial, using 129790 polys (164 A polys)
07/14/09 23:01:04 v1.10 @ 조영욱-PC, on average, sieving found 2.09 rels/poly and 545.80 rels/sec
07/14/09 23:01:04 v1.10 @ 조영욱-PC, trial division touched 3687831 sieve locations out of 119082844160
07/14/09 23:01:04 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
07/14/09 23:01:04 v1.10 @ 조영욱-PC, begin with 270760 relations
07/14/09 23:01:04 v1.10 @ 조영욱-PC, reduce to 65824 relations in 2 passes
07/14/09 23:01:05 v1.10 @ 조영욱-PC, recovered 65824 relations
07/14/09 23:01:05 v1.10 @ 조영욱-PC, recovered 51617 polynomials
07/14/09 23:01:05 v1.10 @ 조영욱-PC, attempting to build 46066 cycles
07/14/09 23:01:05 v1.10 @ 조영욱-PC, found 46066 cycles in 1 passes
07/14/09 23:01:05 v1.10 @ 조영욱-PC, distribution of cycle lengths:
07/14/09 23:01:05 v1.10 @ 조영욱-PC,    length 1 : 23464
07/14/09 23:01:05 v1.10 @ 조영욱-PC,    length 2 : 22602
07/14/09 23:01:05 v1.10 @ 조영욱-PC, largest cycle: 2 relations
07/14/09 23:01:05 v1.10 @ 조영욱-PC, matrix is 45938 x 46066 (7.0 MB) with weight 1467122 (31.85/col)
07/14/09 23:01:05 v1.10 @ 조영욱-PC, sparse part has weight 1467122 (31.85/col)
07/14/09 23:01:05 v1.10 @ 조영욱-PC, filtering completed in 3 passes
07/14/09 23:01:05 v1.10 @ 조영욱-PC, matrix is 33395 x 33459 (5.5 MB) with weight 1182778 (35.35/col)
07/14/09 23:01:05 v1.10 @ 조영욱-PC, sparse part has weight 1182778 (35.35/col)
07/14/09 23:01:05 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
07/14/09 23:01:05 v1.10 @ 조영욱-PC, matrix is 33347 x 33459 (3.8 MB) with weight 882310 (26.37/col)
07/14/09 23:01:05 v1.10 @ 조영욱-PC, sparse part has weight 673096 (20.12/col)
07/14/09 23:01:05 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
07/14/09 23:01:05 v1.10 @ 조영욱-PC, using block size 13383 for processor cache size 4096 kB
07/14/09 23:01:05 v1.10 @ 조영욱-PC, commencing Lanczos iteration
07/14/09 23:01:05 v1.10 @ 조영욱-PC, memory use: 3.7 MB
07/14/09 23:01:08 v1.10 @ 조영욱-PC, lanczos halted after 529 iterations (dim = 33343)
07/14/09 23:01:08 v1.10 @ 조영욱-PC, recovered 16 nontrivial dependencies
07/14/09 23:01:08 v1.10 @ 조영욱-PC, prp44 = 12369996045565239429686508194506888049892077
07/14/09 23:01:10 v1.10 @ 조영욱-PC, prp38 = 41430417338281880250147847818250316533
07/14/09 23:01:10 v1.10 @ 조영욱-PC, Lanczos elapsed time = 4.2900 seconds.
07/14/09 23:01:10 v1.10 @ 조영욱-PC, Sqrt elapsed time = 1.2940 seconds.
07/14/09 23:01:10 v1.10 @ 조영욱-PC, SIQS elapsed time = 501.6600 seconds.
07/14/09 23:01:10 v1.10 @ 조영욱-PC, 
07/14/09 23:01:10 v1.10 @ 조영욱-PC,

(58·10¹⁵⁰+23)/9 = 6(4)₁₄₉7_<151> = 3 · 2003 · 92551 · 107201 · 3391945245606732612163_<22> · C116

C116 = P46 · P71

P46 = 2399679341298100809951191715143165897321865029_<46>

P71 = 13280098068807257841052877871669566506875479890479596261399064850887679_<71>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 31867976986129581142577553204069184977118961756426749952446804034640512899999263466243557329301492399086906477077691 (116 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4284733017
Step 1 took 3806ms
Step 2 took 3307ms
********** Factor found in step 2: 2399679341298100809951191715143165897321865029
Found probable prime factor of 46 digits: 2399679341298100809951191715143165897321865029
Probable prime cofactor 13280098068807257841052877871669566506875479890479596261399064850887679 has 71 digits

Jul 14, 2009 (4th)

By JPascoa / Chris Monico ggnfs-0.77.1, Msieve / Jul 14, 2009

(58·10¹²³+23)/9 = 6(4)₁₂₂7_<124> = 3 · 7 · 24391 · 13990433 · C111

C111 = P50 · P62

P50 = 50773799828332712760339199634604292107704204758339_<50>

P62 = 17711924842507332373590758448378995774984298667244766404457271_<62>

Number: 64447_123
N=899301726527940702964232341357666906090579560911871755134417338433041568548838314131597612984873335457006432869
  ( 111 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=50773799828332712760339199634604292107704204758339 (pp50)
 r2=17711924842507332373590758448378995774984298667244766404457271 (pp62)
Version: Msieve-1.40
Total time: 1.92 hours.
Scaled time: 2.28 units (timescale=1.188).
Factorization parameters were as follows:
n: 899301726527940702964232341357666906090579560911871755134417338433041568548838314131597612984873335457006432869
m: 5000000000000000000000000
deg: 5
c5: 464
c0: 575
skew: 1.04
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 795001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 121689 x 121919
Total sieving time: 1.84 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 1.92 hours.
 --------- CPU info (if available) ----------

(58·10¹⁴²+23)/9 = 6(4)₁₄₁7_<143> = 1249 · 2347 · 24919 · 466183 · 15523710638280211453_<20> · C108

C108 = P37 · P71

P37 = 5264538448831778063739858965185820207_<37>

P71 = 23156188327031872626489300434370560937362355885611469744116956097040047_<71>

Number: 64447_142
N=121906643776048900653845760483176682051303097738362726296929265059517001216762243933421499551133248620829729
  ( 108 digits)
Divisors found:
 r1=5264538448831778063739858965185820207 (pp37)
 r2=23156188327031872626489300434370560937362355885611469744116956097040047 (pp71)
Version: Msieve-1.40
Total time: 10.92 hours.
Scaled time: 13.02 units (timescale=1.192).
Factorization parameters were as follows:
name: 64447_142
n: 121906643776048900653845760483176682051303097738362726296929265059517001216762243933421499551133248620829729
skew: 10330.88
# norm 2.86e+014
c5: 64620
c4: 1239404382
c3: -30319770518560
c2: -91176158701992677
c1: 1056015459864830190240
c0: 2423349024698880698893011
# alpha -5.08
Y1: 331395755999
Y0: -285187278252824020054
# Murphy_E 1.38e-009
# M 121691403354176194190776471266168161078137481667477963639797578008571176758933027729971584524949945150524271
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 324103 x 324347
Polynomial selection time: 1.12 hours.
Total sieving time: 9.47 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 10.92 hours.
 --------- CPU info (if available) ----------

(58·10¹⁴⁶+23)/9 = 6(4)₁₄₅7_<147> = 225240727286207539_<18> · C130

C130 = P40 · P90

P40 = 7984979862480793926125756973956199182887_<40>

P90 = 358314792650653686950640911375423315769676174740273424441797231618837823936703464982949779_<90>

Number: 64447_146
N=2861136403744450867384364181988944676233621211196267931286517974372854120293817015912673374579164624145954637643177163066757231973
  ( 130 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=7984979862480793926125756973956199182887 (pp40)
 r2=358314792650653686950640911375423315769676174740273424441797231618837823936703464982949779 (pp90)
Version: Msieve-1.40
Total time: 22.89 hours.
Scaled time: 20.49 units (timescale=0.895).
Factorization parameters were as follows:
n: 2861136403744450867384364181988944676233621211196267931286517974372854120293817015912673374579164624145954637643177163066757231973
m: 200000000000000000000000000000
deg: 5
c5: 145
c0: 184
skew: 1.05
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 344816 x 345049
Total sieving time: 21.95 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.69 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,148.000,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 22.89 hours.
 --------- CPU info (if available) ----------

Jul 14, 2009 (3rd)

By Robert Backstrom / GGNFS / Jul 14, 2009

(58·10¹²⁰+23)/9 = 6(4)₁₁₉7_<121> = 3 · 16481 · 670037 · C111

C111 = P52 · P59

P52 = 3592422000876207144080797101689943790151669878642591_<52>

P59 = 54149510756258711112608068985210572030309207474345155051487_<59>

Number: n
N=194527893777466619665691553316121652261080764904403871430472308721459150022852335874986627652427044538276082817
  ( 111 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=3592422000876207144080797101689943790151669878642591 (pp52)
 r2=54149510756258711112608068985210572030309207474345155051487 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.72 hours.
Scaled time: 3.13 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_4_119_7
n: 194527893777466619665691553316121652261080764904403871430472308721459150022852335874986627652427044538276082817
m: 1000000000000000000000000
deg: 5
c5: 58
c0: 23
skew: 0.83
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 10000
Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [280000, 540001)
Primes: RFBsize:46072, AFBsize:45556, largePrimes:3217734 encountered
Relations: rels:2682895, finalFF:110424
Max relations in full relation-set: 48
Initial matrix: 91694 x 110424 with sparse part having weight 10891784.
Pruned matrix : 88456 x 88978 with weight 6502223.
Total sieving time: 1.60 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.03 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,560000,560000,28,28,56,56,2.3,2.3,50000
total time: 1.72 hours.
 --------- CPU info (if available) ----------

Jul 14, 2009 (2nd)

By Sinkiti Sibata / Msieve / Jul 14, 2009

(58·10¹³⁹+23)/9 = 6(4)₁₃₈7_<140> = C140

C140 = P67 · P74

P67 = 1938058158904057175420875818268265892536340598520596225753765591909_<67>

P74 = 33252069422357691954035197580335551879441443411363876229822358630860524083_<74>

Number: 64447_139
N=64444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447
  ( 140 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=1938058158904057175420875818268265892536340598520596225753765591909 (pp67)
 r2=33252069422357691954035197580335551879441443411363876229822358630860524083 (pp74)
Version: Msieve-1.40
Total time: 6.74 hours.
Scaled time: 17.36 units (timescale=2.575).
Factorization parameters were as follows:
name: 64447_139
n: 64444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447
m: 10000000000000000000000000000
deg: 5
c5: 29
c0: 115
skew: 1.32
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 240937 x 241174
Total sieving time: 6.55 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 6.74 hours.
 --------- CPU info (if available) ----------

Jul 14, 2009

By Dmitry Domanov / ECMNET / Jul 14, 2009

(58·10¹⁷⁹+23)/9 = 6(4)₁₇₈7_<180> = C180

C180 = P39 · P141

P39 = 672685683356861337041796175253604246571_<39>

P141 = 958017184531880621373920860801042598243408868260257248390356768611005235992717460853265486439899270704857151033067923579387134911377797556957_<141>

C180=P39*P141
C180=672685683356861337041796175253604246571<39>*958017184531880621373920860801042598243408868260257248390356768611005235992717460853265486439899270704857151033067923579387134911377797556957<141>

(58·10¹⁸⁴+23)/9 = 6(4)₁₈₃7_<185> = C185

C185 = P36 · C150

P36 = 176588117670435309434329024092440363_<36>

C150 = [364942133675814393150109614547698249357635271656814604537174727470973783441581875210983228248347867250016918641191589005044762359987857325025874363869_<150>]

C185=P36*C150
C185=176588117670435309434329024092440363<36>*364942133675814393150109614547698249357635271656814604537174727470973783441581875210983228248347867250016918641191589005044762359987857325025874363869<150>

Jul 13, 2009 (6th)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Jul 13, 2009

(58·10¹⁶¹+23)/9 = 6(4)₁₆₀7_<162> = C162

C162 = P38 · C125

P38 = 41119327973436033475483754806134272837_<38>

C125 = [15672543210355221701053940350577676484197328922241828151784149179051334607839580596202241048609582134533477776622521732064531_<125>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 644444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 (162 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1512772174
Step 1 took 4876ms
Step 2 took 2675ms
********** Factor found in step 2: 41119327973436033475483754806134272837
Found probable prime factor of 38 digits: 41119327973436033475483754806134272837
Composite cofactor 15672543210355221701053940350577676484197328922241828151784149179051334607839580596202241048609582134533477776622521732064531 has 125 digits

(58·10¹⁰⁶+23)/9 = 6(4)₁₀₅7_<107> = 492161744461753_<15> · C93

C93 = P35 · P58

P35 = 78129326361730982026375097231768957_<35>

P58 = 1675959621960563483941991874954435017512192924461523251107_<58>

Number: 64447_106
N=130941596273240143468946640593072846211856885990677267608981904319231734474929512919318485399
  ( 93 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=78129326361730982026375097231768957 (pp35)
 r2=1675959621960563483941991874954435017512192924461523251107 (pp58)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.43 hours.
Scaled time: 1.01 units (timescale=2.378).
Factorization parameters were as follows:
n: 130941596273240143468946640593072846211856885990677267608981904319231734474929512919318485399
m: 1000000000000000000000
deg: 5
c5: 580
c0: 23
skew: 0.52
type: snfs
lss: 1
rlim: 280000
alim: 280000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 280000/280000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [140000, 260001)
Primes: RFBsize:24432, AFBsize:24500, largePrimes:879266 encountered
Relations: rels:775786, finalFF:56964
Max relations in full relation-set: 28
Initial matrix: 48999 x 56964 with sparse part having weight 2637228.
Pruned matrix : 46847 x 47155 with weight 1733764.
Total sieving time: 0.41 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,280000,280000,25,25,44,44,2.2,2.2,20000
total time: 0.43 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356)
Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(58·10¹⁷⁵+23)/9 = 6(4)₁₇₄7_<176> = 1613 · 35656160338682906683_<20> · 1247169141570102577601527931_<28> · 1096361019585145532582908854881_<31> · C96

C96 = P47 · P50

P47 = 14983018931158829173921366367260641067839096419_<47>

P50 = 54693821851703361473715645811927745590131721657777_<50>

Number: 64447_175
N=819478568221499914100326001606299190096919170281909322951110135326279607201011575509404424200563
  ( 96 digits)
Divisors found:
 r1=14983018931158829173921366367260641067839096419
 r2=54693821851703361473715645811927745590131721657777
Version: 
Total time: 1.73 hours.
Scaled time: 4.14 units (timescale=2.389).
Factorization parameters were as follows:
name: 64447_175
n: 819478568221499914100326001606299190096919170281909322951110135326279607201011575509404424200563
skew: 1272.92
# norm 1.92e+13
c5: 558540
c4: 521847935
c3: -5408470572471
c2: 351181997744970
c1: 2401135397826069759
c0: 347351341918533091555
# alpha -5.04
Y1: 1132506419
Y0: -1079683784185786326
# Murphy_E 5.04e-09
# M 584362212936005472064082310212869558798949791281506276000328577915598457378327795135603722194649
type: gnfs
rlim: 800000
alim: 800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 40000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [400000, 760001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3757091
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 133248 x 133496
Polynomial selection time: 0.10 hours.
Total sieving time: 1.42 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
gnfs,95,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,800000,800000,26,26,48,48,2.5,2.5,40000
total time: 1.73 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672356)
Calibrating delay using timer specific routine.. 5344.52 BogoMIPS (lpj=2672263)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

Jul 13, 2009 (5th)

By Dmitry Domanov / GGNFS/msieve 1.41, ECMNET / Jul 13, 2009

(58·10¹³⁵+23)/9 = 6(4)₁₃₄7_<136> = 3² · 7 · C135

C135 = P35 · P48 · P53

P35 = 23082255542566823599333086556290313_<35>

P48 = 186979259626794060686307795753842713194685315639_<48>

P53 = 23701359305376003078608706474526261487024092056393967_<53>

N=102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292769
  ( 135 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=23082255542566823599333086556290313 (pp35)
 r2=186979259626794060686307795753842713194685315639 (pp48)
 r3=23701359305376003078608706474526261487024092056393967 (pp53)
Version: Msieve v. 1.41
Total time: 3.57 hours.
Scaled time: 7.10 units (timescale=1.988).
Factorization parameters were as follows:
n: 102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292768959435626102292769
m: 1000000000000000000000000000
deg: 5
c5: 58
c0: 23
skew: 0.83
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1340001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 221572 x 221820
Total sieving time: 3.39 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 3.57 hours.
 --------- CPU info (if available) ----------

(58·10¹⁸⁷+23)/9 = 6(4)₁₈₆7_<188> = 19 · C187

C187 = P39 · P149

P39 = 191379776483330109719074784422593962641_<39>

P149 = 17722942976644742493298788382265098427947056575301551556533727688497872316694355856538018670950859864388326426079285337993714319660444511908472818293_<149>

C187=P39*P149
C187=191379776483330109719074784422593962641<39>*17722942976644742493298788382265098427947056575301551556533727688497872316694355856538018670950859864388326426079285337993714319660444511908472818293<149>

(58·10¹⁵⁴+23)/9 = 6(4)₁₅₃7_<155> = 2221 · 64282310843_<11> · C141

C141 = P48 · P93

P48 = 826950947036232072542160696882965155619752449697_<48>

P93 = 545840424644446244851714823114328414970104900490414450438285896386706980952189028867721389217_<93>

N=451383256090383890332880823304054936956210199597621515127139018576080529748946023299415520701134993942877093671512974234181514772719750717249
  ( 141 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=826950947036232072542160696882965155619752449697 (pp48)
 r2=545840424644446244851714823114328414970104900490414450438285896386706980952189028867721389217 (pp93)
Version: Msieve v. 1.41
Total time: 19.28 hours.
Scaled time: 38.21 units (timescale=1.982).
Factorization parameters were as follows:
n: 451383256090383890332880823304054936956210199597621515127139018576080529748946023299415520701134993942877093671512974234181514772719750717249
m: 10000000000000000000000000000000
deg: 5
c5: 29
c0: 115
skew: 1.32
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 531694 x 531942
Total sieving time: 18.65 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.41 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 19.28 hours.
 --------- CPU info (if available) ----------

Jul 13, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jul 13, 2009

(14·10¹⁸²+1)/3 = 4(6)₁₈₁7_<183> = 71 · 359 · C179

C179 = P80 · P99

P80 = 99337268011377573858694433257182813159834985248138871718472604050896795517134809_<80>

P99 = 184306975295123807994275531879649282427027278526009180015853910534954578635427995339599927648804467_<99>

Number: n
N=18308551401258059032000732342056050322361280029293682242012894451201171747289680515778048046869891587220631121921874795663488825244876874991826539553009795074999673061582120391803
  ( 179 digits)
SNFS difficulty: 185 digits.
Divisors found:

Mon Jul 13 22:15:46 2009  prp80 factor: 99337268011377573858694433257182813159834985248138871718472604050896795517134809
Mon Jul 13 22:15:46 2009  prp99 factor: 184306975295123807994275531879649282427027278526009180015853910534954578635427995339599927648804467
Mon Jul 13 22:15:46 2009  elapsed time 02:40:38 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 150.06 hours.
Scaled time: 397.50 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_4_6_181_7
n: 18308551401258059032000732342056050322361280029293682242012894451201171747289680515778048046869891587220631121921874795663488825244876874991826539553009795074999673061582120391803
m: 5000000000000000000000000000000000000
deg: 5
c5: 56
c0: 125
skew: 1.17
type: snfs
lss: 1
rlim: 8600000
alim: 8600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8600000/8600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4300000, 6900977)
Primes: RFBsize:577439, AFBsize:576914, largePrimes:20806339 encountered
Relations: rels:20705108, finalFF:1024227
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1805413 hash collisions in 21853565 relations
Msieve: matrix is 1379817 x 1380065 (373.7 MB)

Total sieving time: 149.50 hours.
Total relation processing time: 0.56 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,8600000,8600000,28,28,56,56,2.5,2.5,100000
total time: 150.06 hours.
 --------- CPU info (if available) ----------

(58·10¹¹¹+23)/9 = 6(4)₁₁₀7_<112> = 3 · 7² · 32789 · 48039247 · 577672633 · C89

C89 = P38 · P51

P38 = 50196008649124066760669118985278755117_<38>

P51 = 959826657005513846552635296036664574714149430138227_<51>

Number: n
N=48179467176708612066383883797455042200586297273188553625101637577681136825893259793557559
  ( 89 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=50196008649124066760669118985278755117 (pp38)
 r2=959826657005513846552635296036664574714149430138227 (pp51)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.65 hours.
Scaled time: 1.18 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_4_110_7
n: 48179467176708612066383883797455042200586297273188553625101637577681136825893259793557559
m: 10000000000000000000000
deg: 5
c5: 580
c0: 23
skew: 0.52
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 10000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [250000, 360001)
Primes: RFBsize:41538, AFBsize:41462, largePrimes:2818335 encountered
Relations: rels:2338662, finalFF:106501
Max relations in full relation-set: 48
Initial matrix: 83067 x 106501 with sparse part having weight 7902956.
Pruned matrix : 75721 x 76200 with weight 3818881.
Total sieving time: 0.57 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.02 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.3,2.3,50000
total time: 0.65 hours.
 --------- CPU info (if available) ----------

Jul 13, 2009 (3rd)

By Sinkiti Sibata / Msieve / Jul 13, 2009

3·10¹⁶⁹-1 = 2(9)₁₆₉_<170> = 29 · 257 · 1187 · 893281 · 162352619114966156197_<21> · C137

C137 = P55 · P83

P55 = 2228251805235709353313536175233325312147783871786905403_<55>

P83 = 10493678433883386533453073734793889071910451026636427224419520005990497132630462879_<83>

Number: 29999_169
N=23382557913863687360210358549889939699253493723541318867971867107182684122332981322256389039762608813026488643802138025103343450876035237
  ( 137 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=2228251805235709353313536175233325312147783871786905403 (pp55)
 r2=10493678433883386533453073734793889071910451026636427224419520005990497132630462879 (pp83)
Version: Msieve-1.40
Total time: 59.94 hours.
Scaled time: 154.35 units (timescale=2.575).
Factorization parameters were as follows:
name: 29999_169
n: 23382557913863687360210358549889939699253493723541318867971867107182684122332981322256389039762608813026488643802138025103343450876035237
m: 10000000000000000000000000000000000
deg: 5
c5: 3
c0: -10
skew: 1.27
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 4850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 871097 x 871345
Total sieving time: 57.67 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.72 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 59.94 hours.
 --------- CPU info (if available) ----------

(58·10¹¹⁴+23)/9 = 6(4)₁₁₃7_<115> = 3 · C115

C115 = P37 · P78

P37 = 4335063118793507391728654777432128393_<37>

P78 = 495528689959651579368664634248240159079415334936580114911985607106035232953293_<78>

Number: 64447_114
N=2148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149
  ( 115 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=4335063118793507391728654777432128393 (pp37)
 r2=495528689959651579368664634248240159079415334936580114911985607106035232953293 (pp78)
Version: Msieve-1.40
Total time: 1.16 hours.
Scaled time: 2.98 units (timescale=2.564).
Factorization parameters were as follows:
name: 64447_114
n: 2148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149
m: 100000000000000000000000
deg: 5
c5: 29
c0: 115
skew: 1.32
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [305000, 505001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 63265 x 63492
Total sieving time: 1.13 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116.000,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000
total time: 1.16 hours.
 --------- CPU info (if available) ----------

(58·10¹²⁵+23)/9 = 6(4)₁₂₄7_<126> = C126

C126 = P45 · P81

P45 = 974736791340018918589686620786549510151975781_<45>

P81 = 661147142664528713748930535458851545304856790693588371526999971594298072964481587_<81>

Number: 64447_125
N=644444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447
  ( 126 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=974736791340018918589686620786549510151975781 (pp45)
 r2=661147142664528713748930535458851545304856790693588371526999971594298072964481587 (pp81)
Version: Msieve-1.40
Total time: 2.33 hours.
Scaled time: 5.98 units (timescale=2.564).
Factorization parameters were as follows:
name: 64447_125
n: 644444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447
m: 10000000000000000000000000
deg: 5
c5: 58
c0: 23
skew: 0.83
type: snfs
lss: 1
rlim: 910000
alim: 910000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 910000/910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [455000, 805001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 131857 x 132089
Total sieving time: 2.24 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000
total time: 2.33 hours.
 --------- CPU info (if available) ----------

(58·10¹³²+23)/9 = 6(4)₁₃₁7_<133> = 3 · 17 · 83 · 107 · 113 · 9377839 · 54324469205731_<14> · 131229719259439253_<18> · C88

C88 = P40 · P48

P40 = 4760339406616587863684474719485370271377_<40>

P48 = 395645847713421982074206853379199386478310056581_<48>

Mon Jul 13 17:31:00 2009  Msieve v. 1.41
Mon Jul 13 17:31:00 2009  random seeds: 9c99e448 049c84d4
Mon Jul 13 17:31:00 2009  factoring 1883408519934428084391724377309822647511270420467472934806096807678123332226068194782037 (88 digits)
Mon Jul 13 17:31:01 2009  searching for 15-digit factors
Mon Jul 13 17:31:02 2009  commencing quadratic sieve (88-digit input)
Mon Jul 13 17:31:02 2009  using multiplier of 1
Mon Jul 13 17:31:02 2009  using 32kb Intel Core sieve core
Mon Jul 13 17:31:02 2009  sieve interval: 24 blocks of size 32768
Mon Jul 13 17:31:02 2009  processing polynomials in batches of 9
Mon Jul 13 17:31:02 2009  using a sieve bound of 1507487 (57333 primes)
Mon Jul 13 17:31:02 2009  using large prime bound of 120598960 (26 bits)
Mon Jul 13 17:31:02 2009  using double large prime bound of 351899202753840 (42-49 bits)
Mon Jul 13 17:31:02 2009  using trial factoring cutoff of 49 bits
Mon Jul 13 17:31:02 2009  polynomial 'A' values have 11 factors
Mon Jul 13 18:26:51 2009  57588 relations (15601 full + 41987 combined from 609488 partial), need 57429
Mon Jul 13 18:26:52 2009  begin with 625089 relations
Mon Jul 13 18:26:53 2009  reduce to 139946 relations in 10 passes
Mon Jul 13 18:26:53 2009  attempting to read 139946 relations
Mon Jul 13 18:26:54 2009  recovered 139946 relations
Mon Jul 13 18:26:54 2009  recovered 119557 polynomials
Mon Jul 13 18:26:55 2009  attempting to build 57588 cycles
Mon Jul 13 18:26:55 2009  found 57588 cycles in 6 passes
Mon Jul 13 18:26:55 2009  distribution of cycle lengths:
Mon Jul 13 18:26:55 2009     length 1 : 15601
Mon Jul 13 18:26:55 2009     length 2 : 10874
Mon Jul 13 18:26:55 2009     length 3 : 10150
Mon Jul 13 18:26:55 2009     length 4 : 7660
Mon Jul 13 18:26:55 2009     length 5 : 5469
Mon Jul 13 18:26:55 2009     length 6 : 3342
Mon Jul 13 18:26:55 2009     length 7 : 2101
Mon Jul 13 18:26:55 2009     length 9+: 2391
Mon Jul 13 18:26:55 2009  largest cycle: 17 relations
Mon Jul 13 18:26:55 2009  matrix is 57333 x 57588 (13.4 MB) with weight 3275321 (56.88/col)
Mon Jul 13 18:26:55 2009  sparse part has weight 3275321 (56.88/col)
Mon Jul 13 18:26:56 2009  filtering completed in 4 passes
Mon Jul 13 18:26:56 2009  matrix is 53263 x 53327 (12.5 MB) with weight 3057108 (57.33/col)
Mon Jul 13 18:26:56 2009  sparse part has weight 3057108 (57.33/col)
Mon Jul 13 18:26:56 2009  saving the first 48 matrix rows for later
Mon Jul 13 18:26:56 2009  matrix is 53215 x 53327 (8.0 MB) with weight 2418609 (45.35/col)
Mon Jul 13 18:26:56 2009  sparse part has weight 1776241 (33.31/col)
Mon Jul 13 18:26:56 2009  matrix includes 64 packed rows
Mon Jul 13 18:26:56 2009  using block size 21330 for processor cache size 1024 kB
Mon Jul 13 18:26:56 2009  commencing Lanczos iteration
Mon Jul 13 18:26:56 2009  memory use: 7.9 MB
Mon Jul 13 18:27:14 2009  lanczos halted after 843 iterations (dim = 53212)
Mon Jul 13 18:27:14 2009  recovered 14 nontrivial dependencies
Mon Jul 13 18:27:15 2009  prp40 factor: 4760339406616587863684474719485370271377
Mon Jul 13 18:27:15 2009  prp48 factor: 395645847713421982074206853379199386478310056581
Mon Jul 13 18:27:15 2009  elapsed time 00:56:15

Jul 13, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3 / Jul 13, 2009

(58·10¹⁷¹+23)/9 = 6(4)₁₇₀7_<172> = 3² · 7 · 163 · 229 · 43607 · 355636003 · 1269791928287_<13> · 111929378928377_<15> · C127

C127 = P29 · C98

P29 = 29987432328229516862586197167_<29>

C98 = [41461401722079143647924150625301340578093020537184821796736112311143710226687952818709906878188779_<98>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3348063929
Step 1 took 2525ms
Step 2 took 2580ms
********** Factor found in step 2: 29987432328229516862586197167
Found probable prime factor of 29 digits: 29987432328229516862586197167
Composite cofactor has 98 digits

(58·10¹⁷⁰+23)/9 = 6(4)₁₆₉7_<171> = 1153 · 2213 · 123493 · 466866407317_<12> · C148

C148 = P32 · P117

P32 = 19446241608838036363980356232313_<32>

P117 = 225270393946095807438626231453873038111507697639127097761464724268163034474733434977524246262956615989308890849723891_<117>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3684692784
Step 1 took 3013ms
Step 2 took 2936ms
********** Factor found in step 2: 19446241608838036363980356232313
Found probable prime factor of 32 digits: 19446241608838036363980356232313
Probable prime cofactor has 117 digits

Jul 13, 2009

Factorizations of 644...447 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jul 12, 2009 (3rd)

By Dmitry Domanov / ECMNET / Jul 12, 2009

2·10¹⁹⁵+9 = 2(0)₁₉₄9_<196> = 7 · 263 · 5309 · 376787 · 398925029 · C175

C175 = P45 · C130

P45 = 208929543907045046083316767984164355764039923_<45>

C130 = [6515930300278598936340223067286726695961677601878157142390817149184366337340674057734940096025365308355623172051113615953328308609_<130>]

C175=P45*C130
C175=208929543907045046083316767984164355764039923<45>6515930300278598936340223067286726695961677601878157142390817149184366337340674057734940096025365308355623172051113615953328308609<130>
B1: 3000000 sigma: 4163169800 (found in step 2)

Jul 12, 2009 (2nd)

By Wataru Sakai / Msieve / Jul 12, 2009

(49·10¹⁸⁴-13)/9 = 5(4)₁₈₃3_<185> = 107 · C183

C183 = P60 · P124

P60 = 108429772521892036019932427297734099076545943820349377756029_<60>

P124 = 4692683307900570769148796885419169826114104309020076727251929872520649206197793144002184678282254116463836283410737873023781_<124>

Number: 54443_184
N=508826583592938733125649013499480789200415368639667705088265835929387331256490134994807892004153686396677050882658359293873312564901349948078920041536863966770508826583592938733125649
  ( 183 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=108429772521892036019932427297734099076545943820349377756029
 r2=4692683307900570769148796885419169826114104309020076727251929872520649206197793144002184678282254116463836283410737873023781
Version: 
Total time: 345.65 hours.
Scaled time: 693.38 units (timescale=2.006).
Factorization parameters were as follows:
n: 508826583592938733125649013499480789200415368639667705088265835929387331256490134994807892004153686396677050882658359293873312564901349948078920041536863966770508826583592938733125649
m: 10000000000000000000000000000000000000
deg: 5
c5: 49
c0: -130
skew: 1.22
type: snfs
lss: 1
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 7800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1552391 x 1552639
Total sieving time: 345.65 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000
total time: 345.65 hours.
 --------- CPU info (if available) ----------

(53·10¹⁸¹-71)/9 = 5(8)₁₈₀1_<182> = 3 · 2879 · C178

C178 = P53 · P126

P53 = 24081340990091404175861057053153272486112035432620191_<53>

P126 = 283132532303703333726830050085836989037702953632307132314359052811450789821802506909621984361284526068569973287653670838199643_<126>

Number: 58881_181
N=6818211055793549715050236064477120399315605984588270104074202719565692820295112757773403831062740406262462532000566040163122483372570208277050930750131861628909214876564650791813
  ( 178 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=24081340990091404175861057053153272486112035432620191
 r2=283132532303703333726830050085836989037702953632307132314359052811450789821802506909621984361284526068569973287653670838199643
Version: 
Total time: 303.42 hours.
Scaled time: 610.18 units (timescale=2.011).
Factorization parameters were as follows:
n: 6818211055793549715050236064477120399315605984588270104074202719565692820295112757773403831062740406262462532000566040163122483372570208277050930750131861628909214876564650791813
m: 1000000000000000000000000000000000000
deg: 5
c5: 530
c0: -71
skew: 0.67
type: snfs
lss: 1
rlim: 7800000
alim: 7800000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 7800000/7800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3900000, 7500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1382118 x 1382366
Total sieving time: 303.42 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,7800000,7800000,28,28,53,53,2.5,2.5,100000
total time: 303.42 hours.
 --------- CPU info (if available) ----------

7·10¹⁹⁴+3 = 7(0)₁₉₃3_<195> = 37 · 89 · C192

C192 = P48 · P144

P48 = 711549423651204178804703845878926067199337895119_<48>

P144 = 298745407724036587596846553046331517575087722040410770709987309288456174674024401314163963624147750872498764458224098031975479126729720370314609_<144>

Number: 70003_194
N=212572122684482235044032796841785605830549650774369875493470999088976617066504706954145156392347403583358639538414819313695718190100212572122684482235044032796841785605830549650774369875493471
  ( 192 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=711549423651204178804703845878926067199337895119
 r2=298745407724036587596846553046331517575087722040410770709987309288456174674024401314163963624147750872498764458224098031975479126729720370314609
Version: 
Total time: 644.03 hours.
Scaled time: 1297.07 units (timescale=2.014).
Factorization parameters were as follows:
n: 212572122684482235044032796841785605830549650774369875493470999088976617066504706954145156392347403583358639538414819313695718190100212572122684482235044032796841785605830549650774369875493471
m: 1000000000000000000000000000000000000000
deg: 5
c5: 7
c0: 30
skew: 1.34
type: snfs
lss: 1
rlim: 12900000
alim: 12900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 12900000/12900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6450000, 13550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2257343 x 2257591
Total sieving time: 644.03 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,12900000,12900000,28,28,55,55,2.5,2.5,100000
total time: 644.03 hours.
 --------- CPU info (if available) ----------

Jul 12, 2009

By Robert Backstrom / GGNFS, Msieve / Jul 12, 2009

(47·10¹⁸¹+43)/9 = 5(2)₁₈₀7_<182> = 3 · 19 · 53 · 67 · C177

C177 = P67 · P110

P67 = 3094835724684298386572815120341122852673816403442738454046575319003_<67>

P110 = 83366624838085431210186778249034161471498200759267403583313199233944387222928835815581162767824210168479063087_<110>

Number: n
N=258006008795260155143953629183883078264201446700075700060878439096583725969073313779771560381914766891571053482449827437896032361638788293992906481604994996330276236603586942261
  ( 177 digits)
SNFS difficulty: 182 digits.
Divisors found:

Sun Jul 12 05:10:16 2009  prp67 factor: 3094835724684298386572815120341122852673816403442738454046575319003
Sun Jul 12 05:10:16 2009  prp110 factor: 83366624838085431210186778249034161471498200759267403583313199233944387222928835815581162767824210168479063087
Sun Jul 12 05:10:16 2009  elapsed time 02:20:56 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 173.15 hours.
Scaled time: 449.34 units (timescale=2.595).
Factorization parameters were as follows:
name: KA_5_2_180_7
n: 258006008795260155143953629183883078264201446700075700060878439096583725969073313779771560381914766891571053482449827437896032361638788293992906481604994996330276236603586942261
m: 1000000000000000000000000000000000000
deg: 5
c5: 470
c0: 43
skew: 0.62
type: snfs
lss: 1
rlim: 7800000
alim: 7800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 7800000/7800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [3900000, 6919261)
Primes: RFBsize:527154, AFBsize:526275, largePrimes:21057951 encountered
Relations: rels:21147738, finalFF:896232
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2222770 hash collisions in 23551262 relations
Msieve: matrix is 1239049 x 1239297 (334.1 MB)

Total sieving time: 172.51 hours.
Total relation processing time: 0.64 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,7800000,7800000,28,28,56,56,2.5,2.5,100000
total time: 173.15 hours.
 --------- CPU info (if available) ----------

Jul 11, 2009

By Dmitry Domanov / ECMNET / Jul 11, 2009

(16·10²⁰³-7)/9 = 1(7)₂₀₃_<204> = 3² · 31 · 181 · 433 · 1262321 · 131918527086451153_<18> · 16900507086168024103951_<23> · C151

C151 = P43 · P109

P43 = 1984302645679619731376987460864431244810793_<43>

P109 = 1455873198199023485232568455687174282481878946320103856260317493093157285145974619345505379447385520317097309_<109>

C151=P43*P109
C151=1984302645679619731376987460864431244810793<43>*1455873198199023485232568455687174282481878946320103856260317493093157285145974619345505379447385520317097309<109>

(16·10²²⁹-7)/9 = 1(7)₂₂₉_<230> = 37517 · 90221661740474669_<17> · 332893959945287358687593_<24> · C185

C185 = P40 · P145

P40 = 7535122564049591986328629082758999170461_<40>

P145 = 2093834309762269347842472452170929506605387419506516970926981601603119887876945670672882976345795440384666710964898063989946892665696919631391413_<145>

C185=P40*P145
C185=7535122564049591986328629082758999170461<40>*2093834309762269347842472452170929506605387419506516970926981601603119887876945670672882976345795440384666710964898063989946892665696919631391413<145>

2·10¹⁸⁹+9 = 2(0)₁₈₈9_<190> = 7 · 601769500435849_<15> · 262389630418130593543987483_<27> · C148

C148 = P30 · P118

P30 = 231192776199581655479023863569_<30>

P118 = 7826739065615167308219291506990415678354983695078282263339825293001255086110103549843948541000279804194903492659561669_<118>

С148=P30*P118
C148=231192776199581655479023863569<30>*7826739065615167308219291506990415678354983695078282263339825293001255086110103549843948541000279804194903492659561669<118>

2·10¹⁷⁹+9 = 2(0)₁₇₈9_<180> = 71174055487_<11> · C169

C169 = P34 · P136

P34 = 1456349062809436989167539279826921_<34>

P136 = 1929491201087555608892709636519787278782502149025926069860554864817462889929790905160468424725930351070637487831883300700726830778091167_<136>

C169=P34*P136
C169=1456349062809436989167539279826921<34>*1929491201087555608892709636519787278782502149025926069860554864817462889929790905160468424725930351070637487831883300700726830778091167<136>

2·10¹⁷⁸+9 = 2(0)₁₇₇9_<179> = 11 · 41 · 2011 · 2559497 · C166

C166 = P40 · P127

P40 = 3607936990392616468032632672857678386811_<40>

P127 = 2387964213017067719981893822914230918809066561665386940290151207986766746538763247553089857459596549258060136674347450493027907_<127>

C166=P40*P127
C166=3607936990392616468032632672857678386811<40>*2387964213017067719981893822914230918809066561665386940290151207986766746538763247553089857459596549258060136674347450493027907<127>

Jul 10, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jul 10, 2009

(2·10¹⁹⁸+61)/9 = (2)₁₉₇9_<198> = 7 · 29 · 2083 · C192

C192 = P37 · P155

P37 = 5689948804110787089471594196039551347_<37>

P155 = 92362104428415880975825131451967519518894020450568859764644147577928065166772145782496981113824330367418104744872686986693051596921000832713247614731925143_<155>

C192=P37*P155
C192=5689948804110787089471594196039551347<37>*92362104428415880975825131451967519518894020450568859764644147577928065166772145782496981113824330367418104744872686986693051596921000832713247614731925143<155>

(2·10¹⁹⁷+43)/9 = (2)₁₉₆7_<197> = 3 · 157 · C194

C194 = P40 · C154

P40 = 4830297726724849664432111078077719825109_<40>

C154 = [9767708238695844640979066239202354443960649371290018537019416802234300736463213550385464206052611393709860351340957430875026878358838457653530043363189393_<154>]

C194=P40*C154
C194=4830297726724849664432111078077719825109<40>*9767708238695844640979066239202354443960649371290018537019416802234300736463213550385464206052611393709860351340957430875026878358838457653530043363189393<154>

Jul 10, 2009

By Robert Backstrom / GGNFS, Msieve / Jul 10, 2009

(89·10¹⁸¹+1)/9 = 9(8)₁₈₀9_<182> = 3⁵ · 11 · C179

C179 = P44 · P55 · P81

P44 = 40086795901480525822645927616850833828200151_<44>

P55 = 4401347710531047444920804384243769376286461546304783503_<55>

P81 = 209682175547011199524064175561135108760786096939706109059852576036837707179292081_<81>

Number: n
N=36995469094234526333291765390530822629588061686827118925884357983123415222180654279419711518476950575716007814773246872012304111069543168308600407365839464604896703662135760901193
  ( 179 digits)
SNFS difficulty: 184 digits.
Divisors found:

Fri Jul 10 06:11:59 2009  prp44 factor: 40086795901480525822645927616850833828200151
Fri Jul 10 06:11:59 2009  prp55 factor: 4401347710531047444920804384243769376286461546304783503
Fri Jul 10 06:11:59 2009  prp81 factor: 209682175547011199524064175561135108760786096939706109059852576036837707179292081
Fri Jul 10 06:11:59 2009  elapsed time 02:39:51 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 141.03 hours.
Scaled time: 375.14 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_9_8_180_9
n: 36995469094234526333291765390530822629588061686827118925884357983123415222180654279419711518476950575716007814773246872012304111069543168308600407365839464604896703662135760901193
m: 2000000000000000000000000000000000000
deg: 5
c5: 445
c0: 16
skew: 0.51
type: snfs
lss: 1
rlim: 8200000
alim: 8200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8200000/8200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4100000, 6500029)
Primes: RFBsize:552319, AFBsize:551788, largePrimes:20639948 encountered
Relations: rels:20319258, finalFF:1160014
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1760100 hash collisions in 21647752 relations
Msieve: matrix is 1348819 x 1349067 (365.5 MB)

Total sieving time: 140.52 hours.
Total relation processing time: 0.51 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,184,5,0,0,0,0,0,0,0,0,8200000,8200000,28,28,56,56,2.5,2.5,100000
total time: 141.03 hours.
 --------- CPU info (if available) ----------

Jul 9, 2009

By Dmitry Domanov / GGNFS/msieve 1.42beta, ECMNET / Jul 9, 2009

(10²²²+17)/9 = (1)₂₂₁3_<222> = C222

C222 = P51 · P51 · P120

P51 = 551004498127928469834445340613015226657914601778213_<51>

P51 = 676677276408056094567102599764052489094573413056051_<51>

P120 = 298003080664845879339921984943623072483939555335465806206783935206506443967104530715870831039336178009293998396643169751_<120>

Sieving took about 150  cpu-days on various cpu's. Using siever 14e for sieving on rational side in 5M-43M for 57.7M relations.
Postprocessing took 6 days on Xeon E5430 x 1 thread. Factors found in 6th dependency: C222=P51 ・ P51 ・ P120. 
I'm very surprised that this split is similar to Serge Batalov's С222=P55 ・ P55 ・ P114
Postprocessing log below.

=================================
Wed Jul 01 14:11:35 2009  Msieve v. 1.42
Wed Jul 01 14:11:35 2009  random seeds: f8ebc210 61bba000
Wed Jul 01 14:11:35 2009  factoring 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113 (222 digits)
Wed Jul 01 14:11:37 2009  searching for 15-digit factors
Wed Jul 01 14:11:41 2009  commencing number field sieve (222-digit input)
Wed Jul 01 14:11:41 2009  R0: -10000000000000000000000000000000000000
Wed Jul 01 14:11:41 2009  R1:  1
Wed Jul 01 14:11:41 2009  A0:  17
Wed Jul 01 14:11:41 2009  A1:  0
Wed Jul 01 14:11:41 2009  A2:  0
Wed Jul 01 14:11:41 2009  A3:  0
Wed Jul 01 14:11:41 2009  A4:  0
Wed Jul 01 14:11:41 2009  A5:  0
Wed Jul 01 14:11:41 2009  A6:  1
Wed Jul 01 14:11:41 2009  skew 1.60, size 6.533884e-011, alpha 1.099275, combined = 2.482264e-012
Wed Jul 01 14:11:41 2009  
Wed Jul 01 14:11:41 2009  commencing relation filtering
Wed Jul 01 14:11:41 2009  commencing duplicate removal, pass 1
...
<errors skipped>
...
Wed Jul 01 14:20:30 2009  found 12936357 hash collisions in 57701157 relations
Wed Jul 01 14:20:56 2009  added 9 free relations
Wed Jul 01 14:20:56 2009  commencing duplicate removal, pass 2
Wed Jul 01 14:23:12 2009  found 11910252 duplicates and 45790914 unique relations
Wed Jul 01 14:23:12 2009  memory use: 298.4 MB
Wed Jul 01 14:23:12 2009  reading rational ideals above 42926080
Wed Jul 01 14:23:12 2009  reading algebraic ideals above 42926080
Wed Jul 01 14:23:12 2009  commencing singleton removal, pass 1
Wed Jul 01 14:30:55 2009  relations with 0 large ideals: 1510351
Wed Jul 01 14:30:55 2009  relations with 1 large ideals: 6811639
Wed Jul 01 14:30:55 2009  relations with 2 large ideals: 14796919
Wed Jul 01 14:30:55 2009  relations with 3 large ideals: 15230713
Wed Jul 01 14:30:55 2009  relations with 4 large ideals: 6426946
Wed Jul 01 14:30:55 2009  relations with 5 large ideals: 11119
Wed Jul 01 14:30:55 2009  relations with 6 large ideals: 0
Wed Jul 01 14:30:55 2009  relations with 7+ large ideals: 1003227
Wed Jul 01 14:30:55 2009  45790914 relations and about 35545167 large ideals
Wed Jul 01 14:30:55 2009  commencing singleton removal, pass 2
Wed Jul 01 14:38:32 2009  found 10279629 singletons
Wed Jul 01 14:38:32 2009  current dataset: 35511285 relations and about 24146004 large ideals
Wed Jul 01 14:38:32 2009  commencing singleton removal, pass 3
Wed Jul 01 14:44:37 2009  found 2264708 singletons
Wed Jul 01 14:44:37 2009  current dataset: 33246577 relations and about 21818327 large ideals
Wed Jul 01 14:44:37 2009  commencing singleton removal, pass 4
Wed Jul 01 14:50:24 2009  found 493843 singletons
Wed Jul 01 14:50:24 2009  current dataset: 32752734 relations and about 21321359 large ideals
Wed Jul 01 14:50:24 2009  commencing singleton removal, final pass
Wed Jul 01 14:56:34 2009  memory use: 542.2 MB
Wed Jul 01 14:56:34 2009  commencing in-memory singleton removal
Wed Jul 01 14:56:38 2009  begin with 32752734 relations and 26008754 unique ideals
Wed Jul 01 14:57:39 2009  reduce to 25669667 relations and 18602735 ideals in 15 passes
Wed Jul 01 14:57:39 2009  max relations containing the same ideal: 29
Wed Jul 01 14:57:47 2009  reading rational ideals above 720000
Wed Jul 01 14:57:47 2009  reading algebraic ideals above 720000
Wed Jul 01 14:57:47 2009  commencing singleton removal, final pass
Wed Jul 01 15:04:42 2009  keeping 21666592 ideals with weight <= 20, new excess is 2133916
Wed Jul 01 15:05:28 2009  memory use: 695.6 MB
Wed Jul 01 15:05:28 2009  commencing in-memory singleton removal
Wed Jul 01 15:05:34 2009  begin with 25669677 relations and 21666592 unique ideals
Wed Jul 01 15:06:28 2009  reduce to 25657866 relations and 21654721 ideals in 10 passes
Wed Jul 01 15:06:28 2009  max relations containing the same ideal: 20
Wed Jul 01 15:06:56 2009  removing 3005017 relations and 2605017 ideals in 400000 cliques
Wed Jul 01 15:06:58 2009  commencing in-memory singleton removal
Wed Jul 01 15:07:03 2009  begin with 22652849 relations and 21654721 unique ideals
Wed Jul 01 15:07:46 2009  reduce to 22377318 relations and 18768304 ideals in 9 passes
Wed Jul 01 15:07:46 2009  max relations containing the same ideal: 20
Wed Jul 01 15:08:10 2009  removing 2232892 relations and 1832892 ideals in 400000 cliques
Wed Jul 01 15:08:12 2009  commencing in-memory singleton removal
Wed Jul 01 15:08:16 2009  begin with 20144426 relations and 18768304 unique ideals
Wed Jul 01 15:08:54 2009  reduce to 19976966 relations and 16764856 ideals in 9 passes
Wed Jul 01 15:08:54 2009  max relations containing the same ideal: 20
Wed Jul 01 15:09:16 2009  removing 1985426 relations and 1585426 ideals in 400000 cliques
Wed Jul 01 15:09:17 2009  commencing in-memory singleton removal
Wed Jul 01 15:09:21 2009  begin with 17991540 relations and 16764856 unique ideals
Wed Jul 01 15:09:51 2009  reduce to 17842569 relations and 15027706 ideals in 8 passes
Wed Jul 01 15:09:51 2009  max relations containing the same ideal: 20
Wed Jul 01 15:10:10 2009  removing 1626832 relations and 1287312 ideals in 339520 cliques
Wed Jul 01 15:10:11 2009  commencing in-memory singleton removal
Wed Jul 01 15:10:15 2009  begin with 16215737 relations and 15027706 unique ideals
Wed Jul 01 15:10:41 2009  reduce to 16105168 relations and 13627906 ideals in 8 passes
Wed Jul 01 15:10:41 2009  max relations containing the same ideal: 20
Wed Jul 01 15:11:00 2009  relations with 0 large ideals: 188734
Wed Jul 01 15:11:00 2009  relations with 1 large ideals: 934969
Wed Jul 01 15:11:00 2009  relations with 2 large ideals: 2781036
Wed Jul 01 15:11:00 2009  relations with 3 large ideals: 4487783
Wed Jul 01 15:11:00 2009  relations with 4 large ideals: 4224982
Wed Jul 01 15:11:00 2009  relations with 5 large ideals: 2362319
Wed Jul 01 15:11:00 2009  relations with 6 large ideals: 790965
Wed Jul 01 15:11:00 2009  relations with 7+ large ideals: 334380
Wed Jul 01 15:11:00 2009  commencing 2-way merge
Wed Jul 01 15:11:25 2009  reduce to 10513011 relation sets and 8035749 unique ideals
Wed Jul 01 15:11:25 2009  commencing full merge
Wed Jul 01 15:14:22 2009  memory use: 668.7 MB
Wed Jul 01 15:14:24 2009  found 5321363 cycles, need 4983949
Wed Jul 01 15:14:25 2009  weight of 4983949 cycles is about 348959609 (70.02/cycle)
Wed Jul 01 15:14:25 2009  distribution of cycle lengths:
Wed Jul 01 15:14:25 2009  1 relations: 646624
Wed Jul 01 15:14:25 2009  2 relations: 592897
Wed Jul 01 15:14:25 2009  3 relations: 585016
Wed Jul 01 15:14:25 2009  4 relations: 540378
Wed Jul 01 15:14:25 2009  5 relations: 485992
Wed Jul 01 15:14:25 2009  6 relations: 431904
Wed Jul 01 15:14:25 2009  7 relations: 374722
Wed Jul 01 15:14:25 2009  8 relations: 322521
Wed Jul 01 15:14:25 2009  9 relations: 271731
Wed Jul 01 15:14:25 2009  10+ relations: 732164
Wed Jul 01 15:14:25 2009  heaviest cycle: 17 relations
Wed Jul 01 15:14:27 2009  commencing cycle optimization
Wed Jul 01 15:14:40 2009  start with 26812971 relations
Wed Jul 01 15:15:54 2009  pruned 764649 relations
Wed Jul 01 15:15:54 2009  memory use: 702.9 MB
Wed Jul 01 15:15:54 2009  distribution of cycle lengths:
Wed Jul 01 15:15:54 2009  1 relations: 646624
Wed Jul 01 15:15:54 2009  2 relations: 608083
Wed Jul 01 15:15:54 2009  3 relations: 609511
Wed Jul 01 15:15:54 2009  4 relations: 558036
Wed Jul 01 15:15:54 2009  5 relations: 502517
Wed Jul 01 15:15:54 2009  6 relations: 441832
Wed Jul 01 15:15:54 2009  7 relations: 381306
Wed Jul 01 15:15:54 2009  8 relations: 323543
Wed Jul 01 15:15:54 2009  9 relations: 269057
Wed Jul 01 15:15:54 2009  10+ relations: 643440
Wed Jul 01 15:15:54 2009  heaviest cycle: 17 relations
Wed Jul 01 15:16:18 2009  RelProcTime: 3714
Wed Jul 01 15:16:18 2009  
Wed Jul 01 15:16:18 2009  commencing linear algebra
Wed Jul 01 15:16:34 2009  read 4983949 cycles
Wed Jul 01 15:16:48 2009  cycles contain 14619558 unique relations
Wed Jul 01 15:24:04 2009  read 14619558 relations
Wed Jul 01 15:24:44 2009  using 20 quadratic characters above 536870730
Wed Jul 01 15:26:02 2009  building initial matrix
Wed Jul 01 15:30:16 2009  memory use: 1620.3 MB
Wed Jul 01 15:30:38 2009  read 4983949 cycles
Wed Jul 01 15:34:16 2009  matrix is 4983422 x 4983949 (1411.7 MB) with weight 433789956 (87.04/col)
Wed Jul 01 15:34:16 2009  sparse part has weight 335172179 (67.25/col)
Wed Jul 01 15:37:37 2009  filtering completed in 3 passes
Wed Jul 01 15:37:39 2009  matrix is 4960805 x 4961005 (1408.5 MB) with weight 432669651 (87.21/col)
Wed Jul 01 15:37:39 2009  sparse part has weight 334512750 (67.43/col)
Wed Jul 01 15:38:37 2009  read 4961005 cycles
Wed Jul 01 16:11:38 2009  matrix is 4960805 x 4961005 (1408.5 MB) with weight 432669651 (87.21/col)
Wed Jul 01 16:11:38 2009  sparse part has weight 334512750 (67.43/col)
Wed Jul 01 16:11:39 2009  saving the first 48 matrix rows for later
Wed Jul 01 16:11:42 2009  matrix is 4960757 x 4961005 (1336.0 MB) with weight 344782488 (69.50/col)
Wed Jul 01 16:11:42 2009  sparse part has weight 320465925 (64.60/col)
Wed Jul 01 16:11:42 2009  matrix includes 64 packed rows
Wed Jul 01 16:11:42 2009  using block size 65536 for processor cache size 6144 kB
Wed Jul 01 16:12:22 2009  commencing Lanczos iteration
Wed Jul 01 16:12:22 2009  memory use: 1379.2 MB
Tue Jul 07 06:20:38 2009  lanczos halted after 78450 iterations (dim = 4960755)
Tue Jul 07 06:21:31 2009  recovered 34 nontrivial dependencies
Tue Jul 07 06:21:51 2009  BLanczosTime: 486333
Tue Jul 07 06:21:51 2009  
Tue Jul 07 06:21:51 2009  commencing square root phase
Tue Jul 07 06:21:51 2009  reading relations for dependency 1
Tue Jul 07 06:22:29 2009  read 2480662 cycles
Tue Jul 07 06:22:37 2009  cycles contain 8947738 unique relations
Tue Jul 07 06:37:31 2009  read 8947738 relations
Tue Jul 07 06:38:47 2009  multiplying 7302868 relations
Tue Jul 07 07:01:05 2009  multiply complete, coefficients have about 177.09 million bits
Tue Jul 07 07:01:07 2009  initial square root is modulo 2265643
Tue Jul 07 07:30:25 2009  reading relations for dependency 2
Tue Jul 07 07:30:27 2009  read 2481818 cycles
Tue Jul 07 07:30:35 2009  cycles contain 8947960 unique relations
Tue Jul 07 07:44:37 2009  read 8947960 relations
Tue Jul 07 07:45:54 2009  multiplying 7304400 relations
Tue Jul 07 08:07:55 2009  multiply complete, coefficients have about 177.13 million bits
Tue Jul 07 08:07:57 2009  initial square root is modulo 2273239
Tue Jul 07 08:37:11 2009  reading relations for dependency 3
Tue Jul 07 08:37:13 2009  read 2482950 cycles
Tue Jul 07 08:37:21 2009  cycles contain 8953002 unique relations
Tue Jul 07 08:51:19 2009  read 8953002 relations
Tue Jul 07 08:52:29 2009  multiplying 7306608 relations
Tue Jul 07 09:15:24 2009  multiply complete, coefficients have about 177.18 million bits
Tue Jul 07 09:15:26 2009  initial square root is modulo 2282737
Tue Jul 07 09:40:26 2009  reading relations for dependency 4
Tue Jul 07 09:40:29 2009  read 2481076 cycles
Tue Jul 07 09:40:36 2009  cycles contain 8944839 unique relations
Tue Jul 07 09:52:26 2009  read 8944839 relations
Tue Jul 07 09:53:35 2009  multiplying 7300174 relations
Tue Jul 07 10:13:57 2009  multiply complete, coefficients have about 177.03 million bits
Tue Jul 07 10:13:59 2009  initial square root is modulo 2254477
Tue Jul 07 10:39:07 2009  reading relations for dependency 5
Tue Jul 07 10:39:09 2009  read 2482085 cycles
Tue Jul 07 10:39:16 2009  cycles contain 8950605 unique relations
Tue Jul 07 10:51:17 2009  read 8950605 relations
Tue Jul 07 10:52:27 2009  multiplying 7305078 relations
Tue Jul 07 11:14:34 2009  multiply complete, coefficients have about 177.14 million bits
Tue Jul 07 11:14:36 2009  initial square root is modulo 2276503
Tue Jul 07 11:43:26 2009  reading relations for dependency 6
Tue Jul 07 11:43:28 2009  read 2478711 cycles
Tue Jul 07 11:43:35 2009  cycles contain 8941063 unique relations
Tue Jul 07 11:57:15 2009  read 8941063 relations
Tue Jul 07 11:58:30 2009  multiplying 7295494 relations
Tue Jul 07 12:20:25 2009  multiply complete, coefficients have about 176.91 million bits
Tue Jul 07 12:20:27 2009  initial square root is modulo 2233243
Tue Jul 07 12:48:44 2009  sqrtTime: 23213
Tue Jul 07 12:48:44 2009  prp51 factor: 551004498127928469834445340613015226657914601778213
Tue Jul 07 12:48:44 2009  prp51 factor: 676677276408056094567102599764052489094573413056051
Tue Jul 07 12:48:44 2009  prp120 factor: 298003080664845879339921984943623072483939555335465806206783935206506443967104530715870831039336178009293998396643169751
Tue Jul 07 12:48:44 2009  elapsed time 142:37:09

c222 is the second largest number factored by SNFS in our tables so far. Congratulations!

8·10¹⁹⁸+3 = 8(0)₁₉₇3_<199> = 11 · 53 · C197

C197 = P43 · P155

P43 = 1350678383321052486001773788083398163612589_<43>

P155 = 10159433288577617053454552915986316337776945515442442225397613087026136705762770406500515286186663991881893416281217389552885939501195077102302205387682969_<155>

C197=P43*P155
C197=1350678383321052486001773788083398163612589<43>*10159433288577617053454552915986316337776945515442442225397613087026136705762770406500515286186663991881893416281217389552885939501195077102302205387682969<155>

Jul 8, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jul 8, 2009

(56·10¹⁸⁰+61)/9 = 6(2)₁₇₉9_<181> = 13 · 7789 · C176

C176 = P41 · P136

P41 = 26838646500920498855907522727441822854563_<41>

P136 = 2289601238125406496463685953870925367871067431406768811372523359546903375516654651574265382783432990689047815439704473437274675097675119_<136>

Number: n
N=61449798258117682947571251589739200472285592326675906082761905075424140772709266739309106750370070436831253367394078653547134738558541357360204452257347365833692704921360717997
  ( 176 digits)
SNFS difficulty: 181 digits.
Divisors found:

Wed Jul 08 12:08:03 2009  prp41 factor: 26838646500920498855907522727441822854563
Wed Jul 08 12:08:03 2009  prp136 factor: 2289601238125406496463685953870925367871067431406768811372523359546903375516654651574265382783432990689047815439704473437274675097675119
Wed Jul 08 12:08:03 2009  elapsed time 02:00:02 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 131.47 hours.
Scaled time: 349.70 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_2_179_9
n: 61449798258117682947571251589739200472285592326675906082761905075424140772709266739309106750370070436831253367394078653547134738558541357360204452257347365833692704921360717997
m: 1000000000000000000000000000000000000
deg: 5
c5: 56
c0: 61
skew: 1.02
type: snfs
lss: 1
rlim: 7600000
alim: 7600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 7600000/7600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [3800000, 6049990)
Primes: RFBsize:514565, AFBsize:514353, largePrimes:20842136 encountered
Relations: rels:20918964, finalFF:999667
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1886231 hash collisions in 22789853 relations
Msieve: matrix is 1141759 x 1142007 (307.6 MB)

Total sieving time: 130.96 hours.
Total relation processing time: 0.51 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7600000,7600000,28,28,56,56,2.5,2.5,100000
total time: 131.47 hours.
 --------- CPU info (if available) ----------

Jul 8, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM / Jul 8, 2009

(16·10²¹³-7)/9 = 1(7)₂₁₃_<214> = C214

C214 = P37 · C177

P37 = 8468548142759467301501936286449486551_<37>

C177 = [209927102947128172255527477476720550184027075544562096491537855794730425872278030664899902187563513228333907561760924717146946260073314975849230630876994684540632973031211495927_<177>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 1777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777 (214 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=623747480
Step 1 took 23282ms
Step 2 took 8537ms
********** Factor found in step 2: 8468548142759467301501936286449486551
Found probable prime factor of 37 digits: 8468548142759467301501936286449486551
Composite cofactor 209927102947128172255527477476720550184027075544562096491537855794730425872278030664899902187563513228333907561760924717146946260073314975849230630876994684540632973031211495927 has 177 digits

Jul 8, 2009 (2nd)

By Dmitry Domanov / ECMNET, GMP-ECM 6.2.3 / Jul 8, 2009

(16·10²²²-7)/9 = 1(7)₂₂₂_<223> = 199 · 12149 · 98448869 · 54361144210102643223435316458471837889181_<41> · C168

C168 = P37 · P131

P37 = 2235567584419681037453681562092795977_<37>

P131 = 61460592182154974496730933652470829014663740816329411758327108206469005324682537072299516656101839833858534462709909285629495029859_<131>

C168=P37*P131
C168=2235567584419681037453681562092795977<37>*61460592182154974496730933652470829014663740816329411758327108206469005324682537072299516656101839833858534462709909285629495029859<131>

(4·10²³⁹-1)/3 = 1(3)₂₃₉_<240> = 4667580867677873203_<19> · 24503401321619517515329_<23> · C199

C199 = P46 · C153

P46 = 7376676687266393712046503536607829252598737391_<46>

C153 = [158037358971372761393703399726706499974585107747002750603566153342837853221986516569540101910758293615058417151095031685002002369382801730594252944626649_<153>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=4266053392
Step 1 took 358031ms
Step 2 took 112531ms
********** Factor found in step 2: 7376676687266393712046503536607829252598737391
Found probable prime factor of 46 digits: 7376676687266393712046503536607829252598737391
Composite cofactor 158037358971372761393703399726706499974585107747002750603566153342837853221986516569540101910758293615058417151095031685002002369382801730594252944626649 has 153 digits

Jul 8, 2009

By Dmitry Domanov / GGNFS/msieve 1.41 / Jul 8, 2009

(44·10¹⁷¹-71)/9 = 4(8)₁₇₀1_<172> = 3 · 41 · 5153 · C166

C166 = P70 · P97

P70 = 5271981044836967768271841973392602581073085695664717820937384152442373_<70>

P97 = 1463090104635461951610590987260210884486775026240659609393710273204440955431228652088681530430663_<97>

N=7713383298526691198731639299056810996339473712351458206347378177190789308759896577554300027119554460956343828267831808274742298493558711381149648225895545713979683299
  ( 166 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=5271981044836967768271841973392602581073085695664717820937384152442373 (pp70)
 r2=1463090104635461951610590987260210884486775026240659609393710273204440955431228652088681530430663 (pp97)
Version: Msieve v. 1.41
Total time: 78.11 hours.
Scaled time: 154.35 units (timescale=1.976).
Factorization parameters were as follows:
n: 7713383298526691198731639299056810996339473712351458206347378177190789308759896577554300027119554460956343828267831808274742298493558711381149648225895545713979683299
m: 20000000000000000000000000000000000
deg: 5
c5: 55
c0: -284
skew: 1.39
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2700000, 6700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 865106 x 865354
Total sieving time: 76.66 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.19 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,173.000,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000
total time: 78.11 hours.
 --------- CPU info (if available) ----------

(58·10¹⁷⁷-13)/9 = 6(4)₁₇₆3_<178> = 43 · 1549 · C173

C173 = P42 · P132

P42 = 320496404483144759257844472217374390250391_<42>

P132 = 301885635787849997076654250208736448301418211103547828735709980133081356860492761093044763198026788449829497936680286375958621773939_<132>

N=96753260835114093780600303938691795823929083196127200511124122756533764385791950462330452421583984332644383389800538148309403582873338304449148654712634474521363286808360149
  ( 173 digits)
SNFS difficulty: 179 digits.
Divisors found:
 r1=320496404483144759257844472217374390250391 (pp42)
 r2=301885635787849997076654250208736448301418211103547828735709980133081356860492761093044763198026788449829497936680286375958621773939 (pp132)
Version: Msieve v. 1.41
Total time: 124.28 hours.
Scaled time: 246.33 units (timescale=1.982).
Factorization parameters were as follows:
n: 96753260835114093780600303938691795823929083196127200511124122756533764385791950462330452421583984332644383389800538148309403582873338304449148654712634474521363286808360149
m: 200000000000000000000000000000000000
deg: 5
c5: 725
c0: -52
skew: 0.59
type: snfs
lss: 1
rlim: 6800000
alim: 6800000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 6800000/6800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3400000, 9100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1433017 x 1433265
Total sieving time: 119.07 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 4.49 hours.
Time per square root: 0.41 hours.
Prototype def-par.txt line would be:
snfs,179.000,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000
total time: 124.28 hours.
 --------- CPU info (if available) ----------

Jul 7, 2009 (4th)

By Dmitry Domanov / ECMNET / Jul 7, 2009

(16·10²¹⁰-7)/9 = 1(7)₂₁₀_<211> = 2306753 · 707999891526611_<15> · C190

C190 = P38 · C152

P38 = 34982088008588268790615606126668383363_<38>

C152 = [31116981374511626666850275119962721699651581221812870177327853705301792800990178959233683888734687635721087961901222646746337176618805370691748725153913_<152>]

C190=P38*C152
C190=34982088008588268790615606126668383363<38>*31116981374511626666850275119962721699651581221812870177327853705301792800990178959233683888734687635721087961901222646746337176618805370691748725153913<152>

(16·10²²²-7)/9 = 1(7)₂₂₂_<223> = 199 · 12149 · 98448869 · C208

C208 = P41 · C168

P41 = 54361144210102643223435316458471837889181_<41>

C168 = [137399307601663329338762819303363451250324761459293058906011655115908353350470871508735481361435253702571547696510840260773732323164290945411600641942028811070410077243_<168>]

C208=P41*C168
C208=54361144210102643223435316458471837889181<41>*137399307601663329338762819303363451250324761459293058906011655115908353350470871508735481361435253702571547696510840260773732323164290945411600641942028811070410077243<168>

Jul 7, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM / Jul 7, 2009

(44·10¹⁶⁹-71)/9 = 4(8)₁₆₈1_<170> = 19 · 1171 · 22455238546372133233_<20> · 74729759475524672408129_<23> · C124

C124 = P40 · P84

P40 = 3267030704112780993938561807475804129877_<40>

P84 = 400806907449015252453908806551676977356384665542185400498682627662013210514398914421_<84>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 1309448473056422545730772508368357667208736293707271039656288264706133216883595462837863086408288211165694921802757292256217 (124 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1407767135
Step 1 took 9999ms
Step 2 took 4851ms
********** Factor found in step 2: 3267030704112780993938561807475804129877
Found probable prime factor of 40 digits: 3267030704112780993938561807475804129877
Probable prime cofactor 400806907449015252453908806551676977356384665542185400498682627662013210514398914421 has 84 digits

Jul 7, 2009 (2nd)

By Tyler Cadigan / GGNFS and Msieve / Jul 7, 2009

6·10¹⁷⁷+1 = 6(0)₁₇₆1_<178> = 1711983023_<10> · C169

C169 = P72 · P98

P72 = 130909460131276140628552263669024355006100394847355624263188932213877563_<72>

P98 = 26771996829082488321535109586807695003489696065663320871538381541557110996579284791617298469559549_<98>

Number: 60001_177
N=3504707651531425262270255585355766696758884857236110570939931569636832783008269352446726920609188774648263553487352543682321317037966912128660752496258837024694023499087
  ( 169 digits)
SNFS difficulty: 178 digits.
Divisors found:
 r1=130909460131276140628552263669024355006100394847355624263188932213877563 (pp72)
 r2=26771996829082488321535109586807695003489696065663320871538381541557110996579284791617298469559549 (pp98)
Version: Msieve v. 1.41
Total time: 97.06 hours.
Scaled time: 242.85 units (timescale=2.502).
Factorization parameters were as follows:
n: 3504707651531425262270255585355766696758884857236110570939931569636832783008269352446726920609188774648263553487352543682321317037966912128660752496258837024694023499087
m: 200000000000000000000000000000000000
deg: 5
c5: 75
c0: 4
skew: 0.56
type: snfs
lss: 1
rlim: 6600000
alim: 6600000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 6600000/6600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3300000, 7300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1080232 x 1080480
Total sieving time: 93.75 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 2.27 hours.
Time per square root: 0.77 hours.
Prototype def-par.txt line would be:
snfs,178.000,5,0,0,0,0,0,0,0,0,6600000,6600000,28,28,53,53,2.5,2.5,100000
total time: 97.06 hours.
 --------- CPU info (if available) ----------

Jul 7, 2009

By Serge Batalov / GMP-ECM 6.2.3 / Jul 7, 2009

(16·10²⁰⁴-7)/9 = 1(7)₂₀₄_<205> = 709 · 2971 · 7477 · 120847 · 374635434906319_<15> · C175

C175 = P38 · P137

P38 = 92895077195030726821601908997157473833_<38>

P137 = 26838842347296090104640832675754230252174815008475997450915157004722749871051392000924279403189951850376102607159797256027317218632935411_<137>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3235440799
Step 1 took 13861ms
Step 2 took 12025ms
********** Factor found in step 2: 92895077195030726821601908997157473833
Found probable prime factor of 38 digits: 92895077195030726821601908997157473833
Probable prime cofactor has 137 digits

Jul 6, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Jul 6, 2009

(8·10¹⁸⁰+7)/3 = 2(6)₁₇₉9_<181> = 31053624792761_<14> · C167

C167 = P71 · P97

P71 = 18555315928842020306493901187909913884372345209699756189928787759669539_<71>

P97 = 4627943814599199983007985544839411028986120597910669643331539446594085228777254658333014535246311_<97>

Number: n
N=85872959580818437049970776116010943591051241377859585751193600043739729134078369036913847819945516023470865699406926030247953668830042774115289314260254925621328820629
  ( 167 digits)
SNFS difficulty: 180 digits.
Divisors found:

Mon Jul 06 14:14:43 2009  prp71 factor: 18555315928842020306493901187909913884372345209699756189928787759669539
Mon Jul 06 14:14:43 2009  prp97 factor: 4627943814599199983007985544839411028986120597910669643331539446594085228777254658333014535246311
Mon Jul 06 14:14:43 2009  elapsed time 01:38:07 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 131.74 hours.
Scaled time: 344.63 units (timescale=2.616).
Factorization parameters were as follows:
name: KA_2_6_179_9
n: 85872959580818437049970776116010943591051241377859585751193600043739729134078369036913847819945516023470865699406926030247953668830042774115289314260254925621328820629
m: 1000000000000000000000000000000000000
deg: 5
c5: 8
c0: 7
skew: 0.97
type: snfs
lss: 1
rlim: 7200000
alim: 7200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 7200000/7200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [3600000, 5849990)
Primes: RFBsize:489319, AFBsize:488218, largePrimes:20564182 encountered
Relations: rels:20278778, finalFF:1064369
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2117894 hash collisions in 24343356 relations
Msieve: matrix is 1015493 x 1015741 (270.0 MB)

Total sieving time: 131.24 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,56,56,2.5,2.5,100000
total time: 131.74 hours.
 --------- CPU info (if available) ----------

(53·10¹⁸⁰+1)/9 = 5(8)₁₇₉9_<181> = 3 · 67 · 7753 · C175

C175 = P36 · P40 · P99

P36 = 467712874948997340147347573908507417_<36>

P40 = 9277642778843380347719533680822774228073_<40>

P99 = 870864419203635722315194328196734611935239863623475289867757749407372405846045984600645870268689193_<99>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 3778918440744098987128647289085906010312739725138584703779495973562401387162529214426313478967146011775822864837998122947040169261321978325122028762988160505924452860737515113 (175 digits)
Using B1=746000, B2=696728352, polynomial Dickson(3), sigma=338678068
Step 1 took 11500ms
Step 2 took 4765ms
********** Factor found in step 2: 467712874948997340147347573908507417
Found probable prime factor of 36 digits: 467712874948997340147347573908507417
Composite cofactor 8079568990176245407164908138855960352414027399430389385104249725327392997027699414008883250333152166638569639697780145903076291872132315089 has 139 digits

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 8079568990176245407164908138855960352414027399430389385104249725327392997027699414008883250333152166638569639697780145903076291872132315089 (139 digits)
Using B1=2958000, B2=4281751120, polynomial Dickson(6), sigma=314658206
Step 1 took 31781ms
Step 2 took 12547ms
********** Factor found in step 2: 9277642778843380347719533680822774228073
Found probable prime factor of 40 digits: 9277642778843380347719533680822774228073
Probable prime cofactor 870864419203635722315194328196734611935239863623475289867757749407372405846045984600645870268689193 has 99 digits

Jul 6, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jul 6, 2009

(16·10²³²-7)/9 = 1(7)₂₃₂_<233> = 19 · 104953 · 1986217 · 34068054807426322294331_<23> · 13848896772790568546388233869_<29> · C169

C169 = P35 · C135

P35 = 56772616833085221976414195028964401_<35>

C135 = [167571783671037912466408452319759362185008616848696629101669918550562953076710717850252795352341060164798120833972449628332765915929797_<135>]

C169=P35*C135
C169=56772616833085221976414195028964401<35>*167571783671037912466408452319759362185008616848696629101669918550562953076710717850252795352341060164798120833972449628332765915929797<135>

(16·10²⁴²-7)/9 = 1(7)₂₄₂_<243> = 3 · 1377031 · 60563440146936004113491_<23> · C213

C213 = P39 · C175

P39 = 199420903525207265891662998119875755307_<39>

C175 = [3563126863272287848309474508421502859292999903007398926700694144385671714094680930698204166079585664849282637049457051242987232608454018562371651837455217182196840947072062397_<175>]

C213=P39*C175
C213=199420903525207265891662998119875755307<39>*3563126863272287848309474508421502859292999903007398926700694144385671714094680930698204166079585664849282637049457051242987232608454018562371651837455217182196840947072062397<175>

Jul 6, 2009

By Serge Batalov / PFGW / Jul 6, 2009

(2·10⁸⁴²³⁹+1)/3 = (6)₈₄₂₃₈7_<84239> is PRP.

This is the largest unprovable near-repdigit PRP in our tables so far. Congratulations!

Jul 5, 2009 (5th)

By Wataru Sakai / GMP-ECM 6.2.1 / Jul 5, 2009

(2·10¹⁷¹-17)/3 = (6)₁₇₀1_<171> = 19 · 87468884265379_<14> · 13595175907013101_<17> · C140

C140 = P48 · P93

P48 = 138014820965046102634644206118683890867588471483_<48>

P93 = 213791776249621319224967337487968765723499969651474502298025592355774144477612711702325518067_<93>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1868644906
Step 1 took 42626ms
Step 2 took 14881ms
********** Factor found in step 2: 138014820965046102634644206118683890867588471483
Found probable prime factor of 48 digits: 138014820965046102634644206118683890867588471483
Probable prime cofactor 213791776249621319224967337487968765723499969651474502298025592355774144477612711702325518067 has 93 digits

Jul 5, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jul 5, 2009

(49·10¹⁸⁹+23)/9 = 5(4)₁₈₈7_<190> = 13 · C189

C189 = P59 · P130

P59 = 53523756078031042692936382182191372168741504118891852257677_<59>

P130 = 7824626847802964571499691889298350464401845544687833939953026301943157931919076380865693694386248286843653044176844425312737763847_<130>

Number: n
N=418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803419
  ( 189 digits)
SNFS difficulty: 191 digits.
Divisors found:

Sun Jul 05 02:18:18 2009  prp59 factor: 53523756078031042692936382182191372168741504118891852257677
Sun Jul 05 02:18:18 2009  prp130 factor: 7824626847802964571499691889298350464401845544687833939953026301943157931919076380865693694386248286843653044176844425312737763847
Sun Jul 05 02:18:18 2009  elapsed time 06:28:34 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 339.86 hours.
Scaled time: 878.55 units (timescale=2.585).
Factorization parameters were as follows:
name: KA_5_4_188_7
n: 418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803419
m: 100000000000000000000000000000000000000
deg: 5
c5: 49
c0: 230
skew: 1.36
type: snfs
lss: 1
rlim: 11000000
alim: 11000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [5500000, 11549990)
Primes: RFBsize:726517, AFBsize:725473, largePrimes:21473915 encountered
Relations: rels:21946074, finalFF:1409691
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2757639 hash collisions in 24407207 relations
Msieve: matrix is 1838300 x 1838548 (495.2 MB)

Total sieving time: 338.97 hours.
Total relation processing time: 0.89 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,56,56,2.5,2.5,100000
total time: 339.86 hours.
 --------- CPU info (if available) ----------

2·10²¹⁶-1 = 1(9)₂₁₆_<217> = 71 · 1801 · C212

C212 = P87 · P125

P87 = 361107090626796555790432520736349127614104388447835771607771886723658185918374320268583_<87>

P125 = 43313364268944003504537958096108351815974418622703052728674628970748248006983423154634967569396860724808442556827278605720343_<125>

Number: n
N=15640762956417014021943990427853070672787418570277858153920748254099834989950809800502068490900986150104402092734083568596476136105919246740856018956604703177420994596116398557921655418351307176764082551946883969
  ( 212 digits)
SNFS difficulty: 216 digits.
Divisors found:

Sun Jul  5 17:47:36 2009  prp87 factor: 361107090626796555790432520736349127614104388447835771607771886723658185918374320268583
Sun Jul  5 17:47:36 2009  prp125 factor: 43313364268944003504537958096108351815974418622703052728674628970748248006983423154634967569396860724808442556827278605720343
Sun Jul  5 17:47:36 2009  elapsed time 48:29:06 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 137.94 hours.
Scaled time: 277.95 units (timescale=2.015).
Factorization parameters were as follows:
name: KA_1_9_216
n: 15640762956417014021943990427853070672787418570277858153920748254099834989950809800502068490900986150104402092734083568596476136105919246740856018956604703177420994596116398557921655418351307176764082551946883969
m: 1000000000000000000000000000000000000
deg: 6
c6: 2
c0: -1
skew: 0.89
type: snfs
lss: 1
rlim: 28000000
alim: 28000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 28000000/28000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [14000000, 39599990)
Primes: RFBsize:1741430, AFBsize:1740559, largePrimes:38050311 encountered
Relations: rels:34729186, finalFF:1144510
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 8345464 hash collisions in 49109482 relations
Msieve: matrix is 4939937 x 4940185 (1333.9 MB)

Total sieving time: 136.84 hours.
Total relation processing time: 1.10 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,216,6,0,0,0,0,0,0,0,0,28000000,28000000,29,29,58,58,2.6,2.6,100000
total time: 137.94 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3352056k/3407296k available (3119k kernel code, 53956k reserved, 1894k data, 424k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.68 BogoMIPS (lpj=2830844)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22644.41 BogoMIPS).

Jul 5, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve 1.41 / Jul 5, 2009

(19·10¹⁶⁹+11)/3 = 6(3)₁₆₈7_<170> = 419 · 17359 · 435144769 · 1092261451_<10> · 46604867967947_<14> · 6863100712193171991021877484483863219321_<40> · C92

C92 = P46 · P47

P46 = 1460642205399019519450717523391965728267997741_<46>

P47 = 39213693243907045538796060396726173069533192289_<47>

N=57277175381621018844894128396734834310011455677358063497176811475656530660931802849970619149
  ( 92 digits)
Divisors found:
 r1=1460642205399019519450717523391965728267997741 (pp46)
 r2=39213693243907045538796060396726173069533192289 (pp47)
Version: Msieve v. 1.41
Total time: 3.16 hours.
Scaled time: 6.26 units (timescale=1.982).
Factorization parameters were as follows:
name: 0028
n:  57277175381621018844894128396734834310011455677358063497176811475656530660931802849970619149
m:  1144412806986536595868
deg: 4
c4: 33392640
c3: 219871128503
c2: -93123226998648841
c1: -905220131677318023
c0: 65367225897505650092961
skew: 1635.250
type: gnfs
# adj. I(F,S) = 53.225
# E(F1,F2) = 1.050945e-004
# GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=58.00000000, seed=1246725776.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 700000
alim: 700000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.4
alambda: 2.4
qintsize: 40000

type: gnfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [350000, 1030001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 111083 x 111313
Polynomial selection time: 0.17 hours.
Total sieving time: 2.91 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
gnfs,91,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000
total time: 3.16 hours.
 --------- CPU info (if available) ----------

Jul 5, 2009 (2nd)

By Tyler Cadigan / GGNFS, Msieve / Jul 5, 2009

6·10¹⁸⁰+1 = 6(0)₁₇₉1_<181> = 7 · 53 · 5189 · 1530654942827_<13> · C163

C163 = P80 · P83

P80 = 77961257465282390200811842235367085099161175733216672157092688181205275825630537_<80>

P83 = 26117856802019915612096483598867398142659189050194588384216401897862531400938257621_<83>

Number: 60001_180
N=2036180958583651599919324369895283334276379392748411313706838298632139875636431258517052429423184385967502888554627103436454845173306061562588430970166718470572477
  ( 163 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=77961257465282390200811842235367085099161175733216672157092688181205275825630537 (pp80)
 r2=26117856802019915612096483598867398142659189050194588384216401897862531400938257621 (pp83)
Version: Msieve v. 1.41
Total time: 143.05 hours.
Scaled time: 363.92 units (timescale=2.544).
Factorization parameters were as follows:
n: 2036180958583651599919324369895283334276379392748411313706838298632139875636431258517052429423184385967502888554627103436454845173306061562588430970166718470572477
m: 1000000000000000000000000000000000000
deg: 5
c5: 6
c0: 1
skew: 0.70
type: snfs
lss: 1
rlim: 7200000
alim: 7200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 7200000/7200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3600000, 5600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 948967 x 949215
Total sieving time: 141.12 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 1.53 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,180.000,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,53,53,2.5,2.5,100000
total time: 143.05 hours.
 --------- CPU info (if available) ----------

Jul 5, 2009

By Sinkiti Sibata / Msieve / Jul 5, 2009

(58·10¹⁶⁹-13)/9 = 6(4)₁₆₈3_<170> = 3 · 7 · 179 · 147853 · 236891 · 338197 · 4258508879_<10> · C141

C141 = P66 · P75

P66 = 408116836703356135186758597068735340933347535194023264090041406897_<66>

P75 = 832765330571507511987519992376332246212140238340768446412802228965601239809_<75>

Number: 64443_169
N=339865552429068321970877680355397427709972520150182950223233553657884687447900712560490043251329534766131338706168982613469177225889843562673
  ( 141 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=408116836703356135186758597068735340933347535194023264090041406897 (pp66)
 r2=832765330571507511987519992376332246212140238340768446412802228965601239809 (pp75)
Version: Msieve-1.40
Total time: 83.78 hours.
Scaled time: 172.42 units (timescale=2.058).
Factorization parameters were as follows:
name: 64443_169
n: 339865552429068321970877680355397427709972520150182950223233553657884687447900712560490043251329534766131338706168982613469177225889843562673
m: 10000000000000000000000000000000000
deg: 5
c5: 29
c0: -65
skew: 1.18
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 976748 x 976996
Total sieving time: 79.62 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.71 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 83.78 hours.
 --------- CPU info (if available) ----------

Jul 4, 2009 (5th)

By Dmitry Domanov / ECMNET / Jul 4, 2009

(52·10²⁰¹+11)/9 = 5(7)₂₀₀9_<202> = 61 · 9439 · C197

C197 = P36 · P161

P36 = 327574010996440651174881028085255183_<36>

P161 = 30633426295854463882304563603886870527666531320541302771617844658424271598181095302778430382149016907140565796158720390106944926598693879577187939072797793406847_<161>

C197=P36*P161
C197=327574010996440651174881028085255183<36>*30633426295854463882304563603886870527666531320541302771617844658424271598181095302778430382149016907140565796158720390106944926598693879577187939072797793406847<161>

Jul 4, 2009 (4th)

By Sinkiti Sibata / GGNFS / Jul 4, 2009

(58·10¹⁶⁴-13)/9 = 6(4)₁₆₃3_<165> = 634425495437_<12> · 34223943495856159696154680142313760883_<38> · C116

C116 = P40 · P77

P40 = 1039702390453237753079616431433676773883_<40>

P77 = 28547347651007753290977819563148421178571364515389527937841544853464340338951_<77>

Number: 64443_164
N=29680745593852382710885424670845104038289735607516074357223266600260200692718744499668077307158865998260008404416733
  ( 116 digits)
Divisors found:
 r1=1039702390453237753079616431433676773883 (pp40)
 r2=28547347651007753290977819563148421178571364515389527937841544853464340338951 (pp77)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 68.52 hours.
Scaled time: 32.48 units (timescale=0.474).
Factorization parameters were as follows:
name: 64443_164
n: 29680745593852382710885424670845104038289735607516074357223266600260200692718744499668077307158865998260008404416733
skew: 37882.17
# norm 2.16e+15
c5: 28080
c4: -1783304174
c3: -106987684895637
c2: 3254798532959727963
c1: 69333921661141863276279
c0: 311328355938046670337322130
# alpha -5.10
Y1: 1694242071773
Y0: -16025667352605280542669
# Murphy_E 5.09e-10
# M 725564486423152580698825252463775544412007927936381050353624717871811877831131875924797212721560785860023394686973
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3630001)
Primes: RFBsize:315948, AFBsize:315817, largePrimes:7563902 encountered
Relations: rels:7629959, finalFF:773927
Max relations in full relation-set: 28
Initial matrix: 631846 x 773927 with sparse part having weight 60032329.
Pruned matrix : 507204 x 510427 with weight 34236305.
Total sieving time: 56.96 hours.
Total relation processing time: 0.79 hours.
Matrix solve time: 10.35 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 68.52 hours.
 --------- CPU info (if available) ----------

Jul 4, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM / Jul 4, 2009

(19·10¹⁶⁹+11)/3 = 6(3)₁₆₈7_<170> = 419 · 17359 · 435144769 · 1092261451_<10> · 46604867967947_<14> · C132

C132 = P40 · C92

P40 = 6863100712193171991021877484483863219321_<40>

C92 = [57277175381621018844894128396734834310011455677358063497176811475656530660931802849970619149_<92>]

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 393099023154016432157135307697657905002456098719696585711733263469545952679141551813013727666722143370112848288521607667698749377829 (132 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4273467981
Step 1 took 4228ms
Step 2 took 1341ms
********** Factor found in step 2: 6863100712193171991021877484483863219321
Found probable prime factor of 40 digits: 6863100712193171991021877484483863219321
Composite cofactor 57277175381621018844894128396734834310011455677358063497176811475656530660931802849970619149 has 92 digits

Jul 4, 2009 (2nd)

By Tyler Cadigan / PRIMO 3.0.7 / Jun 30, 2009

(10²⁵⁷⁶+53)/9 = (1)₂₅₇₅7_<2576> is prime.

Jul 4, 2009

By Dmitry Domanov / GGNFS/msieve 1.41 / Jul 4, 2009

(16·10²³⁹-7)/9 = 1(7)₂₃₉_<240> = 3⁵ · 15217 · 3990316637461614359759_<22> · 13273181924432571534347_<23> · 17417511129931705819879_<23> · 72157436681702848816201_<23> · 155862880557226828959411237263_<30> · C115

C115 = P52 · P64

P52 = 1242805601725594914246288145126368484394847860891111_<52>

P64 = 3728607415830210175214413350865767470697342530579606832265121657_<64>

N=4633934183029379848911059683421025765683695811198960419440580945122087499442227338278163891999244250812708844890927
  ( 115 digits)
Divisors found:
 r1=1242805601725594914246288145126368484394847860891111 (pp52)
 r2=3728607415830210175214413350865767470697342530579606832265121657 (pp64)
Version: Msieve v. 1.41
Total time: 33.30 hours.
Scaled time: 65.56 units (timescale=1.969).
Factorization parameters were as follows:
name: 0024
n: 4633934183029379848911059683421025765683695811198960419440580945122087499442227338278163891999244250812708844890927
skew: 52277.85
# norm 1.53e+016
c5: 49140
c4: 2023517382
c3: -770576692952680
c2: -6669643093844814455
c1: 675255332437029036418800
c0: -3360776601203873812598149827
# alpha -6.82
Y1: 530957486939
Y0: -9883317554939838314860
# Murphy_E 5.71e-010
# M 453967889756118697662348222666525420739985869353770678696114680314130139019054861861552037690994500371427353763936
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 527177 x 527424
Polynomial selection time: 2.72 hours.
Total sieving time: 29.25 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 1.00 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 33.30 hours.
 --------- CPU info (if available) ----------

Jul 3, 2009 (3rd)

By Jo Yeong Uk / Msieve / Jul 2, 2009

(19·10¹⁷⁰+11)/3 = 6(3)₁₆₉7_<171> = 7² · 13 · 2423 · 5407 · 225212486252296836198773323_<27> · 362095319198698267549534353999723137_<36> · C99

C99 = P32 · P68

P32 = 41530639745908770097077908377763_<32>

P68 = 22407795549198754888680238994593224139411080039444874423497865033157_<68>

Number: 63337_170
N=930610084453751447220883859937900406192855431428364710420148846824731721127839963619056184076487791
  ( 99 digits)
Divisors found:
 r1=41530639745908770097077908377763
 r2=22407795549198754888680238994593224139411080039444874423497865033157
Version: 
Total time: 2.38 hours.
Scaled time: 5.69 units (timescale=2.391).
Factorization parameters were as follows:
name: 63337_170
n: 930610084453751447220883859937900406192855431428364710420148846824731721127839963619056184076487791
skew: 5805.56
# norm 3.75e+13
c5: 45540
c4: -576098332
c3: -4840732325267
c2: 15563382954064314
c1: 66030856022033971056
c0: -120065763798487403936640
# alpha -5.08
Y1: 10461064597
Y0: -7279080541546534673
# Murphy_E 3.46e-09
# M 887173262205881371076995863496444461793338535162077103711482507558309594394743821872645967092394012
type: gnfs
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [500000, 1000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4147948
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 183967 x 184215
Polynomial selection time: 0.14 hours.
Total sieving time: 1.96 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000
total time: 2.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)

By Jo Yeong Uk / GMP-ECM / Jul 3, 2009

(16·10²²⁵-7)/9 = 1(7)₂₂₅_<226> = 17 · 5705120952499567_<16> · 7113174568135224977_<19> · 1430577548090886473232512029_<28> · 23372859706894522584303715363_<29> · C134

C134 = P32 · P103

P32 = 41233351031948151692868641186159_<32>

P103 = 1869081935791828972707833126568044399578183366750010335624802395418611310169927142305210058932642675863_<103>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 77068511565977660174709421461132555031362999146292468101240450879997543709927873527529777203465840908885241587100820037642140078980217 (134 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5175414927
Step 1 took 4227ms
Step 2 took 5835ms
********** Factor found in step 2: 41233351031948151692868641186159
Found probable prime factor of 32 digits: 41233351031948151692868641186159
Probable prime cofactor 1869081935791828972707833126568044399578183366750010335624802395418611310169927142305210058932642675863 has 103 digits

Jul 3, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jul 3, 2009

(16·10²²⁶-7)/9 = 1(7)₂₂₆_<227> = 131 · 6181811 · 132752221159_<12> · C207

C207 = P38 · P170

P38 = 12500755410149652578208142530844687751_<38>

P170 = 13228554790752363275540751728437998199424055178673431699716124390155931820330522849342635457892494755615875231329856621245128124011040693202135088807739033447001924553033_<170>

C207=P38*P170
C207=12500755410149652578208142530844687751<38>*13228554790752363275540751728437998199424055178673431699716124390155931820330522849342635457892494755615875231329856621245128124011040693202135088807739033447001924553033<170>

Jul 3, 2009

By Sinkiti Sibata / Msieve / Jul 3, 2009

(58·10¹⁶³-13)/9 = 6(4)₁₆₂3_<164> = 3² · 7 · 17 · 94951763 · 1450443787417_<13> · C141

C141 = P62 · P80

P62 = 15200010854050980264951294490005750472092205391836031200627031_<62>

P80 = 28744064597297114282228101355955883403740289127783595364008637430740971151148233_<80>

Number: 64443_163
N=436910093868458656181692890758665810048223451661281827184511045317685332128359134867190394080416164666242215892704309860218883494745227686223
  ( 141 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=15200010854050980264951294490005750472092205391836031200627031 (pp62)
 r2=28744064597297114282228101355955883403740289127783595364008637430740971151148233 (pp80)
Version: Msieve-1.40
Total time: 50.73 hours.
Scaled time: 130.08 units (timescale=2.564).
Factorization parameters were as follows:
name: 64443_163
n: 436910093868458656181692890758665810048223451661281827184511045317685332128359134867190394080416164666242215892704309860218883494745227686223
m: 500000000000000000000000000000000
deg: 5
c5: 464
c0: -325
skew: 0.93
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 751768 x 752016
Total sieving time: 49.14 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.27 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 50.73 hours.
 --------- CPU info (if available) ----------

Jul 2, 2009 (4th)

By Dmitry Domanov / ECMNET / Jul 2, 2009

(4·10²²⁷-1)/3 = 1(3)₂₂₇_<228> = 495976721 · C219

C219 = P34 · P185

P34 = 7182449182846041226834457037788413_<34>

P185 = 37428711930030411787026467533746685794015580944665280706076447106637077636188492634909171909470494931514913929830815389062003443743128089759181928735384732113688639097074216322185271721_<185>

C219=P34*P185
C219=7182449182846041226834457037788413<34>*37428711930030411787026467533746685794015580944665280706076447106637077636188492634909171909470494931514913929830815389062003443743128089759181928735384732113688639097074216322185271721<185>

Jul 2, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM, GGNFS, MSieve v1.39 / Jul 2, 2009

(17·10¹⁶⁹-11)/3 = 5(6)₁₆₈3_<170> = 47 · 131 · 149 · 33340437841741841839489_<23> · C142

C142 = P36 · P106

P36 = 588740553020417727859616696880760387_<36>

P106 = 3146856900197104709044954193359079359458730289636307786252071116222364226809318587050803371596885848515837_<106>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 1852682271698160903203411897901451415112616705715726434096600854560620468380525285725615537888596666176564066317954738261417293548183971748919 (142 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3541219365
Step 1 took 4157ms
Step 2 took 2373ms
********** Factor found in step 2: 588740553020417727859616696880760387
Found probable prime factor of 36 digits: 588740553020417727859616696880760387
Probable prime cofactor 3146856900197104709044954193359079359458730289636307786252071116222364226809318587050803371596885848515837 has 106 digits

(19·10¹⁷⁰+11)/3 = 6(3)₁₆₉7_<171> = 7² · 13 · 2423 · 5407 · 225212486252296836198773323_<27> · C135

C135 = P36 · C99

P36 = 362095319198698267549534353999723137_<36>

C99 = [930610084453751447220883859937900406192855431428364710420148846824731721127839963619056184076487791_<99>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 336969555579808682573243870523617049873844489586121451739694245328141713281148910920472473599665329157656373568688539063780045360720367 (135 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6088997955
Step 1 took 3440ms
Step 2 took 2148ms
********** Factor found in step 2: 362095319198698267549534353999723137
Found probable prime factor of 36 digits: 362095319198698267549534353999723137
Composite cofactor 930610084453751447220883859937900406192855431428364710420148846824731721127839963619056184076487791 has 99 digits

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 336969555579808682573243870523617049873844489586121451739694245328141713281148910920472473599665329157656373568688539063780045360720367 (135 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6088997955
Step 1 took 3440ms
Step 2 took 2148ms
********** Factor found in step 2: 362095319198698267549534353999723137
Found probable prime factor of 36 digits: 362095319198698267549534353999723137
Composite cofactor 930610084453751447220883859937900406192855431428364710420148846824731721127839963619056184076487791 has 99 digits

Jul 2, 2009 (2nd)

By Tyler Cadigan / GGNFS, Msieve / Jul 2, 2009

6·10¹⁸¹+1 = 6(0)₁₈₀1_<182> = 23 · 61 · 22921 · 1872699346433998020537767237_<28> · C147

C147 = P52 · P96

P52 = 3221817407318169274057683443449767963151785037276817_<52>

P96 = 309236703947623304730799733324982576204663378968922310111028745418217199315661984343512735564463_<96>

Number: 60001_181
N=996304195760147997067562108673821534929496595129015951823604834209205894024502191944842412261659576950028689198887149061532283496510397260878954271
  ( 147 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=3221817407318169274057683443449767963151785037276817 (pp52)
 r2=309236703947623304730799733324982576204663378968922310111028745418217199315661984343512735564463 (pp96)
Version: Msieve v. 1.41
Total time: 223.86 hours.
Scaled time: 573.97 units (timescale=2.564).
Factorization parameters were as follows:
n: 996304195760147997067562108673821534929496595129015951823604834209205894024502191944842412261659576950028689198887149061532283496510397260878954271
m: 2000000000000000000000000000000000000
deg: 5
c5: 15
c0: 8
skew: 0.88
type: snfs
lss: 1
rlim: 7800000
alim: 7800000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 7800000/7800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3900000, 6900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 851034 x 851282
Total sieving time: 221.71 hours.
Total relation processing time: 0.83 hours.
Matrix solve time: 1.22 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,182.000,5,0,0,0,0,0,0,0,0,7800000,7800000,28,28,53,53,2.5,2.5,100000
total time: 223.86 hours.
 --------- CPU info (if available) ----------

Jul 2, 2009

Factorizations of 177...77 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jul 1, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jul 1, 2009

(53·10²⁰³+1)/9 = 5(8)₂₀₂9_<204> = 7 · 281 · C201

C201 = P40 · C161

P40 = 6991094456219571760445366554492296155281_<40>

C161 = [42823664738654024146753494596611162996197643707455475080552632365269730895208935483894078392027330205442062850153313457655994824376155448514431058020416853642407_<161>]

C201=P40*C161
C201=6991094456219571760445366554492296155281<40>*42823664738654024146753494596611162996197643707455475080552632365269730895208935483894078392027330205442062850153313457655994824376155448514431058020416853642407<161>

(4·10²³¹-1)/3 = 1(3)₂₃₁_<232> = 2917 · 51824844853_<11> · 23692560197239551081270833387477_<32> · C186

C186 = P37 · C150

P37 = 1862546921637290351531952691671776489_<37>

C150 = [199868835314352006303616101691173511035981142016504847269115886853153738185472417870991193724827260514112019164316369241384478739018564658717340450161_<150>]

C186=P37*C150
C186=1862546921637290351531952691671776489<37>*1998688353143520063036161016911735110359811420165048472691158868531537381854724178709911937248272605
14112019164316369241384478739018564658717340450161<150>

Jul 1, 2009

By Sinkiti Sibata / Msieve / Jul 1, 2009

(58·10¹⁴⁹-13)/9 = 6(4)₁₄₈3_<150> = 17680101259_<11> · 612631184541141230147_<21> · C119

C119 = P52 · P68

P52 = 5449278379117159731544956271485792375419509366641329_<52>

P68 = 10918491534763876929867522805580453713263965653671863520590735670379_<68>

Number: 64443_149
N=59497899852962528961232804765393480978112046870788785804578711096597251999116268207960584747284901586476215186462493691
  ( 119 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=5449278379117159731544956271485792375419509366641329 (pp52)
 r2=10918491534763876929867522805580453713263965653671863520590735670379 (pp68)
Version: Msieve-1.40
Total time: 16.99 hours.
Scaled time: 43.57 units (timescale=2.564).
Factorization parameters were as follows:
name: 64443_149
n: 59497899852962528961232804765393480978112046870788785804578711096597251999116268207960584747284901586476215186462493691
m: 1000000000000000000000000000000
deg: 5
c5: 29
c0: -65
skew: 1.18
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 379906 x 380154
Total sieving time: 16.47 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 16.99 hours.
 --------- CPU info (if available) ----------

(58·10¹⁴⁷-13)/9 = 6(4)₁₄₆3_<148> = 17 · 3963777162971_<13> · 334646085665334337_<18> · C117

C117 = P52 · P66

P52 = 1724643839436206727262081314038604977199883913024927_<52>

P66 = 165707498267325136214000770286795308021181237711990781533096525551_<66>

Number: 64443_147
N=285786416035128196683289121621064667771773532733338769241158392752477998247710329546637739266886534072113858155409777
  ( 117 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=1724643839436206727262081314038604977199883913024927 (pp52)
 r2=165707498267325136214000770286795308021181237711990781533096525551 (pp66)
Version: Msieve-1.40
Total time: 14.66 hours.
Scaled time: 30.67 units (timescale=2.092).
Factorization parameters were as follows:
name: 64443_147
n: 285786416035128196683289121621064667771773532733338769241158392752477998247710329546637739266886534072113858155409777
m: 200000000000000000000000000000
deg: 5
c5: 725
c0: -52
skew: 0.59
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 2800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 397682 x 397930
Total sieving time: 13.68 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.54 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,149.000,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000
total time: 14.66 hours.
 --------- CPU info (if available) ----------

June 2009

Jun 30, 2009 (3rd)

By Sinkiti Sibata / Msieve / Jun 30, 2009

(58·10¹⁴³-13)/9 = 6(4)₁₄₂3_<144> = 113 · 223 · 77023 · C135

C135 = P64 · P72

P64 = 1652337627292589379706191532069268484497360291057948743864303033_<64>

P72 = 200947660644812862508216274233245205166132877847788787856034118266055523_<72>

Number: 64443_143
N=332033380799846526477379417918328852033073705607452776566870643319489211252896617924602015943659826695384126147432305894890078475301259
  ( 135 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1652337627292589379706191532069268484497360291057948743864303033 (pp64)
 r2=200947660644812862508216274233245205166132877847788787856034118266055523 (pp72)
Version: Msieve-1.40
Total time: 10.20 hours.
Scaled time: 26.14 units (timescale=2.564).
Factorization parameters were as follows:
name: 64443_143
n: 332033380799846526477379417918328852033073705607452776566870643319489211252896617924602015943659826695384126147432305894890078475301259
m: 50000000000000000000000000000
deg: 5
c5: 464
c0: -325
skew: 0.93
type: snfs
lss: 1
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [955000, 2255001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 341670 x 341918
Total sieving time: 9.82 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 10.20 hours.
 --------- CPU info (if available) ----------

(58·10¹⁵⁵-13)/9 = 6(4)₁₅₄3_<156> = 227 · 42416069 · 2974192430852304989290612183_<28> · C119

C119 = P38 · P81

P38 = 23571159999526622109100196347300471721_<38>

P81 = 954726968014034137402089586947817032218884506562192209056620458034761171420831227_<81>

Number: 64443_155
N=22504022118921734259662990204779762049959337208129694385777166920187136905382202309246021844159118798649720943027231667
  ( 119 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=23571159999526622109100196347300471721 (pp38)
 r2=954726968014034137402089586947817032218884506562192209056620458034761171420831227 (pp81)
Version: Msieve-1.40
Total time: 25.30 hours.
Scaled time: 51.56 units (timescale=2.038).
Factorization parameters were as follows:
name: 64443_155
n: 22504022118921734259662990204779762049959337208129694385777166920187136905382202309246021844159118798649720943027231667
m: 10000000000000000000000000000000
deg: 5
c5: 58
c0: -13
skew: 0.74
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1450000, 2450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 527291 x 527539
Total sieving time: 24.05 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.99 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000
total time: 25.30 hours.
 --------- CPU info (if available) ----------

Jun 30, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 30, 2009

(58·10¹⁶¹-13)/9 = 6(4)₁₆₀3_<162> = 653319345451_<12> · C150

C150 = P52 · P99

P52 = 1575237244329951942400489897260475329452903303322367_<52>

P99 = 626201342405418301153045845166292234087621760837772895460574802045257424597728085044658561255896879_<99>

Number: 64443_161
N=986415677006427804635947990417506924988037544295951487502593886272837369809392052611588638503606484328606433676386764357014430239213162142871046192593
  ( 150 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=1575237244329951942400489897260475329452903303322367
 r2=626201342405418301153045845166292234087621760837772895460574802045257424597728085044658561255896879
Version: 
Total time: 20.20 hours.
Scaled time: 48.26 units (timescale=2.389).
Factorization parameters were as follows:
n: 986415677006427804635947990417506924988037544295951487502593886272837369809392052611588638503606484328606433676386764357014430239213162142871046192593
m: 100000000000000000000000000000000
deg: 5
c5: 580
c0: -13
skew: 0.47
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 3700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9541464
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 736941 x 737189
Total sieving time: 18.04 hours.
Total relation processing time: 0.78 hours.
Matrix solve time: 1.11 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 20.20 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673802)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)

Jun 30, 2009

By Andreas Tete / Msieve v. 1.42, GGNFS / Jun 30, 2009

(58·10¹⁷¹-13)/9 = 6(4)₁₇₀3_<172> = 267800740964923_<15> · 136821051590356663_<18> · 23486273512771613646940357632313_<32> · C109

C109 = P49 · P61

P49 = 1680685663562710108755241113940108250558188502759_<49>

P61 = 4455743436763288668170528477507378349835514471314046357878921_<61>

Mon Jun 29 21:25:16 2009  Msieve v. 1.42
Mon Jun 29 21:25:16 2009  random seeds: bbef2658 2c483f2b
Mon Jun 29 21:25:16 2009  factoring 7488704114681698263211093624793715429841463355073981832582681151912872857638281873870764124988601995996443039 (109 digits)
Mon Jun 29 21:25:17 2009  searching for 15-digit factors
Mon Jun 29 21:25:18 2009  commencing number field sieve (109-digit input)
Mon Jun 29 21:25:18 2009  R0: -1200755848565647964360
Mon Jun 29 21:25:18 2009  R1:  277561682419
Mon Jun 29 21:25:18 2009  A0:  765270029707707158906661
Mon Jun 29 21:25:18 2009  A1:  4592249298769793133290
Mon Jun 29 21:25:18 2009  A2: -476743582276620277
Mon Jun 29 21:25:18 2009  A3: -11323319301534
Mon Jun 29 21:25:18 2009  A4:  354533780
Mon Jun 29 21:25:18 2009  A5:  3000
Mon Jun 29 21:25:18 2009  skew 32429.05, size 2.389419e-010, alpha -5.307571, combined = 1.238732e-009
Mon Jun 29 21:25:19 2009  
Mon Jun 29 21:25:19 2009  commencing relation filtering
Mon Jun 29 21:25:19 2009  commencing duplicate removal, pass 1
Mon Jun 29 21:26:31 2009  found 490481 hash collisions in 5342536 relations
Mon Jun 29 21:26:45 2009  added 36477 free relations
Mon Jun 29 21:26:45 2009  commencing duplicate removal, pass 2
Mon Jun 29 21:26:54 2009  found 476302 duplicates and 4902710 unique relations
Mon Jun 29 21:26:54 2009  memory use: 41.3 MB
Mon Jun 29 21:26:54 2009  reading rational ideals above 3080192
Mon Jun 29 21:26:54 2009  reading algebraic ideals above 3080192
Mon Jun 29 21:26:54 2009  commencing singleton removal, pass 1
Mon Jun 29 21:27:49 2009  relations with 0 large ideals: 119050
Mon Jun 29 21:27:49 2009  relations with 1 large ideals: 753244
Mon Jun 29 21:27:49 2009  relations with 2 large ideals: 1732248
Mon Jun 29 21:27:49 2009  relations with 3 large ideals: 1672371
Mon Jun 29 21:27:49 2009  relations with 4 large ideals: 570809
Mon Jun 29 21:27:49 2009  relations with 5 large ideals: 20278
Mon Jun 29 21:27:49 2009  relations with 6 large ideals: 34710
Mon Jun 29 21:27:49 2009  relations with 7+ large ideals: 0
Mon Jun 29 21:27:49 2009  4902710 relations and about 4779680 large ideals
Mon Jun 29 21:27:49 2009  commencing singleton removal, pass 2
Mon Jun 29 21:28:47 2009  found 2126072 singletons
Mon Jun 29 21:28:47 2009  current dataset: 2776638 relations and about 2200364 large ideals
Mon Jun 29 21:28:47 2009  commencing singleton removal, pass 3
Mon Jun 29 21:29:34 2009  found 500480 singletons
Mon Jun 29 21:29:34 2009  current dataset: 2276158 relations and about 1665007 large ideals
Mon Jun 29 21:29:34 2009  commencing singleton removal, pass 4
Mon Jun 29 21:30:18 2009  found 148691 singletons
Mon Jun 29 21:30:18 2009  current dataset: 2127467 relations and about 1512452 large ideals
Mon Jun 29 21:30:18 2009  commencing singleton removal, final pass
Mon Jun 29 21:31:04 2009  memory use: 33.3 MB
Mon Jun 29 21:31:04 2009  commencing in-memory singleton removal
Mon Jun 29 21:31:04 2009  begin with 2127467 relations and 1560650 unique ideals
Mon Jun 29 21:31:06 2009  reduce to 1935741 relations and 1366206 ideals in 15 passes
Mon Jun 29 21:31:06 2009  max relations containing the same ideal: 46
Mon Jun 29 21:31:07 2009  reading rational ideals above 720000
Mon Jun 29 21:31:07 2009  reading algebraic ideals above 720000
Mon Jun 29 21:31:07 2009  commencing singleton removal, final pass
Mon Jun 29 21:31:52 2009  keeping 1670936 ideals with weight <= 20, new excess is 200601
Mon Jun 29 21:31:54 2009  memory use: 47.7 MB
Mon Jun 29 21:31:54 2009  commencing in-memory singleton removal
Mon Jun 29 21:31:54 2009  begin with 1946275 relations and 1670936 unique ideals
Mon Jun 29 21:31:56 2009  reduce to 1927241 relations and 1600494 ideals in 10 passes
Mon Jun 29 21:31:56 2009  max relations containing the same ideal: 20
Mon Jun 29 21:31:58 2009  removing 322019 relations and 274994 ideals in 47025 cliques
Mon Jun 29 21:31:58 2009  commencing in-memory singleton removal
Mon Jun 29 21:31:58 2009  begin with 1605222 relations and 1600494 unique ideals
Mon Jun 29 21:31:59 2009  reduce to 1571407 relations and 1290716 ideals in 7 passes
Mon Jun 29 21:31:59 2009  max relations containing the same ideal: 20
Mon Jun 29 21:32:00 2009  removing 241602 relations and 194577 ideals in 47025 cliques
Mon Jun 29 21:32:00 2009  commencing in-memory singleton removal
Mon Jun 29 21:32:00 2009  begin with 1329805 relations and 1290716 unique ideals
Mon Jun 29 21:32:01 2009  reduce to 1304264 relations and 1069911 ideals in 8 passes
Mon Jun 29 21:32:01 2009  max relations containing the same ideal: 20
Mon Jun 29 21:32:02 2009  relations with 0 large ideals: 17810
Mon Jun 29 21:32:02 2009  relations with 1 large ideals: 117111
Mon Jun 29 21:32:02 2009  relations with 2 large ideals: 310411
Mon Jun 29 21:32:02 2009  relations with 3 large ideals: 412635
Mon Jun 29 21:32:02 2009  relations with 4 large ideals: 296443
Mon Jun 29 21:32:02 2009  relations with 5 large ideals: 118042
Mon Jun 29 21:32:02 2009  relations with 6 large ideals: 27975
Mon Jun 29 21:32:02 2009  relations with 7+ large ideals: 3837
Mon Jun 29 21:32:02 2009  commencing 2-way merge
Mon Jun 29 21:32:03 2009  reduce to 804300 relation sets and 569947 unique ideals
Mon Jun 29 21:32:03 2009  commencing full merge
Mon Jun 29 21:32:12 2009  memory use: 43.1 MB
Mon Jun 29 21:32:12 2009  found 376706 cycles, need 346147
Mon Jun 29 21:32:12 2009  weight of 346147 cycles is about 24613171 (71.11/cycle)
Mon Jun 29 21:32:12 2009  distribution of cycle lengths:
Mon Jun 29 21:32:12 2009  1 relations: 36446
Mon Jun 29 21:32:12 2009  2 relations: 33802
Mon Jun 29 21:32:13 2009  3 relations: 34003
Mon Jun 29 21:32:13 2009  4 relations: 31923
Mon Jun 29 21:32:13 2009  5 relations: 30349
Mon Jun 29 21:32:13 2009  6 relations: 27713
Mon Jun 29 21:32:13 2009  7 relations: 25349
Mon Jun 29 21:32:13 2009  8 relations: 23008
Mon Jun 29 21:32:13 2009  9 relations: 20155
Mon Jun 29 21:32:13 2009  10+ relations: 83399
Mon Jun 29 21:32:13 2009  heaviest cycle: 18 relations
Mon Jun 29 21:32:13 2009  commencing cycle optimization
Mon Jun 29 21:32:13 2009  start with 2229788 relations
Mon Jun 29 21:32:20 2009  pruned 77903 relations
Mon Jun 29 21:32:20 2009  memory use: 56.0 MB
Mon Jun 29 21:32:20 2009  distribution of cycle lengths:
Mon Jun 29 21:32:20 2009  1 relations: 36446
Mon Jun 29 21:32:20 2009  2 relations: 34796
Mon Jun 29 21:32:20 2009  3 relations: 35589
Mon Jun 29 21:32:20 2009  4 relations: 33220
Mon Jun 29 21:32:20 2009  5 relations: 31692
Mon Jun 29 21:32:20 2009  6 relations: 28752
Mon Jun 29 21:32:20 2009  7 relations: 26007
Mon Jun 29 21:32:20 2009  8 relations: 23590
Mon Jun 29 21:32:20 2009  9 relations: 20541
Mon Jun 29 21:32:20 2009  10+ relations: 75514
Mon Jun 29 21:32:20 2009  heaviest cycle: 18 relations
Mon Jun 29 21:32:21 2009  RelProcTime: 298
Mon Jun 29 21:32:21 2009  
Mon Jun 29 21:32:21 2009  commencing linear algebra
Mon Jun 29 21:32:21 2009  read 346147 cycles
Mon Jun 29 21:32:21 2009  cycles contain 1137287 unique relations
Mon Jun 29 21:32:57 2009  read 1137287 relations
Mon Jun 29 21:32:58 2009  using 20 quadratic characters above 118112012
Mon Jun 29 21:33:06 2009  building initial matrix
Mon Jun 29 21:33:22 2009  memory use: 126.8 MB
Mon Jun 29 21:33:22 2009  read 346147 cycles
Mon Jun 29 21:33:23 2009  matrix is 345913 x 346147 (97.7 MB) with weight 32532069 (93.98/col)
Mon Jun 29 21:33:23 2009  sparse part has weight 23181247 (66.97/col)
Mon Jun 29 21:33:28 2009  filtering completed in 3 passes
Mon Jun 29 21:33:28 2009  matrix is 344348 x 344548 (97.4 MB) with weight 32420368 (94.10/col)
Mon Jun 29 21:33:28 2009  sparse part has weight 23116687 (67.09/col)
Mon Jun 29 21:33:29 2009  read 344548 cycles
Mon Jun 29 21:33:30 2009  matrix is 344348 x 344548 (97.4 MB) with weight 32420368 (94.10/col)
Mon Jun 29 21:33:30 2009  sparse part has weight 23116687 (67.09/col)
Mon Jun 29 21:33:30 2009  saving the first 48 matrix rows for later
Mon Jun 29 21:33:30 2009  matrix is 344300 x 344548 (93.4 MB) with weight 25498522 (74.01/col)
Mon Jun 29 21:33:30 2009  sparse part has weight 22429237 (65.10/col)
Mon Jun 29 21:33:30 2009  matrix includes 64 packed rows
Mon Jun 29 21:33:30 2009  using block size 65536 for processor cache size 3072 kB
Mon Jun 29 21:33:33 2009  commencing Lanczos iteration
Mon Jun 29 21:33:33 2009  memory use: 91.0 MB
Mon Jun 29 21:50:21 2009  lanczos halted after 5445 iterations (dim = 344300)
Mon Jun 29 21:50:21 2009  recovered 30 nontrivial dependencies
Mon Jun 29 21:50:22 2009  BLanczosTime: 1081
Mon Jun 29 21:50:22 2009  
Mon Jun 29 21:50:22 2009  commencing square root phase
Mon Jun 29 21:50:22 2009  reading relations for dependency 1
Mon Jun 29 21:50:22 2009  read 172326 cycles
Mon Jun 29 21:50:22 2009  cycles contain 703698 unique relations
Mon Jun 29 21:50:56 2009  read 703698 relations
Mon Jun 29 21:50:59 2009  multiplying 567642 relations
Mon Jun 29 21:52:27 2009  multiply complete, coefficients have about 22.77 million bits
Mon Jun 29 21:52:28 2009  initial square root is modulo 3467819
Mon Jun 29 21:54:35 2009  sqrtTime: 253
Mon Jun 29 21:54:35 2009  prp49 factor: 1680685663562710108755241113940108250558188502759
Mon Jun 29 21:54:35 2009  prp61 factor: 4455743436763288668170528477507378349835514471314046357878921
Mon Jun 29 21:54:35 2009  elapsed time 00:29:19
total time ~ 11 hours

Jun 29, 2009 (4th)

By Sinkiti Sibata / Msieve, GGNFS / Jun 29, 2009

(58·10¹³³-13)/9 = 6(4)₁₃₂3_<134> = 3 · 7 · 1489 · 68003251 · 16251891980953498210510658603_<29> · C94

C94 = P46 · P48

P46 = 3332366710852869308417885511991106085178367213_<46>

P48 = 559609530053519556611176759097123548994837054123_<48>

Sun Jun 28 20:57:37 2009  Msieve v. 1.41
Sun Jun 28 20:57:37 2009  random seeds: a9bdadcc 57a2d679
Sun Jun 28 20:57:37 2009  factoring 1864824169026366881665848988133902606847100055810034881259952154184029473528657675188049669199 (94 digits)
Sun Jun 28 20:57:38 2009  searching for 15-digit factors
Sun Jun 28 20:57:39 2009  commencing quadratic sieve (94-digit input)
Sun Jun 28 20:57:39 2009  using multiplier of 19
Sun Jun 28 20:57:39 2009  using 32kb Intel Core sieve core
Sun Jun 28 20:57:39 2009  sieve interval: 36 blocks of size 32768
Sun Jun 28 20:57:39 2009  processing polynomials in batches of 6
Sun Jun 28 20:57:39 2009  using a sieve bound of 1986839 (74118 primes)
Sun Jun 28 20:57:39 2009  using large prime bound of 256302231 (27 bits)
Sun Jun 28 20:57:39 2009  using double large prime bound of 1366955142352932 (42-51 bits)
Sun Jun 28 20:57:39 2009  using trial factoring cutoff of 51 bits
Sun Jun 28 20:57:39 2009  polynomial 'A' values have 12 factors
Sun Jun 28 23:52:08 2009  74244 relations (18184 full + 56060 combined from 1032634 partial), need 74214
Sun Jun 28 23:52:10 2009  begin with 1050818 relations
Sun Jun 28 23:52:11 2009  reduce to 192288 relations in 11 passes
Sun Jun 28 23:52:11 2009  attempting to read 192288 relations
Sun Jun 28 23:52:13 2009  recovered 192288 relations
Sun Jun 28 23:52:13 2009  recovered 175552 polynomials
Sun Jun 28 23:52:14 2009  attempting to build 74244 cycles
Sun Jun 28 23:52:14 2009  found 74244 cycles in 6 passes
Sun Jun 28 23:52:14 2009  distribution of cycle lengths:
Sun Jun 28 23:52:14 2009     length 1 : 18184
Sun Jun 28 23:52:14 2009     length 2 : 13292
Sun Jun 28 23:52:14 2009     length 3 : 12515
Sun Jun 28 23:52:14 2009     length 4 : 9850
Sun Jun 28 23:52:14 2009     length 5 : 7471
Sun Jun 28 23:52:14 2009     length 6 : 5174
Sun Jun 28 23:52:14 2009     length 7 : 3312
Sun Jun 28 23:52:14 2009     length 9+: 4446
Sun Jun 28 23:52:14 2009  largest cycle: 19 relations
Sun Jun 28 23:52:14 2009  matrix is 74118 x 74244 (19.4 MB) with weight 4794826 (64.58/col)
Sun Jun 28 23:52:14 2009  sparse part has weight 4794826 (64.58/col)
Sun Jun 28 23:52:15 2009  filtering completed in 3 passes
Sun Jun 28 23:52:15 2009  matrix is 70508 x 70572 (18.6 MB) with weight 4594906 (65.11/col)
Sun Jun 28 23:52:15 2009  sparse part has weight 4594906 (65.11/col)
Sun Jun 28 23:52:15 2009  saving the first 48 matrix rows for later
Sun Jun 28 23:52:15 2009  matrix is 70460 x 70572 (12.0 MB) with weight 3588469 (50.85/col)
Sun Jun 28 23:52:15 2009  sparse part has weight 2713229 (38.45/col)
Sun Jun 28 23:52:15 2009  matrix includes 64 packed rows
Sun Jun 28 23:52:15 2009  using block size 28228 for processor cache size 1024 kB
Sun Jun 28 23:52:16 2009  commencing Lanczos iteration
Sun Jun 28 23:52:16 2009  memory use: 11.4 MB
Sun Jun 28 23:52:49 2009  lanczos halted after 1116 iterations (dim = 70458)
Sun Jun 28 23:52:49 2009  recovered 16 nontrivial dependencies
Sun Jun 28 23:52:50 2009  prp46 factor: 3332366710852869308417885511991106085178367213
Sun Jun 28 23:52:50 2009  prp48 factor: 559609530053519556611176759097123548994837054123
Sun Jun 28 23:52:50 2009  elapsed time 02:55:13

(58·10¹¹⁷-13)/9 = 6(4)₁₁₆3_<118> = C118

C118 = P45 · P73

P45 = 675790396195456442895915104432949740666991523_<45>

P73 = 9536158668020699116745173193884730385667768369512984877372857570707904041_<73>

Number: 64443_117
N=6444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
  ( 118 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=675790396195456442895915104432949740666991523 (pp45)
 r2=9536158668020699116745173193884730385667768369512984877372857570707904041 (pp73)
Version: Msieve-1.40
Total time: 1.62 hours.
Scaled time: 3.37 units (timescale=2.085).
Factorization parameters were as follows:
name: 64443_117
n: 6444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
m: 200000000000000000000000
deg: 5
c5: 725
c0: -52
skew: 0.59
type: snfs
lss: 1
rlim: 680000
alim: 680000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 680000/680000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [340000, 590001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 80828 x 81054
Total sieving time: 1.56 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,119.000,5,0,0,0,0,0,0,0,0,680000,680000,25,25,45,45,2.2,2.2,50000
total time: 1.62 hours.
 --------- CPU info (if available) ----------

(58·10¹⁴⁴-13)/9 = 6(4)₁₄₃3_<145> = 970493 · C139

C139 = P37 · P103

P37 = 2093179992515501466190084387420835861_<37>

P103 = 3172389486725938777025473977276200607103207453371670538718534881764544597885610351738781046647527068891_<103>

Number: 64443_144
N=6640382202081256067219902095578684693701494440912448049027086691449031002227161292708390935786702680436071609423709851018445722374550300151
  ( 139 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=2093179992515501466190084387420835861 (pp37)
 r2=3172389486725938777025473977276200607103207453371670538718534881764544597885610351738781046647527068891 (pp103)
Version: Msieve-1.40
Total time: 10.37 hours.
Scaled time: 26.59 units (timescale=2.564).
Factorization parameters were as follows:
name: 64443_144
n: 6640382202081256067219902095578684693701494440912448049027086691449031002227161292708390935786702680436071609423709851018445722374550300151
m: 100000000000000000000000000000
deg: 5
c5: 29
c0: -65
skew: 1.18
type: snfs
lss: 1
rlim: 1930000
alim: 1930000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1930000/1930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [965000, 2265001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 342546 x 342794
Total sieving time: 9.86 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000
total time: 10.37 hours.
 --------- CPU info (if available) ----------

(58·10¹³⁶-13)/9 = 6(4)₁₃₅3_<137> = 3² · 58871741 · C129

C129 = P48 · P81

P48 = 235727953664055447319411949797137297749012365291_<48>

P81 = 515970662989061743281594639447232372573905136516236978628437287176925324434133117_<81>

Number: 64443_136
N=121628708537097515549276754481585550988894550055186814114440641854985974122295683886102397195294323420136221674852351099324442047
  ( 129 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=235727953664055447319411949797137297749012365291 (pp48)
 r2=515970662989061743281594639447232372573905136516236978628437287176925324434133117 (pp81)
Version: Msieve-1.40
Total time: 5.51 hours.
Scaled time: 14.12 units (timescale=2.564).
Factorization parameters were as follows:
name: 64443_136
n: 121628708537097515549276754481585550988894550055186814114440641854985974122295683886102397195294323420136221674852351099324442047
m: 2000000000000000000000000000
deg: 5
c5: 145
c0: -104
skew: 0.94
type: snfs
lss: 1
rlim: 1430000
alim: 1430000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1430000/1430000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [715000, 1465001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 223069 x 223300
Total sieving time: 5.25 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,138.000,5,0,0,0,0,0,0,0,0,1430000,1430000,26,26,48,48,2.3,2.3,75000
total time: 5.51 hours.
 --------- CPU info (if available) ----------

(58·10¹³⁹-13)/9 = 6(4)₁₃₈3_<140> = 3 · 7 · 19 · 1231 · 1060570349_<10> · 1193524663_<10> · 83228320831_<11> · C106

C106 = P53 · P53

P53 = 32502218758975974264690934359203256203943891833157149_<53>

P53 = 38317707245925041958237144145989843140569750883793499_<53>

Number: 64443_139
N=1245410503249454513950936539400601771642350901839495372749797874484849665147960918528578908546230931574351
  ( 106 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=32502218758975974264690934359203256203943891833157149 (pp53)
 r2=38317707245925041958237144145989843140569750883793499 (pp53)
Version: Msieve-1.40
Total time: 7.24 hours.
Scaled time: 15.19 units (timescale=2.099).
Factorization parameters were as follows:
name: 64443_139
n: 1245410503249454513950936539400601771642350901839495372749797874484849665147960918528578908546230931574351
m: 10000000000000000000000000000
deg: 5
c5: 29
c0: -65
skew: 1.18
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 237619 x 237853
Total sieving time: 6.89 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 7.24 hours.
 --------- CPU info (if available) ----------

(58·10¹⁶²-13)/9 = 6(4)₁₆₁3_<163> = 498670553 · 868251372853531_<15> · 2403433417659585403_<19> · 1519135220149328937011_<22> · C100

C100 = P40 · P61

P40 = 3978007396055070106886225840980948818901_<40>

P61 = 1024783602569126724040280540933691019026235418901075033484997_<61>

Number: 64443_162
N=4076596750375945652022220384779745370572439383193580743868681381671398185956334119178766833053528297
  ( 100 digits)
Divisors found:
 r1=3978007396055070106886225840980948818901 (pp40)
 r2=1024783602569126724040280540933691019026235418901075033484997 (pp61)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 7.99 hours.
Scaled time: 3.78 units (timescale=0.473).
Factorization parameters were as follows:
name: 64443_162
n: 4076596750375945652022220384779745370572439383193580743868681381671398185956334119178766833053528297
skew: 2809.15
# norm 1.60e+14
c5: 875880
c4: 4607514726
c3: -15446799894661
c2: 2133887816628030
c1: 514909499414304834
c0: -27061090266943223903321
# alpha -6.39
Y1: 32280451331
Y0: -5414619025710030114
# Murphy_E 3.38e-09
# M 3423235280954909331517329139689087262865239008060333048147151500659748101870819046725204686439576175
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: RFBsize:135072, AFBsize:134813, largePrimes:3983622 encountered
Relations: rels:4123288, finalFF:497538
Max relations in full relation-set: 28
Initial matrix: 269969 x 497538 with sparse part having weight 35933016.
Pruned matrix : 142475 x 143888 with weight 12612276.
Total sieving time: 7.22 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 7.99 hours.
 --------- CPU info (if available) ----------

Jun 29, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve 1.41, ECMNET / Jun 29, 2009

(58·10¹⁶⁷-13)/9 = 6(4)₁₆₆3_<168> = 907 · 9309593 · 616323772949751279227_<21> · 253974892032742945956761_<24> · 284996068419181591076316632267_<30> · C85

C85 = P39 · P46

P39 = 173896095349135933269424744970466539597_<39>

P46 = 9838278194508804532101741831512619052600114781_<46>

Number: 0011
N=1710838162983627990454857587732199143565178607498223962752146552456866980922081483257
  ( 85 digits)
Divisors found:
 r1=173896095349135933269424744970466539597 (pp39)
 r2=9838278194508804532101741831512619052600114781 (pp46)
Version: Msieve v. 1.41
Total time: 1.39 hours.
Scaled time: 2.76 units (timescale=1.976).
Factorization parameters were as follows:
name: 0011
n:  1710838162983627990454857587732199143565178607498223962752146552456866980922081483257
m:  25598906778006399254
deg: 4
c4: 3984036
c3: -6341237708
c2: -5106462467755171
c1: 19869950659843206
c0: 4617545228137607483265
skew: 1379.250
type: gnfs
# adj. I(F,S) = 47.861
# E(F1,F2) = 1.101643e-003
# GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect.
# Options were: 
# lcd=1, enumLCD=12, maxS1=56.00000000, seed=1246215921.
# maxskew=1500.0
# These parameters should be manually set:
rlim: 550000
alim: 550000
lpbr: 24
lpba: 24
mfbr: 40
mfba: 40
rlambda: 1.9
alambda: 1.9
qintsize: 10000

type: gnfs
Factor base limits: 550000/550000
Large primes per side: 3
Large prime bits: 24/24
Max factor residue bits: 40/40
Sieved algebraic special-q in [275000, 605001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 46853 x 47079
Polynomial selection time: 0.14 hours.
Total sieving time: 1.23 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,84,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,550000,550000,24,24,40,40,1.9,1.9,10000
total time: 1.39 hours.
 --------- CPU info (if available) ----------

6·10²¹³+1 = 6(0)₂₁₂1_<214> = 887 · C211

C211 = P33 · C178

P33 = 710379914267074902446340727571899_<33>

C178 = [9522192505057989196554921686963471449090843139265281936834912784663455668678513277670521436604345942154664018593294330166634222414359055518446450597428054285995444333986164085477_<178>]

C211=P133*C178
C211=710379914267074902446340727571899<33>*9522192505057989196554921686963471449090843139265281936834912784663455668678513277670521436604345942154664018593294330166634222414359055518446450597428054285995444333986164085477<178>

Jun 29, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 29, 2009

(58·10¹³⁵-13)/9 = 6(4)₁₃₄3_<136> = 43 · 1605169 · C128

C128 = P41 · P88

P41 = 16684801071616165742858411059235412368987_<41>

P88 = 5595968120588461964689090820225357668914533447115863619998466725214360596278094821062067_<88>

Number: 64443_135
N=93367614895124271192721682764265688990546260157529228132197460921479794983326821827576953455389178168321310635080190055832916129
  ( 128 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=16684801071616165742858411059235412368987
 r2=5595968120588461964689090820225357668914533447115863619998466725214360596278094821062067
Version: 
Total time: 2.32 hours.
Scaled time: 5.53 units (timescale=2.389).
Factorization parameters were as follows:
n: 93367614895124271192721682764265688990546260157529228132197460921479794983326821827576953455389178168321310635080190055832916129
m: 1000000000000000000000000000
deg: 5
c5: 58
c0: -13
skew: 0.74
type: snfs
lss: 1
rlim: 1400000
alim: 1400000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [700000, 1300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3643747
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 195461 x 195709
Total sieving time: 2.04 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,26,26,48,48,2.3,2.3,50000
total time: 2.32 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673809)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672376)
Calibrating delay using timer specific routine.. 5430.28 BogoMIPS (lpj=2715140)

Jun 29, 2009

By Robert Backstrom / GGNFS / Jun 29, 2009

(58·10¹⁴⁵-13)/9 = 6(4)₁₄₄3_<146> = 3² · 7 · 701 · 745210479281_<12> · 8730110436289447812154290169607_<31> · C99

C99 = P44 · P55

P44 = 81209611999697626708180466005454678658771007_<44>

P55 = 2761981658215742112136342325393296828876923189500830369_<55>

Number: n
N=224299458813981879732712982352694968415152384821436552669343237460916892743989333004630031522311583
  ( 99 digits)
Divisors found:
 r1=81209611999697626708180466005454678658771007 (pp44)
 r2=2761981658215742112136342325393296828876923189500830369 (pp55)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.02 hours.
Scaled time: 7.33 units (timescale=1.823).
Factorization parameters were as follows:
n: 224299458813981879732712982352694968415152384821436552669343237460916892743989333004630031522311583
Y0: -14418171140978802868
Y1:  6052927273
c0:  10863423250545833835634935
c1: -878321344639862200188
c2: -38824411212279790
c3:  973149801761
c4: -49670352
c5:  360
skew: 22477.80
type: gnfs
name: KA_6_4_144_3
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [900000, 1300001)
Primes: RFBsize:135072, AFBsize:134465, largePrimes:10029840 encountered
Relations: rels:8639337, finalFF:328863
Max relations in full relation-set: 48
Initial matrix: 269621 x 328863 with sparse part having weight 31872885.
Pruned matrix : 227953 x 229365 with weight 16672392.
Total sieving time: 3.22 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.37 hours.
Total square root time: 0.17 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,28,28,56,56,2.5,2.5,100000
total time: 4.02 hours.
 --------- CPU info (if available) ----------

(58·10¹³⁰-13)/9 = 6(4)₁₂₉3_<131> = 3 · 23 · 233 · 191051625186109_<15> · C113

C113 = P37 · P76

P37 = 9787483305184856962017021595435426277_<37>

P76 = 2143673808252724180424039293341153908233557786918513112730116683447368346263_<76>

Number: n
N=20981171610035582164419150272767266755882901911373431794670668008723701373071536696140282554060983673945944952851
  ( 113 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=9787483305184856962017021595435426277 (pp37)
 r2=2143673808252724180424039293341153908233557786918513112730116683447368346263 (pp76)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.47 hours.
Scaled time: 4.50 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_4_129_3
n: 20981171610035582164419150272767266755882901911373431794670668008723701373071536696140282554060983673945944952851
m: 100000000000000000000000000
deg: 5
c5: 58
c0: -13
skew: 0.74
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [600000, 980001)
Primes: RFBsize:92938, AFBsize:92609, largePrimes:4750730 encountered
Relations: rels:4127468, finalFF:213711
Max relations in full relation-set: 48
Initial matrix: 185613 x 213711 with sparse part having weight 18258528.
Pruned matrix : 174221 x 175213 with weight 11392735.
Total sieving time: 2.07 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.17 hours.
Total square root time: 0.16 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,56,56,2.3,2.3,50000
total time: 2.47 hours.
 --------- CPU info (if available) ----------

Jun 28, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 28, 2009

(58·10¹²⁸-13)/9 = 6(4)₁₂₇3_<129> = 61 · 154046456857541_<15> · C113

C113 = P56 · P58

P56 = 14261505825626082595820373781089104840019592878166331551_<56>

P58 = 4808820337208844827360136163259599581637949123534929470293_<58>

Number: 64443_128
N=68581019253493123466471220014200095653837774179925416620219999548337191520566357504095160518146710794723443114443
  ( 113 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=14261505825626082595820373781089104840019592878166331551
 r2=4808820337208844827360136163259599581637949123534929470293
Version: 
Total time: 1.58 hours.
Scaled time: 3.78 units (timescale=2.390).
Factorization parameters were as follows:
n: 68581019253493123466471220014200095653837774179925416620219999548337191520566357504095160518146710794723443114443
m: 100000000000000000000000000
deg: 5
c5: 29
c0: -650
skew: 1.86
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2835190
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 156420 x 156668
Total sieving time: 1.38 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 1.58 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673809)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672376)
Calibrating delay using timer specific routine.. 5430.28 BogoMIPS (lpj=2715140)

Jun 28, 2009 (6th)

By Sinkiti Sibata / Msieve / Jun 28, 2009

(58·10¹¹⁴-13)/9 = 6(4)₁₁₃3_<115> = 43 · 47 · 89 · 563 · 16090520573459_<14> · C94

C94 = P38 · P57

P38 = 11253044703352173797806298790102967343_<38>

P57 = 351463824057779343280271448782487763478579276272297536337_<57>

Sun Jun 28 16:54:01 2009  Msieve v. 1.41
Sun Jun 28 16:54:01 2009  random seeds: ffdefb00 e3939988
Sun Jun 28 16:54:01 2009  factoring 3955038123733294154552830225937839027981089639074561881089832913509377721150125554052066842591 (94 digits)
Sun Jun 28 16:54:01 2009  searching for 15-digit factors
Sun Jun 28 16:54:03 2009  commencing quadratic sieve (94-digit input)
Sun Jun 28 16:54:03 2009  using multiplier of 5
Sun Jun 28 16:54:03 2009  using 32kb Intel Core sieve core
Sun Jun 28 16:54:03 2009  sieve interval: 36 blocks of size 32768
Sun Jun 28 16:54:03 2009  processing polynomials in batches of 6
Sun Jun 28 16:54:03 2009  using a sieve bound of 2025307 (75235 primes)
Sun Jun 28 16:54:03 2009  using large prime bound of 271391138 (28 bits)
Sun Jun 28 16:54:03 2009  using double large prime bound of 1515207662043732 (42-51 bits)
Sun Jun 28 16:54:03 2009  using trial factoring cutoff of 51 bits
Sun Jun 28 16:54:03 2009  polynomial 'A' values have 12 factors
Sun Jun 28 20:42:43 2009  75336 relations (18180 full + 57156 combined from 1080234 partial), need 75331
Sun Jun 28 20:42:44 2009  begin with 1098414 relations
Sun Jun 28 20:42:45 2009  reduce to 197110 relations in 9 passes
Sun Jun 28 20:42:45 2009  attempting to read 197110 relations
Sun Jun 28 20:42:48 2009  recovered 197110 relations
Sun Jun 28 20:42:48 2009  recovered 183003 polynomials
Sun Jun 28 20:42:48 2009  attempting to build 75336 cycles
Sun Jun 28 20:42:49 2009  found 75336 cycles in 6 passes
Sun Jun 28 20:42:49 2009  distribution of cycle lengths:
Sun Jun 28 20:42:49 2009     length 1 : 18180
Sun Jun 28 20:42:49 2009     length 2 : 13127
Sun Jun 28 20:42:49 2009     length 3 : 12543
Sun Jun 28 20:42:49 2009     length 4 : 10283
Sun Jun 28 20:42:49 2009     length 5 : 7819
Sun Jun 28 20:42:49 2009     length 6 : 5228
Sun Jun 28 20:42:49 2009     length 7 : 3525
Sun Jun 28 20:42:49 2009     length 9+: 4631
Sun Jun 28 20:42:49 2009  largest cycle: 23 relations
Sun Jun 28 20:42:49 2009  matrix is 75235 x 75336 (20.1 MB) with weight 4962914 (65.88/col)
Sun Jun 28 20:42:49 2009  sparse part has weight 4962914 (65.88/col)
Sun Jun 28 20:42:50 2009  filtering completed in 3 passes
Sun Jun 28 20:42:50 2009  matrix is 72005 x 72069 (19.3 MB) with weight 4777877 (66.30/col)
Sun Jun 28 20:42:50 2009  sparse part has weight 4777877 (66.30/col)
Sun Jun 28 20:42:50 2009  saving the first 48 matrix rows for later
Sun Jun 28 20:42:50 2009  matrix is 71957 x 72069 (12.2 MB) with weight 3788035 (52.56/col)
Sun Jun 28 20:42:50 2009  sparse part has weight 2761797 (38.32/col)
Sun Jun 28 20:42:50 2009  matrix includes 64 packed rows
Sun Jun 28 20:42:50 2009  using block size 28827 for processor cache size 1024 kB
Sun Jun 28 20:42:51 2009  commencing Lanczos iteration
Sun Jun 28 20:42:51 2009  memory use: 11.7 MB
Sun Jun 28 20:43:28 2009  lanczos halted after 1139 iterations (dim = 71951)
Sun Jun 28 20:43:28 2009  recovered 13 nontrivial dependencies
Sun Jun 28 20:43:29 2009  prp38 factor: 11253044703352173797806298790102967343
Sun Jun 28 20:43:29 2009  prp57 factor: 351463824057779343280271448782487763478579276272297536337
Sun Jun 28 20:43:29 2009  elapsed time 03:49:28

(55·10¹⁶⁸+53)/9 = 6(1)₁₆₇7_<169> = 3² · 23 · 8597 · 60736241 · 48550887541806695475431280614507_<32> · C124

C124 = P60 · P64

P60 = 409276563277414763663135352084046268821974277482384997407629_<60>

P64 = 2845384416537614405451040024545314866333284940268230907212204201_<64>

Number: 61117_168
N=1164549155203626829526840703770057776331666897044154747749189812937458891968038623377040295732783853980802775338775983249429
  ( 124 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=409276563277414763663135352084046268821974277482384997407629 (pp60)
 r2=2845384416537614405451040024545314866333284940268230907212204201 (pp64)
Version: Msieve-1.40
Total time: 80.05 hours.
Scaled time: 204.46 units (timescale=2.554).
Factorization parameters were as follows:
name: 61117_168
n: 1164549155203626829526840703770057776331666897044154747749189812937458891968038623377040295732783853980802775338775983249429
m: 5000000000000000000000000000000000
deg: 5
c5: 88
c0: 265
skew: 1.25
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 5750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1020457 x 1020705
Total sieving time: 77.37 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.40 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 80.05 hours.
 --------- CPU info (if available) ----------

Jun 28, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Jun 28, 2009

(19·10¹⁸⁵+11)/3 = 6(3)₁₈₄7_<186> = 23 · C185

C185 = P78 · P108

P78 = 273631349641806731525848462476809281476079559226376744837229076093340563539867_<78>

P108 = 100632591697200952849656764311882330854240620551378358640057703218893173694556069027234501070088318306649757_<108>

Number: n
N=27536231884057971014492753623188405797101449275362318840579710144927536231884057971014492753623188405797101449275362318840579710144927536231884057971014492753623188405797101449275362319
  ( 185 digits)
SNFS difficulty: 186 digits.
Divisors found:

Sun Jun 28 17:31:53 2009  prp78 factor: 273631349641806731525848462476809281476079559226376744837229076093340563539867
Sun Jun 28 17:31:53 2009  prp108 factor: 100632591697200952849656764311882330854240620551378358640057703218893173694556069027234501070088318306649757
Sun Jun 28 17:31:53 2009  elapsed time 03:29:19 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 190.82 hours.
Scaled time: 503.58 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_6_3_184_7
n: 27536231884057971014492753623188405797101449275362318840579710144927536231884057971014492753623188405797101449275362318840579710144927536231884057971014492753623188405797101449275362319
m: 10000000000000000000000000000000000000
deg: 5
c5: 19
c0: 11
skew: 0.90
type: snfs
lss: 1
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [4500000, 8500027)
Primes: RFBsize:602489, AFBsize:603121, largePrimes:21076591 encountered
Relations: rels:21063612, finalFF:1223628
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2072055 hash collisions in 22483145 relations
Msieve: matrix is 1553384 x 1553632 (420.8 MB)

Total sieving time: 190.28 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,56,56,2.5,2.5,100000
total time: 190.82 hours.
 --------- CPU info (if available) ----------

(58·10¹⁰¹-13)/9 = 6(4)₁₀₀3_<102> = 1069 · C99

C99 = P42 · P58

P42 = 378980653168484429716330805966707908641167_<42>

P58 = 1590709002596225501218237944810237612242622890947590032041_<58>

Number: n
N=602847936804905934933998544849807712296019124831098638395177216505560752520528011641201538301631847
  ( 99 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=378980653168484429716330805966707908641167 (pp42)
 r2=1590709002596225501218237944810237612242622890947590032041 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.35 hours.
Scaled time: 0.64 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_6_4_100_3
n: 602847936804905934933998544849807712296019124831098638395177216505560752520528011641201538301631847
m: 20000000000000000000000000
deg: 4
c4: 145
c0: -52
skew: 0.77
type: snfs
lss: 1
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2
qintsize: 10000
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [200000, 260001)
Primes: RFBsize:33860, AFBsize:33714, largePrimes:1034002 encountered
Relations: rels:968213, finalFF:100967
Max relations in full relation-set: 48
Initial matrix: 67641 x 100967 with sparse part having weight 4053842.
Pruned matrix : 52459 x 52861 with weight 1539494.
Total sieving time: 0.31 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.02 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,103,4,0,0,0,0,0,0,0,0,400000,400000,25,25,43,43,2.2,2.2,10000
total time: 0.35 hours.
 --------- CPU info (if available) ----------

Jun 28, 2009 (4th)

By Dmitry Domanov / ECMNET, GGNFS/msieve 1.41 / Jun 28, 2009

(2·10¹⁷²-17)/3 = (6)₁₇₁1_<172> = 17310897119749_<14> · C159

C159 = P34 · C126

P34 = 1198926844780485953297393643793523_<34>

C126 = [321215490763403568953802801349834582946542687658223456641360521873909777640871296136079965295434494691834967162688081300105243_<126>]

C159=P34*C126
C159=1198926844780485953297393643793523<34>*321215490763403568953802801349834582946542687658223456641360521873909777640871296136079965295434494691834967162688081300105243<126>

(56·10²⁰²+43)/9 = 6(2)₂₀₁7_<203> = 11 · C202

C202 = P60 · P143

P60 = 430270091015054667643764166187119702272619904315042374067203_<60>

P143 = 13146546261724103154134734048449804194958643080538462991695579386437701046476401588101268264567193940577012483460643381470898174364294389389619_<143>

Total sieving time: ~28 CPU-days
Total postprocessing time: 32:20 hours
prp60 factor: 430270091015054667643764166187119702272619904315042374067203
prp143 factor: 13146546261724103154134734048449804194958643080538462991695579386437701046476401588101268264567193940577012483460643381470898174364294389389619

Jun 28, 2009 (3rd)

By Wataru Sakai / Msieve / Jun 28, 2009

(47·10¹⁹¹+7)/9 = 5(2)₁₉₀3_<192> = 13 · 19 · C190

C190 = P90 · P101

P90 = 157199391414811481308413123039831010800549348549055356443631902777496014250523799578529659_<90>

P101 = 13449543220035923396736531400707244067808735111856700550761352132101359599419084915660120869479028651_<101>

Number: 52223_191
N=2114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260009
  ( 190 digits)
SNFS difficulty: 193 digits.
Divisors found:
 r1=157199391414811481308413123039831010800549348549055356443631902777496014250523799578529659
 r2=13449543220035923396736531400707244067808735111856700550761352132101359599419084915660120869479028651
Version: 
Total time: 619.85 hours.
Scaled time: 1242.18 units (timescale=2.004).
Factorization parameters were as follows:
n: 2114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260008996851102114260009
m: 200000000000000000000000000000000000000
deg: 5
c5: 235
c0: 112
skew: 0.86
type: snfs
lss: 1
rlim: 11900000
alim: 11900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 11900000/11900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [5950000, 12350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2061084 x 2061332
Total sieving time: 619.85 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,193,5,0,0,0,0,0,0,0,0,11900000,11900000,28,28,55,55,2.5,2.5,100000
total time: 619.85 hours.
 --------- CPU info (if available) ----------

(53·10¹⁹¹-17)/9 = 5(8)₁₉₀7_<192> = 13 · 3077325253235247465155976615079042868201_<40> · C152

C152 = P38 · P42 · P73

P38 = 30955878554994429517866299495278628197_<38>

P42 = 260830264234883533140803293326399923032711_<42>

P73 = 1823120991418613541878724349970952485904020949548098505262099347038089097_<73>

Number: 58887_191
N=45299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299
  ( 191 digits)
SNFS difficulty: 193 digits.
Divisors found:
 r1=30955878554994429517866299495278628197
 r2=3077325253235247465155976615079042868201
 r3=260830264234883533140803293326399923032711
 r4=1823120991418613541878724349970952485904020949548098505262099347038089097
Version:
Total time: 627.02 hours.
Scaled time: 1254.04 units (timescale=2.000).
Factorization parameters were as follows:
n: 45299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299
m: 200000000000000000000000000000000000000
deg: 5
c5: 265
c0: -272
skew: 1.01
type: snfs
lss: 1
rlim: 11900000
alim: 11900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 11900000/11900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [5950000, 13050001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 2074170 x 2074418
Total sieving time: 627.02 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,193,5,0,0,0,0,0,0,0,0,11900000,11900000,28,28,55,55,2.5,2.5,100000
total time: 627.02 hours.
 --------- CPU info (if available) ----------

Jun 28, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / Jun 28, 2009

(58·10¹¹⁹-13)/9 = 6(4)₁₁₈3_<120> = 877 · 2153 · 16433 · 124229663974013057_<18> · C93

C93 = P32 · P61

P32 = 31626202427768372681682563838197_<32>

P61 = 5286310259872520471610188001300077202533865033368128652932579_<61>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1236900711
Step 1 took 5784ms
Step 2 took 4948ms
********** Factor found in step 2: 31626202427768372681682563838197
Found probable prime factor of 32 digits: 31626202427768372681682563838197
Probable prime cofactor 5286310259872520471610188001300077202533865033368128652932579 has 61 digits

(58·10¹⁶⁷-13)/9 = 6(4)₁₆₆3_<168> = 907 · 9309593 · 616323772949751279227_<21> · 253974892032742945956761_<24> · C114

C114 = P30 · C85

P30 = 284996068419181591076316632267_<30>

C85 = [1710838162983627990454857587732199143565178607498223962752146552456866980922081483257_<85>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=578427496
Step 1 took 2408ms
********** Factor found in step 1: 284996068419181591076316632267
Found probable prime factor of 30 digits: 284996068419181591076316632267
Composite cofactor 1710838162983627990454857587732199143565178607498223962752146552456866980922081483257 has 85 digits

(58·10¹⁷⁴-13)/9 = 6(4)₁₇₃3_<175> = 23 · 2003 · 109917710069_<12> · 2561799797279_<13> · C147

C147 = P29 · P119

P29 = 28060415355482968596031509529_<29>

P119 = 17703932477233971993285289597402034285856075678888714104981748648524578359619999237243122567152169494477870888624600693_<119>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=380138816
Step 1 took 3284ms
Step 2 took 3172ms
********** Factor found in step 2: 28060415355482968596031509529
Found probable prime factor of 29 digits: 28060415355482968596031509529
Probable prime cofactor has 119 digits

(58·10¹⁷³-13)/9 = 6(4)₁₇₂3_<174> = 3636439 · C168

C168 = P28 · P34 · C106

P28 = 5201072681589129941159853013_<28>

P34 = 4151220228381396271312783062791689_<34>

C106 = [8208059208418425479971505016759308076623141385702515597077892607382839099391926518651326516913860567839841_<106>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=619016146
Step 1 took 3924ms
Step 2 took 3676ms
********** Factor found in step 2: 4151220228381396271312783062791689
Found probable prime factor of 34 digits: 4151220228381396271312783062791689
Composite cofactor 

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=4219703845
Step 1 took 3853ms
Step 2 took 3548ms
********** Factor found in step 2: 5201072681589129941159853013
Found probable prime factor of 28 digits: 5201072681589129941159853013

(58·10¹⁵⁵-13)/9 = 6(4)₁₅₄3_<156> = 227 · 42416069 · C146

C146 = P28 · C119

P28 = 2974192430852304989290612183_<28>

C119 = [22504022118921734259662990204779762049959337208129694385777166920187136905382202309246021844159118798649720943027231667_<119>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=697347838
Step 1 took 9721ms
Step 2 took 9808ms
********** Factor found in step 2: 2974192430852304989290612183
Found probable prime factor of 28 digits: 2974192430852304989290612183
Composite cofactor has 119 digits

(58·10¹¹²-13)/9 = 6(4)₁₁₁3_<113> = 3 · 31 · C111

C111 = P45 · P67

P45 = 652436120450225810366755666771025792484664531_<45>

P67 = 1062097872590924024217052162548785136776202179702201158841319923821_<67>

SNFS difficulty: 114 digits.
Divisors found:
 r1=652436120450225810366755666771025792484664531 (pp45)
 r2=1062097872590924024217052162548785136776202179702201158841319923821 (pp67)
Version: Msieve v. 1.42
Total time: 0.71 hours.
Scaled time: 1.91 units (timescale=2.699).
Factorization parameters were as follows:
n: 692951015531660692951015531660692951015531660692951015531660692951015531660692951015531660692951015531660692951
m: 20000000000000000000000
deg: 5
c5: 725
c0: -52
skew: 0.59
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [280000, 530001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 57409 x 57635
Total sieving time: 0.67 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,114.000,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000
total time: 0.71 hours.

(58·10¹¹⁶-13)/9 = 6(4)₁₁₅3_<117> = C117

C117 = P56 · P62

P56 = 36666873968480742387982057101824145634673636068789484339_<56>

P62 = 17575658208507661253565689505378100610551179018660768260310137_<62>

SNFS difficulty: 118 digits.
Divisors found:
 r1=36666873968480742387982057101824145634673636068789484339 (pp56)
 r2=17575658208507661253565689505378100610551179018660768260310137 (pp62)
Version: Msieve v. 1.42
Total time: 0.72 hours.
Scaled time: 1.97 units (timescale=2.739).
Factorization parameters were as follows:
n: 644444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
m: 200000000000000000000000
deg: 5
c5: 145
c0: -104
skew: 0.94
type: snfs
lss: 1
rlim: 670000
alim: 670000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 670000/670000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [335000, 585001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 70823 x 71049
Total sieving time: 0.67 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,118.000,5,0,0,0,0,0,0,0,0,670000,670000,25,25,45,45,2.2,2.2,50000
total time: 0.72 hours.

(58·10¹²²-13)/9 = 6(4)₁₂₁3_<123> = 63694693 · C116

C116 = P32 · P84

P32 = 20739698165441745472143977056603_<32>

P84 = 487842692297273949867459723857663010869242116718559328343030013911282591596902649517_<84>

SNFS difficulty: 124 digits.
Divisors found:
 r1=20739698165441745472143977056603 (pp32)
 r2=487842692297273949867459723857663010869242116718559328343030013911282591596902649517 (pp84)
Version: Msieve v. 1.42
Total time: 1.07 hours.
Scaled time: 2.92 units (timescale=2.738).
Factorization parameters were as follows:
n: 10117710190461934473009304628321930124452353423611672709442911428185146358181590488935152642064613521952989779610751
m: 2000000000000000000000000
deg: 5
c5: 725
c0: -52
skew: 0.59
type: snfs
lss: 1
rlim: 830000
alim: 830000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 830000/830000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [415000, 765001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 105540 x 105788
Total sieving time: 0.97 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,124.000,5,0,0,0,0,0,0,0,0,830000,830000,25,25,46,46,2.2,2.2,50000
total time: 1.07 hours.

(58·10¹⁵⁰-13)/9 = 6(4)₁₄₉3_<151> = 91520629 · 44412318343_<11> · 5279210260962477050762476446083_<31> · C102

C102 = P37 · P65

P37 = 9080338989895340087399783131537142371_<37>

P65 = 33074403639492669396853934308598204613343777969269022112121857233_<65>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1156783142
Step 1 took 6716ms
Step 2 took 7148ms
********** Factor found in step 2: 9080338989895340087399783131537142371
Found probable prime factor of 37 digits: 9080338989895340087399783131537142371
Probable prime cofactor has 65 digits

(58·10¹⁴¹-13)/9 = 6(4)₁₄₀3_<142> = 439 · 3083 · 5531 · 297691 · 120686142884170765021_<21> · C107

C107 = P29 · P78

P29 = 44671237448007050301716904523_<29>

P78 = 536404836594779201210885696729897207146989810269196135430698329060421809691473_<78>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=288397723
Step 1 took 6948ms
Step 2 took 264ms
********** Factor found in step 2: 44671237448007050301716904523
Found probable prime factor of 29 digits: 44671237448007050301716904523
Probable prime cofactor has 78 digits

(58·10¹⁹⁰-13)/9 = 6(4)₁₈₉3_<191> = 3² · 509² · 3547 · 1265377 · 12500658557_<11> · 189748339830808583554936738487_<30> · C136

C136 = P31 · P105

P31 = 8859562242390101042337256758079_<31>

P105 = 293023967158645378132168017909583983083045335220259236533576678613996132987368553614771402092617621838013_<105>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=60059875
Step 1 took 9684ms
Step 2 took 9073ms
********** Factor found in step 2: 8859562242390101042337256758079
Found probable prime factor of 31 digits: 8859562242390101042337256758079
Probable prime cofactor has 105 digits

(58·10¹⁶⁴-13)/9 = 6(4)₁₆₃3_<165> = 634425495437_<12> · C154

C154 = P38 · C116

P38 = 34223943495856159696154680142313760883_<38>

C116 = [29680745593852382710885424670845104038289735607516074357223266600260200692718744499668077307158865998260008404416733_<116>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1920900515
Step 1 took 9293ms
Step 2 took 9241ms
********** Factor found in step 2: 34223943495856159696154680142313760883
Found probable prime factor of 38 digits: 34223943495856159696154680142313760883
Composite cofactor has 116 digits

(58·10¹⁷²-13)/9 = 6(4)₁₇₁3_<173> = 3² · 31 · 41865383430599_<14> · C157

C157 = P34 · P123

P34 = 6908239763065591955895879222911977_<34>

P123 = 798654247269250625821363125778243854007703628918987098880286209849549880972564009269875503432979327263787634758461031670979_<123>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=526144718
Step 1 took 11613ms
Step 2 took 10593ms
********** Factor found in step 2: 6908239763065591955895879222911977
Found probable prime factor of 34 digits: 6908239763065591955895879222911977
Probable prime cofactor has 123 digits

(58·10¹⁸³-13)/9 = 6(4)₁₈₂3_<184> = 25919 · 5252563412071_<13> · C167

C167 = P39 · P128

P39 = 961420063382696913845039546496705687743_<39>

P128 = 49235999353202946808007492839763276913494801029546625572470190315605759777492573030933345460372056027724551909999157757321602349_<128>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1633217857
Step 1 took 10608ms
Step 2 took 10413ms
********** Factor found in step 2: 961420063382696913845039546496705687743
Found probable prime factor of 39 digits: 961420063382696913845039546496705687743
Probable prime cofactor has 128 digits

(58·10¹⁹⁶-13)/9 = 6(4)₁₉₅3_<197> = 3 · 23 · 257 · 24169 · C189

C189 = P30 · C160

P30 = 103847259321610372073924050253_<30>

C160 = [1447936609718760749360067535781392847535511656388177962890118978787031768606123874361301183998193725780863669969923596746060603885509742425909266190788773872803_<160>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2549112822
Step 1 took 12280ms
Step 2 took 11289ms
********** Factor found in step 2: 103847259321610372073924050253
Found probable prime factor of 30 digits: 103847259321610372073924050253
Composite cofactor has 160 digits

(58·10¹⁹⁸-13)/9 = 6(4)₁₉₇3_<199> = 43 · 1117 · 19237 · 24821 · 2784569 · 59237954935041703_<17> · C163

C163 = P32 · P132

P32 = 11886551500859734818658620538271_<32>

P132 = 143315551274420434222213373947337563362940576038866710475231323622530913839047854154795199333394648781320634451598336144835705100237_<132>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=581503178
Step 1 took 10729ms
Step 2 took 9936ms
********** Factor found in step 2: 11886551500859734818658620538271
Found probable prime factor of 32 digits: 11886551500859734818658620538271
Probable prime cofactor has 132 digits

Jun 28, 2009

Factorizations of 644...443 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jun 27, 2009 (5th)

By Andreas Tete / Msieve v. 1.42, GGNFS / Jun 27, 2009

(47·10¹⁸⁴+7)/9 = 5(2)₁₈₃3_<185> = 37663 · 135409 · 1588687 · 1021756909_<10> · 15578211305893_<14> · 1203431099965687585292929_<25> · C123

C123 = P56 · P67

P56 = 58503555637351580708422043524842421283873937516824943479_<56>

P67 = 5751563245817234489103450552093888364306272232411751491982339846761_<67>

Fri Jun 26 23:31:17 2009  Msieve v. 1.42
Fri Jun 26 23:31:17 2009  random seeds: a6acf584 39c875ea
Fri Jun 26 23:31:17 2009  factoring 336486900353415024147237600989002997396746148444863813675164649764209038471473839837535695797853611852188481025423346221519 (123 digits)
Fri Jun 26 23:31:18 2009  searching for 15-digit factors
Fri Jun 26 23:31:20 2009  commencing number field sieve (123-digit input)
Fri Jun 26 23:31:20 2009  R0: -487824567839495206772299
Fri Jun 26 23:31:20 2009  R1:  14668679888561
Fri Jun 26 23:31:20 2009  A0: -50331570058330244910862222320
Fri Jun 26 23:31:20 2009  A1:  768380589069646930261796
Fri Jun 26 23:31:20 2009  A2: -8962274101419223348
Fri Jun 26 23:31:20 2009  A3: -707850425755693
Fri Jun 26 23:31:20 2009  A4:  2360485890
Fri Jun 26 23:31:20 2009  A5:  12180
Fri Jun 26 23:31:20 2009  skew 126238.69, size 9.298006e-012, alpha -5.586956, combined = 2.122476e-010
Fri Jun 26 23:31:20 2009  
Fri Jun 26 23:31:20 2009  commencing relation filtering
Fri Jun 26 23:31:20 2009  commencing duplicate removal, pass 1
Fri Jun 26 23:31:20 2009  error -15 reading relation 69
Fri Jun 26 23:31:20 2009  error -15 reading relation 27248
Fri Jun 26 23:33:01 2009  found 1043150 hash collisions in 8851963 relations
Fri Jun 26 23:33:26 2009  added 58672 free relations
Fri Jun 26 23:33:26 2009  commencing duplicate removal, pass 2
Fri Jun 26 23:34:11 2009  found 999794 duplicates and 7910840 unique relations
Fri Jun 26 23:34:11 2009  memory use: 50.6 MB
Fri Jun 26 23:34:11 2009  reading rational ideals above 6094848
Fri Jun 26 23:34:11 2009  reading algebraic ideals above 6094848
Fri Jun 26 23:34:11 2009  commencing singleton removal, pass 1
Fri Jun 26 23:35:56 2009  relations with 0 large ideals: 212256
Fri Jun 26 23:35:56 2009  relations with 1 large ideals: 1376046
Fri Jun 26 23:35:56 2009  relations with 2 large ideals: 2997314
Fri Jun 26 23:35:56 2009  relations with 3 large ideals: 2528754
Fri Jun 26 23:35:56 2009  relations with 4 large ideals: 716094
Fri Jun 26 23:35:56 2009  relations with 5 large ideals: 25114
Fri Jun 26 23:35:56 2009  relations with 6 large ideals: 55262
Fri Jun 26 23:35:56 2009  relations with 7+ large ideals: 0
Fri Jun 26 23:35:56 2009  7910840 relations and about 7542439 large ideals
Fri Jun 26 23:35:56 2009  commencing singleton removal, pass 2
Fri Jun 26 23:37:42 2009  found 3526496 singletons
Fri Jun 26 23:37:42 2009  current dataset: 4384344 relations and about 3347379 large ideals
Fri Jun 26 23:37:42 2009  commencing singleton removal, pass 3
Fri Jun 26 23:38:55 2009  found 708171 singletons
Fri Jun 26 23:38:55 2009  current dataset: 3676173 relations and about 2596928 large ideals
Fri Jun 26 23:38:55 2009  commencing singleton removal, pass 4
Fri Jun 26 23:40:04 2009  found 188233 singletons
Fri Jun 26 23:40:04 2009  current dataset: 3487940 relations and about 2404927 large ideals
Fri Jun 26 23:40:04 2009  commencing singleton removal, final pass
Fri Jun 26 23:41:13 2009  memory use: 53.4 MB
Fri Jun 26 23:41:13 2009  commencing in-memory singleton removal
Fri Jun 26 23:41:13 2009  begin with 3487940 relations and 2532650 unique ideals
Fri Jun 26 23:41:17 2009  reduce to 3111783 relations and 2149870 ideals in 14 passes
Fri Jun 26 23:41:17 2009  max relations containing the same ideal: 37
Fri Jun 26 23:41:18 2009  reading rational ideals above 720000
Fri Jun 26 23:41:18 2009  reading algebraic ideals above 720000
Fri Jun 26 23:41:18 2009  commencing singleton removal, final pass
Fri Jun 26 23:42:25 2009  keeping 2757965 ideals with weight <= 20, new excess is 296631
Fri Jun 26 23:42:30 2009  memory use: 91.6 MB
Fri Jun 26 23:42:30 2009  commencing in-memory singleton removal
Fri Jun 26 23:42:30 2009  begin with 3123556 relations and 2757965 unique ideals
Fri Jun 26 23:42:35 2009  reduce to 3089558 relations and 2666631 ideals in 13 passes
Fri Jun 26 23:42:35 2009  max relations containing the same ideal: 20
Fri Jun 26 23:42:38 2009  removing 321434 relations and 282016 ideals in 39418 cliques
Fri Jun 26 23:42:38 2009  commencing in-memory singleton removal
Fri Jun 26 23:42:38 2009  begin with 2768124 relations and 2666631 unique ideals
Fri Jun 26 23:42:41 2009  reduce to 2746885 relations and 2363049 ideals in 7 passes
Fri Jun 26 23:42:41 2009  max relations containing the same ideal: 20
Fri Jun 26 23:42:43 2009  removing 240115 relations and 200697 ideals in 39418 cliques
Fri Jun 26 23:42:43 2009  commencing in-memory singleton removal
Fri Jun 26 23:42:43 2009  begin with 2506770 relations and 2363049 unique ideals
Fri Jun 26 23:42:45 2009  reduce to 2492837 relations and 2148206 ideals in 7 passes
Fri Jun 26 23:42:45 2009  max relations containing the same ideal: 20
Fri Jun 26 23:42:47 2009  relations with 0 large ideals: 13137
Fri Jun 26 23:42:47 2009  relations with 1 large ideals: 106816
Fri Jun 26 23:42:47 2009  relations with 2 large ideals: 367021
Fri Jun 26 23:42:47 2009  relations with 3 large ideals: 664916
Fri Jun 26 23:42:47 2009  relations with 4 large ideals: 697372
Fri Jun 26 23:42:47 2009  relations with 5 large ideals: 436442
Fri Jun 26 23:42:47 2009  relations with 6 large ideals: 165605
Fri Jun 26 23:42:47 2009  relations with 7+ large ideals: 41528
Fri Jun 26 23:42:47 2009  commencing 2-way merge
Fri Jun 26 23:42:50 2009  reduce to 1533730 relation sets and 1189099 unique ideals
Fri Jun 26 23:42:50 2009  commencing full merge
Fri Jun 26 23:43:13 2009  memory use: 103.6 MB
Fri Jun 26 23:43:14 2009  found 759285 cycles, need 713299
Fri Jun 26 23:43:14 2009  weight of 713299 cycles is about 50132409 (70.28/cycle)
Fri Jun 26 23:43:14 2009  distribution of cycle lengths:
Fri Jun 26 23:43:14 2009  1 relations: 81341
Fri Jun 26 23:43:14 2009  2 relations: 80416
Fri Jun 26 23:43:14 2009  3 relations: 79712
Fri Jun 26 23:43:14 2009  4 relations: 73116
Fri Jun 26 23:43:14 2009  5 relations: 67623
Fri Jun 26 23:43:14 2009  6 relations: 59640
Fri Jun 26 23:43:14 2009  7 relations: 52283
Fri Jun 26 23:43:14 2009  8 relations: 44735
Fri Jun 26 23:43:14 2009  9 relations: 38808
Fri Jun 26 23:43:14 2009  10+ relations: 135625
Fri Jun 26 23:43:14 2009  heaviest cycle: 18 relations
Fri Jun 26 23:43:14 2009  commencing cycle optimization
Fri Jun 26 23:43:16 2009  start with 4176779 relations
Fri Jun 26 23:43:27 2009  pruned 122566 relations
Fri Jun 26 23:43:27 2009  memory use: 108.8 MB
Fri Jun 26 23:43:27 2009  distribution of cycle lengths:
Fri Jun 26 23:43:27 2009  1 relations: 81341
Fri Jun 26 23:43:27 2009  2 relations: 82483
Fri Jun 26 23:43:27 2009  3 relations: 83177
Fri Jun 26 23:43:27 2009  4 relations: 75664
Fri Jun 26 23:43:27 2009  5 relations: 69884
Fri Jun 26 23:43:27 2009  6 relations: 60818
Fri Jun 26 23:43:27 2009  7 relations: 53164
Fri Jun 26 23:43:27 2009  8 relations: 44844
Fri Jun 26 23:43:27 2009  9 relations: 38867
Fri Jun 26 23:43:27 2009  10+ relations: 123057
Fri Jun 26 23:43:27 2009  heaviest cycle: 18 relations
Fri Jun 26 23:43:28 2009  RelProcTime: 517
Fri Jun 26 23:43:28 2009  
Fri Jun 26 23:43:28 2009  commencing linear algebra
Fri Jun 26 23:43:28 2009  read 713299 cycles
Fri Jun 26 23:43:30 2009  cycles contain 2252275 unique relations
Fri Jun 26 23:44:06 2009  read 2252275 relations
Fri Jun 26 23:44:10 2009  using 20 quadratic characters above 134214012
Fri Jun 26 23:44:24 2009  building initial matrix
Fri Jun 26 23:45:01 2009  memory use: 262.0 MB
Fri Jun 26 23:45:02 2009  read 713299 cycles
Fri Jun 26 23:45:04 2009  matrix is 713058 x 713299 (201.5 MB) with weight 67363351 (94.44/col)
Fri Jun 26 23:45:04 2009  sparse part has weight 47840390 (67.07/col)
Fri Jun 26 23:45:19 2009  filtering completed in 3 passes
Fri Jun 26 23:45:19 2009  matrix is 709979 x 710179 (201.1 MB) with weight 67172917 (94.59/col)
Fri Jun 26 23:45:19 2009  sparse part has weight 47741684 (67.22/col)
Fri Jun 26 23:45:21 2009  read 710179 cycles
Fri Jun 26 23:45:22 2009  matrix is 709979 x 710179 (201.1 MB) with weight 67172917 (94.59/col)
Fri Jun 26 23:45:22 2009  sparse part has weight 47741684 (67.22/col)
Fri Jun 26 23:45:22 2009  saving the first 48 matrix rows for later
Fri Jun 26 23:45:23 2009  matrix is 709931 x 710179 (194.0 MB) with weight 53262504 (75.00/col)
Fri Jun 26 23:45:23 2009  sparse part has weight 46602145 (65.62/col)
Fri Jun 26 23:45:23 2009  matrix includes 64 packed rows
Fri Jun 26 23:45:23 2009  using block size 65536 for processor cache size 3072 kB
Fri Jun 26 23:45:29 2009  commencing Lanczos iteration
Fri Jun 26 23:45:29 2009  memory use: 191.5 MB
Sat Jun 27 01:00:51 2009  lanczos halted after 11229 iterations (dim = 709931)
Sat Jun 27 01:00:53 2009  recovered 32 nontrivial dependencies
Sat Jun 27 01:00:53 2009  BLanczosTime: 4645
Sat Jun 27 01:00:53 2009  
Sat Jun 27 01:00:53 2009  commencing square root phase
Sat Jun 27 01:00:53 2009  reading relations for dependency 1
Sat Jun 27 01:00:54 2009  read 354935 cycles
Sat Jun 27 01:00:55 2009  cycles contain 1379817 unique relations
Sat Jun 27 01:01:45 2009  read 1379817 relations
Sat Jun 27 01:01:53 2009  multiplying 1124500 relations
Sat Jun 27 01:05:21 2009  multiply complete, coefficients have about 49.76 million bits
Sat Jun 27 01:05:22 2009  initial square root is modulo 13925531
Sat Jun 27 01:09:52 2009  sqrtTime: 539
Sat Jun 27 01:09:52 2009  prp56 factor: 58503555637351580708422043524842421283873937516824943479
Sat Jun 27 01:09:52 2009  prp67 factor: 5751563245817234489103450552093888364306272232411751491982339846761
Sat Jun 27 01:09:52 2009  elapsed time 01:38:35
total time ~ 56 hours 40 minutes

Jun 27, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jun 27, 2009

4·10²¹⁷-9 = 3(9)₂₁₆1_<218> = C218

C218 = P54 · P165

P54 = 153138923096637815337324392839746144304740150626975813_<54>

P165 = 261200739767238216403031051949070797540409290687764527939818984072695012732362463527871657040814436595996243277659214477992470411020857002428756477130421386528676107_<165>

Number: n
N=39999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 218 digits)
SNFS difficulty: 217 digits.
Divisors found:

Sat Jun 27 16:32:05 2009  prp54 factor: 153138923096637815337324392839746144304740150626975813
Sat Jun 27 16:32:05 2009  prp165 factor: 261200739767238216403031051949070797540409290687764527939818984072695012732362463527871657040814436595996243277659214477992470411020857002428756477130421386528676107
Sat Jun 27 16:32:05 2009  elapsed time 62:55:06 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20050930-k8
Total time: 201.57 hours.
Scaled time: 406.36 units (timescale=2.016).
Factorization parameters were as follows:
name: KA_3_9_216_1
n: 39999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 1000000000000000000000000000000000000
deg: 6
c6: 40
c0: -9
skew: 0.78
type: snfs
lss: 1
rlim: 30000000
alim: 30000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 30000000/30000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [15000000, 51099990)
Primes: RFBsize:1857859, AFBsize:1857909, largePrimes:38359729 encountered
Relations: rels:35364571, finalFF:1138388
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 9231841 hash collisions in 50553036 relations
Msieve: matrix is 5454062 x 5454310 (1490.4 MB)

Total sieving time: 200.07 hours.
Total relation processing time: 1.49 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,217,6,0,0,0,0,0,0,0,0,30000000,30000000,29,29,58,58,2.6,2.6,100000
total time: 201.57 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3352056k/3407296k available (3119k kernel code, 53956k reserved, 1894k data, 424k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.68 BogoMIPS (lpj=2830844)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22644.41 BogoMIPS).

Jun 27, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Jun 27, 2009

(14·10¹⁶⁹-17)/3 = 4(6)₁₆₈1_<170> = 215880244364499579382801212799_<30> · C141

C141 = P39 · P47 · P56

P39 = 164987940471911919931720360662845119279_<39>

P47 = 32526795988018253979416672362657704392943753593_<47>

P56 = 40281013844684900168945533327602460233451320127931079037_<56>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 216169232177971192501955249216876153564299586479509590522860815653381675214844760678296009204006289701356974365633658790823919329922476632539 (141 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5538504349
Step 1 took 4012ms
Step 2 took 2371ms
********** Factor found in step 2: 164987940471911919931720360662845119279
Found probable prime factor of 39 digits: 164987940471911919931720360662845119279
Composite cofactor 1310212319516604554737041668268993579654865949023704998524458434780684269585853050111262206001535729941 has 103 digits

Number: 46661_169
N=1310212319516604554737041668268993579654865949023704998524458434780684269585853050111262206001535729941
  ( 103 digits)
Divisors found:
 r1=32526795988018253979416672362657704392943753593
 r2=40281013844684900168945533327602460233451320127931079037
Version: 
Total time: 3.63 hours.
Scaled time: 8.68 units (timescale=2.390).
Factorization parameters were as follows:
name: 46661_169
n: 1310212319516604554737041668268993579654865949023704998524458434780684269585853050111262206001535729941
skew: 7580.79
# norm 2.17e+13
c5: 11640
c4: 80574174
c3: -2644906284335
c2: -10484031778600973
c1: 62593522390370734919
c0: -62150029590737475022585
# alpha -4.06
Y1: 57271184329
Y0: -40764009580135475262
# Murphy_E 2.53e-09
# M 1010454591132022271215501380240311892732052755553949690211722162287652266129439944490048921978649313790
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4804835
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 257647 x 257895
Polynomial selection time: 0.25 hours.
Total sieving time: 2.93 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 3.63 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672386)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5237.73 BogoMIPS (lpj=2618866)

Jun 27, 2009 (2nd)

By Dmitry Domanov / GGNFS/Msieve 1.41 / Jun 27, 2009

(16·10¹⁸⁴-7)/9 = 1(7)₁₈₄_<185> = 4639 · 2208469987_<10> · 122889553861_<12> · 2043810257434261739_<19> · C142

C142 = P61 · P82

P61 = 3963965902151640309444352830053938422744024270549330775181009_<61>

P82 = 1742914757078340982220330559551431495030549136659252945881611664525081678798945299_<82>

N=6908854667415452929349067257832242713851174690747514804546818467887473298594120925395357875176704646282864437854825702195352929879995014626691
  ( 142 digits)
SNFS difficulty: 185 digits.
Divisors found:
r1=3963965902151640309444352830053938422744024270549330775181009 (pp61)
r2=1742914757078340982220330559551431495030549136659252945881611664525081678798945299 (pp82)
Version: Msieve v. 1.41
Total time: 203.60 hours.
Scaled time: 404.75 units (timescale=1.988).
Factorization parameters were as follows:
n: 6908854667415452929349067257832242713851174690747514804546818467887473298594120925395357875176704646282864437854825702195352929879995014626691
m: 10000000000000000000000000000000000000
deg: 5
c5: 8
c0: -35
skew: 1.34
type: snfs
lss: 1
rlim: 8800000
alim: 8800000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8800000/8800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4400000, 7400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1652077 x 1652325
Total sieving time: 198.57 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 4.38 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
snfs,185.000,5,0,0,0,0,0,0,0,0,8800000,8800000,28,28,54,54,2.5,2.5,100000
total time: 203.60 hours.
 --------- CPU info (if available) ----------

Jun 27, 2009

By Tyler Cadigan / PRIMO 3.0.7 / Jun 27, 2009

(10²⁹⁵²+17)/9 = (1)₂₉₅₁3_<2952> is prime.

Jun 26, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jun 26, 2009

(8·10¹⁷⁴+7)/3 = 2(6)₁₇₃9_<175> = 9291193902637_<13> · 35960739752300141123644395023_<29> · C133

C133 = P42 · P92

P42 = 147246485091491533084862542850273174082841_<42>

P92 = 54203041264768699675736191181175423376382598279706791561135352844935913636053459860335938759_<92>

C133=P42*P92
C133=147246485091491533084862542850273174082841<42>*54203041264768699675736191181175423376382598279706791561135352844935913636053459860335938759<92>

Jun 26, 2009

By Robert Backstrom / GGNFS, Msieve / Jun 26, 2009

(35·10¹⁶⁷-17)/9 = 3(8)₁₆₆7_<168> = 3 · 219943721724751_<15> · 25906357094181540237749_<23> · C131

C131 = P57 · P74

P57 = 996244817379145944395119476840665614982629783547816089009_<57>

P74 = 22836013332760580540298944200610015633803921232860776910122536509987443319_<74>

Number: n
N=22750259932363806506452932866536434963285158584917848593353721346670116012441195229750928624948194947776451081125903243713646380871
  ( 131 digits)
SNFS difficulty: 169 digits.
Divisors found:

Fri Jun 26 01:01:57 2009  prp57 factor: 996244817379145944395119476840665614982629783547816089009
Fri Jun 26 01:01:57 2009  prp74 factor: 22836013332760580540298944200610015633803921232860776910122536509987443319
Fri Jun 26 01:01:57 2009  elapsed time 01:14:28 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 49.98 hours.
Scaled time: 132.95 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_3_8_166_7
n: 22750259932363806506452932866536434963285158584917848593353721346670116012441195229750928624948194947776451081125903243713646380871
m: 5000000000000000000000000000000000
deg: 5
c5: 28
c0: -425
skew: 1.72
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2400000, 5202913)
Primes: RFBsize:335439, AFBsize:335322, largePrimes:16921186 encountered
Relations: rels:16583215, finalFF:748495
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2030599 hash collisions in 18840257 relations
Msieve: matrix is 793962 x 794210 (211.7 MB)

Total sieving time: 49.54 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000
total time: 49.98 hours.
 --------- CPU info (if available) ----------

(85·10¹⁶⁸+41)/9 = 9(4)₁₆₇9_<169> = 7 · 30130007026272762236778552242458213_<35> · C134

C134 = P39 · P95

P39 = 646081469853325946280782791194467559557_<39>

P95 = 69309355117636896116388768379746577518566014665395648129726751071650431763506721291831801078927_<95>

Number: n
N=44779490028988984693345170298727232692672656093119287564674642677206820719270872412399590798774417897156369411429035099199813230155339
  ( 134 digits)
SNFS difficulty: 170 digits.
Divisors found:

Fri Jun 26 12:38:16 2009  prp39 factor: 646081469853325946280782791194467559557
Fri Jun 26 12:38:16 2009  prp95 factor: 69309355117636896116388768379746577518566014665395648129726751071650431763506721291831801078927
Fri Jun 26 12:38:16 2009  elapsed time 01:40:25 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 45.19 hours.
Scaled time: 120.22 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_9_4_167_9
n: 44779490028988984693345170298727232692672656093119287564674642677206820719270872412399590798774417897156369411429035099199813230155339
m: 5000000000000000000000000000000000
deg: 5
c5: 136
c0: 205
skew: 1.09
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 4983701)
Primes: RFBsize:348513, AFBsize:348092, largePrimes:16608879 encountered
Relations: rels:15751124, finalFF:670651
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1838346 hash collisions in 18598297 relations
Msieve: matrix is 800495 x 800743 (213.7 MB)

Total sieving time: 44.69 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 45.19 hours.
 --------- CPU info (if available) ----------

(32·10¹⁶⁸+31)/9 = 3(5)₁₆₇9_<169> = 7 · 61 · 39983209801_<11> · 111470331997295376701_<21> · C136

C136 = P61 · P76

P61 = 1073104304815526983816771184467768044461214238015586531509631_<61>

P76 = 1741007758140672565912344588362661612431195406392316590249384001939025425007_<76>

Number: n
N=1868282919977985573733322020556574078433082808304869247090505648965219877477967805693204420862322587884350227847740147854847247088742417
  ( 136 digits)
SNFS difficulty: 170 digits.
Divisors found:

Fri Jun 26 12:41:03 2009  prp61 factor: 1073104304815526983816771184467768044461214238015586531509631
Fri Jun 26 12:41:03 2009  prp76 factor: 1741007758140672565912344588362661612431195406392316590249384001939025425007
Fri Jun 26 12:41:03 2009  elapsed time 01:41:17 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 45.35 hours.
Scaled time: 120.14 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_3_5_167_9
n: 1868282919977985573733322020556574078433082808304869247090505648965219877477967805693204420862322587884350227847740147854847247088742417
m: 4000000000000000000000000000000000
deg: 5
c5: 125
c0: 124
skew: 1.00
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2400000, 4894117)
Primes: RFBsize:335439, AFBsize:335383, largePrimes:15896129 encountered
Relations: rels:14761745, finalFF:507282
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1791801 hash collisions in 17666333 relations
Msieve: matrix is 827896 x 828144 (222.0 MB)

Total sieving time: 44.92 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000
total time: 45.35 hours.
 --------- CPU info (if available) ----------

Jun 25, 2009 (2nd)

By matsui / GMP-ECM / Jun 25, 2009

(55·10¹⁹²+17)/9 = 6(1)₁₉₁3_<193> = 83 · C191

C191 = P37 · P155

P37 = 1554680079421055663241309632741999791_<37>

P155 = 47358839729650484514213082265957188539646153312865411770034607331778178504222288115743334089402845551750039467061001611721179865193092780024997006733901821_<155>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
73627844712182061579651941097724230254350736278447121820615796519410977242302543507362784471218206157965194109772423025435073627844712182061579651941097724230254350736278447121820615796519411
=
1554680079421055663241309632741999791* 47358839729650484514213082265957188539646153312865411770034607331778178504222288115743334089402845551750039467061001611721179865193092780024997006733901821

(53·10¹⁹¹-17)/9 = 5(8)₁₉₀7_<192> = 13 · C191

C191 = P40 · C152

P40 = 3077325253235247465155976615079042868201_<40>

C152 = [14720298171771570716723886854991671208898715252902464943556125290604128965082355315462245187807878703850020843469774087345493414370248002017144961313499_<152>]

45299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299
=
3077325253235247465155976615079042868201* 14720298171771570716723886854991671208898715252902464943556125290604128965082355315462245187807878703850020843469774087345493414370248002017144961313499

Jun 25, 2009

By Jo Yeong Uk / GMP-ECM / Jun 25, 2009

(4·10¹⁷⁰-7)/3 = 1(3)₁₆₉1_<171> = 31 · 109789 · 9312411211130847248950201_<25> · C139

C139 = P40 · P100

P40 = 1502800256281439263857988805655344280607_<40>

P100 = 2799334573149479855515889170258387660810275368454048558247681468213445701259426026270237351262891687_<100>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 4206840713946531714695528183547906105304724835861710639562086194419321364323506470619518559763137831380386962778321740712084950551575614009 (139 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4784109703
Step 1 took 4633ms
Step 2 took 4431ms
********** Factor found in step 2: 1502800256281439263857988805655344280607
Found probable prime factor of 40 digits: 1502800256281439263857988805655344280607
Probable prime cofactor 2799334573149479855515889170258387660810275368454048558247681468213445701259426026270237351262891687 has 100 digits

Jun 24, 2009 (6th)

By Serge Batalov / PFGW / Jun 23, 2009

(14·10²⁸¹⁷-17)/3 = 4(6)₂₈₁₆1_<2818> is prime.

(22·10³⁵²⁰-13)/9 = 2(4)₃₅₁₉3_<3521> is prime.

Jun 24, 2009 (5th)

By Robert Backstrom / GMP-ECM / Jun 24, 2009

(22·10¹⁶⁸-31)/9 = 2(4)₁₆₇1_<169> = 8873219 · 11099060621790018608384460043_<29> · C134

C134 = P42 · P92

P42 = 371200625538831365829940284569021747043127_<42>

P92 = 66865800468067413875508513185834603191397073474295317096215322040316133061063996555098731599_<92>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 24820626960901307166243457286366035083079281210552737892128741525214711320317507910090012420833207935695272455422603107378826450670073 (134 digits)
Using B1=5878000, B2=11417264050, polynomial Dickson(12), sigma=4081711366
Step 1 took 72790ms
********** Factor found in step 1: 371200625538831365829940284569021747043127
Found probable prime factor of 42 digits: 371200625538831365829940284569021747043127
Probable prime cofactor 66865800468067413875508513185834603191397073474295317096215322040316133061063996555098731599 has 92 digits

Jun 24, 2009 (4th)

By Andreas Tete / Syd`s Database workers / Jun 24, 2009

6·10²⁰⁵+1 = 6(0)₂₀₄1_<206> = 31 · 47 · 107 · 321588220688443027059385703_<27> · C175

C175 = P32 · P143

P32 = 52608200965763511019049070037321_<32>

P143 = 22748582359849985239621437062492301500654660877058842699222608390850103339364205134046046593760422318845790606886535630528076929599435895212973_<143>

This factor is from Syd`s Database
52608200965763511019049070037321

Jun 24, 2009 (3rd)

By Jo Yeong Uk / GMP-ECM / Jun 24, 2009

(22·10¹⁶⁷-13)/9 = 2(4)₁₆₆3_<168> = 3 · 103 · 180519949 · 99146963869_<11> · 20757436223520443_<17> · C130

C130 = P42 · P89

P42 = 167490769827406767572595332518138087825351_<42>

P89 = 12713129747157146466674781904758060906332193817674471949615764473430324022539144529420019_<89>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 2129331888267055615375292847991745991122250793026866418237055157471572765868882564504408062284213491426581138168217340664995101669 (130 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1892633111
Step 1 took 9996ms
Step 2 took 5101ms
********** Factor found in step 2: 167490769827406767572595332518138087825351
Found probable prime factor of 42 digits: 167490769827406767572595332518138087825351
Probable prime cofactor 12713129747157146466674781904758060906332193817674471949615764473430324022539144529420019 has 89 digits

(68·10¹⁶⁷+13)/9 = 7(5)₁₆₆7_<168> = 11 · 6133 · 3692624693_<10> · 3515568961760680937252533_<25> · C129

C129 = P40 · P90

P40 = 1277051303251277396745439863477632923199_<40>

P90 = 675556407842777457227772829257886093211284966360659547830383521551498877804611413980290869_<90>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 862720191055370426409187832685236228895646134693978735857012571110151934022354543430530334015543289916386083309198010532757969931 (129 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1210827030
Step 1 took 10042ms
Step 2 took 5075ms
********** Factor found in step 2: 1277051303251277396745439863477632923199
Found probable prime factor of 40 digits: 1277051303251277396745439863477632923199
Probable prime cofactor 675556407842777457227772829257886093211284966360659547830383521551498877804611413980290869 has 90 digits

Jun 24, 2009 (2nd)

By Dmitry Domanov / ECMNET / Jun 24, 2009

10²¹⁷-9 = (9)₂₁₆1_<217> = 277 · 1597 · 209837 · 26201554231_<11> · 28091934741523_<14> · 6880830160720697642858093533_<28> · C155

C155 = P32 · P123

P32 = 63325093119323060926195351466951_<32>

P123 = 335898346710792594131217225602531441026219994792367522422800950405251569979293410168943832776047737138867077267300064073493_<123>

C155=P32*P123
C155=63325093119323060926195351466951<32>*335898346710792594131217225602531441026219994792367522422800950405251569979293410168943832776047737138867077267300064073493<123>

Jun 24, 2009

By Tyler Cadigan / GGNFS, Msieve / Jun 24, 2009

6·10¹⁸⁵+1 = 6(0)₁₈₄1_<186> = 19 · 167 · 3149035144740077_<16> · 30217523095511560432976100709_<29> · C139

C139 = P66 · P74

P66 = 123251687544331276107061304469530687861827519667502885428574726923_<66>

P74 = 16123225707827282939353513239821935387962162632669892472730626095154698983_<74>

Number: 60001_185
N=1987214777147857751405440882712878768498289240274665943254488411740605391914998115487412671203360049610514137987060572328808885079490819309
  ( 139 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=123251687544331276107061304469530687861827519667502885428574726923 (pp66)
 r2=16123225707827282939353513239821935387962162632669892472730626095154698983 (pp74)
Version: Msieve v. 1.41
Total time: 216.99 hours.
Scaled time: 550.28 units (timescale=2.536).
Factorization parameters were as follows:
n: 1987214777147857751405440882712878768498289240274665943254488411740605391914998115487412671203360049610514137987060572328808885079490819309
m: 10000000000000000000000000000000000000
deg: 5
c5: 6
c0: 1
skew: 0.70
type: snfs
lss: 1
rlim: 8700000
alim: 8700000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 8700000/8700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4350000, 7350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1090015 x 1090262
Total sieving time: 213.24 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 2.48 hours.
Time per square root: 0.79 hours.
Prototype def-par.txt line would be:
snfs,185.000,5,0,0,0,0,0,0,0,0,8700000,8700000,28,28,54,54,2.5,2.5,100000
total time: 216.99 hours.
 --------- CPU info (if available) ----------

Jun 23, 2009 (5th)

By Jo Yeong Uk / GGNFS, GMP-ECM 6.2.3, Msieve v1.39/YAFU 1.10 / Jun 23, 2009

(4·10¹⁷²-7)/3 = 1(3)₁₇₁1_<173> = 1979 · 13289227921_<11> · 162833506738538029_<18> · 11712824240851604859171398762414514649183_<41> · C102

C102 = P43 · P59

P43 = 5134015334759491232232164584639017885994807_<43>

P59 = 51776254296606631877254403452223499612447702177657692377141_<59>

Number: 13331_172
N=265820083535185443400012989979500246927574859540043887531215591340458372270487885471414380147411506787
  ( 102 digits)
Divisors found:
 r1=5134015334759491232232164584639017885994807
 r2=51776254296606631877254403452223499612447702177657692377141
Version: 
Total time: 3.25 hours.
Scaled time: 7.75 units (timescale=2.385).
Factorization parameters were as follows:
name: 13331_172
n: 265820083535185443400012989979500246927574859540043887531215591340458372270487885471414380147411506787
skew: 12643.51
# norm 3.65e+14
c5: 38880
c4: -845394138
c3: -33007101816765
c2: 73320781261222582
c1: 1557463663881869440290
c0: -4414460967845638019542375
# alpha -6.49
Y1: 12393727643
Y0: -23279481991745479608
# Murphy_E 2.72e-09
# M 141911435455571799952981958314235858806500151888383279234915351745234001551558863634711718448352602713
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4792695
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 216449 x 216697
Polynomial selection time: 0.22 hours.
Total sieving time: 2.65 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 3.25 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673796)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672351)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)

(89·10¹⁹⁴+1)/9 = 9(8)₁₉₃9_<195> = 19 · 787 · 1478629721_<10> · 1769297203_<10> · 2283368889277607_<16> · 38346165072677325477768700865603_<32> · C126

C126 = P34 · P43 · P49

P34 = 9097052437296664414776212359460597_<34>

P43 = 3374615834793386611677694152332672045296747_<43>

P49 = 9404503802431255949573827788376837390651779708209_<49>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 288709400214039153514611082816280322399269582988374671238906295467466961967639668368802541858848488578358621719840471080565431 (126 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6364061278
Step 1 took 4180ms
********** Factor found in step 1: 9097052437296664414776212359460597
Found probable prime factor of 34 digits: 9097052437296664414776212359460597
Composite cofactor 31736587450059131430259469757449683794651893754830576115125492366442558497351134990476896123 has 92 digits

06/23/09 22:31:38 v1.10 @ 조영욱-PC, starting SIQS on c92: 31736587450059131430259469757449683794651893754830576115125492366442558497351134990476896123
06/23/09 22:31:38 v1.10 @ 조영욱-PC, random seeds: 552356298, 3598319296
06/23/09 22:31:38 v1.10 @ 조영욱-PC, ==== sieve params ====
06/23/09 22:31:38 v1.10 @ 조영욱-PC, n = 92 digits, 306 bits
06/23/09 22:31:38 v1.10 @ 조영욱-PC, factor base: 71746 primes (max prime = 1914439)
06/23/09 22:31:38 v1.10 @ 조영욱-PC, single large prime cutoff: 229732680 (120 * pmax)
06/23/09 22:31:38 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
06/23/09 22:31:38 v1.10 @ 조영욱-PC, double large prime cutoff: 1122537872193945
06/23/09 22:31:38 v1.10 @ 조영욱-PC, using 16 large prime slices of factor base
06/23/09 22:31:38 v1.10 @ 조영욱-PC, buckets hold 1024 elements
06/23/09 22:31:38 v1.10 @ 조영욱-PC, sieve interval: 11 blocks of size 65536
06/23/09 22:31:38 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors
06/23/09 22:31:38 v1.10 @ 조영욱-PC, using multiplier of 3
06/23/09 22:31:38 v1.10 @ 조영욱-PC, using small prime variation correction of 17 bits
06/23/09 22:31:38 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
06/23/09 22:31:38 v1.10 @ 조영욱-PC, trial factoring cutoff at 100 bits
06/23/09 22:31:38 v1.10 @ 조영욱-PC, ==== sieving started ====
06/23/09 23:55:14 v1.10 @ 조영욱-PC, sieve time = 2424.8690, relation time = 833.1370, poly_time = 1757.1540
06/23/09 23:55:14 v1.10 @ 조영욱-PC, 71833 relations found: 19062 full + 52771 from 910631 partial, using 753626 polys (368 A polys)
06/23/09 23:55:14 v1.10 @ 조영욱-PC, on average, sieving found 1.23 rels/poly and 185.33 rels/sec
06/23/09 23:55:14 v1.10 @ 조영욱-PC, trial division touched 29908181 sieve locations out of 1086571937792
06/23/09 23:55:14 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
06/23/09 23:55:15 v1.10 @ 조영욱-PC, begin with 929693 relations
06/23/09 23:55:15 v1.10 @ 조영욱-PC, reduce to 175623 relations in 10 passes
06/23/09 23:55:17 v1.10 @ 조영욱-PC, recovered 175623 relations
06/23/09 23:55:17 v1.10 @ 조영욱-PC, recovered 156791 polynomials
06/23/09 23:55:17 v1.10 @ 조영욱-PC, attempting to build 71833 cycles
06/23/09 23:55:17 v1.10 @ 조영욱-PC, found 71833 cycles in 5 passes
06/23/09 23:55:17 v1.10 @ 조영욱-PC, distribution of cycle lengths:
06/23/09 23:55:17 v1.10 @ 조영욱-PC,    length 1 : 19062
06/23/09 23:55:17 v1.10 @ 조영욱-PC,    length 2 : 14133
06/23/09 23:55:17 v1.10 @ 조영욱-PC,    length 3 : 12724
06/23/09 23:55:17 v1.10 @ 조영욱-PC,    length 4 : 9637
06/23/09 23:55:17 v1.10 @ 조영욱-PC,    length 5 : 6676
06/23/09 23:55:17 v1.10 @ 조영욱-PC,    length 6 : 4215
06/23/09 23:55:17 v1.10 @ 조영욱-PC,    length 7 : 2381
06/23/09 23:55:17 v1.10 @ 조영욱-PC,    length 9+: 3005
06/23/09 23:55:17 v1.10 @ 조영욱-PC, largest cycle: 21 relations
06/23/09 23:55:17 v1.10 @ 조영욱-PC, matrix is 71746 x 71833 (18.7 MB) with weight 4332676 (60.32/col)
06/23/09 23:55:17 v1.10 @ 조영욱-PC, sparse part has weight 4332676 (60.32/col)
06/23/09 23:55:18 v1.10 @ 조영욱-PC, filtering completed in 3 passes
06/23/09 23:55:18 v1.10 @ 조영욱-PC, matrix is 67865 x 67929 (17.9 MB) with weight 4138642 (60.93/col)
06/23/09 23:55:18 v1.10 @ 조영욱-PC, sparse part has weight 4138642 (60.93/col)
06/23/09 23:55:18 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
06/23/09 23:55:18 v1.10 @ 조영욱-PC, matrix is 67817 x 67929 (12.2 MB) with weight 3300446 (48.59/col)
06/23/09 23:55:18 v1.10 @ 조영욱-PC, sparse part has weight 2517689 (37.06/col)
06/23/09 23:55:18 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
06/23/09 23:55:18 v1.10 @ 조영욱-PC, using block size 27171 for processor cache size 4096 kB
06/23/09 23:55:18 v1.10 @ 조영욱-PC, commencing Lanczos iteration
06/23/09 23:55:18 v1.10 @ 조영욱-PC, memory use: 10.7 MB
06/23/09 23:55:39 v1.10 @ 조영욱-PC, lanczos halted after 1074 iterations (dim = 67814)
06/23/09 23:55:39 v1.10 @ 조영욱-PC, recovered 16 nontrivial dependencies
06/23/09 23:55:40 v1.10 @ 조영욱-PC, prp49 = 9404503802431255949573827788376837390651779708209
06/23/09 23:55:44 v1.10 @ 조영욱-PC, prp43 = 3374615834793386611677694152332672045296747
06/23/09 23:55:44 v1.10 @ 조영욱-PC, Lanczos elapsed time = 24.9760 seconds.
06/23/09 23:55:44 v1.10 @ 조영욱-PC, Sqrt elapsed time = 4.9760 seconds.
06/23/09 23:55:44 v1.10 @ 조영욱-PC, SIQS elapsed time = 5046.4850 seconds.
06/23/09 23:55:44 v1.10 @ 조영욱-PC, 
06/23/09 23:55:44 v1.10 @ 조영욱-PC,

Jun 23, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Jun 23, 2009

5·10¹⁶⁹+9 = 5(0)₁₆₈9_<170> = 601 · 240050495558407698763546267_<27> · C141

C141 = P47 · P94

P47 = 41281411513583644762377184791184555905650687227_<47>

P94 = 8395341891024184763633786646465985958174272838380095043933734588514621669155826987694109067001_<94>

Number: n
N=346571563400596869585973019313910592991068897473874180601102588897696004361669211747830725681790090285548632257724403837334518143947437896227
  ( 141 digits)
SNFS difficulty: 170 digits.
Divisors found:

Tue Jun 23 03:22:08 2009  prp47 factor: 41281411513583644762377184791184555905650687227
Tue Jun 23 03:22:08 2009  prp94 factor: 8395341891024184763633786646465985958174272838380095043933734588514621669155826987694109067001
Tue Jun 23 03:22:08 2009  elapsed time 01:53:33 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 34.53 hours.
Scaled time: 92.22 units (timescale=2.671).
Factorization parameters were as follows:
name: KA_5_0_168_9
n: 346571563400596869585973019313910592991068897473874180601102588897696004361669211747830725681790090285548632257724403837334518143947437896227
m: 10000000000000000000000000000000000
deg: 5
c5: 1
c0: 18
skew: 1.78
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2400000, 4312493)
Primes: RFBsize:335439, AFBsize:335377, largePrimes:15839972 encountered
Relations: rels:14929612, finalFF:644433
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1396892 hash collisions in 16096513 relations
Msieve: matrix is 859768 x 860016 (230.2 MB)

Total sieving time: 34.09 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000
total time: 34.53 hours.
 --------- CPU info (if available) ----------

(47·10¹⁶⁷+61)/9 = 5(2)₁₆₆9_<168> = 73 · 83 · 4889 · 2368801 · 17554369602202312039753_<23> · C132

C132 = P64 · P68

P64 = 5079837261726309477074870937453617318273958408771046998347443561_<64>

P68 = 83458532416670736671267228864304174336696566851849644029351322951463_<68>

Number: n
N=423955762779197108748010664666559127694051691975812539877069526095525968365910818624458358288204930884391825958098258024391334879743
  ( 132 digits)
SNFS difficulty: 169 digits.
Divisors found:

Tue Jun 23 03:49:36 2009  prp64 factor: 5079837261726309477074870937453617318273958408771046998347443561
Tue Jun 23 03:49:36 2009  prp68 factor: 83458532416670736671267228864304174336696566851849644029351322951463
Tue Jun 23 03:49:36 2009  elapsed time 02:21:21 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 74.52 hours.
Scaled time: 198.22 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_2_166_9
n: 423955762779197108748010664666559127694051691975812539877069526095525968365910818624458358288204930884391825958098258024391334879743
m: 2000000000000000000000000000000000
deg: 5
c5: 1175
c0: 488
skew: 0.84
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2400000, 6868387)
Primes: RFBsize:335439, AFBsize:335523, largePrimes:18006057 encountered
Relations: rels:18460657, finalFF:659503
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2776050 hash collisions in 21096983 relations
Msieve: matrix is 847467 x 847715 (222.3 MB)

Total sieving time: 73.33 hours.
Total relation processing time: 1.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000
total time: 74.52 hours.
 --------- CPU info (if available) ----------

(23·10¹⁷¹-41)/9 = 2(5)₁₇₀1_<172> = 562003853 · C163

C163 = P43 · P120

P43 = 9819478707452999260663842216145669618164917_<43>

P120 = 463081680659769326936886310127931535214424803461949022560762005197836495742479612235092546488980256930797094956201310351_<120>

Number: n
N=4547220703050154276354321641199772264827436255237836519878015063280278890820265525040013481109631388159816682885901060816313577045094663355547413934821467417155867
  ( 163 digits)
SNFS difficulty: 172 digits.
Divisors found:

Tue Jun 23 13:07:13 2009  prp43 factor: 9819478707452999260663842216145669618164917
Tue Jun 23 13:07:13 2009  prp120 factor: 463081680659769326936886310127931535214424803461949022560762005197836495742479612235092546488980256930797094956201310351
Tue Jun 23 13:07:13 2009  elapsed time 01:27:20 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 83.31 hours.
Scaled time: 113.38 units (timescale=1.361).
Factorization parameters were as follows:
name: KA_2_5_170_1
n: 4547220703050154276354321641199772264827436255237836519878015063280278890820265525040013481109631388159816682885901060816313577045094663355547413934821467417155867
m: 10000000000000000000000000000000000
deg: 5
c5: 230
c0: -41
skew: 0.71
type: snfs
lss: 1
rlim: 5200000
alim: 5200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2600000, 7388737)
Primes: RFBsize:361407, AFBsize:360913, largePrimes:18867095 encountered
Relations: rels:19622703, finalFF:765979
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2982267 hash collisions in 22477415 relations
Msieve: matrix is 899270 x 899518 (235.4 MB)

Total sieving time: 81.95 hours.
Total relation processing time: 1.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,56,56,2.4,2.4,100000
total time: 83.31 hours.
 --------- CPU info (if available) ----------

Jun 23, 2009 (3rd)

By Dmitry Domanov / ECMNET / Jun 23, 2009

(2·10²³⁴+1)/3 = (6)₂₃₃7_<234> = 11393 · 25339 · C226

C226 = P39 · P187

P39 = 729812897211517853487632354670094565923_<39>

P187 = 3164241616437046679403827475768447797264211271061761553933740453597778289635577612191476954130503242628832673837317052776146482706548181034700795185780339672202760023332942933779133885627_<187>

C226=P39*P187
C226=729812897211517853487632354670094565923<39>*3164241616437046679403827475768447797264211271061761553933740453597778289635577612191476954130503242628832673837317052776146482706548181034700795185780339672202760023332942933779133885627<187>

Jun 23, 2009 (2nd)

By Serge Batalov / Msieve-1.42 / Jun 23, 2009

(49·10¹⁶⁷-13)/9 = 5(4)₁₆₆3_<168> = 3 · 59 · 1105171 · 403536238013_<12> · 374925660096668543699_<21> · C128

C128 = P60 · P69

P60 = 154366586188854324678105391045950947662796027385267558778367_<60>

P69 = 119170789977225348190653974594475835745955100338192207667847653826801_<69>

SNFS difficulty: 169 digits.
Divisors found:
 r1=154366586188854324678105391045950947662796027385267558778367 (pp60)
 r2=119170789977225348190653974594475835745955100338192207667847653826801 (pp69)
Version: Msieve-1.42
Total time: 28.81 hours.
Scaled time: 82.02 units (timescale=2.847).
Factorization parameters were as follows:
n: 18395988022213213815357754832451835276664855589756973035375079343242696253657629170109553860881160095980243731307550988163613967
m: 2000000000000000000000000000000000
deg: 5
c5: 1225
c0: -104
skew: 0.61
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 5450001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 914075 x 914323
Total sieving time: 27.23 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 1.28 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,169.000,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000
total time: 28.81 hours.

Jun 23, 2009

By Serge Batalov / PFGW / Jun 22, 2009

(16·10³⁰¹⁰-7)/9 = 1(7)₃₀₁₀_<3011> is prime.

(16·10¹⁷⁸³⁹-7)/9 = 1(7)₁₇₈₃₉_<17840> is PRP.

(52·10⁹⁰¹⁵-43)/9 = 5(7)₉₀₁₄3_<9016> is prime.

Jun 22, 2009 (4th)

By Dmitry Domanov / ECMNET / Jun 22, 2009

(89·10¹⁸⁵+1)/9 = 9(8)₁₈₄9_<186> = 11 · 1987 · 616943 · C176

C176 = P29 · P148

P29 = 40940401384167441808899155767_<29>

P148 = 1791264866192661432732845062852095165264741708650930105086935795122598812517413884118459537265905771919543758665292146582186543306950429077800614017_<148>

[2009-06-21 02:52:13 GMT] a: Factor found!  / (probable) 40940401384167441808899155767  B1: 11000000 sigma: 2019692168 (found in step 2)
[2009-06-21 02:52:13 GMT] a:    Co-factor:  / (Probable) 1791264866192661432732845062852095165264741708650930105086935795122598812517413884118459537265905771919543758665292146582186543306950429077800614017

(89·10¹⁹⁴+1)/9 = 9(8)₁₉₃9_<195> = 19 · 787 · 1478629721_<10> · 1769297203_<10> · 2283368889277607_<16> · C158

C158 = P32 · C126

P32 = 38346165072677325477768700865603_<32>

C126 = [288709400214039153514611082816280322399269582988374671238906295467466961967639668368802541858848488578358621719840471080565431_<126>]

[2009-06-21 00:32:28 GMT] a: Factor found!  / (probable) 38346165072677325477768700865603  B1: 11000000 sigma: 2792758941 (found in step 2)
[2009-06-21 00:32:28 GMT] a:    Co-factor:  / (Composite) 288709400214039153514611082816280322399269582988374671238906295467466961967639668368802541858848488578358621719840471080565431

(46·10¹⁸⁴+71)/9 = 5(1)₁₈₃9_<185> = 31 · C184

C184 = P36 · C149

P36 = 109950766165990238619142052692775317_<36>

C149 = [14995307238006754970142095290739002827809014572111810162500899017717459167125063659570942091364689704175545066490272917015118441624190530505317102797_<149>]

C184=P36*C149
C184=109950766165990238619142052692775317<36>*14995307238006754970142095290739002827809014572111810162500899017717459167125063659570942091364689704175545066490272917015118441624190530505317102797<149>

(89·10¹⁹⁹+1)/9 = 9(8)₁₉₈9_<200> = 3² · 11 · 29 · 173 · 421 · 3013553 · C186

C186 = P35 · P151

P35 = 75505703827954394348190142512190813_<35>

P151 = 2078392237191109696799707468604509557501015179027375428569828921512009119409343165258187588687754438966150764624796567341773480588321102772113091935307_<151>

C186=P35*P151
C186=75505703827954394348190142512190813<35>*2078392237191109696799707468604509557501015179027375428569828921512009119409343165258187588687754438
966150764624796567341773480588321102772113091935307<151>

Jun 22, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Jun 22, 2009

(34·10¹⁶⁷-43)/9 = 3(7)₁₆₆3_<168> = 11 · 79 · 2212123 · 688065433235990265046158859_<27> · C132

C132 = P53 · P80

P53 = 11607192724957470109727382625443317990290621072844033_<53>

P80 = 24606532827049850789319866486334883175438181692662700048777546004311547846632257_<80>

Number: n
N=285612768816560198153005074423318240175774326559723692726855192453231155131923257812510152266159767651064662586228076782756067772481
  ( 132 digits)
SNFS difficulty: 169 digits.
Divisors found:

Mon Jun 22 05:13:22 2009  prp53 factor: 11607192724957470109727382625443317990290621072844033
Mon Jun 22 05:13:22 2009  prp80 factor: 24606532827049850789319866486334883175438181692662700048777546004311547846632257
Mon Jun 22 05:13:22 2009  elapsed time 01:22:41 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 39.08 hours.
Scaled time: 100.64 units (timescale=2.575).
Factorization parameters were as follows:
name: KA_3_7_166_3
n: 285612768816560198153005074423318240175774326559723692726855192453231155131923257812510152266159767651064662586228076782756067772481
m: 2000000000000000000000000000000000
deg: 5
c5: 425
c0: -172
skew: 0.83
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2300000, 4535147)
Primes: RFBsize:322441, AFBsize:321656, largePrimes:15842237 encountered
Relations: rels:14942542, finalFF:595563
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1561562 hash collisions in 16410559 relations
Msieve: matrix is 845581 x 845829 (229.1 MB)

Total sieving time: 38.59 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,56,56,2.4,2.4,100000
total time: 39.08 hours.
 --------- CPU info (if available) ----------

(19·10¹⁶⁹+71)/9 = 2(1)₁₆₈9_<170> = 17 · 29 · 157 · 401 · 1202690777_<10> · 11917016737_<11> · C143

C143 = P34 · P109

P34 = 5953901394817602332266795990080373_<34>

P109 = 7970709470626566079289325522510715490264808474915393724092566519897218412184343046077211774275868043748116947_<109>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 47456818234849384485919149010234197237043999182472042017612061274694520497973354897231898436283664885858051334911013044250936917790809933381231 (143 digits)
Using B1=1792000, B2=2140281790, polynomial Dickson(6), sigma=4224226140
Step 1 took 24913ms
Step 2 took 8362ms
********** Factor found in step 2: 5953901394817602332266795990080373
Found probable prime factor of 34 digits: 5953901394817602332266795990080373
Probable prime cofactor 7970709470626566079289325522510715490264808474915393724092566519897218412184343046077211774275868043748116947 has 109 digits

Jun 22, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Jun 22, 2009

(4·10¹⁷²-7)/3 = 1(3)₁₇₁1_<173> = 1979 · 13289227921_<11> · 162833506738538029_<18> · C142

C142 = P41 · C102

P41 = 11712824240851604859171398762414514649183_<41>

C102 = [265820083535185443400012989979500246927574859540043887531215591340458372270487885471414380147411506787_<102>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4085455744
Step 1 took 42653ms
Step 2 took 14897ms
********** Factor found in step 2: 11712824240851604859171398762414514649183
Found probable prime factor of 41 digits: 11712824240851604859171398762414514649183
Composite cofactor 265820083535185443400012989979500246927574859540043887531215591340458372270487885471414380147411506787 has 102 digits

Jun 22, 2009

By Jo Yeong Uk / GMP-ECM / Jun 21, 2009

(13·10¹⁶⁷-7)/3 = 4(3)₁₆₆1_<168> = 5959318178397209_<16> · 10739075572896235220891_<23> · C130

C130 = P39 · P92

P39 = 278840979899609144669916444484675755961_<39>

P92 = 24282982392014604316378653148216272453420429843296842734094382957632012796139059509470390809_<92>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 6771090605074307069591549228648573420714999216153608492489545679884278552852674684314455216639986692541470079887690700098181362449 (130 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3881612235
Step 1 took 4274ms
Step 2 took 5819ms
********** Factor found in step 2: 278840979899609144669916444484675755961
Found probable prime factor of 39 digits: 278840979899609144669916444484675755961
Probable prime cofactor 24282982392014604316378653148216272453420429843296842734094382957632012796139059509470390809 has 92 digits

(41·10¹⁶⁷+13)/9 = 4(5)₁₆₆7_<168> = 430279 · 338623573 · 18003240719_<11> · 7832365170209_<13> · C131

C131 = P35 · P96

P35 = 38994801836476403223875236485088157_<35>

P96 = 568622021797804765367548597934605439349622589855711387016954054617774589676260150974346419105693_<96>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 22173303059861962649674962465807468961083598829975529901522059915208172285205905279352766464136854475819255274008388042078205577801 (131 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3093000109
Step 1 took 4196ms
********** Factor found in step 1: 38994801836476403223875236485088157
Found probable prime factor of 35 digits: 38994801836476403223875236485088157
Probable prime cofactor 568622021797804765367548597934605439349622589855711387016954054617774589676260150974346419105693 has 96 digits

Jun 21, 2009

By Serge Batalov / PFGW / Jun 20, 2009

(2·10³⁹⁶⁰⁶+1)/3 = (6)₃₉₆₀₅7_<39606> is PRP.

Jun 20, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Jun 20, 2009

9·10¹⁶⁸+1 = 9(0)₁₆₇1_<169> = 193 · 183122333 · 1365503329_<10> · 70195540469_<11> · C139

C139 = P54 · P85

P54 = 803534758897924386932162437579226018617463265776195233_<54>

P85 = 3306259477416131198963892436083070510480940866548861316188259476731788862020584275713_<85>

Number: n
N=2656694412039548462553232526428776317534088841928298827414634961259564708940735214813108191929447902768879073075808499186281445628188276129
  ( 139 digits)
SNFS difficulty: 170 digits.
Divisors found:

Sat Jun 20 12:49:06 2009  prp54 factor: 803534758897924386932162437579226018617463265776195233
Sat Jun 20 12:49:06 2009  prp85 factor: 3306259477416131198963892436083070510480940866548861316188259476731788862020584275713
Sat Jun 20 12:49:06 2009  elapsed time 01:55:16 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 43.37 hours.
Scaled time: 112.12 units (timescale=2.585).
Factorization parameters were as follows:
name: KA_9_0_167_1
n: 2656694412039548462553232526428776317534088841928298827414634961259564708940735214813108191929447902768879073075808499186281445628188276129
m: 5000000000000000000000000000000000
deg: 5
c5: 72
c0: 25
skew: 0.81
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2400000, 4868657)
Primes: RFBsize:335439, AFBsize:335327, largePrimes:16134981 encountered
Relations: rels:15152762, finalFF:557837
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1660784 hash collisions in 16908306 relations
Msieve: matrix is 905009 x 905257 (241.5 MB)

Total sieving time: 42.92 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000
total time: 43.37 hours.
 --------- CPU info (if available) ----------

Jun 20, 2009 (4th)

By Andreas Tete / Syd`s Database / Jun 20, 2009

2·10¹⁷⁶-9 = 1(9)₁₇₅1_<177> = 977 · 30422398200031601_<17> · C157

C157 = P27 · C131

P27 = 671851302766021349481441049_<27>

C131 = [10015412055048508505562981822117361493985212600568876345607115690865494900174994593465034317095895575473501050630145079867266172367_<131>]

this faktor is from the database http://factordb.com/search.php
671851302766021349481441049

Jun 20, 2009 (3rd)

By Dmitry Domanov / ECMNET / Jun 20, 2009

(2·10²⁴⁸+1)/3 = (6)₂₄₇7_<248> = 163 · 44179 · C241

C241 = P35 · C207

P35 = 41158940460267795191725127905610171_<35>

C207 = [224926729683557925143732786282199759731260062609772664415477620172801666485846605924960352715932697003118406528404722564383235862597511428194310219734798101447346433956246920912393774411884500256114875326201_<207>]

C241=P35*C207
C241=41158940460267795191725127905610171<35>*224926729683557925143732786282199759731260062609772664415477620172801666485846605924960352715932697003118406528404722564383235862597511428194310219734798101447346433956246920912393774411884500256114875326201<207>

Jun 20, 2009 (2nd)

By Jo Yeong Uk / GMP-ECM / Jun 20, 2009

(2·10²⁴⁵+1)/3 = (6)₂₄₄7_<245> = 23 · 153669121 · 869061193254415949_<18> · 38056099737006898261987_<23> · 39366916868321772201193201_<26> · 143367365426738090002045861251553483338881_<42> · C129

C129 = P43 · P86

P43 = 6214754527728988809452793868940752428182767_<43>

P86 = 16259754221608044527762712435800332789719768404154926526062152292523869431586832367349_<86>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 101050381168499134820535981759329661173475719716918113615492884413715003106991408503990025473220959006588553102747390264655274683 (129 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=69261048
Step 1 took 10110ms
Step 2 took 5103ms
********** Factor found in step 2: 6214754527728988809452793868940752428182767
Found probable prime factor of 43 digits: 6214754527728988809452793868940752428182767
Probable prime cofactor 16259754221608044527762712435800332789719768404154926526062152292523869431586832367349 has 86 digits

Jun 20, 2009

By Wataru Sakai / GMP-ECM 6.2.1 / Jun 20, 2009

(19·10²⁰²+11)/3 = 6(3)₂₀₁7_<203> = 54127212709_<11> · 2197913408641_<13> · 64728150351148599673_<20> · 82174869021302388567870545099_<29> · C132

C132 = P40 · P92

P40 = 2453756815506768300255949590474181892893_<40>

P92 = 40788935163953970485133759532334003772942726766052495834782985563446394535091642055266233843_<92>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=463793176
Step 1 took 38271ms
********** Factor found in step 1: 2453756815506768300255949590474181892893
Found probable prime factor of 40 digits: 2453756815506768300255949590474181892893
Probable prime cofactor 40788935163953970485133759532334003772942726766052495834782985563446394535091642055266233843 has 92 digits

Jun 19, 2009 (3rd)

By Dmitry Domanov / ECMNET, ggnfs/msieve 1.41, GMP-ECM 6.2.3 / Jun 18, 2009

(13·10¹⁷⁷-31)/9 = 1(4)₁₇₆1_<178> = 11 · 29 · 348544794317_<12> · 1148063635439185721_<19> · C146

C146 = P44 · P102

P44 = 25033842181419094771095940168167426214644379_<44>

P102 = 452020454928961964652287587071087355520379293916864910615544580991786263169013953137748282195897806913_<102>

C146=P44*P102
C146=25033842181419094771095940168167426214644379<44>*452020454928961964652287587071087355520379293916864910615544580991786263169013953137748282195897806913<102>

(52·10¹⁸⁷-61)/9 = 5(7)₁₈₆1_<188> = 3 · C188

C188 = P45 · P143

P45 = 997793808332543677053158286151927821814822559_<45>

P143 = 19301842824064261453747979950422179754811960550020042043615918104333792084576947186435597860092240404685797062886895860454794938508264046395623_<143>

N=19259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257
  ( 188 digits)
SNFS difficulty: 189 digits.
Divisors found:
r1=997793808332543677053158286151927821814822559 (pp45)
r2=19301842824064261453747979950422179754811960550020042043615918104333792084576947186435597860092240404685797062886895860454794938508264046395623 (pp143)
Version: Msieve v. 1.41
Total time: 282.71 hours.
Scaled time: 562.03 units (timescale=1.988).
Factorization parameters were as follows:
n: 19259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257
m: 20000000000000000000000000000000000000
deg: 5
c5: 325
c0: -122
skew: 0.82
type: snfs
lss: 1
rlim: 9900000
alim: 9900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 9900000/9900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4950000, 9550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1870949 x 1871196
Total sieving time: 276.07 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 5.54 hours.
Time per square root: 0.76 hours.
Prototype def-par.txt line would be:
snfs,189.000,5,0,0,0,0,0,0,0,0,9900000,9900000,28,28,54,54,2.5,2.5,100000
total time: 282.71 hours.
 --------- CPU info (if available) ----------

(56·10¹⁸²-11)/9 = 6(2)₁₈₁1_<183> = 3² · 17 · C181

C181 = P64 · P118

P64 = 2554359733901468190141458804443443258365734902731179951456506049_<64>

P118 = 1592106176735574063902134000268509870312626111202742168378927583346294201956929891804436477420044365348350553606283093_<118>

N=4066811909949164851125635439360929557007988380537400145243282498184458968772694262890341321713870733478576615831517792302106027596223674655047204066811909949164851125635439360929557
  ( 181 digits)
SNFS difficulty: 183 digits.
Divisors found:
r1=2554359733901468190141458804443443258365734902731179951456506049 (pp64)
r2=1592106176735574063902134000268509870312626111202742168378927583346294201956929891804436477420044365348350553606283093 (pp118)
Version: Msieve v. 1.41
Total time: 150.33 hours.
Scaled time: 296.00 units (timescale=1.969).
Factorization parameters were as follows:
n: 4066811909949164851125635439360929557007988380537400145243282498184458968772694262890341321713870733478576615831517792302106027596223674655047204066811909949164851125635439360929557
m: 2000000000000000000000000000000000000
deg: 5
c5: 175
c0: -11
skew: 0.58
type: snfs
lss: 1
rlim: 8100000
alim: 8100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 8100000/8100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [4050000, 6450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1499532 x 1499780
Total sieving time: 146.32 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 3.54 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,183.000,5,0,0,0,0,0,0,0,0,8100000,8100000,28,28,53,53,2.5,2.5,100000
total time: 150.33 hours.
 --------- CPU info (if available) ----------

(2·10²⁰⁷+1)/3 = (6)₂₀₆7_<207> = 11870767 · C200

C200 = P32 · C169

P32 = 12351258440178597743332350167861_<32>

C169 = [4546935055405781507044615238355866287232446105157119558592794940265286537341198984719464906928858883530666741572376981390043297745552656048588332199211361207357791391441_<169>]

GMP-ECM 6.2.3 [powered by GMP 4.3.0] [ECM]
Input number is 56160369980024598803654950574521988904901146376360235751124309546861349958824620739895464772130281612524840784649102005512084153169434347979929743938758689027142615693380778737099857714894637108677701 (200 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=572703295
Step 1 took 224907ms
Step 2 took 55328ms
********** Factor found in step 2: 12351258440178597743332350167861
Found probable prime factor of 32 digits: 12351258440178597743332350167861
Composite cofactor 4546935055405781507044615238355866287232446105157119558592794940265286537341198984719464906928858883530666741572376981390043297745552656048588332199211361207357791391441 has 169 digits

By Dmitry Domanov / ECMNET, ggnfs/msieve 1.41, GMP-ECM 6.2.3 / Jun 19, 2009

(16·10¹⁷¹-61)/9 = 1(7)₁₇₀1_<172> = 7 · 11 · 6869 · 478273 · C160

C160 = P58 · P103

P58 = 1326288982702582673029121665373066080254716222864506558111_<58>

P103 = 5298820469813085006548338151874038728594716331197631203696580068921274591131231214539222639337102417189_<103>

N=7027767210432017693197162292111583596851847704497755291936070419810200093347522268321872666523258643695391096428782659743696661732069745996297465301960793769979
  ( 160 digits)
SNFS difficulty: 172 digits.
Divisors found:
r1=1326288982702582673029121665373066080254716222864506558111 (pp58)
r2=5298820469813085006548338151874038728594716331197631203696580068921274591131231214539222639337102417189 (pp103)
Version: Msieve v. 1.41
Total time: 43.23 hours.
Scaled time: 85.93 units (timescale=1.988).
Factorization parameters were as follows:
n: 7027767210432017693197162292111583596851847704497755291936070419810200093347522268321872666523258643695391096428782659743696661732069745996297465301960793769979
m: 20000000000000000000000000000000000
deg: 5
c5: 5
c0: -61
skew: 1.65
type: snfs
lss: 1
rlim: 5200000
alim: 5200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2600000, 4800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 870887 x 871135
Total sieving time: 41.66 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.04 hours.
Time per square root: 0.37 hours.
Prototype def-par.txt line would be:
snfs,172.000,5,0,0,0,0,0,0,0,0,5200000,5200000,27,27,52,52,2.4,2.4,100000
total time: 43.23 hours.
 --------- CPU info (if available) ----------

(2·10²³²+1)/3 = (6)₂₃₁7_<232> = 491 · 54681433 · C222

C222 = P34 · C188

P34 = 7430349296958259255009925644985843_<34>

C188 = [33417821221541330852542188413689425137725811211108368838101480074258853205202674229068504165866529215131936272245109112256704331846203516632198560835389525811428095563532128787664936663923_<188>]

C222=P34*C188
C222=7430349296958259255009925644985843<34>*33417821221541330852542188413689425137725811211108368838101480074258853205202674229068504165866529215131936272245109112256704331846203516632198560835389525811428095563532128787664936663923<188>

Jun 19, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jun 18, 2009

(58·10¹⁶²-31)/9 = 6(4)₁₆₁1_<163> = 3 · 47 · 641 · 2767 · 130829 · 494051 · 271311440270983020815509571_<27> · C118

C118 = P53 · P65

P53 = 24954118155618919079580333638817425652891937701291029_<53>

P65 = 58886134193713359403521657026257990804220556027035516543340997003_<65>

Number: n
N=1469451550397554580732676837059180360646094335779406648161528362300117656219537283085352644318514476025995697119786087
  ( 118 digits)
Divisors found:

Thu Jun 18 14:54:49 2009  prp53 factor: 24954118155618919079580333638817425652891937701291029
Thu Jun 18 14:54:49 2009  prp65 factor: 58886134193713359403521657026257990804220556027035516543340997003
Thu Jun 18 14:54:49 2009  elapsed time 00:47:19 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 26.24 hours.
Scaled time: 69.80 units (timescale=2.660).
Factorization parameters were as follows:
n: 1469451550397554580732676837059180360646094335779406648161528362300117656219537283085352644318514476025995697119786087
Y0: -46893879102853055658803
Y1:  3141268982191
c0: -3760144619058917366194126238400
c1:  68800418075202982299435180
c2:  44964992749753915636
c3: -1417804088061757
c4: -118330278
c5:  6480
skew: 268641.15
type: gnfs
name: KA_6_4_161_1
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2250000, 3700000)
Primes: RFBsize:315948, AFBsize:316236, largePrimes:14559686 encountered
Relations: rels:13791475, finalFF:805925
Max relations in full relation-set: 28
Initial matrix: 632261 x 805925 with sparse part having weight 75126954.
Pruned matrix : 490038 x 493263 with weight 46026915.

Msieve: found 1187436 hash collisions in 14695534 relations
Msieve: matrix is 563385 x 563633 (154.8 MB)

Total sieving time: 25.17 hours.
Total relation processing time: 0.67 hours.
Matrix solve time: 0.41 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,56,56,2.4,2.4,60000
total time: 26.24 hours.
 --------- CPU info (if available) ----------

(13·10¹⁷¹-31)/9 = 1(4)₁₇₀1_<172> = 11 · 845599 · 14030443675276817_<17> · 256462931804549017510633552397_<30> · C119

C119 = P57 · P63

P57 = 116063407036321876724157657256907246256483937762664427391_<57>

P63 = 371836804863893294145143569503109186718694143977647172218587591_<63>

Number: n
N=43156646434003437590709513779974321417811490608715284910791365906651077456606782151395693253101947622545235176793105081
  ( 119 digits)
Divisors found:

Thu Jun 18 22:22:17 2009  prp57 factor: 116063407036321876724157657256907246256483937762664427391
Thu Jun 18 22:22:17 2009  prp63 factor: 371836804863893294145143569503109186718694143977647172218587591
Thu Jun 18 22:22:17 2009  elapsed time 00:45:54 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 33.10 hours.
Scaled time: 88.40 units (timescale=2.671).
Factorization parameters were as follows:
n: 43156646434003437590709513779974321417811490608715284910791365906651077456606782151395693253101947622545235176793105081
Y0: -82873704940012508645811
Y1:  5558225810587
c0:  390332349543191292661504637720
c1:  11283470990773849387345742
c2:  27771274009983295117
c3: -848230578916907
c4: -1954794837
c5:  11040
skew: 148251.93
type: gnfs
name: KA_1_4_170_1
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2250000, 4100000)
Primes: RFBsize:315948, AFBsize:315748, largePrimes:14766964 encountered
Relations: rels:14062877, finalFF:788445
Max relations in full relation-set: 28
Initial matrix: 631777 x 788445 with sparse part having weight 79095519.
Pruned matrix : 509527 x 512749 with weight 52748937.

Msieve: found 1396489 hash collisions in 15182031 relations
Msieve: matrix is 605319 x 605567 (165.1 MB)

Total sieving time: 31.45 hours.
Total relation processing time: 0.85 hours.
Matrix solve time: 0.80 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,56,56,2.4,2.4,60000
total time: 33.10 hours.
 --------- CPU info (if available) ----------

By Robert Backstrom / GGNFS, Msieve / Jun 19, 2009

(14·10¹⁷¹-41)/9 = 1(5)₁₇₀1_<172> = 3 · 11 · 144264311 · C162

C162 = P58 · P104

P58 = 8422572196437277344165892625074975797910517101552896422569_<58>

P104 = 38794301624236914293793808123357843854869719962248434313381337905654704362886863912964954781426002751633_<104>

Number: n
N=326747806240499343230759596100293564963118613154761041676746005032714834420399700505602789363046603661020070633672157059323827132394838374455190425704435922805177
  ( 162 digits)
SNFS difficulty: 172 digits.
Divisors found:

Fri Jun 19 11:40:48 2009  prp58 factor: 8422572196437277344165892625074975797910517101552896422569
Fri Jun 19 11:40:48 2009  prp104 factor: 38794301624236914293793808123357843854869719962248434313381337905654704362886863912964954781426002751633
Fri Jun 19 11:40:48 2009  elapsed time 01:16:46 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 55.33 hours.
Scaled time: 143.58 units (timescale=2.595).
Factorization parameters were as follows:
name: KA_1_5_170_1
n: 326747806240499343230759596100293564963118613154761041676746005032714834420399700505602789363046603661020070633672157059323827132394838374455190425704435922805177
m: 10000000000000000000000000000000000
deg: 5
c5: 140
c0: -41
skew: 0.78
type: snfs
lss: 1
rlim: 5200000
alim: 5200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2600000, 5682731)
Primes: RFBsize:361407, AFBsize:361488, largePrimes:17700805 encountered
Relations: rels:17570935, finalFF:657599
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2124084 hash collisions in 19715067 relations
Msieve: matrix is 839295 x 839543 (222.4 MB)

Total sieving time: 54.53 hours.
Total relation processing time: 0.80 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,56,56,2.4,2.4,100000
total time: 55.33 hours.
 --------- CPU info (if available) ----------

Jun 19, 2009

By Jo Yeong Uk / GGNFS/Msieve v1.39, GMP-ECM 6.2.3, YAFU 1.10, Msieve 1.38 / Jun 18, 2009

(2·10¹⁸⁹+1)/3 = (6)₁₈₈7_<189> = 258925710247_<12> · 697907276489069_<15> · 103472810660886766470523_<24> · C140

C140 = P55 · P85

P55 = 4746350295580571237653643884883727173586562822307651507_<55>

P85 = 7511900121266661845814589063433511839761657945042526497565623384799661040038440081329_<85>

Number: 66667_189
N=35654109360945749376081662769339983989787406080664915477018647301233533367134903422592365407581183879146350856255226267556261179388069412803
  ( 140 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=4746350295580571237653643884883727173586562822307651507
 r2=7511900121266661845814589063433511839761657945042526497565623384799661040038440081329
Version: 
Total time: 121.93 hours.
Scaled time: 291.79 units (timescale=2.393).
Factorization parameters were as follows:
n: 35654109360945749376081662769339983989787406080664915477018647301233533367134903422592365407581183879146350856255226267556261179388069412803
m: 100000000000000000000000000000000000000
deg: 5
c5: 1
c0: 5
skew: 1.38
type: snfs
lss: 1
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 7700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 20417084
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1659788 x 1660036
Total sieving time: 112.16 hours.
Total relation processing time: 3.42 hours.
Matrix solve time: 6.18 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000
total time: 121.93 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672386)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672306)
Calibrating delay using timer specific routine.. 5237.81 BogoMIPS (lpj=2618905)

(2·10²²⁹+1)/3 = (6)₂₂₈7_<229> = 7² · 23321 · 23767 · 322159063 · 78124519400027_<14> · 1738216785948389_<16> · 13256504103154300738627_<23> · C159

C159 = P34 · P37 · P41 · P49

P34 = 1237470824271985512472690448473327_<34>

P37 = 3750161593708449394591669208868139007_<37>

P41 = 18395753866925715147248317212109801384969_<41>

P49 = 4957901829527390747060609927610231043240041489103_<49>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 423253407774740648022246108235966296444851118790323740603674354528601384880202632965018613844937841027261734318817645520742415810378445164456463254205170583223 (159 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=704297402
Step 1 took 5585ms
Step 2 took 4914ms
********** Factor found in step 2: 1237470824271985512472690448473327
Found probable prime factor of 34 digits: 1237470824271985512472690448473327
Composite cofactor 342031019619185111284341039676048075550210964995684373883223922629868991470538634305390046991088073329628622395980813626622649 has 126 digits

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 342031019619185111284341039676048075550210964995684373883223922629868991470538634305390046991088073329628622395980813626622649 (126 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4528562233
Step 1 took 4165ms
Step 2 took 4103ms
********** Factor found in step 2: 3750161593708449394591669208868139007
Found probable prime factor of 37 digits: 3750161593708449394591669208868139007
Composite cofactor 91204341752366576110296493038317865627250705073055612416739775293441219621456530521492807 has 89 digits

06/18/09 22:22:38 v1.10 @ 조영욱-PC, starting SIQS on c89: 91204341752366576110296493038317865627250705073055612416739775293441219621456530521492807
06/18/09 22:22:38 v1.10 @ 조영욱-PC, random seeds: 1827674413, 2265870248
06/18/09 22:22:38 v1.10 @ 조영욱-PC, ==== sieve params ====
06/18/09 22:22:38 v1.10 @ 조영욱-PC, n = 89 digits, 302 bits
06/18/09 22:22:38 v1.10 @ 조영욱-PC, factor base: 64055 primes (max prime = 1699001)
06/18/09 22:22:38 v1.10 @ 조영욱-PC, single large prime cutoff: 186890110 (110 * pmax)
06/18/09 22:22:38 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
06/18/09 22:22:38 v1.10 @ 조영욱-PC, double large prime cutoff: 774203936799977
06/18/09 22:22:38 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base
06/18/09 22:22:38 v1.10 @ 조영욱-PC, buckets hold 1024 elements
06/18/09 22:22:38 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536
06/18/09 22:22:38 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors
06/18/09 22:22:38 v1.10 @ 조영욱-PC, using multiplier of 55
06/18/09 22:22:38 v1.10 @ 조영욱-PC, using small prime variation correction of 21 bits
06/18/09 22:22:38 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
06/18/09 22:22:38 v1.10 @ 조영욱-PC, trial factoring cutoff at 101 bits
06/18/09 22:22:38 v1.10 @ 조영욱-PC, ==== sieving started ====
06/18/09 23:09:51 v1.10 @ 조영욱-PC, sieve time = 1414.9750, relation time = 346.6610, poly_time = 1070.8390
06/18/09 23:09:51 v1.10 @ 조영욱-PC, 64149 relations found: 22732 full + 41417 from 529677 partial, using 563791 polys (276 A polys)
06/18/09 23:09:51 v1.10 @ 조영욱-PC, on average, sieving found 0.98 rels/poly and 194.96 rels/sec
06/18/09 23:09:51 v1.10 @ 조영욱-PC, trial division touched 12214549 sieve locations out of 665074925568
06/18/09 23:09:51 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
06/18/09 23:09:52 v1.10 @ 조영욱-PC, begin with 552409 relations
06/18/09 23:09:52 v1.10 @ 조영욱-PC, reduce to 123820 relations in 8 passes
06/18/09 23:09:53 v1.10 @ 조영욱-PC, recovered 123820 relations
06/18/09 23:09:53 v1.10 @ 조영욱-PC, recovered 111157 polynomials
06/18/09 23:09:53 v1.10 @ 조영욱-PC, attempting to build 64149 cycles
06/18/09 23:09:53 v1.10 @ 조영욱-PC, found 64149 cycles in 4 passes
06/18/09 23:09:53 v1.10 @ 조영욱-PC, distribution of cycle lengths:
06/18/09 23:09:53 v1.10 @ 조영욱-PC,    length 1 : 22732
06/18/09 23:09:53 v1.10 @ 조영욱-PC,    length 2 : 19952
06/18/09 23:09:53 v1.10 @ 조영욱-PC,    length 3 : 11344
06/18/09 23:09:53 v1.10 @ 조영욱-PC,    length 4 : 5697
06/18/09 23:09:53 v1.10 @ 조영욱-PC,    length 5 : 2597
06/18/09 23:09:53 v1.10 @ 조영욱-PC,    length 6 : 1045
06/18/09 23:09:53 v1.10 @ 조영욱-PC,    length 7 : 482
06/18/09 23:09:53 v1.10 @ 조영욱-PC,    length 9+: 300
06/18/09 23:09:53 v1.10 @ 조영욱-PC, largest cycle: 16 relations
06/18/09 23:09:53 v1.10 @ 조영욱-PC, matrix is 64055 x 64149 (13.5 MB) with weight 3021778 (47.11/col)
06/18/09 23:09:53 v1.10 @ 조영욱-PC, sparse part has weight 3021778 (47.11/col)
06/18/09 23:09:54 v1.10 @ 조영욱-PC, filtering completed in 3 passes
06/18/09 23:09:54 v1.10 @ 조영욱-PC, matrix is 56373 x 56437 (12.1 MB) with weight 2721078 (48.21/col)
06/18/09 23:09:54 v1.10 @ 조영욱-PC, sparse part has weight 2721078 (48.21/col)
06/18/09 23:09:54 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
06/18/09 23:09:54 v1.10 @ 조영욱-PC, matrix is 56325 x 56437 (8.0 MB) with weight 2068248 (36.65/col)
06/18/09 23:09:54 v1.10 @ 조영욱-PC, sparse part has weight 1535318 (27.20/col)
06/18/09 23:09:54 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
06/18/09 23:09:54 v1.10 @ 조영욱-PC, using block size 22574 for processor cache size 4096 kB
06/18/09 23:09:54 v1.10 @ 조영욱-PC, commencing Lanczos iteration
06/18/09 23:09:54 v1.10 @ 조영욱-PC, memory use: 7.4 MB
06/18/09 23:10:06 v1.10 @ 조영욱-PC, lanczos halted after 892 iterations (dim = 56323)
06/18/09 23:10:06 v1.10 @ 조영욱-PC, recovered 18 nontrivial dependencies
06/18/09 23:10:06 v1.10 @ 조영욱-PC, prp49 = 4957901829527390747060609927610231043240041489103
06/18/09 23:10:07 v1.10 @ 조영욱-PC, prp41 = 18395753866925715147248317212109801384969
06/18/09 23:10:07 v1.10 @ 조영욱-PC, Lanczos elapsed time = 14.3360 seconds.
06/18/09 23:10:07 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.9360 seconds.
06/18/09 23:10:07 v1.10 @ 조영욱-PC, SIQS elapsed time = 2848.7480 seconds.
06/18/09 23:10:07 v1.10 @ 조영욱-PC, 
06/18/09 23:10:07 v1.10 @ 조영욱-PC,

By Jo Yeong Uk / GMP-ECM 6.2.3, YAFU 1.10, Msieve 1.38 / Jun 19, 2009

(2·10²⁴⁵+1)/3 = (6)₂₄₄7_<245> = 23 · 153669121 · 869061193254415949_<18> · 38056099737006898261987_<23> · 39366916868321772201193201_<26> · C170

C170 = P42 · C129

P42 = 143367365426738090002045861251553483338881_<42>

C129 = [101050381168499134820535981759329661173475719716918113615492884413715003106991408503990025473220959006588553102747390264655274683_<129>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 14487326923495388617824015611778517505155899148341968548636740762719170987406338312232633735870766518958322657602899284502551991614008890281311729164701564107015028849723 (170 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3765053233
Step 1 took 4782ms
Step 2 took 2800ms
********** Factor found in step 2: 143367365426738090002045861251553483338881
Found probable prime factor of 42 digits: 143367365426738090002045861251553483338881
Composite cofactor 101050381168499134820535981759329661173475719716918113615492884413715003106991408503990025473220959006588553102747390264655274683 has 129 digits

(2·10²¹³+1)/3 = (6)₂₁₂7_<213> = 642623 · 68623043 · 1464084467605343_<16> · 4409891276148706861866704821_<28> · 118009803355233384577031249267259421_<36> · C122

C122 = P34 · P42 · P47

P34 = 7115150503396792667994916837952063_<34>

P42 = 166507482518017499178086786863171180756723_<42>

P47 = 16747599071352727268207577662937259514746886269_<47>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 19841312675353812400480170290920785443960159561950228060042177768467208735513015756609844426709640725339681886570157222681 (122 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2561369874
Step 1 took 4197ms
Step 2 took 4383ms
********** Factor found in step 2: 7115150503396792667994916837952063
Found probable prime factor of 34 digits: 7115150503396792667994916837952063
Composite cofactor 2788600559592030339441370842570956136373448758960749300573053163294910487916335438136487 has 88 digits

06/19/09 10:49:18 v1.10 @ 조영욱-PC, starting SIQS on c88: 2788600559592030339441370842570956136373448758960749300573053163294910487916335438136487
06/19/09 10:49:18 v1.10 @ 조영욱-PC, random seeds: 3105731754, 2216531008
06/19/09 10:49:18 v1.10 @ 조영욱-PC, ==== sieve params ====
06/19/09 10:49:18 v1.10 @ 조영욱-PC, n = 88 digits, 294 bits
06/19/09 10:49:18 v1.10 @ 조영욱-PC, factor base: 61083 primes (max prime = 1621237)
06/19/09 10:49:18 v1.10 @ 조영욱-PC, single large prime cutoff: 178336070 (110 * pmax)
06/19/09 10:49:18 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits
06/19/09 10:49:18 v1.10 @ 조영욱-PC, double large prime cutoff: 711591161729305
06/19/09 10:49:18 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base
06/19/09 10:49:18 v1.10 @ 조영욱-PC, buckets hold 1024 elements
06/19/09 10:49:18 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536
06/19/09 10:49:18 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors
06/19/09 10:49:18 v1.10 @ 조영욱-PC, using multiplier of 7
06/19/09 10:49:18 v1.10 @ 조영욱-PC, using small prime variation correction of 21 bits
06/19/09 10:49:18 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning
06/19/09 10:49:18 v1.10 @ 조영욱-PC, trial factoring cutoff at 97 bits
06/19/09 10:49:18 v1.10 @ 조영욱-PC, ==== sieving started ====
06/19/09 11:14:09 v1.10 @ 조영욱-PC, sieve time = 705.0230, relation time = 283.2280, poly_time = 502.4320
06/19/09 11:14:09 v1.10 @ 조영욱-PC, 61155 relations found: 22477 full + 38678 from 495499 partial, using 270969 polys (264 A polys)
06/19/09 11:14:09 v1.10 @ 조영욱-PC, on average, sieving found 1.91 rels/poly and 347.31 rels/sec
06/19/09 11:14:09 v1.10 @ 조영욱-PC, trial division touched 11124401 sieve locations out of 319648038912
06/19/09 11:14:09 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ====
06/19/09 11:14:09 v1.10 @ 조영욱-PC, begin with 517976 relations
06/19/09 11:14:09 v1.10 @ 조영욱-PC, reduce to 116716 relations in 7 passes
06/19/09 11:14:10 v1.10 @ 조영욱-PC, failed to read relation 31420
06/19/09 11:14:10 v1.10 @ 조영욱-PC, failed to read relation 63878
06/19/09 11:14:10 v1.10 @ 조영욱-PC, recovered 116714 relations
06/19/09 11:14:10 v1.10 @ 조영욱-PC, recovered 95103 polynomials
06/19/09 11:14:10 v1.10 @ 조영욱-PC, attempting to build 61153 cycles
06/19/09 11:14:10 v1.10 @ 조영욱-PC, found 61153 cycles in 4 passes
06/19/09 11:14:10 v1.10 @ 조영욱-PC, distribution of cycle lengths:
06/19/09 11:14:10 v1.10 @ 조영욱-PC,    length 1 : 22477
06/19/09 11:14:10 v1.10 @ 조영욱-PC,    length 2 : 18718
06/19/09 11:14:10 v1.10 @ 조영욱-PC,    length 3 : 10834
06/19/09 11:14:10 v1.10 @ 조영욱-PC,    length 4 : 5187
06/19/09 11:14:10 v1.10 @ 조영욱-PC,    length 5 : 2310
06/19/09 11:14:10 v1.10 @ 조영욱-PC,    length 6 : 994
06/19/09 11:14:10 v1.10 @ 조영욱-PC,    length 7 : 410
06/19/09 11:14:10 v1.10 @ 조영욱-PC,    length 9+: 223
06/19/09 11:14:10 v1.10 @ 조영욱-PC, largest cycle: 13 relations
06/19/09 11:14:11 v1.10 @ 조영욱-PC, matrix is 61083 x 61153 (12.3 MB) with weight 2744311 (44.88/col)
06/19/09 11:14:11 v1.10 @ 조영욱-PC, sparse part has weight 2744311 (44.88/col)
06/19/09 11:14:11 v1.10 @ 조영욱-PC, filtering completed in 4 passes
06/19/09 11:14:11 v1.10 @ 조영욱-PC, matrix is 52042 x 52106 (10.8 MB) with weight 2412409 (46.30/col)
06/19/09 11:14:11 v1.10 @ 조영욱-PC, sparse part has weight 2412409 (46.30/col)
06/19/09 11:14:11 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later
06/19/09 11:14:11 v1.10 @ 조영욱-PC, matrix is 51994 x 52106 (7.5 MB) with weight 1883866 (36.15/col)
06/19/09 11:14:11 v1.10 @ 조영욱-PC, sparse part has weight 1455034 (27.92/col)
06/19/09 11:14:11 v1.10 @ 조영욱-PC, matrix includes 64 packed rows
06/19/09 11:14:11 v1.10 @ 조영욱-PC, using block size 20842 for processor cache size 4096 kB
06/19/09 11:14:11 v1.10 @ 조영욱-PC, commencing Lanczos iteration
06/19/09 11:14:11 v1.10 @ 조영욱-PC, memory use: 6.9 MB
06/19/09 11:14:21 v1.10 @ 조영욱-PC, lanczos halted after 824 iterations (dim = 51989)
06/19/09 11:14:21 v1.10 @ 조영욱-PC, recovered 14 nontrivial dependencies
06/19/09 11:14:22 v1.10 @ 조영욱-PC, prp42 = 166507482518017499178086786863171180756723
06/19/09 11:14:22 v1.10 @ 조영욱-PC, prp47 = 16747599071352727268207577662937259514746886269
06/19/09 11:14:22 v1.10 @ 조영욱-PC, Lanczos elapsed time = 12.3240 seconds.
06/19/09 11:14:22 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.5620 seconds.
06/19/09 11:14:22 v1.10 @ 조영욱-PC, SIQS elapsed time = 1504.2710 seconds.
06/19/09 11:14:22 v1.10 @ 조영욱-PC, 
06/19/09 11:14:22 v1.10 @ 조영욱-PC,

Jun 18, 2009

By Serge Batalov / PFGW / Jun 17, 2009

(2·10⁵⁵⁵⁴⁴+1)/3 = (6)₅₅₅₄₃7_<55544> is PRP.

Jun 17, 2009 (6th)

By Andreas Tete / Msieve 1.42/GGNFS / Jun 17, 2009

(68·10¹⁷⁰+13)/9 = 7(5)₁₆₉7_<171> = 139 · 29473 · 290911573 · 32154519786569_<14> · 23839585429968260174265553579269018490660487_<44> · C99

C99 = P49 · P51

P49 = 3094951329199020842510313392944073185116931701059_<49>

P51 = 267221692159180547256882648639110381886247612020911_<51>

Tue Jun 16 22:04:28 2009  Msieve v. 1.42
Tue Jun 16 22:04:28 2009  random seeds: ea0da198 42de2300
Tue Jun 16 22:04:28 2009  factoring 827038131338867400594187976741748355884015349016991665314607084014181746469763768683616779908844749 (99 digits)
Tue Jun 16 22:04:28 2009  searching for 15-digit factors
Tue Jun 16 22:04:30 2009  commencing quadratic sieve (99-digit input)
Tue Jun 16 22:04:30 2009  using multiplier of 5
Tue Jun 16 22:04:30 2009  using 32kb Intel Core sieve core
Tue Jun 16 22:04:30 2009  sieve interval: 36 blocks of size 32768
Tue Jun 16 22:04:30 2009  processing polynomials in batches of 6
Tue Jun 16 22:04:30 2009  using a sieve bound of 2642771 (96471 primes)
Tue Jun 16 22:04:30 2009  using large prime bound of 396415650 (28 bits)
Tue Jun 16 22:04:30 2009  using double large prime bound of 2996893989271350 (43-52 bits)
Tue Jun 16 22:04:30 2009  using trial factoring cutoff of 52 bits
Tue Jun 16 22:04:30 2009  polynomial 'A' values have 13 factors
Tue Jun 16 22:04:42 2009  restarting with 20829 full and 1327127 partial relations
Tue Jun 16 22:45:30 2009  96657 relations (22826 full + 73831 combined from 1456926 partial), need 96567
Tue Jun 16 22:45:42 2009  begin with 1479752 relations
Tue Jun 16 22:45:43 2009  reduce to 256034 relations in 11 passes
Tue Jun 16 22:45:43 2009  attempting to read 256034 relations
Tue Jun 16 22:45:47 2009  recovered 256034 relations
Tue Jun 16 22:45:47 2009  recovered 247013 polynomials
Tue Jun 16 22:45:47 2009  attempting to build 96657 cycles
Tue Jun 16 22:45:47 2009  found 96655 cycles in 5 passes
Tue Jun 16 22:45:47 2009  distribution of cycle lengths:
Tue Jun 16 22:45:47 2009     length 1 : 22826
Tue Jun 16 22:45:47 2009     length 2 : 16496
Tue Jun 16 22:45:47 2009     length 3 : 16148
Tue Jun 16 22:45:47 2009     length 4 : 13213
Tue Jun 16 22:45:47 2009     length 5 : 10056
Tue Jun 16 22:45:47 2009     length 6 : 7061
Tue Jun 16 22:45:47 2009     length 7 : 4484
Tue Jun 16 22:45:47 2009     length 9+: 6371
Tue Jun 16 22:45:47 2009  largest cycle: 19 relations
Tue Jun 16 22:45:47 2009  matrix is 96471 x 96655 (25.0 MB) with weight 6159330 (63.72/col)
Tue Jun 16 22:45:47 2009  sparse part has weight 6159330 (63.72/col)
Tue Jun 16 22:45:48 2009  filtering completed in 3 passes
Tue Jun 16 22:45:48 2009  matrix is 92701 x 92765 (24.1 MB) with weight 5939028 (64.02/col)
Tue Jun 16 22:45:48 2009  sparse part has weight 5939028 (64.02/col)
Tue Jun 16 22:45:48 2009  saving the first 48 matrix rows for later
Tue Jun 16 22:45:48 2009  matrix is 92653 x 92765 (13.4 MB) with weight 4416948 (47.61/col)
Tue Jun 16 22:45:48 2009  sparse part has weight 2953275 (31.84/col)
Tue Jun 16 22:45:48 2009  matrix includes 64 packed rows
Tue Jun 16 22:45:48 2009  using block size 37106 for processor cache size 2048 kB
Tue Jun 16 22:45:49 2009  commencing Lanczos iteration
Tue Jun 16 22:45:49 2009  memory use: 14.2 MB
Tue Jun 16 22:46:25 2009  lanczos halted after 1466 iterations (dim = 92652)
Tue Jun 16 22:46:25 2009  recovered 17 nontrivial dependencies
Tue Jun 16 22:46:26 2009  prp49 factor: 3094951329199020842510313392944073185116931701059
Tue Jun 16 22:46:26 2009  prp51 factor: 267221692159180547256882648639110381886247612020911
Tue Jun 16 22:46:26 2009  elapsed time 00:41:58
Tue Jun 16 22:46:26 2009  total time 07:44:45

(17·10¹⁷⁰+7)/3 = 5(6)₁₆₉9_<171> = 559631 · 104675792068314853_<18> · 322875512531802497_<18> · 162573751231188186196793586329_<30> · C102

C102 = P39 · P64

P39 = 102486391641802624865794677615608882159_<39>

P64 = 1798158246875135173916969236304899898630006002386192375498498449_<64>

Wed Jun 17 10:43:02 2009  Msieve v. 1.42
Wed Jun 17 10:43:02 2009  random seeds: 433ed298 64d9e482
Wed Jun 17 10:43:02 2009  factoring 184286750323182314380444905316628685751186302523555068558316595554862239297139529533915383571885271391 (102 digits)
Wed Jun 17 10:43:03 2009  searching for 15-digit factors
Wed Jun 17 10:43:04 2009  commencing number field sieve (102-digit input)
Wed Jun 17 10:43:04 2009  R0: -48886729453583034047
Wed Jun 17 10:43:04 2009  R1:  27538271657
Wed Jun 17 10:43:04 2009  A0:  1655221487135049353428650
Wed Jun 17 10:43:04 2009  A1:  139986539947248807243
Wed Jun 17 10:43:04 2009  A2: -493487056659667
Wed Jun 17 10:43:04 2009  A3: -286852384879
Wed Jun 17 10:43:04 2009  A4: -12793664
Wed Jun 17 10:43:04 2009  A5:  660
Wed Jun 17 10:43:04 2009  skew 23388.86, size 1.238991e-009, alpha -4.826938, combined = 2.969698e-009
Wed Jun 17 10:43:04 2009  
Wed Jun 17 10:43:04 2009  commencing relation filtering
Wed Jun 17 10:43:04 2009  commencing duplicate removal, pass 1
Wed Jun 17 10:43:38 2009  found 226641 hash collisions in 3981204 relations
Wed Jun 17 10:43:49 2009  added 30399 free relations
Wed Jun 17 10:43:49 2009  commencing duplicate removal, pass 2
Wed Jun 17 10:43:54 2009  found 206333 duplicates and 3805269 unique relations
Wed Jun 17 10:43:54 2009  memory use: 36.7 MB
Wed Jun 17 10:43:54 2009  reading rational ideals above 2162688
Wed Jun 17 10:43:54 2009  reading algebraic ideals above 2162688
Wed Jun 17 10:43:54 2009  commencing singleton removal, pass 1
Wed Jun 17 10:44:30 2009  relations with 0 large ideals: 87613
Wed Jun 17 10:44:30 2009  relations with 1 large ideals: 607266
Wed Jun 17 10:44:30 2009  relations with 2 large ideals: 1422964
Wed Jun 17 10:44:30 2009  relations with 3 large ideals: 1293039
Wed Jun 17 10:44:30 2009  relations with 4 large ideals: 365325
Wed Jun 17 10:44:30 2009  relations with 5 large ideals: 0
Wed Jun 17 10:44:30 2009  relations with 6 large ideals: 29062
Wed Jun 17 10:44:30 2009  relations with 7+ large ideals: 0
Wed Jun 17 10:44:30 2009  3805269 relations and about 3828438 large ideals
Wed Jun 17 10:44:30 2009  commencing singleton removal, pass 2
Wed Jun 17 10:45:06 2009  found 1847305 singletons
Wed Jun 17 10:45:06 2009  current dataset: 1957964 relations and about 1579102 large ideals
Wed Jun 17 10:45:06 2009  commencing singleton removal, pass 3
Wed Jun 17 10:45:31 2009  found 388897 singletons
Wed Jun 17 10:45:31 2009  current dataset: 1569067 relations and about 1160524 large ideals
Wed Jun 17 10:45:31 2009  commencing singleton removal, final pass
Wed Jun 17 10:45:50 2009  memory use: 24.2 MB
Wed Jun 17 10:45:50 2009  commencing in-memory singleton removal
Wed Jun 17 10:45:50 2009  begin with 1569067 relations and 1190472 unique ideals
Wed Jun 17 10:45:51 2009  reduce to 1319249 relations and 933729 ideals in 13 passes
Wed Jun 17 10:45:51 2009  max relations containing the same ideal: 16
Wed Jun 17 10:45:51 2009  reading rational ideals above 100000
Wed Jun 17 10:45:51 2009  reading algebraic ideals above 100000
Wed Jun 17 10:45:51 2009  commencing singleton removal, final pass
Wed Jun 17 10:46:09 2009  keeping 1233284 ideals with weight <= 25, new excess is 99584
Wed Jun 17 10:46:11 2009  memory use: 34.3 MB
Wed Jun 17 10:46:11 2009  commencing in-memory singleton removal
Wed Jun 17 10:46:11 2009  begin with 1332898 relations and 1233284 unique ideals
Wed Jun 17 10:46:12 2009  reduce to 1310030 relations and 1144254 ideals in 12 passes
Wed Jun 17 10:46:12 2009  max relations containing the same ideal: 25
Wed Jun 17 10:46:13 2009  removing 196021 relations and 170892 ideals in 25129 cliques
Wed Jun 17 10:46:13 2009  commencing in-memory singleton removal
Wed Jun 17 10:46:13 2009  begin with 1114009 relations and 1144254 unique ideals
Wed Jun 17 10:46:14 2009  reduce to 1095209 relations and 954131 ideals in 9 passes
Wed Jun 17 10:46:14 2009  max relations containing the same ideal: 25
Wed Jun 17 10:46:15 2009  removing 146412 relations and 121283 ideals in 25129 cliques
Wed Jun 17 10:46:15 2009  commencing in-memory singleton removal
Wed Jun 17 10:46:15 2009  begin with 948797 relations and 954131 unique ideals
Wed Jun 17 10:46:15 2009  reduce to 934995 relations and 818721 ideals in 7 passes
Wed Jun 17 10:46:15 2009  max relations containing the same ideal: 25
Wed Jun 17 10:46:16 2009  relations with 0 large ideals: 4286
Wed Jun 17 10:46:16 2009  relations with 1 large ideals: 38985
Wed Jun 17 10:46:16 2009  relations with 2 large ideals: 142845
Wed Jun 17 10:46:16 2009  relations with 3 large ideals: 264588
Wed Jun 17 10:46:16 2009  relations with 4 large ideals: 270213
Wed Jun 17 10:46:16 2009  relations with 5 large ideals: 154225
Wed Jun 17 10:46:16 2009  relations with 6 large ideals: 50521
Wed Jun 17 10:46:16 2009  relations with 7+ large ideals: 9332
Wed Jun 17 10:46:16 2009  commencing 2-way merge
Wed Jun 17 10:46:16 2009  reduce to 557916 relation sets and 441642 unique ideals
Wed Jun 17 10:46:16 2009  commencing full merge
Wed Jun 17 10:46:24 2009  memory use: 36.4 MB
Wed Jun 17 10:46:24 2009  found 262675 cycles, need 247842
Wed Jun 17 10:46:24 2009  weight of 247842 cycles is about 17409653 (70.24/cycle)
Wed Jun 17 10:46:24 2009  distribution of cycle lengths:
Wed Jun 17 10:46:24 2009  1 relations: 23301
Wed Jun 17 10:46:24 2009  2 relations: 24561
Wed Jun 17 10:46:24 2009  3 relations: 24959
Wed Jun 17 10:46:24 2009  4 relations: 23784
Wed Jun 17 10:46:24 2009  5 relations: 22348
Wed Jun 17 10:46:24 2009  6 relations: 19801
Wed Jun 17 10:46:24 2009  7 relations: 18209
Wed Jun 17 10:46:24 2009  8 relations: 16045
Wed Jun 17 10:46:24 2009  9 relations: 14195
Wed Jun 17 10:46:24 2009  10+ relations: 60639
Wed Jun 17 10:46:24 2009  heaviest cycle: 19 relations
Wed Jun 17 10:46:24 2009  commencing cycle optimization
Wed Jun 17 10:46:25 2009  start with 1626188 relations
Wed Jun 17 10:46:29 2009  pruned 47838 relations
Wed Jun 17 10:46:29 2009  memory use: 41.4 MB
Wed Jun 17 10:46:29 2009  distribution of cycle lengths:
Wed Jun 17 10:46:29 2009  1 relations: 23301
Wed Jun 17 10:46:29 2009  2 relations: 25154
Wed Jun 17 10:46:29 2009  3 relations: 26000
Wed Jun 17 10:46:29 2009  4 relations: 24495
Wed Jun 17 10:46:29 2009  5 relations: 23048
Wed Jun 17 10:46:29 2009  6 relations: 20446
Wed Jun 17 10:46:29 2009  7 relations: 18605
Wed Jun 17 10:46:29 2009  8 relations: 16292
Wed Jun 17 10:46:29 2009  9 relations: 14364
Wed Jun 17 10:46:29 2009  10+ relations: 56137
Wed Jun 17 10:46:29 2009  heaviest cycle: 19 relations
Wed Jun 17 10:46:29 2009  RelProcTime: 193
Wed Jun 17 10:46:29 2009  
Wed Jun 17 10:46:29 2009  commencing linear algebra
Wed Jun 17 10:46:29 2009  read 247842 cycles
Wed Jun 17 10:46:30 2009  cycles contain 843980 unique relations
Wed Jun 17 10:46:43 2009  read 843980 relations
Wed Jun 17 10:46:44 2009  using 20 quadratic characters above 67106562
Wed Jun 17 10:46:49 2009  building initial matrix
Wed Jun 17 10:47:00 2009  memory use: 91.7 MB
Wed Jun 17 10:47:01 2009  read 247842 cycles
Wed Jun 17 10:47:01 2009  matrix is 247647 x 247842 (70.5 MB) with weight 23537024 (94.97/col)
Wed Jun 17 10:47:01 2009  sparse part has weight 16510401 (66.62/col)
Wed Jun 17 10:47:04 2009  filtering completed in 2 passes
Wed Jun 17 10:47:04 2009  matrix is 246637 x 246832 (70.4 MB) with weight 23478090 (95.12/col)
Wed Jun 17 10:47:04 2009  sparse part has weight 16482270 (66.78/col)
Wed Jun 17 10:47:05 2009  read 246832 cycles
Wed Jun 17 10:47:06 2009  matrix is 246637 x 246832 (70.4 MB) with weight 23478090 (95.12/col)
Wed Jun 17 10:47:06 2009  sparse part has weight 16482270 (66.78/col)
Wed Jun 17 10:47:06 2009  saving the first 48 matrix rows for later
Wed Jun 17 10:47:06 2009  matrix is 246589 x 246832 (67.2 MB) with weight 18694202 (75.74/col)
Wed Jun 17 10:47:06 2009  sparse part has weight 16146110 (65.41/col)
Wed Jun 17 10:47:06 2009  matrix includes 64 packed rows
Wed Jun 17 10:47:06 2009  using block size 65536 for processor cache size 3072 kB
Wed Jun 17 10:47:08 2009  commencing Lanczos iteration
Wed Jun 17 10:47:08 2009  memory use: 65.0 MB
Wed Jun 17 10:55:12 2009  lanczos halted after 3903 iterations (dim = 246589)
Wed Jun 17 10:55:13 2009  recovered 36 nontrivial dependencies
Wed Jun 17 10:55:13 2009  BLanczosTime: 524
Wed Jun 17 10:55:13 2009  
Wed Jun 17 10:55:13 2009  commencing square root phase
Wed Jun 17 10:55:13 2009  reading relations for dependency 1
Wed Jun 17 10:55:13 2009  read 123117 cycles
Wed Jun 17 10:55:14 2009  cycles contain 520801 unique relations
Wed Jun 17 10:55:20 2009  read 520801 relations
Wed Jun 17 10:55:22 2009  multiplying 420376 relations
Wed Jun 17 10:56:05 2009  multiply complete, coefficients have about 15.35 million bits
Wed Jun 17 10:56:06 2009  initial square root is modulo 656468557
Wed Jun 17 10:57:29 2009  reading relations for dependency 2
Wed Jun 17 10:57:30 2009  read 123574 cycles
Wed Jun 17 10:57:30 2009  cycles contain 523003 unique relations
Wed Jun 17 10:57:43 2009  read 523003 relations
Wed Jun 17 10:57:45 2009  multiplying 421782 relations
Wed Jun 17 10:58:28 2009  multiply complete, coefficients have about 15.40 million bits
Wed Jun 17 10:58:29 2009  initial square root is modulo 703063901
Wed Jun 17 10:59:51 2009  sqrtTime: 278
Wed Jun 17 10:59:51 2009  prp39 factor: 102486391641802624865794677615608882159
Wed Jun 17 10:59:51 2009  prp64 factor: 1798158246875135173916969236304899898630006002386192375498498449
Wed Jun 17 10:59:51 2009  elapsed time 00:16:49
total time 4,5 hours

Jun 17, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Jun 17, 2009

(58·10¹⁵²-31)/9 = 6(4)₁₅₁1_<153> = 43 · 59 · 1387660273_<10> · 6622312771_<10> · 2204947328723_<13> · C119

C119 = P50 · P69

P50 = 29094058807903755108349233484470242778633421481941_<50>

P69 = 430893200761032977032832794015273047754856060570037729587831660047397_<69>

Number: n
N=12536432122867372519200253053164652442871301443065502726646145676657703651611969289789345370155994930176926330039557577
  ( 119 digits)
SNFS difficulty: 154 digits.
Divisors found:

Wed Jun 17 16:40:36 2009  prp50 factor: 29094058807903755108349233484470242778633421481941
Wed Jun 17 16:40:36 2009  prp69 factor: 430893200761032977032832794015273047754856060570037729587831660047397
Wed Jun 17 16:40:36 2009  elapsed time 00:30:16 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 15.52 hours.
Scaled time: 41.27 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_4_151_1
n: 12536432122867372519200253053164652442871301443065502726646145676657703651611969289789345370155994930176926330039557577
m: 2000000000000000000000000000000
deg: 5
c5: 725
c0: -124
skew: 0.70
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1300000, 2305363)
Primes: RFBsize:189880, AFBsize:190566, largePrimes:11573313 encountered
Relations: rels:10680437, finalFF:303015
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 939344 hash collisions in 11511210 relations
Msieve: matrix is 472487 x 472735 (126.7 MB)

Total sieving time: 15.33 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,28,28,56,56,2.4,2.4,100000
total time: 15.52 hours.
 --------- CPU info (if available) ----------

Jun 17, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.3 / Jun 17, 2009

(2·10²¹³+1)/3 = (6)₂₁₂7_<213> = 642623 · 68623043 · 1464084467605343_<16> · 4409891276148706861866704821_<28> · C157

C157 = P36 · C122

P36 = 118009803355233384577031249267259421_<36>

C122 = [19841312675353812400480170290920785443960159561950228060042177768467208735513015756609844426709640725339681886570157222681_<122>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=2629839573
Step 1 took 3869ms
Step 2 took 3416ms
********** Factor found in step 2: 118009803355233384577031249267259421
Found probable prime factor of 36 digits: 118009803355233384577031249267259421
Composite cofactor has 122 digits

Jun 17, 2009 (3rd)

Factorizations of 66...667 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jun 17, 2009 (2nd)

By Andreas Tete / Msieve 1.42/GGNFS / Jun 17, 2009

2·10²⁰⁷-1 = 1(9)₂₀₇_<208> = 59 · 3094811768747411_<16> · 617154916981980493532291_<24> · 1381098786990645604063367397059_<31> · C137

C137 = P47 · P91

P47 = 10018631606052288287701622273517610992315312691_<47>

P91 = 1282674318787362762030604322874622092382640612854027342323747789696130963429438316715523069_<91>

Tue Jun 16 08:41:15 2009  Msieve v. 1.42
Tue Jun 16 08:41:15 2009  random seeds: e7048544 5712ebb3
Tue Jun 16 08:41:15 2009  factoring 12850641470474661004875505196236329003404849262692486716060856559801450057354066892544499120803880203791248408541006698806056308358968679 (137 digits)
Tue Jun 16 08:41:16 2009  searching for 15-digit factors
Tue Jun 16 08:41:19 2009  commencing number field sieve (137-digit input)
Tue Jun 16 08:41:19 2009  R0: -184938694941958480622306328
Tue Jun 16 08:41:19 2009  R1:  1210976711056969
Tue Jun 16 08:41:19 2009  A0: -389193885300554948797063324008702305
Tue Jun 16 08:41:19 2009  A1:  317170412277137560002579632698
Tue Jun 16 08:41:19 2009  A2:  342990442362395307028433
Tue Jun 16 08:41:19 2009  A3: -98772152073117598
Tue Jun 16 08:41:19 2009  A4: -12135218028
Tue Jun 16 08:41:19 2009  A5:  59400
Tue Jun 16 08:41:19 2009  skew 1751330.93, size 3.148758e-013, alpha -8.406469, combined = 3.071070e-011
Tue Jun 16 08:41:19 2009  
Tue Jun 16 08:41:19 2009  commencing relation filtering
Tue Jun 16 08:41:19 2009  commencing duplicate removal, pass 1
Tue Jun 16 08:42:58 2009  error -5 reading relation 7150400
Tue Jun 16 08:45:52 2009  found 4303051 hash collisions in 21013118 relations
Tue Jun 16 08:46:53 2009  added 117519 free relations
Tue Jun 16 08:46:53 2009  commencing duplicate removal, pass 2
Tue Jun 16 08:48:02 2009  found 4382890 duplicates and 16747746 unique relations
Tue Jun 16 08:48:02 2009  memory use: 106.6 MB
Tue Jun 16 08:48:02 2009  reading rational ideals above 15663104
Tue Jun 16 08:48:02 2009  reading algebraic ideals above 15663104
Tue Jun 16 08:48:02 2009  commencing singleton removal, pass 1
Tue Jun 16 08:51:52 2009  relations with 0 large ideals: 487570
Tue Jun 16 08:51:52 2009  relations with 1 large ideals: 2808823
Tue Jun 16 08:51:52 2009  relations with 2 large ideals: 5803004
Tue Jun 16 08:51:52 2009  relations with 3 large ideals: 5237520
Tue Jun 16 08:51:52 2009  relations with 4 large ideals: 2029946
Tue Jun 16 08:51:52 2009  relations with 5 large ideals: 271692
Tue Jun 16 08:51:52 2009  relations with 6 large ideals: 109191
Tue Jun 16 08:51:52 2009  relations with 7+ large ideals: 0
Tue Jun 16 08:51:52 2009  16747746 relations and about 15351641 large ideals
Tue Jun 16 08:51:52 2009  commencing singleton removal, pass 2
Tue Jun 16 08:56:10 2009  found 6725926 singletons
Tue Jun 16 08:56:10 2009  current dataset: 10021820 relations and about 7447053 large ideals
Tue Jun 16 08:56:10 2009  commencing singleton removal, pass 3
Tue Jun 16 08:58:55 2009  found 1478173 singletons
Tue Jun 16 08:58:55 2009  current dataset: 8543647 relations and about 5886766 large ideals
Tue Jun 16 08:58:55 2009  commencing singleton removal, pass 4
Tue Jun 16 09:01:34 2009  found 397854 singletons
Tue Jun 16 09:01:34 2009  current dataset: 8145793 relations and about 5481664 large ideals
Tue Jun 16 09:01:34 2009  commencing singleton removal, final pass
Tue Jun 16 09:04:43 2009  memory use: 133.2 MB
Tue Jun 16 09:04:43 2009  commencing in-memory singleton removal
Tue Jun 16 09:04:44 2009  begin with 8145793 relations and 6066424 unique ideals
Tue Jun 16 09:04:53 2009  reduce to 6656410 relations and 4531042 ideals in 14 passes
Tue Jun 16 09:04:53 2009  max relations containing the same ideal: 24
Tue Jun 16 09:04:55 2009  reading rational ideals above 720000
Tue Jun 16 09:04:55 2009  reading algebraic ideals above 720000
Tue Jun 16 09:04:55 2009  commencing singleton removal, final pass
Tue Jun 16 09:07:42 2009  keeping 6066245 ideals with weight <= 20, new excess is 496511
Tue Jun 16 09:07:53 2009  memory use: 182.1 MB
Tue Jun 16 09:07:53 2009  commencing in-memory singleton removal
Tue Jun 16 09:07:54 2009  begin with 6660230 relations and 6066245 unique ideals
Tue Jun 16 09:08:06 2009  reduce to 6551115 relations and 5938488 ideals in 12 passes
Tue Jun 16 09:08:06 2009  max relations containing the same ideal: 20
Tue Jun 16 09:08:11 2009  removing 247011 relations and 228674 ideals in 18337 cliques
Tue Jun 16 09:08:11 2009  commencing in-memory singleton removal
Tue Jun 16 09:08:12 2009  begin with 6304104 relations and 5938488 unique ideals
Tue Jun 16 09:08:20 2009  reduce to 6298481 relations and 5704165 ideals in 8 passes
Tue Jun 16 09:08:20 2009  max relations containing the same ideal: 20
Tue Jun 16 09:08:25 2009  removing 179348 relations and 161011 ideals in 18337 cliques
Tue Jun 16 09:08:25 2009  commencing in-memory singleton removal
Tue Jun 16 09:08:26 2009  begin with 6119133 relations and 5704165 unique ideals
Tue Jun 16 09:08:31 2009  reduce to 6115696 relations and 5539705 ideals in 6 passes
Tue Jun 16 09:08:31 2009  max relations containing the same ideal: 20
Tue Jun 16 09:08:33 2009  relations with 0 large ideals: 8428
Tue Jun 16 09:08:33 2009  relations with 1 large ideals: 98147
Tue Jun 16 09:08:33 2009  relations with 2 large ideals: 511881
Tue Jun 16 09:08:33 2009  relations with 3 large ideals: 1359789
Tue Jun 16 09:08:33 2009  relations with 4 large ideals: 1976358
Tue Jun 16 09:08:33 2009  relations with 5 large ideals: 1508005
Tue Jun 16 09:08:33 2009  relations with 6 large ideals: 549511
Tue Jun 16 09:08:33 2009  relations with 7+ large ideals: 103577
Tue Jun 16 09:08:33 2009  commencing 2-way merge
Tue Jun 16 09:08:40 2009  reduce to 3654554 relation sets and 3078563 unique ideals
Tue Jun 16 09:08:40 2009  commencing full merge
Tue Jun 16 09:09:49 2009  memory use: 277.3 MB
Tue Jun 16 09:09:50 2009  found 1863902 cycles, need 1788763
Tue Jun 16 09:09:50 2009  weight of 1788763 cycles is about 125390665 (70.10/cycle)
Tue Jun 16 09:09:50 2009  distribution of cycle lengths:
Tue Jun 16 09:09:50 2009  1 relations: 214445
Tue Jun 16 09:09:50 2009  2 relations: 230761
Tue Jun 16 09:09:50 2009  3 relations: 226678
Tue Jun 16 09:09:50 2009  4 relations: 200070
Tue Jun 16 09:09:50 2009  5 relations: 173029
Tue Jun 16 09:09:50 2009  6 relations: 144276
Tue Jun 16 09:09:50 2009  7 relations: 120117
Tue Jun 16 09:09:50 2009  8 relations: 100783
Tue Jun 16 09:09:50 2009  9 relations: 82547
Tue Jun 16 09:09:50 2009  10+ relations: 296057
Tue Jun 16 09:09:50 2009  heaviest cycle: 19 relations
Tue Jun 16 09:09:51 2009  commencing cycle optimization
Tue Jun 16 09:09:55 2009  start with 9955039 relations
Tue Jun 16 09:10:24 2009  pruned 243613 relations
Tue Jun 16 09:10:24 2009  memory use: 266.1 MB
Tue Jun 16 09:10:24 2009  distribution of cycle lengths:
Tue Jun 16 09:10:24 2009  1 relations: 214445
Tue Jun 16 09:10:24 2009  2 relations: 236371
Tue Jun 16 09:10:24 2009  3 relations: 235532
Tue Jun 16 09:10:24 2009  4 relations: 204943
Tue Jun 16 09:10:24 2009  5 relations: 176486
Tue Jun 16 09:10:24 2009  6 relations: 145380
Tue Jun 16 09:10:24 2009  7 relations: 120359
Tue Jun 16 09:10:24 2009  8 relations: 99668
Tue Jun 16 09:10:24 2009  9 relations: 80917
Tue Jun 16 09:10:24 2009  10+ relations: 274662
Tue Jun 16 09:10:24 2009  heaviest cycle: 19 relations
Tue Jun 16 09:10:27 2009  RelProcTime: 1388
Tue Jun 16 09:10:27 2009  
Tue Jun 16 09:10:27 2009  commencing linear algebra
Tue Jun 16 09:10:28 2009  read 1788763 cycles
Tue Jun 16 09:10:33 2009  cycles contain 5592553 unique relations
Tue Jun 16 09:12:10 2009  read 5592553 relations
Tue Jun 16 09:12:22 2009  using 20 quadratic characters above 268435034
Tue Jun 16 09:13:00 2009  building initial matrix
Tue Jun 16 09:14:39 2009  memory use: 666.8 MB
Tue Jun 16 09:15:01 2009  read 1788763 cycles
Tue Jun 16 09:15:04 2009  matrix is 1788464 x 1788763 (515.1 MB) with weight 170626373 (95.39/col)
Tue Jun 16 09:15:04 2009  sparse part has weight 120728082 (67.49/col)
Tue Jun 16 09:15:46 2009  filtering completed in 3 passes
Tue Jun 16 09:15:47 2009  matrix is 1778355 x 1778555 (513.7 MB) with weight 170014583 (95.59/col)
Tue Jun 16 09:15:47 2009  sparse part has weight 120432214 (67.71/col)
Tue Jun 16 09:16:17 2009  read 1778555 cycles
Tue Jun 16 09:16:20 2009  matrix is 1778355 x 1778555 (513.7 MB) with weight 170014583 (95.59/col)
Tue Jun 16 09:16:20 2009  sparse part has weight 120432214 (67.71/col)
Tue Jun 16 09:16:20 2009  saving the first 48 matrix rows for later
Tue Jun 16 09:16:21 2009  matrix is 1778307 x 1778555 (491.3 MB) with weight 135611324 (76.25/col)
Tue Jun 16 09:16:21 2009  sparse part has weight 118111865 (66.41/col)
Tue Jun 16 09:16:21 2009  matrix includes 64 packed rows
Tue Jun 16 09:16:21 2009  using block size 65536 for processor cache size 3072 kB
Tue Jun 16 09:16:37 2009  commencing Lanczos iteration
Tue Jun 16 09:16:37 2009  memory use: 489.2 MB
Tue Jun 16 18:00:35 2009  lanczos halted after 28124 iterations (dim = 1778306)
Tue Jun 16 18:00:41 2009  recovered 30 nontrivial dependencies
Tue Jun 16 18:00:41 2009  BLanczosTime: 31814
Tue Jun 16 18:00:41 2009  
Tue Jun 16 18:00:41 2009  commencing square root phase
Tue Jun 16 18:00:41 2009  reading relations for dependency 1
Tue Jun 16 18:00:43 2009  read 889064 cycles
Tue Jun 16 18:00:46 2009  cycles contain 3390342 unique relations
Tue Jun 16 18:01:49 2009  read 3390342 relations
Tue Jun 16 18:02:12 2009  multiplying 2790492 relations
Tue Jun 16 18:10:35 2009  multiply complete, coefficients have about 135.95 million bits
Tue Jun 16 18:10:41 2009  initial square root is modulo 75679
Tue Jun 16 18:24:12 2009  sqrtTime: 1411
Tue Jun 16 18:24:12 2009  prp47 factor: 10018631606052288287701622273517610992315312691
Tue Jun 16 18:24:12 2009  prp91 factor: 1282674318787362762030604322874622092382640612854027342323747789696130963429438316715523069
Tue Jun 16 18:24:12 2009  elapsed time 09:42:57
total time 358,5 hours

Jun 17, 2009

By Markus Tervooren / lasieve/msieve / Jun 17, 2009

(52·10²⁰⁴+11)/9 = 5(7)₂₀₃9_<205> = 7 · C204

C204 = P52 · P153

P52 = 3489796835931103361689260396347023065416395122343361_<52>

P153 = 236517156786464756205308903707715975525031761922301258980101045633547768238421296759011363918993807438685658380715328301003618543542563650318286959170677_<153>

Msieve v. 1.41
Mon Jun 15 11:30:04 2009
random seeds: 15203ffb 1cd35f9e
factoring 825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825397 (204 digits)
searching for 15-digit factors
commencing number field sieve (204-digit input)
R0: -100000000000000000000000000000000000000000
R1:  1
A0:  55
A1:  0
A2:  0
A3:  0
A4:  0
A5:  26
skew 1.16, size 2.311556e-14, alpha 1.167854, combined = 8.053847e-12

commencing relation filtering
commencing duplicate removal, pass 1
error -11 reading relation 4747171
error -11 reading relation 36981095
error -11 reading relation 37269830
error -9 reading relation 37529624
error -15 reading relation 37808078
found 6615974 hash collisions in 41847181 relations
added 36 free relations
commencing duplicate removal, pass 2
found 5189566 duplicates and 36657651 unique relations
memory use: 165.2 MB
reading rational ideals above 27066368
reading algebraic ideals above 27066368
commencing singleton removal, pass 1
relations with 0 large ideals: 854492
relations with 1 large ideals: 4838519
relations with 2 large ideals: 11747822
relations with 3 large ideals: 12974157
relations with 4 large ideals: 5544950
relations with 5 large ideals: 51281
relations with 6 large ideals: 646430
relations with 7+ large ideals: 0
36657651 relations and about 31746105 large ideals
commencing singleton removal, pass 2
found 11657926 singletons
current dataset: 24999725 relations and about 18520428 large ideals
commencing singleton removal, pass 3
found 2458512 singletons
current dataset: 22541213 relations and about 15954383 large ideals
commencing singleton removal, pass 4
found 610781 singletons
current dataset: 21930432 relations and about 15335945 large ideals
commencing singleton removal, pass 5
found 151119 singletons
current dataset: 21779313 relations and about 15184347 large ideals
commencing singleton removal, final pass
memory use: 360.3 MB
commencing in-memory singleton removal
begin with 21779313 relations and 18395015 unique ideals
reduce to 15354339 relations and 11633580 ideals in 18 passes
max relations containing the same ideal: 46
reading rational ideals above 720000
reading algebraic ideals above 720000
commencing singleton removal, final pass
keeping 13441317 ideals with weight <= 20, new excess is 1564387
memory use: 489.2 MB
commencing in-memory singleton removal
begin with 15354376 relations and 13441317 unique ideals
reduce to 15313044 relations and 13399791 ideals in 13 passes
max relations containing the same ideal: 20
removing 728555 relations and 679273 ideals in 49282 cliques
commencing in-memory singleton removal
begin with 14584489 relations and 13399791 unique ideals
reduce to 14556496 relations and 12692371 ideals in 8 passes
max relations containing the same ideal: 20
removing 524992 relations and 475710 ideals in 49282 cliques
commencing in-memory singleton removal
begin with 14031504 relations and 12692371 unique ideals
reduce to 14016019 relations and 12201099 ideals in 8 passes
max relations containing the same ideal: 20
relations with 0 large ideals: 121410
relations with 1 large ideals: 784824
relations with 2 large ideals: 2483536
relations with 3 large ideals: 4142115
relations with 4 large ideals: 3815762
relations with 5 large ideals: 1924327
relations with 6 large ideals: 648133
relations with 7+ large ideals: 95912
commencing 2-way merge
reduce to 8245211 relation sets and 6430293 unique ideals
ignored 2 oversize relation sets
commencing full merge
memory use: 604.6 MB
found 4064935 cycles, need 3832493
weight of 3832493 cycles is about 268453437 (70.05/cycle)
distribution of cycle lengths:
1 relations: 555724
2 relations: 487158
3 relations: 462672
4 relations: 405356
5 relations: 357807
6 relations: 296266
7 relations: 254182
8 relations: 213886
9 relations: 178724
10+ relations: 620718
heaviest cycle: 20 relations
commencing cycle optimization
start with 20801266 relations
pruned 493110 relations
memory use: 717.1 MB
distribution of cycle lengths:
1 relations: 555724
2 relations: 498808
3 relations: 479788
4 relations: 414965
5 relations: 364985
6 relations: 299239
7 relations: 255275
8 relations: 212681
9 relations: 175573
10+ relations: 575455
heaviest cycle: 20 relations
RelProcTime: 1843

commencing linear algebra
read 3832493 cycles
cycles contain 12267129 unique relations
read 12267129 relations
using 20 quadratic characters above 536870840
building initial matrix
memory use: 1538.9 MB
read 3832493 cycles
matrix is 3830980 x 3832493 (1149.3 MB) with weight 338758144 (88.39/col)
sparse part has weight 259136904 (67.62/col)
filtering completed in 3 passes
matrix is 3777859 x 3778059 (1139.2 MB) with weight 335479132 (88.80/col)
sparse part has weight 257071186 (68.04/col)
read 3778059 cycles
matrix is 3777859 x 3778059 (1139.2 MB) with weight 335479132 (88.80/col)
sparse part has weight 257071186 (68.04/col)
saving the first 48 matrix rows for later
matrix is 3777811 x 3778059 (1080.2 MB) with weight 265630651 (70.31/col)
sparse part has weight 245398470 (64.95/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (4 threads)
memory use: 1135.5 MB
linear algebra completed 3777680 of 3778059 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 59744 iterations (dim = 3777811)
recovered 37 nontrivial dependencies
BLanczosTime: 95960

commencing square root phase
reading relations for dependency 1
read 1889489 cycles
cycles contain 7358025 unique relations
read 7358025 relations
multiplying 6101724 relations
multiply complete, coefficients have about 175.74 million bits
initial square root is modulo 2028101
reading relations for dependency 2
read 1888830 cycles
cycles contain 7354128 unique relations
read 7354128 relations
multiplying 6099464 relations
multiply complete, coefficients have about 175.68 million bits
initial square root is modulo 2017991
reading relations for dependency 3
read 1888847 cycles
cycles contain 7355319 unique relations
read 7355319 relations
multiplying 6101654 relations
multiply complete, coefficients have about 175.74 million bits
initial square root is modulo 2027561
sqrtTime: 4290
prp52 factor: 3489796835931103361689260396347023065416395122343361
prp153 factor: 236517156786464756205308903707715975525031761922301258980101045633547768238421296759011363918993807438685658380715328301003618543542563650318286959170677
elapsed time 28:21:58
Sieving CPU time 551:45:01

Jun 16, 2009 (3rd)

By Wataru Sakai / Msieve, GMP-ECM 6.2.1 / Jun 16, 2009

(32·10¹⁹⁰+31)/9 = 3(5)₁₈₉9_<191> = 3 · 229 · C188

C188 = P86 · P102

P86 = 52311355555847030303143653332060151795995423261951000945838450963825453383089608706687_<86>

P102 = 989360933782077602757730767136340057134054664376326080972807007427391485597216486100369325941804525111_<102>

Number: 35559_190
N=51754811580139091056121623807213326863981885815946951318130357431667475335597606339964418567038654374898916383632540837781012453501536470968785379265728610706776645641274462235160925117257
  ( 188 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=52311355555847030303143653332060151795995423261951000945838450963825453383089608706687
 r2=989360933782077602757730767136340057134054664376326080972807007427391485597216486100369325941804525111
Version: 
Total time: 386.28 hours.
Scaled time: 721.57 units (timescale=1.868).
Factorization parameters were as follows:
n: 51754811580139091056121623807213326863981885815946951318130357431667475335597606339964418567038654374898916383632540837781012453501536470968785379265728610706776645641274462235160925117257
m: 200000000000000000000000000000000000000
deg: 5
c5: 1
c0: 31
skew: 1.99
type: snfs
lss: 1
rlim: 10900000
alim: 10900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10900000/10900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5450000, 9050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1769931 x 1770179
Total sieving time: 386.28 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,10900000,10900000,28,28,54,54,2.5,2.5,100000
total time: 386.28 hours.
 --------- CPU info (if available) ----------

(17·10¹⁷⁰+7)/3 = 5(6)₁₆₉9_<171> = 559631 · 104675792068314853_<18> · 322875512531802497_<18> · C131

C131 = P30 · C102

P30 = 162573751231188186196793586329_<30>

C102 = [184286750323182314380444905316628685751186302523555068558316595554862239297139529533915383571885271391_<102>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3231751289
Step 1 took 38311ms
Step 2 took 14187ms
********** Factor found in step 2: 162573751231188186196793586329
Found probable prime factor of 30 digits: 162573751231188186196793586329
Composite cofactor 184286750323182314380444905316628685751186302523555068558316595554862239297139529533915383571885271391 has 102 digits

Jun 16, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jun 16, 2009

(7·10²⁰⁷-43)/9 = (7)₂₀₆3_<207> = 29 · C206

C206 = P58 · P148

P58 = 3525612691841796717716571447742461396593977021280549090597_<58>

P148 = 7607166673102896895035924993239057602596719975676720837964603242247454297832536031682543083611128181134404747535699168691579388841629444804314983421_<148>

Number: n
N=26819923371647509578544061302681992337164750957854406130268199233716475095785440613026819923371647509578544061302681992337164750957854406130268199233716475095785440613026819923371647509578544061302681992337
  ( 206 digits)
SNFS difficulty: 208 digits.
Divisors found:

Tue Jun 16 14:27:57 2009  prp58 factor: 3525612691841796717716571447742461396593977021280549090597
Tue Jun 16 14:27:57 2009  prp148 factor: 7607166673102896895035924993239057602596719975676720837964603242247454297832536031682543083611128181134404747535699168691579388841629444804314983421
Tue Jun 16 14:27:57 2009  elapsed time 34:01:05 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20050930-k8
Total time: 109.38 hours.
Scaled time: 161.56 units (timescale=1.477).
Factorization parameters were as follows:
name: KA_7_206_3
n: 26819923371647509578544061302681992337164750957854406130268199233716475095785440613026819923371647509578544061302681992337164750957854406130268199233716475095785440613026819923371647509578544061302681992337
m: 200000000000000000000000000000000000000000
deg: 5
c5: 175
c0: -344
skew: 1.14
type: snfs
lss: 1
rlim: 21000000
alim: 21000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 21000000/21000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 57/57
Sieved  special-q in [10500000, 31534423)
Primes: RFBsize:1329943, AFBsize:1329867, largePrimes:40241582 encountered
Relations: rels:40602379, finalFF:1267324
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 7729398 hash collisions in 46531126 relations
Msieve: matrix is 4107666 x 4107914 (1109.4 MB)

Total sieving time: 108.14 hours.
Total relation processing time: 1.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,208,5,0,0,0,0,0,0,0,0,21000000,21000000,29,29,57,57,2.6,2.6,100000
total time: 109.38 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2748k kernel code, 36964k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830496)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Total of 4 processors activated (22643.71 BogoMIPS).

Jun 16, 2009

By Sinkiti Sibata / Msieve / Jun 16, 2009

(58·10¹⁶⁹-31)/9 = 6(4)₁₆₈1_<170> = 4759 · 990345030902428049_<18> · 1040962582350012886277401_<25> · C125

C125 = P44 · P81

P44 = 36034728933765103515768049208221872190779947_<44>

P81 = 364524626825221980305319507663534157249009284349617294059232336100323699966871333_<81>

Number: 64441_169
N=13135546117328753501423666515409815427710732848545414983081187338314684998812020480051106583513231610413546102918990665559351
  ( 125 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=36034728933765103515768049208221872190779947 (pp44)
 r2=364524626825221980305319507663534157249009284349617294059232336100323699966871333 (pp81)
Version: Msieve-1.40
Total time: 93.24 hours.
Scaled time: 193.10 units (timescale=2.071).
Factorization parameters were as follows:
name: 64441_169
n: 13135546117328753501423666515409815427710732848545414983081187338314684998812020480051106583513231610413546102918990665559351
m: 10000000000000000000000000000000000
deg: 5
c5: 29
c0: -155
skew: 1.40
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 6000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 984133 x 984381
Total sieving time: 88.91 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.87 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 93.24 hours.
 --------- CPU info (if available) ----------

Jun 15, 2009 (4th)

By Sinkiti Sibata / Msieve / Jun 15, 2009

(58·10¹⁷¹-31)/9 = 6(4)₁₇₀1_<172> = 3 · 131 · 1072439 · C164

C164 = P45 · P120

P45 = 152397504383392681380161331359317911517374557_<45>

P120 = 100332695395700957993833618354525485896082262537839241810909027600644295331161884483270160049035739884288720424176670819_<120>

Number: 64441_171
N=15290452386363939446525848048541105999225523296178280103094019270493344440033228019525273934498184829930241610767876967583025349943732440179203332172996263714952183
  ( 164 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=152397504383392681380161331359317911517374557 (pp45)
 r2=100332695395700957993833618354525485896082262537839241810909027600644295331161884483270160049035739884288720424176670819 (pp120)
Version: Msieve-1.40
Total time: 101.26 hours.
Scaled time: 257.59 units (timescale=2.544).
Factorization parameters were as follows:
name: 64441_171
n: 15290452386363939446525848048541105999225523296178280103094019270493344440033228019525273934498184829930241610767876967583025349943732440179203332172996263714952183
m: 20000000000000000000000000000000000
deg: 5
c5: 145
c0: -248
skew: 1.11
type: snfs
lss: 1
rlim: 5500000
alim: 5500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2750000, 6950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1067207 x 1067455
Total sieving time: 101.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,173.000,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,52,52,2.4,2.4,100000
total time: 101.26 hours.
 --------- CPU info (if available) ----------

Jun 15, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Jun 15, 2009

(68·10¹⁷⁰+13)/9 = 7(5)₁₆₉7_<171> = 139 · 29473 · 290911573 · 32154519786569_<14> · C143

C143 = P44 · C99

P44 = 23839585429968260174265553579269018490660487_<44>

C99 = [827038131338867400594187976741748355884015349016991665314607084014181746469763768683616779908844749_<99>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1694953640
Step 1 took 42454ms
Step 2 took 14836ms
********** Factor found in step 2: 23839585429968260174265553579269018490660487
Found probable prime factor of 44 digits: 23839585429968260174265553579269018490660487
Composite cofactor 827038131338867400594187976741748355884015349016991665314607084014181746469763768683616779908844749 has 99 digits

(58·10¹⁸⁹-31)/9 = 6(4)₁₈₈1_<190> = 3 · 1298969585567877829600303_<25> · 104526430293899563124851798413289_<33> · C134

C134 = P35 · P99

P35 = 27851355416234957710219931262472333_<35>

P99 = 568058146616729197426787256156526078124017948322299569993098655486669818175582047103675908213848777_<99>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=98376821
Step 1 took 38188ms
Step 2 took 14478ms
********** Factor found in step 2: 27851355416234957710219931262472333
Found probable prime factor of 35 digits: 27851355416234957710219931262472333
Probable prime cofactor 568058146616729197426787256156526078124017948322299569993098655486669818175582047103675908213848777 has 99 digits

(32·10²⁰⁵+13)/9 = 3(5)₂₀₄7_<206> = 37 · 967379807683_<12> · 1184417920426891_<16> · 795593320256493401773149644687597_<33> · C145

C145 = P51 · P94

P51 = 523543438969426161642554706724547076253559125346249_<51>

P94 = 2013538358755604989175086781461802433222124306874954367100349986369529759283778641199459395229_<94>

Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=3446144840
Step 1 took 1563441ms
Step 2 took 378657ms
********** Factor found in step 2: 523543438969426161642554706724547076253559125346249
Found probable prime factor of 51 digits: 523543438969426161642554706724547076253559125346249
Probable prime cofactor 2013538358755604989175086781461802433222124306874954367100349986369529759283778641199459395229 has 94 digits

(17·10¹⁶⁹+7)/3 = 5(6)₁₆₈9_<170> = 23 · 12541 · 14323 · 87332633531070045486751_<23> · C138

C138 = P37 · P101

P37 = 2324768203435506363366226453197815069_<37>

P101 = 67558104709023990501069888186016245427948179198146067231684361193242776832285202310303887339358758159_<101>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2047747038
Step 1 took 42655ms
Step 2 took 14967ms
********** Factor found in step 2: 2324768203435506363366226453197815069
Found probable prime factor of 37 digits: 2324768203435506363366226453197815069
Probable prime cofactor 67558104709023990501069888186016245427948179198146067231684361193242776832285202310303887339358758159 has 101 digits

(52·10¹⁶⁹-61)/9 = 5(7)₁₆₈1_<170> = 3 · 89 · 278903 · 3279377 · 32360346197_<11> · 4451979143044721_<16> · C130

C130 = P47 · P83

P47 = 53078376861500775441655726585136757521797989163_<47>

P83 = 30940058238615665313403938893991266571394807926612012937315069117082296436341232033_<83>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=616297871
Step 1 took 38399ms
Step 2 took 6654ms
********** Factor found in step 2: 53078376861500775441655726585136757521797989163
Found probable prime factor of 47 digits: 53078376861500775441655726585136757521797989163
Probable prime cofactor 30940058238615665313403938893991266571394807926612012937315069117082296436341232033 has 83 digits

Jun 15, 2009 (2nd)

By Robert Backstrom / GMP-ECM / Jun 15, 2009

(11·10¹⁷¹-17)/3 = 3(6)₁₇₀1_<172> = 7 · 83 · 89 · 37879493 · 83385999899891719865878511313987222461_<38> · C122

C122 = P43 · P79

P43 = 4418221078669137442616872879018688733164741_<43>

P79 = 5081132846877830440997852063020506750789351211654669138222845010685572422958853_<79>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 22449568247593753184083167533291975290884854540034547605076554357224725377782546501707146485392713868517979960233913402073 (122 digits)
Using B1=7962000, B2=23420528050, polynomial Dickson(12), sigma=3300305035
Step 1 took 88764ms
Step 2 took 30982ms
********** Factor found in step 2: 4418221078669137442616872879018688733164741
Found probable prime factor of 43 digits: 4418221078669137442616872879018688733164741
Probable prime cofactor 5081132846877830440997852063020506750789351211654669138222845010685572422958853 has 79 digits

Jun 15, 2009

By Andreas Tete / Msieve v. 1.42 / Jun 15, 2009

(16·10¹⁹⁹-7)/9 = 1(7)₁₉₉_<200> = 264007 · 6353173 · 23291472982858333436228811919662999043691_<41> · 1502739138045835488243594532007091714625588183_<46> · C102

C102 = P42 · P60

P42 = 452241368214969009042683359968470074470559_<42>

P60 = 669607810762702090792985421889647833991658340054391761378041_<60>

Sun Jun 14 14:08:47 2009  Msieve v. 1.42
Sun Jun 14 14:08:47 2009  random seeds: c7bcd9dc 96bf054c
Sun Jun 14 14:08:47 2009  factoring 302824352506754444443578645843911185284478634106196572443295670733987494299384968724155242087323594919 (102 digits)
Sun Jun 14 14:08:48 2009  searching for 15-digit factors
Sun Jun 14 14:08:49 2009  commencing quadratic sieve (102-digit input)
Sun Jun 14 14:08:49 2009  using multiplier of 1
Sun Jun 14 14:08:49 2009  using 32kb Intel Core sieve core
Sun Jun 14 14:08:49 2009  sieve interval: 36 blocks of size 32768
Sun Jun 14 14:08:49 2009  processing polynomials in batches of 6
Sun Jun 14 14:08:49 2009  using a sieve bound of 3198347 (114987 primes)
Sun Jun 14 14:08:49 2009  using large prime bound of 479752050 (28 bits)
Sun Jun 14 14:08:49 2009  using double large prime bound of 4225034777495250 (44-52 bits)
Sun Jun 14 14:08:49 2009  using trial factoring cutoff of 52 bits
Sun Jun 14 14:08:49 2009  polynomial 'A' values have 13 factors
Sun Jun 14 14:08:59 2009  restarting with 17685 full and 1114340 partial relations
Sun Jun 14 18:09:23 2009  115177 relations (27268 full + 87909 combined from 1713973 partial), need 115083
Sun Jun 14 18:09:39 2009  begin with 1741241 relations
Sun Jun 14 18:09:40 2009  reduce to 304006 relations in 15 passes
Sun Jun 14 18:09:40 2009  attempting to read 304006 relations
Sun Jun 14 18:09:48 2009  recovered 304006 relations
Sun Jun 14 18:09:48 2009  recovered 294904 polynomials
Sun Jun 14 18:09:48 2009  attempting to build 115177 cycles
Sun Jun 14 18:09:48 2009  found 115177 cycles in 6 passes
Sun Jun 14 18:09:48 2009  distribution of cycle lengths:
Sun Jun 14 18:09:48 2009     length 1 : 27268
Sun Jun 14 18:09:48 2009     length 2 : 19448
Sun Jun 14 18:09:48 2009     length 3 : 19360
Sun Jun 14 18:09:48 2009     length 4 : 15827
Sun Jun 14 18:09:49 2009     length 5 : 12078
Sun Jun 14 18:09:49 2009     length 6 : 8314
Sun Jun 14 18:09:49 2009     length 7 : 5356
Sun Jun 14 18:09:49 2009     length 9+: 7526
Sun Jun 14 18:09:49 2009  largest cycle: 20 relations
Sun Jun 14 18:09:49 2009  matrix is 114987 x 115177 (32.8 MB) with weight 8128071 (70.57/col)
Sun Jun 14 18:09:49 2009  sparse part has weight 8128071 (70.57/col)
Sun Jun 14 18:09:50 2009  filtering completed in 3 passes
Sun Jun 14 18:09:50 2009  matrix is 110432 x 110496 (31.6 MB) with weight 7844676 (71.00/col)
Sun Jun 14 18:09:50 2009  sparse part has weight 7844676 (71.00/col)
Sun Jun 14 18:09:50 2009  saving the first 48 matrix rows for later
Sun Jun 14 18:09:50 2009  matrix is 110384 x 110496 (20.4 MB) with weight 6291124 (56.94/col)
Sun Jun 14 18:09:50 2009  sparse part has weight 4671682 (42.28/col)
Sun Jun 14 18:09:50 2009  matrix includes 64 packed rows
Sun Jun 14 18:09:50 2009  using block size 44198 for processor cache size 2048 kB
Sun Jun 14 18:09:51 2009  commencing Lanczos iteration
Sun Jun 14 18:09:51 2009  memory use: 19.2 MB
Sun Jun 14 18:10:58 2009  lanczos halted after 1747 iterations (dim = 110382)
Sun Jun 14 18:10:58 2009  recovered 17 nontrivial dependencies
Sun Jun 14 18:10:59 2009  prp42 factor: 452241368214969009042683359968470074470559
Sun Jun 14 18:10:59 2009  prp60 factor: 669607810762702090792985421889647833991658340054391761378041
Sun Jun 14 18:10:59 2009  elapsed time 04:02:12
total time 11:33:01

Jun 14, 2009 (2nd)

By Justin Card / ggnfs, msieve 1.41 / Jun 14, 2009

(56·10¹⁷³+61)/9 = 6(2)₁₇₂9_<174> = 37 · 1456321 · 223735397 · 47438213027_<11> · 6724817532511251616845931_<25> · C123

C123 = P58 · P66

P58 = 1076573811006174078255496603425369798195157247908414024513_<58>

P66 = 150279363077127682942036206681415950498349083088117034520490825661_<66>

Sieving with ggnfs over 2 days.

post processing:

Fri Jun 12 19:58:59 2009  
Fri Jun 12 19:58:59 2009  
Fri Jun 12 19:58:59 2009  Msieve v. 1.41
Fri Jun 12 19:58:59 2009  random seeds: d4231cb1 94d197db
Fri Jun 12 19:58:59 2009  factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits)
Fri Jun 12 19:59:01 2009  searching for 15-digit factors
Fri Jun 12 19:59:01 2009  commencing number field sieve (123-digit input)
Fri Jun 12 19:59:01 2009  R0: -403531707038578195679824
Fri Jun 12 19:59:01 2009  R1:  18400543438849
Fri Jun 12 19:59:01 2009  A0:  288596986503835432574359753965
Fri Jun 12 19:59:01 2009  A1: -7558628649210801901609443
Fri Jun 12 19:59:01 2009  A2: -90495200746547881266
Fri Jun 12 19:59:01 2009  A3:  367691967788437
Fri Jun 12 19:59:01 2009  A4:  2322968419
Fri Jun 12 19:59:01 2009  A5:  15120
Fri Jun 12 19:59:01 2009  skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12
Fri Jun 12 19:59:02 2009  generating factor base
Fri Jun 12 19:59:07 2009  factor base complete:
Fri Jun 12 19:59:07 2009  424490 rational roots (max prime = 6181811)
Fri Jun 12 19:59:07 2009  425953 algebraic roots (max prime = 6181753)
Fri Jun 12 19:59:07 2009  a range: [-28363636, 28363636]
Fri Jun 12 19:59:07 2009  b range: [1, 4294967295]
Fri Jun 12 19:59:07 2009  number of hash buckets: 95
Fri Jun 12 19:59:07 2009  sieve block size: 65536
Fri Jun 12 19:59:07 2009  
Fri Jun 12 19:59:07 2009  maximum RFB prime: 6181811
Fri Jun 12 19:59:07 2009  RFB entries: 424490
Fri Jun 12 19:59:07 2009  medium RFB entries: 6542
Fri Jun 12 19:59:07 2009  resieved RFB entries: 6374
Fri Jun 12 19:59:07 2009  small RFB prime powers: 25
Fri Jun 12 19:59:07 2009  projective RFB roots: 5
Fri Jun 12 19:59:07 2009  RFB trial factoring cutoff: 59 or 88 bits
Fri Jun 12 19:59:07 2009  single large prime RFB range: 23 - 27 bits
Fri Jun 12 19:59:07 2009  double large prime RFB range: 46 - 52 bits
Fri Jun 12 19:59:07 2009  triple large prime RFB range: 71 - 79 bits
Fri Jun 12 19:59:07 2009  
Fri Jun 12 19:59:07 2009  maximum AFB prime: 6181753
Fri Jun 12 19:59:07 2009  AFB entries: 425953
Fri Jun 12 19:59:07 2009  medium AFB entries: 6520
Fri Jun 12 19:59:07 2009  resieved AFB entries: 6275
Fri Jun 12 19:59:07 2009  small AFB prime powers: 131
Fri Jun 12 19:59:07 2009  projective AFB roots: 4
Fri Jun 12 19:59:07 2009  AFB trial factoring cutoff: 59 or 88 bits
Fri Jun 12 19:59:07 2009  single large prime AFB range: 23 - 27 bits
Fri Jun 12 19:59:07 2009  double large prime AFB range: 46 - 52 bits
Fri Jun 12 19:59:07 2009  triple large prime AFB range: 71 - 79 bits
Fri Jun 12 19:59:07 2009  
Fri Jun 12 19:59:08 2009  multiplying 1639202 primes from 6181753 to 33554432
Fri Jun 12 19:59:40 2009  
Fri Jun 12 19:59:40 2009  
Fri Jun 12 19:59:40 2009  Msieve v. 1.41
Fri Jun 12 19:59:40 2009  random seeds: 2353b878 c382ae6b
Fri Jun 12 19:59:40 2009  factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits)
Fri Jun 12 19:59:42 2009  searching for 15-digit factors
Fri Jun 12 19:59:43 2009  commencing number field sieve (123-digit input)
Fri Jun 12 19:59:43 2009  R0: -403531707038578195679824
Fri Jun 12 19:59:43 2009  R1:  18400543438849
Fri Jun 12 19:59:43 2009  A0:  288596986503835432574359753965
Fri Jun 12 19:59:43 2009  A1: -7558628649210801901609443
Fri Jun 12 19:59:43 2009  A2: -90495200746547881266
Fri Jun 12 19:59:43 2009  A3:  367691967788437
Fri Jun 12 19:59:43 2009  A4:  2322968419
Fri Jun 12 19:59:43 2009  A5:  15120
Fri Jun 12 19:59:43 2009  skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12
Fri Jun 12 19:59:43 2009  
Fri Jun 12 19:59:43 2009  commencing relation filtering
Fri Jun 12 19:59:43 2009  commencing duplicate removal, pass 1
Fri Jun 12 19:59:43 2009  found 0 hash collisions in 0 relations
Fri Jun 12 19:59:43 2009  reading rational ideals above 327680
Fri Jun 12 19:59:43 2009  reading algebraic ideals above 327680
Fri Jun 12 19:59:43 2009  commencing singleton removal, pass 1
Fri Jun 12 19:59:43 2009  relations with 0 large ideals: 0
Fri Jun 12 19:59:43 2009  relations with 1 large ideals: 0
Fri Jun 12 19:59:43 2009  relations with 2 large ideals: 0
Fri Jun 12 19:59:43 2009  relations with 3 large ideals: 0
Fri Jun 12 19:59:43 2009  relations with 4 large ideals: 0
Fri Jun 12 19:59:43 2009  relations with 5 large ideals: 0
Fri Jun 12 19:59:43 2009  relations with 6 large ideals: 0
Fri Jun 12 19:59:43 2009  relations with 7+ large ideals: 0
Fri Jun 12 19:59:43 2009  0 relations and about 0 large ideals
Fri Jun 12 19:59:43 2009  commencing singleton removal, pass 2
Fri Jun 12 19:59:43 2009  found 0 singletons
Fri Jun 12 19:59:43 2009  current dataset: 0 relations and about 0 large ideals
Fri Jun 12 19:59:43 2009  commencing singleton removal, final pass
Fri Jun 12 19:59:43 2009  memory use: 0.1 MB
Fri Jun 12 19:59:43 2009  commencing in-memory singleton removal
Fri Jun 12 19:59:43 2009  begin with 0 relations and 0 unique ideals
Fri Jun 12 19:59:43 2009  reduce to 0 relations and 0 ideals in 1 passes
Fri Jun 12 19:59:43 2009  max relations containing the same ideal: 0
Fri Jun 12 19:59:44 2009  reading rational ideals above 100000
Fri Jun 12 19:59:44 2009  reading algebraic ideals above 100000
Fri Jun 12 19:59:44 2009  commencing singleton removal, final pass
Fri Jun 12 19:59:44 2009  keeping 0 ideals with weight <= 25, new excess is 19224
Fri Jun 12 20:00:21 2009  
Fri Jun 12 20:00:21 2009  
Fri Jun 12 20:00:21 2009  Msieve v. 1.41
Fri Jun 12 20:00:21 2009  random seeds: bf533eb4 9b4b30df
Fri Jun 12 20:00:21 2009  factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits)
Fri Jun 12 20:00:22 2009  searching for 15-digit factors
Fri Jun 12 20:00:23 2009  commencing number field sieve (123-digit input)
Fri Jun 12 20:00:23 2009  R0: -403531707038578195679824
Fri Jun 12 20:00:23 2009  R1:  18400543438849
Fri Jun 12 20:00:23 2009  A0:  288596986503835432574359753965
Fri Jun 12 20:00:23 2009  A1: -7558628649210801901609443
Fri Jun 12 20:00:23 2009  A2: -90495200746547881266
Fri Jun 12 20:00:23 2009  A3:  367691967788437
Fri Jun 12 20:00:23 2009  A4:  2322968419
Fri Jun 12 20:00:23 2009  A5:  15120
Fri Jun 12 20:00:23 2009  skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12
Fri Jun 12 20:00:23 2009  
Fri Jun 12 20:00:23 2009  commencing relation filtering
Fri Jun 12 20:00:23 2009  commencing duplicate removal, pass 1
Fri Jun 12 20:01:23 2009  found 245218 hash collisions in 4342759 relations
Fri Jun 12 20:01:48 2009  added 32761 free relations
Fri Jun 12 20:01:48 2009  commencing duplicate removal, pass 2
Fri Jun 12 20:01:52 2009  found 221724 duplicates and 4153796 unique relations
Fri Jun 12 20:01:52 2009  memory use: 36.7 MB
Fri Jun 12 20:01:52 2009  reading rational ideals above 7929856
Fri Jun 12 20:01:52 2009  reading algebraic ideals above 7929856
Fri Jun 12 20:01:52 2009  commencing singleton removal, pass 1
Fri Jun 12 20:02:51 2009  relations with 0 large ideals: 225807
Fri Jun 12 20:02:51 2009  relations with 1 large ideals: 904826
Fri Jun 12 20:02:51 2009  relations with 2 large ideals: 1503333
Fri Jun 12 20:02:51 2009  relations with 3 large ideals: 1135579
Fri Jun 12 20:02:51 2009  relations with 4 large ideals: 345538
Fri Jun 12 20:02:51 2009  relations with 5 large ideals: 10406
Fri Jun 12 20:02:51 2009  relations with 6 large ideals: 28307
Fri Jun 12 20:02:51 2009  relations with 7+ large ideals: 0
Fri Jun 12 20:02:51 2009  4153796 relations and about 4466316 large ideals
Fri Jun 12 20:02:51 2009  commencing singleton removal, pass 2
Fri Jun 12 20:03:49 2009  found 2073269 singletons
Fri Jun 12 20:03:49 2009  current dataset: 2080527 relations and about 1761280 large ideals
Fri Jun 12 20:03:49 2009  commencing singleton removal, pass 3
Fri Jun 12 20:04:20 2009  found 669977 singletons
Fri Jun 12 20:04:20 2009  current dataset: 1410550 relations and about 987820 large ideals
Fri Jun 12 20:04:20 2009  commencing singleton removal, pass 4
Fri Jun 12 20:04:42 2009  found 251716 singletons
Fri Jun 12 20:04:42 2009  current dataset: 1158834 relations and about 716140 large ideals
Fri Jun 12 20:04:42 2009  commencing singleton removal, final pass
Fri Jun 12 20:04:59 2009  memory use: 16.6 MB
Fri Jun 12 20:04:59 2009  commencing in-memory singleton removal
Fri Jun 12 20:04:59 2009  begin with 1158834 relations and 737995 unique ideals
Fri Jun 12 20:05:01 2009  reduce to 901584 relations and 471390 ideals in 19 passes
Fri Jun 12 20:05:01 2009  max relations containing the same ideal: 19
Fri Jun 12 20:05:01 2009  reading rational ideals above 720000
Fri Jun 12 20:05:01 2009  reading algebraic ideals above 720000
Fri Jun 12 20:05:01 2009  commencing singleton removal, final pass
Fri Jun 12 20:05:18 2009  keeping 1394025 ideals with weight <= 20, new excess is 116433
Fri Jun 12 20:05:19 2009  memory use: 34.6 MB
Fri Jun 12 20:05:19 2009  commencing in-memory singleton removal
Fri Jun 12 20:05:19 2009  begin with 913236 relations and 1394025 unique ideals
Fri Jun 12 20:05:19 2009  reduce to 525 relations and 19 ideals in 8 passes
Fri Jun 12 20:05:19 2009  max relations containing the same ideal: 2
Fri Jun 12 20:05:19 2009  filtering wants 403668 more relations
Fri Jun 12 20:05:19 2009  elapsed time 00:04:58
Fri Jun 12 22:19:23 2009  
Fri Jun 12 22:19:23 2009  
Fri Jun 12 22:19:23 2009  Msieve v. 1.41
Fri Jun 12 22:19:23 2009  random seeds: bfd03f0f 5f41b48a
Fri Jun 12 22:19:23 2009  factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits)
Fri Jun 12 22:19:25 2009  searching for 15-digit factors
Fri Jun 12 22:19:26 2009  commencing number field sieve (123-digit input)
Fri Jun 12 22:19:26 2009  R0: -403531707038578195679824
Fri Jun 12 22:19:26 2009  R1:  18400543438849
Fri Jun 12 22:19:26 2009  A0:  288596986503835432574359753965
Fri Jun 12 22:19:26 2009  A1: -7558628649210801901609443
Fri Jun 12 22:19:26 2009  A2: -90495200746547881266
Fri Jun 12 22:19:26 2009  A3:  367691967788437
Fri Jun 12 22:19:26 2009  A4:  2322968419
Fri Jun 12 22:19:26 2009  A5:  15120
Fri Jun 12 22:19:26 2009  skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12
Fri Jun 12 22:19:26 2009  
Fri Jun 12 22:19:26 2009  commencing relation filtering
Fri Jun 12 22:19:26 2009  commencing duplicate removal, pass 1
Fri Jun 12 22:20:40 2009  error -15 reading relation 4853261
Fri Jun 12 22:20:44 2009  found 332870 hash collisions in 5121689 relations
Fri Jun 12 22:21:10 2009  added 32874 free relations
Fri Jun 12 22:21:10 2009  commencing duplicate removal, pass 2
Fri Jun 12 22:21:15 2009  found 302652 duplicates and 4851911 unique relations
Fri Jun 12 22:21:15 2009  memory use: 40.3 MB
Fri Jun 12 22:21:15 2009  reading rational ideals above 8192000
Fri Jun 12 22:21:15 2009  reading algebraic ideals above 8192000
Fri Jun 12 22:21:15 2009  commencing singleton removal, pass 1
Fri Jun 12 22:22:24 2009  relations with 0 large ideals: 264315
Fri Jun 12 22:22:24 2009  relations with 1 large ideals: 1052504
Fri Jun 12 22:22:24 2009  relations with 2 large ideals: 1735144
Fri Jun 12 22:22:24 2009  relations with 3 large ideals: 1319991
Fri Jun 12 22:22:24 2009  relations with 4 large ideals: 424942
Fri Jun 12 22:22:24 2009  relations with 5 large ideals: 26723
Fri Jun 12 22:22:24 2009  relations with 6 large ideals: 28292
Fri Jun 12 22:22:24 2009  relations with 7+ large ideals: 0
Fri Jun 12 22:22:24 2009  4851911 relations and about 4759380 large ideals
Fri Jun 12 22:22:24 2009  commencing singleton removal, pass 2
Fri Jun 12 22:23:33 2009  found 2063490 singletons
Fri Jun 12 22:23:33 2009  current dataset: 2788421 relations and about 2200671 large ideals
Fri Jun 12 22:23:33 2009  commencing singleton removal, pass 3
Fri Jun 12 22:24:15 2009  found 656390 singletons
Fri Jun 12 22:24:15 2009  current dataset: 2132031 relations and about 1474736 large ideals
Fri Jun 12 22:24:15 2009  commencing singleton removal, pass 4
Fri Jun 12 22:24:46 2009  found 242361 singletons
Fri Jun 12 22:24:46 2009  current dataset: 1889670 relations and about 1220553 large ideals
Fri Jun 12 22:24:46 2009  commencing singleton removal, final pass
Fri Jun 12 22:25:15 2009  memory use: 26.0 MB
Fri Jun 12 22:25:15 2009  commencing in-memory singleton removal
Fri Jun 12 22:25:15 2009  begin with 1889670 relations and 1258949 unique ideals
Fri Jun 12 22:25:18 2009  reduce to 1593421 relations and 955497 ideals in 16 passes
Fri Jun 12 22:25:18 2009  max relations containing the same ideal: 27
Fri Jun 12 22:25:19 2009  reading rational ideals above 720000
Fri Jun 12 22:25:19 2009  reading algebraic ideals above 720000
Fri Jun 12 22:25:19 2009  commencing singleton removal, final pass
Fri Jun 12 22:25:48 2009  keeping 1913424 ideals with weight <= 20, new excess is 125729
Fri Jun 12 22:25:49 2009  memory use: 64.8 MB
Fri Jun 12 22:25:49 2009  commencing in-memory singleton removal
Fri Jun 12 22:25:49 2009  begin with 1596892 relations and 1913424 unique ideals
Fri Jun 12 22:26:08 2009  reduce to 1013701 relations and 1301558 ideals in 73 passes
Fri Jun 12 22:26:08 2009  max relations containing the same ideal: 20
Fri Jun 12 22:26:08 2009  filtering wants 1000000 more relations
Fri Jun 12 22:26:08 2009  elapsed time 00:06:45
Fri Jun 12 23:46:27 2009  
Fri Jun 12 23:46:27 2009  
Fri Jun 12 23:46:27 2009  Msieve v. 1.41
Fri Jun 12 23:46:27 2009  random seeds: deb8b6cc 2e1ca6cf
Fri Jun 12 23:46:27 2009  factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits)
Fri Jun 12 23:46:28 2009  searching for 15-digit factors
Fri Jun 12 23:46:29 2009  commencing number field sieve (123-digit input)
Fri Jun 12 23:46:29 2009  R0: -403531707038578195679824
Fri Jun 12 23:46:29 2009  R1:  18400543438849
Fri Jun 12 23:46:29 2009  A0:  288596986503835432574359753965
Fri Jun 12 23:46:29 2009  A1: -7558628649210801901609443
Fri Jun 12 23:46:29 2009  A2: -90495200746547881266
Fri Jun 12 23:46:29 2009  A3:  367691967788437
Fri Jun 12 23:46:29 2009  A4:  2322968419
Fri Jun 12 23:46:29 2009  A5:  15120
Fri Jun 12 23:46:29 2009  skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12
Fri Jun 12 23:46:29 2009  
Fri Jun 12 23:46:29 2009  commencing relation filtering
Fri Jun 12 23:46:29 2009  commencing duplicate removal, pass 1
Fri Jun 12 23:47:47 2009  error -15 reading relation 5041416
Fri Jun 12 23:47:53 2009  found 378687 hash collisions in 5493173 relations
Fri Jun 12 23:48:20 2009  added 32906 free relations
Fri Jun 12 23:48:20 2009  commencing duplicate removal, pass 2
Fri Jun 12 23:48:25 2009  found 345149 duplicates and 5180930 unique relations
Fri Jun 12 23:48:25 2009  memory use: 40.3 MB
Fri Jun 12 23:48:25 2009  reading rational ideals above 9109504
Fri Jun 12 23:48:25 2009  reading algebraic ideals above 9109504
Fri Jun 12 23:48:25 2009  commencing singleton removal, pass 1
Fri Jun 12 23:49:39 2009  relations with 0 large ideals: 345545
Fri Jun 12 23:49:39 2009  relations with 1 large ideals: 1266516
Fri Jun 12 23:49:39 2009  relations with 2 large ideals: 1888794
Fri Jun 12 23:49:39 2009  relations with 3 large ideals: 1282726
Fri Jun 12 23:49:39 2009  relations with 4 large ideals: 355464
Fri Jun 12 23:49:39 2009  relations with 5 large ideals: 13999
Fri Jun 12 23:49:39 2009  relations with 6 large ideals: 27886
Fri Jun 12 23:49:39 2009  relations with 7+ large ideals: 0
Fri Jun 12 23:49:39 2009  5180930 relations and about 4783311 large ideals
Fri Jun 12 23:49:39 2009  commencing singleton removal, pass 2
Fri Jun 12 23:50:52 2009  found 2032546 singletons
Fri Jun 12 23:50:52 2009  current dataset: 3148384 relations and about 2315356 large ideals
Fri Jun 12 23:50:52 2009  commencing singleton removal, pass 3
Fri Jun 12 23:51:37 2009  found 618234 singletons
Fri Jun 12 23:51:37 2009  current dataset: 2530150 relations and about 1643805 large ideals
Fri Jun 12 23:51:37 2009  commencing singleton removal, pass 4
Fri Jun 12 23:52:14 2009  found 211011 singletons
Fri Jun 12 23:52:14 2009  current dataset: 2319139 relations and about 1425302 large ideals
Fri Jun 12 23:52:14 2009  commencing singleton removal, final pass
Fri Jun 12 23:52:48 2009  memory use: 33.3 MB
Fri Jun 12 23:52:48 2009  commencing in-memory singleton removal
Fri Jun 12 23:52:48 2009  begin with 2319138 relations and 1470374 unique ideals
Fri Jun 12 23:52:51 2009  reduce to 2065653 relations and 1212121 ideals in 14 passes
Fri Jun 12 23:52:51 2009  max relations containing the same ideal: 32
Fri Jun 12 23:52:52 2009  reading rational ideals above 720000
Fri Jun 12 23:52:52 2009  reading algebraic ideals above 720000
Fri Jun 12 23:52:52 2009  commencing singleton removal, final pass
Fri Jun 12 23:53:27 2009  keeping 2244398 ideals with weight <= 20, new excess is 151810
Fri Jun 12 23:53:29 2009  memory use: 66.1 MB
Fri Jun 12 23:53:29 2009  commencing in-memory singleton removal
Fri Jun 12 23:53:30 2009  begin with 2065846 relations and 2244398 unique ideals
Fri Jun 12 23:53:40 2009  reduce to 1751486 relations and 1923897 ideals in 24 passes
Fri Jun 12 23:53:40 2009  max relations containing the same ideal: 20
Fri Jun 12 23:53:40 2009  filtering wants 1000000 more relations
Fri Jun 12 23:53:40 2009  elapsed time 00:07:13
Sat Jun 13 01:02:32 2009  
Sat Jun 13 01:02:32 2009  
Sat Jun 13 01:02:32 2009  Msieve v. 1.41
Sat Jun 13 01:02:32 2009  random seeds: 82748a4d d51598b3
Sat Jun 13 01:02:32 2009  factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits)
Sat Jun 13 01:02:33 2009  searching for 15-digit factors
Sat Jun 13 01:02:34 2009  commencing number field sieve (123-digit input)
Sat Jun 13 01:02:34 2009  R0: -403531707038578195679824
Sat Jun 13 01:02:34 2009  R1:  18400543438849
Sat Jun 13 01:02:34 2009  A0:  288596986503835432574359753965
Sat Jun 13 01:02:34 2009  A1: -7558628649210801901609443
Sat Jun 13 01:02:34 2009  A2: -90495200746547881266
Sat Jun 13 01:02:34 2009  A3:  367691967788437
Sat Jun 13 01:02:34 2009  A4:  2322968419
Sat Jun 13 01:02:34 2009  A5:  15120
Sat Jun 13 01:02:34 2009  skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12
Sat Jun 13 01:02:34 2009  
Sat Jun 13 01:02:34 2009  commencing relation filtering
Sat Jun 13 01:02:34 2009  commencing duplicate removal, pass 1
Sat Jun 13 01:03:48 2009  error -15 reading relation 5182393
Sat Jun 13 01:03:55 2009  found 414465 hash collisions in 5772298 relations
Sat Jun 13 01:04:22 2009  added 32928 free relations
Sat Jun 13 01:04:22 2009  commencing duplicate removal, pass 2
Sat Jun 13 01:04:27 2009  found 378446 duplicates and 5426780 unique relations
Sat Jun 13 01:04:27 2009  memory use: 40.3 MB
Sat Jun 13 01:04:27 2009  reading rational ideals above 9240576
Sat Jun 13 01:04:27 2009  reading algebraic ideals above 9240576
Sat Jun 13 01:04:27 2009  commencing singleton removal, pass 1
Sat Jun 13 01:05:43 2009  relations with 0 large ideals: 377155
Sat Jun 13 01:05:43 2009  relations with 1 large ideals: 1362769
Sat Jun 13 01:05:43 2009  relations with 2 large ideals: 1994385
Sat Jun 13 01:05:43 2009  relations with 3 large ideals: 1314888
Sat Jun 13 01:05:43 2009  relations with 4 large ideals: 342912
Sat Jun 13 01:05:43 2009  relations with 5 large ideals: 6832
Sat Jun 13 01:05:43 2009  relations with 6 large ideals: 27839
Sat Jun 13 01:05:43 2009  relations with 7+ large ideals: 0
Sat Jun 13 01:05:43 2009  5426780 relations and about 4859513 large ideals
Sat Jun 13 01:05:43 2009  commencing singleton removal, pass 2
Sat Jun 13 01:06:59 2009  found 2010559 singletons
Sat Jun 13 01:06:59 2009  current dataset: 3416221 relations and about 2450810 large ideals
Sat Jun 13 01:06:59 2009  commencing singleton removal, pass 3
Sat Jun 13 01:07:49 2009  found 597342 singletons
Sat Jun 13 01:07:49 2009  current dataset: 2818879 relations and about 1808301 large ideals
Sat Jun 13 01:07:49 2009  commencing singleton removal, pass 4
Sat Jun 13 01:08:29 2009  found 196450 singletons
Sat Jun 13 01:08:29 2009  current dataset: 2622429 relations and about 1605872 large ideals
Sat Jun 13 01:08:29 2009  commencing singleton removal, final pass
Sat Jun 13 01:09:08 2009  memory use: 35.7 MB
Sat Jun 13 01:09:08 2009  commencing in-memory singleton removal
Sat Jun 13 01:09:08 2009  begin with 2622429 relations and 1656743 unique ideals
Sat Jun 13 01:09:11 2009  reduce to 2379143 relations and 1409509 ideals in 13 passes
Sat Jun 13 01:09:11 2009  max relations containing the same ideal: 34
Sat Jun 13 01:09:12 2009  reading rational ideals above 720000
Sat Jun 13 01:09:12 2009  reading algebraic ideals above 720000
Sat Jun 13 01:09:12 2009  commencing singleton removal, final pass
Sat Jun 13 01:09:54 2009  keeping 2439301 ideals with weight <= 20, new excess is 178904
Sat Jun 13 01:09:56 2009  memory use: 89.9 MB
Sat Jun 13 01:09:56 2009  commencing in-memory singleton removal
Sat Jun 13 01:09:56 2009  begin with 2379242 relations and 2439301 unique ideals
Sat Jun 13 01:10:04 2009  reduce to 2157977 relations and 2214963 ideals in 16 passes
Sat Jun 13 01:10:04 2009  max relations containing the same ideal: 20
Sat Jun 13 01:10:05 2009  filtering wants 1000000 more relations
Sat Jun 13 01:10:05 2009  elapsed time 00:07:33
Sat Jun 13 09:20:57 2009  
Sat Jun 13 09:20:57 2009  
Sat Jun 13 09:20:57 2009  Msieve v. 1.41
Sat Jun 13 09:20:57 2009  random seeds: d4f72b0d 5f6e8dac
Sat Jun 13 09:20:57 2009  factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits)
Sat Jun 13 09:20:59 2009  searching for 15-digit factors
Sat Jun 13 09:21:00 2009  commencing number field sieve (123-digit input)
Sat Jun 13 09:21:00 2009  R0: -403531707038578195679824
Sat Jun 13 09:21:00 2009  R1:  18400543438849
Sat Jun 13 09:21:00 2009  A0:  288596986503835432574359753965
Sat Jun 13 09:21:00 2009  A1: -7558628649210801901609443
Sat Jun 13 09:21:00 2009  A2: -90495200746547881266
Sat Jun 13 09:21:00 2009  A3:  367691967788437
Sat Jun 13 09:21:00 2009  A4:  2322968419
Sat Jun 13 09:21:00 2009  A5:  15120
Sat Jun 13 09:21:00 2009  skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12
Sat Jun 13 09:21:00 2009  
Sat Jun 13 09:21:00 2009  commencing relation filtering
Sat Jun 13 09:21:00 2009  commencing duplicate removal, pass 1
Sat Jun 13 09:22:35 2009  error -15 reading relation 6135277
Sat Jun 13 09:22:57 2009  found 693492 hash collisions in 7649825 relations
Sat Jun 13 09:23:25 2009  added 32973 free relations
Sat Jun 13 09:23:25 2009  commencing duplicate removal, pass 2
Sat Jun 13 09:23:32 2009  found 641368 duplicates and 7041430 unique relations
Sat Jun 13 09:23:32 2009  memory use: 48.6 MB
Sat Jun 13 09:23:32 2009  reading rational ideals above 9633792
Sat Jun 13 09:23:32 2009  reading algebraic ideals above 9633792
Sat Jun 13 09:23:32 2009  commencing singleton removal, pass 1
Sat Jun 13 09:25:14 2009  relations with 0 large ideals: 506739
Sat Jun 13 09:25:14 2009  relations with 1 large ideals: 1797606
Sat Jun 13 09:25:14 2009  relations with 2 large ideals: 2579855
Sat Jun 13 09:25:14 2009  relations with 3 large ideals: 1674934
Sat Jun 13 09:25:14 2009  relations with 4 large ideals: 440116
Sat Jun 13 09:25:14 2009  relations with 5 large ideals: 14500
Sat Jun 13 09:25:14 2009  relations with 6 large ideals: 27680
Sat Jun 13 09:25:14 2009  relations with 7+ large ideals: 0
Sat Jun 13 09:25:14 2009  7041430 relations and about 5295063 large ideals
Sat Jun 13 09:25:14 2009  commencing singleton removal, pass 2
Sat Jun 13 09:27:01 2009  found 1790083 singletons
Sat Jun 13 09:27:01 2009  current dataset: 5251347 relations and about 3286858 large ideals
Sat Jun 13 09:27:01 2009  commencing singleton removal, pass 3
Sat Jun 13 09:28:24 2009  found 425197 singletons
Sat Jun 13 09:28:24 2009  current dataset: 4826150 relations and about 2847189 large ideals
Sat Jun 13 09:28:24 2009  commencing singleton removal, final pass
Sat Jun 13 09:29:36 2009  memory use: 69.3 MB
Sat Jun 13 09:29:37 2009  commencing in-memory singleton removal
Sat Jun 13 09:29:37 2009  begin with 4826149 relations and 2931993 unique ideals
Sat Jun 13 09:29:43 2009  reduce to 4568128 relations and 2670795 ideals in 11 passes
Sat Jun 13 09:29:43 2009  max relations containing the same ideal: 42
Sat Jun 13 09:29:44 2009  reading rational ideals above 720000
Sat Jun 13 09:29:44 2009  reading algebraic ideals above 720000
Sat Jun 13 09:29:44 2009  commencing singleton removal, final pass
Sat Jun 13 09:31:07 2009  keeping 3506550 ideals with weight <= 20, new excess is 444702
Sat Jun 13 09:31:12 2009  memory use: 127.2 MB
Sat Jun 13 09:31:12 2009  commencing in-memory singleton removal
Sat Jun 13 09:31:13 2009  begin with 4568195 relations and 3506550 unique ideals
Sat Jun 13 09:31:21 2009  reduce to 4532733 relations and 3470763 ideals in 9 passes
Sat Jun 13 09:31:21 2009  max relations containing the same ideal: 20
Sat Jun 13 09:31:26 2009  removing 1083262 relations and 810204 ideals in 273058 cliques
Sat Jun 13 09:31:27 2009  commencing in-memory singleton removal
Sat Jun 13 09:31:27 2009  begin with 3449471 relations and 3470763 unique ideals
Sat Jun 13 09:31:32 2009  reduce to 3299683 relations and 2500727 ideals in 7 passes
Sat Jun 13 09:31:32 2009  max relations containing the same ideal: 20
Sat Jun 13 09:31:36 2009  removing 833905 relations and 560847 ideals in 273058 cliques
Sat Jun 13 09:31:36 2009  commencing in-memory singleton removal
Sat Jun 13 09:31:37 2009  begin with 2465778 relations and 2500727 unique ideals
Sat Jun 13 09:31:40 2009  reduce to 2332272 relations and 1795523 ideals in 8 passes
Sat Jun 13 09:31:40 2009  max relations containing the same ideal: 19
Sat Jun 13 09:31:43 2009  removing 106458 relations and 85564 ideals in 20894 cliques
Sat Jun 13 09:31:43 2009  commencing in-memory singleton removal
Sat Jun 13 09:31:43 2009  begin with 2225814 relations and 1795523 unique ideals
Sat Jun 13 09:31:45 2009  reduce to 2223285 relations and 1707413 ideals in 5 passes
Sat Jun 13 09:31:45 2009  max relations containing the same ideal: 18
Sat Jun 13 09:31:46 2009  relations with 0 large ideals: 35555
Sat Jun 13 09:31:46 2009  relations with 1 large ideals: 212163
Sat Jun 13 09:31:46 2009  relations with 2 large ideals: 514722
Sat Jun 13 09:31:46 2009  relations with 3 large ideals: 659685
Sat Jun 13 09:31:46 2009  relations with 4 large ideals: 493889
Sat Jun 13 09:31:46 2009  relations with 5 large ideals: 226498
Sat Jun 13 09:31:46 2009  relations with 6 large ideals: 67432
Sat Jun 13 09:31:46 2009  relations with 7+ large ideals: 13341
Sat Jun 13 09:31:46 2009  commencing 2-way merge
Sat Jun 13 09:31:49 2009  reduce to 1578507 relation sets and 1062635 unique ideals
Sat Jun 13 09:31:49 2009  commencing full merge
Sat Jun 13 09:32:19 2009  memory use: 104.7 MB
Sat Jun 13 09:32:19 2009  found 793018 cycles, need 722835
Sat Jun 13 09:32:20 2009  weight of 722835 cycles is about 51025720 (70.59/cycle)
Sat Jun 13 09:32:20 2009  distribution of cycle lengths:
Sat Jun 13 09:32:20 2009  1 relations: 70009
Sat Jun 13 09:32:20 2009  2 relations: 75914
Sat Jun 13 09:32:20 2009  3 relations: 81835
Sat Jun 13 09:32:20 2009  4 relations: 78723
Sat Jun 13 09:32:20 2009  5 relations: 74097
Sat Jun 13 09:32:20 2009  6 relations: 67368
Sat Jun 13 09:32:20 2009  7 relations: 59972
Sat Jun 13 09:32:20 2009  8 relations: 52597
Sat Jun 13 09:32:20 2009  9 relations: 44793
Sat Jun 13 09:32:20 2009  10+ relations: 117527
Sat Jun 13 09:32:20 2009  heaviest cycle: 15 relations
Sat Jun 13 09:32:20 2009  commencing cycle optimization
Sat Jun 13 09:32:22 2009  start with 4135027 relations
Sat Jun 13 09:32:36 2009  pruned 184148 relations
Sat Jun 13 09:32:36 2009  memory use: 126.0 MB
Sat Jun 13 09:32:36 2009  distribution of cycle lengths:
Sat Jun 13 09:32:36 2009  1 relations: 70009
Sat Jun 13 09:32:36 2009  2 relations: 78957
Sat Jun 13 09:32:36 2009  3 relations: 87287
Sat Jun 13 09:32:36 2009  4 relations: 83219
Sat Jun 13 09:32:36 2009  5 relations: 78985
Sat Jun 13 09:32:36 2009  6 relations: 70517
Sat Jun 13 09:32:36 2009  7 relations: 62392
Sat Jun 13 09:32:36 2009  8 relations: 53131
Sat Jun 13 09:32:36 2009  9 relations: 43708
Sat Jun 13 09:32:36 2009  10+ relations: 94630
Sat Jun 13 09:32:36 2009  heaviest cycle: 15 relations
Sat Jun 13 09:32:37 2009  RelProcTime: 578
Sat Jun 13 09:32:37 2009  elapsed time 00:11:40
Sat Jun 13 10:08:45 2009  
Sat Jun 13 10:08:45 2009  
Sat Jun 13 10:08:45 2009  Msieve v. 1.41
Sat Jun 13 10:08:45 2009  random seeds: b95777f6 913f57c4
Sat Jun 13 10:08:45 2009  factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits)
Sat Jun 13 10:08:46 2009  searching for 15-digit factors
Sat Jun 13 10:08:47 2009  commencing number field sieve (123-digit input)
Sat Jun 13 10:08:47 2009  R0: -403531707038578195679824
Sat Jun 13 10:08:47 2009  R1:  18400543438849
Sat Jun 13 10:08:47 2009  A0:  288596986503835432574359753965
Sat Jun 13 10:08:47 2009  A1: -7558628649210801901609443
Sat Jun 13 10:08:47 2009  A2: -90495200746547881266
Sat Jun 13 10:08:47 2009  A3:  367691967788437
Sat Jun 13 10:08:47 2009  A4:  2322968419
Sat Jun 13 10:08:47 2009  A5:  15120
Sat Jun 13 10:08:47 2009  skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12
Sat Jun 13 10:08:47 2009  
Sat Jun 13 10:08:47 2009  commencing linear algebra
Sat Jun 13 10:08:48 2009  read 722835 cycles
Sat Jun 13 10:08:50 2009  cycles contain 1990579 unique relations
Sat Jun 13 10:09:22 2009  read 1990579 relations
Sat Jun 13 10:09:27 2009  using 20 quadratic characters above 67108668
Sat Jun 13 10:09:48 2009  building initial matrix
Sat Jun 13 10:10:31 2009  memory use: 267.2 MB
Sat Jun 13 10:10:32 2009  read 722835 cycles
Sat Jun 13 10:10:33 2009  matrix is 722618 x 722835 (213.2 MB) with weight 67963204 (94.02/col)
Sat Jun 13 10:10:33 2009  sparse part has weight 47938517 (66.32/col)
Sat Jun 13 10:11:07 2009  filtering completed in 3 passes
Sat Jun 13 10:11:07 2009  matrix is 721430 x 721630 (213.0 MB) with weight 67890760 (94.08/col)
Sat Jun 13 10:11:07 2009  sparse part has weight 47901032 (66.38/col)
Sat Jun 13 10:11:15 2009  read 721630 cycles
Sat Jun 13 10:11:16 2009  matrix is 721430 x 721630 (213.0 MB) with weight 67890760 (94.08/col)
Sat Jun 13 10:11:16 2009  sparse part has weight 47901032 (66.38/col)
Sat Jun 13 10:11:16 2009  saving the first 48 matrix rows for later
Sat Jun 13 10:11:16 2009  matrix is 721382 x 721630 (205.5 MB) with weight 53354728 (73.94/col)
Sat Jun 13 10:11:16 2009  sparse part has weight 46662784 (64.66/col)
Sat Jun 13 10:11:16 2009  matrix includes 64 packed rows
Sat Jun 13 10:11:16 2009  using block size 10922 for processor cache size 256 kB
Sat Jun 13 10:11:22 2009  commencing Lanczos iteration
Sat Jun 13 10:11:22 2009  memory use: 192.6 MB
Sat Jun 13 12:59:06 2009  lanczos halted after 11408 iterations (dim = 721381)
Sat Jun 13 12:59:08 2009  recovered 32 nontrivial dependencies
Sat Jun 13 12:59:08 2009  BLanczosTime: 10221
Sat Jun 13 12:59:08 2009  elapsed time 02:50:23
Sat Jun 13 17:14:02 2009  
Sat Jun 13 17:14:02 2009  
Sat Jun 13 17:14:02 2009  Msieve v. 1.41
Sat Jun 13 17:14:02 2009  random seeds: 705341fb cc3403da
Sat Jun 13 17:14:02 2009  factoring 161786826623523873106331984288573086057036069356281984589662923023302881395583523319398596356535562638667735369803263428093 (123 digits)
Sat Jun 13 17:14:03 2009  searching for 15-digit factors
Sat Jun 13 17:14:04 2009  commencing number field sieve (123-digit input)
Sat Jun 13 17:14:04 2009  R0: -403531707038578195679824
Sat Jun 13 17:14:04 2009  R1:  18400543438849
Sat Jun 13 17:14:04 2009  A0:  288596986503835432574359753965
Sat Jun 13 17:14:04 2009  A1: -7558628649210801901609443
Sat Jun 13 17:14:04 2009  A2: -90495200746547881266
Sat Jun 13 17:14:04 2009  A3:  367691967788437
Sat Jun 13 17:14:04 2009  A4:  2322968419
Sat Jun 13 17:14:04 2009  A5:  15120
Sat Jun 13 17:14:04 2009  skew 1.00, size 1.029077e-11, alpha -6.403071, combined = 5.274824e-12
Sat Jun 13 17:14:04 2009  
Sat Jun 13 17:14:04 2009  commencing square root phase
Sat Jun 13 17:14:04 2009  reading relations for dependency 1
Sat Jun 13 17:14:05 2009  read 360628 cycles
Sat Jun 13 17:14:05 2009  cycles contain 1248013 unique relations
Sat Jun 13 17:14:23 2009  read 1248013 relations
Sat Jun 13 17:14:33 2009  multiplying 994200 relations
Sat Jun 13 17:18:41 2009  multiply complete, coefficients have about 44.73 million bits
Sat Jun 13 17:18:43 2009  initial square root is modulo 2645257
Sat Jun 13 17:24:35 2009  reading relations for dependency 2
Sat Jun 13 17:24:35 2009  read 360316 cycles
Sat Jun 13 17:24:36 2009  cycles contain 1248281 unique relations
Sat Jun 13 17:24:54 2009  read 1248281 relations
Sat Jun 13 17:25:03 2009  multiplying 995182 relations
Sat Jun 13 17:29:11 2009  multiply complete, coefficients have about 44.78 million bits
Sat Jun 13 17:29:13 2009  initial square root is modulo 2683463
Sat Jun 13 17:35:12 2009  sqrtTime: 1268
Sat Jun 13 17:35:12 2009  prp58 factor: 1076573811006174078255496603425369798195157247908414024513
Sat Jun 13 17:35:12 2009  prp66 factor: 150279363077127682942036206681415950498349083088117034520490825661
Sat Jun 13 17:35:12 2009  elapsed time 00:21:10

Jun 14, 2009

By Dmitry Domanov

3·10¹⁷⁰+1 = 3(0)₁₆₉1_<171> = 7 · 43 · 199 · 57529 · 1526651229058273_<16> · C146

C146 = P42 · P105

P42 = 261968755177133227477927295381326837835413_<42>

P105 = 217683509057887059702713392168572709659690627314116574373411276814837715368246493032016769217598949465919_<105>

C146=P42*P105
261968755177133227477927295381326837835413<42>*217683509057887059702713392168572709659690627314116574373411276814837715368246493032016769217598949465919<105>

Jun 13, 2009

By Dmitry Domanov / GMP-ECM 6.2.3/GGNFS/msieve 1.41 / Jun 13, 2009

(16·10¹⁹⁸-7)/9 = 1(7)₁₉₈_<199> = 1549 · 838171 · 125956137380071_<15> · 419305834596410850871_<21> · C155

C155 = P43 · P51 · P62

P43 = 2304592382652143961731264096224704807494453_<43>

P51 = 970232895675790774671967182467598265874128054928869_<51>

P62 = 11595061808911655986014839901941482182826165063259278842132599_<62>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=359511029
Step 1 took 596172ms
********** Factor found in step 1: 2304592382652143961731264096224704807494453
Found probable prime factor of 43 digits: 2304592382652143961731264096224704807494453
Composite cofactor 11249910394400128588769006741704920966079711840343348528218384849373111775151335952807607620202060052645211100531 has 113 digits

Number: 113
N=11249910394400128588769006741704920966079711840343348528218384849373111775151335952807607620202060052645211100531
  ( 113 digits)
Divisors found:
 r1=970232895675790774671967182467598265874128054928869 (pp51)
 r2=11595061808911655986014839901941482182826165063259278842132599 (pp62)

Version: Msieve v. 1.41
Total time: 22.41 hours.
Scaled time: 43.85 units (timescale=1.957).
Factorization parameters were as follows:
name: 113
n: 11249910394400128588769006741704920966079711840343348528218384849373111775151335952807607620202060052645211100531
skew: 59745.59
# norm 3.15e+015
c5: 5160
c4: -1695445366
c3: -45700015886565
c2: 3212891314605306753
c1: 22427336187626592335133
c0: 681835847596764281493583285
# alpha -6.11
Y1: 71639820263
Y0: -4652649231129391287936
# Murphy_E 7.55e-010
# M 1907449802102492470588219400247055954751799605254586842573274650345131418013743453796202936420222481907727438553
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 364394 x 364642
Polynomial selection time: 2.11 hours.
Total sieving time: 19.77 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.31 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 22.41 hours.
 --------- CPU info (if available) ----------

(16·10¹⁹⁰-7)/9 = 1(7)₁₉₀_<191> = 6067 · 376882183 · C178

C178 = P58 · P59 · P62

P58 = 6945950415193564269695115861239077510702586733059382852791_<58>

P59 = 64441391317514719880046737523653294644667708778777048133109_<59>

P62 = 17370058629430105732971321653115633962410075240228083185104703_<62>

N=7774954774392157161927067104500558023545269774120869069685490738315009061192661033202790969577883277483294279822564047287532151045058863141496220336288440400519147292742336300957
  ( 178 digits)
SNFS difficulty: 191 digits.
Divisors found:
r1=6945950415193564269695115861239077510702586733059382852791 (pp58)
r2=64441391317514719880046737523653294644667708778777048133109 (pp59)
r3=17370058629430105732971321653115633962410075240228083185104703 (pp62)
Version: Msieve v. 1.41
Total time: 237.40 hours.
Scaled time: 467.44 units (timescale=1.969).
Factorization parameters were as follows:
n: 7774954774392157161927067104500558023545269774120869069685490738315009061192661033202790969577883277483294279822564047287532151045058863141496220336288440400519147292742336300957
m: 200000000000000000000000000000000000000
deg: 5
c5: 1
c0: -14
skew: 1.70
type: snfs
lss: 1
rlim: 10900000
alim: 10900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10900000/10900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5450000, 9050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1830662 x 1830910
Total sieving time: 230.22 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 6.34 hours.
Time per square root: 0.49 hours.
Prototype def-par.txt line would be:
snfs,191.000,5,0,0,0,0,0,0,0,0,10900000,10900000,28,28,54,54,2.5,2.5,100000
total time: 237.40 hours.
 --------- CPU info (if available) ----------

(13·10¹⁸⁵-31)/9 = 1(4)₁₈₄1_<186> = 3² · 11 · 43² · 145650497 · 616424391175458370238527_<24> · C148

C148 = P29 · P120

P29 = 65179480030846277956271414089_<29>

P120 = 134842271464926635129442045399461515806781710308343035529982485877975632051921808466844841500311919558453436567204757101_<120>

C148=P29*P120
C148=65179480030846277956271414089<29>*134842271464926635129442045399461515806781710308343035529982485877975632051921808466844841500311919558453436567204757101<120>

(13·10¹⁸⁴-31)/9 = 1(4)₁₈₃1_<185> = 7 · 34283 · 55249 · C175

C175 = P28 · C147

P28 = 8073813069587996438988098243_<28>

C147 = [134933837651912564103374368384507680483444062389797150170691343744949834607546660900113391183180100724265992335560088217959448485874274082253775023_<147>]

C175=P28*C147
C175=8073813069587996438988098243<28>*134933837651912564103374368384507680483444062389797150170691343744949834607546660900113391183180100724265992335560088217959448485874274082253775023<147>

Jun 12, 2009 (4th)

By Justin Card / GGNFS, msieve / Jun 12, 2009

(65·10¹⁶⁶+43)/9 = 7(2)₁₆₅7_<167> = 12263 · 603213984515802900576681227024393_<33> · C130

C130 = P57 · P74

P57 = 450631373675458452337775455499947328084685648775502985779_<57>

P74 = 21666127415793961010964729859371091707932535791390299034807201472008220607_<74>

Sieving performed over 2.5 days manually

Postprocessing log:

Thu Jun 11 22:15:03 2009  
Thu Jun 11 22:15:03 2009  
Thu Jun 11 22:15:03 2009  Msieve v. 1.41
Thu Jun 11 22:15:03 2009  random seeds: 891788b7 6f9284bd
Thu Jun 11 22:15:03 2009  factoring 9763436759606743427904739583306785308462946373464374213867612168717174093348236091973396634356359866256404708584327307961415747853 (130 digits)
Thu Jun 11 22:15:04 2009  searching for 15-digit factors
Thu Jun 11 22:15:05 2009  commencing number field sieve (130-digit input)
Thu Jun 11 22:15:05 2009  R0: -1000000000000000000000000000000000
Thu Jun 11 22:15:05 2009  R1:  1
Thu Jun 11 22:15:05 2009  A0:  43
Thu Jun 11 22:15:05 2009  A1:  0
Thu Jun 11 22:15:05 2009  A2:  0
Thu Jun 11 22:15:05 2009  A3:  0
Thu Jun 11 22:15:05 2009  A4:  0
Thu Jun 11 22:15:05 2009  A5:  650
Thu Jun 11 22:15:05 2009  skew 1.00, size 9.555107e-12, alpha -0.317313, combined = 3.222005e-10
Thu Jun 11 22:15:05 2009  
Thu Jun 11 22:15:05 2009  commencing relation filtering
Thu Jun 11 22:15:05 2009  commencing duplicate removal, pass 1
Thu Jun 11 22:17:35 2009  found 2090217 hash collisions in 13684980 relations
Thu Jun 11 22:18:13 2009  added 357929 free relations
Thu Jun 11 22:18:13 2009  commencing duplicate removal, pass 2
Thu Jun 11 22:18:27 2009  found 2030428 duplicates and 12012481 unique relations
Thu Jun 11 22:18:27 2009  memory use: 69.3 MB
Thu Jun 11 22:18:27 2009  reading rational ideals above 6094848
Thu Jun 11 22:18:27 2009  reading algebraic ideals above 6094848
Thu Jun 11 22:18:27 2009  commencing singleton removal, pass 1
Thu Jun 11 22:20:57 2009  relations with 0 large ideals: 299061
Thu Jun 11 22:20:57 2009  relations with 1 large ideals: 1856276
Thu Jun 11 22:20:57 2009  relations with 2 large ideals: 4373394
Thu Jun 11 22:20:57 2009  relations with 3 large ideals: 4053181
Thu Jun 11 22:20:57 2009  relations with 4 large ideals: 1048259
Thu Jun 11 22:20:57 2009  relations with 5 large ideals: 39190
Thu Jun 11 22:20:57 2009  relations with 6 large ideals: 343119
Thu Jun 11 22:20:57 2009  relations with 7+ large ideals: 1
Thu Jun 11 22:20:57 2009  12012481 relations and about 9765690 large ideals
Thu Jun 11 22:20:57 2009  commencing singleton removal, pass 2
Thu Jun 11 22:23:39 2009  found 3384675 singletons
Thu Jun 11 22:23:39 2009  current dataset: 8627806 relations and about 5627344 large ideals
Thu Jun 11 22:23:39 2009  commencing singleton removal, pass 3
Thu Jun 11 22:25:22 2009  found 877593 singletons
Thu Jun 11 22:25:22 2009  current dataset: 7750213 relations and about 4725529 large ideals
Thu Jun 11 22:25:22 2009  commencing singleton removal, pass 4
Thu Jun 11 22:26:57 2009  found 139102 singletons
Thu Jun 11 22:26:57 2009  current dataset: 7611111 relations and about 4585593 large ideals
Thu Jun 11 22:26:57 2009  commencing singleton removal, final pass
Thu Jun 11 22:28:37 2009  memory use: 123.1 MB
Thu Jun 11 22:28:37 2009  commencing in-memory singleton removal
Thu Jun 11 22:28:38 2009  begin with 7611111 relations and 4846475 unique ideals
Thu Jun 11 22:28:45 2009  reduce to 7238441 relations and 4470046 ideals in 8 passes
Thu Jun 11 22:28:45 2009  max relations containing the same ideal: 31
Thu Jun 11 22:28:46 2009  reading rational ideals above 720000
Thu Jun 11 22:28:46 2009  reading algebraic ideals above 720000
Thu Jun 11 22:28:46 2009  commencing singleton removal, final pass
Thu Jun 11 22:30:40 2009  keeping 4652011 ideals with weight <= 20, new excess is 661449
Thu Jun 11 22:30:45 2009  memory use: 177.4 MB
Thu Jun 11 22:30:45 2009  commencing in-memory singleton removal
Thu Jun 11 22:30:46 2009  begin with 7239473 relations and 4652011 unique ideals
Thu Jun 11 22:30:50 2009  reduce to 7238347 relations and 4645988 ideals in 4 passes
Thu Jun 11 22:30:50 2009  max relations containing the same ideal: 20
Thu Jun 11 22:30:55 2009  removing 1370225 relations and 970225 ideals in 400000 cliques
Thu Jun 11 22:30:56 2009  commencing in-memory singleton removal
Thu Jun 11 22:30:56 2009  begin with 5868122 relations and 4645988 unique ideals
Thu Jun 11 22:31:02 2009  reduce to 5763246 relations and 3565026 ideals in 7 passes
Thu Jun 11 22:31:02 2009  max relations containing the same ideal: 20
Thu Jun 11 22:31:06 2009  removing 1048359 relations and 648359 ideals in 400000 cliques
Thu Jun 11 22:31:06 2009  commencing in-memory singleton removal
Thu Jun 11 22:31:07 2009  begin with 4714887 relations and 3565026 unique ideals
Thu Jun 11 22:31:10 2009  reduce to 4612574 relations and 2807796 ideals in 6 passes
Thu Jun 11 22:31:10 2009  max relations containing the same ideal: 20
Thu Jun 11 22:31:13 2009  removing 958972 relations and 558972 ideals in 400000 cliques
Thu Jun 11 22:31:14 2009  commencing in-memory singleton removal
Thu Jun 11 22:31:14 2009  begin with 3653602 relations and 2807796 unique ideals
Thu Jun 11 22:31:17 2009  reduce to 3546460 relations and 2133022 ideals in 6 passes
Thu Jun 11 22:31:17 2009  max relations containing the same ideal: 19
Thu Jun 11 22:31:19 2009  removing 927820 relations and 527820 ideals in 400000 cliques
Thu Jun 11 22:31:20 2009  commencing in-memory singleton removal
Thu Jun 11 22:31:20 2009  begin with 2618640 relations and 2133022 unique ideals
Thu Jun 11 22:31:22 2009  reduce to 2502532 relations and 1476617 ideals in 7 passes
Thu Jun 11 22:31:22 2009  max relations containing the same ideal: 16
Thu Jun 11 22:31:24 2009  removing 617081 relations and 358447 ideals in 258634 cliques
Thu Jun 11 22:31:24 2009  commencing in-memory singleton removal
Thu Jun 11 22:31:24 2009  begin with 1885451 relations and 1476617 unique ideals
Thu Jun 11 22:31:25 2009  reduce to 1796412 relations and 1019287 ideals in 7 passes
Thu Jun 11 22:31:25 2009  max relations containing the same ideal: 14
Thu Jun 11 22:31:26 2009  removing 44809 relations and 34965 ideals in 9844 cliques
Thu Jun 11 22:31:27 2009  commencing in-memory singleton removal
Thu Jun 11 22:31:27 2009  begin with 1751603 relations and 1019287 unique ideals
Thu Jun 11 22:31:27 2009  reduce to 1750837 relations and 983553 ideals in 4 passes
Thu Jun 11 22:31:27 2009  max relations containing the same ideal: 14
Thu Jun 11 22:31:28 2009  relations with 0 large ideals: 174112
Thu Jun 11 22:31:28 2009  relations with 1 large ideals: 583484
Thu Jun 11 22:31:28 2009  relations with 2 large ideals: 636673
Thu Jun 11 22:31:28 2009  relations with 3 large ideals: 282529
Thu Jun 11 22:31:28 2009  relations with 4 large ideals: 64640
Thu Jun 11 22:31:28 2009  relations with 5 large ideals: 7757
Thu Jun 11 22:31:28 2009  relations with 6 large ideals: 1629
Thu Jun 11 22:31:28 2009  relations with 7+ large ideals: 13
Thu Jun 11 22:31:28 2009  commencing 2-way merge
Thu Jun 11 22:31:29 2009  reduce to 1298618 relation sets and 531334 unique ideals
Thu Jun 11 22:31:29 2009  commencing full merge
Thu Jun 11 22:31:35 2009  memory use: 52.1 MB
Thu Jun 11 22:31:35 2009  found 764728 cycles, need 661649
Thu Jun 11 22:31:35 2009  weight of 661649 cycles is about 32721827 (49.45/cycle)
Thu Jun 11 22:31:35 2009  distribution of cycle lengths:
Thu Jun 11 22:31:35 2009  1 relations: 174112
Thu Jun 11 22:31:35 2009  2 relations: 97968
Thu Jun 11 22:31:35 2009  3 relations: 80875
Thu Jun 11 22:31:35 2009  4 relations: 65935
Thu Jun 11 22:31:35 2009  5 relations: 56261
Thu Jun 11 22:31:35 2009  6 relations: 46805
Thu Jun 11 22:31:35 2009  7 relations: 40424
Thu Jun 11 22:31:35 2009  8 relations: 33366
Thu Jun 11 22:31:35 2009  9 relations: 27756
Thu Jun 11 22:31:35 2009  10+ relations: 38147
Thu Jun 11 22:31:35 2009  heaviest cycle: 14 relations
Thu Jun 11 22:31:35 2009  matrix can improve, retrying
Thu Jun 11 22:31:36 2009  reading rational ideals above 720000
Thu Jun 11 22:31:36 2009  reading algebraic ideals above 720000
Thu Jun 11 22:31:36 2009  commencing singleton removal, final pass
Thu Jun 11 22:33:29 2009  keeping 4741281 ideals with weight <= 25, new excess is 572179
Thu Jun 11 22:33:34 2009  memory use: 177.4 MB
Thu Jun 11 22:33:34 2009  commencing in-memory singleton removal
Thu Jun 11 22:33:35 2009  begin with 7239473 relations and 4741281 unique ideals
Thu Jun 11 22:33:40 2009  reduce to 7238347 relations and 4735258 ideals in 4 passes
Thu Jun 11 22:33:40 2009  max relations containing the same ideal: 25
Thu Jun 11 22:33:45 2009  removing 1370225 relations and 970225 ideals in 400000 cliques
Thu Jun 11 22:33:46 2009  commencing in-memory singleton removal
Thu Jun 11 22:33:47 2009  begin with 5868122 relations and 4735258 unique ideals
Thu Jun 11 22:33:52 2009  reduce to 5763246 relations and 3654296 ideals in 7 passes
Thu Jun 11 22:33:52 2009  max relations containing the same ideal: 25
Thu Jun 11 22:33:57 2009  removing 1048359 relations and 648359 ideals in 400000 cliques
Thu Jun 11 22:33:57 2009  commencing in-memory singleton removal
Thu Jun 11 22:33:58 2009  begin with 4714887 relations and 3654296 unique ideals
Thu Jun 11 22:34:02 2009  reduce to 4612548 relations and 2897043 ideals in 6 passes
Thu Jun 11 22:34:02 2009  max relations containing the same ideal: 24
Thu Jun 11 22:34:05 2009  removing 958960 relations and 558960 ideals in 400000 cliques
Thu Jun 11 22:34:05 2009  commencing in-memory singleton removal
Thu Jun 11 22:34:06 2009  begin with 3653588 relations and 2897043 unique ideals
Thu Jun 11 22:34:09 2009  reduce to 3546576 relations and 2222376 ideals in 6 passes
Thu Jun 11 22:34:09 2009  max relations containing the same ideal: 23
Thu Jun 11 22:34:12 2009  removing 927863 relations and 527863 ideals in 400000 cliques
Thu Jun 11 22:34:12 2009  commencing in-memory singleton removal
Thu Jun 11 22:34:13 2009  begin with 2618713 relations and 2222376 unique ideals
Thu Jun 11 22:34:15 2009  reduce to 2502567 relations and 1565849 ideals in 7 passes
Thu Jun 11 22:34:15 2009  max relations containing the same ideal: 19
Thu Jun 11 22:34:17 2009  removing 645878 relations and 372888 ideals in 272990 cliques
Thu Jun 11 22:34:17 2009  commencing in-memory singleton removal
Thu Jun 11 22:34:18 2009  begin with 1856689 relations and 1565849 unique ideals
Thu Jun 11 22:34:19 2009  reduce to 1761413 relations and 1086714 ideals in 7 passes
Thu Jun 11 22:34:19 2009  max relations containing the same ideal: 17
Thu Jun 11 22:34:20 2009  removing 49978 relations and 39007 ideals in 10971 cliques
Thu Jun 11 22:34:21 2009  commencing in-memory singleton removal
Thu Jun 11 22:34:21 2009  begin with 1711435 relations and 1086714 unique ideals
Thu Jun 11 22:34:22 2009  reduce to 1710437 relations and 1046700 ideals in 5 passes
Thu Jun 11 22:34:22 2009  max relations containing the same ideal: 16
Thu Jun 11 22:34:22 2009  relations with 0 large ideals: 113635
Thu Jun 11 22:34:22 2009  relations with 1 large ideals: 443963
Thu Jun 11 22:34:22 2009  relations with 2 large ideals: 615026
Thu Jun 11 22:34:22 2009  relations with 3 large ideals: 381062
Thu Jun 11 22:34:22 2009  relations with 4 large ideals: 128224
Thu Jun 11 22:34:22 2009  relations with 5 large ideals: 24417
Thu Jun 11 22:34:22 2009  relations with 6 large ideals: 3945
Thu Jun 11 22:34:22 2009  relations with 7+ large ideals: 165
Thu Jun 11 22:34:22 2009  commencing 2-way merge
Thu Jun 11 22:34:23 2009  reduce to 1266153 relation sets and 602416 unique ideals
Thu Jun 11 22:34:23 2009  commencing full merge
Thu Jun 11 22:34:38 2009  memory use: 58.1 MB
Thu Jun 11 22:34:38 2009  found 666737 cycles, need 584616
Thu Jun 11 22:34:39 2009  weight of 584616 cycles is about 41139292 (70.37/cycle)
Thu Jun 11 22:34:39 2009  distribution of cycle lengths:
Thu Jun 11 22:34:39 2009  1 relations: 113778
Thu Jun 11 22:34:39 2009  2 relations: 61154
Thu Jun 11 22:34:39 2009  3 relations: 53353
Thu Jun 11 22:34:39 2009  4 relations: 47482
Thu Jun 11 22:34:39 2009  5 relations: 44643
Thu Jun 11 22:34:39 2009  6 relations: 40899
Thu Jun 11 22:34:39 2009  7 relations: 38087
Thu Jun 11 22:34:39 2009  8 relations: 34576
Thu Jun 11 22:34:39 2009  9 relations: 31157
Thu Jun 11 22:34:39 2009  10+ relations: 119487
Thu Jun 11 22:34:39 2009  heaviest cycle: 18 relations
Thu Jun 11 22:34:39 2009  matrix can improve, retrying
Thu Jun 11 22:34:40 2009  reading rational ideals above 720000
Thu Jun 11 22:34:40 2009  reading algebraic ideals above 720000
Thu Jun 11 22:34:40 2009  commencing singleton removal, final pass
Thu Jun 11 22:37:12 2009  keeping 4838805 ideals with weight <= 30, new excess is 474655
Thu Jun 11 22:37:20 2009  memory use: 177.4 MB
Thu Jun 11 22:37:20 2009  commencing in-memory singleton removal
Thu Jun 11 22:37:22 2009  begin with 7239473 relations and 4838805 unique ideals
Thu Jun 11 22:37:29 2009  reduce to 7238347 relations and 4832782 ideals in 4 passes
Thu Jun 11 22:37:29 2009  max relations containing the same ideal: 30
Thu Jun 11 22:37:39 2009  removing 1370225 relations and 970225 ideals in 400000 cliques
Thu Jun 11 22:37:40 2009  commencing in-memory singleton removal
Thu Jun 11 22:37:42 2009  begin with 5868122 relations and 4832782 unique ideals
Thu Jun 11 22:37:53 2009  reduce to 5763246 relations and 3751820 ideals in 7 passes
Thu Jun 11 22:37:53 2009  max relations containing the same ideal: 30
Thu Jun 11 22:38:01 2009  removing 1048359 relations and 648359 ideals in 400000 cliques
Thu Jun 11 22:38:02 2009  commencing in-memory singleton removal
Thu Jun 11 22:38:03 2009  begin with 4714887 relations and 3751820 unique ideals
Thu Jun 11 22:38:11 2009  reduce to 4612549 relations and 2994568 ideals in 6 passes
Thu Jun 11 22:38:11 2009  max relations containing the same ideal: 28
Thu Jun 11 22:38:17 2009  removing 958958 relations and 558958 ideals in 400000 cliques
Thu Jun 11 22:38:18 2009  commencing in-memory singleton removal
Thu Jun 11 22:38:19 2009  begin with 3653591 relations and 2994568 unique ideals
Thu Jun 11 22:38:25 2009  reduce to 3546538 relations and 2319864 ideals in 6 passes
Thu Jun 11 22:38:25 2009  max relations containing the same ideal: 26
Thu Jun 11 22:38:30 2009  removing 927846 relations and 527846 ideals in 400000 cliques
Thu Jun 11 22:38:31 2009  commencing in-memory singleton removal
Thu Jun 11 22:38:31 2009  begin with 2618692 relations and 2319864 unique ideals
Thu Jun 11 22:38:36 2009  reduce to 2502397 relations and 1663234 ideals in 7 passes
Thu Jun 11 22:38:36 2009  max relations containing the same ideal: 21
Thu Jun 11 22:38:39 2009  removing 676969 relations and 388406 ideals in 288563 cliques
Thu Jun 11 22:38:40 2009  commencing in-memory singleton removal
Thu Jun 11 22:38:41 2009  begin with 1825428 relations and 1663234 unique ideals
Thu Jun 11 22:38:44 2009  reduce to 1723810 relations and 1160990 ideals in 7 passes
Thu Jun 11 22:38:44 2009  max relations containing the same ideal: 18
Thu Jun 11 22:38:46 2009  removing 55463 relations and 43243 ideals in 12220 cliques
Thu Jun 11 22:38:47 2009  commencing in-memory singleton removal
Thu Jun 11 22:38:47 2009  begin with 1668347 relations and 1160990 unique ideals
Thu Jun 11 22:38:49 2009  reduce to 1667063 relations and 1116452 ideals in 5 passes
Thu Jun 11 22:38:49 2009  max relations containing the same ideal: 18
Thu Jun 11 22:38:49 2009  relations with 0 large ideals: 65458
Thu Jun 11 22:38:49 2009  relations with 1 large ideals: 297828
Thu Jun 11 22:38:49 2009  relations with 2 large ideals: 530856
Thu Jun 11 22:38:49 2009  relations with 3 large ideals: 462549
Thu Jun 11 22:38:49 2009  relations with 4 large ideals: 229066
Thu Jun 11 22:38:49 2009  relations with 5 large ideals: 67346
Thu Jun 11 22:38:49 2009  relations with 6 large ideals: 12804
Thu Jun 11 22:38:49 2009  relations with 7+ large ideals: 1156
Thu Jun 11 22:38:49 2009  commencing 2-way merge
Thu Jun 11 22:38:52 2009  reduce to 1233370 relation sets and 682759 unique ideals
Thu Jun 11 22:38:52 2009  commencing full merge
Thu Jun 11 22:39:14 2009  memory use: 65.7 MB
Thu Jun 11 22:39:14 2009  found 634387 cycles, need 560959
Thu Jun 11 22:39:15 2009  weight of 560959 cycles is about 39428217 (70.29/cycle)
Thu Jun 11 22:39:15 2009  distribution of cycle lengths:
Thu Jun 11 22:39:15 2009  1 relations: 72319
Thu Jun 11 22:39:15 2009  2 relations: 52148
Thu Jun 11 22:39:15 2009  3 relations: 55635
Thu Jun 11 22:39:15 2009  4 relations: 54694
Thu Jun 11 22:39:15 2009  5 relations: 54247
Thu Jun 11 22:39:15 2009  6 relations: 49707
Thu Jun 11 22:39:15 2009  7 relations: 45747
Thu Jun 11 22:39:15 2009  8 relations: 40721
Thu Jun 11 22:39:15 2009  9 relations: 35481
Thu Jun 11 22:39:15 2009  10+ relations: 100260
Thu Jun 11 22:39:15 2009  heaviest cycle: 16 relations
Thu Jun 11 22:39:15 2009  commencing cycle optimization
Thu Jun 11 22:39:17 2009  start with 3244833 relations
Thu Jun 11 22:39:31 2009  pruned 210947 relations
Thu Jun 11 22:39:31 2009  memory use: 93.5 MB
Thu Jun 11 22:39:31 2009  distribution of cycle lengths:
Thu Jun 11 22:39:31 2009  1 relations: 72319
Thu Jun 11 22:39:31 2009  2 relations: 54853
Thu Jun 11 22:39:31 2009  3 relations: 60718
Thu Jun 11 22:39:31 2009  4 relations: 60060
Thu Jun 11 22:39:31 2009  5 relations: 60069
Thu Jun 11 22:39:31 2009  6 relations: 54268
Thu Jun 11 22:39:31 2009  7 relations: 49024
Thu Jun 11 22:39:31 2009  8 relations: 42072
Thu Jun 11 22:39:31 2009  9 relations: 35161
Thu Jun 11 22:39:31 2009  10+ relations: 72415
Thu Jun 11 22:39:31 2009  heaviest cycle: 16 relations
Thu Jun 11 22:39:34 2009  RelProcTime: 1326
Thu Jun 11 22:39:34 2009  elapsed time 00:24:31
Thu Jun 11 22:39:45 2009  
Thu Jun 11 22:39:45 2009  
Thu Jun 11 22:39:45 2009  Msieve v. 1.41
Thu Jun 11 22:39:45 2009  random seeds: 2f7019d3 c696b041
Thu Jun 11 22:39:45 2009  factoring 9763436759606743427904739583306785308462946373464374213867612168717174093348236091973396634356359866256404708584327307961415747853 (130 digits)
Thu Jun 11 22:39:47 2009  searching for 15-digit factors
Thu Jun 11 22:39:48 2009  commencing number field sieve (130-digit input)
Thu Jun 11 22:39:48 2009  R0: -1000000000000000000000000000000000
Thu Jun 11 22:39:48 2009  R1:  1
Thu Jun 11 22:39:48 2009  A0:  43
Thu Jun 11 22:39:48 2009  A1:  0
Thu Jun 11 22:39:48 2009  A2:  0
Thu Jun 11 22:39:48 2009  A3:  0
Thu Jun 11 22:39:48 2009  A4:  0
Thu Jun 11 22:39:48 2009  A5:  650
Thu Jun 11 22:39:48 2009  skew 1.00, size 9.555107e-12, alpha -0.317313, combined = 3.222005e-10
Thu Jun 11 22:39:48 2009  
Thu Jun 11 22:39:48 2009  commencing linear algebra
Thu Jun 11 22:39:48 2009  read 560959 cycles
Thu Jun 11 22:39:51 2009  cycles contain 1460370 unique relations
Thu Jun 11 22:40:18 2009  
Thu Jun 11 22:40:18 2009  
Thu Jun 11 22:40:18 2009  Msieve v. 1.41
Thu Jun 11 22:40:18 2009  random seeds: 896479b4 8c2297c6
Thu Jun 11 22:40:18 2009  factoring 9763436759606743427904739583306785308462946373464374213867612168717174093348236091973396634356359866256404708584327307961415747853 (130 digits)
Thu Jun 11 22:40:19 2009  searching for 15-digit factors
Thu Jun 11 22:40:20 2009  commencing number field sieve (130-digit input)
Thu Jun 11 22:40:20 2009  R0: -1000000000000000000000000000000000
Thu Jun 11 22:40:20 2009  R1:  1
Thu Jun 11 22:40:20 2009  A0:  43
Thu Jun 11 22:40:20 2009  A1:  0
Thu Jun 11 22:40:20 2009  A2:  0
Thu Jun 11 22:40:20 2009  A3:  0
Thu Jun 11 22:40:20 2009  A4:  0
Thu Jun 11 22:40:20 2009  A5:  650
Thu Jun 11 22:40:20 2009  skew 1.00, size 9.555107e-12, alpha -0.317313, combined = 3.222005e-10
Thu Jun 11 22:40:20 2009  
Thu Jun 11 22:40:20 2009  commencing linear algebra
Thu Jun 11 22:40:20 2009  read 560959 cycles
Thu Jun 11 22:40:21 2009  cycles contain 1460370 unique relations
Thu Jun 11 22:40:43 2009  read 1460370 relations
Thu Jun 11 22:40:46 2009  using 20 quadratic characters above 134210724
Thu Jun 11 22:41:00 2009  building initial matrix
Thu Jun 11 22:41:26 2009  memory use: 185.1 MB
Thu Jun 11 22:41:27 2009  read 560959 cycles
Thu Jun 11 22:41:27 2009  matrix is 560744 x 560959 (161.1 MB) with weight 48786446 (86.97/col)
Thu Jun 11 22:41:27 2009  sparse part has weight 36056943 (64.28/col)
Thu Jun 11 22:41:43 2009  filtering completed in 2 passes
Thu Jun 11 22:41:43 2009  matrix is 559754 x 559954 (160.9 MB) with weight 48736748 (87.04/col)
Thu Jun 11 22:41:43 2009  sparse part has weight 36028515 (64.34/col)
Thu Jun 11 22:41:47 2009  read 559954 cycles
Thu Jun 11 22:41:48 2009  matrix is 559754 x 559954 (160.9 MB) with weight 48736748 (87.04/col)
Thu Jun 11 22:41:48 2009  sparse part has weight 36028515 (64.34/col)
Thu Jun 11 22:41:48 2009  saving the first 48 matrix rows for later
Thu Jun 11 22:41:48 2009  matrix is 559706 x 559954 (153.0 MB) with weight 38273617 (68.35/col)
Thu Jun 11 22:41:48 2009  sparse part has weight 34501380 (61.61/col)
Thu Jun 11 22:41:48 2009  matrix includes 64 packed rows
Thu Jun 11 22:41:48 2009  using block size 10922 for processor cache size 256 kB
Thu Jun 11 22:41:52 2009  commencing Lanczos iteration (2 threads)
Thu Jun 11 22:41:52 2009  memory use: 149.8 MB
Thu Jun 11 23:37:37 2009  lanczos halted after 8855 iterations (dim = 559706)
Thu Jun 11 23:37:38 2009  recovered 39 nontrivial dependencies
Thu Jun 11 23:37:38 2009  BLanczosTime: 3438
Thu Jun 11 23:37:38 2009  elapsed time 00:57:20
Thu Jun 11 23:42:07 2009  
Thu Jun 11 23:42:07 2009  
Thu Jun 11 23:42:07 2009  Msieve v. 1.41
Thu Jun 11 23:42:07 2009  random seeds: f3d8e841 ee630f48
Thu Jun 11 23:42:07 2009  factoring 9763436759606743427904739583306785308462946373464374213867612168717174093348236091973396634356359866256404708584327307961415747853 (130 digits)
Thu Jun 11 23:42:09 2009  searching for 15-digit factors
Thu Jun 11 23:42:09 2009  commencing number field sieve (130-digit input)
Thu Jun 11 23:42:09 2009  R0: -1000000000000000000000000000000000
Thu Jun 11 23:42:09 2009  R1:  1
Thu Jun 11 23:42:09 2009  A0:  43
Thu Jun 11 23:42:09 2009  A1:  0
Thu Jun 11 23:42:09 2009  A2:  0
Thu Jun 11 23:42:09 2009  A3:  0
Thu Jun 11 23:42:09 2009  A4:  0
Thu Jun 11 23:42:09 2009  A5:  650
Thu Jun 11 23:42:09 2009  skew 1.00, size 9.555107e-12, alpha -0.317313, combined = 3.222005e-10
Thu Jun 11 23:42:10 2009  
Thu Jun 11 23:42:10 2009  commencing square root phase
Thu Jun 11 23:42:10 2009  reading relations for dependency 1
Thu Jun 11 23:42:10 2009  read 279367 cycles
Thu Jun 11 23:42:10 2009  cycles contain 921779 unique relations
Thu Jun 11 23:42:27 2009  read 921779 relations
Thu Jun 11 23:42:33 2009  multiplying 729442 relations
Thu Jun 11 23:44:19 2009  multiply complete, coefficients have about 22.36 million bits
Thu Jun 11 23:44:20 2009  initial square root is modulo 2636251
Thu Jun 11 23:47:12 2009  reading relations for dependency 2
Thu Jun 11 23:47:12 2009  read 279179 cycles
Thu Jun 11 23:47:13 2009  cycles contain 921197 unique relations
Thu Jun 11 23:47:29 2009  read 921197 relations
Thu Jun 11 23:47:35 2009  multiplying 728430 relations
Thu Jun 11 23:49:22 2009  multiply complete, coefficients have about 22.33 million bits
Thu Jun 11 23:49:22 2009  initial square root is modulo 2586791
Thu Jun 11 23:52:15 2009  sqrtTime: 605
Thu Jun 11 23:52:15 2009  prp57 factor: 450631373675458452337775455499947328084685648775502985779
Thu Jun 11 23:52:15 2009  prp74 factor: 21666127415793961010964729859371091707932535791390299034807201472008220607
Thu Jun 11 23:52:15 2009  elapsed time 00:10:08

Jun 12, 2009 (3rd)

By Dmitry Domanov / ECM / Jun 12, 2009

(13·10¹⁷¹-31)/9 = 1(4)₁₇₀1_<172> = 11 · 845599 · 14030443675276817_<17> · C149

C149 = P30 · C119

P30 = 256462931804549017510633552397_<30>

C119 = [43156646434003437590709513779974321417811490608715284910791365906651077456606782151395693253101947622545235176793105081_<119>]

C149=P30*C119
C140=256462931804549017510633552397<30>*43156646434003437590709513779974321417811490608715284910791365906651077456606782151395693253101947622545235176793105081<119>

(19·10²⁰⁵+11)/3 = 6(3)₂₀₄7_<206> = 47 · 1049 · 28439 · 301073 · 226406454334346351603_<21> · 1677465659365970615668154819_<28> · C144

C144 = P33 · P111

P33 = 720739136192652754793757399275881_<33>

P111 = 548090560221826880156372241250752203241766441099323845908077403370902283241257961429117324365891642207569996921_<111>

C144=P33*P111
C144=720739136192652754793757399275881<33>*548090560221826880156372241250752203241766441099323845908077403370902283241257961429117324365891642207569996921<111>

(31·10¹⁷⁰-13)/9 = 3(4)₁₆₉3_<171> = 7² · 4629920455654758013498867_<25> · C145

C145 = P42 · P103

P42 = 232031625289267285997872846548274872654251_<42>

P103 = 6543383771920925262771313657337423017658900689973818172304650431186996923388887223462560916516787337371_<103>

C145=P42*P103
C145=232031625289267285997872846548274872654251<42>*6543383771920925262771313657337423017658900689973818172304650431186996923388887223462560916516787337371<103>

Jun 12, 2009 (2nd)

By Sinkiti Sibata / Msieve / Jun 12, 2009

(19·10¹⁶³+11)/3 = 6(3)₁₆₂7_<164> = 23 · 212240551 · 507368374445072909_<18> · C137

C137 = P50 · P87

P50 = 78154045810066885489839026558465998531596120691381_<50>

P87 = 327190953676735888663357517665468214766548405810117447443857596565381215359865497358761_<87>

Number: 63337_163
N=25571296782291088901074669831696584997219804892506777450351526895074193322549230921193042451835425230969964312171558082984763036717538941
  ( 137 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=78154045810066885489839026558465998531596120691381 (pp50)
 r2=327190953676735888663357517665468214766548405810117447443857596565381215359865497358761 (pp87)
Version: Msieve-1.40
Total time: 52.38 hours.
Scaled time: 109.58 units (timescale=2.092).
Factorization parameters were as follows:
name: 63337_163
n: 25571296782291088901074669831696584997219804892506777450351526895074193322549230921193042451835425230969964312171558082984763036717538941
m: 500000000000000000000000000000000
deg: 5
c5: 152
c0: 275
skew: 1.13
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 4000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 737427 x 737675
Total sieving time: 49.68 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.06 hours.
Time per square root: 0.45 hours.
Prototype def-par.txt line would be:
snfs,165.000,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 52.38 hours.
 --------- CPU info (if available) ----------

Jun 12, 2009

By Robert Backstrom / GMP-ECM / Jun 12, 2009

(58·10¹⁷³-31)/9 = 6(4)₁₇₂1_<174> = 7 · 43 · 10141 · 39563 · 48491 · 212579 · 154774691 · 34627365762419_<14> · 80771274582319_<14> · C118

C118 = P37 · P81

P37 = 3252686432044830575611644891450269629_<37>

P81 = 367662177813584306398113689094894372531220364516609385149063751165849999660842617_<81>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 1195889777350299605771289107018392405410588807124263934343162265572375663837663946874692414404316491260057477983979093 (118 digits)
Using B1=4518000, B2=8562077170, polynomial Dickson(6), sigma=2004421685
Step 1 took 50653ms
Step 2 took 14851ms
********** Factor found in step 2: 3252686432044830575611644891450269629
Found probable prime factor of 37 digits: 3252686432044830575611644891450269629
Probable prime cofactor 367662177813584306398113689094894372531220364516609385149063751165849999660842617 has 81 digits

Jun 11, 2009 (6th)

By Robert Backstrom / GGNFS / Jun 11, 2009

(58·10¹⁴⁷-31)/9 = 6(4)₁₄₆1_<148> = 3 · 19 · 4099 · 9319 · C139

C139 = P52 · P88

P52 = 1676223678292203960049128169722890860607910437181707_<52>

P88 = 1765758994698086055170520278368619003216331480155940049496103700209244596464918718463639_<88>

Number: n
N=2959807037070370077701588675503483600950004631059528994363964170551323205253630464699789086748024196236570518498067476640101738676115451773
  ( 139 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=1676223678292203960049128169722890860607910437181707 (pp52)
 r2=1765758994698086055170520278368619003216331480155940049496103700209244596464918718463639 (pp88)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 12.28 hours.
Scaled time: 32.52 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_6_4_146_1
n: 2959807037070370077701588675503483600950004631059528994363964170551323205253630464699789086748024196236570518498067476640101738676115451773
m: 200000000000000000000000000000
deg: 5
c5: 725
c0: -124
skew: 0.70
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 100000
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [1100000, 3200001)
Primes: RFBsize:162662, AFBsize:163211, largePrimes:8173952 encountered
Relations: rels:7706656, finalFF:392959
Max relations in full relation-set: 28
Initial matrix: 325940 x 392959 with sparse part having weight 44229416.
Pruned matrix : 301299 x 302992 with weight 32110514.
Total sieving time: 11.27 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.42 hours.
Total square root time: 0.44 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,56,56,2.3,2.3,100000
total time: 12.28 hours.
 --------- CPU info (if available) ----------

Jun 11, 2009 (5th)

By Dmitry Domanov / GGNFS/msieve 1.41 / Jun 11, 2009

(26·10²⁰³+1)/9 = 2(8)₂₀₂9_<204> = 61 · 9819918737_<10> · 37287396313_<11> · 100744959165252560987_<21> · 5394637429152624442511_<22> · C140

C140 = P49 · P92

P49 = 1591392095289804421962004160362504930638566818651_<49>

P92 = 14954375035445075432517592802281751545607225577975759746369031858970547474844079393319097347_<92>

N=23798274221406481862937388696721507629375257074001696626340245646231006728544866514463627094525111474872935700567490601892062846556764218897
  ( 140 digits)
Divisors found:
r1=1591392095289804421962004160362504930638566818651 (pp49)
r2=14954375035445075432517592802281751545607225577975759746369031858970547474844079393319097347 (pp92)
Version: Msieve v. 1.41
Total time: 484.30 hours.
Scaled time: 959.88 units (timescale=1.982).
Factorization parameters were as follows:
n: 23798274221406481862937388696721507629375257074001696626340245646231006728544866514463627094525111474872935700567490601892062846556764218897

Y0: -734848807318907386147773470
Y1:  3828307784904209
c0: -575676726393303313640246491759215387
c1:  241313731949091829399125074778
c2:  679634942601726569804696
c3: -345838423607777188
c4: -106656386559
c5:  111060
skew: 1624324.30
type: gnfs
# size 1.397696e-013, alpha -7.351016, combined = 1.920798e-011

rlim: 12000000
alim: 12000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved algebraic special-q in [6000000, 13400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2138724 x 2138969
Total sieving time: 470.62 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 10.64 hours.
Time per square root: 2.62 hours.
Prototype def-par.txt line would be:
gnfs,139,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12000000,12000000,28,28,55,55,2.6,2.6,100000
total time: 484.30 hours.
 --------- CPU info (if available) ----------

(55·10¹⁷⁰+71)/9 = 6(1)₁₆₉9_<171> = 5867 · 1686669207321401057_<19> · C149

C149 = P41 · P109

P41 = 15417904565595260846145189831758985988853_<41>

P109 = 4005427012872325335566780151439560381843187368300758259621127417374298478093358344498755291601015884297338617_<109>

C149=P41*P109
C149=15417904565595260846145189831758985988853<41>*4005427012872325335566780151439560381843187368300758259621127417374298478093358344498755291601015884297338617<109>

Jun 11, 2009 (4th)

By Wataru Sakai / Msieve / Jun 11, 2009

8·10¹⁷⁰+9 = 8(0)₁₆₉9_<171> = 113 · 452926193 · 3182006963_<10> · 3558984497657_<13> · C139

C139 = P52 · P87

P52 = 3739349584888004768232061820906349177229967138340283_<52>

P87 = 369114253681640613419529242815258516418059888685901830643751071825955380199942725832817_<87>

Number: 80009_170
N=1380247231280688513519537236207908295619969438829829240186899926792486920831167751357193427318708350016115652627084598605877702542314467211
  ( 139 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=3739349584888004768232061820906349177229967138340283
 r2=369114253681640613419529242815258516418059888685901830643751071825955380199942725832817
Version: 
Total time: 70.90 hours.
Scaled time: 129.39 units (timescale=1.825).
Factorization parameters were as follows:
n: 1380247231280688513519537236207908295619969438829829240186899926792486920831167751357193427318708350016115652627084598605877702542314467211
m: 10000000000000000000000000000000000
deg: 5
c5: 8
c0: 9
skew: 1.02
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 4650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 617808 x 618056
Total sieving time: 70.90 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 70.90 hours.
 --------- CPU info (if available) ----------

Jun 11, 2009 (3rd)

By matsui / GGNFS / Jun 11, 2009

(46·10²⁰²+17)/9 = 5(1)₂₀₁3_<203> = 1933 · C200

C200 = P41 · P76 · P84

P41 = 25095474208856818167520252174989158442949_<41>

P76 = 3297726093382206271419702874019435673426517286346071139459697077025086546391_<76>

P84 = 319501926354791297344734539988594417282060450051494131411273826097979565702137229279_<84>

N=26441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340461
  ( 200 digits)
SNFS difficulty: 204 digits.
Divisors found:
 r1=25095474208856818167520252174989158442949 (pp41)
 r2=3297726093382206271419702874019435673426517286346071139459697077025086546391 (pp76)
 r3=319501926354791297344734539988594417282060450051494131411273826097979565702137229279 (pp84)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 1246.67 hours.
Scaled time: 2805.00 units (timescale=2.250).
Factorization parameters were as follows:
n: 26441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340460999022820026441340461
m: 20000000000000000000000000000000000000000
deg: 5
c5: 575
c0: 68
skew: 0.65
type: snfs
lss: 1
rlim: 17800000
alim: 17800000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6

Factor base limits: 17800000/17800000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [8900000, 25100001)
Primes: RFBsize:1139344, AFBsize:1139550, largePrimes:39498154 encountered
Relations: rels:43640536, finalFF:2563810
Max relations in full relation-set: 32
Initial matrix: 2278961 x 2563810 with sparse part having weight 390927558.
Pruned matrix : 2046135 x 2057593 with weight 354661269.
Total sieving time: 1150.15 hours.
Total relation processing time: 5.81 hours.
Matrix solve time: 90.28 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
snfs,204,5,0,0,0,0,0,0,0,0,17800000,17800000,29,29,56,56,2.6,2.6,100000
total time: 1246.67 hours.

Jun 11, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 11, 2009

(58·10¹⁵³-31)/9 = 6(4)₁₅₂1_<154> = 3 · 367 · 112967 · 2319381799539473_<16> · 165136459534555368901_<21> · C111

C111 = P50 · P61

P50 = 17078280205792035788335884856822731960474470615281_<50>

P61 = 7921131453941733646557818615716638624170555497980778464200671_<61>

Number: 64441_153
N=135279302517329798555025774871892764507712533727343188426012269005859259034731526227526481196165806601223053551
  ( 111 digits)
Divisors found:
 r1=17078280205792035788335884856822731960474470615281
 r2=7921131453941733646557818615716638624170555497980778464200671
Version: 
Total time: 10.01 hours.
Scaled time: 23.92 units (timescale=2.390).
Factorization parameters were as follows:
name: 64441_153
n: 135279302517329798555025774871892764507712533727343188426012269005859259034731526227526481196165806601223053551
skew: 23605.40
# norm 1.03e+15
c5: 22800
c4: 2606101498
c3: -45023322297711
c2: -1636176262836888459
c1: 13673763986598234398219
c0: -27225391059235964049208347
# alpha -5.58
Y1: 181355987777
Y0: -1427769303683968481770
# Murphy_E 9.32e-10
# M 81165317231035287838596792647390099905123823365903785899096838405611340060018680107531939427877027642720548542
type: gnfs
rlim: 2100000
alim: 2100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1050000, 1800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8141639
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 387419 x 387667
Polynomial selection time: 0.76 hours.
Total sieving time: 8.27 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 0.31 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000
total time: 10.01 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673795)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339)

2·10¹⁷¹-9 = 1(9)₁₇₀1_<172> = 11² · 541 · 77524813986331865479_<20> · 334794278410722364007416315208828631701999789_<45> · C103

C103 = P40 · P63

P40 = 5034377696798900669436721889289682064351_<40>

P63 = 233820618672097095012926459422107581471500507709899340258393951_<63>

Number: 19991_171
N=1177141307694526201464716642183051523982966901517506432181852284630204945543901005711357960481491140801
  ( 103 digits)
Divisors found:
 r1=5034377696798900669436721889289682064351
 r2=233820618672097095012926459422107581471500507709899340258393951
Version: 
Total time: 3.55 hours.
Scaled time: 8.41 units (timescale=2.373).
Factorization parameters were as follows:
name: 19991_171
n: 1177141307694526201464716642183051523982966901517506432181852284630204945543901005711357960481491140801
skew: 5404.07
# norm 2.21e+13
c5: 43680
c4: -5969942
c3: -1865578457695
c2: -7134246430272257
c1: 9256714106389184315
c0: 106135789530131846696475
# alpha -5.04
Y1: 78574733761
Y0: -30627336107087582486
# Murphy_E 2.77e-09
# M 912930077984427313258403547379730171018387886625134225735594264395813050211885657140230567293533718485
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4960858
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 221323 x 221571
Polynomial selection time: 0.28 hours.
Total sieving time: 2.84 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 3.55 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673795)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339)

Jun 11, 2009

By Sinkiti Sibata / GGNFS / Jun 11, 2009

(58·10¹⁵⁹-31)/9 = 6(4)₁₅₈1_<160> = 3² · 199 · 1093443781_<10> · C148

C148 = P42 · P107

P42 = 209900031606919638060250968011950579085083_<42>

P107 = 15677648943826422381981429129925161545478792495477603112103677976852749787973098495048186703923564765299937_<107>

Number: 64441_159
N=3290739008831356339219803947719937682395452958069035022616313113583137251250683536978098961627564466067632336829533503848993054608278016739537539771
  ( 148 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=209900031606919638060250968011950579085083 (pp42)
 r2=15677648943826422381981429129925161545478792495477603112103677976852749787973098495048186703923564765299937 (pp107)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 63.25 hours.
Scaled time: 162.17 units (timescale=2.564).
Factorization parameters were as follows:
name: 64441_159
n: 3290739008831356339219803947719937682395452958069035022616313113583137251250683536978098961627564466067632336829533503848993054608278016739537539771
m: 100000000000000000000000000000000
deg: 5
c5: 29
c0: -155
skew: 1.40
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1200000, 3700001)
Primes: RFBsize:176302, AFBsize:176834, largePrimes:9998293 encountered
Relations: rels:11718185, finalFF:504709
Max relations in full relation-set: 28
Initial matrix: 353201 x 504709 with sparse part having weight 72785254.
Pruned matrix : 312059 x 313889 with weight 49222426.
Total sieving time: 61.84 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.08 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,51,51,2.4,2.4,100000
total time: 63.25 hours.
 --------- CPU info (if available) ----------

Jun 10, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM 6.2.3 / Jun 10, 2009

(58·10¹⁴²-31)/9 = 6(4)₁₄₁1_<143> = 13 · 23 · 16921 · 9524591 · C130

C130 = P37 · P93

P37 = 1527327053387300561922655200517536151_<37>

P93 = 875608341824785328181448860447816700700338797768291942567678323978198356949700451593224781019_<93>

Number: 64441_142
N=1337340308640589620461913848808391038150893661277969899138772830138477829834862994727105090713233954169870052955561019646391117869
  ( 130 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=1527327053387300561922655200517536151
 r2=875608341824785328181448860447816700700338797768291942567678323978198356949700451593224781019
Version: 
Total time: 5.36 hours.
Scaled time: 12.80 units (timescale=2.390).
Factorization parameters were as follows:
n: 1337340308640589620461913848808391038150893661277969899138772830138477829834862994727105090713233954169870052955561019646391117869
m: 20000000000000000000000000000
deg: 5
c5: 725
c0: -124
skew: 0.70
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 2350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4659016
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 353852 x 354100
Total sieving time: 4.60 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,2400000,2400000,26,26,49,49,2.3,2.3,50000
total time: 5.36 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673795)
Calibrating delay using timer specific routine.. 5344.71 BogoMIPS (lpj=2672355)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672378)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339)

(58·10¹⁵⁷-31)/9 = 6(4)₁₅₆1_<158> = 2648031729249449_<16> · 361382784217781834150297587_<27> · C116

C116 = P35 · P37 · P46

P35 = 37727530996966089900393367642062277_<35>

P37 = 1174640614178015563795193560615453921_<37>

P46 = 1519607549694666831724736274979975973591058671_<46>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 67343369134565438844901431185162974421508417199500632120324380433626581713504247852334181996419224033954426575162507 (116 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3241163861
Step 1 took 4758ms
Step 2 took 4056ms
********** Factor found in step 2: 37727530996966089900393367642062277
Found probable prime factor of 35 digits: 37727530996966089900393367642062277
Composite cofactor 1784992745482892754448907629357284460115231211814851591365797111193768269607998991 has 82 digits
Wed Jun 10 20:58:37 2009  
Wed Jun 10 20:58:37 2009  
Wed Jun 10 20:58:37 2009  Msieve v. 1.39
Wed Jun 10 20:58:37 2009  random seeds: 09b54ec4 e4f52600
Wed Jun 10 20:58:37 2009  factoring 1784992745482892754448907629357284460115231211814851591365797111193768269607998991 (82 digits)
Wed Jun 10 20:58:38 2009  searching for 15-digit factors
Wed Jun 10 20:58:39 2009  commencing quadratic sieve (82-digit input)
Wed Jun 10 20:58:39 2009  using multiplier of 2
Wed Jun 10 20:58:39 2009  using VC8 32kb sieve core
Wed Jun 10 20:58:39 2009  sieve interval: 12 blocks of size 32768
Wed Jun 10 20:58:39 2009  processing polynomials in batches of 17
Wed Jun 10 20:58:39 2009  using a sieve bound of 1334353 (51039 primes)
Wed Jun 10 20:58:39 2009  using large prime bound of 126763535 (26 bits)
Wed Jun 10 20:58:39 2009  using trial factoring cutoff of 27 bits
Wed Jun 10 20:58:39 2009  polynomial 'A' values have 10 factors
Wed Jun 10 21:12:23 2009  51267 relations (26158 full + 25109 combined from 276608 partial), need 51135
Wed Jun 10 21:12:26 2009  begin with 302766 relations
Wed Jun 10 21:12:26 2009  reduce to 73151 relations in 2 passes
Wed Jun 10 21:12:26 2009  attempting to read 73151 relations
Wed Jun 10 21:12:26 2009  recovered 73151 relations
Wed Jun 10 21:12:26 2009  recovered 63902 polynomials
Wed Jun 10 21:12:26 2009  attempting to build 51267 cycles
Wed Jun 10 21:12:26 2009  found 51267 cycles in 1 passes
Wed Jun 10 21:12:26 2009  distribution of cycle lengths:
Wed Jun 10 21:12:26 2009     length 1 : 26158
Wed Jun 10 21:12:26 2009     length 2 : 25109
Wed Jun 10 21:12:26 2009  largest cycle: 2 relations
Wed Jun 10 21:12:26 2009  matrix is 51039 x 51267 (7.7 MB) with weight 1598396 (31.18/col)
Wed Jun 10 21:12:26 2009  sparse part has weight 1598396 (31.18/col)
Wed Jun 10 21:12:27 2009  filtering completed in 4 passes
Wed Jun 10 21:12:27 2009  matrix is 36342 x 36406 (6.0 MB) with weight 1273006 (34.97/col)
Wed Jun 10 21:12:27 2009  sparse part has weight 1273006 (34.97/col)
Wed Jun 10 21:12:27 2009  saving the first 48 matrix rows for later
Wed Jun 10 21:12:27 2009  matrix is 36294 x 36406 (4.5 MB) with weight 1009038 (27.72/col)
Wed Jun 10 21:12:27 2009  sparse part has weight 825277 (22.67/col)
Wed Jun 10 21:12:27 2009  matrix includes 64 packed rows
Wed Jun 10 21:12:27 2009  using block size 14562 for processor cache size 4096 kB
Wed Jun 10 21:12:27 2009  commencing Lanczos iteration
Wed Jun 10 21:12:27 2009  memory use: 4.3 MB
Wed Jun 10 21:12:31 2009  lanczos halted after 576 iterations (dim = 36292)
Wed Jun 10 21:12:31 2009  recovered 17 nontrivial dependencies
Wed Jun 10 21:12:31 2009  prp37 factor: 1174640614178015563795193560615453921
Wed Jun 10 21:12:31 2009  prp46 factor: 1519607549694666831724736274979975973591058671
Wed Jun 10 21:12:31 2009  elapsed time 00:13:54

(58·10¹⁹⁵-31)/9 = 6(4)₁₉₄1_<196> = 3³ · 121205741 · 843725777 · 3449383496233_<13> · 131039417139088721513_<21> · 43268274902688917839656473_<26> · C120

C120 = P34 · P86

P34 = 3808947365887241518949456612924387_<34>

P86 = 31331358494823262828693743658366323430037124627429151340540267581059886550031789827861_<86>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 119339495408525915193752433668177694063200767597864676491438032551608032555488259949937499272744109343579204370538946207 (120 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2513972108
Step 1 took 4243ms
Step 2 took 4087ms
********** Factor found in step 2: 3808947365887241518949456612924387
Found probable prime factor of 34 digits: 3808947365887241518949456612924387
Probable prime cofactor 31331358494823262828693743658366323430037124627429151340540267581059886550031789827861 has 86 digits

Jun 10, 2009 (3rd)

By Sinkiti Sibata / Msieve / Jun 10, 2009

(58·10¹³⁹-31)/9 = 6(4)₁₃₈1_<140> = 107 · 80387 · C133

C133 = P62 · P72

P62 = 30526319028262238359498114223427853590308640702586934246165653_<62>

P72 = 245437798286995703352529829459865094652787031237088609961669260962599733_<72>

Number: 64441_139
N=7492312532103105949786185547559062061162821631251861694339200059483794392807555650992115878275808584900967323428573672574393851570649
  ( 133 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=30526319028262238359498114223427853590308640702586934246165653 (pp62)
 r2=245437798286995703352529829459865094652787031237088609961669260962599733 (pp72)
Version: Msieve-1.40
Total time: 7.19 hours.
Scaled time: 18.43 units (timescale=2.564).
Factorization parameters were as follows:
name: 64441_139
n: 7492312532103105949786185547559062061162821631251861694339200059483794392807555650992115878275808584900967323428573672574393851570649
m: 10000000000000000000000000000
deg: 5
c5: 29
c0: -155
skew: 1.40
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 254885 x 255133
Total sieving time: 7.19 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 7.19 hours.
 --------- CPU info (if available) ----------

(58·10¹³⁶-31)/9 = 6(4)₁₃₅1_<137> = 13 · 47939 · 4176817 · 5558906216847676501769_<22> · C103

C103 = P39 · P64

P39 = 633355274586104563509265411646604936091_<39>

P64 = 7031872289102237803989792955009556850261052778421728047172153941_<64>

Number: 64441_136
N=4453673404518767477016279696608870096235646732603416366253344277217826059089646595306167583295118784631
  ( 103 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=633355274586104563509265411646604936091 (pp39)
 r2=7031872289102237803989792955009556850261052778421728047172153941 (pp64)
Version: Msieve-1.40
Total time: 6.33 hours.
Scaled time: 13.23 units (timescale=2.092).
Factorization parameters were as follows:
name: 64441_136
n: 4453673404518767477016279696608870096235646732603416366253344277217826059089646595306167583295118784631
m: 2000000000000000000000000000
deg: 5
c5: 145
c0: -248
skew: 1.11
type: snfs
lss: 1
rlim: 1430000
alim: 1430000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1430000/1430000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [715000, 1540001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 221217 x 221449
Total sieving time: 6.01 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,138.000,5,0,0,0,0,0,0,0,0,1430000,1430000,26,26,48,48,2.3,2.3,75000
total time: 6.33 hours.
 --------- CPU info (if available) ----------

Jun 10, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Jun 10, 2009

(58·10¹⁴³-31)/9 = 6(4)₁₄₂1_<144> = 7 · 26683 · C139

C139 = P48 · P92

P48 = 342602696066354823193997798573370772650604826459_<48>

P92 = 10070754559295277760249566975349829558487644575316533280632068011095277845540303297091747479_<92>

Number: n
N=3450267663437097158942528653580634242478862649008434714689633551830456226513641347055880654051774240658549019677828282557885675975845746861
  ( 139 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=342602696066354823193997798573370772650604826459 (pp48)
 r2=10070754559295277760249566975349829558487644575316533280632068011095277845540303297091747479 (pp92)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 9.29 hours.
Scaled time: 24.72 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_4_142_1
n: 3450267663437097158942528653580634242478862649008434714689633551830456226513641347055880654051774240658549019677828282557885675975845746861
m: 50000000000000000000000000000
deg: 5
c5: 464
c0: -775
skew: 1.11
type: snfs
lss: 1
rlim: 1920000
alim: 1920000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 100000
Factor base limits: 1920000/1920000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [960000, 2560001)
Primes: RFBsize:143414, AFBsize:143328, largePrimes:7362448 encountered
Relations: rels:6792022, finalFF:324534
Max relations in full relation-set: 28
Initial matrix: 286809 x 324534 with sparse part having weight 33806415.
Pruned matrix : 273676 x 275174 with weight 26500476.
Total sieving time: 8.45 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.31 hours.
Total square root time: 0.36 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1920000,1920000,28,28,56,56,2.3,2.3,100000
total time: 9.29 hours.
 --------- CPU info (if available) ----------

(64·10²¹¹-1)/9 = 7(1)₂₁₁_<212> = 71 · 236879 · C205

C205 = P51 · P73 · P82

P51 = 643057363391772539930509437073292784585159499609363_<51>

P73 = 1745172861926735098113731730696839166480106417061262769272337987121179921_<73>

P82 = 3767596531307051231311670269449565300807368866581972286491213685667330975891607973_<82>

Number: n
N=4228171113635725656993542677616599234274247410151050025665989637373613111151661914697823742490214806353627808142322565179091025263513992977047419355250018661759926941431327488296372808576073462781830975279
  ( 205 digits)
SNFS difficulty: 212 digits.
Divisors found:

Wed Jun 10 10:00:33 2009  prp51 factor: 643057363391772539930509437073292784585159499609363
Wed Jun 10 10:00:33 2009  prp73 factor: 1745172861926735098113731730696839166480106417061262769272337987121179921
Wed Jun 10 10:00:33 2009  prp82 factor: 3767596531307051231311670269449565300807368866581972286491213685667330975891607973
Wed Jun 10 10:00:33 2009  elapsed time 31:29:32 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20050930-k8
Total time: 113.30 hours.
Scaled time: 173.69 units (timescale=1.533).
Factorization parameters were as follows:
name: KA_7_1_211
n: 4228171113635725656993542677616599234274247410151050025665989637373613111151661914697823742490214806353627808142322565179091025263513992977047419355250018661759926941431327488296372808576073462781830975279
m: 200000000000000000000000000000000000
deg: 6
c6: 10
c0: -1
skew: 0.68
type: snfs
lss: 1
rlim: 25000000
alim: 25000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 25000000/25000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 57/57
Sieved  special-q in [12500000, 33599990)
Primes: RFBsize:1565927, AFBsize:1564806, largePrimes:38685477 encountered
Relations: rels:38036155, finalFF:2004157
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 7242530 hash collisions in 46516704 relations
Msieve: matrix is 4096749 x 4096997 (1112.1 MB)

Total sieving time: 112.10 hours.
Total relation processing time: 1.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,212,6,0,0,0,0,0,0,0,0,25000000,25000000,29,29,57,57,2.6,2.6,100000
total time: 113.30 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2748k kernel code, 36964k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830496)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Total of 4 processors activated (22643.71 BogoMIPS).

(58·10¹⁶⁶-31)/9 = 6(4)₁₆₅1_<167> = 13 · 3673 · 29669 · 237791 · C153

C153 = P39 · P114

P39 = 278920477089003851435716097376075149113_<39>

P114 = 685871066084268679784539153202401450105862248666859370968796776773667518547705937015346850643694246601536809957367_<114>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 191303484973767908831484385073305410609307331952420749269253261812451372451202115512906550164548598382034855111281939724339195680624834936274137697865471 (153 digits)
Using B1=2144000, B2=2854157680, polynomial Dickson(6), sigma=333789588
Step 1 took 32822ms
Step 2 took 10920ms
********** Factor found in step 2: 278920477089003851435716097376075149113
Found probable prime factor of 39 digits: 278920477089003851435716097376075149113
Probable prime cofactor 685871066084268679784539153202401450105862248666859370968796776773667518547705937015346850643694246601536809957367 has 114 digits

(32·10¹⁶⁸-23)/9 = 3(5)₁₆₇3_<169> = 99787 · 35110973901895945362440267_<26> · C139

C139 = P59 · P80

P59 = 25148140795056499081497427625137336246538170970339484970739_<59>

P80 = 40353828462554322758429865388999567026694081322219443685122757666884960343307763_<80>

Number: n
N=1014823759795874448307906099141215069716476101479601314893226854770980254415688256799200840659055310493204808095612598493667121316526546857
  ( 139 digits)
SNFS difficulty: 170 digits.
Divisors found:

Wed Jun 10 22:39:16 2009  prp59 factor: 25148140795056499081497427625137336246538170970339484970739
Wed Jun 10 22:39:16 2009  prp80 factor: 40353828462554322758429865388999567026694081322219443685122757666884960343307763
Wed Jun 10 22:39:16 2009  elapsed time 01:42:21 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 40.62 hours.
Scaled time: 63.49 units (timescale=1.563).
Factorization parameters were as follows:
name: KA_3_5_167_3
n: 1014823759795874448307906099141215069716476101479601314893226854770980254415688256799200840659055310493204808095612598493667121316526546857
m: 4000000000000000000000000000000000
deg: 5
c5: 125
c0: -92
skew: 0.94
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2400000, 4648807)
Primes: RFBsize:335439, AFBsize:335677, largePrimes:16462283 encountered
Relations: rels:15982118, finalFF:631639
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1679083 hash collisions in 17631665 relations
Msieve: matrix is 762700 x 762948 (205.3 MB)

Total sieving time: 40.05 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000
total time: 40.62 hours.
 --------- CPU info (if available) ----------

(46·10¹⁶⁸+53)/9 = 5(1)₁₆₇7_<169> = 11 · 2383919 · 404892423714526201213_<21> · C141

C141 = P57 · P85

P57 = 130013906438737421609827744440291958180593859853561963893_<57>

P85 = 3702556412970577933431326070205991960265739985195153009374566172308595834356085499657_<85>

Number: n
N=481383823060103954194458622525066612872526569817422802914373422723167098834287235699476136882982546717677639945688012941180066526049097884701
  ( 141 digits)
SNFS difficulty: 171 digits.
Divisors found:

Wed Jun 10 23:32:14 2009  prp57 factor: 130013906438737421609827744440291958180593859853561963893
Wed Jun 10 23:32:14 2009  prp85 factor: 3702556412970577933431326070205991960265739985195153009374566172308595834356085499657
Wed Jun 10 23:32:14 2009  elapsed time 02:34:18 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 52.58 hours.
Scaled time: 139.85 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_1_167_7
n: 481383823060103954194458622525066612872526569817422802914373422723167098834287235699476136882982546717677639945688012941180066526049097884701
m: 5000000000000000000000000000000000
deg: 5
c5: 368
c0: 1325
skew: 1.29
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 5496571)
Primes: RFBsize:348513, AFBsize:348491, largePrimes:16732815 encountered
Relations: rels:16217712, finalFF:697188
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1947970 hash collisions in 18297886 relations
Msieve: matrix is 856679 x 856927 (229.3 MB)

Total sieving time: 51.90 hours.
Total relation processing time: 0.67 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 52.58 hours.
 --------- CPU info (if available) ----------

Jun 10, 2009

By Dmitry Domanov / ggnfs/msieve 1.41 / Jun 10, 2009

(58·10¹⁶¹-31)/9 = 6(4)₁₆₀1_<162> = 7 · 67 · C160

C160 = P58 · P102

P58 = 4093134095623509822924789862483442313088777192093517929121_<58>

P102 = 335704117919347485954227762146677853991802972588438738421183653051486156771646723097088789614286700309_<102>

N=1374081971096896470030798389007344231224828239753612887941246150201374081971096896470030798389007344231224828239753612887941246150201374081971096896470030798389
  ( 160 digits)
SNFS difficulty: 163 digits.
Divisors found:
r1=4093134095623509822924789862483442313088777192093517929121 (pp58)
r2=335704117919347485954227762146677853991802972588438738421183653051486156771646723097088789614286700309 (pp102)
Version: Msieve v. 1.41
Total time: 34.54 hours.
Scaled time: 68.66 units (timescale=1.988).
Factorization parameters were as follows:
n: 1374081971096896470030798389007344231224828239753612887941246150201374081971096896470030798389007344231224828239753612887941246150201374081971096896470030798389
m: 200000000000000000000000000000000
deg: 5
c5: 145
c0: -248
skew: 1.11
type: snfs
lss: 1
rlim: 3700000
alim: 3700000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3700000/3700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1850000, 3750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 703581 x 703829
Total sieving time: 33.57 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.76 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,163.000,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,51,51,2.4,2.4,100000
total time: 34.54 hours.
 --------- CPU info (if available) ----------

(58·10¹²¹-31)/9 = 6(4)₁₂₀1_<122> = 61 · C121

C121 = P51 · P70

P51 = 464920469417375193572200232662861103514882907303691_<51>

P70 = 2272359192297716094864344333471243185707117555901008894066572651550791_<70>

N=1056466302367941712204007285974499089253187613843351548269581056466302367941712204007285974499089253187613843351548269581
  ( 121 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=464920469417375193572200232662861103514882907303691 (pp51)
 r2=2272359192297716094864344333471243185707117555901008894066572651550791 (pp70)
Version: Msieve v. 1.41
Total time: 2.40 hours.
Scaled time: 4.75 units (timescale=1.982).
Factorization parameters were as follows:
n: 1056466302367941712204007285974499089253187613843351548269581056466302367941712204007285974499089253187613843351548269581
m: 2000000000000000000000000
deg: 5
c5: 145
c0: -248
skew: 1.11
type: snfs
lss: 1
rlim: 810000
alim: 810000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 810000/810000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [405000, 955001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 89180 x 89409
Total sieving time: 2.31 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,123.000,5,0,0,0,0,0,0,0,0,810000,810000,25,25,46,46,2.2,2.2,50000
total time: 2.40 hours.
 --------- CPU info (if available) ----------

2·10¹⁷¹+9 = 2(0)₁₇₀9_<172> = 7² · 3181 · 55360013450292649181_<20> · C147

C147 = P36 · C111

P36 = 332698364302461530229511915253909389_<36>

C111 = [696664039882704701975721828063080480151348232344868154988400858011494357876797914528601178091872120507409021829_<111>]

C147=P36*C111
C147=332698364302461530229511915253909389<36>*6966640398827047019757218280630804801513482323448681549884008580114943578767979145286011780918721205
07409021829<111>

2·10¹⁷¹-9 = 1(9)₁₇₀1_<172> = 11² · 541 · 77524813986331865479_<20> · C147

C147 = P45 · C103

P45 = 334794278410722364007416315208828631701999789_<45>

C103 = [1177141307694526201464716642183051523982966901517506432181852284630204945543901005711357960481491140801_<103>]

C147=P45*C103
C147=334794278410722364007416315208828631701999789<45>*1177141307694526201464716642183051523982966901517506432181852284630204945543901005711357960481491140801<103>

(19·10¹⁷¹+11)/3 = 6(3)₁₇₀7_<172> = 17 · C171

C171 = P38 · P134

P38 = 25310355343227723063527451248702974397_<38>

P134 = 14719233078943155176128039350114423645313440687246188053637990114166597188559130734521853858080446251446814489501657905107267542908413_<134>

N=372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901961
  ( 171 digits)
SNFS difficulty: 172 digits.
Divisors found:
r1=25310355343227723063527451248702974397 (pp38)
r2=14719233078943155176128039350114423645313440687246188053637990114166597188559130734521853858080446251446814489501657905107267542908413 (pp134)
Version: Msieve v. 1.41
Total time: 60.02 hours.
Scaled time: 118.95 units (timescale=1.982).
Factorization parameters were as follows:
n: 372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901961
m: 10000000000000000000000000000000000
deg: 5
c5: 190
c0: 11
skew: 0.57
type: snfs
lss: 1
rlim: 5200000
alim: 5200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2600000, 5600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 968092 x 968339
Total sieving time: 58.28 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.44 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,172.000,5,0,0,0,0,0,0,0,0,5200000,5200000,27,27,52,52,2.4,2.4,100000
total time: 60.02 hours.
 --------- CPU info (if available) ----------

Jun 9, 2009 (6th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Jun 9, 2009

(19·10¹⁶⁸-7)/3 = 6(3)₁₆₇1_<169> = 2194638858649_<13> · 40919237740408367_<17> · C140

C140 = P33 · P43 · P65

P33 = 241612742823526534650909688816909_<33>

P43 = 6233028353893749389383907598437941819707581_<43>

P65 = 46829854524857710207917680811999264463722603395805706199658829933_<65>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 70524781078454483013796349470455628281280408219714768823579374956912502233135840477646284348677885337018782934159342461747464081084903832357 (140 digits)
Using B1=1046000, B2=1045563762, polynomial Dickson(6), sigma=4279458543
Step 1 took 14398ms
Step 2 took 6069ms
********** Factor found in step 2: 241612742823526534650909688816909
Found probable prime factor of 33 digits: 241612742823526534650909688816909
Composite cofactor 291891811062157604903137230387297274730508932417381545453883499198383081542958422133134293492730462669822073 has 108 digits

Number: n
N=291891811062157604903137230387297274730508932417381545453883499198383081542958422133134293492730462669822073
  ( 108 digits)
Divisors found:
 r1=6233028353893749389383907598437941819707581 (pp43)
 r2=46829854524857710207917680811999264463722603395805706199658829933 (pp65)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 10.60 hours.
Scaled time: 27.41 units (timescale=2.585).
Factorization parameters were as follows:
n: 291891811062157604903137230387297274730508932417381545453883499198383081542958422133134293492730462669822073
name: KA_6_3_167_1
Y0: -561705156206669121855
Y1:  197076323297
c0:  203638276723910946303732994
c1:  11325872543009262796133
c2: -569264334750724044
c3: -25179488545454
c4:  320512286
c5:  5220
skew: 30973.96
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1250000, 2400001)
Primes: RFBsize:183072, AFBsize:183947, largePrimes:15902600 encountered
Relations: rels:14110942, finalFF:413269
Max relations in full relation-set: 28
Initial matrix: 367098 x 413269 with sparse part having weight 38019278.
Pruned matrix : 336788 x 338687 with weight 28286917.
Total sieving time: 9.14 hours.
Total relation processing time: 0.52 hours.
Matrix solve time: 0.52 hours.
Total square root time: 0.42 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000
total time: 10.60 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶⁸+11)/9 = 5(7)₁₆₇9_<169> = 7 · 3631 · 18695220169_<11> · 4918399219037_<13> · C142

C142 = P65 · P78

P65 = 22052280975865092692525800150982807244061830250598730578589972079_<65>

P78 = 112105950947613006602391329605195305461345950480308802909553359992427651958801_<78>

Number: n
N=2472191929363311566113899520147805286457413223560785065597047238434828374391621498727947661965678444475466010146628383966893721000200248317279
  ( 142 digits)
SNFS difficulty: 171 digits.
Divisors found:

Tue Jun 09 23:43:23 2009  prp65 factor: 22052280975865092692525800150982807244061830250598730578589972079
Tue Jun 09 23:43:23 2009  prp78 factor: 112105950947613006602391329605195305461345950480308802909553359992427651958801
Tue Jun 09 23:43:23 2009  elapsed time 01:16:52 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 47.54 hours.
Scaled time: 125.47 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_5_7_167_9
n: 2472191929363311566113899520147805286457413223560785065597047238434828374391621498727947661965678444475466010146628383966893721000200248317279
m: 10000000000000000000000000000000000
deg: 5
c5: 13
c0: 275
skew: 1.84
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 5174293)
Primes: RFBsize:348513, AFBsize:348622, largePrimes:16908539 encountered
Relations: rels:16337061, finalFF:749922
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1847517 hash collisions in 18248277 relations
Msieve: matrix is 844859 x 845107 (224.0 MB)

Total sieving time: 47.00 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 47.54 hours.
 --------- CPU info (if available) ----------

Jun 9, 2009 (5th)

By Sinkiti Sibata / Msieve, GGNFS / Jun 9, 2009

(58·10¹²⁶-31)/9 = 6(4)₁₂₅1_<127> = 3 · 7411 · 17231 · 149711 · 151643837421842767195511_<24> · C90

C90 = P33 · P58

P33 = 230317917783472779280908801355139_<33>

P58 = 3217145707328322487608679926740369461372781503408846476493_<58>

Tue Jun 09 05:40:41 2009  Msieve v. 1.39
Tue Jun 09 05:40:41 2009  random seeds: dba3cd58 e3fe0ec0
Tue Jun 09 05:40:41 2009  factoring 740966300517896959122455501051949913568949425089984203468076083503353610890837643708247527 (90 digits)
Tue Jun 09 05:40:42 2009  searching for 15-digit factors
Tue Jun 09 05:40:44 2009  commencing quadratic sieve (90-digit input)
Tue Jun 09 05:40:44 2009  using multiplier of 23
Tue Jun 09 05:40:44 2009  using 64kb Pentium 4 sieve core
Tue Jun 09 05:40:44 2009  sieve interval: 18 blocks of size 65536
Tue Jun 09 05:40:44 2009  processing polynomials in batches of 6
Tue Jun 09 05:40:44 2009  using a sieve bound of 1611319 (61176 primes)
Tue Jun 09 05:40:44 2009  using large prime bound of 135350796 (27 bits)
Tue Jun 09 05:40:44 2009  using double large prime bound of 433141090259052 (42-49 bits)
Tue Jun 09 05:40:44 2009  using trial factoring cutoff of 49 bits
Tue Jun 09 05:40:44 2009  polynomial 'A' values have 12 factors
Tue Jun 09 07:58:27 2009  61458 relations (16936 full + 44522 combined from 659490 partial), need 61272
Tue Jun 09 07:58:28 2009  begin with 676426 relations
Tue Jun 09 07:58:28 2009  reduce to 148302 relations in 10 passes
Tue Jun 09 07:58:28 2009  attempting to read 148302 relations
Tue Jun 09 07:58:30 2009  recovered 148302 relations
Tue Jun 09 07:58:30 2009  recovered 127865 polynomials
Tue Jun 09 07:58:31 2009  attempting to build 61458 cycles
Tue Jun 09 07:58:31 2009  found 61458 cycles in 5 passes
Tue Jun 09 07:58:31 2009  distribution of cycle lengths:
Tue Jun 09 07:58:31 2009     length 1 : 16936
Tue Jun 09 07:58:31 2009     length 2 : 11789
Tue Jun 09 07:58:31 2009     length 3 : 10877
Tue Jun 09 07:58:31 2009     length 4 : 8015
Tue Jun 09 07:58:31 2009     length 5 : 5699
Tue Jun 09 07:58:31 2009     length 6 : 3616
Tue Jun 09 07:58:31 2009     length 7 : 2045
Tue Jun 09 07:58:31 2009     length 9+: 2481
Tue Jun 09 07:58:31 2009  largest cycle: 17 relations
Tue Jun 09 07:58:31 2009  matrix is 61176 x 61458 (14.8 MB) with weight 3643194 (59.28/col)
Tue Jun 09 07:58:31 2009  sparse part has weight 3643194 (59.28/col)
Tue Jun 09 07:58:33 2009  filtering completed in 3 passes
Tue Jun 09 07:58:33 2009  matrix is 57138 x 57201 (13.9 MB) with weight 3410202 (59.62/col)
Tue Jun 09 07:58:33 2009  sparse part has weight 3410202 (59.62/col)
Tue Jun 09 07:58:33 2009  saving the first 48 matrix rows for later
Tue Jun 09 07:58:33 2009  matrix is 57090 x 57201 (8.7 MB) with weight 2676739 (46.80/col)
Tue Jun 09 07:58:33 2009  sparse part has weight 1950038 (34.09/col)
Tue Jun 09 07:58:33 2009  matrix includes 64 packed rows
Tue Jun 09 07:58:33 2009  using block size 21845 for processor cache size 512 kB
Tue Jun 09 07:58:33 2009  commencing Lanczos iteration
Tue Jun 09 07:58:33 2009  memory use: 8.6 MB
Tue Jun 09 07:59:05 2009  lanczos halted after 905 iterations (dim = 57090)
Tue Jun 09 07:59:05 2009  recovered 18 nontrivial dependencies
Tue Jun 09 07:59:06 2009  prp33 factor: 230317917783472779280908801355139
Tue Jun 09 07:59:06 2009  prp58 factor: 3217145707328322487608679926740369461372781503408846476493
Tue Jun 09 07:59:06 2009  elapsed time 02:18:25

(58·10¹²⁴-31)/9 = 6(4)₁₂₃1_<125> = 13 · 35495845603181599_<17> · C108

C108 = P44 · P65

P44 = 10365682454341659712247078164498849241329819_<44>

P65 = 13473074299298846240802412667099780125728616836040931580302460697_<65>

Number: 64441_124
N=139657609870283601668911375940815747186350774436336032162631242504400623898265616657709917390014558261623843
  ( 108 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=10365682454341659712247078164498849241329819 (pp44)
 r2=13473074299298846240802412667099780125728616836040931580302460697 (pp65)
Version: Msieve-1.40
Total time: 2.53 hours.
Scaled time: 5.12 units (timescale=2.026).
Factorization parameters were as follows:
name: 64441_124
n: 139657609870283601668911375940815747186350774436336032162631242504400623898265616657709917390014558261623843
m: 10000000000000000000000000
deg: 5
c5: 29
c0: -155
skew: 1.40
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 118575 x 118811
Total sieving time: 2.43 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 2.53 hours.
 --------- CPU info (if available) ----------

(58·10¹²⁷-31)/9 = 6(4)₁₂₆1_<128> = 125311 · 609769384018041241_<18> · C105

C105 = P37 · P69

P37 = 4563387659778388937693511871883853581_<37>

P69 = 184817592939026058870817741062463000395240787066825512930841487415611_<69>

Number: 64441_127
N=843394322927897026365377549418668488290321211203191730227702468445885249759060112943616393213835217652991
  ( 105 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=4563387659778388937693511871883853581 (pp37)
 r2=184817592939026058870817741062463000395240787066825512930841487415611 (pp69)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 5.20 hours.
Scaled time: 2.46 units (timescale=0.473).
Factorization parameters were as follows:
name: 64441_127
n: 843394322927897026365377549418668488290321211203191730227702468445885249759060112943616393213835217652991
m: 20000000000000000000000000
deg: 5
c5: 725
c0: -124
skew: 0.70
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 950001)
Primes: RFBsize:78498, AFBsize:78647, largePrimes:2613755 encountered
Relations: rels:2478315, finalFF:176856
Max relations in full relation-set: 28
Initial matrix: 157212 x 176856 with sparse part having weight 13708487.
Pruned matrix : 151509 x 152359 with weight 9984418.
Total sieving time: 4.70 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 5.20 hours.
 --------- CPU info (if available) ----------

(58·10¹³²-31)/9 = 6(4)₁₃₁1_<133> = 3² · 1129 · 1621 · 16858112517613651_<17> · C110

C110 = P44 · P66

P44 = 34466753311020998457630093985809224389075193_<44>

P66 = 673374543227464904583619694013355768942795706554365875033955504127_<66>

Number: 64441_132
N=23209034267342478453008918977902204295017917623204003350478450858683155607960876824016810806416786769624821511
  ( 110 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=34466753311020998457630093985809224389075193 (pp44)
 r2=673374543227464904583619694013355768942795706554365875033955504127 (pp66)
Version: Msieve-1.40
Total time: 4.57 hours.
Scaled time: 9.65 units (timescale=2.112).
Factorization parameters were as follows:
name: 64441_132
n: 23209034267342478453008918977902204295017917623204003350478450858683155607960876824016810806416786769624821511
m: 200000000000000000000000000
deg: 5
c5: 725
c0: -124
skew: 0.70
type: snfs
lss: 1
rlim: 1210000
alim: 1210000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1210000/1210000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [605000, 1205001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 205047 x 205295
Total sieving time: 4.22 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,134.000,5,0,0,0,0,0,0,0,0,1210000,1210000,26,26,47,47,2.3,2.3,75000
total time: 4.57 hours.
 --------- CPU info (if available) ----------

(19·10¹⁶²+11)/3 = 6(3)₁₆₁7_<163> = 29 · 29308250296927268355754842857_<29> · C133

C133 = P49 · P85

P49 = 1291194527858043387638211121856667727905724778137_<49>

P85 = 5771022661503775565834617477507816177513092462939509440235021835776577960538998268717_<85>

Number: 63337_162
N=7451512880678436435055571220951791531103776927461414651478143238821216572496591422500580442134129208413266665885995744128931932640229
  ( 133 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=1291194527858043387638211121856667727905724778137 (pp49)
 r2=5771022661503775565834617477507816177513092462939509440235021835776577960538998268717 (pp85)
Version: Msieve-1.40
Total time: 44.28 hours.
Scaled time: 113.54 units (timescale=2.564).
Factorization parameters were as follows:
name: 63337_162
n: 7451512880678436435055571220951791531103776927461414651478143238821216572496591422500580442134129208413266665885995744128931932640229
m: 200000000000000000000000000000000
deg: 5
c5: 475
c0: 88
skew: 0.71
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 3900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 718107 x 718355
Total sieving time: 44.28 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164.000,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 44.28 hours.
 --------- CPU info (if available) ----------

(58·10¹³⁴-31)/9 = 6(4)₁₃₃1_<135> = 197 · 1217 · 2011 · C127

C127 = P48 · P79

P48 = 271751257225613675644169237643916573741484702123_<48>

P79 = 4918640111763998771075163673454473204834564360412556035749135411931945947164253_<79>

Number: 64441_134
N=1336646634212199628172054116219545703948108311669051107140593065931122376318243861956011152390469522275355700445792232258809119
  ( 127 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=271751257225613675644169237643916573741484702123 (pp48)
 r2=4918640111763998771075163673454473204834564360412556035749135411931945947164253 (pp79)
Version: Msieve-1.40
Total time: 5.11 hours.
Scaled time: 10.66 units (timescale=2.085).
Factorization parameters were as follows:
name: 64441_134
n: 1336646634212199628172054116219545703948108311669051107140593065931122376318243861956011152390469522275355700445792232258809119
m: 1000000000000000000000000000
deg: 5
c5: 29
c0: -155
skew: 1.40
type: snfs
lss: 1
rlim: 1320000
alim: 1320000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1320000/1320000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [660000, 1335001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 204143 x 204372
Total sieving time: 4.89 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1320000,1320000,26,26,48,48,2.3,2.3,75000
total time: 5.11 hours.
 --------- CPU info (if available) ----------

Jun 9, 2009 (4th)

By Wataru Sakai / Msieve / Jun 9, 2009

8·10¹⁹⁷-3 = 7(9)₁₉₆7_<198> = 11 · 23873 · C193

C193 = P54 · P140

P54 = 140821602104944344191203976546352435011228207631215297_<54>

P140 = 21633212827108175193600382697413167083794938983381715227587944143322409584255496805513095712742862874312277348366992788638949071288208626967_<140>

Number: 79997_197
N=3046423688990605590949075220008910789290297521353526045018526064058674120249959063681679188737371621801731130261268911627056811993770063556014211566509141175081777435901341568832039237937114199
  ( 193 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=140821602104944344191203976546352435011228207631215297
 r2=21633212827108175193600382697413167083794938983381715227587944143322409584255496805513095712742862874312277348366992788638949071288208626967
Version: 
Total time: 576.63 hours.
Scaled time: 1145.20 units (timescale=1.986).
Factorization parameters were as follows:
n: 3046423688990605590949075220008910789290297521353526045018526064058674120249959063681679188737371621801731130261268911627056811993770063556014211566509141175081777435901341568832039237937114199
m: 2000000000000000000000000000000000000000
deg: 5
c5: 25
c0: -3
skew: 0.65
type: snfs
lss: 1
rlim: 13900000
alim: 13900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 13900000/13900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6950000, 12650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1981883 x 1982131
Total sieving time: 576.63 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,13900000,13900000,28,28,55,55,2.5,2.5,100000
total time: 576.63 hours.
 --------- CPU info (if available) ----------

(19·10²⁰⁵-7)/3 = 6(3)₂₀₄1_<206> = C206

C206 = P50 · P157

P50 = 14447627005804904645234614420982884085254814760187_<50>

P157 = 4383649529980713498048347690027570917080963555852230233404851224727836970133139701807922977479993415798243544960995282024391148278612096474108353621266360713_<157>

Number: 63331_205
N=63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
  ( 206 digits)
SNFS difficulty: 206 digits.
Divisors found:
 r1=14447627005804904645234614420982884085254814760187
 r2=4383649529980713498048347690027570917080963555852230233404851224727836970133139701807922977479993415798243544960995282024391148278612096474108353621266360713
Version: 
Total time: 968.77 hours.
Scaled time: 1886.19 units (timescale=1.947).
Factorization parameters were as follows:
n: 63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
m: 100000000000000000000000000000000000000000
deg: 5
c5: 19
c0: -7
skew: 0.82
type: snfs
lss: 1
rlim: 19200000
alim: 19200000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 19200000/19200000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [9600000, 18800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3340362 x 3340609
Total sieving time: 968.77 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,19200000,19200000,29,29,56,56,2.6,2.6,100000
total time: 968.77 hours.
 --------- CPU info (if available) ----------

5·10¹⁸³-1 = 4(9)₁₈₃_<184> = 23 · 11633 · C179

C179 = P78 · P101

P78 = 945200151001218657635011445058228730913844677283075507271374283027271720740913_<78>

P101 = 19770909942771694388069711525503787363511760112454424254375327438641837630246346547998813862502042297_<101>

Number: 49999_183
N=18687467063339300864482226350076057990947790954518442661244809556023157509184890061631266374893014251062382502550839254145814568001823896785381915764373465291767423259916504397161
  ( 179 digits)
SNFS difficulty: 184 digits.
Divisors found:
 r1=945200151001218657635011445058228730913844677283075507271374283027271720740913
 r2=19770909942771694388069711525503787363511760112454424254375327438641837630246346547998813862502042297
Version: 
Total time: 197.96 hours.
Scaled time: 379.48 units (timescale=1.917).
Factorization parameters were as follows:
n: 18687467063339300864482226350076057990947790954518442661244809556023157509184890061631266374893014251062382502550839254145814568001823896785381915764373465291767423259916504397161
m: 5000000000000000000000000000000000000
deg: 5
c5: 8
c0: -5
skew: 0.91
type: snfs
lss: 1
rlim: 8300000
alim: 8300000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8300000/8300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4150000, 6050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1592809 x 1593055
Total sieving time: 197.96 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,184,5,0,0,0,0,0,0,0,0,8300000,8300000,28,28,54,54,2.5,2.5,100000
total time: 197.96 hours.
 --------- CPU info (if available) ----------

Jun 9, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / Jun 9, 2009

(58·10¹⁷⁵-31)/9 = 6(4)₁₇₄1_<176> = 55714679 · 5235442620557_<13> · 6232928151786767_<16> · 232729247283047481153469816271_<30> · C111

C111 = P30 · P81

P30 = 454908773934063966445433989859_<30>

P81 = 334807400088451839410571141352346615537487208329487130708430760155293207884291769_<81>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3320324933
Step 1 took 5604ms
Step 2 took 6120ms
********** Factor found in step 2: 454908773934063966445433989859
Found probable prime factor of 30 digits: 454908773934063966445433989859
Probable prime cofactor has 81 digits

(58·10¹⁷⁸-31)/9 = 6(4)₁₇₇1_<179> = 13 · 2985950646001_<13> · 103729544616818033_<18> · C149

C149 = P32 · P118

P32 = 15760309062369653259657044097511_<32>

P118 = 1015528943204105616882829519823718893580572556570303575730382698748439447747013081058056037752739634733914242599226139_<118>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1343471373
Step 1 took 8065ms
Step 2 took 7684ms
********** Factor found in step 2: 15760309062369653259657044097511
Found probable prime factor of 32 digits: 15760309062369653259657044097511
Probable prime cofactor has 118 digits

(58·10¹⁶⁴-31)/9 = 6(4)₁₆₃1_<165> = 23² · 383 · 1106512672418801_<16> · C145

C145 = P34 · P112

P34 = 2153842407797207605842854513620151_<34>

P112 = 1334629507037536053292771611266454391010528184018975178657665649995918628661229565400499790650495782091540687313_<112>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3471677956
Step 1 took 9761ms
Step 2 took 9648ms
********** Factor found in step 2: 2153842407797207605842854513620151
Found probable prime factor of 34 digits: 2153842407797207605842854513620151
Probable prime cofactor has 112 digits

(58·10¹¹⁰-31)/9 = 6(4)₁₀₉1_<111> = 43 · 89 · 709 · 63516017 · C97

C97 = P44 · P53

P44 = 64029904137894160699939453653382583511076709_<44>

P53 = 58400246311501793633262292351880538367399994103824779_<53>

SNFS difficulty: 111 digits.
Divisors found:
 r1=64029904137894160699939453653382583511076709 (pp44)
 r2=58400246311501793633262292351880538367399994103824779 (pp53)
Version: Msieve v. 1.42
Total time: 0.44 hours.
Scaled time: 1.20 units (timescale=2.739).
Factorization parameters were as follows:
n: 3739362172954866891959870454158433811546691347795804580424247967542367672806713155626329363972311
m: 10000000000000000000000
deg: 5
c5: 58
c0: -31
skew: 0.88
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [255000, 405001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 49264 x 49504
Total sieving time: 0.41 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.44 hours.

(58·10¹¹⁷-31)/9 = 6(4)₁₁₆1_<118> = 3 · 151 · C116

C116 = P57 · P59

P57 = 335590386834784504387239992197852758626517636211067047607_<57>

P59 = 42391401048926704326708187457225970435707174842995360025571_<59>

SNFS difficulty: 119 digits.
Divisors found:
 r1=335590386834784504387239992197852758626517636211067047607 (pp57)
 r2=42391401048926704326708187457225970435707174842995360025571 (pp59)
Version: Msieve v. 1.42
Total time: 0.87 hours.
Scaled time: 2.38 units (timescale=2.736).
Factorization parameters were as follows:
n: 14226146676477802305616875153298994358597007603630120186411577140053961246014226146676477802305616875153298994358597
m: 200000000000000000000000
deg: 5
c5: 725
c0: -124
skew: 0.70
type: snfs
lss: 1
rlim: 680000
alim: 680000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 680000/680000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [340000, 640001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 76358 x 76584
Total sieving time: 0.82 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,119.000,5,0,0,0,0,0,0,0,0,680000,680000,25,25,45,45,2.2,2.2,50000
total time: 0.87 hours.

Jun 9, 2009 (2nd)

By Dmitry Domanov / ECMNET/GMP-ECM 6.2.3 / Jun 9, 2009

(58·10²⁰⁴-31)/9 = 6(4)₂₀₃1_<205> = 3² · 227 · 4337 · 8581 · 522523 · 92090216387547454209696971_<26> · C163

C163 = P33 · C130

P33 = 225681106744058840576374317838111_<33>

C130 = [7805049924632190975500473119323412038681495890816226485855611592217951151934608322814868752014324502254708615145997800942003863817_<130>]

[2009-06-08 19:49:16 GMT] a: Factor found! / (probable) 225681106744058840576374317838111  B1: 3000000 sigma: 2193550413 (found in step 2)
[2009-06-08 19:49:16 GMT] a:    Co-factor:  / (Composite) 7805049924632190975500473119323412038681495890816226485855611592217951151934608322814868752014324502254708615145997800942003863817

Jun 9, 2009

Factorizations of 644...441 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jun 8, 2009 (4th)

By Sinkiti Sibata / GGNFS / Jun 8, 2009

(19·10¹⁶⁷+11)/3 = 6(3)₁₆₆7_<168> = 43 · 293 · 377329 · 453317541319_<12> · 59752351280420531883007677311069_<32> · C115

C115 = P33 · P83

P33 = 451635143998643094798214056395897_<33>

P83 = 10890074034432660056461130378390738916429422879842755660108083810782993459835053541_<83>

Number: 63337_167
N=4918340154696878584797715035296828294757600408247419664161466612691457251945246728276473762673861793707090487721277
  ( 115 digits)
Divisors found:
 r1=451635143998643094798214056395897 (pp33)
 r2=10890074034432660056461130378390738916429422879842755660108083810782993459835053541 (pp83)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 56.94 hours.
Scaled time: 26.88 units (timescale=0.472).
Factorization parameters were as follows:
name: 63337_167
n: 4918340154696878584797715035296828294757600408247419664161466612691457251945246728276473762673861793707090487721277
skew: 41061.75
# norm 3.68e+15
c5: 19440
c4: 21217646
c3: -194470098863967
c2: 312840910399259543
c1: 91867653659978829575663
c0: 671399258331606106211358267
# alpha -5.86
Y1: 124570391
Y0: -12039943812266001523120
# Murphy_E 6.16e-10
# M 954209243953220357002622527516688316195460346728018691553675653695772336926992012472982582020705135658684704564758
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2950001)
Primes: RFBsize:250150, AFBsize:250374, largePrimes:7767187 encountered
Relations: rels:7848397, finalFF:722910
Max relations in full relation-set: 28
Initial matrix: 500605 x 722910 with sparse part having weight 66809160.
Pruned matrix : 337685 x 340252 with weight 39640429.
Total sieving time: 50.55 hours.
Total relation processing time: 0.60 hours.
Matrix solve time: 5.44 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 56.94 hours.
 --------- CPU info (if available) ----------

Jun 8, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 8, 2009

(2·10¹⁸⁷+1)/3 = (6)₁₈₆7_<187> = 7³ · 509 · 6807883 · C175

C175 = P48 · P127

P48 = 832957047027425833335054553975046273267520991369_<48>

P127 = 6733830004153306475052063018140541113462683578069214987182885775529843283897925895868514070483631862407825839272911409226010683_<127>

Number: 66667_187
N=5608991155444216796145843881216219198330238812809990245289610633020319055475951327318681109826779298887702399873401084096868614468301634210121695696972944460387689897144795027
  ( 175 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=832957047027425833335054553975046273267520991369
 r2=6733830004153306475052063018140541113462683578069214987182885775529843283897925895868514070483631862407825839272911409226010683
Version: 
Total time: 114.35 hours.
Scaled time: 272.96 units (timescale=2.387).
Factorization parameters were as follows:
n: 5608991155444216796145843881216219198330238812809990245289610633020319055475951327318681109826779298887702399873401084096868614468301634210121695696972944460387689897144795027
m: 20000000000000000000000000000000000000
deg: 5
c5: 25
c0: 4
skew: 0.69
type: snfs
lss: 1
rlim: 8400000
alim: 8400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4200000, 7200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 20006057
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1668637 x 1668883
Total sieving time: 103.50 hours.
Total relation processing time: 3.18 hours.
Matrix solve time: 6.64 hours.
Time per square root: 1.03 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,54,54,2.5,2.5,100000
total time: 114.35 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 8, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Jun 8, 2009

(19·10¹⁶⁵+11)/3 = 6(3)₁₆₄7_<166> = 13127 · 13229 · 1605041 · C152

C152 = P67 · P85

P67 = 2791700755882992873339918737978119310151779702113163525509754308843_<67>

P85 = 8139258648311733962685908037081497873764129440073504717377547968433533826435397148353_<85>

Number: n
N=22722374520819054559718952394116308190104376321680853380543504496639755831541448161475981772137990356697581047755307729999750673967210420073896650785579
  ( 152 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Jun 08 04:39:24 2009  prp67 factor: 2791700755882992873339918737978119310151779702113163525509754308843
Mon Jun 08 04:39:24 2009  prp85 factor: 8139258648311733962685908037081497873764129440073504717377547968433533826435397148353
Mon Jun 08 04:39:24 2009  elapsed time 01:42:10 (Msieve 1.39 - dependency 6)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 33.04 hours.
Scaled time: 54.02 units (timescale=1.635).
Factorization parameters were as follows:
name: KA_6_3_164_7
n: 22722374520819054559718952394116308190104376321680853380543504496639755831541448161475981772137990356697581047755307729999750673967210420073896650785579
m: 1000000000000000000000000000000000
deg: 5
c5: 19
c0: 11
skew: 0.90
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2100000, 4000907)
Primes: RFBsize:296314, AFBsize:296017, largePrimes:15395159 encountered
Relations: rels:14739602, finalFF:489099
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1463873 hash collisions in 15897279 relations
Msieve: matrix is 737574 x 737822 (197.4 MB)

Total sieving time: 32.56 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,56,56,2.4,2.4,100000
total time: 33.04 hours.
 --------- CPU info (if available) ----------

(56·10¹⁶⁹+61)/9 = 6(2)₁₆₈9_<170> = 3³ · 212332831 · C161

C161 = P39 · P39 · P42 · P42

P39 = 424274908169666727454295410341629377361_<39>

P39 = 744256981543256710605164151127424339141_<39>

P42 = 142246468831973644407334999953831883982951_<42>

P42 = 241631107074584670119388266251172464439467_<42>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 10853369863331184124031483771365186333201545340097971388628670188884701563828629413905976457174413200556159317183157365669906297429153018284425120160496591494417 (161 digits)
Using B1=3094000, B2=5707048630, polynomial Dickson(6), sigma=3228879520
Step 1 took 52338ms
Step 2 took 16848ms
********** Factor found in step 2: 424274908169666727454295410341629377361
Found probable prime factor of 39 digits: 424274908169666727454295410341629377361
Composite cofactor 25580984532299850721733509754897028278292393878345135113886787454119781358631871189418843479083638795833911078559833986497 has 122 digits

Number: n
N=25580984532299850721733509754897028278292393878345135113886787454119781358631871189418843479083638795833911078559833986497
  ( 122 digits)
SNFS difficulty: 171 digits.
Divisors found:

Mon Jun 08 05:04:28 2009  prp39 factor: 744256981543256710605164151127424339141
Mon Jun 08 05:04:28 2009  prp42 factor: 142246468831973644407334999953831883982951
Mon Jun 08 05:04:28 2009  prp42 factor: 241631107074584670119388266251172464439467
Mon Jun 08 05:04:28 2009  elapsed time 01:46:24 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 57.37 hours.
Scaled time: 151.98 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_6_2_168_9

# n: 10853369863331184124031483771365186333201545340097971388628670188884701563828629413905976457174413200556159317183157365669906297429153018284425120160496591494417

n: 25580984532299850721733509754897028278292393878345135113886787454119781358631871189418843479083638795833911078559833986497

m: 10000000000000000000000000000000000
deg: 5
c5: 28
c0: 305
skew: 1.61
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 5711327)
Primes: RFBsize:348513, AFBsize:348667, largePrimes:17581904 encountered
Relations: rels:17491753, finalFF:578623
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2140410 hash collisions in 19295644 relations
Msieve: matrix is 855294 x 855542 (227.4 MB)

Total sieving time: 56.51 hours.
Total relation processing time: 0.86 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 57.37 hours.
 --------- CPU info (if available) ----------

Jun 8, 2009

By Serge Batalov / PFGW / Jun 7, 2009

(23·10⁸¹²¹⁴+1)/3 = 7(6)₈₁₂₁₃7_<81215> is PRP.

Jun 7, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jun 7, 2009

(89·10¹⁶⁸+1)/9 = 9(8)₁₆₇9_<169> = 31 · 15467 · 14156321914008218389_<20> · C145

C145 = P46 · P100

P46 = 1197741581225809551137206782460379046419207957_<46>

P100 = 1216371290130096965390512251725852109764456594341931436026498758415155508058087929946270416461522909_<100>

Number: n
N=1456898472398100290050596745119217016354672758605044647270127522188882139954015967734324164186163472619789554745096128190882591606939001790586913
  ( 145 digits)
SNFS difficulty: 171 digits.
Divisors found:

Sun Jun 07 06:14:32 2009  prp46 factor: 1197741581225809551137206782460379046419207957
Sun Jun 07 06:14:32 2009  prp100 factor: 1216371290130096965390512251725852109764456594341931436026498758415155508058087929946270416461522909
Sun Jun 07 06:14:32 2009  elapsed time 01:18:27 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 37.15 hours.
Scaled time: 96.40 units (timescale=2.595).
Factorization parameters were as follows:
name: KA_9_8_167_9
n: 1456898472398100290050596745119217016354672758605044647270127522188882139954015967734324164186163472619789554745096128190882591606939001790586913
m: 10000000000000000000000000000000000
deg: 5
c5: 89
c0: 100
skew: 1.02
type: snfs
lss: 1
rlim: 5200000
alim: 5200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2600000, 4572629)
Primes: RFBsize:361407, AFBsize:361067, largePrimes:16319409 encountered
Relations: rels:15511318, finalFF:797908
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1476171 hash collisions in 17185281 relations
Msieve: matrix is 795559 x 795807 (216.5 MB)

Total sieving time: 36.66 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,56,56,2.4,2.4,100000
total time: 37.15 hours.
 --------- CPU info (if available) ----------

(56·10¹⁷¹-11)/9 = 6(2)₁₇₀1_<172> = 18289 · C168

C168 = P52 · P117

P52 = 1688756690963537752408473787951585430593702236955631_<52>

P117 = 201459835463477766709930841456375992587398927045022191791163930369390792616322549362470313523356697387941237086565619_<117>

Number: n
N=340216645099361486260715305496321407524863153929806015759321024781137417148133972454602341419553951677085801422834612183401072897491509772115600755766975899295873050589
  ( 168 digits)
SNFS difficulty: 173 digits.
Divisors found:

Sun Jun 07 20:39:56 2009  prp52 factor: 1688756690963537752408473787951585430593702236955631
Sun Jun 07 20:39:56 2009  prp117 factor: 201459835463477766709930841456375992587398927045022191791163930369390792616322549362470313523356697387941237086565619
Sun Jun 07 20:39:56 2009  elapsed time 01:43:30 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 62.43 hours.
Scaled time: 166.07 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_2_170_1
n: 340216645099361486260715305496321407524863153929806015759321024781137417148133972454602341419553951677085801422834612183401072897491509772115600755766975899295873050589
m: 20000000000000000000000000000000000
deg: 5
c5: 35
c0: -22
skew: 0.91
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2700000, 6139019)
Primes: RFBsize:374362, AFBsize:374788, largePrimes:18470689 encountered
Relations: rels:18863544, finalFF:793404
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2353896 hash collisions in 20946880 relations
Msieve: matrix is 847908 x 848156 (224.6 MB)

Total sieving time: 61.47 hours.
Total relation processing time: 0.97 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,5400000,5400000,28,28,56,56,2.4,2.4,100000
total time: 62.43 hours.
 --------- CPU info (if available) ----------

(19·10¹⁵⁸+11)/3 = 6(3)₁₅₇7_<159> = 7 · 13 · 109 · 139 · 12507541 · 14102089 · C139

C139 = P48 · P91

P48 = 890298629966988697335260273638928061736248977777_<48>

P91 = 2925220203141326850950535511175349840756501552381707616474921977213766925742775925795078409_<91>

Number: n
N=2604319539208479662296566196626281659401273439107427083867761096506661355606572402680653377381481359641859195173125630014326233603813516793
  ( 139 digits)
SNFS difficulty: 160 digits.
Divisors found:

Sun Jun 07 20:45:45 2009  prp48 factor: 890298629966988697335260273638928061736248977777
Sun Jun 07 20:45:45 2009  prp91 factor: 2925220203141326850950535511175349840756501552381707616474921977213766925742775925795078409
Sun Jun 07 20:45:45 2009  elapsed time 01:45:45 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.03 hours.
Scaled time: 43.80 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_3_157_7
n: 2604319539208479662296566196626281659401273439107427083867761096506661355606572402680653377381481359641859195173125630014326233603813516793
m: 50000000000000000000000000000000
deg: 5
c5: 152
c0: 275
skew: 1.13
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1700000, 3000000)
Primes: RFBsize:243539, AFBsize:243160, largePrimes:13719071 encountered
Relations: rels:13002746, finalFF:619676
Max relations in full relation-set: 28
Initial matrix: 486766 x 619676 with sparse part having weight 94340976.
Pruned matrix : 439537 x 442034 with weight 58453176.

Msieve: found 1164952 hash collisions in 13921564 relations
Msieve: matrix is 561281 x 561529 (150.0 MB)

Total sieving time: 23.75 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,28,28,56,56,2.4,2.4,100000
total time: 24.03 hours.
 --------- CPU info (if available) ----------

Jun 7, 2009

By Sinkiti Sibata / Msieve / Jun 7, 2009

(19·10¹⁶⁰+11)/3 = 6(3)₁₅₉7_<161> = 71 · 78858923431_<11> · 2376673566823_<13> · 19232519182912433163629_<23> · C114

C114 = P49 · P65

P49 = 5145544189689853686084609914300609465992312536511_<49>

P65 = 48093471998115581878663595761747484801061854861862293238174882901_<65>

Number: 63337_160
N=247467085401915310220618172014915005673608575042370220062176194352664913172346163743395659359667859872701712098411
  ( 114 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=5145544189689853686084609914300609465992312536511 (pp49)
 r2=48093471998115581878663595761747484801061854861862293238174882901 (pp65)
Version: Msieve-1.40
Total time: 29.14 hours.
Scaled time: 75.04 units (timescale=2.575).
Factorization parameters were as follows:
name: 63337_160
n: 247467085401915310220618172014915005673608575042370220062176194352664913172346163743395659359667859872701712098411
m: 100000000000000000000000000000000
deg: 5
c5: 19
c0: 11
skew: 0.90
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 640283 x 640531
Total sieving time: 29.14 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 29.14 hours.
 --------- CPU info (if available) ----------

(19·10¹⁵⁵+11)/3 = 6(3)₁₅₄7_<156> = 17 · 2819 · 90377489523395579_<17> · C135

C135 = P47 · P88

P47 = 34157108083670710906043469808823415090877040147_<47>

P88 = 4281017286969461896442622204066901741881371785859940186877570995394406015230096372670563_<88>

Number: 63337_155
N=146227170179078662500471844618178651924786228401446376604148500459079741163926619676302325596862400065732441170848197134506827356092761
  ( 135 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=34157108083670710906043469808823415090877040147 (pp47)
 r2=4281017286969461896442622204066901741881371785859940186877570995394406015230096372670563 (pp88)
Version: Msieve-1.40
Total time: 23.07 hours.
Scaled time: 47.79 units (timescale=2.071).
Factorization parameters were as follows:
name: 63337_155
n: 146227170179078662500471844618178651924786228401446376604148500459079741163926619676302325596862400065732441170848197134506827356092761
m: 10000000000000000000000000000000
deg: 5
c5: 19
c0: 11
skew: 0.90
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 513105 x 513353
Total sieving time: 21.77 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.94 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 23.07 hours.
 --------- CPU info (if available) ----------

Jun 6, 2009 (3rd)

By Sinkiti Sibata / Msieve / Jun 6, 2009

(19·10¹⁴¹+11)/3 = 6(3)₁₄₀7_<142> = 23 · 3424151153_<10> · 254758733191_<12> · C120

C120 = P46 · P74

P46 = 5050129058517986723316852587290974346406186227_<46>

P74 = 62505757846387088561289339012886665141712282005484871401793013435241437139_<74>

Number: 63337_141
N=315662144024728088954673401382175903113016566302661569618687283007998859457218463561321830356053124278841664279548084553
  ( 120 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=5050129058517986723316852587290974346406186227 (pp46)
 r2=62505757846387088561289339012886665141712282005484871401793013435241437139 (pp74)
Version: Msieve-1.40
Total time: 6.59 hours.
Scaled time: 13.82 units (timescale=2.098).
Factorization parameters were as follows:
name: 63337_141
n: 315662144024728088954673401382175903113016566302661569618687283007998859457218463561321830356053124278841664279548084553
m: 10000000000000000000000000000
deg: 5
c5: 190
c0: 11
skew: 0.57
type: snfs
lss: 1
rlim: 1650000
alim: 1650000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1650000/1650000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [825000, 1625001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 277291 x 277539
Total sieving time: 6.17 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,142.000,5,0,0,0,0,0,0,0,0,1650000,1650000,26,26,48,48,2.3,2.3,100000
total time: 6.59 hours.
 --------- CPU info (if available) ----------

(19·10¹⁴⁵+11)/3 = 6(3)₁₄₄7_<146> = 133183 · 818689 · 1404005417_<10> · 121490964551680697_<18> · C109

C109 = P39 · P70

P39 = 512414144904096443350797214360954687769_<39>

P70 = 6645546857480804860225968131089235254175762793540245993870446512951071_<70>

Number: 63337_145
N=3405272210396131896853192046880242928373403317362054445048532704581653759643181140672663734035062647579150599
  ( 109 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=512414144904096443350797214360954687769 (pp39)
 r2=6645546857480804860225968131089235254175762793540245993870446512951071 (pp70)
Version: Msieve-1.40
Total time: 9.27 hours.
Scaled time: 23.67 units (timescale=2.554).
Factorization parameters were as follows:
name: 63337_145
n: 3405272210396131896853192046880242928373403317362054445048532704581653759643181140672663734035062647579150599
m: 100000000000000000000000000000
deg: 5
c5: 19
c0: 11
skew: 0.90
type: snfs
lss: 1
rlim: 1920000
alim: 1920000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1920000/1920000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [960000, 2160001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 296008 x 296256
Total sieving time: 9.27 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1920000,1920000,26,26,49,49,2.3,2.3,100000
total time: 9.27 hours.
 --------- CPU info (if available) ----------

(19·10¹⁴⁴+11)/3 = 6(3)₁₄₃7_<145> = 1439 · 58897 · 2161819295110817870598641_<25> · C113

C113 = P41 · P73

P41 = 16608864835497717889409845648017981835361_<41>

P73 = 2081225022557446636993986742266210526066920283027389665865883672099304039_<73>

Number: 63337_144
N=34566785091912320142172687249517564182023491309663939642348715633880788938470418987969605576911440066471980323079
  ( 113 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=16608864835497717889409845648017981835361 (pp41)
 r2=2081225022557446636993986742266210526066920283027389665865883672099304039 (pp73)
Version: Msieve-1.40
Total time: 11.32 hours.
Scaled time: 23.76 units (timescale=2.099).
Factorization parameters were as follows:
name: 63337_144
n: 34566785091912320142172687249517564182023491309663939642348715633880788938470418987969605576911440066471980323079
m: 100000000000000000000000000000
deg: 5
c5: 19
c0: 110
skew: 1.42
type: snfs
lss: 1
rlim: 1920000
alim: 1920000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1920000/1920000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [960000, 2360001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 338620 x 338848
Total sieving time: 10.80 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.39 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1920000,1920000,26,26,49,49,2.3,2.3,100000
total time: 11.32 hours.
 --------- CPU info (if available) ----------

Jun 6, 2009 (2nd)

By Jo Yeong Uk / GGNFS / Msieve v1.39 / Jun 6, 2009

(19·10¹⁶⁶+11)/3 = 6(3)₁₆₅7_<167> = 67 · 3911 · 14202604430369_<14> · 86380538071123_<14> · 8368840124326806116601083_<25> · C110

C110 = P49 · P61

P49 = 6262082223742718300440148144843541334567401119143_<49>

P61 = 3759255070882753743580420042857440550706597169458132984067267_<61>

Number: 63337_166
N=23540764353889564672128696226443881624693799593278057392043683758795636761529340169115771824957267483793392181
  ( 110 digits)
Divisors found:
 r1=6262082223742718300440148144843541334567401119143
 r2=3759255070882753743580420042857440550706597169458132984067267
Version: 
Total time: 8.56 hours.
Scaled time: 20.44 units (timescale=2.389).
Factorization parameters were as follows:
name: 63337_166
n: 23540764353889564672128696226443881624693799593278057392043683758795636761529340169115771824957267483793392181
skew: 29345.35
# norm 1.91e+15
c5: 40080
c4: 1978609108
c3: -130421089236824
c2: -1597893340708739207
c1: 37398680496777286640604
c0: 277920807332288752590379839
# alpha -6.54
Y1: 138689822447
Y0: -899037708825546047086
# Murphy_E 1.11e-09
# M 19367926142172829006431938429769541855506380602628362297909528725610931992982566228734831217917220084588038212
type: gnfs
rlim: 2100000
alim: 2100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1050000, 1650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7917419
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 364689 x 364937
Polynomial selection time: 0.66 hours.
Total sieving time: 7.02 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000
total time: 8.56 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 6, 2009

By Dmitry Domanov / GGNFS / Jun 6, 2009

(56·10¹⁷⁸+43)/9 = 6(2)₁₇₇7_<179> = 11 · C178

C178 = P59 · P120

P59 = 11344343380024260457115967605538423116332562634899263825067_<59>

P120 = 498624333474077167029242363855886817081848222640868644668813635343289283688929391503016030544074083603519829915383917771_<120>

[06/05 12:08:29] GGNFS-0.77.1-VC8(Sat 01/17/2009) : procrels
[06/05 12:18:07] There were 328787/9999999 duplicates.
[06/05 12:18:07] RelProcTime: 538.1
[06/05 12:19:22] GGNFS-0.77.1-VC8(Sat 01/17/2009) : procrels
[06/05 12:32:10] There were 821816/9694483 duplicates.
[06/05 12:32:10] RelProcTime: 702.5
[06/05 12:33:33] largePrimes: 17825819 , relations: 18543879
[06/05 12:33:50] GGNFS-0.77.1-VC8(Sat 01/17/2009) : matbuild
[06/05 12:36:44] largePrimes: 17825819 , relations: 18543879
[06/05 12:47:26] reduceRelSets dropped relation-set weight from 38957706 to 29025895.
[06/05 12:51:32] reduceRelSets dropped relation-set weight from 29025895 to 28948873.
[06/05 12:51:32] After removing heavy rel-sets, weight is 26752953.
[06/05 12:59:09] Heap stats for matbuild run.
[06/05 12:59:09] Max heap usage: 0 MB
[06/05 12:59:09] malloc/realloc errors: 0 
[06/05 12:59:09] total malloc's : 991 
[06/05 12:59:09] total realloc's: 569 
[06/05 12:59:09] rels:18543879, initialFF:0, finalFF:1674782
[06/05 12:59:09] depinf file written. Run matprune.
[06/05 13:03:14] GGNFS-0.77.1-VC8(Sat 01/17/2009) : matprune
[06/05 13:03:25] Pruning matrix with wt=0.700
[06/05 13:03:25] Initial matrix is 992017 x 1674782 with sparse part having weight 266215805.
[06/05 13:03:26] (total weight is 401811151)
[06/05 13:56:36] Matrix pruned to 813338 x 818362 with weight 93403634.
[06/05 13:56:40] Matrix is pruned. Run matsolve.
[06/05 13:56:40] Heap stats for matprune run:
[06/05 13:56:40] Max heap usage: 0 MB
[06/05 13:56:40] malloc/realloc errors: 0 
[06/05 13:56:40] total malloc's : 16 
[06/05 13:56:40] total realloc's: 0 
[06/05 13:56:55] GGNFS-0.77.1-VC8(Sat 01/17/2009) : matsolve (seed=2116475424)
[06/05 22:37:42] BLanczosTime: 31246.1
[06/05 22:37:42] Heap stats for matsolve run:
[06/05 22:37:42] Max heap usage: 0 MB
[06/05 22:37:42] malloc/realloc errors: 0 
[06/05 22:37:42] total malloc's : 14 
[06/05 22:37:42] total realloc's: 0 
[06/05 22:42:59] GGNFS-0.77.1-VC8(Sat 01/17/2009) : sqrt
[06/05 22:43:01] bmultiplier=1
[06/05 23:07:38] From dependence 0, sqrt obtained:
[06/05 23:07:38]   r1=1
[06/05 23:07:38]   r2=5656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565657
[06/05 23:07:38] sqrtTime: 1478.7
[06/05 23:12:12] GGNFS-0.77.1-VC8(Sat 01/17/2009) : sqrt
[06/05 23:12:13] bmultiplier=1
[06/05 23:36:49] From dependence 1, sqrt obtained:
[06/05 23:36:49]   r1=498624333474077167029242363855886817081848222640868644668813635343289283688929391503016030544074083603519829915383917771 (pp120)
[06/05 23:36:49]   r2=11344343380024260457115967605538423116332562634899263825067 (pp59)
[06/05 23:36:49] (pp=probable prime, c=composite)
[06/05 23:36:49] sqrtTime: 1477.0

Jun 5, 2009 (5th)

By Sinkiti Sibata / Msieve, GGNFS / Jun 5, 2009

(19·10¹²⁷+11)/3 = 6(3)₁₂₆7_<128> = 3457 · 29392248791_<11> · C114

C114 = P41 · P73

P41 = 64869638554838628758245001081530634426441_<41>

P73 = 9608568122148198650049870148335148191834916510556873243141924230269946711_<73>

Number: 63337_127
N=623304341113298190003715456304851113044797613882178039296795487508371893944858702136693299304697768174591119385551
  ( 114 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=64869638554838628758245001081530634426441 (pp41)
 r2=9608568122148198650049870148335148191834916510556873243141924230269946711 (pp73)
Version: Msieve-1.40
Total time: 3.08 hours.
Scaled time: 5.95 units (timescale=1.934).
Factorization parameters were as follows:
name: 63337_127
n: 623304341113298190003715456304851113044797613882178039296795487508371893944858702136693299304697768174591119385551
m: 20000000000000000000000000
deg: 5
c5: 475
c0: 88
skew: 0.71
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 150689 x 150919
Total sieving time: 2.90 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,129.000,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 3.08 hours.
 --------- CPU info (if available) ----------

(55·10¹⁹⁹+53)/9 = 6(1)₁₉₈7_<200> = 67 · 127 · 149 · 15271 · 32537 · 64951 · 3491419 · 76893119 · 2984002608911_<13> · 73272202678356361_<17> · C137

C137 = P49 · P88

P49 = 4646275918046474726914070102202746441538122559419_<49>

P88 = 5476355976757986022100975097151083556451371821389834131152133448924920125725709745151429_<88>

Number: 61117_199
N=25444660893460510317172439394273556297338846060840182666903667766609275787693643836357738825942267824554292636529889428645386199205259751
  ( 137 digits)
Divisors found:
 r1=4646275918046474726914070102202746441538122559419 (pp49)
 r2=5476355976757986022100975097151083556451371821389834131152133448924920125725709745151429 (pp88)
Version: Msieve-1.40
Total time: 455.10 hours.
Scaled time: 1153.23 units (timescale=2.534).
Factorization parameters were as follows:
name: 61117_199
# Murphy_E = 3.193184e-11, selected by Jeff Gilchrist
n: 25444660893460510317172439394273556297338846060840182666903667766609275787693643836357738825942267824554292636529889428645386199205259751
Y0: -195340899491540177501362945
Y1: 1646830578424513
c0: -17264089700630042706198979052928
c1: 4053148267436222996637322534
c2: -5446174057260405430633
c3: -42244614185732804
c4: 45385993146
c5: 89460
skew: 431663.49
type: gnfs
# selected mechanically
rlim: 14600000
alim: 14600000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6
Factor base limits: 14600000/14600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved algebraic special-q in [7300000, 13000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2006714 x 2006962
Total sieving time: 455.10 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,136,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,14600000,14600000,28,28,55,55,2.6,2.6,100000
total time: 455.10 hours.
 --------- CPU info (if available) ----------

(19·10¹²¹+11)/3 = 6(3)₁₂₀7_<122> = 337972093300564182992672797_<27> · C96

C96 = P35 · P61

P35 = 62733293684483999236989225276611999_<35>

P61 = 2987125124779044111070216291606218084493743214162216434936179_<61>

Fri Jun 05 06:31:30 2009  Msieve v. 1.39
Fri Jun 05 06:31:30 2009  random seeds: 2323b060 822852cc
Fri Jun 05 06:31:30 2009  factoring 187392197725064686109742995863136748941619341863639505659853720451164022359704784009624910611821 (96 digits)
Fri Jun 05 06:31:31 2009  searching for 15-digit factors
Fri Jun 05 06:31:33 2009  commencing quadratic sieve (96-digit input)
Fri Jun 05 06:31:33 2009  using multiplier of 61
Fri Jun 05 06:31:33 2009  using 64kb Pentium 4 sieve core
Fri Jun 05 06:31:33 2009  sieve interval: 18 blocks of size 65536
Fri Jun 05 06:31:33 2009  processing polynomials in batches of 6
Fri Jun 05 06:31:33 2009  using a sieve bound of 2231297 (82353 primes)
Fri Jun 05 06:31:33 2009  using large prime bound of 334694550 (28 bits)
Fri Jun 05 06:31:33 2009  using double large prime bound of 2209873982808450 (43-51 bits)
Fri Jun 05 06:31:33 2009  using trial factoring cutoff of 51 bits
Fri Jun 05 06:31:33 2009  polynomial 'A' values have 13 factors
Fri Jun 05 13:06:47 2009  82566 relations (20793 full + 61773 combined from 1213021 partial), need 82449
Fri Jun 05 13:06:51 2009  begin with 1233814 relations
Fri Jun 05 13:06:53 2009  reduce to 211552 relations in 11 passes
Fri Jun 05 13:06:53 2009  attempting to read 211552 relations
Fri Jun 05 13:06:56 2009  recovered 211552 relations
Fri Jun 05 13:06:56 2009  recovered 195515 polynomials
Fri Jun 05 13:06:56 2009  attempting to build 82566 cycles
Fri Jun 05 13:06:57 2009  found 82566 cycles in 7 passes
Fri Jun 05 13:06:57 2009  distribution of cycle lengths:
Fri Jun 05 13:06:57 2009     length 1 : 20793
Fri Jun 05 13:06:57 2009     length 2 : 15102
Fri Jun 05 13:06:57 2009     length 3 : 14124
Fri Jun 05 13:06:57 2009     length 4 : 11079
Fri Jun 05 13:06:57 2009     length 5 : 8138
Fri Jun 05 13:06:57 2009     length 6 : 5400
Fri Jun 05 13:06:57 2009     length 7 : 3467
Fri Jun 05 13:06:57 2009     length 9+: 4463
Fri Jun 05 13:06:57 2009  largest cycle: 22 relations
Fri Jun 05 13:06:57 2009  matrix is 82353 x 82566 (22.0 MB) with weight 5433208 (65.80/col)
Fri Jun 05 13:06:57 2009  sparse part has weight 5433208 (65.80/col)
Fri Jun 05 13:06:59 2009  filtering completed in 3 passes
Fri Jun 05 13:06:59 2009  matrix is 77904 x 77968 (20.9 MB) with weight 5161906 (66.21/col)
Fri Jun 05 13:06:59 2009  sparse part has weight 5161906 (66.21/col)
Fri Jun 05 13:07:00 2009  saving the first 48 matrix rows for later
Fri Jun 05 13:07:00 2009  matrix is 77856 x 77968 (13.2 MB) with weight 4086517 (52.41/col)
Fri Jun 05 13:07:00 2009  sparse part has weight 2989211 (38.34/col)
Fri Jun 05 13:07:00 2009  matrix includes 64 packed rows
Fri Jun 05 13:07:00 2009  using block size 21845 for processor cache size 512 kB
Fri Jun 05 13:07:01 2009  commencing Lanczos iteration
Fri Jun 05 13:07:01 2009  memory use: 12.6 MB
Fri Jun 05 13:08:06 2009  lanczos halted after 1233 iterations (dim = 77852)
Fri Jun 05 13:08:06 2009  recovered 15 nontrivial dependencies
Fri Jun 05 13:08:08 2009  prp35 factor: 62733293684483999236989225276611999
Fri Jun 05 13:08:08 2009  prp61 factor: 2987125124779044111070216291606218084493743214162216434936179
Fri Jun 05 13:08:08 2009  elapsed time 06:36:38

(19·10¹²⁹+11)/3 = 6(3)₁₂₈7_<130> = 62851 · 139720167823_<12> · 58002654641443_<14> · C101

C101 = P35 · P66

P35 = 17449273243471122496481234616760253_<35>

P66 = 712583630602248633508269573326866172600331656507196538198864101611_<66>

Number: 63337_129
N=12434066479203327235310154754897020409422523293225327204362332170782668264539997328386255596218067583
  ( 101 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=17449273243471122496481234616760253 (pp35)
 r2=712583630602248633508269573326866172600331656507196538198864101611 (pp66)
Version: Msieve-1.40
Total time: 3.35 hours.
Scaled time: 7.01 units (timescale=2.092).
Factorization parameters were as follows:
name: 63337_129
n: 12434066479203327235310154754897020409422523293225327204362332170782668264539997328386255596218067583
m: 100000000000000000000000000
deg: 5
c5: 19
c0: 110
skew: 1.42
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 990001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 176273 x 176521
Total sieving time: 3.17 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,131.000,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 3.35 hours.
 --------- CPU info (if available) ----------

(19·10¹³⁸+11)/3 = 6(3)₁₃₇7_<139> = 9539 · 1061453 · C129

C129 = P30 · P100

P30 = 205884879028525378989717723409_<30>

P100 = 3038115476624172547568021652027874523576378588114643432322765099118331016365199930349650938900052879_<100>

Number: 63337_138
N=625502037379458488816395300931864859727403089208807473972117605577143483778134905225062631923110042485477446199442955993596144511
  ( 129 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=205884879028525378989717723409 (pp30)
 r2=3038115476624172547568021652027874523576378588114643432322765099118331016365199930349650938900052879 (pp100)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 9.07 hours.
Scaled time: 23.25 units (timescale=2.564).
Factorization parameters were as follows:
name: 63337_138
n: 625502037379458488816395300931864859727403089208807473972117605577143483778134905225062631923110042485477446199442955993596144511
m: 5000000000000000000000000000
deg: 5
c5: 152
c0: 275
skew: 1.13
type: snfs
lss: 1
rlim: 1550000
alim: 1550000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1550000/1550000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [775000, 1675001)
Primes: RFBsize:117663, AFBsize:117528, largePrimes:3737414 encountered
Relations: rels:3888763, finalFF:406792
Max relations in full relation-set: 28
Initial matrix: 235258 x 406792 with sparse part having weight 39309693.
Pruned matrix : 190098 x 191338 with weight 15984031.
Total sieving time: 8.74 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1550000,1550000,26,26,48,48,2.3,2.3,100000
total time: 9.07 hours.
 --------- CPU info (if available) ----------

(19·10¹³⁵+11)/3 = 6(3)₁₃₄7_<136> = 157 · 1193 · 7127 · 182309 · C122

C122 = P38 · P84

P38 = 65553528374184830411681549262167408477_<38>

P84 = 396991593279050907298492993278089931927123423048089785475114566024909213674236773267_<84>

Number: 63337_135
N=26024199674331107471002085266667364048678991074073173613246618562363142575922389775938957979867675799494856731304022784359
  ( 122 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=65553528374184830411681549262167408477 (pp38)
 r2=396991593279050907298492993278089931927123423048089785475114566024909213674236773267 (pp84)
Version: Msieve-1.40
Total time: 4.12 hours.
Scaled time: 8.62 units (timescale=2.092).
Factorization parameters were as follows:
name: 63337_135
n: 26024199674331107471002085266667364048678991074073173613246618562363142575922389775938957979867675799494856731304022784359
m: 1000000000000000000000000000
deg: 5
c5: 19
c0: 11
skew: 0.90
type: snfs
lss: 1
rlim: 1310000
alim: 1310000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1310000/1310000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [655000, 1180001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 203473 x 203721
Total sieving time: 3.90 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1310000,1310000,26,26,48,48,2.3,2.3,75000
total time: 4.12 hours.
 --------- CPU info (if available) ----------

(19·10¹⁴⁰+11)/3 = 6(3)₁₃₉7_<141> = 7 · 13 · 3407 · 171823361 · 221764604227301363_<18> · C110

C110 = P43 · P68

P43 = 1710045167050240022231811529388514487003039_<43>

P68 = 31349946151692462001498077827253531605274742451697616985120067166313_<68>

Number: 63337_140
N=53609823903986965507620058340145593869320117918452590610271899609036796485551947681698832409120418760549425207
  ( 110 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=1710045167050240022231811529388514487003039 (pp43)
 r2=31349946151692462001498077827253531605274742451697616985120067166313 (pp68)
Version: Msieve-1.40
Total time: 5.90 hours.
Scaled time: 15.13 units (timescale=2.564).
Factorization parameters were as follows:
name: 63337_140
n: 53609823903986965507620058340145593869320117918452590610271899609036796485551947681698832409120418760549425207
m: 10000000000000000000000000000
deg: 5
c5: 19
c0: 11
skew: 0.90
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 1590001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 223122 x 223370
Total sieving time: 5.90 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000
total time: 5.90 hours.
 --------- CPU info (if available) ----------

Jun 5, 2009 (4th)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Jun 5, 2009

(19·10¹⁴⁹+11)/3 = 6(3)₁₄₈7_<150> = 472669 · 2502376448875356964523_<22> · 108515729007503118966010501_<27> · C97

C97 = P33 · P65

P33 = 412263120561519252622656422088931_<33>

P65 = 11968932109377920243791744162779339493133905057285675419912761321_<65>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 4934349301201108471565949482849373763257646188675193487984795052436076161688151809042115239037851 (97 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3312505575
Step 1 took 3051ms
Step 2 took 1822ms
********** Factor found in step 2: 412263120561519252622656422088931
Found probable prime factor of 33 digits: 412263120561519252622656422088931
Probable prime cofactor 11968932109377920243791744162779339493133905057285675419912761321 has 65 digits

(19·10¹⁰⁸+11)/3 = 6(3)₁₀₇7_<109> = 8161 · C105

C105 = P41 · P64

P41 = 91472206780727469444733176114899308261069_<41>

P64 = 8483983432303508769598845872763266181025177265418747924732236893_<64>

Number: 63337_108
N=776048686843932524608912306498386635624719192909365682310174406731201241677898950292039374259690397418617
  ( 105 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=91472206780727469444733176114899308261069
 r2=8483983432303508769598845872763266181025177265418747924732236893
Version: 
Total time: 0.39 hours.
Scaled time: 0.89 units (timescale=2.299).
Factorization parameters were as follows:
n: 776048686843932524608912306498386635624719192909365682310174406731201241677898950292039374259690397418617
m: 10000000000000000000000
deg: 5
c5: 19
c0: 1100
skew: 2.25
type: snfs
lss: 1
rlim: 360000
alim: 360000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [180000, 320001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 1030824
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 46772 x 47014
Total sieving time: 0.34 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.39 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(19·10¹¹⁶+11)/3 = 6(3)₁₁₅7_<117> = 7 · 13 · 31 · C114

C114 = P40 · P74

P40 = 2432404320102848256993656968416427973341_<40>

P74 = 92298255789188300181247940446582418073169321267278450482509633620109979017_<74>

Number: 63337_116
N=224506676119579345385796998700224506676119579345385796998700224506676119579345385796998700224506676119579345385797
  ( 114 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=2432404320102848256993656968416427973341
 r2=92298255789188300181247940446582418073169321267278450482509633620109979017
Version: 
Total time: 0.50 hours.
Scaled time: 1.20 units (timescale=2.385).
Factorization parameters were as follows:
n: 224506676119579345385796998700224506676119579345385796998700224506676119579345385796998700224506676119579345385797
m: 100000000000000000000000
deg: 5
c5: 190
c0: 11
skew: 0.57
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [250000, 425001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 1180696
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 61967 x 62215
Total sieving time: 0.45 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,500000,500000,25,25,45,45,2.2,2.2,25000
total time: 0.50 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 5, 2009 (3rd)

By Dmitry Domanov / ECMNET/GMP-ECM 6.2.3, ggnfs/msieve 1.41 / Jun 5, 2009

(19·10¹⁸¹+11)/3 = 6(3)₁₈₀7_<182> = C182

C182 = P32 · P151

P32 = 11159287224414433102572369164279_<32>

P151 = 5675392348963995343600513340549846572758077864937588438849066954047336838627831641100426017661512177938167043255580512712225275971080992889921645619503_<151>

[2009-06-05 02:29:53 GMT] a: Factor found!  new2 / (probable) 11159287224414433102572369164279  B1: 11000000 sigma: 2433365336 (found in step 2)
[2009-06-05 02:29:53 GMT] a:    Co-factor:  new2 / (Probable) 5675392348963995343600513340549846572758077864937588438849066954047336838627831641100426017661512177938167043255580512712225275971080992889921645619503

(19·10¹⁴⁸+11)/3 = 6(3)₁₄₇7_<149> = C149

C149 = P38 · P112

P38 = 14440446545037476137898408596542568433_<38>

P112 = 4385829284143440551081787553942088343816297920166421201719640736203533717033343955624721785579707213468219251689_<112>

Number: 149
N=63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337
  ( 149 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=14440446545037476137898408596542568433 (pp38)
 r2=4385829284143440551081787553942088343816297920166421201719640736203533717033343955624721785579707213468219251689 (pp112)
Version: Msieve v. 1.41
Total time: 12.22 hours.
Scaled time: 24.23 units (timescale=1.982).
Factorization parameters were as follows:
n: 63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337
m: 500000000000000000000000000000
deg: 5
c5: 152
c0: 275
skew: 1.13
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 386066 x 386314
Total sieving time: 11.85 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,150.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 12.22 hours.
 --------- CPU info (if available) ----------

Jun 5, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jun 5, 2009

(19·10¹¹⁴+11)/3 = 6(3)₁₁₃7_<115> = 37380337049761321074077_<23> · C93

C93 = P40 · P54

P40 = 1256600447385245073338384160128201847119_<40>

P54 = 134831672979018180497816847883716523804858773842922499_<54>

Number: n
N=169429540587135304979822222408703249896601171683279232545042066240429357482811986336963430381
  ( 93 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=1256600447385245073338384160128201847119 (pp40)
 r2=134831672979018180497816847883716523804858773842922499 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.38 hours.
Scaled time: 2.52 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_3_113_7
n: 169429540587135304979822222408703249896601171683279232545042066240429357482811986336963430381
m: 100000000000000000000000
deg: 5
c5: 19
c0: 110
skew: 1.42
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 10000
Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [305000, 425001)
Primes: RFBsize:49861, AFBsize:50010, largePrimes:5545888 encountered
Relations: rels:4848782, finalFF:124010
Max relations in full relation-set: 48
Initial matrix: 99936 x 124010 with sparse part having weight 16116609.
Pruned matrix : 94670 x 95233 with weight 9564276.
Total sieving time: 1.21 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.06 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,28,28,56,56,2.6,2.6,50000
total time: 1.38 hours.
 --------- CPU info (if available) ----------

(56·10¹⁶⁹+43)/9 = 6(2)₁₆₈7_<170> = 179 · 135743941 · C160

C160 = P74 · P87

P74 = 19333098532550373816686399052437320026075307008972428010009612629104605191_<74>

P87 = 132455674486371148046277269230562934350373310994141895370938879096275193417660466241323_<87>

Number: n
N=2560778606040432031409473120026286862842617515944645726231703028047780271030618289067540422150066760117190517505152551127225133147724890763191178312489644507693
  ( 160 digits)
SNFS difficulty: 171 digits.
Divisors found:

Fri Jun 05 16:15:56 2009  prp74 factor: 19333098532550373816686399052437320026075307008972428010009612629104605191
Fri Jun 05 16:15:56 2009  prp87 factor: 132455674486371148046277269230562934350373310994141895370938879096275193417660466241323
Fri Jun 05 16:15:56 2009  elapsed time 01:29:54 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 43.15 hours.
Scaled time: 112.46 units (timescale=2.606).
Factorization parameters were as follows:
name: KA_6_2_168_7
n: 2560778606040432031409473120026286862842617515944645726231703028047780271030618289067540422150066760117190517505152551127225133147724890763191178312489644507693
m: 10000000000000000000000000000000000
deg: 5
c5: 28
c0: 215
skew: 1.50
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 4900589)
Primes: RFBsize:348513, AFBsize:347706, largePrimes:16552047 encountered
Relations: rels:15738848, finalFF:690603
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1615751 hash collisions in 17010335 relations
Msieve: matrix is 911803 x 912051 (244.8 MB)

Total sieving time: 42.67 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 43.15 hours.
 --------- CPU info (if available) ----------

Jun 5, 2009

By Serge Batalov / GMP-ECM 6.2.3, Msieve / Jun 5, 2009

(19·10¹⁵⁹+11)/3 = 6(3)₁₅₈7_<160> = 47 · 2777 · 55488371 · 83963507 · 12461087964323018107_<20> · 47012464426731479399_<20> · C101

C101 = P30 · P71

P30 = 279929909870966847008523066101_<30>

P71 = 63510828694745285306996073091706073394019137483384890813990419744277463_<71>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=3996634525
Step 1 took 4696ms
Step 2 took 4261ms
********** Factor found in step 2: 279929909870966847008523066101
Found probable prime factor of 30 digits: 279929909870966847008523066101
Probable prime cofactor has 71 digits

(19·10¹⁷⁶+11)/3 = 6(3)₁₇₅7_<177> = 7 · 13 · 31 · 329711 · C168

C168 = P33 · P136

P33 = 380411345154635513542806482329393_<33>

P136 = 1789956030815979787160246186972967745910411150766357772414416278341751433525261220762485364988957571956424883773305352022454824614214139_<136>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=1431286068
Step 1 took 7581ms
Step 2 took 6112ms
********** Factor found in step 2: 380411345154635513542806482329393
Found probable prime factor of 33 digits: 380411345154635513542806482329393
Probable prime cofactor has 136 digits

(19·10¹²³+11)/3 = 6(3)₁₂₂7_<124> = 17 · 2221 · C120

C120 = P31 · P89

P31 = 2123006000891924143214151384847_<31>

P89 = 79010287948575789367851766818808637179491229043894459004745091157379088266646782235367203_<89>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=1215604976
Step 1 took 5396ms
Step 2 took 4761ms
********** Factor found in step 2: 2123006000891924143214151384847
Found probable prime factor of 31 digits: 2123006000891924143214151384847
Probable prime cofactor has 89 digits

(19·10¹¹⁹+11)/3 = 6(3)₁₁₈7_<120> = 23 · C119

C119 = P54 · P65

P54 = 886378704567425127996664373012529164481079650712500457_<54>

P65 = 31065989900441411912454637184703297301511811585122769130099098167_<65>

SNFS difficulty: 121 digits.
Divisors found:
 r1=886378704567425127996664373012529164481079650712500457 (pp54)
 r2=31065989900441411912454637184703297301511811585122769130099098167 (pp65)
Version: Msieve v. 1.41
Total time: 0.88 hours.
Scaled time: 2.39 units (timescale=2.734).
Factorization parameters were as follows:
n: 27536231884057971014492753623188405797101449275362318840579710144927536231884057971014492753623188405797101449275362319
m: 1000000000000000000000000
deg: 5
c5: 19
c0: 110
skew: 1.42
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 670001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 83360 x 83587
Total sieving time: 0.82 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 0.88 hours.

Jun 4, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Jun 4, 2009

(56·10¹⁷³-11)/9 = 6(2)₁₇₂1_<174> = 3² · C173

C173 = P48 · P125

P48 = 738564409141079321357570371709279096815335359017_<48>

P125 = 93608359153858981426105610055260809112478522633363061217130806551642027574933883449218513789486636057611681994106049642990557_<125>

Number: n
N=69135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469
  ( 173 digits)
SNFS difficulty: 176 digits.
Divisors found:

Thu Jun 04 06:39:25 2009  prp48 factor: 738564409141079321357570371709279096815335359017
Thu Jun 04 06:39:25 2009  prp125 factor: 93608359153858981426105610055260809112478522633363061217130806551642027574933883449218513789486636057611681994106049642990557
Thu Jun 04 06:39:25 2009  elapsed time 01:57:21 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 77.32 hours.
Scaled time: 206.51 units (timescale=2.671).
Factorization parameters were as follows:
name: KA_6_2_172_1
n: 69135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469
m: 100000000000000000000000000000000000
deg: 5
c5: 14
c0: -275
skew: 1.81
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [3000000, 6930323)
Primes: RFBsize:412849, AFBsize:413097, largePrimes:20590929 encountered
Relations: rels:20331002, finalFF:783769
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2478742 hash collisions in 22397806 relations
Msieve: matrix is 1058956 x 1059204 (283.3 MB)

Total sieving time: 76.03 hours.
Total relation processing time: 1.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,56,56,2.5,2.5,100000
total time: 77.32 hours.
 --------- CPU info (if available) ----------

Jun 4, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 4, 2009

(2·10¹⁸⁶+1)/3 = (6)₁₈₅7_<186> = 251 · 6985625296223599274700793_<25> · C159

C159 = P52 · P107

P52 = 4206917503932403168642670324369591892367492856212867_<52>

P107 = 90378626505701927771029832024922188717613437390639233047108160799437912965230133400154778880592650723086707_<107>

Number: 66667_186
N=380215425828206486972276085410708135299591961689712370600918694125902131065848858643968804230144200389046038423936391956686137469192075622992358872536490058969
  ( 159 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=4206917503932403168642670324369591892367492856212867
 r2=90378626505701927771029832024922188717613437390639233047108160799437912965230133400154778880592650723086707
Version: 
Total time: 98.62 hours.
Scaled time: 235.31 units (timescale=2.386).
Factorization parameters were as follows:
n: 380215425828206486972276085410708135299591961689712370600918694125902131065848858643968804230144200389046038423936391956686137469192075622992358872536490058969
m: 10000000000000000000000000000000000000
deg: 5
c5: 20
c0: 1
skew: 0.55
type: snfs
lss: 1
rlim: 7800000
alim: 7800000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 7800000/7800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [3900000, 6500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 19636934
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1626273 x 1626520
Total sieving time: 89.24 hours.
Total relation processing time: 2.68 hours.
Matrix solve time: 6.01 hours.
Time per square root: 0.68 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,7800000,7800000,28,28,54,54,2.5,2.5,100000
total time: 98.62 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 4, 2009

Factorizations of 633...337 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Jun 3, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 3, 2009

(56·10¹⁶⁴+61)/9 = 6(2)₁₆₃9_<165> = 37 · 107143243 · 827738769862247647289_<21> · C135

C135 = P67 · P68

P67 = 6359269268231973633385412363501308099138996129477289618088897243227_<67>

P68 = 29817998891046624165279119258269213521683566428481920044352290969873_<68>

Number: 62229_164
N=189620683988007866952443937748701417479265735985124731986169809683284375738554208691520381887964237839718019582607285916537475810300171
  ( 135 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=6359269268231973633385412363501308099138996129477289618088897243227
 r2=29817998891046624165279119258269213521683566428481920044352290969873
Version: 
Total time: 25.86 hours.
Scaled time: 61.83 units (timescale=2.391).
Factorization parameters were as follows:
n: 189620683988007866952443937748701417479265735985124731986169809683284375738554208691520381887964237839718019582607285916537475810300171
m: 1000000000000000000000000000000000
deg: 5
c5: 28
c0: 305
skew: 1.61
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2400000, 4500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9806459
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 818905 x 819153
Total sieving time: 23.34 hours.
Total relation processing time: 1.00 hours.
Matrix solve time: 1.43 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000
total time: 25.86 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 3, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jun 3, 2009

(19·10¹⁶⁶-7)/3 = 6(3)₁₆₅1_<167> = 1251201797773_<13> · C155

C155 = P40 · P115

P40 = 5222677376389994113737654403622761109617_<40>

P115 = 9691963898668385579244490463221708208315417143422065550154610103602175046798755781909933417277472713444234030147791_<115>

Number: n
N=50618000586363942762203374279640780451317566357735062091510191730164175208514686857624038716426133302249351141792345827911123123457306830339243153661406047
  ( 155 digits)
SNFS difficulty: 168 digits.
Divisors found:

Wed Jun 03 10:22:45 2009  prp40 factor: 5222677376389994113737654403622761109617
Wed Jun 03 10:22:45 2009  prp115 factor: 9691963898668385579244490463221708208315417143422065550154610103602175046798755781909933417277472713444234030147791
Wed Jun 03 10:22:45 2009  elapsed time 01:10:24 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 34.34 hours.
Scaled time: 90.96 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_6_3_165_1
n: 50618000586363942762203374279640780451317566357735062091510191730164175208514686857624038716426133302249351141792345827911123123457306830339243153661406047
m: 2000000000000000000000000000000000
deg: 5
c5: 95
c0: -112
skew: 1.03
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2300000, 4218517)
Primes: RFBsize:322441, AFBsize:321861, largePrimes:15963971 encountered
Relations: rels:15425943, finalFF:635132
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1491550 hash collisions in 16716161 relations
Msieve: matrix is 728875 x 729123 (196.3 MB)

Total sieving time: 33.78 hours.
Total relation processing time: 0.55 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,56,56,2.4,2.4,100000
total time: 34.34 hours.
 --------- CPU info (if available) ----------

(56·10¹⁶⁸+61)/9 = 6(2)₁₆₇9_<169> = 13 · 331 · C166

C166 = P53 · P113

P53 = 96209819631831239463458686211657549363576689560960517_<53>

P113 = 15029854316755953449386612574288835256536189192545473764862710443914088338103651872711772544550625231249480134879_<113>

Number: n
N=1446019572907790430449040720944044206884086038164588013530611717922896170630309603119270792986805071397216412322152503421385596612182714901748134376533168073953572443
  ( 166 digits)
SNFS difficulty: 170 digits.
Divisors found:

Wed Jun 03 17:30:16 2009  prp53 factor: 96209819631831239463458686211657549363576689560960517
Wed Jun 03 17:30:16 2009  prp113 factor: 15029854316755953449386612574288835256536189192545473764862710443914088338103651872711772544550625231249480134879
Wed Jun 03 17:30:16 2009  elapsed time 01:53:45 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 63.55 hours.
Scaled time: 167.40 units (timescale=2.634).
Factorization parameters were as follows:
name: KA_6_2_167_9
n: 1446019572907790430449040720944044206884086038164588013530611717922896170630309603119270792986805071397216412322152503421385596612182714901748134376533168073953572443
m: 4000000000000000000000000000000000
deg: 5
c5: 875
c0: 976
skew: 1.02
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 6236533)
Primes: RFBsize:348513, AFBsize:348732, largePrimes:17394588 encountered
Relations: rels:17199344, finalFF:648711
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2276774 hash collisions in 19262903 relations
Msieve: matrix is 898230 x 898478 (237.4 MB)

Total sieving time: 62.63 hours.
Total relation processing time: 0.92 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 63.55 hours.
 --------- CPU info (if available) ----------

Jun 3, 2009

By Dmitry Domanov / ECM / Jun 3, 2009

(16·10¹⁹⁹-7)/9 = 1(7)₁₉₉_<200> = 264007 · 6353173 · 23291472982858333436228811919662999043691_<41> · C147

C147 = P46 · C102

P46 = 1502739138045835488243594532007091714625588183_<46>

C102 = [302824352506754444443578645843911185284478634106196572443295670733987494299384968724155242087323594919_<102>]

[2009-06-02 23:45:23 GMT] a: Factor found!  test61 / (probable) 1502739138045835488243594532007091714625588183  B1: 11000000 sigma: 540716867 (found in step 2)
[2009-06-02 23:45:23 GMT] a:    Co-factor:  test61 / (Composite) 302824352506754444443578645843911185284478634106196572443295670733987494299384968724155242087323594919

Jun 2, 2009 (2nd)

By Dmitry Domanov / ggnfs, msieve / Jun 2, 2009

(19·10¹⁶⁹-7)/3 = 6(3)₁₆₈1_<170> = C170

C170 = P42 · P129

P42 = 454291383041177479146316118799864631194049_<42>

P129 = 139411258275160216175498607426380186850484941194923576476093434398091509434652722681972425582202165365944458263133700328849433619_<129>

Sieving in [2400000;5700000] took about 20hours on Xeon E5310 @ 4 cores

Mon Jun 01 23:57:37 2009  Msieve v. 1.41
Mon Jun 01 23:57:37 2009  random seeds: d61aa0a0 238188c0
Mon Jun 01 23:57:37 2009  factoring 63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 (170 digits)
Mon Jun 01 23:57:39 2009  searching for 15-digit factors
Mon Jun 01 23:57:41 2009  commencing number field sieve (170-digit input)
Mon Jun 01 23:57:41 2009  R0: -10000000000000000000000000000000000
Mon Jun 01 23:57:41 2009  R1:  1
Mon Jun 01 23:57:41 2009  A0: -70
Mon Jun 01 23:57:41 2009  A1:  0
Mon Jun 01 23:57:41 2009  A2:  0
Mon Jun 01 23:57:41 2009  A3:  0
Mon Jun 01 23:57:41 2009  A4:  0
Mon Jun 01 23:57:41 2009  A5:  19
Mon Jun 01 23:57:41 2009  skew 1.30, size 4.593843e-012, alpha 1.501780, combined = 2.087721e-010
Mon Jun 01 23:57:41 2009  
Mon Jun 01 23:57:41 2009  commencing relation filtering
Mon Jun 01 23:57:41 2009  commencing duplicate removal, pass 1
Mon Jun 01 23:59:18 2009  found 1777090 hash collisions in 12098448 relations
Mon Jun 01 23:59:39 2009  added 2707 free relations
Mon Jun 01 23:59:39 2009  commencing duplicate removal, pass 2
Tue Jun 02 00:00:03 2009  found 1797917 duplicates and 10303238 unique relations
Tue Jun 02 00:00:03 2009  memory use: 69.3 MB
Tue Jun 02 00:00:03 2009  reading rational ideals above 5701632
Tue Jun 02 00:00:03 2009  reading algebraic ideals above 5701632
Tue Jun 02 00:00:03 2009  commencing singleton removal, pass 1
Tue Jun 02 00:01:33 2009  relations with 0 large ideals: 174319
Tue Jun 02 00:01:33 2009  relations with 1 large ideals: 1092040
Tue Jun 02 00:01:33 2009  relations with 2 large ideals: 3004490
Tue Jun 02 00:01:33 2009  relations with 3 large ideals: 3791203
Tue Jun 02 00:01:33 2009  relations with 4 large ideals: 1864703
Tue Jun 02 00:01:33 2009  relations with 5 large ideals: 22017
Tue Jun 02 00:01:33 2009  relations with 6 large ideals: 354460
Tue Jun 02 00:01:33 2009  relations with 7+ large ideals: 6
Tue Jun 02 00:01:33 2009  10303238 relations and about 10061091 large ideals
Tue Jun 02 00:01:33 2009  commencing singleton removal, pass 2
Tue Jun 02 00:03:06 2009  found 3638251 singletons
Tue Jun 02 00:03:06 2009  current dataset: 6664987 relations and about 5540314 large ideals
Tue Jun 02 00:03:06 2009  commencing singleton removal, pass 3
Tue Jun 02 00:04:14 2009  found 1113381 singletons
Tue Jun 02 00:04:14 2009  current dataset: 5551606 relations and about 4351780 large ideals
Tue Jun 02 00:04:14 2009  commencing singleton removal, pass 4
Tue Jun 02 00:05:12 2009  found 330238 singletons
Tue Jun 02 00:05:12 2009  current dataset: 5221368 relations and about 4013429 large ideals
Tue Jun 02 00:05:12 2009  commencing singleton removal, final pass
Tue Jun 02 00:06:12 2009  memory use: 88.2 MB
Tue Jun 02 00:06:12 2009  commencing in-memory singleton removal
Tue Jun 02 00:06:12 2009  begin with 5221368 relations and 4249847 unique ideals
Tue Jun 02 00:06:20 2009  reduce to 4512893 relations and 3525902 ideals in 14 passes
Tue Jun 02 00:06:20 2009  max relations containing the same ideal: 17
Tue Jun 02 00:06:21 2009  reading rational ideals above 720000
Tue Jun 02 00:06:21 2009  reading algebraic ideals above 720000
Tue Jun 02 00:06:21 2009  commencing singleton removal, final pass
Tue Jun 02 00:07:23 2009  keeping 3861899 ideals with weight <= 20, new excess is 468053
Tue Jun 02 00:07:29 2009  memory use: 128.6 MB
Tue Jun 02 00:07:29 2009  commencing in-memory singleton removal
Tue Jun 02 00:07:30 2009  begin with 4515600 relations and 3861899 unique ideals
Tue Jun 02 00:07:34 2009  reduce to 4511494 relations and 3844466 ideals in 8 passes
Tue Jun 02 00:07:34 2009  max relations containing the same ideal: 20
Tue Jun 02 00:07:38 2009  removing 543410 relations and 481367 ideals in 62043 cliques
Tue Jun 02 00:07:38 2009  commencing in-memory singleton removal
Tue Jun 02 00:07:39 2009  begin with 3968084 relations and 3844466 unique ideals
Tue Jun 02 00:07:44 2009  reduce to 3918567 relations and 3312614 ideals in 10 passes
Tue Jun 02 00:07:44 2009  max relations containing the same ideal: 20
Tue Jun 02 00:07:47 2009  removing 403681 relations and 341638 ideals in 62043 cliques
Tue Jun 02 00:07:47 2009  commencing in-memory singleton removal
Tue Jun 02 00:07:48 2009  begin with 3514886 relations and 3312614 unique ideals
Tue Jun 02 00:07:51 2009  reduce to 3483225 relations and 2938714 ideals in 7 passes
Tue Jun 02 00:07:51 2009  max relations containing the same ideal: 20
Tue Jun 02 00:07:54 2009  relations with 0 large ideals: 41806
Tue Jun 02 00:07:54 2009  relations with 1 large ideals: 262264
Tue Jun 02 00:07:54 2009  relations with 2 large ideals: 761751
Tue Jun 02 00:07:54 2009  relations with 3 large ideals: 1115630
Tue Jun 02 00:07:54 2009  relations with 4 large ideals: 857838
Tue Jun 02 00:07:54 2009  relations with 5 large ideals: 342096
Tue Jun 02 00:07:54 2009  relations with 6 large ideals: 93408
Tue Jun 02 00:07:54 2009  relations with 7+ large ideals: 8432
Tue Jun 02 00:07:54 2009  commencing 2-way merge
Tue Jun 02 00:07:57 2009  reduce to 2116068 relation sets and 1571558 unique ideals
Tue Jun 02 00:07:57 2009  ignored 1 oversize relation sets
Tue Jun 02 00:07:57 2009  commencing full merge
Tue Jun 02 00:08:27 2009  memory use: 117.7 MB
Tue Jun 02 00:08:28 2009  found 1009501 cycles, need 937758
Tue Jun 02 00:08:28 2009  weight of 937758 cycles is about 65932017 (70.31/cycle)
Tue Jun 02 00:08:28 2009  distribution of cycle lengths:
Tue Jun 02 00:08:28 2009  1 relations: 117955
Tue Jun 02 00:08:28 2009  2 relations: 103087
Tue Jun 02 00:08:28 2009  3 relations: 101087
Tue Jun 02 00:08:28 2009  4 relations: 92485
Tue Jun 02 00:08:28 2009  5 relations: 84611
Tue Jun 02 00:08:28 2009  6 relations: 75708
Tue Jun 02 00:08:28 2009  7 relations: 66535
Tue Jun 02 00:08:28 2009  8 relations: 57923
Tue Jun 02 00:08:28 2009  9 relations: 50477
Tue Jun 02 00:08:28 2009  10+ relations: 187890
Tue Jun 02 00:08:28 2009  heaviest cycle: 18 relations
Tue Jun 02 00:08:28 2009  commencing cycle optimization
Tue Jun 02 00:08:30 2009  start with 5543854 relations
Tue Jun 02 00:08:44 2009  pruned 157739 relations
Tue Jun 02 00:08:44 2009  memory use: 145.8 MB
Tue Jun 02 00:08:44 2009  distribution of cycle lengths:
Tue Jun 02 00:08:44 2009  1 relations: 117955
Tue Jun 02 00:08:44 2009  2 relations: 105792
Tue Jun 02 00:08:44 2009  3 relations: 105257
Tue Jun 02 00:08:44 2009  4 relations: 95447
Tue Jun 02 00:08:44 2009  5 relations: 87378
Tue Jun 02 00:08:44 2009  6 relations: 77385
Tue Jun 02 00:08:44 2009  7 relations: 67623
Tue Jun 02 00:08:44 2009  8 relations: 58211
Tue Jun 02 00:08:44 2009  9 relations: 50641
Tue Jun 02 00:08:44 2009  10+ relations: 172069
Tue Jun 02 00:08:44 2009  heaviest cycle: 18 relations
Tue Jun 02 00:08:47 2009  RelProcTime: 612
Tue Jun 02 00:08:47 2009  elapsed time 00:11:10
Tue Jun 02 00:18:36 2009  
Tue Jun 02 00:18:36 2009  
Tue Jun 02 00:18:36 2009  Msieve v. 1.41
Tue Jun 02 00:18:36 2009  random seeds: 08740858 38647e30
Tue Jun 02 00:18:36 2009  factoring 63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 (170 digits)
Tue Jun 02 00:18:37 2009  searching for 15-digit factors
Tue Jun 02 00:18:40 2009  commencing number field sieve (170-digit input)
Tue Jun 02 00:18:40 2009  R0: -10000000000000000000000000000000000
Tue Jun 02 00:18:40 2009  R1:  1
Tue Jun 02 00:18:40 2009  A0: -70
Tue Jun 02 00:18:40 2009  A1:  0
Tue Jun 02 00:18:40 2009  A2:  0
Tue Jun 02 00:18:40 2009  A3:  0
Tue Jun 02 00:18:40 2009  A4:  0
Tue Jun 02 00:18:40 2009  A5:  19
Tue Jun 02 00:18:40 2009  skew 1.30, size 4.593843e-012, alpha 1.501780, combined = 2.087721e-010
Tue Jun 02 00:18:40 2009  
Tue Jun 02 00:18:40 2009  commencing linear algebra
Tue Jun 02 00:18:40 2009  read 937758 cycles
Tue Jun 02 00:18:42 2009  cycles contain 3063344 unique relations
Tue Jun 02 00:19:16 2009  read 3063344 relations
Tue Jun 02 00:19:21 2009  using 20 quadratic characters above 134217402
Tue Jun 02 00:19:37 2009  building initial matrix
Tue Jun 02 00:20:17 2009  memory use: 335.2 MB
Tue Jun 02 00:20:18 2009  read 937758 cycles
Tue Jun 02 00:20:22 2009  matrix is 937406 x 937758 (265.7 MB) with weight 82805041 (88.30/col)
Tue Jun 02 00:20:22 2009  sparse part has weight 63082269 (67.27/col)
Tue Jun 02 00:20:44 2009  filtering completed in 3 passes
Tue Jun 02 00:20:44 2009  matrix is 929761 x 929961 (264.4 MB) with weight 82352811 (88.56/col)
Tue Jun 02 00:20:44 2009  sparse part has weight 62803128 (67.53/col)
Tue Jun 02 00:20:49 2009  read 929961 cycles
Tue Jun 02 00:23:59 2009  matrix is 929761 x 929961 (264.4 MB) with weight 82352811 (88.56/col)
Tue Jun 02 00:23:59 2009  sparse part has weight 62803128 (67.53/col)
Tue Jun 02 00:24:00 2009  saving the first 48 matrix rows for later
Tue Jun 02 00:24:00 2009  matrix is 929713 x 929961 (249.3 MB) with weight 64976976 (69.87/col)
Tue Jun 02 00:24:00 2009  sparse part has weight 59762482 (64.26/col)
Tue Jun 02 00:24:00 2009  matrix includes 64 packed rows
Tue Jun 02 00:24:00 2009  using block size 65536 for processor cache size 6144 kB
Tue Jun 02 00:24:07 2009  commencing Lanczos iteration (4 threads)
Tue Jun 02 00:24:07 2009  memory use: 272.7 MB
Tue Jun 02 01:46:04 2009  lanczos halted after 14705 iterations (dim = 929711)
Tue Jun 02 01:46:06 2009  recovered 35 nontrivial dependencies
Tue Jun 02 01:46:06 2009  BLanczosTime: 5246
Tue Jun 02 01:46:06 2009  elapsed time 01:27:30
Tue Jun 02 11:13:35 2009  
Tue Jun 02 11:13:35 2009  
Tue Jun 02 11:13:35 2009  Msieve v. 1.41
Tue Jun 02 11:13:35 2009  random seeds: 81a95a80 200be138
Tue Jun 02 11:13:35 2009  factoring 63333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 (170 digits)
Tue Jun 02 11:13:37 2009  searching for 15-digit factors
Tue Jun 02 11:13:39 2009  commencing number field sieve (170-digit input)
Tue Jun 02 11:13:39 2009  R0: -10000000000000000000000000000000000
Tue Jun 02 11:13:39 2009  R1:  1
Tue Jun 02 11:13:39 2009  A0: -70
Tue Jun 02 11:13:39 2009  A1:  0
Tue Jun 02 11:13:39 2009  A2:  0
Tue Jun 02 11:13:39 2009  A3:  0
Tue Jun 02 11:13:39 2009  A4:  0
Tue Jun 02 11:13:39 2009  A5:  19
Tue Jun 02 11:13:39 2009  skew 1.30, size 4.593843e-012, alpha 1.501780, combined = 2.087721e-010
Tue Jun 02 11:13:39 2009  
Tue Jun 02 11:13:39 2009  commencing square root phase
Tue Jun 02 11:13:39 2009  reading relations for dependency 1
Tue Jun 02 11:13:40 2009  read 465397 cycles
Tue Jun 02 11:13:40 2009  cycles contain 1871002 unique relations
Tue Jun 02 11:14:08 2009  read 1871002 relations
Tue Jun 02 11:14:18 2009  multiplying 1528186 relations
Tue Jun 02 11:16:21 2009  multiply complete, coefficients have about 40.14 million bits
Tue Jun 02 11:16:22 2009  initial square root is modulo 579011
Tue Jun 02 11:20:27 2009  sqrtTime: 408
Tue Jun 02 11:20:27 2009  prp42 factor: 454291383041177479146316118799864631194049
Tue Jun 02 11:20:27 2009  prp129 factor: 139411258275160216175498607426380186850484941194923576476093434398091509434652722681972425582202165365944458263133700328849433619
Tue Jun 02 11:20:27 2009  elapsed time 00:06:52

Jun 2, 2009

By Robert Backstrom / GGNFS, Msieve / Jun 2, 2009

(19·10¹⁶³-7)/3 = 6(3)₁₆₂1_<164> = 1528115427195860226452144519734181_<34> · C131

C131 = P42 · P90

P42 = 375054753555520893395695609169760004067579_<42>

P90 = 110504893874187591596413409495017682935672393337348376387307423814825042765064498801134869_<90>

Number: n
N=41445385738662417611442928814986924314473384202452265032125295618316543566091246353416032258371712530792430821849165330461369312151
  ( 131 digits)
SNFS difficulty: 165 digits.
Divisors found:

Tue Jun 02 12:58:47 2009  prp42 factor: 375054753555520893395695609169760004067579
Tue Jun 02 12:58:47 2009  prp90 factor: 110504893874187591596413409495017682935672393337348376387307423814825042765064498801134869
Tue Jun 02 12:58:47 2009  elapsed time 01:07:01 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 39.96 hours.
Scaled time: 105.85 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_6_3_162_1
n: 41445385738662417611442928814986924314473384202452265032125295618316543566091246353416032258371712530792430821849165330461369312151
m: 500000000000000000000000000000000
deg: 5
c5: 152
c0: -175
skew: 1.03
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2000000, 4425397)
Primes: RFBsize:283146, AFBsize:283092, largePrimes:15709237 encountered
Relations: rels:15287211, finalFF:613633
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1801663 hash collisions in 16935383 relations
Msieve: matrix is 712265 x 712513 (188.5 MB)

Total sieving time: 39.44 hours.
Total relation processing time: 0.51 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.4,2.4,100000
total time: 39.96 hours.
 --------- CPU info (if available) ----------

(53·10²⁰³-17)/9 = 5(8)₂₀₂7_<204> = 13 · C203

C203 = P42 · P59 · P102

P42 = 987350730914620921690289987203621855954963_<42>

P59 = 92566848900864095239779213632802017565483126475597474270379_<59>

P102 = 495636265293798401196317143432651643488247579932991797044874163185512392872923768166698869239772113987_<102>

Number: n
N=45299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299
  ( 203 digits)
SNFS difficulty: 206 digits.
Divisors found:

Tue Jun  2 14:05:48 2009  prp42 factor: 987350730914620921690289987203621855954963
Tue Jun  2 14:05:48 2009  prp59 factor: 92566848900864095239779213632802017565483126475597474270379
Tue Jun  2 14:05:48 2009  prp102 factor: 495636265293798401196317143432651643488247579932991797044874163185512392872923768166698869239772113987
Tue Jun  2 14:05:48 2009  elapsed time 19:30:16 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20050930-k8
Total time: 99.56 hours.
Scaled time: 200.62 units (timescale=2.015).
Factorization parameters were as follows:
name: KA_5_8_202_7
n: 45299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299
m: 50000000000000000000000000000000000000000
deg: 5
c5: 424
c0: -425
skew: 1.00
type: snfs
lss: 1
rlim: 19000000
alim: 19000000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 19000000/19000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved  special-q in [9500000, 29099990)
Primes: RFBsize:1211050, AFBsize:1212352, largePrimes:35419729 encountered
Relations: rels:33177779, finalFF:834914
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 7395621 hash collisions in 44885691 relations
Msieve: matrix is 3359630 x 3359878 (905.5 MB)

Total sieving time: 98.57 hours.
Total relation processing time: 0.99 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,19000000,19000000,29,29,56,56,2.6,2.6,100000
total time: 99.56 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2748k kernel code, 36964k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830496)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Total of 4 processors activated (22643.71 BogoMIPS).

Jun 1, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve / Jun 1, 2009

(16·10¹⁷⁸-7)/9 = 1(7)₁₇₈_<179> = 19 · 67247 · 6779280532223_<13> · 17847077925229148671_<20> · C141

C141 = P63 · P78

P63 = 351285801553477998259072973907150185197704089795714956495320427_<63>

P78 = 327370570697273242447130450554318941139597272631318183807575568975566864956879_<78>

Number: 577
N=115000633332411167647364546083294741615775101260141430479997902227306590463854471282709871778389721057965754878001756662197647499816642867333
  ( 141 digits)
SNFS difficulty: 180 digits.
Divisors found:
r1=351285801553477998259072973907150185197704089795714956495320427 (pp63)
r2=327370570697273242447130450554318941139597272631318183807575568975566864956879 (pp78)
Version: Msieve v. 1.41
Total time: 106.90 hours.
Scaled time: 211.87 units (timescale=1.982).
Factorization parameters were as follows:
n: 115000633332411167647364546083294741615775101260141430479997902227306590463854471282709871778389721057965754878001756662197647499816642867333
m: 400000000000000000000000000000000000
deg: 5
c5: 125
c0: -56
skew: 0.85
type: snfs
lss: 1
rlim: 7000000
alim: 7000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3500000, 5300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1198873 x 1199121
Total sieving time: 104.20 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 1.98 hours.
Time per square root: 0.43 hours.
Prototype def-par.txt line would be:
snfs,180.000,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,53,53,2.5,2.5,100000
total time: 106.90 hours.
 --------- CPU info (if available) ----------

(16·10¹⁸⁰-7)/9 = 1(7)₁₈₀_<181> = 1038694808570917_<16> · C166

C166 = P60 · P107

P60 = 137718772401945611066139183172563078616174576033116838801957_<60>

P107 = 12427860489216359333700314673797681425104380541244459983868501418546968585363216500853083110304729687523033_<107>

Number: 677
N=1711549690157520228330742557808063317961315632644673179819320806670356053994984550359977522136522021367570978466533605186365590753577246918825184595149011146562975581
  ( 166 digits)
SNFS difficulty: 181 digits.
Divisors found:
r1=137718772401945611066139183172563078616174576033116838801957 (pp60)
r2=12427860489216359333700314673797681425104380541244459983868501418546968585363216500853083110304729687523033 (pp107)
Version: Msieve v. 1.41
Total time: 101.21 hours.
Scaled time: 201.21 units (timescale=1.988).
Factorization parameters were as follows:
n: 1711549690157520228330742557808063317961315632644673179819320806670356053994984550359977522136522021367570978466533605186365590753577246918825184595149011146562975581
m: 2000000000000000000000000000000000000
deg: 5
c5: 1
c0: -14
skew: 1.70
type: snfs
lss: 1
rlim: 7400000
alim: 7400000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3700000, 5400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1390191 x 1390439
Total sieving time: 98.04 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 2.77 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,181.000,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,53,53,2.5,2.5,100000
total time: 101.21 hours.
 --------- CPU info (if available) ----------

Jun 1, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.3 / Jun 1, 2009

(7·10²²⁷-43)/9 = (7)₂₂₆3_<227> = 3559 · C224

C224 = P28 · C196

P28 = 8458505971912909206817868981_<28>

C196 = [2583651199824609680034453819884625327726724648528050962698862538834572380539968219106118313227233933547355672372029262918293850733930449356683602772128068063946794992912419603436233160706908852287_<196>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3642532168
Step 1 took 16621ms
Step 2 took 13553ms
********** Factor found in step 2: 8458505971912909206817868981
Found probable prime factor of 28 digits: 8458505971912909206817868981
Composite cofactor has 196 digits

(7·10²¹⁵-43)/9 = (7)₂₁₄3_<215> = 2081 · 1504051683081685150327_<22> · 4344239786129705012158373_<25> · C166

C166 = P34 · C133

P34 = 3024223307536720085994159843093307_<34>

C133 = [1891442074356078127435530811303209306810261564412542247972987797125896592894268399142579972662858268228984818353299092343914997992589_<133>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3496836667
Step 1 took 3564ms
Step 2 took 3300ms
********** Factor found in step 2: 3024223307536720085994159843093307
Found probable prime factor of 34 digits: 3024223307536720085994159843093307
Composite cofactor has 133 digits

(7·10²⁴⁵-43)/9 = (7)₂₄₄3_<245> = 53² · C242

C242 = P30 · C213

P30 = 147803791508418175555074273469_<30>

C213 = [187334694537922847786332374691014861222601208364833920555120484053811064039560744117770151237267789426518709898544015747455022079756915518534598493789954675170924442769261275475794400002491732103243135770913504313_<213>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=624630945
Step 1 took 6221ms
Step 2 took 4776ms
********** Factor found in step 2: 147803791508418175555074273469
Found probable prime factor of 30 digits: 147803791508418175555074273469
Composite cofactor has 213 digits

(7·10²³⁴-43)/9 = (7)₂₃₃3_<234> = 73 · C233

C233 = P32 · P201

P32 = 70162570395366838677237918643007_<32>

P201 = 151854329830089387276948123171475465368043900564395635574907640527902177725953130967084760080446859468423858471494840344280032942052563119440955147796605889957623924505089000655025798808544614240070843_<201>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=762880277
Step 1 took 18957ms
Step 2 took 8053ms
********** Factor found in step 2: 70162570395366838677237918643007
Found probable prime factor of 32 digits: 70162570395366838677237918643007
Probable prime cofactor has 201 digits

Jun 1, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jun 1, 2009

(7·10²²¹-43)/9 = (7)₂₂₀3_<221> = 17 · 281 · 1933050226305217_<16> · 7065680627293703578348517_<25> · 21626847603702295660286951_<26> · 94971446179866949702602973_<26> · 17941218631370458475790313427_<29> · C98

C98 = P35 · P63

P35 = 83917164802182940110279805322856967_<35>

P63 = 385490904422208015412208301554642767311267505646360635649004263_<63>

Number: 77773_221
N=32349303756140982366638500632066141116319673464587062506666215628176801423560827981638307922250321
  ( 98 digits)
Divisors found:
 r1=83917164802182940110279805322856967
 r2=385490904422208015412208301554642767311267505646360635649004263
Version: 
Total time: 2.25 hours.
Scaled time: 5.38 units (timescale=2.390).
Factorization parameters were as follows:
name: 77773_221
n: 32349303756140982366638500632066141116319673464587062506666215628176801423560827981638307922250321
skew: 2071.43
# norm 3.18e+13
c5: 786480
c4: -909597786
c3: -6090742551109
c2: 5271076042794314
c1: 5464881154623239836
c0: -8918248740224616729200
# alpha -5.76
Y1: 861948791
Y0: -2102981693400790119
# Murphy_E 4.30e-09
# M 13704586428295265528822636952842921510667563363553767895424173946931554241498540878006403524405789
type: gnfs
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [500000, 950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4218915
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 163307 x 163555
Polynomial selection time: 0.13 hours.
Total sieving time: 1.82 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000
total time: 2.25 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

Jun 1, 2009

By Robert Backstrom / GGNFS, Msieve / Jun 1, 2009

(56·10¹⁶²+43)/9 = 6(2)₁₆₁7_<163> = 11 · 47 · 10296567877_<11> · 123990940208683_<15> · C136

C136 = P50 · P87

P50 = 23983976853277442191852487114470582321131826167551_<50>

P87 = 393053201540223607796745824158765838141928859295078242639142682262167967738704645960991_<87>

Number: n
N=9426978887847316499591259177339751369402284659743241181896586427524629168471443390568790396652331861718178838223408061486266734976003041
  ( 136 digits)
SNFS difficulty: 163 digits.
Divisors found:

Mon Jun 01 03:05:09 2009  prp50 factor: 23983976853277442191852487114470582321131826167551
Mon Jun 01 03:05:09 2009  prp87 factor: 393053201540223607796745824158765838141928859295078242639142682262167967738704645960991
Mon Jun 01 03:05:09 2009  elapsed time 00:56:26 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 24.18 hours.
Scaled time: 63.81 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_6_2_161_7
n: 9426978887847316499591259177339751369402284659743241181896586427524629168471443390568790396652331861718178838223408061486266734976003041
m: 200000000000000000000000000000000
deg: 5
c5: 175
c0: 43
skew: 0.76
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1900000, 3302917)
Primes: RFBsize:269987, AFBsize:270282, largePrimes:14135902 encountered
Relations: rels:13111233, finalFF:534265
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1138162 hash collisions in 14020541 relations
Msieve: matrix is 699147 x 699395 (188.5 MB)

Total sieving time: 23.90 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3800000,3800000,28,28,56,56,2.4,2.4,100000
total time: 24.18 hours.
 --------- CPU info (if available) ----------

May 2009

May 31, 2009 (4th)

By Sinkiti Sibata / GGNFS, Msieve / May 31, 2009

(19·10¹⁵⁵-7)/3 = 6(3)₁₅₄1_<156> = 164235667 · 1740417311_<10> · 111425777511793_<15> · 250229323067441_<15> · C110

C110 = P49 · P62

P49 = 5281247843943756323575345174974322075624622245631_<49>

P62 = 15047039119267587349572218682986674068056537222113859655843521_<62>

Number: 63331_155
N=79467142906369303749636744937281745129764539117988920683892994469122391287838213736204396907027827898561906751
  ( 110 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=5281247843943756323575345174974322075624622245631 (pp49)
 r2=15047039119267587349572218682986674068056537222113859655843521 (pp62)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 36.68 hours.
Scaled time: 17.31 units (timescale=0.472).
Factorization parameters were as follows:
name: 63331_155
n: 79467142906369303749636744937281745129764539117988920683892994469122391287838213736204396907027827898561906751
m: 10000000000000000000000000000000
deg: 5
c5: 19
c0: -7
skew: 0.82
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2200001)
Primes: RFBsize:203362, AFBsize:203482, largePrimes:7899338 encountered
Relations: rels:7979074, finalFF:587339
Max relations in full relation-set: 28
Initial matrix: 406909 x 587339 with sparse part having weight 60082132.
Pruned matrix : 326722 x 328820 with weight 32423960.
Total sieving time: 32.08 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 4.14 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 36.68 hours.
 --------- CPU info (if available) ----------

(56·10¹⁶²+61)/9 = 6(2)₁₆₁9_<163> = 13 · 17 · 333169659657218214943445880431_<30> · C131

C131 = P44 · P88

P44 = 58777162300699886134806717903601862679409189_<44>

P88 = 1437736120496800403800748865253742711720255061341109233283383300163142470662643993317611_<88>

Number: 62229_162
N=84506049300019045541148664177605664932560143115156293509081093839740279885169035460356133555067936173292757082359105087321508927479
  ( 131 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=58777162300699886134806717903601862679409189 (pp44)
 r2=1437736120496800403800748865253742711720255061341109233283383300163142470662643993317611 (pp88)
Version: Msieve-1.40
Total time: 40.03 hours.
Scaled time: 83.47 units (timescale=2.085).
Factorization parameters were as follows:
name: 62229_162
n: 84506049300019045541148664177605664932560143115156293509081093839740279885169035460356133555067936173292757082359105087321508927479
m: 200000000000000000000000000000000
deg: 5
c5: 175
c0: 61
skew: 0.81
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 3400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 732299 x 732547
Total sieving time: 37.56 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 2.01 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,163.000,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 40.03 hours.
 --------- CPU info (if available) ----------

May 31, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 31, 2009

(2·10¹⁸³+1)/3 = (6)₁₈₂7_<183> = 83 · 127 · 166561 · 45500165622286770651251939807357753869_<38> · C136

C136 = P58 · P79

P58 = 1768102116358568726804059735346898250979675156958250450963_<58>

P79 = 4719905315980089354175144342714435067318349425166521859528612903312864663830561_<79>

Number: 66667_183
N=8345274578196455040772840047280934924400950145019956077371379711181517748470254840649874990874138242711129166964755686037538473271280243
  ( 136 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=1768102116358568726804059735346898250979675156958250450963
 r2=4719905315980089354175144342714435067318349425166521859528612903312864663830561
Version: 
Total time: 84.74 hours.
Scaled time: 202.26 units (timescale=2.387).
Factorization parameters were as follows:
n: 8345274578196455040772840047280934924400950145019956077371379711181517748470254840649874990874138242711129166964755686037538473271280243
m: 10000000000000000000000000000000000000
deg: 5
c5: 1
c0: 50
skew: 2.19
type: snfs
lss: 1
rlim: 6800000
alim: 6800000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 6800000/6800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [3400000, 5700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 19866084
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1321278 x 1321526
Total sieving time: 78.16 hours.
Total relation processing time: 2.42 hours.
Matrix solve time: 4.00 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,54,54,2.5,2.5,100000
total time: 84.74 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 31, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / May 30, 2009

(19·10¹⁶⁰-7)/3 = 6(3)₁₅₉1_<161> = 205559 · 166690938181_<12> · 4739551742255273_<16> · C129

C129 = P60 · P70

P60 = 192953010834035420920565005161094023397748898317016682693703_<60>

P70 = 2021133639555239274004216421272326134198633923821597116449982793956831_<70>

Number: n
N=389983821050135524992495811598954671852428778933960144116705863669289820317650361573801619260957749190958138592224628970977535193
  ( 129 digits)
SNFS difficulty: 161 digits.
Divisors found:

Sat May 30 17:51:49 2009  prp60 factor: 192953010834035420920565005161094023397748898317016682693703
Sat May 30 17:51:49 2009  prp70 factor: 2021133639555239274004216421272326134198633923821597116449982793956831
Sat May 30 17:51:49 2009  elapsed time 01:13:25 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.86 hours.
Scaled time: 36.20 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_3_159_1
n: 389983821050135524992495811598954671852428778933960144116705863669289820317650361573801619260957749190958138592224628970977535193
m: 100000000000000000000000000000000
deg: 5
c5: 19
c0: -7
skew: 0.82
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 100000
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1700000, 2802749)
Primes: RFBsize:243539, AFBsize:243539, largePrimes:9127528 encountered
Relations: rels:8394159, finalFF:515146
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 677135 hash collisions in 8972024 relations
Msieve: matrix is 526245 x 526493 (141.7 MB)

Total sieving time: 19.72 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,28,28,56,56,2.3,2.3,100000
total time: 19.86 hours.
 --------- CPU info (if available) ----------

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 31, 2009

(19·10¹⁶⁴-7)/3 = 6(3)₁₆₃1_<165> = 521 · C163

C163 = P31 · P133

P31 = 1030395146901575232482318153521_<31>

P133 = 1179752261192165436937509834268451367995427496483506345869434991137876794024756627575257376550528314299971500543436800664584942621291_<133>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 1215611004478566858605246321177223288547664747280870121561100447856685860524632117722328854766474728087012156110044785668586052463211772232885476647472808701215611 (163 digits)
Using B1=910000, B2=871204962, polynomial Dickson(3), sigma=3339709975
Step 1 took 11609ms
Step 2 took 5078ms
********** Factor found in step 2: 1030395146901575232482318153521
Found probable prime factor of 31 digits: 1030395146901575232482318153521
Probable prime cofactor 1179752261192165436937509834268451367995427496483506345869434991137876794024756627575257376550528314299971500543436800664584942621291 has 133 digits

(56·10¹⁶³+61)/9 = 6(2)₁₆₂9_<164> = 3 · 547 · 36583739 · 8911817542531_<13> · C141

C141 = P41 · P100

P41 = 42597891454673060505110716648489489874029_<41>

P100 = 2730199970499644357975731595205926704022982681290973431824354119749840881511693404859673560174062129_<100>

Number: n
N=116300761992895442277851487983159703948805793485901191608307239656827728210759065722462137843313433918613770797238045307858287214837429547741
  ( 141 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sun May 31 01:41:53 2009  prp41 factor: 42597891454673060505110716648489489874029
Sun May 31 01:41:53 2009  prp100 factor: 2730199970499644357975731595205926704022982681290973431824354119749840881511693404859673560174062129
Sun May 31 01:41:53 2009  elapsed time 01:13:17 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 45.29 hours.
Scaled time: 82.02 units (timescale=1.811).
Factorization parameters were as follows:
name: KA_6_2_162_9
n: 116300761992895442277851487983159703948805793485901191608307239656827728210759065722462137843313433918613770797238045307858287214837429547741
m: 400000000000000000000000000000000
deg: 5
c5: 875
c0: 976
skew: 1.02
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2000000, 4800193)
Primes: RFBsize:283146, AFBsize:283248, largePrimes:16000975 encountered
Relations: rels:15979828, finalFF:489412
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2015568 hash collisions in 17683124 relations
Msieve: matrix is 693919 x 694167 (182.0 MB)

Total sieving time: 44.58 hours.
Total relation processing time: 0.71 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.4,2.4,100000
total time: 45.29 hours.
 --------- CPU info (if available) ----------

(56·10¹⁷⁵-11)/9 = 6(2)₁₇₄1_<176> = 47 · C175

C175 = P54 · P121

P54 = 192125247010041170809174670779335744201118561259127269_<54>

P121 = 6890698068894240356891730438060670874910112730143005165653589033348984895253689710744878953349272012244501560105878095047_<121>

Number: n
N=1323877068557919621749408983451536643026004728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749408983451536643
  ( 175 digits)
SNFS difficulty: 177 digits.
Divisors found:

Sun May 31 02:43:55 2009  prp54 factor: 192125247010041170809174670779335744201118561259127269
Sun May 31 02:43:55 2009  prp121 factor: 6890698068894240356891730438060670874910112730143005165653589033348984895253689710744878953349272012244501560105878095047
Sun May 31 02:43:55 2009  elapsed time 02:23:38 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 42.54 hours.
Scaled time: 113.16 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_2_174_1
n: 1323877068557919621749408983451536643026004728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749408983451536643
m: 200000000000000000000000000000000000
deg: 5
c5: 7
c0: -44
skew: 1.44
type: snfs
lss: 1
rlim: 6400000
alim: 6400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 6400000/6400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [3200000, 7810333)
Primes: RFBsize:438410, AFBsize:438596, largePrimes:21022405 encountered
Relations: rels:21220839, finalFF:870178
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2947888 hash collisions in 24544932 relations
Msieve: matrix is 1052560 x 1052808 (277.6 MB)

Total sieving time: 41.68 hours.
Total relation processing time: 0.86 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,6400000,6400000,28,28,56,56,2.5,2.5,100000
total time: 42.54 hours.
 --------- CPU info (if available) ----------

May 31, 2009

Factorizations of 77...773 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 30, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 30, 2009

(19·10¹⁸³-7)/3 = 6(3)₁₈₂1_<184> = 13 · 2372462713_<10> · 8468765729_<10> · 69592743691_<11> · 129057352081045693_<18> · 261750565597678834213_<21> · C116

C116 = P47 · P69

P47 = 20918814650880279245782585898866372921751427107_<47>

P69 = 493058067701339029668726835528369070385382676527854413996834196777607_<69>

Number: 63331_183
N=10314190330365491502414101471530176218118047462207183441475087326449818983417302428137450255427811591623312950392949
  ( 116 digits)
Divisors found:
 r1=20918814650880279245782585898866372921751427107
 r2=493058067701339029668726835528369070385382676527854413996834196777607
Version: 
Total time: 16.07 hours.
Scaled time: 38.20 units (timescale=2.377).
Factorization parameters were as follows:
name: 63331_183
n: 10314190330365491502414101471530176218118047462207183441475087326449818983417302428137450255427811591623312950392949
skew: 41613.59
# norm 9.10e+15
c5: 28500
c4: 3554644580
c3: 158727902980021
c2: -3174603706020844408
c1: 21891353313746581626744
c0: -727582156817515135345185867
# alpha -6.13
Y1: 362105387977
Y0: -12933550196069224996114
# Murphy_E 5.18e-10
# M 2313767235390905646823578484813923700899760471601142099600885784234612345003558293700337149488837071365532915777600
type: gnfs
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1650000, 2850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8690691
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 505767 x 506015
Polynomial selection time: 1.53 hours.
Total sieving time: 13.18 hours.
Total relation processing time: 0.65 hours.
Matrix solve time: 0.53 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3300000,3300000,27,27,52,52,2.4,2.4,75000
total time: 16.07 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 30, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.3 / May 30, 2009

(73·10²⁴¹-1)/9 = 8(1)₂₄₁_<242> = 3 · 1553 · 3142163203150529_<16> · C223

C223 = P40 · C183

P40 = 9738217033362438978257872010279769567827_<40>

C183 = [568957009763349750886082427078689969120509026254399618771016802246504288678284189495990001284085372062009919964865734459369038780656037994148639766044103725733477699960823359523909263_<183>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1553818478
Step 1 took 16365ms
Step 2 took 7596ms
********** Factor found in step 2: 9738217033362438978257872010279769567827
Found probable prime factor of 40 digits: 9738217033362438978257872010279769567827
Composite cofactor has 183 digits

May 30, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 30, 2009

(56·10¹⁶⁵+43)/9 = 6(2)₁₆₄7_<166> = 13² · 97 · C162

C162 = P54 · P109

P54 = 309696278400778819235156054633314885731808278757399009_<54>

P109 = 1225606603322051740069831254149400184276453879353393307568364058398997457686804434974933893594153486691097371_<109>

Number: n
N=379565803832259026549272385909975124883927421595938645898994828415922785470763266163741976588923456488880755335949626195462833052047960850498519015568975917905339
  ( 162 digits)
SNFS difficulty: 166 digits.
Divisors found:

Sat May 30 01:58:34 2009  prp54 factor: 309696278400778819235156054633314885731808278757399009
Sat May 30 01:58:34 2009  prp109 factor: 1225606603322051740069831254149400184276453879353393307568364058398997457686804434974933893594153486691097371
Sat May 30 01:58:34 2009  elapsed time 00:54:25 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 28.06 hours.
Scaled time: 74.05 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_6_2_164_7
n: 379565803832259026549272385909975124883927421595938645898994828415922785470763266163741976588923456488880755335949626195462833052047960850498519015568975917905339
m: 1000000000000000000000000000000000
deg: 5
c5: 56
c0: 43
skew: 0.95
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2100000, 3676151)
Primes: RFBsize:296314, AFBsize:296021, largePrimes:14911125 encountered
Relations: rels:14135788, finalFF:539450
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1346121 hash collisions in 15874367 relations
Msieve: matrix is 638603 x 638851 (171.0 MB)

Total sieving time: 27.68 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,56,56,2.4,2.4,100000
total time: 28.06 hours.
 --------- CPU info (if available) ----------

(19·10¹⁶⁵-7)/3 = 6(3)₁₆₄1_<166> = 13 · 994133839 · C156

C156 = P37 · P120

P37 = 1585869221747468828672050826992090487_<37>

P120 = 309013011562915854221734443449651727484814802076522487369928457645392098079175692205271336122167806548220047231911529559_<120>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 490054224157122952020527174892280454289193034077464070194656644395229342441867615754187379077013278470130800453699763035113001004263659492519477035103205233 (156 digits)
Using B1=1216000, B2=1426326730, polynomial Dickson(6), sigma=900906112
Step 1 took 20670ms
Step 2 took 7519ms
********** Factor found in step 2: 1585869221747468828672050826992090487
Found probable prime factor of 37 digits: 1585869221747468828672050826992090487
Probable prime cofactor 309013011562915854221734443449651727484814802076522487369928457645392098079175692205271336122167806548220047231911529559 has 120 digits

May 30, 2009

By Sinkiti Sibata / Msieve / May 30, 2009

(19·10¹⁴³-7)/3 = 6(3)₁₄₂1_<144> = 17 · 686946041 · 5004379399496219_<16> · C119

C119 = P49 · P70

P49 = 6064675005431407597682140703583328855985936884427_<49>

P70 = 1786911481999335182645866206956164102877404014783178509521822170053571_<70>

Number: 63331_143
N=10837037401799762698529461554216170185290795964322502951936154198933444977066459208793255063177504764001758971425638817
  ( 119 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=6064675005431407597682140703583328855985936884427 (pp49)
 r2=1786911481999335182645866206956164102877404014783178509521822170053571 (pp70)
Version: Msieve-1.40
Total time: 11.21 hours.
Scaled time: 23.45 units (timescale=2.092).
Factorization parameters were as follows:
name: 63331_143
n: 10837037401799762698529461554216170185290795964322502951936154198933444977066459208793255063177504764001758971425638817
m: 50000000000000000000000000000
deg: 5
c5: 152
c0: -175
skew: 1.03
type: snfs
lss: 1
rlim: 1880000
alim: 1880000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1880000/1880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [940000, 2340001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 324522 x 324752
Total sieving time: 10.66 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,145.000,5,0,0,0,0,0,0,0,0,1880000,1880000,26,26,49,49,2.3,2.3,100000
total time: 11.21 hours.
 --------- CPU info (if available) ----------

May 29, 2009 (7th)

By Andreas Tete / GMP-ECM 6.2.3, Msieve v. 1.41 / May 29, 2009

(19·10¹⁵⁶-7)/3 = 6(3)₁₅₅1_<157> = 31² · 592451 · 43888913 · 2128275991521061911960831276960508639_<37> · C105

C105 = P32 · P73

P32 = 42922832558351566227042018293831_<32>

P73 = 2774504138001681732261294798409783710382595552789039859654944907699312713_<73>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1091934915
Step 1 took 8814ms
Step 2 took 4103ms
********** Factor found in step 2: 42922832558351566227042018293831
Found probable prime factor of 32 digits: 42922832558351566227042018293831
Probable prime cofactor 2774504138001681732261294798409783710382595552789039859654944907699312713 has 73 digits

(19·10¹³⁴-7)/3 = 6(3)₁₃₃1_<135> = 3255290605655383_<16> · 1564191755329938983_<19> · C102

C102 = P44 · P58

P44 = 43633958034178706867946687302128801578332407_<44>

P58 = 2850545511538911509758997306144163361132986931822475337797_<58>

Fri May 29 01:46:11 2009  Msieve v. 1.41
Fri May 29 01:46:11 2009  random seeds: 7a0386d4 e2e4a5c6
Fri May 29 01:46:11 2009  factoring 124380583225005339635170276374626881553544663883508895938724024594535921167555826580114650203277087379 (102 digits)
Fri May 29 01:46:12 2009  searching for 15-digit factors
Fri May 29 01:46:13 2009  commencing number field sieve (102-digit input)
Fri May 29 01:46:13 2009  R0: -41927590673415626285
Fri May 29 01:46:13 2009  R1:  31763566207
Fri May 29 01:46:13 2009  A0:  36772747658165768275752
Fri May 29 01:46:13 2009  A1: -174000147123189357426
Fri May 29 01:46:13 2009  A2: -11206915547828719
Fri May 29 01:46:13 2009  A3:  150414980036
Fri May 29 01:46:13 2009  A4: -53039818
Fri May 29 01:46:13 2009  A5:  960
Fri May 29 01:46:13 2009  skew 18483.41, size 1.224183e-009, alpha -4.909780, combined = 2.906612e-009
Fri May 29 01:46:14 2009  
Fri May 29 01:46:14 2009  commencing relation filtering
Fri May 29 01:46:14 2009  commencing duplicate removal, pass 1
Fri May 29 01:47:30 2009  found 392433 hash collisions in 4779022 relations
Fri May 29 01:47:43 2009  added 30939 free relations
Fri May 29 01:47:43 2009  commencing duplicate removal, pass 2
Fri May 29 01:48:03 2009  found 376855 duplicates and 4433105 unique relations
Fri May 29 01:48:03 2009  memory use: 40.3 MB
Fri May 29 01:48:03 2009  reading rational ideals above 2031616
Fri May 29 01:48:03 2009  reading algebraic ideals above 2031616
Fri May 29 01:48:03 2009  commencing singleton removal, pass 1
Fri May 29 01:48:49 2009  relations with 0 large ideals: 80551
Fri May 29 01:48:49 2009  relations with 1 large ideals: 590268
Fri May 29 01:48:49 2009  relations with 2 large ideals: 1517218
Fri May 29 01:48:49 2009  relations with 3 large ideals: 1590960
Fri May 29 01:48:49 2009  relations with 4 large ideals: 586066
Fri May 29 01:48:49 2009  relations with 5 large ideals: 38047
Fri May 29 01:48:49 2009  relations with 6 large ideals: 29992
Fri May 29 01:48:49 2009  relations with 7+ large ideals: 3
Fri May 29 01:48:49 2009  4433105 relations and about 4216507 large ideals
Fri May 29 01:48:49 2009  commencing singleton removal, pass 2
Fri May 29 01:49:36 2009  found 1920217 singletons
Fri May 29 01:49:36 2009  current dataset: 2512888 relations and about 1933737 large ideals
Fri May 29 01:49:36 2009  commencing singleton removal, pass 3
Fri May 29 01:50:12 2009  found 390516 singletons
Fri May 29 01:50:12 2009  current dataset: 2122372 relations and about 1520986 large ideals
Fri May 29 01:50:12 2009  commencing singleton removal, final pass
Fri May 29 01:50:53 2009  memory use: 34.5 MB
Fri May 29 01:50:53 2009  commencing in-memory singleton removal
Fri May 29 01:50:53 2009  begin with 2122372 relations and 1562809 unique ideals
Fri May 29 01:50:55 2009  reduce to 1898971 relations and 1334953 ideals in 10 passes
Fri May 29 01:50:55 2009  max relations containing the same ideal: 67
Fri May 29 01:50:55 2009  reading rational ideals above 100000
Fri May 29 01:50:55 2009  reading algebraic ideals above 100000
Fri May 29 01:50:55 2009  commencing singleton removal, final pass
Fri May 29 01:51:43 2009  keeping 1538216 ideals with weight <= 25, new excess is 126334
Fri May 29 01:51:46 2009  memory use: 47.3 MB
Fri May 29 01:51:46 2009  commencing in-memory singleton removal
Fri May 29 01:51:46 2009  begin with 1903679 relations and 1538216 unique ideals
Fri May 29 01:51:48 2009  reduce to 1897608 relations and 1509334 ideals in 8 passes
Fri May 29 01:51:48 2009  max relations containing the same ideal: 25
Fri May 29 01:51:49 2009  removing 522496 relations and 401633 ideals in 120863 cliques
Fri May 29 01:51:49 2009  commencing in-memory singleton removal
Fri May 29 01:51:49 2009  begin with 1375112 relations and 1509334 unique ideals
Fri May 29 01:51:51 2009  reduce to 1297128 relations and 1024266 ideals in 8 passes
Fri May 29 01:51:51 2009  max relations containing the same ideal: 25
Fri May 29 01:51:51 2009  removing 397287 relations and 276424 ideals in 120863 cliques
Fri May 29 01:51:51 2009  commencing in-memory singleton removal
Fri May 29 01:51:52 2009  begin with 899841 relations and 1024266 unique ideals
Fri May 29 01:51:52 2009  reduce to 824971 relations and 666110 ideals in 8 passes
Fri May 29 01:51:52 2009  max relations containing the same ideal: 21
Fri May 29 01:51:53 2009  removing 67837 relations and 55524 ideals in 12313 cliques
Fri May 29 01:51:53 2009  commencing in-memory singleton removal
Fri May 29 01:51:53 2009  begin with 757134 relations and 666110 unique ideals
Fri May 29 01:51:53 2009  reduce to 753786 relations and 607197 ideals in 6 passes
Fri May 29 01:51:53 2009  max relations containing the same ideal: 21
Fri May 29 01:51:53 2009  relations with 0 large ideals: 11066
Fri May 29 01:51:53 2009  relations with 1 large ideals: 73648
Fri May 29 01:51:53 2009  relations with 2 large ideals: 190050
Fri May 29 01:51:53 2009  relations with 3 large ideals: 242532
Fri May 29 01:51:53 2009  relations with 4 large ideals: 162951
Fri May 29 01:51:53 2009  relations with 5 large ideals: 59782
Fri May 29 01:51:53 2009  relations with 6 large ideals: 12446
Fri May 29 01:51:53 2009  relations with 7+ large ideals: 1311
Fri May 29 01:51:53 2009  commencing 2-way merge
Fri May 29 01:51:53 2009  reduce to 487336 relation sets and 340747 unique ideals
Fri May 29 01:51:53 2009  commencing full merge
Fri May 29 01:51:59 2009  memory use: 25.5 MB
Fri May 29 01:51:59 2009  found 230072 cycles, need 210947
Fri May 29 01:51:59 2009  weight of 210947 cycles is about 14775600 (70.04/cycle)
Fri May 29 01:51:59 2009  distribution of cycle lengths:
Fri May 29 01:51:59 2009  1 relations: 18697
Fri May 29 01:51:59 2009  2 relations: 18637
Fri May 29 01:51:59 2009  3 relations: 19991
Fri May 29 01:51:59 2009  4 relations: 19889
Fri May 29 01:51:59 2009  5 relations: 19620
Fri May 29 01:51:59 2009  6 relations: 18220
Fri May 29 01:51:59 2009  7 relations: 16848
Fri May 29 01:51:59 2009  8 relations: 15336
Fri May 29 01:51:59 2009  9 relations: 13673
Fri May 29 01:51:59 2009  10+ relations: 50036
Fri May 29 01:51:59 2009  heaviest cycle: 18 relations
Fri May 29 01:51:59 2009  commencing cycle optimization
Fri May 29 01:51:59 2009  start with 1374954 relations
Fri May 29 01:52:03 2009  pruned 52307 relations
Fri May 29 01:52:03 2009  memory use: 33.9 MB
Fri May 29 01:52:03 2009  distribution of cycle lengths:
Fri May 29 01:52:03 2009  1 relations: 18697
Fri May 29 01:52:03 2009  2 relations: 19181
Fri May 29 01:52:03 2009  3 relations: 21002
Fri May 29 01:52:03 2009  4 relations: 20738
Fri May 29 01:52:03 2009  5 relations: 20663
Fri May 29 01:52:03 2009  6 relations: 19137
Fri May 29 01:52:03 2009  7 relations: 17544
Fri May 29 01:52:03 2009  8 relations: 15854
Fri May 29 01:52:03 2009  9 relations: 13910
Fri May 29 01:52:03 2009  10+ relations: 44221
Fri May 29 01:52:03 2009  heaviest cycle: 18 relations
Fri May 29 01:52:03 2009  RelProcTime: 249
Fri May 29 01:52:03 2009  
Fri May 29 01:52:03 2009  commencing linear algebra
Fri May 29 01:52:03 2009  read 210947 cycles
Fri May 29 01:52:04 2009  cycles contain 673540 unique relations
Fri May 29 01:52:25 2009  read 673540 relations
Fri May 29 01:52:26 2009  using 20 quadratic characters above 67108290
Fri May 29 01:52:30 2009  building initial matrix
Fri May 29 01:52:40 2009  memory use: 75.2 MB
Fri May 29 01:52:40 2009  read 210947 cycles
Fri May 29 01:52:40 2009  matrix is 210749 x 210947 (58.5 MB) with weight 19798822 (93.86/col)
Fri May 29 01:52:40 2009  sparse part has weight 13848264 (65.65/col)
Fri May 29 01:52:43 2009  filtering completed in 2 passes
Fri May 29 01:52:43 2009  matrix is 210230 x 210428 (58.4 MB) with weight 19766738 (93.94/col)
Fri May 29 01:52:43 2009  sparse part has weight 13831777 (65.73/col)
Fri May 29 01:52:44 2009  read 210428 cycles
Fri May 29 01:52:45 2009  matrix is 210230 x 210428 (58.4 MB) with weight 19766738 (93.94/col)
Fri May 29 01:52:45 2009  sparse part has weight 13831777 (65.73/col)
Fri May 29 01:52:45 2009  saving the first 48 matrix rows for later
Fri May 29 01:52:45 2009  matrix is 210182 x 210428 (55.9 MB) with weight 15466001 (73.50/col)
Fri May 29 01:52:45 2009  sparse part has weight 13378511 (63.58/col)
Fri May 29 01:52:45 2009  matrix includes 64 packed rows
Fri May 29 01:52:45 2009  using block size 65536 for processor cache size 3072 kB
Fri May 29 01:52:47 2009  commencing Lanczos iteration
Fri May 29 01:52:47 2009  memory use: 53.9 MB
Fri May 29 01:58:49 2009  lanczos halted after 3325 iterations (dim = 210182)
Fri May 29 01:58:50 2009  recovered 32 nontrivial dependencies
Fri May 29 01:58:50 2009  BLanczosTime: 407
Fri May 29 01:58:50 2009  
Fri May 29 01:58:50 2009  commencing square root phase
Fri May 29 01:58:50 2009  reading relations for dependency 1
Fri May 29 01:58:50 2009  read 105203 cycles
Fri May 29 01:58:50 2009  cycles contain 423488 unique relations
Fri May 29 01:58:56 2009  read 423488 relations
Fri May 29 01:58:58 2009  multiplying 336942 relations
Fri May 29 01:59:40 2009  multiply complete, coefficients have about 12.53 million bits
Fri May 29 01:59:40 2009  initial square root is modulo 15873877
Fri May 29 02:00:39 2009  sqrtTime: 109
Fri May 29 02:00:39 2009  prp44 factor: 43633958034178706867946687302128801578332407
Fri May 29 02:00:39 2009  prp58 factor: 2850545511538911509758997306144163361132986931822475337797
Fri May 29 02:00:39 2009  elapsed time 00:14:28
total time ~ 6 hours

May 29, 2009 (6th)

By Sinkiti Sibata / Msieve, GGNFS / May 29, 2009

(19·10¹²⁴-7)/3 = 6(3)₁₂₃1_<125> = 51753967471_<11> · C115

C115 = P42 · P73

P42 = 334097884150240049775907767539422981255259_<42>

P73 = 3662814902318079871210119531219746089941789043300847960174770283548307879_<73>

Number: 63331_124
N=1223738708898438673158498521971862166326037441608479951609106141089519589487113261963145490831491374404224819885661
  ( 115 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=334097884150240049775907767539422981255259 (pp42)
 r2=3662814902318079871210119531219746089941789043300847960174770283548307879 (pp73)
Version: Msieve-1.40
Total time: 2.21 hours.
Scaled time: 4.28 units (timescale=1.939).
Factorization parameters were as follows:
name: 63331_124
n: 1223738708898438673158498521971862166326037441608479951609106141089519589487113261963145490831491374404224819885661
m: 10000000000000000000000000
deg: 5
c5: 19
c0: -70
skew: 1.30
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 745001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 129222 x 129450
Total sieving time: 2.10 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 2.21 hours.
 --------- CPU info (if available) ----------

(19·10¹⁴¹-7)/3 = 6(3)₁₄₀1_<142> = 13 · 31 · 121823874281_<12> · 1054160869936423_<16> · C114

C114 = P47 · P67

P47 = 32436080587219098362111053786648781396373526097_<47>

P67 = 3772763927878618428978561857091666143636833194970166981744931256207_<67>

Number: 63331_141
N=122373674801224129713801839644924727291412501484302854678154146032811270477033116336772352870157465546636307734079
  ( 114 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=32436080587219098362111053786648781396373526097 (pp47)
 r2=3772763927878618428978561857091666143636833194970166981744931256207 (pp67)
Version: Msieve-1.40
Total time: 6.64 hours.
Scaled time: 13.90 units (timescale=2.092).
Factorization parameters were as follows:
name: 63331_141
n: 122373674801224129713801839644924727291412501484302854678154146032811270477033116336772352870157465546636307734079
m: 20000000000000000000000000000
deg: 5
c5: 95
c0: -112
skew: 1.03
type: snfs
lss: 1
rlim: 1720000
alim: 1720000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1720000/1720000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [860000, 1660001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 224336 x 224584
Total sieving time: 6.38 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,143.000,5,0,0,0,0,0,0,0,0,1720000,1720000,26,26,48,48,2.3,2.3,100000
total time: 6.64 hours.
 --------- CPU info (if available) ----------

(19·10¹⁴⁶-7)/3 = 6(3)₁₄₅1_<147> = C147

C147 = P47 · P100

P47 = 77171271388291014287393251838556984620187665647_<47>

P100 = 8206853689719400760471490320870429786719891558871093340652371961062720153762369224195693688837201373_<100>

Number: 63331_146
N=633333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
  ( 147 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=77171271388291014287393251838556984620187665647 (pp47)
 r2=8206853689719400760471490320870429786719891558871093340652371961062720153762369224195693688837201373 (pp100)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 17.57 hours.
Scaled time: 7.56 units (timescale=0.430).
Factorization parameters were as follows:
name: 63331_146
n: 633333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
m: 200000000000000000000000000000
deg: 5
c5: 95
c0: -112
skew: 1.03
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2250001)
Primes: RFBsize:155805, AFBsize:155117, largePrimes:4100927 encountered
Relations: rels:4170193, finalFF:377449
Max relations in full relation-set: 28
Initial matrix: 310989 x 377449 with sparse part having weight 32749524.
Pruned matrix : 283655 x 285273 with weight 21193066.
Total sieving time: 14.85 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.41 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 17.57 hours.
 --------- CPU info (if available) ----------

May 29, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 29, 2009

(56·10¹⁸⁶+61)/9 = 6(2)₁₈₅9_<187> = 13 · 84061 · 1822669 · 443936293 · 203796075559_<12> · 439766607999421_<15> · 386006825772686319809_<21> · C120

C120 = P51 · P69

P51 = 250673953247691140295576769478106793315213729261069_<51>

P69 = 811440899328768309046496122133133937558453179540215891652660246798611_<69>

Number: 62229_186
N=203407098061604120287021780643889425783415179229077710477149813168419812392713855634930663385611053845841843301885575159
  ( 120 digits)
Divisors found:
 r1=250673953247691140295576769478106793315213729261069
 r2=811440899328768309046496122133133937558453179540215891652660246798611
Version: 
Total time: 28.47 hours.
Scaled time: 68.07 units (timescale=2.391).
Factorization parameters were as follows:
name: 62229_186
n: 203407098061604120287021780643889425783415179229077710477149813168419812392713855634930663385611053845841843301885575159
skew: 50983.71
# norm 1.83e+16
c5: 29940
c4: 8871972664
c3: 133501584474317
c2: -18333168317553189533
c1: 397303272440526758105387
c0: -2454440886303536665977967575
# alpha -5.21
Y1: 9371863989197
Y0: -92559341351746858589674
# Murphy_E 2.93e-10
# M 22682978338461827122610808507135925082005800740391586673361601427470149998450196025368237394910875482716387709003550593
type: gnfs
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved algebraic special-q in [2400000, 4400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10199974
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 733110 x 733358
Polynomial selection time: 2.61 hours.
Total sieving time: 23.59 hours.
Total relation processing time: 0.98 hours.
Matrix solve time: 1.13 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4800000,4800000,27,27,53,53,2.4,2.4,100000
total time: 28.47 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 29, 2009 (4th)

By Wataru Sakai / GMP-ECM 6.2.1 / May 29, 2009

(49·10¹⁶⁸-31)/9 = 5(4)₁₆₇1_<169> = 15301755193_<11> · 13943954834566879_<17> · 2810066056947827497_<19> · C124

C124 = P46 · P79

P46 = 2738071186438710195874120880465381105300462749_<46>

P79 = 3316386124839130067412276341415290040498997690391963192414696202873340504719251_<79>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=408812994
Step 1 took 34039ms
Step 2 took 13682ms
********** Factor found in step 2: 2738071186438710195874120880465381105300462749
Found probable prime factor of 46 digits: 2738071186438710195874120880465381105300462749
Probable prime cofactor 3316386124839130067412276341415290040498997690391963192414696202873340504719251 has 79 digits

May 29, 2009 (3rd)

By matsui / Msieve / May 29, 2009

9·10¹⁷¹-1 = 8(9)₁₇₁_<172> = 136963579157_<12> · 429373702687757_<15> · C147

C147 = P47 · P100

P47 = 42679129855580064934964485511968838445123658843_<47>

P100 = 3585802901069120875169780945172816193378262142753545298800676974244410697305766876766285241909080157_<100>

N=153038947651244726688666449207685636156794373899467047177951914194053059387772278586968400747355401308035645995849761200170389692110687828408878351
  ( 147 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=42679129855580064934964485511968838445123658843 (pp47)
 r2=3585802901069120875169780945172816193378262142753545298800676974244410697305766876766285241909080157 (pp100)
Version: Msieve v. 1.41
Total time: 78.73 hours.
Scaled time: 174.07 units (timescale=2.211).
Factorization parameters were as follows:
n: 153038947651244726688666449207685636156794373899467047177951914194053059387772278586968400747355401308035645995849761200170389692110687828408878351
m: 30000000000000000000000000000000000
deg: 5
c5: 10
c0: -27
skew: 1.22
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 300000

Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2700000, 6000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 945937 x 946185
Total sieving time: 76.03 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 2.28 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
snfs,173.000,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000
total time: 78.73 hours.

9·10²⁴⁹-1 = 8(9)₂₄₉_<250> = 1239961 · 17567289930891241_<17> · 2211131180516999698877_<22> · 132852679081112049264025722783994751_<36> · 173971508153106043979381596158458837_<36> · C136

C136 = P59 · P78

P59 = 12401770836281816440614430558156356059434053950562553627081_<59>

P78 = 651903118776272291480393446015384353260696868728533727242356292283467348358521_<78>

N=8084753086520734729835410115388355154353484488692121661133313572891265091227154991684283911329904836521257457036748584838069340122707201
  ( 136 digits)
Divisors found:
 r1=12401770836281816440614430558156356059434053950562553627081 (pp59)
 r2=651903118776272291480393446015384353260696868728533727242356292283467348358521 (pp78)
Version: Msieve v. 1.41
Total time: 226.30 hours.
Scaled time: 501.03 units (timescale=2.214).
Factorization parameters were as follows:
n: 8084753086520734729835410115388355154353484488692121661133313572891265091227154991684283911329904836521257457036748584838069340122707201
m: 
c5: 720360
c4: -1815557350383
c3: -23809703162461182
c2: 28998780185371742771312
c1: 325033929753928457456535728
c0: -26134567168271472059124246564480
Y1: 1303012087128367
Y0: -102335477824812549114012973
skew: 136467.92
type: gnfs
rlim: 9800000
alim: 9800000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

Factor base limits: 9800000/9800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved algebraic special-q in [4900000, 9600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1702773 x 1703021
Total sieving time: 220.58 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 5.01 hours.
Time per square root: 0.44 hours.
Prototype def-par.txt line would be:
gnfs,135,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,9800000,9800000,28,28,55,55,2.5,2.5,100000
total time: 226.30 hours.

May 29, 2009 (2nd)

By Robert Backstrom / GGNFS / May 29, 2009

(19·10¹³³-7)/3 = 6(3)₁₃₂1_<134> = 825593 · C128

C128 = P63 · P66

P63 = 276917410651474473427328257365491996984371079112664023186244621_<63>

P66 = 277023162052734203341720293109298019669320818393106271797699685527_<66>

Number: n
N=76712536726126957633280966933262919299622614694326784908948275158986732364898119694974803969187400248467868953992261723795300267
  ( 128 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=276917410651474473427328257365491996984371079112664023186244621 (pp63)
 r2=277023162052734203341720293109298019669320818393106271797699685527 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.98 hours.
Scaled time: 7.28 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_6_3_132_1
n: 76712536726126957633280966933262919299622614694326784908948275158986732364898119694974803969187400248467868953992261723795300267
m: 500000000000000000000000000
deg: 5
c5: 152
c0: -175
skew: 1.03
type: snfs
lss: 1
rlim: 1280000
alim: 1280000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 100000
Factor base limits: 1280000/1280000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [640000, 1340001)
Primes: RFBsize:98610, AFBsize:98660, largePrimes:5291294 encountered
Relations: rels:4679338, finalFF:255913
Max relations in full relation-set: 48
Initial matrix: 197337 x 255913 with sparse part having weight 27792419.
Pruned matrix : 182759 x 183809 with weight 14545692.
Total sieving time: 3.54 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.25 hours.
Total square root time: 0.12 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1280000,1280000,28,28,56,56,2.3,2.3,75000
total time: 3.98 hours.
 --------- CPU info (if available) ----------

May 29, 2009

By Serge Batalov / GMP-ECM 6.2.3 / May 29, 2009

(19·10¹⁷⁶-7)/3 = 6(3)₁₇₅1_<177> = 3499 · 17881 · 20441 · 79357 · C160

C160 = P37 · P124

P37 = 3163772207346213559008453427361628107_<37>

P124 = 1972440967760531199381211837488119430417008472869108795319192731868746765494186479794291931702613136217821449591778270468311_<124>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2707555263
Step 1 took 11868ms
Step 2 took 11053ms
********** Factor found in step 2: 3163772207346213559008453427361628107
Found probable prime factor of 37 digits: 3163772207346213559008453427361628107
Probable prime cofactor has 124 digits

May 28, 2009 (7th)

By Sinkiti Sibata / Msieve, GGNFS / May 28, 2009

(56·10¹⁶¹+61)/9 = 6(2)₁₆₀9_<162> = 37 · C161

C161 = P68 · P94

P68 = 13048995793706679358357176909020251049647095744876594597880337395921_<68>

P94 = 1288744136535571334391285850180075374337949769163721716371914833115868776095281688468705962977_<94>

Number: 62229_161
N=16816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816817
  ( 161 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=13048995793706679358357176909020251049647095744876594597880337395921 (pp68)
 r2=1288744136535571334391285850180075374337949769163721716371914833115868776095281688468705962977 (pp94)
Version: Msieve-1.40
Total time: 45.84 hours.
Scaled time: 95.57 units (timescale=2.085).
Factorization parameters were as follows:
name: 62229_161
n: 16816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816817
m: 200000000000000000000000000000000
deg: 5
c5: 35
c0: 122
skew: 1.28
type: snfs
lss: 1
rlim: 3700000
alim: 3700000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3700000/3700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1850000, 3650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 660498 x 660746
Total sieving time: 43.92 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.59 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,163.000,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,51,51,2.4,2.4,100000
total time: 45.84 hours.
 --------- CPU info (if available) ----------

(19·10¹⁵⁸-7)/3 = 6(3)₁₅₇1_<159> = 12748061 · 244988506811_<12> · 3945162826217_<13> · 183252155785867837_<18> · 555494520034835752099_<21> · C90

C90 = P28 · P62

P28 = 5576034521395138710161741431_<28>

P62 = 90557254071447654817328327205076133848394476380414258694325861_<62>

Thu May 28 17:28:03 2009  Msieve v. 1.41
Thu May 28 17:28:03 2009  random seeds: f671fa40 5246c742
Thu May 28 17:28:03 2009  factoring 504950374865142600275495635504678889561884596942536208080854606867393688609203766338447091 (90 digits)
Thu May 28 17:28:04 2009  searching for 15-digit factors
Thu May 28 17:28:06 2009  commencing quadratic sieve (90-digit input)
Thu May 28 17:28:06 2009  using multiplier of 3
Thu May 28 17:28:06 2009  using 32kb Intel Core sieve core
Thu May 28 17:28:06 2009  sieve interval: 36 blocks of size 32768
Thu May 28 17:28:06 2009  processing polynomials in batches of 6
Thu May 28 17:28:06 2009  using a sieve bound of 1584931 (59873 primes)
Thu May 28 17:28:06 2009  using large prime bound of 126794480 (26 bits)
Thu May 28 17:28:06 2009  using double large prime bound of 385106280791040 (42-49 bits)
Thu May 28 17:28:06 2009  using trial factoring cutoff of 49 bits
Thu May 28 17:28:06 2009  polynomial 'A' values have 12 factors
Thu May 28 18:45:55 2009  60302 relations (15971 full + 44331 combined from 641278 partial), need 59969
Thu May 28 18:45:56 2009  begin with 657249 relations
Thu May 28 18:45:56 2009  reduce to 147005 relations in 11 passes
Thu May 28 18:45:56 2009  attempting to read 147005 relations
Thu May 28 18:45:58 2009  recovered 147005 relations
Thu May 28 18:45:58 2009  recovered 126900 polynomials
Thu May 28 18:45:58 2009  attempting to build 60302 cycles
Thu May 28 18:45:58 2009  found 60302 cycles in 6 passes
Thu May 28 18:45:58 2009  distribution of cycle lengths:
Thu May 28 18:45:58 2009     length 1 : 15971
Thu May 28 18:45:58 2009     length 2 : 11649
Thu May 28 18:45:58 2009     length 3 : 10712
Thu May 28 18:45:58 2009     length 4 : 8110
Thu May 28 18:45:58 2009     length 5 : 5770
Thu May 28 18:45:58 2009     length 6 : 3416
Thu May 28 18:45:58 2009     length 7 : 2145
Thu May 28 18:45:58 2009     length 9+: 2529
Thu May 28 18:45:58 2009  largest cycle: 20 relations
Thu May 28 18:45:59 2009  matrix is 59873 x 60302 (14.8 MB) with weight 3649006 (60.51/col)
Thu May 28 18:45:59 2009  sparse part has weight 3649006 (60.51/col)
Thu May 28 18:46:00 2009  filtering completed in 3 passes
Thu May 28 18:46:00 2009  matrix is 55912 x 55976 (13.8 MB) with weight 3395133 (60.65/col)
Thu May 28 18:46:00 2009  sparse part has weight 3395133 (60.65/col)
Thu May 28 18:46:00 2009  saving the first 48 matrix rows for later
Thu May 28 18:46:00 2009  matrix is 55864 x 55976 (9.1 MB) with weight 2710920 (48.43/col)
Thu May 28 18:46:00 2009  sparse part has weight 2037212 (36.39/col)
Thu May 28 18:46:00 2009  matrix includes 64 packed rows
Thu May 28 18:46:00 2009  using block size 22390 for processor cache size 1024 kB
Thu May 28 18:46:00 2009  commencing Lanczos iteration
Thu May 28 18:46:00 2009  memory use: 8.6 MB
Thu May 28 18:46:19 2009  lanczos halted after 884 iterations (dim = 55861)
Thu May 28 18:46:19 2009  recovered 16 nontrivial dependencies
Thu May 28 18:46:20 2009  prp28 factor: 5576034521395138710161741431
Thu May 28 18:46:20 2009  prp62 factor: 90557254071447654817328327205076133848394476380414258694325861
Thu May 28 18:46:20 2009  elapsed time 01:18:17

(19·10¹⁰⁷-7)/3 = 6(3)₁₀₆1_<108> = 5063453251223820049_<19> · C90

C90 = P41 · P49

P41 = 27699069066082335842545359049149492434657_<41>

P49 = 4515650990127709404839488960748228699356811540867_<49>

Thu May 28 17:24:09 2009  Msieve v. 1.39
Thu May 28 17:24:09 2009  random seeds: 7f5bdf80 2937e844
Thu May 28 17:24:09 2009  factoring 125079328653870506893939709139555539629227686655558726451828266925280542002683923482627619 (90 digits)
Thu May 28 17:24:10 2009  searching for 15-digit factors
Thu May 28 17:24:12 2009  commencing quadratic sieve (90-digit input)
Thu May 28 17:24:13 2009  using multiplier of 19
Thu May 28 17:24:13 2009  using 64kb Pentium 4 sieve core
Thu May 28 17:24:13 2009  sieve interval: 17 blocks of size 65536
Thu May 28 17:24:13 2009  processing polynomials in batches of 6
Thu May 28 17:24:13 2009  using a sieve bound of 1565693 (59275 primes)
Thu May 28 17:24:13 2009  using large prime bound of 125255440 (26 bits)
Thu May 28 17:24:13 2009  using double large prime bound of 376733166741360 (42-49 bits)
Thu May 28 17:24:13 2009  using trial factoring cutoff of 49 bits
Thu May 28 17:24:13 2009  polynomial 'A' values have 12 factors
Thu May 28 20:01:23 2009  59872 relations (15512 full + 44360 combined from 636070 partial), need 59371
Thu May 28 20:01:23 2009  begin with 651582 relations
Thu May 28 20:01:24 2009  reduce to 147624 relations in 9 passes
Thu May 28 20:01:24 2009  attempting to read 147624 relations
Thu May 28 20:01:26 2009  recovered 147624 relations
Thu May 28 20:01:26 2009  recovered 129772 polynomials
Thu May 28 20:01:26 2009  attempting to build 59872 cycles
Thu May 28 20:01:26 2009  found 59872 cycles in 5 passes
Thu May 28 20:01:26 2009  distribution of cycle lengths:
Thu May 28 20:01:26 2009     length 1 : 15512
Thu May 28 20:01:26 2009     length 2 : 11355
Thu May 28 20:01:26 2009     length 3 : 10603
Thu May 28 20:01:26 2009     length 4 : 8064
Thu May 28 20:01:26 2009     length 5 : 5649
Thu May 28 20:01:26 2009     length 6 : 3749
Thu May 28 20:01:26 2009     length 7 : 2267
Thu May 28 20:01:26 2009     length 9+: 2673
Thu May 28 20:01:26 2009  largest cycle: 17 relations
Thu May 28 20:01:27 2009  matrix is 59275 x 59872 (14.6 MB) with weight 3590614 (59.97/col)
Thu May 28 20:01:27 2009  sparse part has weight 3590614 (59.97/col)
Thu May 28 20:01:28 2009  filtering completed in 3 passes
Thu May 28 20:01:28 2009  matrix is 55768 x 55831 (13.6 MB) with weight 3342235 (59.86/col)
Thu May 28 20:01:28 2009  sparse part has weight 3342235 (59.86/col)
Thu May 28 20:01:28 2009  saving the first 48 matrix rows for later
Thu May 28 20:01:28 2009  matrix is 55720 x 55831 (8.6 MB) with weight 2634322 (47.18/col)
Thu May 28 20:01:28 2009  sparse part has weight 1910383 (34.22/col)
Thu May 28 20:01:28 2009  matrix includes 64 packed rows
Thu May 28 20:01:28 2009  using block size 21845 for processor cache size 512 kB
Thu May 28 20:01:29 2009  commencing Lanczos iteration
Thu May 28 20:01:29 2009  memory use: 8.4 MB
Thu May 28 20:01:58 2009  lanczos halted after 883 iterations (dim = 55718)
Thu May 28 20:01:59 2009  recovered 16 nontrivial dependencies
Thu May 28 20:01:59 2009  prp41 factor: 27699069066082335842545359049149492434657
Thu May 28 20:01:59 2009  prp49 factor: 4515650990127709404839488960748228699356811540867
Thu May 28 20:01:59 2009  elapsed time 02:37:50

(19·10¹¹³-7)/3 = 6(3)₁₁₂1_<114> = 8559317557642312663_<19> · C95

C95 = P36 · P60

P36 = 364273749615784181999930257926974317_<36>

P60 = 203125913174411006540302087331278541353649937784127457423961_<60>

Thu May 28 18:56:30 2009  Msieve v. 1.41
Thu May 28 18:56:31 2009  random seeds: 06c371f0 c3b8ef42
Thu May 28 18:56:31 2009  factoring 73993438036172912506392899516636791785351321648353676280690625853787679718172923974499827409637 (95 digits)
Thu May 28 18:56:31 2009  searching for 15-digit factors
Thu May 28 18:56:33 2009  commencing quadratic sieve (95-digit input)
Thu May 28 18:56:33 2009  using multiplier of 7
Thu May 28 18:56:33 2009  using 32kb Intel Core sieve core
Thu May 28 18:56:33 2009  sieve interval: 36 blocks of size 32768
Thu May 28 18:56:33 2009  processing polynomials in batches of 6
Thu May 28 18:56:33 2009  using a sieve bound of 2189221 (81176 primes)
Thu May 28 18:56:33 2009  using large prime bound of 328383150 (28 bits)
Thu May 28 18:56:33 2009  using double large prime bound of 2135430964341600 (43-51 bits)
Thu May 28 18:56:33 2009  using trial factoring cutoff of 51 bits
Thu May 28 18:56:33 2009  polynomial 'A' values have 12 factors
Thu May 28 22:25:59 2009  81333 relations (20466 full + 60867 combined from 1206902 partial), need 81272
Thu May 28 22:26:01 2009  begin with 1227368 relations
Thu May 28 22:26:02 2009  reduce to 209918 relations in 11 passes
Thu May 28 22:26:02 2009  attempting to read 209918 relations
Thu May 28 22:26:05 2009  recovered 209918 relations
Thu May 28 22:26:05 2009  recovered 192815 polynomials
Thu May 28 22:26:05 2009  attempting to build 81333 cycles
Thu May 28 22:26:06 2009  found 81333 cycles in 6 passes
Thu May 28 22:26:06 2009  distribution of cycle lengths:
Thu May 28 22:26:06 2009     length 1 : 20466
Thu May 28 22:26:06 2009     length 2 : 14388
Thu May 28 22:26:06 2009     length 3 : 13712
Thu May 28 22:26:06 2009     length 4 : 11051
Thu May 28 22:26:06 2009     length 5 : 8178
Thu May 28 22:26:06 2009     length 6 : 5546
Thu May 28 22:26:06 2009     length 7 : 3416
Thu May 28 22:26:06 2009     length 9+: 4576
Thu May 28 22:26:06 2009  largest cycle: 19 relations
Thu May 28 22:26:06 2009  matrix is 81176 x 81333 (22.4 MB) with weight 5559794 (68.36/col)
Thu May 28 22:26:06 2009  sparse part has weight 5559794 (68.36/col)
Thu May 28 22:26:07 2009  filtering completed in 4 passes
Thu May 28 22:26:07 2009  matrix is 77022 x 77086 (21.4 MB) with weight 5309405 (68.88/col)
Thu May 28 22:26:07 2009  sparse part has weight 5309405 (68.88/col)
Thu May 28 22:26:07 2009  saving the first 48 matrix rows for later
Thu May 28 22:26:08 2009  matrix is 76974 x 77086 (15.4 MB) with weight 4400031 (57.08/col)
Thu May 28 22:26:08 2009  sparse part has weight 3582618 (46.48/col)
Thu May 28 22:26:08 2009  matrix includes 64 packed rows
Thu May 28 22:26:08 2009  using block size 30834 for processor cache size 1024 kB
Thu May 28 22:26:09 2009  commencing Lanczos iteration
Thu May 28 22:26:09 2009  memory use: 13.7 MB
Thu May 28 22:26:53 2009  lanczos halted after 1219 iterations (dim = 76972)
Thu May 28 22:26:53 2009  recovered 17 nontrivial dependencies
Thu May 28 22:26:55 2009  prp36 factor: 364273749615784181999930257926974317
Thu May 28 22:26:55 2009  prp60 factor: 203125913174411006540302087331278541353649937784127457423961
Thu May 28 22:26:55 2009  elapsed time 03:30:24

(19·10¹¹⁹-7)/3 = 6(3)₁₁₈1_<120> = 2213 · 5749978691_<10> · C107

C107 = P52 · P55

P52 = 7142565667777428842404199142177757024839466055246647_<52>

P55 = 6968358010744748481904859785034423037844326555299193931_<55>

Number: 63331_119
N=49771954688327260109155339961234952205510402352405246631726248886182137604135641201297364629821392490499357
  ( 107 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=7142565667777428842404199142177757024839466055246647 (pp52)
 r2=6968358010744748481904859785034423037844326555299193931 (pp55)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.02 hours.
Scaled time: 1.43 units (timescale=0.473).
Factorization parameters were as follows:
name: 63331_119
n: 49771954688327260109155339961234952205510402352405246631726248886182137604135641201297364629821392490499357
m: 1000000000000000000000000
deg: 5
c5: 19
c0: -70
skew: 1.30
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 670001)
Primes: RFBsize:59531, AFBsize:59488, largePrimes:1388071 encountered
Relations: rels:1389636, finalFF:174888
Max relations in full relation-set: 28
Initial matrix: 119084 x 174888 with sparse part having weight 8851867.
Pruned matrix : 98634 x 99293 with weight 3731877.
Total sieving time: 2.86 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 3.02 hours.
 --------- CPU info (if available) ----------

May 28, 2009 (6th)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve / May 28, 2009

(32·10¹⁶⁹+31)/9 = 3(5)₁₆₈9_<170> = 3 · 13 · 17 · 3229 · 319549142894958130531092345559_<30> · C134

C134 = P47 · P88

P47 = 36503865295478130758755327213624903058483920561_<47>

P88 = 1423801300523414982742214232334802997389942436426180599813692010039144526423143680899283_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1504946988
Step 1 took 38186ms
Step 2 took 14458ms
********** Factor found in step 2: 36503865295478130758755327213624903058483920561
Found probable prime factor of 47 digits: 36503865295478130758755327213624903058483920561
Probable prime cofactor 1423801300523414982742214232334802997389942436426180599813692010039144526423143680899283 has 88 digits

(52·10²⁰⁰+11)/9 = 5(7)₁₉₉9_<201> = 3 · C201

C201 = P37 · P41 · P123

P37 = 8075439109054338741026365424340286769_<37>

P41 = 46072334646769181132736381886218495737461_<41>

P123 = 517646417427145438243223197026762870951002843055646221049761620790442362955715502310129467442320445073950466702993889063677_<123>

Number: 57779_200
N=192592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593
  ( 201 digits)
SNFS difficulty: 201 digits.
Divisors found:
 r1=8075439109054338741026365424340286769
 r2=46072334646769181132736381886218495737461
 r3=517646417427145438243223197026762870951002843055646221049761620790442362955715502310129467442320445073950466702993889063677
Version: 
Total time: 724.79 hours.
Scaled time: 1437.98 units (timescale=1.984).
Factorization parameters were as follows:
n: 192592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593
m: 10000000000000000000000000000000000000000
deg: 5
c5: 52
c0: 11
skew: 0.73
type: snfs
lss: 1
rlim: 16100000
alim: 16100000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 16100000/16100000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [8050000, 15150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2550504 x 2550752
Total sieving time: 724.79 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,201,5,0,0,0,0,0,0,0,0,16100000,16100000,29,29,56,56,2.6,2.6,100000
total time: 724.79 hours.
 --------- CPU info (if available) ----------

May 28, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / May 28, 2009

(56·10¹⁵⁸+61)/9 = 6(2)₁₅₇9_<159> = 37 · 113 · 223 · 557 · 3527 · 45653899 · C139

C139 = P45 · P95

P45 = 124878684080187282583724105767405939123035029_<45>

P95 = 59584547392283647789639726101806207148068690320073897315957313077500509015687698972674356372107_<95>

Number: n
N=7440839869861936630058067963126918327949604224644175519468827650795213963955279495313110552543506489514537808067602830238665387271519536103
  ( 139 digits)
SNFS difficulty: 160 digits.
Divisors found:

Thu May 28 06:18:05 2009  prp45 factor: 124878684080187282583724105767405939123035029
Thu May 28 06:18:05 2009  prp95 factor: 59584547392283647789639726101806207148068690320073897315957313077500509015687698972674356372107
Thu May 28 06:18:05 2009  elapsed time 01:01:35 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 26.13 hours.
Scaled time: 69.22 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_6_2_157_9
n: 7440839869861936630058067963126918327949604224644175519468827650795213963955279495313110552543506489514537808067602830238665387271519536103
m: 40000000000000000000000000000000
deg: 5
c5: 875
c0: 976
skew: 1.02
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1700000, 3337129)
Primes: RFBsize:243539, AFBsize:243630, largePrimes:13449259 encountered
Relations: rels:12430495, finalFF:445077
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1223572 hash collisions in 13440933 relations
Msieve: matrix is 683080 x 683328 (182.1 MB)

Total sieving time: 25.77 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,28,28,56,56,2.4,2.4,100000
total time: 26.13 hours.
 --------- CPU info (if available) ----------

(56·10²⁰⁰+61)/9 = 6(2)₁₉₉9_<201> = 37 · C200

C200 = P60 · P67 · P73

P60 = 481076100939208673226663917864223084277575369417353564944939_<60>

P67 = 8545755976691122629091211724599067284274966594431886983135257852967_<67>

P73 = 4090529449389188605462156151123695237619192394785337828054066652466473909_<73>

Number: n
N=16816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816817
  ( 200 digits)
SNFS difficulty: 201 digits.
Divisors found:

Thu May 28 09:36:48 2009  prp60 factor: 481076100939208673226663917864223084277575369417353564944939
Thu May 28 09:36:48 2009  prp67 factor: 8545755976691122629091211724599067284274966594431886983135257852967
Thu May 28 09:36:48 2009  prp73 factor: 4090529449389188605462156151123695237619192394785337828054066652466473909
Thu May 28 09:36:48 2009  elapsed time 14:35:01 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20050930-k8
Total time: 41.52 hours.
Scaled time: 83.69 units (timescale=2.016).
Factorization parameters were as follows:
name: KA_6_2_199_9
n: 16816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816816817
m: 10000000000000000000000000000000000000000
deg: 5
c5: 56
c0: 61
skew: 1.02
type: snfs
lss: 1
rlim: 16000000
alim: 16000000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 16000000/16000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved  special-q in [8000000, 15599990)
Primes: RFBsize:1031130, AFBsize:1029484, largePrimes:35216489 encountered
Relations: rels:33331588, finalFF:1260378
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 4741784 hash collisions in 38635157 relations
Msieve: matrix is 2987116 x 2987364 (816.9 MB)

Total sieving time: 40.75 hours.
Total relation processing time: 0.76 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,201,5,0,0,0,0,0,0,0,0,16000000,16000000,29,29,56,56,2.6,2.6,100000
total time: 41.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.97 BogoMIPS (lpj=2830488)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22643.70 BogoMIPS).

(56·10¹⁵⁵+61)/9 = 6(2)₁₅₄9_<156> = 23 · 37 · 251 · 27017372954252618111623_<23> · C129

C129 = P48 · P81

P48 = 177021412931799064494121309758465332060558628233_<48>

P81 = 609078564125640040336170484954565150827351856308547897231649778954045702279685131_<81>

Number: n
N=107819948007992181599739919757114454654783869201061103982701027821480434645578678954568874887411940205225700015025344436526903523
  ( 129 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=177021412931799064494121309758465332060558628233 (pp48)
 r2=609078564125640040336170484954565150827351856308547897231649778954045702279685131 (pp81)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 16.46 hours.
Scaled time: 43.60 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_6_2_154_9
n: 107819948007992181599739919757114454654783869201061103982701027821480434645578678954568874887411940205225700015025344436526903523
m: 10000000000000000000000000000000
deg: 5
c5: 56
c0: 61
skew: 1.02
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [1500000, 2400001)
Primes: RFBsize:216816, AFBsize:216332, largePrimes:13126010 encountered
Relations: rels:12952716, finalFF:813070
Max relations in full relation-set: 28
Initial matrix: 433214 x 813070 with sparse part having weight 92819045.
Pruned matrix : 311917 x 314147 with weight 40066358.
Total sieving time: 15.57 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.49 hours.
Total square root time: 0.13 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000
total time: 16.46 hours.
 --------- CPU info (if available) ----------

(56·10¹⁵⁶-11)/9 = 6(2)₁₅₅1_<157> = 23 · 17083343429_<11> · 77944473401_<11> · 479005799717307893_<18> · C117

C117 = P42 · P76

P42 = 132044681737646078708528335633309997093929_<42>

P76 = 3212164637458965643862477012178193071661944450676327587119744724091254536579_<76>

Number: n
N=424149257242190418021587942433779094384856789451403605718656098432866063576129536769017395811084206441250327629328891
  ( 117 digits)
SNFS difficulty: 158 digits.
Divisors found:

Thu May 28 21:55:08 2009  prp42 factor: 132044681737646078708528335633309997093929
Thu May 28 21:55:08 2009  prp76 factor: 3212164637458965643862477012178193071661944450676327587119744724091254536579
Thu May 28 21:55:08 2009  elapsed time 00:36:31 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 16.38 hours.
Scaled time: 43.74 units (timescale=2.671).
Factorization parameters were as follows:
name: KA_6_2_155_1
n: 424149257242190418021587942433779094384856789451403605718656098432866063576129536769017395811084206441250327629328891
m: 20000000000000000000000000000000
deg: 5
c5: 35
c0: -22
skew: 0.91
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1500000, 2487227)
Primes: RFBsize:216816, AFBsize:216457, largePrimes:11828670 encountered
Relations: rels:10501634, finalFF:290618
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 926649 hash collisions in 12226691 relations
Msieve: matrix is 545545 x 545793 (146.4 MB)

Total sieving time: 16.21 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000
total time: 16.38 hours.
 --------- CPU info (if available) ----------

(19·10¹²⁶-7)/3 = 6(3)₁₂₅1_<127> = 23 · 31 · 149 · 2208204383867_<13> · 550564080566484469_<18> · C92

C92 = P39 · P54

P39 = 274896745903554277016688501088576610443_<39>

P54 = 178377390878943326425099144634565645197695200985423067_<54>

Number: n
N=49035364295387863925479124276192463882986180905219291115366358148835194378188975727205288681
  ( 92 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=274896745903554277016688501088576610443 (pp39)
 r2=178377390878943326425099144634565645197695200985423067 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.66 hours.
Scaled time: 3.02 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_3_125_1
n: 49035364295387863925479124276192463882986180905219291115366358148835194378188975727205288681
m: 10000000000000000000000000
deg: 5
c5: 190
c0: -7
skew: 0.52
type: snfs
lss: 1
rlim: 700000
alim: 700000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [350000, 550001)
Primes: RFBsize:56543, AFBsize:56408, largePrimes:6577217 encountered
Relations: rels:5810183, finalFF:200349
Max relations in full relation-set: 48
Initial matrix: 113018 x 200349 with sparse part having weight 28695026.
Pruned matrix : 99364 x 99993 with weight 9200613.
Total sieving time: 1.49 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.06 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,700000,700000,28,28,56,56,2.5,2.5,50000
total time: 1.66 hours.
 --------- CPU info (if available) ----------

May 28, 2009 (4th)

By Serge Batalov / Msieve, GMP-ECM 6.2.3 / May 28, 2009

(19·10¹²⁷-7)/3 = 6(3)₁₂₆1_<128> = 17 · C127

C127 = P35 · P39 · P54

P35 = 12436519676849010829556240379784957_<35>

P39 = 804710243827567182357245316678847272239_<39>

P54 = 372258851965716799664238973288980795787307673603607441_<54>

SNFS difficulty: 129 digits.
Divisors found:
 r1=12436519676849010829556240379784957 (pp35)
 r2=804710243827567182357245316678847272239 (pp39)
 r3=372258851965716799664238973288980795787307673603607441 (pp54)
Version: Msieve v. 1.41
Total time: 1.53 hours.
Scaled time: 4.15 units (timescale=2.712).
Factorization parameters were as follows:
n: 3725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843
m: 20000000000000000000000000
deg: 5
c5: 475
c0: -56
skew: 0.65
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 950001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 135989 x 136232
Total sieving time: 1.39 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,129.000,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 1.53 hours.

(19·10¹⁷³-7)/3 = 6(3)₁₇₂1_<174> = 29 · C173

C173 = P33 · C141

P33 = 122569446876810816963640019353373_<33>

C141 = [178177196815774311635530949428564880269645047657883031777408413802169831219687056745323086331601289126990624176890263158591874451664925011643_<141>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=156145018
Step 1 took 11573ms
Step 2 took 11276ms
********** Factor found in step 2: 122569446876810816963640019353373
Found probable prime factor of 33 digits: 122569446876810816963640019353373
Composite cofactor has 141 digits

(19·10¹¹⁰-7)/3 = 6(3)₁₀₉1_<111> = 233 · 4483 · 17387 · C101

C101 = P36 · P66

P36 = 188300054736491233677602258486606213_<36>

P66 = 185196419489526548303620514212561505070907195886173707296562972959_<66>

SNFS difficulty: 111 digits.
Divisors found:
 r1=188300054736491233677602258486606213 (pp36)
 r2=185196419489526548303620514212561505070907195886173707296562972959 (pp66)
Version: Msieve v. 1.41
Total time: 0.46 hours.
Scaled time: 1.19 units (timescale=2.575).
Factorization parameters were as follows:
n: 34872495926880040942521501477836754590113782610902400474116000214661062511721881330962317609600394267
m: 10000000000000000000000
deg: 5
c5: 19
c0: -7
skew: 0.82
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [250000, 350001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 42818 x 43051
Total sieving time: 0.43 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 0.46 hours.

May 28, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 28, 2009

(56·10¹⁵⁸-11)/9 = 6(2)₁₅₇1_<159> = 3 · 59 · 203211241393631956722915124219_<30> · C128

C128 = P37 · P42 · P49

P37 = 2537899873573280171017705810844700679_<37>

P42 = 939154026293509730665590837625768055750239_<42>

P49 = 7257937322928077535349031612424282545111610115807_<49>

Number: 62221_158
N=17299140354921275130942878961573349031729110752907845125819804596310155375128869475259027043222450254192642083192090196656125767
  ( 128 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=2537899873573280171017705810844700679
 r2=939154026293509730665590837625768055750239
 r3=7257937322928077535349031612424282545111610115807
Version: 
Total time: 14.96 hours.
Scaled time: 35.76 units (timescale=2.391).
Factorization parameters were as follows:
n: 17299140354921275130942878961573349031729110752907845125819804596310155375128869475259027043222450254192642083192090196656125767
m: 100000000000000000000000000000000
deg: 5
c5: 14
c0: -275
skew: 1.81
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1600000, 2900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9222390
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 594313 x 594561
Total sieving time: 13.51 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 0.73 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,51,51,2.4,2.4,100000
total time: 14.96 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 28, 2009 (2nd)

Factorizations of 633...331 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 28, 2009

By Serge Batalov / PFGW / Mar 27, 2009

(23·10⁹⁵³²⁶+1)/3 = 7(6)₉₅₃₂₅7_<95327> is PRP.

May 27, 2009 (7th)

By Robert Backstrom / GGNFS, Msieve / May 27, 2009

(56·10¹⁴⁷+61)/9 = 6(2)₁₄₆9_<148> = 47 · 257 · 521941369984393_<15> · C129

C129 = P54 · P76

P54 = 465797699955877232314532201968922695556111616869606659_<54>

P76 = 2118826887558452953755045283330372730886493555641871631624937415827575885473_<76>

Number: n
N=986944690829397494891842036788406549333195416034921768446440979831502668989069508880958440112596340641488280029932940203142164707
  ( 129 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=465797699955877232314532201968922695556111616869606659 (pp54)
 r2=2118826887558452953755045283330372730886493555641871631624937415827575885473 (pp76)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 8.43 hours.
Scaled time: 21.11 units (timescale=2.504).
Factorization parameters were as follows:
name: KA_6_2_146_9
n: 986944690829397494891842036788406549333195416034921768446440979831502668989069508880958440112596340641488280029932940203142164707
m: 200000000000000000000000000000
deg: 5
c5: 175
c0: 61
skew: 0.81
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 100000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [1050000, 2550001)
Primes: RFBsize:155805, AFBsize:155723, largePrimes:7753568 encountered
Relations: rels:7266143, finalFF:435765
Max relations in full relation-set: 28
Initial matrix: 311594 x 435765 with sparse part having weight 44152462.
Pruned matrix : 268454 x 270075 with weight 24701362.
Total sieving time: 7.95 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.27 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,28,28,56,56,2.3,2.3,100000
total time: 8.43 hours.
 --------- CPU info (if available) ----------

(56·10¹⁵⁷+61)/9 = 6(2)₁₅₆9_<158> = 3 · 622385760966490075969_<21> · C137

C137 = P47 · P91

P47 = 14069154013962149347549891861752751330227218953_<47>

P91 = 2368626755962424844786981424733173785115155651413561625293563213425932855103394297861451599_<91>

Number: n
N=33324574631226893870084125839523117530322491594485773868792919061646457590097800036857175718446511341481511144550053544984125841384955847
  ( 137 digits)
SNFS difficulty: 158 digits.
Divisors found:

Wed May 27 21:27:35 2009  prp47 factor: 14069154013962149347549891861752751330227218953
Wed May 27 21:27:35 2009  prp91 factor: 2368626755962424844786981424733173785115155651413561625293563213425932855103394297861451599
Wed May 27 21:27:35 2009  elapsed time 00:35:53 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 18.00 hours.
Scaled time: 47.68 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_6_2_156_9
n: 33324574631226893870084125839523117530322491594485773868792919061646457590097800036857175718446511341481511144550053544984125841384955847
m: 20000000000000000000000000000000
deg: 5
c5: 175
c0: 61
skew: 0.81
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1500000, 2631523)
Primes: RFBsize:216816, AFBsize:216897, largePrimes:12484526 encountered
Relations: rels:11502437, finalFF:462209
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1021111 hash collisions in 12654905 relations
Msieve: matrix is 530829 x 531077 (142.1 MB)

Total sieving time: 17.74 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000
total time: 18.00 hours.
 --------- CPU info (if available) ----------

May 27, 2009 (6th)

By Serge Batalov / GMP-ECM 6.2.3 / May 27, 2009

(73·10²²⁷-1)/9 = 8(1)₂₂₇_<228> = 7 · 25247 · 3015815141_<10> · 639055693476556840009_<21> · C193

C193 = P35 · C158

P35 = 36279878564912877449080351436751977_<35>

C158 = [65639200136356610405763222555366392184764170615078420676661341059916251862205399722171206761383798033819165310154860533682523793910413983567476004394037283043_<158>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1381633969
Step 1 took 12653ms
********** Factor found in step 1: 36279878564912877449080351436751977
Found probable prime factor of 35 digits: 36279878564912877449080351436751977
Composite cofactor has 158 digits

May 27, 2009 (5th)

By Jo Yeong Uk / GMP-ECM 6.2.3, GGNFS, Msieve v1.39 / May 27, 2009

(56·10¹⁶¹+43)/9 = 6(2)₁₆₀7_<162> = 3³ · 241 · 523 · 21067 · 35373733327_<11> · C141

C141 = P38 · P44 · P60

P38 = 23731097486702355179310475185816769673_<38>

P44 = 68151158133676074312874348411451777745055799_<44>

P60 = 151700972667842036388110214409589568929986947480698193739649_<60>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 245346252744473392713773264651954391624666663016908687743450233882316596771088286439921866261057056653436602715231332271824612453355358691823 (141 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2122690916
Step 1 took 4181ms
Step 2 took 2446ms
********** Factor found in step 2: 23731097486702355179310475185816769673
Found probable prime factor of 38 digits: 23731097486702355179310475185816769673
Composite cofactor 10338596977318574636609620997004061760631577234451161306507242896988534078032307853523486220823983674551 has 104 digits

Number: 62227_161
N=10338596977318574636609620997004061760631577234451161306507242896988534078032307853523486220823983674551
  ( 104 digits)
Divisors found:
 r1=68151158133676074312874348411451777745055799
 r2=151700972667842036388110214409589568929986947480698193739649
Version: 
Total time: 3.99 hours.
Scaled time: 9.53 units (timescale=2.387).
Factorization parameters were as follows:
name: 62227_161
n: 10338596977318574636609620997004061760631577234451161306507242896988534078032307853523486220823983674551
skew: 21347.68
# norm 3.13e+14
c5: 1800
c4: 223241370
c3: -14927947804901
c2: -49922189142606074
c1: 798958580446369787614
c0: -26568840382120456200144
# alpha -5.80
Y1: 51897908579
Y0: -89501759710446812431
# Murphy_E 2.37e-09
# M 1694559806196192336452944050483858266788892742415679960275701010130132314731881164627205298510258439261
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4950704
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 243927 x 244175
Polynomial selection time: 0.29 hours.
Total sieving time: 3.21 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 3.99 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(2·10¹⁸⁰+1)/3 = (6)₁₇₉7_<180> = 43 · 659 · 7471369 · 51785777 · C161

C161 = P43 · P119

P43 = 1425608464044510496227793232639877013972121_<43>

P119 = 42652444118965609051628435266578532444132686084908100215479465855804466932393039505383096680112378775502273023323954667_<119>

Number: 66667_180
N=60805685348182876641979890690791410598648830455271886745185368187421994147748888627596878591817404759980073838738634174475982237199577653112470341374075805838707
  ( 161 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=1425608464044510496227793232639877013972121
 r2=42652444118965609051628435266578532444132686084908100215479465855804466932393039505383096680112378775502273023323954667
Version: 
Total time: 60.71 hours.
Scaled time: 144.91 units (timescale=2.387).
Factorization parameters were as follows:
n: 60805685348182876641979890690791410598648830455271886745185368187421994147748888627596878591817404759980073838738634174475982237199577653112470341374075805838707
m: 1000000000000000000000000000000000000
deg: 5
c5: 2
c0: 1
skew: 0.87
type: snfs
lss: 1
rlim: 5200000
alim: 5200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [2600000, 4300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 17440824
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1137720 x 1137968
Total sieving time: 55.66 hours.
Total relation processing time: 1.55 hours.
Matrix solve time: 2.86 hours.
Time per square root: 0.64 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,53,53,2.5,2.5,100000
total time: 60.71 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹⁵⁹+61)/9 = 6(2)₁₅₈9_<160> = 136879 · 1401744473_<10> · 1017640607768771362296572005537507_<34> · C113

C113 = P54 · P60

P54 = 193908127945844596110201403564697754328536812293850033_<54>

P60 = 164342314587529651585996443231840529788907444242118587893377_<60>

Number: 62229_159
N=31867310563954942460860793410742458897721802139714768023254519185323949327123209616553915892182082536506231931441
  ( 113 digits)
Divisors found:
 r1=193908127945844596110201403564697754328536812293850033
 r2=164342314587529651585996443231840529788907444242118587893377
Version: 
Total time: 12.13 hours.
Scaled time: 28.98 units (timescale=2.389).
Factorization parameters were as follows:
name: 62229_159
n: 31867310563954942460860793410742458897721802139714768023254519185323949327123209616553915892182082536506231931441
skew: 27061.66
# norm 9.39e+14
c5: 23940
c4: 884131582
c3: -60546641862666
c2: -320075720127746262
c1: 16417652371480033255285
c0: 116175128751983383521569019
# alpha -4.98
Y1: 1292890423231
Y0: -4215443468428684833628
# Murphy_E 7.52e-10
# M 15723322497422548827044109855298921437946360103556637207250493316262810669984092035138974002790496204291964433993
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1200000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8284318
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 452570 x 452818
Polynomial selection time: 1.01 hours.
Total sieving time: 10.02 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000
total time: 12.13 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹⁶⁵+61)/9 = 6(2)₁₆₄9_<166> = 42701 · 1376939 · 133455793 · C147

C147 = P35 · P113

P35 = 57659426044021677634098200461896179_<35>

P113 = 13752606780688174685773011147018886593941074896390490689917340604450663623768311804047072834136008067972436430313_<113>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 792967413583600859697370064059829457020793249634680186515285950164270324042605059768528085343798618048347992595494171085194377886539401081974474027 (147 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5746488418
Step 1 took 4059ms
Step 2 took 2476ms
********** Factor found in step 2: 57659426044021677634098200461896179
Found probable prime factor of 35 digits: 57659426044021677634098200461896179
Probable prime cofactor 13752606780688174685773011147018886593941074896390490689917340604450663623768311804047072834136008067972436430313 has 113 digits

May 27, 2009 (4th)

By Andreas Tete / GGNFS / Msieve v. 1.41 / May 27, 2009

(56·10¹⁷⁰+61)/9 = 6(2)₁₆₉9_<171> = 37 · 67 · 60348354518122561506923_<23> · 50323262668560143510940878296447111_<35> · C110

C110 = P54 · P57

P54 = 311370498917197796572412633772014554924884165146521673_<54>

P57 = 265434460235786313700762170596984220117945146644969782479_<57>

Tue May 26 20:45:04 2009  Msieve v. 1.41
Tue May 26 20:45:04 2009  random seeds: 359fae64 86e64e80
Tue May 26 20:45:04 2009  factoring 82648460313433883981241425769067111639470813131991163858925087068467532014766035327819208292972854598269167367 (110 digits)
Tue May 26 20:45:05 2009  searching for 15-digit factors
Tue May 26 20:45:07 2009  commencing number field sieve (110-digit input)
Tue May 26 20:45:07 2009  R0: -2247903484810375378741
Tue May 26 20:45:07 2009  R1:  231928949747
Tue May 26 20:45:07 2009  A0: -930670227212751277904443904
Tue May 26 20:45:07 2009  A1:  60489629810981899875608
Tue May 26 20:45:07 2009  A2:  3167107438421659766
Tue May 26 20:45:07 2009  A3: -20947784407893
Tue May 26 20:45:07 2009  A4: -515063582
Tue May 26 20:45:07 2009  A5:  1440
Tue May 26 20:45:07 2009  skew 76520.28, size 1.840075e-010, alpha -6.218085, combined = 1.066739e-009
Tue May 26 20:45:07 2009  
Tue May 26 20:45:07 2009  commencing relation filtering
Tue May 26 20:45:07 2009  commencing duplicate removal, pass 1
Tue May 26 20:46:08 2009  found 565242 hash collisions in 5755946 relations
Tue May 26 20:46:25 2009  added 43793 free relations
Tue May 26 20:46:25 2009  commencing duplicate removal, pass 2
Tue May 26 20:46:33 2009  found 554761 duplicates and 5244977 unique relations
Tue May 26 20:46:33 2009  memory use: 41.3 MB
Tue May 26 20:46:33 2009  reading rational ideals above 3080192
Tue May 26 20:46:33 2009  reading algebraic ideals above 3080192
Tue May 26 20:46:33 2009  commencing singleton removal, pass 1
Tue May 26 20:47:24 2009  relations with 0 large ideals: 110843
Tue May 26 20:47:24 2009  relations with 1 large ideals: 727001
Tue May 26 20:47:24 2009  relations with 2 large ideals: 1746135
Tue May 26 20:47:24 2009  relations with 3 large ideals: 1813514
Tue May 26 20:47:24 2009  relations with 4 large ideals: 731433
Tue May 26 20:47:24 2009  relations with 5 large ideals: 72669
Tue May 26 20:47:24 2009  relations with 6 large ideals: 43366
Tue May 26 20:47:24 2009  relations with 7+ large ideals: 16
Tue May 26 20:47:24 2009  5244977 relations and about 5339068 large ideals
Tue May 26 20:47:24 2009  commencing singleton removal, pass 2
Tue May 26 20:48:16 2009  found 2357815 singletons
Tue May 26 20:48:16 2009  current dataset: 2887162 relations and about 2364014 large ideals
Tue May 26 20:48:16 2009  commencing singleton removal, pass 3
Tue May 26 20:48:47 2009  found 586582 singletons
Tue May 26 20:48:47 2009  current dataset: 2300580 relations and about 1730089 large ideals
Tue May 26 20:48:47 2009  commencing singleton removal, pass 4
Tue May 26 20:49:13 2009  found 178268 singletons
Tue May 26 20:49:13 2009  current dataset: 2122312 relations and about 1546296 large ideals
Tue May 26 20:49:13 2009  commencing singleton removal, final pass
Tue May 26 20:49:38 2009  memory use: 33.4 MB
Tue May 26 20:49:38 2009  commencing in-memory singleton removal
Tue May 26 20:49:38 2009  begin with 2122312 relations and 1598652 unique ideals
Tue May 26 20:49:40 2009  reduce to 1891073 relations and 1363286 ideals in 13 passes
Tue May 26 20:49:40 2009  max relations containing the same ideal: 38
Tue May 26 20:49:41 2009  reading rational ideals above 720000
Tue May 26 20:49:41 2009  reading algebraic ideals above 720000
Tue May 26 20:49:41 2009  commencing singleton removal, final pass
Tue May 26 20:50:17 2009  keeping 1720791 ideals with weight <= 20, new excess is 192649
Tue May 26 20:50:19 2009  memory use: 47.9 MB
Tue May 26 20:50:19 2009  commencing in-memory singleton removal
Tue May 26 20:50:20 2009  begin with 1909274 relations and 1720791 unique ideals
Tue May 26 20:50:22 2009  reduce to 1881367 relations and 1603481 ideals in 12 passes
Tue May 26 20:50:22 2009  max relations containing the same ideal: 20
Tue May 26 20:50:23 2009  removing 233093 relations and 205886 ideals in 27207 cliques
Tue May 26 20:50:23 2009  commencing in-memory singleton removal
Tue May 26 20:50:23 2009  begin with 1648274 relations and 1603481 unique ideals
Tue May 26 20:50:25 2009  reduce to 1629103 relations and 1378053 ideals in 8 passes
Tue May 26 20:50:25 2009  max relations containing the same ideal: 20
Tue May 26 20:50:26 2009  removing 173083 relations and 145876 ideals in 27207 cliques
Tue May 26 20:50:26 2009  commencing in-memory singleton removal
Tue May 26 20:50:26 2009  begin with 1456020 relations and 1378053 unique ideals
Tue May 26 20:50:27 2009  reduce to 1443057 relations and 1219015 ideals in 7 passes
Tue May 26 20:50:27 2009  max relations containing the same ideal: 20
Tue May 26 20:50:28 2009  relations with 0 large ideals: 14707
Tue May 26 20:50:28 2009  relations with 1 large ideals: 104047
Tue May 26 20:50:28 2009  relations with 2 large ideals: 298920
Tue May 26 20:50:28 2009  relations with 3 large ideals: 443932
Tue May 26 20:50:28 2009  relations with 4 large ideals: 362506
Tue May 26 20:50:28 2009  relations with 5 large ideals: 166027
Tue May 26 20:50:28 2009  relations with 6 large ideals: 45752
Tue May 26 20:50:28 2009  relations with 7+ large ideals: 7166
Tue May 26 20:50:28 2009  commencing 2-way merge
Tue May 26 20:50:29 2009  reduce to 869629 relation sets and 645587 unique ideals
Tue May 26 20:50:29 2009  commencing full merge
Tue May 26 20:50:40 2009  memory use: 50.0 MB
Tue May 26 20:50:40 2009  found 408007 cycles, need 379787
Tue May 26 20:50:40 2009  weight of 379787 cycles is about 26862121 (70.73/cycle)
Tue May 26 20:50:40 2009  distribution of cycle lengths:
Tue May 26 20:50:40 2009  1 relations: 41647
Tue May 26 20:50:40 2009  2 relations: 38819
Tue May 26 20:50:40 2009  3 relations: 38644
Tue May 26 20:50:40 2009  4 relations: 36329
Tue May 26 20:50:40 2009  5 relations: 33244
Tue May 26 20:50:40 2009  6 relations: 29893
Tue May 26 20:50:40 2009  7 relations: 26931
Tue May 26 20:50:40 2009  8 relations: 23810
Tue May 26 20:50:40 2009  9 relations: 20729
Tue May 26 20:50:40 2009  10+ relations: 89741
Tue May 26 20:50:40 2009  heaviest cycle: 20 relations
Tue May 26 20:50:40 2009  commencing cycle optimization
Tue May 26 20:50:41 2009  start with 2422138 relations
Tue May 26 20:50:47 2009  pruned 76207 relations
Tue May 26 20:50:47 2009  memory use: 61.9 MB
Tue May 26 20:50:47 2009  distribution of cycle lengths:
Tue May 26 20:50:47 2009  1 relations: 41647
Tue May 26 20:50:47 2009  2 relations: 39915
Tue May 26 20:50:47 2009  3 relations: 40326
Tue May 26 20:50:47 2009  4 relations: 37675
Tue May 26 20:50:47 2009  5 relations: 34547
Tue May 26 20:50:47 2009  6 relations: 30630
Tue May 26 20:50:47 2009  7 relations: 27402
Tue May 26 20:50:47 2009  8 relations: 24036
Tue May 26 20:50:47 2009  9 relations: 20893
Tue May 26 20:50:47 2009  10+ relations: 82716
Tue May 26 20:50:47 2009  heaviest cycle: 19 relations
Tue May 26 20:50:48 2009  RelProcTime: 320
Tue May 26 20:50:48 2009  
Tue May 26 20:50:48 2009  commencing linear algebra
Tue May 26 20:50:48 2009  read 379787 cycles
Tue May 26 20:50:49 2009  cycles contain 1272344 unique relations
Tue May 26 20:51:05 2009  read 1272344 relations
Tue May 26 20:51:07 2009  using 20 quadratic characters above 134156108
Tue May 26 20:51:15 2009  building initial matrix
Tue May 26 20:51:32 2009  memory use: 140.2 MB
Tue May 26 20:51:33 2009  read 379787 cycles
Tue May 26 20:51:33 2009  matrix is 379562 x 379787 (107.2 MB) with weight 35505175 (93.49/col)
Tue May 26 20:51:33 2009  sparse part has weight 25441017 (66.99/col)
Tue May 26 20:51:39 2009  filtering completed in 3 passes
Tue May 26 20:51:40 2009  matrix is 377431 x 377631 (106.8 MB) with weight 35365680 (93.65/col)
Tue May 26 20:51:40 2009  sparse part has weight 25363858 (67.17/col)
Tue May 26 20:51:41 2009  read 377631 cycles
Tue May 26 20:51:43 2009  matrix is 377431 x 377631 (106.8 MB) with weight 35365680 (93.65/col)
Tue May 26 20:51:43 2009  sparse part has weight 25363858 (67.17/col)
Tue May 26 20:51:43 2009  saving the first 48 matrix rows for later
Tue May 26 20:51:43 2009  matrix is 377383 x 377631 (102.1 MB) with weight 28015668 (74.19/col)
Tue May 26 20:51:43 2009  sparse part has weight 24504348 (64.89/col)
Tue May 26 20:51:43 2009  matrix includes 64 packed rows
Tue May 26 20:51:43 2009  using block size 65536 for processor cache size 3072 kB
Tue May 26 20:51:47 2009  commencing Lanczos iteration
Tue May 26 20:51:47 2009  memory use: 99.5 MB
Tue May 26 21:12:00 2009  lanczos halted after 5969 iterations (dim = 377383)
Tue May 26 21:12:01 2009  recovered 29 nontrivial dependencies
Tue May 26 21:12:01 2009  BLanczosTime: 1273
Tue May 26 21:12:01 2009  
Tue May 26 21:12:01 2009  commencing square root phase
Tue May 26 21:12:01 2009  reading relations for dependency 1
Tue May 26 21:12:02 2009  read 188904 cycles
Tue May 26 21:12:02 2009  cycles contain 784422 unique relations
Tue May 26 21:12:34 2009  read 784422 relations
Tue May 26 21:12:38 2009  multiplying 635546 relations
Tue May 26 21:14:11 2009  multiply complete, coefficients have about 25.40 million bits
Tue May 26 21:14:12 2009  initial square root is modulo 19765799
Tue May 26 21:16:27 2009  sqrtTime: 266
Tue May 26 21:16:27 2009  prp54 factor: 311370498917197796572412633772014554924884165146521673
Tue May 26 21:16:27 2009  prp57 factor: 265434460235786313700762170596984220117945146644969782479
Tue May 26 21:16:27 2009  elapsed time 00:31:23
total time ~ 29 hours

May 27, 2009 (3rd)

By Erik Branger / GGNFS, Msieve / May 27, 2009

(28·10¹⁶⁷+17)/9 = 3(1)₁₆₆3_<168> = 11² · 23 · 9297531860777_<13> · 5625355375946149097_<19> · C133

C133 = P59 · P74

P59 = 54444563831060370474725702212332871377604421032494991959961_<59>

P74 = 39258179248712943472377998594789236506615356188918297471633268441459167679_<74>

Number: 31113_167
N=2137394445997761510395890241674344962098210020617491226246533753230837511777526481868931497067228733273481388043

052545928179953300519
  ( 133 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=54444563831060370474725702212332871377604421032494991959961 (pp59)
 r2=39258179248712943472377998594789236506615356188918297471633268441459167679 (pp74)
Version: Msieve v. 1.41
Total time: 82.07 hours.
Scaled time: 64.51 units (timescale=0.786).
Factorization parameters were as follows:
n: 

213739444599776151039589024167434496209821002061749122624653375323083751177752648186893149706722873327348138804305

2545928179953300519
m: 2000000000000000000000000000000000
deg: 5
c5: 175
c0: 34
skew: 0.72
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 4250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 797429 x 797677
Total sieving time: 76.93 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 3.93 hours.
Time per square root: 0.95 hours.
Prototype def-par.txt line would be:
snfs,168.000,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000
total time: 82.07 hours.
 --------- CPU info (if available) ----------

May 27, 2009 (2th)

By Jo Yeong Uk / GMP-ECM / May 27, 2009

(56·10¹⁵³+43)/9 = 6(2)₁₅₂7_<154> = 13 · 123289 · 213417229 · 137435871258200903_<18> · C123

C123 = P36 · P87

P36 = 207855748749177702475903581228065689_<36>

P87 = 636775313135541920644661803313139569186068666649278705384340856517311504776930805506077_<87>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 132357409496780157389212183926742930693742441984686316735685449045612894064896546327354637730958479189188077024805444692053 (123 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=6068088808
Step 1 took 9885ms
Step 2 took 4900ms
********** Factor found in step 2: 207855748749177702475903581228065689
Found probable prime factor of 36 digits: 207855748749177702475903581228065689
Probable prime cofactor 636775313135541920644661803313139569186068666649278705384340856517311504776930805506077 has 87 digits

May 27, 2009

By Wataru Sakai / GMP-ECM 6.2.1 / May 27, 2009

(56·10¹⁶⁸-11)/9 = 6(2)₁₆₇1_<169> = 33409 · 682183 · 251073507463_<12> · 21345376764104279543479_<23> · C125

C125 = P37 · P89

P37 = 2010311494190430198841667490889357457_<37>

P89 = 25340377371216548369200872625377112559349060405814187929776061184010278109483909816007387_<89>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1641621734
Step 1 took 11410ms
Step 2 took 5745ms
********** Factor found in step 2: 2010311494190430198841667490889357457
Found probable prime factor of 37 digits: 2010311494190430198841667490889357457
Probable prime cofactor 25340377371216548369200872625377112559349060405814187929776061184010278109483909816007387 has 89 digits

May 26, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / May 26, 2009

(56·10¹⁴⁸+61)/9 = 6(2)₁₄₇9_<149> = 3 · 877 · 1543 · 588079 · 22446283 · 9580622869530879653_<19> · C111

C111 = P51 · P60

P51 = 289514970278927942159258952609383815151082133561159_<51>

P60 = 418614114873860963119831279688454686719068277729444773205067_<60>

Number: 62229_148
N=121195053026045584142394732863532381780659248901094604117009289059680767354936395953884054694505268254893192653
  ( 111 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=289514970278927942159258952609383815151082133561159
 r2=418614114873860963119831279688454686719068277729444773205067
Version: 
Total time: 9.08 hours.
Scaled time: 21.71 units (timescale=2.391).
Factorization parameters were as follows:
n: 121195053026045584142394732863532381780659248901094604117009289059680767354936395953884054694505268254893192653
m: 1000000000000000000000000000000
deg: 5
c5: 14
c0: 1525
skew: 2.56
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7197933
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 374222 x 374470
Total sieving time: 8.38 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000
total time: 9.08 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(64·10³³³-1)/9 = 7(1)₃₃₃_<334> = 13 · 4999 · 228777281 · 1541677987_<10> · 1103253089147723_<16> · 897821565552123255197697079_<27> · 3426549570671671064841267094850481127005282543233354557266456990784769879505493_<79> · C191

C191 = P46 · C146

P46 = 1138685703753966317205547366328393186964066889_<46>

C146 = [80274634692979035236916096891593763332243932346695290164007809815885473899897686446683991310308022576677193511877133845257360068833629111661478111_<146>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 91407578898967392587495646040927113707134826897259567335187608469947492579148685035563607122524857909977897193250344414103264830313965448959782212407733030637049190216830852599866469613366679 (191 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3772275269
Step 1 took 17355ms
Step 2 took 7332ms
********** Factor found in step 2: 1138685703753966317205547366328393186964066889
Found probable prime factor of 46 digits: 1138685703753966317205547366328393186964066889
Composite cofactor 80274634692979035236916096891593763332243932346695290164007809815885473899897686446683991310308022576677193511877133845257360068833629111661478111 has 146 digits

(56·10¹⁶⁰+43)/9 = 6(2)₁₅₉7_<161> = 11 · 29 · 89 · 313 · 92791 · 544139 · 6514435771_<10> · 2061956422574897_<16> · C119

C119 = P38 · P81

P38 = 23586179971590229479094783927097020021_<38>

P81 = 437714449894873609652732767202131105370021782154533893534171532886167160496086903_<81>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 10324011791386102959321469009102640141118795635457083329933205374182497205761640135034992221084890050320448802746884963 (119 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3294267125
Step 1 took 3303ms
Step 2 took 2127ms
********** Factor found in step 2: 23586179971590229479094783927097020021
Found probable prime factor of 38 digits: 23586179971590229479094783927097020021
Probable prime cofactor 437714449894873609652732767202131105370021782154533893534171532886167160496086903 has 81 digits

(56·10¹⁵⁰+61)/9 = 6(2)₁₄₉9_<151> = 13 · 313 · 2117793157_<10> · 11389628087237_<14> · C125

C125 = P56 · P70

P56 = 45880006269511777788728871269771814767906863056900086357_<56>

P70 = 1381787550307658684570025101538845151921121612343299356704173071667957_<70>

Number: 62229_150
N=63396421471248701503774582755485442858010065898672575389777263502026078279011714548384334671616138564383032169071703329762649
  ( 125 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=45880006269511777788728871269771814767906863056900086357
 r2=1381787550307658684570025101538845151921121612343299356704173071667957
Version: 
Total time: 6.36 hours.
Scaled time: 15.22 units (timescale=2.392).
Factorization parameters were as follows:
n: 63396421471248701503774582755485442858010065898672575389777263502026078279011714548384334671616138564383032169071703329762649
m: 2000000000000000000000000000000
deg: 5
c5: 7
c0: 244
skew: 2.03
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 1600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6678090
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 359761 x 360009
Total sieving time: 5.85 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000
total time: 6.36 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹⁵¹+43)/9 = 6(2)₁₅₀7_<152> = 17 · 23 · 4971942883_<10> · 456814079039621_<15> · C125

C125 = P62 · P63

P62 = 93975190122255146831769552633703935437239278355207260903635149_<62>

P63 = 745572594250544127634375047849152507123131772168599590838274471_<63>

Number: 62227_151
N=70065326294637878981668261731991506218824553413226891366512464715316805317115533774559626960853188454863060360342646504981179
  ( 125 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=93975190122255146831769552633703935437239278355207260903635149
 r2=745572594250544127634375047849152507123131772168599590838274471
Version: 
Total time: 6.94 hours.
Scaled time: 16.60 units (timescale=2.391).
Factorization parameters were as follows:
n: 70065326294637878981668261731991506218824553413226891366512464715316805317115533774559626960853188454863060360342646504981179
m: 2000000000000000000000000000000
deg: 5
c5: 35
c0: 86
skew: 1.20
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1100000, 1700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8198304
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 316651 x 316899
Total sieving time: 6.34 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000
total time: 6.94 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 26, 2009 (6th)

By Wataru Sakai / GMP-ECM 6.2.1 / May 26, 2009

(34·10¹⁹³-43)/9 = 3(7)₁₉₂3_<194> = 3³ · 11 · 19² · 79 · 661 · 33889871 · 206690543 · 93566161264769_<14> · 219952497998232711504934775239_<30> · C125

C125 = P41 · P84

P41 = 69424502729465583786896074169319913973389_<41>

P84 = 674206903768606413668523156780015154564362553296911583362292946823897682656330305733_<84>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2671172606
Step 1 took 34040ms
Step 2 took 13572ms
********** Factor found in step 2: 69424502729465583786896074169319913973389
Found probable prime factor of 41 digits: 69424502729465583786896074169319913973389
Probable prime cofactor 674206903768606413668523156780015154564362553296911583362292946823897682656330305733 has 84 digits

May 26, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / May 26, 2009

(56·10¹⁵⁸+43)/9 = 6(2)₁₅₇7_<159> = 3 · 11 · 151 · C156

C156 = P51 · P105

P51 = 131335550907515946628289499737357777353323247025711_<51>

P105 = 950763126802695634262216390025909375472382868521848823716068506070698983337343456509688484625876526536779_<105>

Number: n
N=124868999041184471648047806988204339197716681160389769661292840100787120654670323544495729926193502352442749793743171226614935224206747385555332575200124869
  ( 156 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue May 26 11:51:07 2009  prp51 factor: 131335550907515946628289499737357777353323247025711
Tue May 26 11:51:07 2009  prp105 factor: 950763126802695634262216390025909375472382868521848823716068506070698983337343456509688484625876526536779
Tue May 26 11:51:07 2009  elapsed time 01:00:34 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 17.56 hours.
Scaled time: 46.71 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_2_157_7
n: 124868999041184471648047806988204339197716681160389769661292840100787120654670323544495729926193502352442749793743171226614935224206747385555332575200124869
m: 100000000000000000000000000000000
deg: 5
c5: 14
c0: 1075
skew: 2.38
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1700000, 2719897)
Primes: RFBsize:243539, AFBsize:243744, largePrimes:12847464 encountered
Relations: rels:11612917, finalFF:421044
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 910588 hash collisions in 12545435 relations
Msieve: matrix is 635285 x 635533 (172.0 MB)

Total sieving time: 17.32 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,28,28,56,56,2.4,2.4,100000
total time: 17.56 hours.
 --------- CPU info (if available) ----------

(56·10¹⁵⁷+43)/9 = 6(2)₁₅₆7_<158> = 273028069792489029181_<21> · C138

C138 = P63 · P75

P63 = 320942228218226583907804711929443473075863562997620056114681199_<63>

P75 = 710086662304528289565255283855826775901561463458072754281346535801862830433_<75>

Number: n
N=227896795628058710335314314166424003855735536627830620672743604025471001519443133269242576088187366592345094853326988207142020075590129167
  ( 138 digits)
SNFS difficulty: 158 digits.
Divisors found:

Tue May 26 12:02:33 2009  prp63 factor: 320942228218226583907804711929443473075863562997620056114681199
Tue May 26 12:02:33 2009  prp75 factor: 710086662304528289565255283855826775901561463458072754281346535801862830433
Tue May 26 12:02:33 2009  elapsed time 01:12:33 (Msieve 1.39 - dependency 8)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 17.54 hours.
Scaled time: 46.45 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_6_2_156_7
n: 227896795628058710335314314166424003855735536627830620672743604025471001519443133269242576088187366592345094853326988207142020075590129167
m: 20000000000000000000000000000000
deg: 5
c5: 175
c0: 43
skew: 0.76
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1500000, 2549171)
Primes: RFBsize:216816, AFBsize:217001, largePrimes:12428958 encountered
Relations: rels:11393794, finalFF:436268
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1006927 hash collisions in 12751827 relations
Msieve: matrix is 518804 x 519052 (138.8 MB)

Total sieving time: 17.27 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000
total time: 17.54 hours.
 --------- CPU info (if available) ----------

(29·10¹⁶⁹-11)/9 = 3(2)₁₆₈1_<170> = 739 · 20375213 · 761841315115219_<15> · C145

C145 = P38 · P107

P38 = 30185337815716905249692358934686648943_<38>

P107 = 93056846468806542487059667457037413274973699346875535788608105484856824239552996076515719745447019284007559_<107>

Number: n
N=2808952346726228286607349592413192856250276838617066864027465513158652213003638652734864016020646324259579957110275941513825532651046513191360137
  ( 145 digits)
SNFS difficulty: 171 digits.
Divisors found:

Tue May 26 23:55:05 2009  prp38 factor: 30185337815716905249692358934686648943
Tue May 26 23:55:05 2009  prp107 factor: 93056846468806542487059667457037413274973699346875535788608105484856824239552996076515719745447019284007559
Tue May 26 23:55:05 2009  elapsed time 01:59:15 (Msieve 1.39 - dependency 8)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 65.82 hours.
Scaled time: 166.07 units (timescale=2.523).
Factorization parameters were as follows:
name: KA_3_2_168_1
n: 2808952346726228286607349592413192856250276838617066864027465513158652213003638652734864016020646324259579957110275941513825532651046513191360137
m: 10000000000000000000000000000000000
deg: 5
c5: 29
c0: -110
skew: 1.31
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 6278801)
Primes: RFBsize:348513, AFBsize:349112, largePrimes:17921984 encountered
Relations: rels:17899366, finalFF:670524
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2434863 hash collisions in 20268295 relations
Msieve: matrix is 879292 x 879540 (232.6 MB)

Total sieving time: 64.98 hours.
Total relation processing time: 0.85 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 65.82 hours.
 --------- CPU info (if available) ----------

May 26, 2009 (4th)

By Dmitry Domanov / GGNFS/msieve 1.41 / May 26, 2009

(16·10¹⁹⁷-7)/9 = 1(7)₁₉₇_<198> = 3 · C197

C197 = P52 · P146

P52 = 2492719882705008579729261285974409303651590046350993_<52>

P146 = 23772931595889256247702401807095568187613434909292752523159600299070459234751820679071565671109595402287192339846210282361233657325888516506821963_<146>

Number: big197
N=59259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259
  ( 197 digits)
SNFS difficulty: 198 digits.
Divisors found:
r1=2492719882705008579729261285974409303651590046350993 (pp52)
r2=23772931595889256247702401807095568187613434909292752523159600299070459234751820679071565671109595402287192339846210282361233657325888516506821963 (pp146)
Version: Msieve v. 1.41
Total time: 619.58 hours.
Scaled time: 1231.72 units (timescale=1.988).
Factorization parameters were as follows:
n: 59259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259
m: 2000000000000000000000000000000000000000
deg: 5
c5: 50
c0: -7
skew: 0.67
type: snfs
lss: 1
rlim: 14100000
alim: 14100000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 14100000/14100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [7050000, 15550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2584336 x 2584584
Total sieving time: 607.29 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 11.22 hours.
Time per square root: 0.65 hours.
Prototype def-par.txt line would be:
snfs,198.000,5,0,0,0,0,0,0,0,0,14100000,14100000,28,28,55,55,2.5,2.5,100000
total time: 619.58 hours.
 --------- CPU info (if available) ----------

(16·10¹⁸⁹-7)/9 = 1(7)₁₈₉_<190> = 97 · 565257584232221_<15> · 2894757784480057_<16> · 313874266742039388275321127723139_<33> · C125

C125 = P49 · P76

P49 = 9641915714367601914559833623585613291763136575081_<49>

P76 = 3701076555786604628832541036576489067616431031951291380827268989656764182967_<76>

Number: 477
N=35685468203316383629285285631630576483658593506329090236596327342634932358233727998968557498199790458256613246731307616845327
  ( 125 digits)
Divisors found:
r1=9641915714367601914559833623585613291763136575081 (pp49)
r2=3701076555786604628832541036576489067616431031951291380827268989656764182967 (pp76)
Version: Msieve v. 1.41
Total time: 65.61 hours.
Scaled time: 130.43 units (timescale=1.988).
Factorization parameters were as follows:
# Murphy_E = 1.630694e-10, selected by Jeff Gilchrist
n: 35685468203316383629285285631630576483658593506329090236596327342634932358233727998968557498199790458256613246731307616845327
Y0: -1168519198374191872033102
Y1: 20511124710263
c0: -352577385070769488032860696085
c1: 39647842142184592470391721
c2: 173482975072407524037
c3: -2569127795806573
c4: -3778907800
c5: 16380
skew: 207212.3
type: gnfs
# selected mechanically
rlim: 7000000
alim: 7000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3500000, 6900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 915481 x 915729
Total sieving time: 64.15 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.15 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,124,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,7000000,7000000,27,27,52,52,2.5,2.5,100000
total time: 65.61 hours.
 --------- CPU info (if available) ----------

May 26, 2009 (3rd)

By Andreas Tete / GGNFS, Msieve v. 1.41 / May 26, 2009

(56·10¹⁶⁷+43)/9 = 6(2)₁₆₆7_<168> = 3 · 17 · 107 · 272993143283568505766291_<24> · 202190630619170096698842510247_<30> · C112

C112 = P50 · P63

P50 = 12913859117422035067458198332956795125072403023589_<50>

P63 = 159964183537285427027730694363434784194223930354711288637274587_<63>

Tue May 26 06:09:29 2009  Msieve v. 1.41
Tue May 26 06:09:29 2009  random seeds: 1d19d524 4eadf5fa
Tue May 26 06:09:29 2009  factoring 2065754930033945216243352113649333727221810688018550046454028316144656706557916899127021556696477554587231232743 (112 digits)
Tue May 26 06:09:31 2009  searching for 15-digit factors
Tue May 26 06:09:34 2009  commencing number field sieve (112-digit input)
Tue May 26 06:09:34 2009  R0: -3625033447227194025530
Tue May 26 06:09:34 2009  R1:  336182944457
Tue May 26 06:09:34 2009  A0: -23268323678036412887177004591
Tue May 26 06:09:34 2009  A1: -262632231566139633823819
Tue May 26 06:09:34 2009  A2: -1655649079234538915
Tue May 26 06:09:34 2009  A3:  84999748352463
Tue May 26 06:09:34 2009  A4:  390639850
Tue May 26 06:09:34 2009  A5:  3300
Tue May 26 06:09:34 2009  skew 116347.62, size 1.254584e-010, alpha -7.586029, combined = 8.633661e-010
Tue May 26 06:09:34 2009  
Tue May 26 06:09:34 2009  commencing relation filtering
Tue May 26 06:09:34 2009  commencing duplicate removal, pass 1
Tue May 26 06:11:31 2009  found 435423 hash collisions in 8143655 relations
Tue May 26 06:11:58 2009  added 58787 free relations
Tue May 26 06:11:58 2009  commencing duplicate removal, pass 2
Tue May 26 06:12:53 2009  found 339672 duplicates and 7862769 unique relations
Tue May 26 06:12:53 2009  memory use: 41.3 MB
Tue May 26 06:12:53 2009  reading rational ideals above 3604480
Tue May 26 06:12:53 2009  reading algebraic ideals above 3604480
Tue May 26 06:12:53 2009  commencing singleton removal, pass 1
Tue May 26 06:14:40 2009  relations with 0 large ideals: 138250
Tue May 26 06:14:40 2009  relations with 1 large ideals: 1038561
Tue May 26 06:14:40 2009  relations with 2 large ideals: 2734154
Tue May 26 06:14:40 2009  relations with 3 large ideals: 2897588
Tue May 26 06:14:40 2009  relations with 4 large ideals: 997490
Tue May 26 06:14:40 2009  relations with 5 large ideals: 0
Tue May 26 06:14:40 2009  relations with 6 large ideals: 56726
Tue May 26 06:14:40 2009  relations with 7+ large ideals: 0
Tue May 26 06:14:40 2009  7862769 relations and about 7636607 large ideals
Tue May 26 06:14:40 2009  commencing singleton removal, pass 2
Tue May 26 06:16:31 2009  found 3528605 singletons
Tue May 26 06:16:31 2009  current dataset: 4334164 relations and about 3416603 large ideals
Tue May 26 06:16:31 2009  commencing singleton removal, pass 3
Tue May 26 06:17:39 2009  found 719044 singletons
Tue May 26 06:17:39 2009  current dataset: 3615120 relations and about 2653573 large ideals
Tue May 26 06:17:39 2009  commencing singleton removal, pass 4
Tue May 26 06:18:28 2009  found 189682 singletons
Tue May 26 06:18:28 2009  current dataset: 3425438 relations and about 2460057 large ideals
Tue May 26 06:18:28 2009  commencing singleton removal, final pass
Tue May 26 06:19:21 2009  memory use: 66.6 MB
Tue May 26 06:19:21 2009  commencing in-memory singleton removal
Tue May 26 06:19:21 2009  begin with 3425438 relations and 2588466 unique ideals
Tue May 26 06:19:27 2009  reduce to 3051772 relations and 2208065 ideals in 15 passes
Tue May 26 06:19:27 2009  max relations containing the same ideal: 19
Tue May 26 06:19:28 2009  reading rational ideals above 720000
Tue May 26 06:19:28 2009  reading algebraic ideals above 720000
Tue May 26 06:19:28 2009  commencing singleton removal, final pass
Tue May 26 06:20:24 2009  keeping 2576865 ideals with weight <= 20, new excess is 231323
Tue May 26 06:20:28 2009  memory use: 90.6 MB
Tue May 26 06:20:28 2009  commencing in-memory singleton removal
Tue May 26 06:20:29 2009  begin with 3066465 relations and 2576865 unique ideals
Tue May 26 06:20:32 2009  reduce to 3048947 relations and 2487838 ideals in 8 passes
Tue May 26 06:20:32 2009  max relations containing the same ideal: 20
Tue May 26 06:20:36 2009  removing 749279 relations and 602892 ideals in 146387 cliques
Tue May 26 06:20:36 2009  commencing in-memory singleton removal
Tue May 26 06:20:36 2009  begin with 2299668 relations and 2487838 unique ideals
Tue May 26 06:20:40 2009  reduce to 2192609 relations and 1771961 ideals in 9 passes
Tue May 26 06:20:40 2009  max relations containing the same ideal: 20
Tue May 26 06:20:42 2009  removing 568468 relations and 422081 ideals in 146387 cliques
Tue May 26 06:20:42 2009  commencing in-memory singleton removal
Tue May 26 06:20:42 2009  begin with 1624141 relations and 1771961 unique ideals
Tue May 26 06:20:44 2009  reduce to 1525450 relations and 1244801 ideals in 10 passes
Tue May 26 06:20:44 2009  max relations containing the same ideal: 19
Tue May 26 06:20:45 2009  removing 81649 relations and 69335 ideals in 12314 cliques
Tue May 26 06:20:45 2009  commencing in-memory singleton removal
Tue May 26 06:20:46 2009  begin with 1443801 relations and 1244801 unique ideals
Tue May 26 06:20:47 2009  reduce to 1441089 relations and 1172727 ideals in 5 passes
Tue May 26 06:20:47 2009  max relations containing the same ideal: 18
Tue May 26 06:20:47 2009  relations with 0 large ideals: 25242
Tue May 26 06:20:47 2009  relations with 1 large ideals: 159541
Tue May 26 06:20:47 2009  relations with 2 large ideals: 390608
Tue May 26 06:20:47 2009  relations with 3 large ideals: 466073
Tue May 26 06:20:47 2009  relations with 4 large ideals: 287778
Tue May 26 06:20:47 2009  relations with 5 large ideals: 92935
Tue May 26 06:20:47 2009  relations with 6 large ideals: 17392
Tue May 26 06:20:47 2009  relations with 7+ large ideals: 1520
Tue May 26 06:20:47 2009  commencing 2-way merge
Tue May 26 06:20:50 2009  reduce to 897524 relation sets and 629162 unique ideals
Tue May 26 06:20:50 2009  commencing full merge
Tue May 26 06:21:03 2009  memory use: 45.4 MB
Tue May 26 06:21:03 2009  found 429073 cycles, need 393362
Tue May 26 06:21:03 2009  weight of 393362 cycles is about 27680407 (70.37/cycle)
Tue May 26 06:21:03 2009  distribution of cycle lengths:
Tue May 26 06:21:03 2009  1 relations: 39720
Tue May 26 06:21:03 2009  2 relations: 37268
Tue May 26 06:21:03 2009  3 relations: 39791
Tue May 26 06:21:03 2009  4 relations: 38591
Tue May 26 06:21:03 2009  5 relations: 36964
Tue May 26 06:21:03 2009  6 relations: 34142
Tue May 26 06:21:03 2009  7 relations: 31447
Tue May 26 06:21:03 2009  8 relations: 28300
Tue May 26 06:21:03 2009  9 relations: 24566
Tue May 26 06:21:03 2009  10+ relations: 82573
Tue May 26 06:21:03 2009  heaviest cycle: 17 relations
Tue May 26 06:21:03 2009  commencing cycle optimization
Tue May 26 06:21:04 2009  start with 2426704 relations
Tue May 26 06:21:12 2009  pruned 76457 relations
Tue May 26 06:21:12 2009  memory use: 62.3 MB
Tue May 26 06:21:12 2009  distribution of cycle lengths:
Tue May 26 06:21:12 2009  1 relations: 39720
Tue May 26 06:21:12 2009  2 relations: 38302
Tue May 26 06:21:12 2009  3 relations: 41621
Tue May 26 06:21:12 2009  4 relations: 39935
Tue May 26 06:21:12 2009  5 relations: 38536
Tue May 26 06:21:12 2009  6 relations: 35428
Tue May 26 06:21:12 2009  7 relations: 32474
Tue May 26 06:21:12 2009  8 relations: 28730
Tue May 26 06:21:12 2009  9 relations: 24690
Tue May 26 06:21:12 2009  10+ relations: 73926
Tue May 26 06:21:12 2009  heaviest cycle: 17 relations
Tue May 26 06:21:13 2009  RelProcTime: 530
Tue May 26 06:21:13 2009  
Tue May 26 06:21:13 2009  commencing linear algebra
Tue May 26 06:21:13 2009  read 393362 cycles
Tue May 26 06:21:14 2009  cycles contain 1279167 unique relations
Tue May 26 06:21:37 2009  read 1279167 relations
Tue May 26 06:21:40 2009  using 20 quadratic characters above 134216012
Tue May 26 06:21:50 2009  building initial matrix
Tue May 26 06:22:17 2009  memory use: 144.5 MB
Tue May 26 06:22:19 2009  read 393362 cycles
Tue May 26 06:22:20 2009  matrix is 393137 x 393362 (112.2 MB) with weight 37544918 (95.45/col)
Tue May 26 06:22:20 2009  sparse part has weight 26262120 (66.76/col)
Tue May 26 06:22:29 2009  filtering completed in 3 passes
Tue May 26 06:22:30 2009  matrix is 391430 x 391630 (111.9 MB) with weight 37438270 (95.60/col)
Tue May 26 06:22:30 2009  sparse part has weight 26207109 (66.92/col)
Tue May 26 06:22:31 2009  read 391630 cycles
Tue May 26 06:22:32 2009  matrix is 391430 x 391630 (111.9 MB) with weight 37438270 (95.60/col)
Tue May 26 06:22:32 2009  sparse part has weight 26207109 (66.92/col)
Tue May 26 06:22:32 2009  saving the first 48 matrix rows for later
Tue May 26 06:22:32 2009  matrix is 391382 x 391630 (107.1 MB) with weight 29862902 (76.25/col)
Tue May 26 06:22:32 2009  sparse part has weight 25728315 (65.70/col)
Tue May 26 06:22:32 2009  matrix includes 64 packed rows
Tue May 26 06:22:32 2009  using block size 65536 for processor cache size 3072 kB
Tue May 26 06:22:36 2009  commencing Lanczos iteration
Tue May 26 06:22:36 2009  memory use: 104.1 MB
Tue May 26 06:51:48 2009  lanczos halted after 6191 iterations (dim = 391380)
Tue May 26 06:51:49 2009  recovered 28 nontrivial dependencies
Tue May 26 06:51:49 2009  BLanczosTime: 1836
Tue May 26 06:51:49 2009  
Tue May 26 06:51:49 2009  commencing square root phase
Tue May 26 06:51:49 2009  reading relations for dependency 1
Tue May 26 06:51:49 2009  read 195890 cycles
Tue May 26 06:51:50 2009  cycles contain 791224 unique relations
Tue May 26 06:52:40 2009  read 791224 relations
Tue May 26 06:52:45 2009  multiplying 638908 relations
Tue May 26 06:54:36 2009  multiply complete, coefficients have about 26.49 million bits
Tue May 26 06:54:37 2009  initial square root is modulo 40454321
Tue May 26 06:57:24 2009  reading relations for dependency 2
Tue May 26 06:57:25 2009  read 195289 cycles
Tue May 26 06:57:25 2009  cycles contain 789633 unique relations
Tue May 26 06:58:16 2009  read 789633 relations
Tue May 26 06:58:22 2009  multiplying 638022 relations
Tue May 26 07:00:12 2009  multiply complete, coefficients have about 26.45 million bits
Tue May 26 07:00:13 2009  initial square root is modulo 39556393
Tue May 26 07:02:57 2009  sqrtTime: 668
Tue May 26 07:02:57 2009  prp50 factor: 12913859117422035067458198332956795125072403023589
Tue May 26 07:02:57 2009  prp63 factor: 159964183537285427027730694363434784194223930354711288637274587
Tue May 26 07:02:57 2009  elapsed time 00:53:28

May 26, 2009 (2nd)

By Sinkiti Sibata / Msieve / May 26, 2009

(56·10¹⁴²+61)/9 = 6(2)₁₄₁9_<143> = 3⁴ · 19 · 131 · 42419329483_<11> · 87525447502071318703_<20> · C107

C107 = P38 · P70

P38 = 44872549100086381398779792036441672819_<38>

P70 = 1852493621640036569971842416827656964494493099561502515079759713220051_<70>

Number: 62229_142
N=83126110994639384502124993651960889801899443839353934431248268695470043758248670095884805167694367492493769
  ( 107 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=44872549100086381398779792036441672819 (pp38)
 r2=1852493621640036569971842416827656964494493099561502515079759713220051 (pp70)
Version: Msieve-1.40
Total time: 6.74 hours.
Scaled time: 17.29 units (timescale=2.564).
Factorization parameters were as follows:
name: 62229_142
n: 83126110994639384502124993651960889801899443839353934431248268695470043758248670095884805167694367492493769
m: 20000000000000000000000000000
deg: 5
c5: 175
c0: 61
skew: 0.81
type: snfs
lss: 1
rlim: 1740000
alim: 1740000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1740000/1740000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [870000, 1770001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 282609 x 282857
Total sieving time: 6.74 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,143.000,5,0,0,0,0,0,0,0,0,1740000,1740000,26,26,48,48,2.3,2.3,100000
total time: 6.74 hours.
 --------- CPU info (if available) ----------

(56·10¹⁴⁹+43)/9 = 6(2)₁₄₈7_<150> = 3 · 503 · 521 · 8099537 · 1053083254675877_<16> · C122

C122 = P39 · P84

P39 = 150749794589437620706289474468020105961_<39>

P84 = 615515402049415406036097417507594704876193733951431676017316119220986881163077938187_<84>

Number: 62227_149
N=92788820425584484372450631418906503883926540579412767808945265882752439664813153845210701883662809020035395189181148232707
  ( 122 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=150749794589437620706289474468020105961 (pp39)
 r2=615515402049415406036097417507594704876193733951431676017316119220986881163077938187 (pp84)
Version: Msieve-1.40
Total time: 15.19 hours.
Scaled time: 31.57 units (timescale=2.078).
Factorization parameters were as follows:
name: 62227_149
n: 92788820425584484372450631418906503883926540579412767808945265882752439664813153845210701883662809020035395189181148232707
m: 1000000000000000000000000000000
deg: 5
c5: 28
c0: 215
skew: 1.50
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 370302 x 370550
Total sieving time: 14.54 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 15.19 hours.
 --------- CPU info (if available) ----------

May 26, 2009

Factorizations of 811...11 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 25, 2009 (8th)

By Erik Branger / GGNFS, Msieve / May 25, 2009

(56·10¹¹⁴+61)/9 = 6(2)₁₁₃9_<115> = 13 · 17 · 53 · 16391888269_<11> · C101

C101 = P43 · P58

P43 = 6330526609647274115237024207116463641404217_<43>

P58 = 5119276068573292810156043341228585529455167728488587180721_<58>

Number: 62229_114
N=32407713374233713689381067581298315293249215778887709800371510988289185758861020536966163909590500457
  ( 101 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=6330526609647274115237024207116463641404217 (pp43)
 r2=5119276068573292810156043341228585529455167728488587180721 (pp58)
Version: Msieve v. 1.41
Total time: 1.42 hours.
Scaled time: 1.24 units (timescale=0.873).
Factorization parameters were as follows:
n: 32407713374233713689381067581298315293249215778887709800371510988289185758861020536966163909590500457
m: 100000000000000000000000
deg: 5
c5: 28
c0: 305
skew: 1.61
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [305000, 505001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 59031 x 59258
Total sieving time: 1.38 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116.000,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000
total time: 1.42 hours.
 --------- CPU info (if available) ----------

(56·10¹⁵²+61)/9 = 6(2)₁₅₁9_<153> = 37 · 11186507 · C145

C145 = P32 · P45 · P68

P32 = 28942433849206367671246614943001_<32>

P45 = 595936129032331976442960402461375031323194639_<45>

P68 = 87159459781777493595426241904554628150888105525357079878608434976229_<68>

Number: 62229_152
N=1503312590500038735667605340685597105228362778194910781070160400991731987189282303834147407838462606496989347686173782112398161179071967399369331
  ( 145 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=28942433849206367671246614943001 (pp32)
 r2=595936129032331976442960402461375031323194639 (pp45)
 r3=87159459781777493595426241904554628150888105525357079878608434976229 (pp68)
Version: Msieve v. 1.41
Total time: 23.52 hours.
Scaled time: 21.85 units (timescale=0.929).
Factorization parameters were as follows:
n: 1503312590500038735667605340685597105228362778194910781070160400991731987189282303834147407838462606496989347686173782112398161179071967399369331
m: 2000000000000000000000000000000
deg: 5
c5: 175
c0: 61
skew: 0.81
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 417187 x 417435
Total sieving time: 22.71 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,153.000,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 23.52 hours.
 --------- CPU info (if available) ----------

May 25, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / May 25, 2009

(2·10¹⁷⁶+1)/3 = (6)₁₇₅7_<176> = 891423615315154872538304147_<27> · C149

C149 = P46 · P104

P46 = 1103614510810071915219795913454294436119696473_<46>

P104 = 67765274784633510325405809275250340559244879028941434970319872358880286167373422167498357591651212673457_<104>

Number: 66667_176
N=74786740581353412957536483508702404864499831989498538968548097789732163315742538650870690452878548195480134264825891327689726788458624388437703617161
  ( 149 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=1103614510810071915219795913454294436119696473
 r2=67765274784633510325405809275250340559244879028941434970319872358880286167373422167498357591651212673457
Version: 
Total time: 41.82 hours.
Scaled time: 99.56 units (timescale=2.381).
Factorization parameters were as follows:
n: 74786740581353412957536483508702404864499831989498538968548097789732163315742538650870690452878548195480134264825891327689726788458624388437703617161
m: 100000000000000000000000000000000000
deg: 5
c5: 20
c0: 1
skew: 0.55
type: snfs
lss: 1
rlim: 6800000
alim: 6800000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6800000/6800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3400000, 6200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 17375629
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1270401 x 1270648
Total sieving time: 35.56 hours.
Total relation processing time: 2.43 hours.
Matrix solve time: 3.67 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000
total time: 41.82 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(2·10¹⁸³+1)/3 = (6)₁₈₂7_<183> = 83 · 127 · 166561 · C174

C174 = P38 · C136

P38 = 45500165622286770651251939807357753869_<38>

C136 = [8345274578196455040772840047280934924400950145019956077371379711181517748470254840649874990874138242711129166964755686037538473271280243_<136>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 379711375471398074234106639718109884265998516506006882170335172843003391956211271054661861198218055599683554842890969670141327812629146543076795651919267864113486694516510167 (174 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=249765663
Step 1 took 18603ms
Step 2 took 7278ms
********** Factor found in step 2: 45500165622286770651251939807357753869
Found probable prime factor of 38 digits: 45500165622286770651251939807357753869
Composite cofactor 8345274578196455040772840047280934924400950145019956077371379711181517748470254840649874990874138242711129166964755686037538473271280243 has 136 digits

May 25, 2009 (6th)

By Andreas Tete / Msieve 1.41, GGNFS / May 25, 2009

(56·10¹³⁰+61)/9 = 6(2)₁₂₉9_<131> = 3 · 17 · 31 · 383 · 389 · 22362407201_<11> · 93495249169104112307_<20> · C93

C93 = P35 · P58

P35 = 46247980690072474031252763921167863_<35>

P58 = 2731897511788387797568503987411292236154621175780104218527_<58>

Sun May 24 20:20:45 2009  Msieve v. 1.41
Sun May 24 20:20:45 2009  random seeds: 092395d0 b3c8db31
Sun May 24 20:20:45 2009  factoring 126344743372446397853828500971974809042236413069841939570637101725244189122830500998801597801 (93 digits)
Sun May 24 20:20:46 2009  searching for 15-digit factors
Sun May 24 20:20:48 2009  commencing quadratic sieve (93-digit input)
Sun May 24 20:20:48 2009  using multiplier of 1
Sun May 24 20:20:48 2009  using 32kb Intel Core sieve core
Sun May 24 20:20:48 2009  sieve interval: 36 blocks of size 32768
Sun May 24 20:20:48 2009  processing polynomials in batches of 6
Sun May 24 20:20:48 2009  using a sieve bound of 1855093 (69412 primes)
Sun May 24 20:20:48 2009  using large prime bound of 209625509 (27 bits)
Sun May 24 20:20:48 2009  using double large prime bound of 951917611763851 (42-50 bits)
Sun May 24 20:20:48 2009  using trial factoring cutoff of 50 bits
Sun May 24 20:20:48 2009  polynomial 'A' values have 12 factors
Sun May 24 21:50:51 2009  69988 relations (18807 full + 51181 combined from 878512 partial), need 69508
Sun May 24 21:50:52 2009  begin with 897319 relations
Sun May 24 21:50:53 2009  reduce to 173296 relations in 11 passes
Sun May 24 21:50:53 2009  attempting to read 173296 relations
Sun May 24 21:50:55 2009  recovered 173296 relations
Sun May 24 21:50:55 2009  recovered 149101 polynomials
Sun May 24 21:50:55 2009  attempting to build 69988 cycles
Sun May 24 21:50:55 2009  found 69988 cycles in 6 passes
Sun May 24 21:50:55 2009  distribution of cycle lengths:
Sun May 24 21:50:55 2009     length 1 : 18807
Sun May 24 21:50:55 2009     length 2 : 13230
Sun May 24 21:50:55 2009     length 3 : 12138
Sun May 24 21:50:55 2009     length 4 : 9193
Sun May 24 21:50:55 2009     length 5 : 6597
Sun May 24 21:50:55 2009     length 6 : 4296
Sun May 24 21:50:55 2009     length 7 : 2591
Sun May 24 21:50:55 2009     length 9+: 3136
Sun May 24 21:50:55 2009  largest cycle: 18 relations
Sun May 24 21:50:55 2009  matrix is 69412 x 69988 (16.8 MB) with weight 4113021 (58.77/col)
Sun May 24 21:50:55 2009  sparse part has weight 4113021 (58.77/col)
Sun May 24 21:50:56 2009  filtering completed in 3 passes
Sun May 24 21:50:56 2009  matrix is 64767 x 64831 (15.5 MB) with weight 3813493 (58.82/col)
Sun May 24 21:50:56 2009  sparse part has weight 3813493 (58.82/col)
Sun May 24 21:50:56 2009  saving the first 48 matrix rows for later
Sun May 24 21:50:56 2009  matrix is 64719 x 64831 (9.1 MB) with weight 2880785 (44.44/col)
Sun May 24 21:50:56 2009  sparse part has weight 1985361 (30.62/col)
Sun May 24 21:50:56 2009  matrix includes 64 packed rows
Sun May 24 21:50:56 2009  using block size 25932 for processor cache size 3072 kB
Sun May 24 21:50:57 2009  commencing Lanczos iteration
Sun May 24 21:50:57 2009  memory use: 9.3 MB
Sun May 24 21:51:18 2009  lanczos halted after 1025 iterations (dim = 64716)
Sun May 24 21:51:18 2009  recovered 14 nontrivial dependencies
Sun May 24 21:51:19 2009  prp35 factor: 46247980690072474031252763921167863
Sun May 24 21:51:19 2009  prp58 factor: 2731897511788387797568503987411292236154621175780104218527
Sun May 24 21:51:19 2009  elapsed time 01:30:34

(56·10¹⁴³+61)/9 = 6(2)₁₄₂9_<144> = 37² · 373 · 17957 · 1184131106238803_<16> · 215044693802791697848307401_<27> · C93

C93 = P45 · P48

P45 = 317892978543602332825062735108706473864059569_<45>

P48 = 838281725573898180269529020619937933152992089583_<48>

Sun May 24 20:21:04 2009  Msieve v. 1.41
Sun May 24 20:21:04 2009  random seeds: 122f2e58 cfce9184
Sun May 24 20:21:04 2009  factoring 266483874601357153181251525441014367612362300577944076002637810002542212287393126744496369727 (93 digits)
Sun May 24 20:21:05 2009  searching for 15-digit factors
Sun May 24 20:21:06 2009  commencing quadratic sieve (93-digit input)
Sun May 24 20:21:06 2009  using multiplier of 23
Sun May 24 20:21:06 2009  using 32kb Intel Core sieve core
Sun May 24 20:21:06 2009  sieve interval: 36 blocks of size 32768
Sun May 24 20:21:06 2009  processing polynomials in batches of 6
Sun May 24 20:21:06 2009  using a sieve bound of 1923137 (71682 primes)
Sun May 24 20:21:06 2009  using large prime bound of 232699577 (27 bits)
Sun May 24 20:21:06 2009  using double large prime bound of 1148767303677169 (42-51 bits)
Sun May 24 20:21:06 2009  using trial factoring cutoff of 51 bits
Sun May 24 20:21:06 2009  polynomial 'A' values have 12 factors
Sun May 24 22:15:21 2009  72189 relations (18540 full + 53649 combined from 955622 partial), need 71778
Sun May 24 22:15:22 2009  begin with 974162 relations
Sun May 24 22:15:22 2009  reduce to 182692 relations in 10 passes
Sun May 24 22:15:22 2009  attempting to read 182692 relations
Sun May 24 22:15:24 2009  recovered 182692 relations
Sun May 24 22:15:24 2009  recovered 161726 polynomials
Sun May 24 22:15:24 2009  attempting to build 72189 cycles
Sun May 24 22:15:24 2009  found 72189 cycles in 5 passes
Sun May 24 22:15:24 2009  distribution of cycle lengths:
Sun May 24 22:15:24 2009     length 1 : 18540
Sun May 24 22:15:24 2009     length 2 : 13035
Sun May 24 22:15:24 2009     length 3 : 12364
Sun May 24 22:15:24 2009     length 4 : 9765
Sun May 24 22:15:24 2009     length 5 : 7042
Sun May 24 22:15:24 2009     length 6 : 4696
Sun May 24 22:15:24 2009     length 7 : 2920
Sun May 24 22:15:24 2009     length 9+: 3827
Sun May 24 22:15:24 2009  largest cycle: 22 relations
Sun May 24 22:15:25 2009  matrix is 71682 x 72189 (18.5 MB) with weight 4572493 (63.34/col)
Sun May 24 22:15:25 2009  sparse part has weight 4572493 (63.34/col)
Sun May 24 22:15:25 2009  filtering completed in 4 passes
Sun May 24 22:15:25 2009  matrix is 67624 x 67688 (17.4 MB) with weight 4291973 (63.41/col)
Sun May 24 22:15:25 2009  sparse part has weight 4291973 (63.41/col)
Sun May 24 22:15:25 2009  saving the first 48 matrix rows for later
Sun May 24 22:15:25 2009  matrix is 67576 x 67688 (11.0 MB) with weight 3377687 (49.90/col)
Sun May 24 22:15:25 2009  sparse part has weight 2467530 (36.45/col)
Sun May 24 22:15:25 2009  matrix includes 64 packed rows
Sun May 24 22:15:25 2009  using block size 27075 for processor cache size 3072 kB
Sun May 24 22:15:26 2009  commencing Lanczos iteration
Sun May 24 22:15:26 2009  memory use: 10.6 MB
Sun May 24 22:15:48 2009  lanczos halted after 1069 iterations (dim = 67576)
Sun May 24 22:15:48 2009  recovered 18 nontrivial dependencies
Sun May 24 22:15:49 2009  prp45 factor: 317892978543602332825062735108706473864059569
Sun May 24 22:15:49 2009  prp48 factor: 838281725573898180269529020619937933152992089583
Sun May 24 22:15:49 2009  elapsed time 01:54:45

(56·10¹⁴⁰+61)/9 = 6(2)₁₃₉9_<141> = 37 · 53 · 89 · 963758813 · 54907861729789_<14> · 460872462819125911_<18> · C96

C96 = P39 · P57

P39 = 978943390360530542658966408125707944647_<39>

P57 = 149326430979469122412950225463477963912388764701360493229_<57>

Sun May 24 22:39:56 2009  Msieve v. 1.41
Sun May 24 22:39:56 2009  random seeds: 06f87b70 c674ec23
Sun May 24 22:39:56 2009  factoring 146182122613479262289613169053058939851336705039243163791190781853654247444845783800423750295163 (96 digits)
Sun May 24 22:39:56 2009  searching for 15-digit factors
Sun May 24 22:39:58 2009  commencing quadratic sieve (96-digit input)
Sun May 24 22:39:58 2009  using multiplier of 43
Sun May 24 22:39:58 2009  using 32kb Intel Core sieve core
Sun May 24 22:39:58 2009  sieve interval: 36 blocks of size 32768
Sun May 24 22:39:58 2009  processing polynomials in batches of 6
Sun May 24 22:39:58 2009  using a sieve bound of 2231351 (82021 primes)
Sun May 24 22:39:58 2009  using large prime bound of 334702650 (28 bits)
Sun May 24 22:39:58 2009  using double large prime bound of 2209970306285550 (43-51 bits)
Sun May 24 22:39:58 2009  using trial factoring cutoff of 51 bits
Sun May 24 22:39:58 2009  polynomial 'A' values have 13 factors
Mon May 25 02:48:05 2009  82159 relations (19904 full + 62255 combined from 1225582 partial), need 82117
Mon May 25 02:48:11 2009  begin with 1245486 relations
Mon May 25 02:48:11 2009  reduce to 213522 relations in 10 passes
Mon May 25 02:48:11 2009  attempting to read 213522 relations
Mon May 25 02:48:14 2009  recovered 213522 relations
Mon May 25 02:48:14 2009  recovered 200363 polynomials
Mon May 25 02:48:15 2009  attempting to build 82159 cycles
Mon May 25 02:48:15 2009  found 82159 cycles in 5 passes
Mon May 25 02:48:15 2009  distribution of cycle lengths:
Mon May 25 02:48:15 2009     length 1 : 19904
Mon May 25 02:48:15 2009     length 2 : 14671
Mon May 25 02:48:15 2009     length 3 : 13906
Mon May 25 02:48:15 2009     length 4 : 11285
Mon May 25 02:48:15 2009     length 5 : 8474
Mon May 25 02:48:15 2009     length 6 : 5479
Mon May 25 02:48:15 2009     length 7 : 3542
Mon May 25 02:48:15 2009     length 9+: 4898
Mon May 25 02:48:15 2009  largest cycle: 19 relations
Mon May 25 02:48:15 2009  matrix is 82021 x 82159 (22.0 MB) with weight 5431070 (66.10/col)
Mon May 25 02:48:15 2009  sparse part has weight 5431070 (66.10/col)
Mon May 25 02:48:16 2009  filtering completed in 3 passes
Mon May 25 02:48:16 2009  matrix is 78309 x 78373 (21.1 MB) with weight 5212730 (66.51/col)
Mon May 25 02:48:16 2009  sparse part has weight 5212730 (66.51/col)
Mon May 25 02:48:16 2009  saving the first 48 matrix rows for later
Mon May 25 02:48:16 2009  matrix is 78261 x 78373 (13.2 MB) with weight 4124874 (52.63/col)
Mon May 25 02:48:16 2009  sparse part has weight 2986916 (38.11/col)
Mon May 25 02:48:16 2009  matrix includes 64 packed rows
Mon May 25 02:48:16 2009  using block size 31349 for processor cache size 3072 kB
Mon May 25 02:48:17 2009  commencing Lanczos iteration
Mon May 25 02:48:17 2009  memory use: 12.7 MB
Mon May 25 02:48:51 2009  lanczos halted after 1240 iterations (dim = 78257)
Mon May 25 02:48:51 2009  recovered 15 nontrivial dependencies
Mon May 25 02:48:51 2009  prp39 factor: 978943390360530542658966408125707944647
Mon May 25 02:48:51 2009  prp57 factor: 149326430979469122412950225463477963912388764701360493229
Mon May 25 02:48:51 2009  elapsed time 04:08:55

(56·10¹⁴⁹+61)/9 = 6(2)₁₄₈9_<150> = 37 · 367 · 1051 · 341777 · 77367889 · 31670079807843380454722401_<26> · C104

C104 = P36 · P68

P36 = 832195583129323149983272972560380221_<36>

P68 = 62560018490695800182384977161797681356057234677991482841691500909777_<68>

Mon May 25 05:33:46 2009  Msieve v. 1.41
Mon May 25 05:33:46 2009  random seeds: 018af4c8 d7d4be39
Mon May 25 05:33:46 2009  factoring 52062171068445830162659955825043517121841057140092515963953339641548995481118465125414925940886536320717 (104 digits)
Mon May 25 05:33:47 2009  searching for 15-digit factors
Mon May 25 05:33:48 2009  commencing number field sieve (104-digit input)
Mon May 25 05:33:49 2009  R0: -129310016354264376017
Mon May 25 05:33:49 2009  R1:  37729512247
Mon May 25 05:33:49 2009  A0: -12303180889884472428281196
Mon May 25 05:33:49 2009  A1:  6672523770448843233576
Mon May 25 05:33:49 2009  A2:  8027043772154227
Mon May 25 05:33:49 2009  A3: -9727220638494
Mon May 25 05:33:49 2009  A4: -11933922
Mon May 25 05:33:49 2009  A5:  1440
Mon May 25 05:33:49 2009  skew 42751.50, size 6.886428e-010, alpha -5.640437, combined = 2.142178e-009
Mon May 25 05:33:49 2009  
Mon May 25 05:33:49 2009  commencing relation filtering
Mon May 25 05:33:49 2009  commencing duplicate removal, pass 1
Mon May 25 05:34:50 2009  found 252836 hash collisions in 4403292 relations
Mon May 25 05:35:03 2009  added 31659 free relations
Mon May 25 05:35:03 2009  commencing duplicate removal, pass 2
Mon May 25 05:35:24 2009  found 229075 duplicates and 4205875 unique relations
Mon May 25 05:35:24 2009  memory use: 36.7 MB
Mon May 25 05:35:24 2009  reading rational ideals above 2686976
Mon May 25 05:35:24 2009  reading algebraic ideals above 2686976
Mon May 25 05:35:24 2009  commencing singleton removal, pass 1
Mon May 25 05:36:10 2009  relations with 0 large ideals: 105708
Mon May 25 05:36:10 2009  relations with 1 large ideals: 667887
Mon May 25 05:36:10 2009  relations with 2 large ideals: 1524536
Mon May 25 05:36:10 2009  relations with 3 large ideals: 1433892
Mon May 25 05:36:10 2009  relations with 4 large ideals: 443789
Mon May 25 05:36:10 2009  relations with 5 large ideals: 0
Mon May 25 05:36:10 2009  relations with 6 large ideals: 30063
Mon May 25 05:36:10 2009  relations with 7+ large ideals: 0
Mon May 25 05:36:10 2009  4205875 relations and about 4232833 large ideals
Mon May 25 05:36:10 2009  commencing singleton removal, pass 2
Mon May 25 05:36:57 2009  found 1957334 singletons
Mon May 25 05:36:57 2009  current dataset: 2248541 relations and about 1850202 large ideals
Mon May 25 05:36:57 2009  commencing singleton removal, pass 3
Mon May 25 05:37:22 2009  found 469164 singletons
Mon May 25 05:37:22 2009  current dataset: 1779377 relations and about 1341428 large ideals
Mon May 25 05:37:22 2009  commencing singleton removal, final pass
Mon May 25 05:37:42 2009  memory use: 33.3 MB
Mon May 25 05:37:42 2009  commencing in-memory singleton removal
Mon May 25 05:37:42 2009  begin with 1779377 relations and 1378143 unique ideals
Mon May 25 05:37:44 2009  reduce to 1436060 relations and 1023327 ideals in 17 passes
Mon May 25 05:37:44 2009  max relations containing the same ideal: 15
Mon May 25 05:37:44 2009  reading rational ideals above 100000
Mon May 25 05:37:44 2009  reading algebraic ideals above 100000
Mon May 25 05:37:44 2009  commencing singleton removal, final pass
Mon May 25 05:38:06 2009  keeping 1311028 ideals with weight <= 25, new excess is 105073
Mon May 25 05:38:08 2009  memory use: 46.3 MB
Mon May 25 05:38:08 2009  commencing in-memory singleton removal
Mon May 25 05:38:08 2009  begin with 1436466 relations and 1311028 unique ideals
Mon May 25 05:38:10 2009  reduce to 1418531 relations and 1291094 ideals in 14 passes
Mon May 25 05:38:10 2009  max relations containing the same ideal: 25
Mon May 25 05:38:11 2009  relations with 0 large ideals: 3714
Mon May 25 05:38:11 2009  relations with 1 large ideals: 36679
Mon May 25 05:38:11 2009  relations with 2 large ideals: 154974
Mon May 25 05:38:11 2009  relations with 3 large ideals: 345255
Mon May 25 05:38:11 2009  relations with 4 large ideals: 428854
Mon May 25 05:38:11 2009  relations with 5 large ideals: 297777
Mon May 25 05:38:11 2009  relations with 6 large ideals: 120870
Mon May 25 05:38:11 2009  relations with 7+ large ideals: 30408
Mon May 25 05:38:11 2009  commencing 2-way merge
Mon May 25 05:38:13 2009  reduce to 793834 relation sets and 666539 unique ideals
Mon May 25 05:38:13 2009  ignored 142 oversize relation sets
Mon May 25 05:38:13 2009  commencing full merge
Mon May 25 05:38:26 2009  memory use: 51.8 MB
Mon May 25 05:38:26 2009  found 348548 cycles, need 336739
Mon May 25 05:38:26 2009  weight of 336739 cycles is about 23875670 (70.90/cycle)
Mon May 25 05:38:26 2009  distribution of cycle lengths:
Mon May 25 05:38:26 2009  1 relations: 37628
Mon May 25 05:38:26 2009  2 relations: 36630
Mon May 25 05:38:26 2009  3 relations: 35577
Mon May 25 05:38:26 2009  4 relations: 32071
Mon May 25 05:38:26 2009  5 relations: 28916
Mon May 25 05:38:26 2009  6 relations: 25285
Mon May 25 05:38:26 2009  7 relations: 21939
Mon May 25 05:38:26 2009  8 relations: 18742
Mon May 25 05:38:26 2009  9 relations: 16541
Mon May 25 05:38:26 2009  10+ relations: 83410
Mon May 25 05:38:26 2009  heaviest cycle: 23 relations
Mon May 25 05:38:26 2009  commencing cycle optimization
Mon May 25 05:38:27 2009  start with 2248490 relations
Mon May 25 05:38:33 2009  pruned 62276 relations
Mon May 25 05:38:33 2009  memory use: 57.9 MB
Mon May 25 05:38:33 2009  distribution of cycle lengths:
Mon May 25 05:38:33 2009  1 relations: 37628
Mon May 25 05:38:33 2009  2 relations: 37508
Mon May 25 05:38:33 2009  3 relations: 36957
Mon May 25 05:38:33 2009  4 relations: 32991
Mon May 25 05:38:33 2009  5 relations: 29754
Mon May 25 05:38:33 2009  6 relations: 25609
Mon May 25 05:38:33 2009  7 relations: 22241
Mon May 25 05:38:33 2009  8 relations: 18838
Mon May 25 05:38:33 2009  9 relations: 16417
Mon May 25 05:38:33 2009  10+ relations: 78796
Mon May 25 05:38:33 2009  heaviest cycle: 23 relations
Mon May 25 05:38:34 2009  RelProcTime: 240
Mon May 25 05:38:34 2009  
Mon May 25 05:38:34 2009  commencing linear algebra
Mon May 25 05:38:34 2009  read 336739 cycles
Mon May 25 05:38:35 2009  cycles contain 1199734 unique relations
Mon May 25 05:38:48 2009  read 1199734 relations
Mon May 25 05:38:49 2009  using 20 quadratic characters above 67107320
Mon May 25 05:38:57 2009  building initial matrix
Mon May 25 05:39:13 2009  memory use: 131.8 MB
Mon May 25 05:39:13 2009  read 336739 cycles
Mon May 25 05:39:14 2009  matrix is 336429 x 336739 (95.4 MB) with weight 32260771 (95.80/col)
Mon May 25 05:39:14 2009  sparse part has weight 22649350 (67.26/col)
Mon May 25 05:39:19 2009  filtering completed in 3 passes
Mon May 25 05:39:19 2009  matrix is 333871 x 334071 (94.9 MB) with weight 32048592 (95.93/col)
Mon May 25 05:39:19 2009  sparse part has weight 22527086 (67.43/col)
Mon May 25 05:39:20 2009  read 334071 cycles
Mon May 25 05:39:21 2009  matrix is 333871 x 334071 (94.9 MB) with weight 32048592 (95.93/col)
Mon May 25 05:39:21 2009  sparse part has weight 22527086 (67.43/col)
Mon May 25 05:39:21 2009  saving the first 48 matrix rows for later
Mon May 25 05:39:21 2009  matrix is 333823 x 334071 (91.6 MB) with weight 25399168 (76.03/col)
Mon May 25 05:39:21 2009  sparse part has weight 22011721 (65.89/col)
Mon May 25 05:39:21 2009  matrix includes 64 packed rows
Mon May 25 05:39:21 2009  using block size 65536 for processor cache size 3072 kB
Mon May 25 05:39:24 2009  commencing Lanczos iteration
Mon May 25 05:39:24 2009  memory use: 89.0 MB
Mon May 25 05:55:18 2009  lanczos halted after 5279 iterations (dim = 333823)
Mon May 25 05:55:19 2009  recovered 30 nontrivial dependencies
Mon May 25 05:55:19 2009  BLanczosTime: 1005
Mon May 25 05:55:19 2009  
Mon May 25 05:55:19 2009  commencing square root phase
Mon May 25 05:55:19 2009  reading relations for dependency 1
Mon May 25 05:55:20 2009  read 167116 cycles
Mon May 25 05:55:20 2009  cycles contain 736925 unique relations
Mon May 25 05:55:42 2009  read 736925 relations
Mon May 25 05:55:46 2009  multiplying 597656 relations
Mon May 25 05:57:16 2009  multiply complete, coefficients have about 22.86 million bits
Mon May 25 05:57:17 2009  initial square root is modulo 3683189
Mon May 25 05:59:23 2009  reading relations for dependency 2
Mon May 25 05:59:23 2009  read 166895 cycles
Mon May 25 05:59:24 2009  cycles contain 736574 unique relations
Mon May 25 05:59:43 2009  read 736574 relations
Mon May 25 05:59:47 2009  multiplying 597616 relations
Mon May 25 06:01:16 2009  multiply complete, coefficients have about 22.86 million bits
Mon May 25 06:01:17 2009  initial square root is modulo 3677743
Mon May 25 06:03:23 2009  reading relations for dependency 3
Mon May 25 06:03:23 2009  read 167360 cycles
Mon May 25 06:03:23 2009  cycles contain 737677 unique relations
Mon May 25 06:03:32 2009  read 737677 relations
Mon May 25 06:03:36 2009  multiplying 598594 relations
Mon May 25 06:05:05 2009  multiply complete, coefficients have about 22.89 million bits
Mon May 25 06:05:06 2009  initial square root is modulo 3763663
Mon May 25 06:07:13 2009  reading relations for dependency 4
Mon May 25 06:07:13 2009  read 167048 cycles
Mon May 25 06:07:13 2009  cycles contain 736390 unique relations
Mon May 25 06:07:30 2009  read 736390 relations
Mon May 25 06:07:34 2009  multiplying 598082 relations
Mon May 25 06:09:02 2009  multiply complete, coefficients have about 22.88 million bits
Mon May 25 06:09:03 2009  initial square root is modulo 3720209
Mon May 25 06:11:10 2009  sqrtTime: 951
Mon May 25 06:11:10 2009  prp36 factor: 832195583129323149983272972560380221
Mon May 25 06:11:10 2009  prp68 factor: 62560018490695800182384977161797681356057234677991482841691500909777
Mon May 25 06:11:10 2009  elapsed time 00:37:24
total time 6.5 hours

May 25, 2009 (5th)

By Sinkiti Sibata / GGNFS, Msieve / May 25, 2009

(56·10¹³⁸+43)/9 = 6(2)₁₃₇7_<139> = 11 · 941 · 2081 · 73319904863013559_<17> · C115

C115 = P54 · P62

P54 = 252582742401819496101004032224677833111279988837135163_<54>

P62 = 15597879529518414507388705585990268985508739535035277037248401_<62>

Number: 62227_138
N=3939755187218963168564073683454277537648892061874153338956209989139586816829311362788017536263011469626285242624363
  ( 115 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=252582742401819496101004032224677833111279988837135163 (pp54)
 r2=15597879529518414507388705585990268985508739535035277037248401 (pp62)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 9.47 hours.
Scaled time: 4.48 units (timescale=0.473).
Factorization parameters were as follows:
name: 62227_138
n: 3939755187218963168564073683454277537648892061874153338956209989139586816829311362788017536263011469626285242624363
m: 10000000000000000000000000000
deg: 5
c5: 14
c0: 1075
skew: 2.38
type: snfs
lss: 1
rlim: 1580000
alim: 1580000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1580000/1580000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [790000, 1490001)
Primes: RFBsize:119758, AFBsize:119798, largePrimes:3500496 encountered
Relations: rels:3503621, finalFF:331649
Max relations in full relation-set: 28
Initial matrix: 239623 x 331649 with sparse part having weight 26600511.
Pruned matrix : 205538 x 206800 with weight 12852082.
Total sieving time: 8.47 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.79 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000
total time: 9.47 hours.
 --------- CPU info (if available) ----------

(56·10¹³⁹+43)/9 = 6(2)₁₃₈7_<140> = 36314261237_<11> · C130

C130 = P53 · P78

P53 = 16917846419888696768298044123057919511670201250983773_<53>

P78 = 101279891163629551253563290479520952949599673934425934851975389746050526567827_<78>

Number: 62227_139
N=1713437644129327058688367892522417892364908148116768536706504340616505826625808007270359281141562335294994678738154229856960871271
  ( 130 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=16917846419888696768298044123057919511670201250983773 (pp53)
 r2=101279891163629551253563290479520952949599673934425934851975389746050526567827 (pp78)
Version: Msieve-1.40
Total time: 5.80 hours.
Scaled time: 11.89 units (timescale=2.051).
Factorization parameters were as follows:
name: 62227_139
n: 1713437644129327058688367892522417892364908148116768536706504340616505826625808007270359281141562335294994678738154229856960871271
m: 10000000000000000000000000000
deg: 5
c5: 28
c0: 215
skew: 1.50
type: snfs
lss: 1
rlim: 1590000
alim: 1590000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1590000/1590000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [795000, 1495001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 237030 x 237272
Total sieving time: 5.51 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1590000,1590000,26,26,48,48,2.3,2.3,100000
total time: 5.80 hours.
 --------- CPU info (if available) ----------

(56·10¹³³+61)/9 = 6(2)₁₃₂9_<134> = 3² · 23 · 57791 · 11594399 · C120

C120 = P40 · P81

P40 = 2050093115527204261907231651787933907889_<40>

P81 = 218823083595232013815530432131300867020797233718074161750759354297345178113504747_<81>

Number: 62229_133
N=448607697197019060625892563531944678283091071139362032611439778047028539705459320296028668163660435906071845109662249083
  ( 120 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=2050093115527204261907231651787933907889 (pp40)
 r2=218823083595232013815530432131300867020797233718074161750759354297345178113504747 (pp81)
Version: Msieve-1.40
Total time: 5.02 hours.
Scaled time: 12.86 units (timescale=2.564).
Factorization parameters were as follows:
name: 62229_133
n: 448607697197019060625892563531944678283091071139362032611439778047028539705459320296028668163660435906071845109662249083
m: 400000000000000000000000000
deg: 5
c5: 875
c0: 976
skew: 1.02
type: snfs
lss: 1
rlim: 1290000
alim: 1290000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1290000/1290000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [645000, 1395001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 205047 x 205295
Total sieving time: 5.02 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,135.000,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,47,47,2.3,2.3,75000
total time: 5.02 hours.
 --------- CPU info (if available) ----------

(56·10¹⁴⁴+43)/9 = 6(2)₁₄₃7_<145> = 11 · 1129 · 7321697527_<10> · 74149919989_<11> · 286114807428707_<15> · C106

C106 = P40 · P67

P40 = 1032081249274106458614747291742945237133_<40>

P67 = 3125231534392205434001538433222177150023095481011878101744560218381_<67>

Number: 62227_144
N=3225492866286339988432275090241219659458968821377202212036109173924177050533883647824390348308870310341673
  ( 106 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1032081249274106458614747291742945237133 (pp40)
 r2=3125231534392205434001538433222177150023095481011878101744560218381 (pp67)
Version: Msieve-1.40
Total time: 8.53 hours.
Scaled time: 17.22 units (timescale=2.019).
Factorization parameters were as follows:
name: 62227_144
n: 3225492866286339988432275090241219659458968821377202212036109173924177050533883647824390348308870310341673
m: 100000000000000000000000000000
deg: 5
c5: 28
c0: 215
skew: 1.50
type: snfs
lss: 1
rlim: 1930000
alim: 1930000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1930000/1930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [965000, 1965001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 295553 x 295788
Total sieving time: 8.07 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000
total time: 8.53 hours.
 --------- CPU info (if available) ----------

(56·10¹³¹+61)/9 = 6(2)₁₃₀9_<132> = 37 · 283 · 643883 · C122

C122 = P57 · P66

P57 = 159686308718439159016667656009306239856813271212893922903_<57>

P66 = 577939951522268816742636674750823088926876138623548752575547561151_<66>

Number: 62229_131
N=92289097519504779862952719554869071871120983603499068731655019677004049875514370065206669198915030245941280087690671941353
  ( 122 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=159686308718439159016667656009306239856813271212893922903 (pp57)
 r2=577939951522268816742636674750823088926876138623548752575547561151 (pp66)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 6.12 hours.
Scaled time: 2.90 units (timescale=0.474).
Factorization parameters were as follows:
name: 62229_131
n: 92289097519504779862952719554869071871120983603499068731655019677004049875514370065206669198915030245941280087690671941353
m: 200000000000000000000000000
deg: 5
c5: 35
c0: 122
skew: 1.28
type: snfs
lss: 1
rlim: 1160000
alim: 1160000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1160000/1160000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [580000, 1080001)
Primes: RFBsize:90030, AFBsize:89794, largePrimes:2889130 encountered
Relations: rels:2764091, finalFF:201528
Max relations in full relation-set: 28
Initial matrix: 179890 x 201528 with sparse part having weight 15605433.
Pruned matrix : 172692 x 173655 with weight 11444066.
Total sieving time: 5.44 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.50 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1160000,1160000,26,26,47,47,2.3,2.3,50000
total time: 6.12 hours.
 --------- CPU info (if available) ----------

(56·10¹³⁵+61)/9 = 6(2)₁₃₄9_<136> = 149 · 2769863903_<10> · 121665866875249877_<18> · C108

C108 = P45 · P63

P45 = 209015100514626233074544372015842670379194321_<45>

P63 = 592863072551192271076213234179270899072477314898132518913979571_<63>

Number: 62229_135
N=123917334700697597414242200320681797444203769876573619477198778577783375289171534465147893407700710833216291
  ( 108 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=209015100514626233074544372015842670379194321 (pp45)
 r2=592863072551192271076213234179270899072477314898132518913979571 (pp63)
Version: Msieve-1.40
Total time: 3.83 hours.
Scaled time: 9.81 units (timescale=2.564).
Factorization parameters were as follows:
name: 62229_135
n: 123917334700697597414242200320681797444203769876573619477198778577783375289171534465147893407700710833216291
m: 1000000000000000000000000000
deg: 5
c5: 56
c0: 61
skew: 1.02
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1190001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 171604 x 171852
Total sieving time: 3.83 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 3.83 hours.
 --------- CPU info (if available) ----------

May 25, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / May 25, 2009

(56·10¹⁶⁰-11)/9 = 6(2)₁₅₉1_<161> = 269 · 373 · 1230295747861_<13> · C144

C144 = P63 · P81

P63 = 775846871621927753324108755276601243288486937913721807341743493_<63>

P81 = 649679060495355895325070925859546682086034606213142987112835244431188959754868821_<81>

Number: n
N=504051466643595019894954236222448362647569780846853338415788166117574360723140988666841004315521289230578075817789845038183606421744841645331753
  ( 144 digits)
SNFS difficulty: 162 digits.
Divisors found:

Mon May 25 02:47:00 2009  prp63 factor: 775846871621927753324108755276601243288486937913721807341743493
Mon May 25 02:47:00 2009  prp81 factor: 649679060495355895325070925859546682086034606213142987112835244431188959754868821
Mon May 25 02:47:00 2009  elapsed time 01:07:14 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 24.56 hours.
Scaled time: 65.32 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_2_159_1
n: 504051466643595019894954236222448362647569780846853338415788166117574360723140988666841004315521289230578075817789845038183606421744841645331753
m: 200000000000000000000000000000000
deg: 5
c5: 7
c0: -44
skew: 1.44
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1800000, 3276551)
Primes: RFBsize:256726, AFBsize:256192, largePrimes:13666778 encountered
Relations: rels:12674729, finalFF:493008
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1249037 hash collisions in 14356305 relations
Msieve: matrix is 624633 x 624881 (166.0 MB)

Total sieving time: 24.22 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,56,56,2.4,2.4,100000
total time: 24.56 hours.
 --------- CPU info (if available) ----------

(56·10¹⁶²-11)/9 = 6(2)₁₆₁1_<163> = 197 · 252142207 · 111065768926160413_<18> · C136

C136 = P49 · P87

P49 = 1823252523842627786390503818226391271537327698861_<49>

P87 = 618595406100207642323032126026402169934936034070394900447336655500101739827442920178543_<87>

Number: n
N=1127855635409658852402902632598064353581145150105534602459045513277510690669157474826168615022942292427479973569208316215515613457739523
  ( 136 digits)
SNFS difficulty: 163 digits.
Divisors found:

Mon May 25 02:50:27 2009  prp49 factor: 1823252523842627786390503818226391271537327698861
Mon May 25 02:50:27 2009  prp87 factor: 618595406100207642323032126026402169934936034070394900447336655500101739827442920178543
Mon May 25 02:50:27 2009  elapsed time 01:11:34 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 23.92 hours.
Scaled time: 62.84 units (timescale=2.627).
Factorization parameters were as follows:
name: KA_6_2_161_1
n: 1127855635409658852402902632598064353581145150105534602459045513277510690669157474826168615022942292427479973569208316215515613457739523
m: 200000000000000000000000000000000
deg: 5
c5: 175
c0: -11
skew: 0.58
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1900000, 3274757)
Primes: RFBsize:269987, AFBsize:270713, largePrimes:13952484 encountered
Relations: rels:12951526, finalFF:549074
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1202406 hash collisions in 14619892 relations
Msieve: matrix is 621423 x 621671 (167.0 MB)

Total sieving time: 23.56 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3800000,3800000,28,28,56,56,2.4,2.4,100000
total time: 23.92 hours.
 --------- CPU info (if available) ----------

(56·10¹⁶⁷-11)/9 = 6(2)₁₆₆1_<168> = 3 · 209567 · C162

C162 = P50 · P113

P50 = 19443110822937189264550767307016668556003239123591_<50>

P113 = 50902090040427650194639698198812141669545651810512442623714907082500172503194814420162690721388875673540845020231_<113>

Number: n
N=989694977775162155336514849224388417104827608389715019098462102370160413650085210970273981148784910827598846227733409398461625195796129196903173722043105104369521
  ( 162 digits)
SNFS difficulty: 168 digits.
Divisors found:

Mon May 25 13:47:58 2009  prp50 factor: 19443110822937189264550767307016668556003239123591
Mon May 25 13:47:58 2009  prp113 factor: 50902090040427650194639698198812141669545651810512442623714907082500172503194814420162690721388875673540845020231
Mon May 25 13:47:58 2009  elapsed time 01:17:42 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 34.31 hours.
Scaled time: 91.25 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_2_166_1
n: 989694977775162155336514849224388417104827608389715019098462102370160413650085210970273981148784910827598846227733409398461625195796129196903173722043105104369521
m: 2000000000000000000000000000000000
deg: 5
c5: 175
c0: -11
skew: 0.58
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2250000, 4166023)
Primes: RFBsize:315948, AFBsize:316727, largePrimes:15604488 encountered
Relations: rels:14708231, finalFF:619987
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1424982 hash collisions in 15945458 relations
Msieve: matrix is 805558 x 805806 (218.3 MB)

Total sieving time: 33.73 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000
total time: 34.31 hours.
 --------- CPU info (if available) ----------

May 25, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / May 25, 2009

(10²⁰³-7)/3 = (3)₂₀₂1_<203> = 61 · 137458709 · 74987928326523863886652073_<26> · 10610358077968123193638709904195047_<35> · C133

C133 = P46 · P88

P46 = 4587999570650147356774231952309279185249023649_<46>

P88 = 1089010042319197941814674558968741326938785715705358274243860464565699180298897115436301_<88>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=4169885631
Step 1 took 583777ms
Step 2 took 152715ms
********** Factor found in step 2: 4587999570650147356774231952309279185249023649
Found probable prime factor of 46 digits: 4587999570650147356774231952309279185249023649
Probable prime cofactor 1089010042319197941814674558968741326938785715705358274243860464565699180298897115436301 has 88 digits

(56·10¹⁹⁹+61)/9 = 6(2)₁₉₈9_<200> = 3 · 23 · 579433 · 312051449 · 81427551415291_<14> · 4489531305364324771_<19> · 39767223830636299661_<20> · C132

C132 = P37 · P96

P37 = 1209584055008769471318521911851364117_<37>

P96 = 283617674035040392384807441800220868385912808582004760099992553834346079760320670717642984524689_<96>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1028574052
Step 1 took 41086ms
Step 2 took 15269ms
********** Factor found in step 2: 1209584055008769471318521911851364117
Found probable prime factor of 37 digits: 1209584055008769471318521911851364117
Probable prime cofactor 283617674035040392384807441800220868385912808582004760099992553834346079760320670717642984524689 has 96 digits

May 25, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / May 25, 2009

(56·10¹⁵⁹+61)/9 = 6(2)₁₅₈9_<160> = 136879 · 1401744473_<10> · C146

C146 = P34 · C113

P34 = 1017640607768771362296572005537507_<34>

C113 = [31867310563954942460860793410742458897721802139714768023254519185323949327123209616553915892182082536506231931441_<113>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2708368817
Step 1 took 9001ms
Step 2 took 5336ms
********** Factor found in step 2: 1017640607768771362296572005537507
Found probable prime factor of 34 digits: 1017640607768771362296572005537507
Composite cofactor has 113 digits

(56·10¹⁷⁰+61)/9 = 6(2)₁₆₉9_<171> = 37 · 67 · 60348354518122561506923_<23> · C145

C145 = P35 · C110

P35 = 50323262668560143510940878296447111_<35>

C110 = [82648460313433883981241425769067111639470813131991163858925087068467532014766035327819208292972854598269167367_<110>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3826816614
Step 1 took 9036ms
Step 2 took 4981ms
********** Factor found in step 2: 50323262668560143510940878296447111
Found probable prime factor of 35 digits: 50323262668560143510940878296447111
Composite cofactor has 110 digits

(56·10¹⁹⁵+61)/9 = 6(2)₁₉₄9_<196> = 43 · 3182601396073271461249_<22> · C173

C173 = P32 · C142

P32 = 16693093986305324656984769853199_<32>

C142 = [2723691869854779319603026289539237147981460259414140512173402438206782609228973001831820347551262311828517281485882982830362108368597411785553_<142>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3990195945
Step 1 took 10597ms
Step 2 took 6004ms
********** Factor found in step 2: 16693093986305324656984769853199
Found probable prime factor of 32 digits: 16693093986305324656984769853199
Composite cofactor has 142 digits

(56·10¹⁹¹+61)/9 = 6(2)₁₉₀9_<192> = 37 · 975849195904534229_<18> · C173

C173 = P30 · P143

P30 = 635681258779264596324193416307_<30>

P143 = 27109510583283492081643976278683612870546015190877688257375898962423467107326967638290646508596450189747001674490682798108581473816237145499039_<143>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3303208364
Step 1 took 10609ms
Step 2 took 5792ms
********** Factor found in step 2: 635681258779264596324193416307
Found probable prime factor of 30 digits: 635681258779264596324193416307
Probable prime cofactor has 143 digits

(56·10¹⁰⁷+61)/9 = 6(2)₁₀₆9_<108> = 37 · 379 · 112927 · 55560881 · C91

C91 = P37 · P55

P37 = 2295077568936423863494133074142261789_<37>

P55 = 3081344817769656577369011100621445436455662919402022161_<55>

SNFS difficulty: 108 digits.
Divisors found:
 r1=2295077568936423863494133074142261789 (pp37)
 r2=3081344817769656577369011100621445436455662919402022161 (pp55)
Version: Msieve v. 1.41
Total time: 0.43 hours.
Scaled time: 1.27 units (timescale=2.952).
Factorization parameters were as follows:
n: 7071925373421631420796761079039365887080635651240836510936657912643231821326147396841506029
m: 2000000000000000000000
deg: 5
c5: 175
c0: 61
skew: 0.81
type: snfs
lss: 1
rlim: 450000
alim: 450000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 450000/450000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [225000, 375001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 40775 x 41003
Total sieving time: 0.40 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,108.000,5,0,0,0,0,0,0,0,0,450000,450000,25,25,44,44,2.2,2.2,50000
total time: 0.43 hours.

(56·10¹⁰⁹+61)/9 = 6(2)₁₀₈9_<110> = 3 · 59 · 2377 · 71947 · C100

C100 = P40 · P60

P40 = 2824281279310317588227094570203151997417_<40>

P60 = 727817397218189875999836925903135109554540687624630777625599_<60>

SNFS difficulty: 111 digits.
Divisors found:
 r1=2824281279310317588227094570203151997417 (pp40)
 r2=727817397218189875999836925903135109554540687624630777625599 (pp60)
Version: Msieve v. 1.41
Total time: 0.41 hours.
Scaled time: 1.22 units (timescale=2.953).
Factorization parameters were as follows:
n: 2055561049719694884428140807935064724630352561769741255986414432336507158381803421499204389441077783
m: 10000000000000000000000
deg: 5
c5: 28
c0: 305
skew: 1.61
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [250000, 400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 48123 x 48349
Total sieving time: 0.38 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 0.41 hours.

May 25, 2009

Factorizations of 622...229 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 24, 2009 (7th)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve v. 1.41 / May 24, 2009

(56·10¹⁵⁵+43)/9 = 6(2)₁₅₄7_<156> = 3 · 59 · 2789452241_<10> · 2996112633712301879539_<22> · C123

C123 = P30 · P35 · P59

P30 = 389870705611988238369726947353_<30>

P35 = 92761963956040897493510077601053423_<35>

P59 = 11630667659548072946415545987059571680567690307767207819271_<59>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2813365054
Step 1 took 11317ms
Step 2 took 5645ms
********** Factor found in step 2: 389870705611988238369726947353
Found probable prime factor of 30 digits: 389870705611988238369726947353
Composite cofactor 1078883574219688887059781833004601860775772060817862175000544130711681997737837040792199914633 has 94 digits
----------------------
Sun May 24 19:37:17 2009  Msieve v. 1.41
Sun May 24 19:37:17 2009  random seeds: f1b7c9b4 8e4f20a1
Sun May 24 19:37:17 2009  factoring 1078883574219688887059781833004601860775772060817862175000544130711681997737837040792199914633 (94 digits)
Sun May 24 19:37:18 2009  searching for 15-digit factors
Sun May 24 19:37:19 2009  commencing quadratic sieve (94-digit input)
Sun May 24 19:37:19 2009  using multiplier of 2
Sun May 24 19:37:19 2009  using 32kb Intel Core sieve core
Sun May 24 19:37:19 2009  sieve interval: 36 blocks of size 32768
Sun May 24 19:37:19 2009  processing polynomials in batches of 6
Sun May 24 19:37:19 2009  using a sieve bound of 1980947 (74118 primes)
Sun May 24 19:37:19 2009  using large prime bound of 255542163 (27 bits)
Sun May 24 19:37:19 2009  using double large prime bound of 1359667019806545 (42-51 bits)
Sun May 24 19:37:19 2009  using trial factoring cutoff of 51 bits
Sun May 24 19:37:19 2009  polynomial 'A' values have 12 factors
Sun May 24 22:08:52 2009  74293 relations (17920 full + 56373 combined from 1039979 partial), need 74214
Sun May 24 22:08:53 2009  begin with 1057899 relations
Sun May 24 22:08:54 2009  reduce to 194343 relations in 11 passes
Sun May 24 22:08:54 2009  attempting to read 194343 relations
Sun May 24 22:08:55 2009  recovered 194343 relations
Sun May 24 22:08:55 2009  recovered 178893 polynomials
Sun May 24 22:08:55 2009  attempting to build 74293 cycles
Sun May 24 22:08:55 2009  found 74293 cycles in 5 passes
Sun May 24 22:08:55 2009  distribution of cycle lengths:
Sun May 24 22:08:55 2009     length 1 : 17920
Sun May 24 22:08:55 2009     length 2 : 12771
Sun May 24 22:08:55 2009     length 3 : 12586
Sun May 24 22:08:55 2009     length 4 : 10058
Sun May 24 22:08:55 2009     length 5 : 7860
Sun May 24 22:08:55 2009     length 6 : 5167
Sun May 24 22:08:55 2009     length 7 : 3339
Sun May 24 22:08:55 2009     length 9+: 4592
Sun May 24 22:08:55 2009  largest cycle: 20 relations
Sun May 24 22:08:55 2009  matrix is 74118 x 74293 (19.0 MB) with weight 4686053 (63.08/col)
Sun May 24 22:08:55 2009  sparse part has weight 4686053 (63.08/col)
Sun May 24 22:08:56 2009  filtering completed in 3 passes
Sun May 24 22:08:56 2009  matrix is 70817 x 70881 (18.2 MB) with weight 4498517 (63.47/col)
Sun May 24 22:08:56 2009  sparse part has weight 4498517 (63.47/col)
Sun May 24 22:08:56 2009  saving the first 48 matrix rows for later
Sun May 24 22:08:56 2009  matrix is 70769 x 70881 (10.7 MB) with weight 3460039 (48.81/col)
Sun May 24 22:08:56 2009  sparse part has weight 2390791 (33.73/col)
Sun May 24 22:08:56 2009  matrix includes 64 packed rows
Sun May 24 22:08:56 2009  using block size 28352 for processor cache size 6144 kB
Sun May 24 22:08:56 2009  commencing Lanczos iteration
Sun May 24 22:08:56 2009  memory use: 10.9 MB
Sun May 24 22:09:14 2009  lanczos halted after 1121 iterations (dim = 70765)
Sun May 24 22:09:15 2009  recovered 14 nontrivial dependencies
Sun May 24 22:09:15 2009  prp35 factor: 92761963956040897493510077601053423
Sun May 24 22:09:15 2009  prp59 factor: 11630667659548072946415545987059571680567690307767207819271
Sun May 24 22:09:15 2009  elapsed time 02:31:58

May 24, 2009 (6th)

By Sinkiti Sibata / GMP-ECM 6.2, Msieve / May 24, 2009

(56·10¹⁷¹+43)/9 = 6(2)₁₇₀7_<172> = 13 · 31 · 866555766780581_<15> · 104333591897662925186183537264500679_<36> · C120

C120 = P30 · P90

P30 = 913359407733730867454204942251_<30>

P90 = 186972652452924239112747207858060766215361741312914837100521197879242145306970573282591041_<90>

Run 38 out of 2318:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3857517126
Step 1 took 44672ms
Step 2 took 20984ms
********** Factor found in step 2: 913359407733730867454204942251
Found probable prime factor of 30 digits: 913359407733730867454204942251
Probable prime cofactor 18697265245292423911274720785806076621536174131291483710
0521197879242145306970573282591041 has 90 digits

(56·10¹²¹+43)/9 = 6(2)₁₂₀7_<122> = 220771 · C117

C117 = P49 · P68

P49 = 9837523052183919446566376509856910961364164092149_<49>

P68 = 28649545041019888937504172137615515915556659334640337227186636743213_<68>

Number: 62227_121
N=281840559775614651481499935327657265774138008262961268564359550041546318231208909785353249395175191588669808182334737
  ( 117 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=9837523052183919446566376509856910961364164092149 (pp49)
 r2=28649545041019888937504172137615515915556659334640337227186636743213 (pp68)
Version: Msieve-1.40
Total time: 1.43 hours.
Scaled time: 2.99 units (timescale=2.092).
Factorization parameters were as follows:
name:  62227_121
n: 281840559775614651481499935327657265774138008262961268564359550041546318231208909785353249395175191588669808182334737
m: 2000000000000000000000000
deg: 5
c5: 35
c0: 86
skew: 1.20
type: snfs
lss: 1
rlim: 790000
alim: 790000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 790000/790000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [395000, 595001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 77044 x 77272
Total sieving time: 1.38 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,123.000,5,0,0,0,0,0,0,0,0,790000,790000,25,25,46,46,2.2,2.2,50000
total time: 1.43 hours.
 --------- CPU info (if available) ----------

(56·10¹³¹+43)/9 = 6(2)₁₃₀7_<132> = 3 · 241 · 4974095003_<10> · 12592035475039_<14> · C107

C107 = P36 · P71

P36 = 446751495478926418011405201098840477_<36>

P71 = 30756094804548521464938261943862495082201487416789170131157756023139761_<71>

Number: 62227_131
N=13740331349023691081262371544782048819022677210235262837555319619113317592126935803456752792873718014905997
  ( 107 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=446751495478926418011405201098840477 (pp36)
 r2=30756094804548521464938261943862495082201487416789170131157756023139761 (pp71)
Version: Msieve-1.40
Total time: 2.54 hours.
Scaled time: 5.13 units (timescale=2.019).
Factorization parameters were as follows:
name: 62227_131
n: 13740331349023691081262371544782048819022677210235262837555319619113317592126935803456752792873718014905997
m: 200000000000000000000000000
deg: 5
c5: 35
c0: 86
skew: 1.20
type: snfs
lss: 1
rlim: 1160000
alim: 1160000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1160000/1160000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [580000, 880001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 159075 x 159311
Total sieving time: 2.39 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,133.000,5,0,0,0,0,0,0,0,0,1160000,1160000,26,26,47,47,2.3,2.3,50000
total time: 2.54 hours.
 --------- CPU info (if available) ----------

(56·10¹³⁷+43)/9 = 6(2)₁₃₆7_<138> = 3 · 1019 · 1093 · 185831 · 1994119 · 24351891709373_<14> · C107

C107 = P38 · P70

P38 = 18820540090523760177462888274940089121_<38>

P70 = 1096467833377187138957925392191314902327577642797243965784912605287971_<70>

Number: 62227_137
N=20636116816045076827182019814547604895449093412286731348595867767639030081888155139050751735319042609263491
  ( 107 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=18820540090523760177462888274940089121 (pp38)
 r2=1096467833377187138957925392191314902327577642797243965784912605287971 (pp70)
Version: Msieve-1.40
Total time: 4.85 hours.
Scaled time: 9.91 units (timescale=2.045).
Factorization parameters were as follows:
name: 62227_137
n: 20636116816045076827182019814547604895449093412286731348595867767639030081888155139050751735319042609263491
m: 2000000000000000000000000000
deg: 5
c5: 175
c0: 43
skew: 0.76
type: snfs
lss: 1
rlim: 1440000
alim: 1440000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1440000/1440000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [720000, 1320001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 218250 x 218491
Total sieving time: 4.59 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,138.000,5,0,0,0,0,0,0,0,0,1440000,1440000,26,26,48,48,2.3,2.3,75000
total time: 4.85 hours.
 --------- CPU info (if available) ----------

May 24, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 24, 2009

2·10¹⁹⁰-1 = 1(9)₁₉₀_<191> = 7 · 23 · 151 · 1043761 · C180

C180 = P80 · P101

P80 = 27676127635110233402503730692785558639486036666823955434117813714327581673274833_<80>

P101 = 28478740748702695477340652489819896975660217520497038645376481346236576555545798008200801855853755193_<101>

Number: 19999_190
N=788181263848310569191168289698477608629667806002138500262250231716631429766774029824489209769354914397516489610270580329936650268653863597002338747131096998004045747905232989957769
  ( 180 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=27676127635110233402503730692785558639486036666823955434117813714327581673274833
 r2=28478740748702695477340652489819896975660217520497038645376481346236576555545798008200801855853755193
Version: 
Total time: 128.90 hours.
Scaled time: 308.07 units (timescale=2.390).
Factorization parameters were as follows:
n: 788181263848310569191168289698477608629667806002138500262250231716631429766774029824489209769354914397516489610270580329936650268653863597002338747131096998004045747905232989957769
m: 100000000000000000000000000000000000000
deg: 5
c5: 2
c0: -1
skew: 0.87
type: snfs
lss: 1
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 7900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 20445526
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1710578 x 1710826
Total sieving time: 118.17 hours.
Total relation processing time: 3.65 hours.
Matrix solve time: 6.91 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000
total time: 128.90 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹³⁰+43)/9 = 6(2)₁₂₉7_<131> = 11² · C129

C129 = P56 · P73

P56 = 72233322432718414569232836843550578144966505331853321253_<56>

P73 = 7119058409433545234707650257417296676583573298236685291355068311287769679_<73>

Number: 62227_130
N=514233241505968778696051423324150596877869605142332415059687786960514233241505968778696051423324150596877869605142332415059687787
  ( 129 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=72233322432718414569232836843550578144966505331853321253
 r2=7119058409433545234707650257417296676583573298236685291355068311287769679
Version: 
Total time: 1.19 hours.
Scaled time: 2.84 units (timescale=2.389).
Factorization parameters were as follows:
n: 514233241505968778696051423324150596877869605142332415059687786960514233241505968778696051423324150596877869605142332415059687787
m: 200000000000000000000000000
deg: 5
c5: 7
c0: 172
skew: 1.90
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2835911
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 148128 x 148376
Total sieving time: 1.03 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 1.19 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹³⁴+43)/9 = 6(2)₁₃₃7_<135> = 3⁴ · 11 · C132

C132 = P54 · P79

P54 = 192604255731103436303710965316098343362792567691761203_<54>

P79 = 3625784053583637817608793557180079376482560388589629390866850398023592021991699_<79>

Number: 62227_134
N=698341439082179822920563661304402045142785883526624267365008105748846489587230327971068711809452550193290934031674772415513156253897
  ( 132 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=192604255731103436303710965316098343362792567691761203
 r2=3625784053583637817608793557180079376482560388589629390866850398023592021991699
Version: 
Total time: 1.86 hours.
Scaled time: 4.44 units (timescale=2.390).
Factorization parameters were as follows:
n: 698341439082179822920563661304402045142785883526624267365008105748846489587230327971068711809452550193290934031674772415513156253897
m: 1000000000000000000000000000
deg: 5
c5: 28
c0: 215
skew: 1.50
type: snfs
lss: 1
rlim: 1400000
alim: 1400000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [700000, 1150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3274434
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 203984 x 204232
Total sieving time: 1.59 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,26,26,48,48,2.3,2.3,50000
total time: 1.86 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 24, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / May 24, 2009

(56·10¹⁹⁹+43)/9 = 6(2)₁₉₈7_<200> = 17 · 67 · 302390323 · 54155250493414958844529123_<26> · 5291829120047019899159557464003015689_<37> · C126

C126 = P34 · P93

P34 = 2008749061218436992848565483649771_<34>

P93 = 313820880783536836636772081534716495375043694090733253911265097187774233741468386340143215843_<93>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1829143434
Step 1 took 7572ms
Step 2 took 4445ms
********** Factor found in step 2: 2008749061218436992848565483649771
Found probable prime factor of 34 digits: 2008749061218436992848565483649771
Probable prime cofactor has 93 digits

(56·10¹⁸²+43)/9 = 6(2)₁₈₁7_<183> = 3 · 11 · 19 · 763846635731399196931_<21> · C160

C160 = P35 · C125

P35 = 77070395583281942176460981358816319_<35>

C125 = [16857152605764005065047232676396102366871417751924711712204360137910738853018733972405664108283513247694184519411936056181109_<125>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2792916294
Step 1 took 10817ms
Step 2 took 5524ms
********** Factor found in step 2: 77070395583281942176460981358816319
Found probable prime factor of 35 digits: 77070395583281942176460981358816319
Composite cofactor has 125 digits

(56·10¹⁶⁷+43)/9 = 6(2)₁₆₆7_<168> = 3 · 17 · 107 · 272993143283568505766291_<24> · C141

C141 = P30 · C112

P30 = 202190630619170096698842510247_<30>

C112 = [2065754930033945216243352113649333727221810688018550046454028316144656706557916899127021556696477554587231232743_<112>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2717518823
Step 1 took 9233ms
Step 2 took 4972ms
********** Factor found in step 2: 202190630619170096698842510247
Found probable prime factor of 30 digits: 202190630619170096698842510247
Composite cofactor has 112 digits

(56·10¹⁸⁶+43)/9 = 6(2)₁₈₅7_<187> = 11 · 31 · 20226806889120479159903_<23> · C162

C162 = P35 · P128

P35 = 58045262016572887128888099753888857_<35>

P128 = 15541646783249331782258374772285235272347816600047608549641982111352344802341765058279612308967565859193730460809532798442526657_<128>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3456060348
Step 1 took 10489ms
********** Factor found in step 1: 58045262016572887128888099753888857
Found probable prime factor of 35 digits: 58045262016572887128888099753888857
Probable prime cofactor has 128 digits

(56·10¹⁰⁵+43)/9 = 6(2)₁₀₄7_<106> = 13 · 173 · 191 · C101

C101 = P48 · P53

P48 = 232285334117970032187985184744148944279078916011_<48>

P53 = 62359253040006800401370106387797632463343215746998223_<53>

SNFS difficulty: 106 digits.
Divisors found:
 r1=232285334117970032187985184744148944279078916011 (pp48)
 r2=62359253040006800401370106387797632463343215746998223 (pp53)
Version: Msieve v. 1.41
Total time: 0.30 hours.
Scaled time: 0.90 units (timescale=2.943).
Factorization parameters were as follows:
n: 14485139927745018081851904446705160926024649052219188102733785631827577171522939159049681701983248453
m: 200000000000000000000000000
deg: 4
c4: 35
c0: 43
skew: 1.05
type: snfs
lss: 1
rlim: 420000
alim: 420000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 420000/420000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [210000, 310001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 33412 x 33639
Total sieving time: 0.28 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,106.000,4,0,0,0,0,0,0,0,0,420000,420000,25,25,44,44,2.2,2.2,20000
total time: 0.30 hours.

(56·10¹¹¹+43)/9 = 6(2)₁₁₀7_<112> = 13 · 31 · 71 · 5303 · C104

C104 = P47 · P58

P47 = 13897540214212527692645902486242042976664910799_<47>

P58 = 2950683011130204299615480832638819572472845820061038977007_<58>

SNFS difficulty: 113 digits.
Divisors found:
 r1=13897540214212527692645902486242042976664910799 (pp47)
 r2=2950683011130204299615480832638819572472845820061038977007 (pp58)
Version: Msieve v. 1.41
Total time: 0.48 hours.
Scaled time: 1.42 units (timescale=2.951).
Factorization parameters were as follows:
n: 41007235806575725696026815732831110100780693485242177944644714630722910606662210835069365507803866998593
m: 20000000000000000000000
deg: 5
c5: 35
c0: 86
skew: 1.20
type: snfs
lss: 1
rlim: 540000
alim: 540000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 540000/540000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [270000, 420001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 43248 x 43476
Total sieving time: 0.45 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,113.000,5,0,0,0,0,0,0,0,0,540000,540000,25,25,45,45,2.2,2.2,50000
total time: 0.48 hours.

(56·10¹¹³+43)/9 = 6(2)₁₁₂7_<114> = 3 · 5023929737_<10> · C104

C104 = P36 · P69

P36 = 408348128880194658464406352398206191_<36>

P69 = 101099762660918448367538763269301577394107046179160743691761007449127_<69>

Msieve v. 1.39
Sun May 24 00:22:17 2009
random seeds: 7fbe7db1 de138fc7
factoring 41283898912817818217708765580892400009973986506692143136437221913998955158438237411083324513343488945257 (104 digits)
searching for 15-digit factors
commencing number field sieve (104-digit input)
R0: -100000000000000000000000
R1:  1
A0:  1075
A1:  0
A2:  0
A3:  0
A4:  0
A5:  14
skew 2.38, size 2.597755e-08, alpha -0.612885, combined = 3.186562e-08

commencing square root phase
reading relations for dependency 1
read 28696 cycles
cycles contain 110948 unique relations
read 110948 relations
multiplying 85764 relations
multiply complete, coefficients have about 1.99 million bits
initial square root is modulo 1536515521
Newton iteration failed to converge
algebraic square root failed
reading relations for dependency 2
read 28880 cycles
cycles contain 111389 unique relations
read 111389 relations
multiplying 86004 relations
multiply complete, coefficients have about 2.00 million bits
initial square root is modulo 1639707491
reading relations for dependency 3
read 28924 cycles
cycles contain 111395 unique relations
read 111395 relations
multiplying 86186 relations
multiply complete, coefficients have about 2.00 million bits
initial square root is modulo 1708967971
prp36 factor: 408348128880194658464406352398206191
prp69 factor: 101099762660918448367538763269301577394107046179160743691761007449127
elapsed time 00:30:37

May 24, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / May 24, 2009

(56·10¹⁹⁰-11)/9 = 6(2)₁₈₉1_<191> = C191

C191 = P84 · P108

P84 = 158796307404671877627661739735355205593268234205073217528273831685616486751940901041_<84>

P108 = 391836707283481889552854182532334698780981401663807885131994302605274535384646414268878461059412149522861981_<108>

Number: n
N=62222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
  ( 191 digits)
SNFS difficulty: 192 digits.
Divisors found:

Sun May 24 06:45:23 2009  prp84 factor: 158796307404671877627661739735355205593268234205073217528273831685616486751940901041
Sun May 24 06:45:23 2009  prp108 factor: 391836707283481889552854182532334698780981401663807885131994302605274535384646414268878461059412149522861981
Sun May 24 06:45:23 2009  elapsed time 03:57:52 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20050930-k8
Total time: 28.54 hours.
Scaled time: 57.54 units (timescale=2.016).
Factorization parameters were as follows:
name: KA_6_2_189_1
n: 62222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 200000000000000000000000000000000000000
deg: 5
c5: 7
c0: -44
skew: 1.44
type: snfs
lss: 1
rlim: 11200000
alim: 11200000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 11200000/11200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved  special-q in [5600000, 11699990)
Primes: RFBsize:738873, AFBsize:739548, largePrimes:20146869 encountered
Relations: rels:19495272, finalFF:919837
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 3303101 hash collisions in 27644196 relations
Msieve: matrix is 1604566 x 1604814 (423.0 MB)

Total sieving time: 28.19 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,192,5,0,0,0,0,0,0,0,0,11200000,11200000,28,28,55,55,2.5,2.5,100000
total time: 28.54 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.97 BogoMIPS (lpj=2830488)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22643.70 BogoMIPS).

(56·10¹⁴²+43)/9 = 6(2)₁₄₁7_<143> = 11 · C142

C142 = P47 · P95

P47 = 68896062191871030491723833548784337537918021729_<47>

P95 = 82102887692078698167555009410022945808543510134623548922165046341705571318356455365072720933433_<95>

Number: n
N=5656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565657
  ( 142 digits)
SNFS difficulty: 143 digits.
Divisors found:

Sun May 24 15:38:08 2009  prp47 factor: 68896062191871030491723833548784337537918021729
Sun May 24 15:38:08 2009  prp95 factor: 82102887692078698167555009410022945808543510134623548922165046341705571318356455365072720933433
Sun May 24 15:38:08 2009  elapsed time 00:23:38 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.91 hours.
Scaled time: 8.95 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_6_2_141_7
n: 5656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565657
m: 20000000000000000000000000000
deg: 5
c5: 175
c0: 43
skew: 0.76
type: snfs
lss: 1
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [900000, 1748963)
Primes: RFBsize:135072, AFBsize:135383, largePrimes:5996260 encountered
Relations: rels:5238251, finalFF:247066
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 462130 hash collisions in 5983346 relations
Msieve: matrix is 270478 x 270726 (72.3 MB)

Total sieving time: 4.82 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,56,56,2.3,2.3,100000
total time: 4.91 hours.
 --------- CPU info (if available) ----------

May 24, 2009 (2nd)

By Dmitry Domanov / GMP-ECM 6.2.3 / May 24, 2009

(16·10¹⁸⁸-7)/9 = 1(7)₁₈₈_<189> = 3 · 31 · 2069 · 65398169 · 14567926460916274090418321_<26> · C150

C150 = P39 · P112

P39 = 121896753428115558413310315910630311743_<39>

P112 = 7955703066426815166859690188164155329317259808964297303908057957751323028198357087524600604449363008467485722583_<112>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2616785286
Step 1 took 143375ms
Step 2 took 39250ms
********** Factor found in step 2: 121896753428115558413310315910630311743
Found probable prime factor of 39 digits: 121896753428115558413310315910630311743
Probable prime cofactor 7955703066426815166859690188164155329317259808964297303908057957751323028198357087524600604449363008467485722583 has 112 digits

May 24, 2009

Factorizations of 622...227 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 23, 2009 (5th)

By Dmitry Domanov / GMP-ECM 6.2.3 / May 23, 2009

(73·10¹⁹⁹-1)/9 = 8(1)₁₉₉_<200> = 3² · 4386230489_<10> · 261738156131_<12> · C178

C178 = P37 · C142

P37 = 2356059256180297974755710952450611393_<37>

C142 = [3331909097163411490195797154179506593226135680655488427797409658939627839025957996970418820375433315961414173071731590938360326732797877361517_<142>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1302500274
Step 1 took 296422ms
********** Factor found in step 1: 2356059256180297974755710952450611393
Found probable prime factor of 37 digits: 2356059256180297974755710952450611393
Composite cofactor 3331909097163411490195797154179506593226135680655488427797409658939627839025957996970418820375433315961414173071731590938360326732797877361517 has 142 digits

May 23, 2009 (4th)

By Sinkiti Sibata / Msieve, GMP-ECM 6.2 / May 23, 2009

(56·10¹⁴³-11)/9 = 6(2)₁₄₂1_<144> = 3 · 247812371 · 8791047040390906987_<19> · C116

C116 = P53 · P64

P53 = 52096666235637883534522642520955700372141756844560643_<53>

P64 = 1827472048686128722686279854270138033017141595244865854768896437_<64>

Number: 62221_143
N=95205201375358632669691236626623247521905406835492682061039667657362165007206580925633300445028642999687163233128991
  ( 116 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=52096666235637883534522642520955700372141756844560643 (pp53)
 r2=1827472048686128722686279854270138033017141595244865854768896437 (pp64)
Version: Msieve-1.40
Total time: 9.23 hours.
Scaled time: 19.31 units (timescale=2.092).
Factorization parameters were as follows:
name: 62221_143
n: 95205201375358632669691236626623247521905406835492682061039667657362165007206580925633300445028642999687163233128991
m: 100000000000000000000000000000
deg: 5
c5: 14
c0: -275
skew: 1.81
type: snfs
lss: 1
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [955000, 2055001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 321846 x 322094
Total sieving time: 8.71 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 9.23 hours.
 --------- CPU info (if available) ----------

8·10¹⁹³-9 = 7(9)₁₉₂1_<194> = 19 · 281 · 4418326058451689_<16> · 28635389649731171_<17> · 4005799549560803338611269_<25> · C134

C134 = P50 · P84

P50 = 47530447988775454504196992466925654385332702204589_<50>

P84 = 622025352119764712028843316628216948512092949996598055244945354900245093351541822511_<84>

Number: 79991_193
N=29565143646628214552910727018766282005163877039936094266740542090166082984748527095016519714301140410272311793378686931866644647702979
  ( 134 digits)
Divisors found:
 r1=47530447988775454504196992466925654385332702204589 (pp50)
 r2=622025352119764712028843316628216948512092949996598055244945354900245093351541822511 (pp84)
Version: Msieve-1.40
Total time: 379.04 hours.
Scaled time: 745.57 units (timescale=1.967).
Factorization parameters were as follows:
name: 79991_193
# Murphy_E = 4.630559e-11, selected by Jeff Gilchrist
n: 29565143646628214552910727018766282005163877039936094266740542090166082984748527095016519714301140410272311793378686931866644647702979
Y0: -57543593694049710599247587
Y1: 721718734872989
c0: -90368218213303982886078566019840
c1: 1320429414049798041363608796
c2: 8903540005306081349992
c3: -27320914772887363
c4: -61896802964
c5: 46860
skew: 386466.26
type: gnfs
# selected mechanically
rlim: 12100000
alim: 12100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6
Factor base limits: 12100000/12100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved algebraic special-q in [6050000, 14950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1834899 x 1835147
Total sieving time: 379.04 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,133,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12100000,12100000,28,28,54,54,2.6,2.6,100000
total time: 379.04 hours.
 --------- CPU info (if available) ----------

(56·10¹⁸⁶-11)/9 = 6(2)₁₈₅1_<187> = 599 · 37158634009449941_<17> · 187078422967358237181929_<24> · 291087023629052324337893_<24> · C121

C121 = P37 · P40 · P45

P37 = 8669942536444244537787894218627299087_<37>

P40 = 2294619415855590800799109639269294659123_<40>

P45 = 258039104434055048772680144104698258424326727_<45>

Run 785 out of 2318:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2397597109
Step 1 took 27125ms
Step 2 took 15062ms
********** Factor found in step 2: 2294619415855590800799109639269294659123
Found probable prime factor of 40 digits: 22946194158555908007991096392692946591
23
Probable prime cofactor 258039104434055048772680144104698258424326727msieve has 45 dig
its

May 23, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 23, 2009

(56·10¹⁵⁴-11)/9 = 6(2)₁₅₃1_<155> = 1319 · 99588740355980248700009_<23> · C129

C129 = P36 · P94

P36 = 159529283600937361262720079033676357_<36>

P94 = 2969272580593994736122638271517181885182905451818307218893722397054616314597839349595890387543_<94>

Number: 62221_154
N=473685927598066523811321219743107411021072297995390038378143177362996029747199699549590394307377922267919784079276586320766420851
  ( 129 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=159529283600937361262720079033676357
 r2=2969272580593994736122638271517181885182905451818307218893722397054616314597839349595890387543
Version: 
Total time: 12.57 hours.
Scaled time: 30.06 units (timescale=2.391).
Factorization parameters were as follows:
n: 473685927598066523811321219743107411021072297995390038378143177362996029747199699549590394307377922267919784079276586320766420851
m: 10000000000000000000000000000000
deg: 5
c5: 28
c0: -55
skew: 1.14
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8477784
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 465979 x 466227
Total sieving time: 11.54 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 0.45 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 12.57 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 23, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / May 23, 2009

5·10¹⁷¹+9 = 5(0)₁₇₀9_<172> = 67 · 40378193 · 44404164907_<11> · C152

C152 = P59 · P94

P59 = 30861275933615391341234232012900752504190775857799782307643_<59>

P94 = 1348685652951649280820481874144969335193186551718062790432538324525777278141762353767694766939_<94>

Number: n
N=41622160083449093835715177170359909547044068164867790126481396040503116696826064618716663968196854901778090190322063002576843971520433247969928483414777
  ( 152 digits)
SNFS difficulty: 171 digits.
Divisors found:

Sat May 23 11:46:27 2009  prp59 factor: 30861275933615391341234232012900752504190775857799782307643
Sat May 23 11:46:27 2009  prp94 factor: 1348685652951649280820481874144969335193186551718062790432538324525777278141762353767694766939
Sat May 23 11:46:27 2009  elapsed time 01:19:08 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 45.61 hours.
Scaled time: 60.89 units (timescale=1.335).
Factorization parameters were as follows:
name: KA_5_0_170_9
n: 41622160083449093835715177170359909547044068164867790126481396040503116696826064618716663968196854901778090190322063002576843971520433247969928483414777
m: 10000000000000000000000000000000000
deg: 5
c5: 50
c0: 9
skew: 0.71
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2550000, 5039821)
Primes: RFBsize:354971, AFBsize:354121, largePrimes:16733383 encountered
Relations: rels:16062335, finalFF:753335
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1755175 hash collisions in 18017048 relations
Msieve: matrix is 843918 x 844166 (226.5 MB)

Total sieving time: 45.09 hours.
Total relation processing time: 0.52 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,28,28,56,56,2.4,2.4,100000
total time: 45.61 hours.
 --------- CPU info (if available) ----------

May 23, 2009

By Wataru Sakai / Msieve / May 23, 2009

9·10¹⁹⁸+1 = 9(0)₁₉₇1_<199> = 206641 · C194

C194 = P73 · P122

P73 = 1971332907858188412423521352631276953751910015856265250493673622099401969_<73>

P122 = 22093577408287644837009510470494689478804802552229642889751303060701247374764381532930283372837715454765095820414492639969_<122>

Number: 90001_198
N=43553796197269660909500050812762230147937727750059281555935172594015708402495148591034693018326469577673356207141854714214507285582241665497166583591833179281943080027680857138709162266926698961
  ( 194 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=1971332907858188412423521352631276953751910015856265250493673622099401969
 r2=22093577408287644837009510470494689478804802552229642889751303060701247374764381532930283372837715454765095820414492639969
Version: 
Total time: 761.36 hours.
Scaled time: 1506.74 units (timescale=1.979).
Factorization parameters were as follows:
n: 43553796197269660909500050812762230147937727750059281555935172594015708402495148591034693018326469577673356207141854714214507285582241665497166583591833179281943080027680857138709162266926698961
m: 5000000000000000000000000000000000000000
deg: 5
c5: 72
c0: 25
skew: 0.81
type: snfs
lss: 1
rlim: 15300000
alim: 15300000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 15300000/15300000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7650000, 15450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3112132 x 3112378
Total sieving time: 761.36 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15300000,15300000,29,29,56,56,2.6,2.6,100000
total time: 761.36 hours.
 --------- CPU info (if available) ----------

May 22, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / May 22, 2009

(56·10¹⁴⁷-11)/9 = 6(2)₁₄₆1_<148> = 940357975339_<12> · 4396150383764093_<16> · C121

C121 = P40 · P82

P40 = 1008215810246207129612047042208358145051_<40>

P82 = 1492884680420177799347131923818531569599984632006412804870158351516771646036609673_<82>

Number: 62221_147
N=1505149937673979552320836226405694346794312067193454584388061053324185341450817482913564538855807343552377213503203678323
  ( 121 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=1008215810246207129612047042208358145051
 r2=1492884680420177799347131923818531569599984632006412804870158351516771646036609673
Version: 
Total time: 5.64 hours.
Scaled time: 13.43 units (timescale=2.380).
Factorization parameters were as follows:
n: 1505149937673979552320836226405694346794312067193454584388061053324185341450817482913564538855807343552377213503203678323
m: 200000000000000000000000000000
deg: 5
c5: 175
c0: -11
skew: 0.58
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1500000, 2625001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4957651
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 378093 x 378341
Total sieving time: 4.93 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,3000000,3000000,26,26,49,49,2.3,2.3,75000
total time: 5.64 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹⁸⁹-11)/9 = 6(2)₁₈₈1_<190> = 277 · 25277866982933_<14> · 40398247348837599795974405003_<29> · 54162299091422434499021060679582624167_<38> · C108

C108 = P48 · P61

P48 = 228498442360438340292379803269188129395888720953_<48>

P61 = 1777388907317542637562195901082903456247197584230926518332977_<61>

Number: 62221_189
N=406130596790779999759153981712709459914372909456044656520865406171812435177580766081922259159004770290767081
  ( 108 digits)
Divisors found:
 r1=228498442360438340292379803269188129395888720953
 r2=1777388907317542637562195901082903456247197584230926518332977
Version: 
Total time: 6.46 hours.
Scaled time: 15.42 units (timescale=2.389).
Factorization parameters were as follows:
name: 62221_189
n: 406130596790779999759153981712709459914372909456044656520865406171812435177580766081922259159004770290767081
skew: 14032.91
# norm 1.60e+15
c5: 105840
c4: -4277112308
c3: 61395728235004
c2: 1309518592510891537
c1: -4824049825893490081356
c0: -32284824656823243472412025
# alpha -6.61
Y1: 100307285683
Y0: -328703438188208320058
# Murphy_E 1.28e-09
# M 141094203117980261816754148973220116699568804394140714353111345509640429615565396644228123557747415940163645
type: gnfs
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 2050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7208996
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 348141 x 348389
Polynomial selection time: 0.50 hours.
Total sieving time: 4.80 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000
total time: 6.46 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹⁵³-11)/9 = 6(2)₁₅₂1_<154> = 161038333187_<12> · C143

C143 = P64 · P80

P64 = 3363325659726554254219949158081482055226599127679686333139708977_<64>

P80 = 11488076797017378618898480601030100376760617008747621903303917850030785920234079_<80>

Number: 62221_153
N=38638143472317795247537705888526995749935352454153330768119348134235245226490461527992257076379883719605964665915331039200805176564213777627183
  ( 143 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=3363325659726554254219949158081482055226599127679686333139708977
 r2=11488076797017378618898480601030100376760617008747621903303917850030785920234079
Version: 
Total time: 10.66 hours.
Scaled time: 25.48 units (timescale=2.390).
Factorization parameters were as follows:
n: 38638143472317795247537705888526995749935352454153330768119348134235245226490461527992257076379883719605964665915331039200805176564213777627183
m: 10000000000000000000000000000000
deg: 5
c5: 14
c0: -275
skew: 1.81
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8440039
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 421469 x 421717
Total sieving time: 9.84 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 10.66 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(2·10¹⁹⁵+1)/3 = (6)₁₉₄7_<195> = 643 · 2267 · 591132392867_<12> · C177

C177 = P38 · P140

P38 = 20445535278979404077682352742063245387_<38>

P140 = 37841034812644230659598583398507678171373442415633054522576738535458043251909493707277588574988992770463156691080518508056734230085009425083_<140>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 773680212255005402213215670718471636322872901200645179715616504990970707569170676906984764825388611905986628614026077579135645235380535252670977400250192112030102091574021842121 (177 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2093518856
Step 1 took 17167ms
Step 2 took 7023ms
********** Factor found in step 2: 20445535278979404077682352742063245387
Found probable prime factor of 38 digits: 20445535278979404077682352742063245387
Probable prime cofactor 37841034812644230659598583398507678171373442415633054522576738535458043251909493707277588574988992770463156691080518508056734230085009425083 has 140 digits

(2·10¹⁷²+1)/3 = (6)₁₇₁7_<172> = 19 · 367894099 · C162

C162 = P38 · P125

P38 = 31923954769587137972250253982544737507_<38>

P125 = 29875530881591454506940299770383247214954619398774924636746552858006558949858905691700278509265508508706937584865642995542001_<125>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM]
Input number is 953745096581329347038200775768507611618084673281090437797093323267618218445186838896418777162493147199015389346805459313594862392389699576171077293841543738531507 (162 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3322220783
Step 1 took 14428ms
Step 2 took 6321ms
********** Factor found in step 2: 31923954769587137972250253982544737507
Found probable prime factor of 38 digits: 31923954769587137972250253982544737507
Probable prime cofactor 29875530881591454506940299770383247214954619398774924636746552858006558949858905691700278509265508508706937584865642995542001 has 125 digits

May 22, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(32·10¹⁶⁹-41)/9 = 3(5)₁₆₈1_<170> = 1613 · 13159 · 116981 · 81326373781_<11> · C147

C147 = P45 · P46 · P57

P45 = 140850378091982090577354915876165350338613087_<45>

P46 = 9786966886270901249855494260133478437860029027_<46>

P57 = 127731302497147884438978142065758231658906688736325985177_<57>

Number: n
N=176077343280428722210294933173471602076330384241286510651480244704067065779074311519434584743655131635262384425494570149205597165806500457976278773
  ( 147 digits)
SNFS difficulty: 171 digits.
Divisors found:

Fri May 22 13:03:18 2009  prp45 factor: 140850378091982090577354915876165350338613087
Fri May 22 13:03:18 2009  prp46 factor: 9786966886270901249855494260133478437860029027
Fri May 22 13:03:18 2009  prp57 factor: 127731302497147884438978142065758231658906688736325985177
Fri May 22 13:03:18 2009  elapsed time 01:14:43 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 49.74 hours.
Scaled time: 132.30 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_3_5_168_1
n: 176077343280428722210294933173471602076330384241286510651480244704067065779074311519434584743655131635262384425494570149205597165806500457976278773
m: 10000000000000000000000000000000000
deg: 5
c5: 16
c0: -205
skew: 1.67
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 5261749)
Primes: RFBsize:348513, AFBsize:348852, largePrimes:17302361 encountered
Relations: rels:17224239, finalFF:733473
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1992447 hash collisions in 19178345 relations
Msieve: matrix is 783206 x 783454 (206.8 MB)

Total sieving time: 49.02 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 49.74 hours.
 --------- CPU info (if available) ----------

(56·10¹⁶³-11)/9 = 6(2)₁₆₂1_<164> = 71 · 1212709 · 131517167 · C148

C148 = P34 · P115

P34 = 4653012427420569338623962801251087_<34>

P115 = 1180902142478392291997557302605730893103002830157279589768710079332801129714037937532741668108603105238106040542191_<115>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 5494752344519535146687404917043008612140116501569138078950789948018034611445897276112464677546840828744848284725055003614238674816203386438608111617 (148 digits)
Using B1=804000, B2=696806892, polynomial Dickson(3), sigma=562029734
Step 1 took 12495ms
Step 2 took 4322ms
********** Factor found in step 2: 4653012427420569338623962801251087
Found probable prime factor of 34 digits: 4653012427420569338623962801251087
Probable prime cofactor 1180902142478392291997557302605730893103002830157279589768710079332801129714037937532741668108603105238106040542191 has 115 digits

(56·10¹⁴¹-11)/9 = 6(2)₁₄₀1_<142> = 19 · 179 · C139

C139 = P54 · P85

P54 = 297263336609650968924047699599162922866765769099232391_<54>

P85 = 6154567475724947698759561455579847624574161601456877967507516611787461722048501183731_<85>

Number: n
N=1829527263223234996242935084452285275572544022999771309092097095625469633114443464340553431997125028586363487863046816295860694566957430821
  ( 139 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=297263336609650968924047699599162922866765769099232391 (pp54)
 r2=6154567475724947698759561455579847624574161601456877967507516611787461722048501183731 (pp85)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 4.94 hours.
Scaled time: 13.14 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_2_140_1
n: 1829527263223234996242935084452285275572544022999771309092097095625469633114443464340553431997125028586363487863046816295860694566957430821
m: 20000000000000000000000000000
deg: 5
c5: 35
c0: -22
skew: 0.91
type: snfs
lss: 1
rlim: 1700000
alim: 1700000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 100000
Factor base limits: 1700000/1700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [850000, 1750001)
Primes: RFBsize:128141, AFBsize:127925, largePrimes:6368334 encountered
Relations: rels:5761128, finalFF:316228
Max relations in full relation-set: 28
Initial matrix: 256132 x 316228 with sparse part having weight 27527715.
Pruned matrix : 235172 x 236516 with weight 17145775.
Total sieving time: 4.61 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.16 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1700000,1700000,28,28,56,56,2.3,2.3,100000
total time: 4.94 hours.
 --------- CPU info (if available) ----------

(56·10¹⁴⁶-11)/9 = 6(2)₁₄₅1_<147> = 3² · 1303 · C143

C143 = P63 · P81

P63 = 390636623576473629943499655770771098579496801221468572377451887_<63>

P81 = 135826851857318304777560953992990975187323813555012363701612426250045999154804429_<81>

Number: n
N=53058942800564698748377438579536302739167922079152572884985266668561628909543977336251575187364391764494092455207829983987569047686724842007523
  ( 143 digits)
SNFS difficulty: 148 digits.
Divisors found:

Fri May 22 20:41:04 2009  prp63 factor: 390636623576473629943499655770771098579496801221468572377451887
Fri May 22 20:41:04 2009  prp81 factor: 135826851857318304777560953992990975187323813555012363701612426250045999154804429
Fri May 22 20:41:04 2009  elapsed time 00:17:27 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 6.71 hours.
Scaled time: 17.84 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_2_145_1
n: 53058942800564698748377438579536302739167922079152572884985266668561628909543977336251575187364391764494092455207829983987569047686724842007523
m: 200000000000000000000000000000
deg: 5
c5: 35
c0: -22
skew: 0.91
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 100000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1050000, 2275187)
Primes: RFBsize:155805, AFBsize:155618, largePrimes:6972249 encountered
Relations: rels:6204110, finalFF:309632
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 625424 hash collisions in 6918126 relations
Msieve: matrix is 340345 x 340593 (90.9 MB)

Total sieving time: 6.58 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,28,28,56,56,2.3,2.3,100000
total time: 6.71 hours.
 --------- CPU info (if available) ----------

(5·10¹⁹⁷-11)/3 = 1(6)₁₉₆3_<198> = 7 · C197

C197 = P78 · P119

P78 = 770224136745202272960858853390184251348929602406163327279097423136818113201277_<78>

P119 = 30912461287097049773379532118577710425262942254107754948474511204970390341027073730433138066136695072775834272781147317_<119>

Number: n
N=23809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809
  ( 197 digits)
SNFS difficulty: 198 digits.
Divisors found:

Fri May 22 20:51:57 2009  prp78 factor: 770224136745202272960858853390184251348929602406163327279097423136818113201277
Fri May 22 20:51:57 2009  prp119 factor: 30912461287097049773379532118577710425262942254107754948474511204970390341027073730433138066136695072775834272781147317
Fri May 22 20:51:57 2009  elapsed time 07:26:51 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 11.89 hours.
Scaled time: 23.98 units (timescale=2.016).
Factorization parameters were as follows:
name: KA_1_6_196_3
n: 23809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809523809
m: 2000000000000000000000000000000000000000
deg: 5
c5: 125
c0: -88
skew: 0.93
type: snfs
lss: 1
rlim: 14300000
alim: 14300000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 14300000/14300000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved  special-q in [7150000, 10150057)
Primes: RFBsize:928293, AFBsize:926118, largePrimes:36842353 encountered
Relations: rels:37172595, finalFF:2021767
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 7310015 hash collisions in 43187116 relations
Msieve: matrix is 2219007 x 2219255 (603.4 MB)

Total sieving time: 11.02 hours.
Total relation processing time: 0.87 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,198,5,0,0,0,0,0,0,0,0,14300000,14300000,29,29,56,56,2.5,2.5,100000
total time: 11.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.97 BogoMIPS (lpj=2830488)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22643.70 BogoMIPS).

May 22, 2009 (3rd)

By Sinkiti Sibata / Msieve, GGNFS, GMP-ECM 6.2

(56·10¹⁴⁰-11)/9 = 6(2)₁₃₉1_<141> = 3 · 137029 · C136

C136 = P36 · P100

P36 = 299406853214567406564359036434117307_<36>

P100 = 5055336135400232322529243029621372499820771506159438962856581567533302079098571471572820157443691769_<100>

Number: 62221_140
N=1513602284242075819041278907438625454519900221175133784873329057406880349469144541720419819216424314615208513580391066178746158896346083
  ( 136 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=299406853214567406564359036434117307 (pp36)
 r2=5055336135400232322529243029621372499820771506159438962856581567533302079098571471572820157443691769 (pp100)
Version: Msieve-1.40
Total time: 7.25 hours.
Scaled time: 15.22 units (timescale=2.099).
Factorization parameters were as follows:
name: 62221_140
n: 1513602284242075819041278907438625454519900221175133784873329057406880349469144541720419819216424314615208513580391066178746158896346083
m: 20000000000000000000000000000
deg: 5
c5: 7
c0: -44
skew: 1.44
type: snfs
lss: 1
rlim: 1650000
alim: 1650000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1650000/1650000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [825000, 1725001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 260220 x 260457
Total sieving time: 6.88 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,142.000,5,0,0,0,0,0,0,0,0,1650000,1650000,26,26,48,48,2.3,2.3,100000
total time: 7.25 hours.
 --------- CPU info (if available) ----------

(56·10¹⁴⁴-11)/9 = 6(2)₁₄₃1_<145> = 467 · 1181321 · 34029929 · 2347379653_<10> · 16006457832853967_<17> · C103

C103 = P41 · P63

P41 = 51446154457445281300092961754341423886897_<41>

P63 = 171462117056719624665955830711633870545040915759347599025265181_<63>

Number: 62221_144
N=8821066557700560914707538403741916445191036516315719696291370434325710113707949441060998120603176233357
  ( 103 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=51446154457445281300092961754341423886897 (pp41)
 r2=171462117056719624665955830711633870545040915759347599025265181 (pp63)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 21.11 hours.
Scaled time: 10.01 units (timescale=0.474).
Factorization parameters were as follows:
name: 62221_144
n: 8821066557700560914707538403741916445191036516315719696291370434325710113707949441060998120603176233357
m: 100000000000000000000000000000
deg: 5
c5: 28
c0: -55
skew: 1.14
type: snfs
lss: 1
rlim: 1930000
alim: 1930000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1930000/1930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [965000, 2565001)
Primes: RFBsize:144125, AFBsize:144353, largePrimes:4136963 encountered
Relations: rels:4269862, finalFF:339786
Max relations in full relation-set: 28
Initial matrix: 288544 x 339786 with sparse part having weight 35413273.
Pruned matrix : 270492 x 271998 with weight 25939742.
Total sieving time: 18.45 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 2.34 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000
total time: 21.11 hours.
 --------- CPU info (if available) ----------

(56·10¹⁴²-11)/9 = 6(2)₁₄₁1_<143> = 23911 · 42257 · C134

C134 = P55 · P80

P55 = 1143941411907996700520971946060340262736488878322319963_<55>

P80 = 53832597353146372166288374957906854282217567080482754146364408192442359473749921_<80>

Number: 62221_142
N=61581337422832947042565963830758116002701376652326624198705025783356556057053843625770686217875640758640672397218969955090412007972923
  ( 134 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=1143941411907996700520971946060340262736488878322319963 (pp55)
 r2=53832597353146372166288374957906854282217567080482754146364408192442359473749921 (pp80)
Version: Msieve-1.40
Total time: 6.74 hours.
Scaled time: 13.92 units (timescale=2.065).
Factorization parameters were as follows:
name: 62221_142
n: 61581337422832947042565963830758116002701376652326624198705025783356556057053843625770686217875640758640672397218969955090412007972923
m: 20000000000000000000000000000
deg: 5
c5: 175
c0: -11
skew: 0.58
type: snfs
lss: 1
rlim: 1740000
alim: 1740000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1740000/1740000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [870000, 1670001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 274221 x 274469
Total sieving time: 6.37 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,143.000,5,0,0,0,0,0,0,0,0,1740000,1740000,26,26,48,48,2.3,2.3,100000
total time: 6.74 hours.
 --------- CPU info (if available) ----------

(56·10¹⁷⁴-11)/9 = 6(2)₁₇₃1_<175> = 659 · 8501 · 2621693 · 15087703 · 1862887311324908123884845247211972663_<37> · C119

C119 = P30 · P89

P30 = 452022591052245072685099765541_<30>

P89 = 33345589605560820714725890779712247472160401068383290810785202245000234921008604498692867_<89>

Run 8 out of 2318:
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=432356704
Step 1 took 44297ms
Step 2 took 20875ms
********** Factor found in step 2: 452022591052245072685099765541
Found probable prime factor of 30 digits: 452022591052245072685099765541
Probable prime cofactor 33345589605560820714725890779712247472160401068383290810
785202245000234921008604498692867 has 89 digits

May 22, 2009 (2nd)

By Dmitry Domanov / GMP-ECM 6.2.3, GGNFS/msieve / May 22, 2009

(16·10¹⁷⁶-7)/9 = 1(7)₁₇₆_<177> = 3² · 59 · 615711081072019872468826193588606901197_<39> · C135

C135 = P43 · P93

P43 = 1772012938854214576783047007942566638416973_<43>

P93 = 306859161300820429718744093592872285344754892092073690101163543698285825481837814744085179507_<93>

N=543758404231006280078915314898360251643955593507494702574785941537600961230214196342616452411330988575208199411251642709824917020572311
  ( 135 digits)
SNFS difficulty: 177 digits.
Divisors found:
r1=1772012938854214576783047007942566638416973 (pp43)
r2=306859161300820429718744093592872285344754892092073690101163543698285825481837814744085179507 (pp93)
Version: Msieve v. 1.41
Total time: 83.47 hours.
Scaled time: 165.45 units (timescale=1.982).
Factorization parameters were as follows:
n: 543758404231006280078915314898360251643955593507494702574785941537600961230214196342616452411330988575208199411251642709824917020572311
m: 200000000000000000000000000000000000
deg: 5
c5: 5
c0: -7
skew: 1.07
type: snfs
lss: 1
rlim: 6300000
alim: 6300000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6300000/6300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3150000, 6350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1161103 x 1161351
Total sieving time: 81.17 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 1.94 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,177.000,5,0,0,0,0,0,0,0,0,6300000,6300000,28,28,53,53,2.5,2.5,100000
total time: 83.47 hours.
 --------- CPU info (if available) ----------

(7·10¹⁸⁸-43)/9 = (7)₁₈₇3_<188> = 19 · 227 · 30181 · 1971583899979817205738323467_<28> · C153

C153 = P49 · P104

P49 = 4805550249913806107164545818458971893599632427019_<49>

P104 = 63064369942282470443928890836206937269530197886183657029723257323673694166847341225815396360621173715417_<104>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=3499185670
Step 1 took 524485ms
Step 2 took 113000ms
********** Factor found in step 2: 4805550249913806107164545818458971893599632427019
Found probable prime factor of 49 digits: 4805550249913806107164545818458971893599632427019
Probable prime cofactor 63064369942282470443928890836206937269530197886183657029723257323673694166847341225815396360621173715417 has 104 digits

(73·10¹⁹²-1)/9 = 8(1)₁₉₂_<193> = 73256271947274662782040893968743123700881_<41> · C153

C153 = P47 · P48 · P59

P47 = 12514183981701174831234244754445618634782464551_<47>

P48 = 267288759821310351191537888363735659318239313283_<48>

P59 = 33101853000094382825599338798034443619214831850089105550107_<59>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1770093265
Step 1 took 881297ms
Step 2 took 194656ms
********** Factor found in step 2: 267288759821310351191537888363735659318239313283
Found probable prime factor of 48 digits: 267288759821310351191537888363735659318239313283
Composite cofactor 414242678578408103235078719600045420705685685982987391903794714703925355295201997258318971178094081756957 has 105 digits

N=414242678578408103235078719600045420705685685982987391903794714703925355295201997258318971178094081756957
  ( 105 digits)
Divisors found:
 r1=12514183981701174831234244754445618634782464551 (pp47)
 r2=33101853000094382825599338798034443619214831850089105550107 (pp59)
Version: Msieve v. 1.41
Total time: 8.29 hours.
Scaled time: 16.43 units (timescale=1.982).
Factorization parameters were as follows:
n: 414242678578408103235078719600045420705685685982987391903794714703925355295201997258318971178094081756957
skew: 10245.06
# norm 9.53e+014
c5: 189000
c4: -4228453038
c3: -104481482087957
c2: 329571606307239790
c1: 3722167535783309214524
c0: 192804791565346169927120
# alpha -6.85
Y1: 26624677783
Y0: -73817495856612743163
# Murphy_E 1.91e-009
# M 380244343347328658347174459880259612066021441439257999459704883260043181974659152092827411667820947949767
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 256054 x 256302
Polynomial selection time: 0.74 hours.
Total sieving time: 7.33 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 8.29 hours.
 --------- CPU info (if available) ----------

(73·10¹⁹⁰-1)/9 = 8(1)₁₉₀_<191> = 3³ · 766373 · 576849289308102433339_<21> · 352770971508535022385843411436127_<33> · C131

C131 = P38 · P46 · P47

P38 = 53018587549308860488727446119008638117_<38>

P46 = 9830729640749698698057713596885562332720579109_<46>

P47 = 36957899619439052588389493711338143513746251349_<47>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1641020606
Step 1 took 111219ms
Step 2 took 32437ms
********** Factor found in step 2: 53018587549308860488727446119008638117
Found probable prime factor of 38 digits: 53018587549308860488727446119008638117
Composite cofactor 363323119248671503681840442228888007882580930456529372102126201532931588055727988917152468041 has 93 digits

N=363323119248671503681840442228888007882580930456529372102126201532931588055727988917152468041
  ( 93 digits)
Divisors found:
r1=9830729640749698698057713596885562332720579109 (pp46)
r2=36957899619439052588389493711338143513746251349 (pp47)
Version: Msieve v. 1.41
Total time: 3.56 hours.
Scaled time: 7.03 units (timescale=1.976).
Factorization parameters were as follows:
n:  363323119248671503681840442228888007882580930456529372102126201532931588055727988917152468041
m:  2201437169476072225733
deg: 4
c4: 15469200
c3: 64470243577
c2: -206162652068209327
c1: -157308994180603347
c0: 292072553235282416374746
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.372
# E(F1,F2) = 6.310444e-005
# GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1242934815.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 171992 x 172240
Polynomial selection time: 0.17 hours.
Total sieving time: 3.23 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
gnfs,92,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 3.56 hours.
 --------- CPU info (if available) ----------

May 22, 2009

By Dmitry Domanov / GMP-ECM 6.2.3/GGNFS/Msieve / May 22, 2009

(73·10¹⁷³-1)/9 = 8(1)₁₇₃_<174> = 7 · 4943 · 1059933049229_<13> · 64098166474883233335412841_<26> · C132

C132 = P37 · P45 · P51

P37 = 5651544344073065353949288742526199989_<37>

P45 = 460594228426107287120213438958014196056247359_<45>

P51 = 132550700853026894371155963466907255560307901107449_<51>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1247506212
Step 1 took 184500ms
Step 2 took 57109ms
********** Factor found in step 2: 5651544344073065353949288742526199989
Found probable prime factor of 37 digits: 5651544344073065353949288742526199989
Composite cofactor 61052087786739683422486377745002538362377897736805318143684633775842372114767648010131181477191 has 95 digits

N=61052087786739683422486377745002538362377897736805318143684633775842372114767648010131181477191
  ( 95 digits)
Divisors found:
 r1=460594228426107287120213438958014196056247359 (pp45)
 r2=132550700853026894371155963466907255560307901107449 (pp51)
Version: Msieve v. 1.41
Total time: 4.57 hours.
Scaled time: 8.99 units (timescale=1.969).
Factorization parameters were as follows:
n:  61052087786739683422486377745002538362377897736805318143684633775842372114767648010131181477191
m:  5723651533996740584386
deg: 4
c4: 56886312
c3: -96342723053
c2: -224961695606516291
c1: 242685027110432538
c0: 144224341387033435142535
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.139
# E(F1,F2) = 3.669255e-005
# GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1242912454.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1380001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 168434 x 168662
Polynomial selection time: 0.17 hours.
Total sieving time: 4.19 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 4.57 hours.
 --------- CPU info (if available) ----------

May 21, 2009 (6th)

By Dmitry Domanov / GMP-ECM 6.2.3/GGNFS/Msieve / May 21, 2009

(16·10¹⁷⁴-7)/9 = 1(7)₁₇₄_<175> = 2306250299_<10> · 74898255015998655946498827377_<29> · C137

C137 = P54 · P83

P54 = 478201468652324457339234840573843334174654778416210183_<54>

P83 = 21522287485721472882131698140452420826474012890115270934342109978718916791569225653_<83>

N=10291989484429551876179833835177150162938324601375571356928446368849810743540128602817703724734336895923865775996568943437420300203424499
  ( 137 digits)
SNFS difficulty: 175 digits.
Divisors found:
r1=478201468652324457339234840573843334174654778416210183 (pp54)
r2=21522287485721472882131698140452420826474012890115270934342109978718916791569225653 (pp83)
Version: Msieve v. 1.41
Total time: 84.67 hours.
Scaled time: 168.32 units (timescale=1.988).
Factorization parameters were as follows:
n: 10291989484429551876179833835177150162938324601375571356928446368849810743540128602817703724734336895923865775996568943437420300203424499
m: 100000000000000000000000000000000000
deg: 5
c5: 8
c0: -35
skew: 1.34
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [3000000, 6500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1127939 x 1128187
Total sieving time: 82.45 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 1.77 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,175.000,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,52,52,2.5,2.5,100000
total time: 84.67 hours.
 --------- CPU info (if available) ----------

(73·10¹⁸¹-1)/9 = 8(1)₁₈₁_<182> = 3² · 71 · 401 · 7607 · 72912676783_<11> · 923219843886583_<15> · C147

C147 = P35 · P46 · P68

P35 = 20361161670231525367845505082480057_<35>

P46 = 1251616944363009719621705935812728955500311537_<46>

P68 = 24257137178864474300374832376502570787961784406903986047306381280607_<68>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=767694175
Step 1 took 135641ms
Step 2 took 38156ms
********** Factor found in step 2: 20361161670231525367845505082480057
Found probable prime factor of 35 digits: 20361161670231525367845505082480057
Composite cofactor 30360643914804711280126537478375872549443004895718960937443150897826484577690408044401934796318699204093516462959 has 113 digits

N=30360643914804711280126537478375872549443004895718960937443150897826484577690408044401934796318699204093516462959
  ( 113 digits)
Divisors found:
r1=1251616944363009719621705935812728955500311537 (pp46)
r2=24257137178864474300374832376502570787961784406903986047306381280607 (pp68)
Version: Msieve v. 1.41
Total time: 17.82 hours.
Scaled time: 35.43 units (timescale=1.988).
Factorization parameters were as follows:
name: 007
n: 30360643914804711280126537478375872549443004895718960937443150897826484577690408044401934796318699204093516462959
skew: 56060.73
# norm 4.56e+015
c5: 5400
c4: 925749786
c3: 139144709401328
c2: -2731545790006531265
c1: -191386617501901718109034
c0: -51794230834906778574463800
# alpha -6.75
Y1: 2605339957
Y0: -5623198788990427023859
# Murphy_E 7.80e-010
# M 26026941765268532581501352771223314519362970659436966324429862456488236216574342368172363669966953696988389310169
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 409831 x 410079
Total sieving time: 17.43 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 17.82 hours.
 --------- CPU info (if available) ----------

(16·10¹⁹⁹-7)/9 = 1(7)₁₉₉_<200> = 264007 · 6353173 · C188

C188 = P41 · C147

P41 = 23291472982858333436228811919662999043691_<41>

C147 = [455066006465288415070009733577160112444400511082951782000226631417419627374631140800240793491446540584054470178200734178991550975951296244405242177_<147>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=4270917581
Step 1 took 211781ms
Step 2 took 52875ms
********** Factor found in step 2: 23291472982858333436228811919662999043691
Found probable prime factor of 41 digits: 23291472982858333436228811919662999043691
Composite cofactor 455066006465288415070009733577160112444400511082951782000226631417419627374631140800240793491446540584054470178200734178991550975951296244405242177 has 147 digits

May 21, 2009 (5th)

By matsui / Msieve / May 21, 2009

10¹⁷⁸-3 = (9)₁₇₇7_<178> = 13 · 887 · 10847 · C170

C170 = P41 · P48 · P82

P41 = 52170205801655912072668661692945628873867_<41>

P48 = 791376560196615965346312862807404223815327503783_<48>

P82 = 1936500685368344801593175804002836251063019833454008113128462336831727700966974861_<82>

N=79950905666669947318829189023504982624389597821120354119830593305197383715345289932645119668396902871410393219581156873135110146803694310686357178256548496856214460373321
  ( 170 digits)
SNFS difficulty: 179 digits.
Divisors found:
 r1=52170205801655912072668661692945628873867 (pp41)
 r2=791376560196615965346312862807404223815327503783 (pp48)
 r3=1936500685368344801593175804002836251063019833454008113128462336831727700966974861 (pp82)
Version: Msieve v. 1.41
Total time: 99.44 hours.
Scaled time: 220.85 units (timescale=2.221).
Factorization parameters were as follows:
n: 79950905666669947318829189023504982624389597821120354119830593305197383715345289932645119668396902871410393219581156873135110146803694310686357178256548496856214460373321
m: 500000000000000000000000000000000000
deg: 5
c5: 8
c0: -75
skew: 1.56
type: snfs
lss: 1
rlim: 6800000
alim: 6800000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 200000
Factor base limits: 6800000/6800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3400000, 7800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1275737 x 1275985
Total sieving time: 96.45 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.61 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,179.000,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000
total time: 99.44 hours.

May 21, 2009 (4th)

By Sinkiti Sibata / GGNFS, Msieve / May 21, 2009

(56·10¹²⁶-11)/9 = 6(2)₁₂₅1_<127> = 1217 · 2621 · 196681 · 1314917 · C109

C109 = P50 · P59

P50 = 85460947370226636743108095203141443911505920048757_<50>

P59 = 88259094526073219007075664062010607115306266951250511756577_<59>

Number: 62221_126
N=7542705832236601216063235731698454018477684470697798773233660065331465340664513913820697047502655637555424789
  ( 109 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=85460947370226636743108095203141443911505920048757 (pp50)
 r2=88259094526073219007075664062010607115306266951250511756577 (pp59)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.70 hours.
Scaled time: 1.75 units (timescale=0.474).
Factorization parameters were as follows:
name: 62221_126
n: 7542705832236601216063235731698454018477684470697798773233660065331465340664513913820697047502655637555424789
m: 20000000000000000000000000
deg: 5
c5: 35
c0: -22
skew: 0.91
type: snfs
lss: 1
rlim: 950000
alim: 950000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 950000/950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [475000, 775001)
Primes: RFBsize:74907, AFBsize:74524, largePrimes:2496810 encountered
Relations: rels:2361847, finalFF:177094
Max relations in full relation-set: 28
Initial matrix: 149497 x 177094 with sparse part having weight 12725097.
Pruned matrix : 138823 x 139634 with weight 7970789.
Total sieving time: 3.31 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,950000,950000,26,26,47,47,2.3,2.3,50000
total time: 3.70 hours.
 --------- CPU info (if available) ----------

(17·10¹⁷⁹-11)/3 = 5(6)₁₇₈3_<180> = 31 · 10007 · 53192437 · 105051320748779_<15> · 374955728135539_<15> · 2878942959482939_<16> · C123

C123 = P51 · P72

P51 = 354049920548723132634303957269119976363078994390569_<51>

P72 = 855328836537558036336720562807522226820031225278213794850985182331674257_<72>

Number: 56663_179
N=302829106619154218377716355436978651473579332240491193108600419858021141565254322328800457872695512634703127245357140882233
  ( 123 digits)
Divisors found:
 r1=354049920548723132634303957269119976363078994390569 (pp51)
 r2=855328836537558036336720562807522226820031225278213794850985182331674257 (pp72)
Version: Msieve-1.40
Total time: 75.65 hours.
Scaled time: 151.75 units (timescale=2.006).
Factorization parameters were as follows:
name: 56663_179
# Murphy_E = 2.026034e-10, selected by Jeff Gilchrist
n: 302829106619154218377716355436978651473579332240491193108600419858021141565254322328800457872695512634703127245357140882233
Y0: -433157679004605500978739
Y1: 18225977925839
c0: -18544938211182598116809527360
c1: -2140927006093851150814424
c2: -40473423879282093450
c3: 833121153677281
c4: -12735684640
c5: 19860
skew: 75263.93
type: gnfs
# selected mechanically
rlim: 6100000
alim: 6100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6100000/6100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3050000, 5750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 824469 x 824717
Total sieving time: 72.48 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.63 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6100000,6100000,27,27,52,52,2.5,2.5,100000
total time: 75.65 hours.
 --------- CPU info (if available) ----------

May 21, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 21, 2009

(56·10¹⁰⁵-11)/9 = 6(2)₁₀₄1_<106> = 19 · 275616891313033_<15> · C91

C91 = P35 · P56

P35 = 24330702448592325739955334584339839_<35>

P56 = 48835027773320238922833025911088665344601596148840538457_<56>

Number: 62221_105
N=1188190529821396970209289612592845440044925234583594455283508212115333084445779916636688423
  ( 91 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=24330702448592325739955334584339839 (pp35)
 r2=48835027773320238922833025911088665344601596148840538457 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.42 hours.
Scaled time: 1.00 units (timescale=2.384).
Factorization parameters were as follows:
n: 1188190529821396970209289612592845440044925234583594455283508212115333084445779916636688423
m: 2000000000000000000000
deg: 5
c5: 7
c0: -44
skew: 1.44
type: snfs
lss: 1
rlim: 240000
alim: 240000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 240000/240000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [120000, 240001)
Primes: RFBsize:21221, AFBsize:21035, largePrimes:895240 encountered
Relations: rels:798669, finalFF:63832
Max relations in full relation-set: 28
Initial matrix: 42322 x 63832 with sparse part having weight 3116321.
Pruned matrix : 38783 x 39058 with weight 1292696.
Total sieving time: 0.40 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,240000,240000,25,25,44,44,2.2,2.2,20000
total time: 0.42 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

(56·10¹²⁵-11)/9 = 6(2)₁₂₄1_<126> = 3 · C126

C126 = P52 · P74

P52 = 3806506880294352571346546015603433909291622425036793_<52>

P74 = 54487595564616145799918267616624286940343098904288600520561248151699639399_<74>

Number: 62221_125
N=207407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407
  ( 126 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=3806506880294352571346546015603433909291622425036793
 r2=54487595564616145799918267616624286940343098904288600520561248151699639399
Version: 
Total time: 1.09 hours.
Scaled time: 2.60 units (timescale=2.378).
Factorization parameters were as follows:
n: 207407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407
m: 20000000000000000000000000
deg: 5
c5: 7
c0: -44
skew: 1.44
type: snfs
lss: 1
rlim: 800000
alim: 800000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [400000, 720001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2509555
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 117486 x 117729
Total sieving time: 0.96 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,26,26,46,46,2.3,2.3,40000
total time: 1.09 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 21, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / May 21, 2009

(56·10¹³⁷-11)/9 = 6(2)₁₃₆1_<138> = 3⁴ · 23789 · 31963 · 36405263 · 49736621128429_<14> · C106

C106 = P34 · P73

P34 = 1042522064367890213390144229142147_<34>

P73 = 5351937971935949863412995979448075596857523038286721401050467570506870027_<73>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2962973428
Step 1 took 7013ms
Step 2 took 4220ms
********** Factor found in step 2: 1042522064367890213390144229142147
Found probable prime factor of 34 digits: 1042522064367890213390144229142147
Probable prime cofactor has 73 digits

(56·10¹⁹⁸-11)/9 = 6(2)₁₉₇1_<199> = 17 · 71 · 1877691063628923919_<19> · 39317325018936102524429_<23> · 100727673887609352544951_<24> · C132

C132 = P29 · P103

P29 = 71349951368303820813792160667_<29>

P103 = 9716003423286518136366458101254813472031564320708621201225088809711249287119537530935122345120997784109_<103>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3031718808
Step 1 took 8297ms
Step 2 took 4920ms
********** Factor found in step 2: 71349951368303820813792160667
Found probable prime factor of 29 digits: 71349951368303820813792160667
Probable prime cofactor has 103 digits

(56·10¹⁸⁹-11)/9 = 6(2)₁₈₈1_<190> = 277 · 25277866982933_<14> · 40398247348837599795974405003_<29> · C146

C146 = P38 · C108

P38 = 54162299091422434499021060679582624167_<38>

C108 = [406130596790779999759153981712709459914372909456044656520865406171812435177580766081922259159004770290767081_<108>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=715898463
Step 1 took 9785ms
Step 2 took 5252ms
********** Factor found in step 2: 54162299091422434499021060679582624167
Found probable prime factor of 38 digits: 54162299091422434499021060679582624167
Composite cofactor has 108 digits

(56·10¹⁸³-11)/9 = 6(2)₁₈₂1_<184> = 4093565809_<10> · 49145698624699_<14> · 485601426753367817_<18> · C143

C143 = P28 · P115

P28 = 9736459749091473825931494539_<28>

P115 = 6541497819942903558698373382749994533024229717901469902742645607369605026183770257812764739195205897479634921596237_<115>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2783513680
Step 1 took 9212ms
Step 2 took 4944ms
********** Factor found in step 2: 9736459749091473825931494539
Found probable prime factor of 28 digits: 9736459749091473825931494539
Probable prime cofactor has 115 digits

(56·10¹⁵⁸-11)/9 = 6(2)₁₅₇1_<159> = 3 · 59 · C157

C157 = P30 · C128

P30 = 203211241393631956722915124219_<30>

C128 = [17299140354921275130942878961573349031729110752907845125819804596310155375128869475259027043222450254192642083192090196656125767_<128>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4165293997
Step 1 took 10729ms
Step 2 took 5564ms
********** Factor found in step 2: 203211241393631956722915124219
Found probable prime factor of 30 digits: 203211241393631956722915124219
Composite cofactor has 128 digits

(56·10¹⁶⁹-11)/9 = 6(2)₁₆₈1_<170> = C170

C170 = P35 · P135

P35 = 90825936474910356580445455028314087_<35>

P135 = 685071078121065245380977100774338379718781727188337319868089778466636278967013267581132544372714137499174702411896983346835604803519083_<135>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=123382992
Step 1 took 3481ms
Step 2 took 2488ms
********** Factor found in step 2: 90825936474910356580445455028314087
Found probable prime factor of 35 digits: 90825936474910356580445455028314087
Probable prime cofactor has 135 digits

(56·10¹³⁶-11)/9 = 6(2)₁₃₅1_<137> = C137

C137 = P50 · P88

P50 = 47116193896513763084644758936281326373029576202347_<50>

P88 = 1320612237034413540645554150519798422265330249675924859416078913978284141978929267347943_<88>

SNFS difficulty: 138 digits.
Divisors found:
 r1=47116193896513763084644758936281326373029576202347 (pp50)
 r2=1320612237034413540645554150519798422265330249675924859416078913978284141978929267347943 (pp88)
Version: Msieve v. 1.41
Total time: 2.29 hours.
Scaled time: 6.24 units (timescale=2.723).
Factorization parameters were as follows:
n: 62222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 2000000000000000000000000000
deg: 5
c5: 35
c0: -22
skew: 0.91
type: snfs
lss: 1
rlim: 1400000
alim: 1400000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [700000, 1300001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 222824 x 223072
Total sieving time: 2.05 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138.000,5,0,0,0,0,0,0,0,0,1400000,1400000,26,26,48,48,2.3,2.3,75000
total time: 2.29 hours.

May 21, 2009

By Robert Backstrom / GGNFS, Msieve / May 21, 2009

(52·10¹⁷⁰-7)/9 = 5(7)₁₇₀_<171> = 20852144987_<11> · 79044397577_<11> · C150

C150 = P68 · P83

P68 = 22440932013872133921645504836737591772839461986141299394467185251929_<68>

P83 = 15620614489398361590137207913320714870296064367180578091040472815622493531339189187_<83>

Number: n
N=350541147771494609491011242354777867405296059250495473592326054158821399535045616100799756842524277369580042636792251617397763429972324635079187691723
  ( 150 digits)
SNFS difficulty: 171 digits.
Divisors found:

Thu May 21 12:16:22 2009  prp68 factor: 22440932013872133921645504836737591772839461986141299394467185251929
Thu May 21 12:16:22 2009  prp83 factor: 15620614489398361590137207913320714870296064367180578091040472815622493531339189187
Thu May 21 12:16:22 2009  elapsed time 01:12:26 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 61.66 hours.
Scaled time: 164.02 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_7_170
n: 350541147771494609491011242354777867405296059250495473592326054158821399535045616100799756842524277369580042636792251617397763429972324635079187691723
m: 10000000000000000000000000000000000
deg: 5
c5: 52
c0: -7
skew: 0.67
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2550000, 6067799)
Primes: RFBsize:354971, AFBsize:354331, largePrimes:18240831 encountered
Relations: rels:18861558, finalFF:753290
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2437626 hash collisions in 20937000 relations
Msieve: matrix is 812926 x 813174 (214.4 MB)

Total sieving time: 60.69 hours.
Total relation processing time: 0.97 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,28,28,56,56,2.4,2.4,100000
total time: 61.66 hours.
 --------- CPU info (if available) ----------

(13·10¹⁷⁰+41)/9 = 1(4)₁₆₉9_<171> = 83 · 37643 · 1922390207061151_<16> · C149

C149 = P49 · P101

P49 = 1575121672855345298238023360609906942627058819383_<49>

P101 = 15268025271988546201862798038998621247627449241812295699219585367782233836956990474049954794008106537_<101>

Number: n
N=24048997507612287288102100750520634911112589018110209838926532782366722172082602334303006601667608485021999452619553254832970652887124101622504606671
  ( 149 digits)
SNFS difficulty: 171 digits.
Divisors found:

Thu May 21 14:11:46 2009  prp49 factor: 1575121672855345298238023360609906942627058819383
Thu May 21 14:11:46 2009  prp101 factor: 15268025271988546201862798038998621247627449241812295699219585367782233836956990474049954794008106537
Thu May 21 14:11:46 2009  elapsed time 01:23:14 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 41.94 hours.
Scaled time: 111.09 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_1_4_169_9
n: 24048997507612287288102100750520634911112589018110209838926532782366722172082602334303006601667608485021999452619553254832970652887124101622504606671
m: 10000000000000000000000000000000000
deg: 5
c5: 13
c0: 41
skew: 1.26
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 4812883)
Primes: RFBsize:348513, AFBsize:347692, largePrimes:16399716 encountered
Relations: rels:15549600, finalFF:675814
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1579804 hash collisions in 16873984 relations
Msieve: matrix is 902266 x 902514 (242.4 MB)

Total sieving time: 41.36 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 41.94 hours.
 --------- CPU info (if available) ----------

May 20, 2009 (3rd)

By Dmitry Domanov / GMP-ECM 6.2.3, GGNFS/Msieve / May 20, 2009

(73·10¹⁷³-1)/9 = 8(1)₁₇₃_<174> = 7 · 4943 · 1059933049229_<13> · C158

C158 = P26 · C132

P26 = 64098166474883233335412841_<26>

C132 = [345038581425000928450184633893862071554589588600861750152497688160450839810744310320911058217737288283002897503366245665576907950899_<132>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=460137404
Step 1 took 41172ms
Step 2 took 11828ms
********** Factor found in step 2: 64098166474883233335412841
Found probable prime factor of 26 digits: 64098166474883233335412841
Composite cofactor 345038581425000928450184633893862071554589588600861750152497688160450839810744310320911058217737288283002897503366245665576907950899 has 132 digits

(16·10¹⁷¹-7)/9 = 1(7)₁₇₁_<172> = 2159081 · 6112989193_<10> · 1204075884061927058546730881_<28> · C129

C129 = P56 · P73

P56 = 28439831557188093353879668494862682918380292611871233807_<56>

P73 = 3933453600796913095720722985325855260149941585902703532789048980867241007_<73>

N=111866757844679185887968729281774448067931340871359537390276493296195096332957079943344641551979112580133063024428735821115123649
  ( 129 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=28439831557188093353879668494862682918380292611871233807 (pp56)
r2=3933453600796913095720722985325855260149941585902703532789048980867241007 (pp73)
Version: Msieve v. 1.41
Total time: 55.00 hours.
Scaled time: 109.34 units (timescale=1.988).
Factorization parameters were as follows:
n: 111866757844679185887968729281774448067931340871359537390276493296195096332957079943344641551979112580133063024428735821115123649
m: 20000000000000000000000000000000000
deg: 5
c5: 5
c0: -7
skew: 1.07
type: snfs
lss: 1
rlim: 5200000
alim: 5200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2600000, 5000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 961428 x 961676
Total sieving time: 53.49 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.27 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,172.000,5,0,0,0,0,0,0,0,0,5200000,5200000,27,27,52,52,2.4,2.4,100000
total time: 55.00 hours.
 --------- CPU info (if available) ----------

(73·10¹⁹⁰-1)/9 = 8(1)₁₉₀_<191> = 3³ · 766373 · 576849289308102433339_<21> · C163

C163 = P33 · C131

P33 = 352770971508535022385843411436127_<33>

C131 = [19262878606573673376074258194783601287435893348319362805902003690630345538687715610774754588966646448026626420304138049204776918797_<131>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3579367891
Step 1 took 40735ms
Step 2 took 12609ms
********** Factor found in step 2: 352770971508535022385843411436127
Found probable prime factor of 33 digits: 352770971508535022385843411436127
Composite cofactor 19262878606573673376074258194783601287435893348319362805902003690630345538687715610774754588966646448026626420304138049204776918797 has 131 digits

(73·10¹⁷⁹-1)/9 = 8(1)₁₇₉_<180> = 7 · 29 · 67 · 21269 · C172

C172 = P41 · P131

P41 = 47141841003406331455972300887242733651907_<41>

P131 = 59477937477999248614204295322005295328835826506670111421059365117724762292797146126309564949352193967528628063664436708337272494617_<131>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2284984890
Step 1 took 165109ms
********** Factor found in step 1: 47141841003406331455972300887242733651907
Found probable prime factor of 41 digits: 47141841003406331455972300887242733651907
Probable prime cofactor 59477937477999248614204295322005295328835826506670111421059365117724762292797146126309564949352193967528628063664436708337272494617 has 131 digits

May 20, 2009 (2nd)

By Robert Backstrom / GGNFS / May 20, 2009

4·10¹⁷⁰+7 = 4(0)₁₆₉7_<171> = 11 · 23 · 37 · 2381 · 2531 · 23039 · 1367480531_<10> · C147

C147 = P47 · P101

P47 = 22070578087533539660066827927884256765089556891_<47>

P101 = 10197359262644066179879009668764560198414918046657958570180948390548824665266349600950111435706326543_<101>

Number: n
N=225061613892819300304785905266740211732831812868396480313631702593877904934930918137401620751717308464609538424488999385361130786232218389221857813
  ( 147 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=22070578087533539660066827927884256765089556891 (pp47)
 r2=10197359262644066179879009668764560198414918046657958570180948390548824665266349600950111435706326543 (pp101)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 37.67 hours.
Scaled time: 98.95 units (timescale=2.627).
Factorization parameters were as follows:
name: KA_4_0_169_7
n: 225061613892819300304785905266740211732831812868396480313631702593877904934930918137401620751717308464609538424488999385361130786232218389221857813
m: 10000000000000000000000000000000000
deg: 5
c5: 4
c0: 7
skew: 1.12
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [2450000, 4250001)
Primes: RFBsize:341992, AFBsize:341158, largePrimes:16380774 encountered
Relations: rels:16086164, finalFF:804371
Max relations in full relation-set: 28
Initial matrix: 683214 x 804371 with sparse part having weight 83408290.
Pruned matrix : 597975 x 601455 with weight 63746608.
Total sieving time: 33.20 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 3.16 hours.
Total square root time: 0.82 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,28,28,56,56,2.4,2.4,100000
total time: 37.67 hours.
 --------- CPU info (if available) ----------

May 20, 2009

Factorizations of 622...221 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 19, 2009 (4th)

By Dmitry Domanov / GGNFS/Msieve, GMP-ECM 6.2.3 / May 19, 2009

(7·10¹⁸⁰-43)/9 = (7)₁₇₉3_<180> = 53 · 197 · 422057 · 741131 · 1131199217758037948475947876693_<31> · C135

C135 = P64 · P71

P64 = 2741369082874657399663051277237026829017586667572935865244850717_<64>

P71 = 76796378648023087638003648915673883503681198485916992643055270266992439_<71>

Number: 777
N=210527218102425973724818558615766578439790005099467290507542270053221747074507541204557915603489023170770125680574714982426615122728763
  ( 135 digits)
SNFS difficulty: 180 digits.
Divisors found:
r1=2741369082874657399663051277237026829017586667572935865244850717 (pp64)
r2=76796378648023087638003648915673883503681198485916992643055270266992439 (pp71)
Version: Msieve v. 1.41
Total time: 158.15 hours.
Scaled time: 313.46 units (timescale=1.982).
Factorization parameters were as follows:
n: 210527218102425973724818558615766578439790005099467290507542270053221747074507541204557915603489023170770125680574714982426615122728763
m: 1000000000000000000000000000000000000
deg: 5
c5: 7
c0: -43
skew: 1.44
type: snfs
lss: 1
rlim: 7200000
alim: 7200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7200000/7200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3600000, 5900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1283421 x 1283669
Total sieving time: 155.28 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 2.33 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,180.000,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,53,53,2.5,2.5,100000
total time: 158.15 hours.
 --------- CPU info (if available) ----------

(7·10²⁰⁰-43)/9 = (7)₁₉₉3_<200> = 991073183 · C191

C191 = P40 · C152

P40 = 3937154377208831195317050869489643571199_<40>

C152 = [19932756512603613805537617547909718330804698132888310510455011242343011729605214247504057026096081092532311130097139778827231495420334733940846765405069_<152>]

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1296127361
Step 1 took 829141ms
Step 2 took 159953ms
********** Factor found in step 2: 3937154377208831195317050869489643571199
Found probable prime factor of 40 digits: 3937154377208831195317050869489643571199
Composite cofactor 19932756512603613805537617547909718330804698132888310510455011242343011729605214247504057026096081092532311130097139778827231495420334733940846765405069 has 152 digits

May 19, 2009 (3rd)

By matsui / Msieve / May 19, 2009

8·10¹⁸⁰-9 = 7(9)₁₇₉1_<181> = 826115977894170609050375729157582021497_<39> · C142

C142 = P67 · P75

P67 = 9990207070327391855783197701498143287718371662893791939986474480751_<67>

P75 = 969336296313865853470535064289775123620533028668230038800912477861614266753_<75>

N=9683870320959750397301131599191235511655411576027658067144718311274518875633720728729028560156827649352670707054841461900759820696819277771503
  ( 142 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=9990207070327391855783197701498143287718371662893791939986474480751 (pp67)
 r2=969336296313865853470535064289775123620533028668230038800912477861614266753 (pp75)
Version: Msieve v. 1.41
Total time: 110.65 hours.
Scaled time: 244.98 units (timescale=2.214).
Factorization parameters were as follows:
n: 9683870320959750397301131599191235511655411576027658067144718311274518875633720728729028560156827649352670707054841461900759820696819277771503
m: 1000000000000000000000000000000000000
deg: 5
c5: 8
c0: -9
skew: 1.02
type: snfs
lss: 1
rlim: 7200000
alim: 7200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 200000
Factor base limits: 7200000/7200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3600000, 5400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1294696 x 1294944
Total sieving time: 106.54 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.78 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,180.000,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,53,53,2.5,2.5,100000
total time: 110.65 hours.

May 19, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / May 19, 2009

(82·10¹⁹⁸-1)/9 = 9(1)₁₉₈_<199> = 3² · 347 · C196

C196 = P87 · P109

P87 = 436939136360240984927360625309074935876631115857657607436178934760710293610292472591579_<87>

P109 = 6676954438986529421607213490324435297594479058174569446376089299972729546356176059887751621704278177785185383_<109>

Number: n
N=2917422706087451524531255559113388123954886683032696481303589853061514925107624435194079766606183513003878037499555270928950083609065357384281495712811755078805991390045184473618671505318959689757
  ( 196 digits)
SNFS difficulty: 201 digits.
Divisors found:

Tue May 19 05:13:09 2009  prp87 factor: 436939136360240984927360625309074935876631115857657607436178934760710293610292472591579
Tue May 19 05:13:09 2009  prp109 factor: 6676954438986529421607213490324435297594479058174569446376089299972729546356176059887751621704278177785185383
Tue May 19 05:13:09 2009  elapsed time 13:39:46 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20050930-k8
Total time: 40.20 hours.
Scaled time: 81.00 units (timescale=2.015).
Factorization parameters were as follows:
name: KA_9_1_198
n: 2917422706087451524531255559113388123954886683032696481303589853061514925107624435194079766606183513003878037499555270928950083609065357384281495712811755078805991390045184473618671505318959689757
m: 10000000000000000000000000000000000000000
deg: 5
c5: 41
c0: -50
skew: 1.04
type: snfs
lss: 1
rlim: 16000000
alim: 16000000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 16000000/16000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved  special-q in [8000000, 17000141)
Primes: RFBsize:1031130, AFBsize:1031439, largePrimes:36170229 encountered
Relations: rels:35462145, finalFF:1658980
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 4758809 hash collisions in 38486645 relations
Msieve: matrix is 2854694 x 2854942 (777.1 MB)

Total sieving time: 39.37 hours.
Total relation processing time: 0.82 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,201,5,0,0,0,0,0,0,0,0,16000000,16000000,29,29,56,56,2.6,2.6,100000
total time: 40.20 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.97 BogoMIPS (lpj=2830488)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22643.70 BogoMIPS).

(55·10¹⁶⁶+71)/9 = 6(1)₁₆₅9_<167> = 3² · 285643157 · C158

C158 = P46 · P112

P46 = 4368395824318766408050439945935647525108707809_<46>

P112 = 5441665761123586513039701393455608632083915097455189199613841488885076266307031749893027851414099021773762658907_<112>

Number: n
N=23771349988230677119949782157008310396142707023750348259839893370139875105742944357634737445469850540792487658964375109431112528945069238224822787510794304763
  ( 158 digits)
SNFS difficulty: 167 digits.
Divisors found:

Tue May 19 17:51:37 2009  prp46 factor: 4368395824318766408050439945935647525108707809
Tue May 19 17:51:37 2009  prp112 factor: 5441665761123586513039701393455608632083915097455189199613841488885076266307031749893027851414099021773762658907
Tue May 19 17:51:37 2009  elapsed time 00:59:13 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 46.95 hours.
Scaled time: 124.89 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_1_165_9
n: 23771349988230677119949782157008310396142707023750348259839893370139875105742944357634737445469850540792487658964375109431112528945069238224822787510794304763
m: 1000000000000000000000000000000000
deg: 5
c5: 550
c0: 71
skew: 0.66
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2200000, 4930207)
Primes: RFBsize:309335, AFBsize:308675, largePrimes:16930723 encountered
Relations: rels:17097659, finalFF:662576
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2077248 hash collisions in 18962584 relations
Msieve: matrix is 711056 x 711304 (188.0 MB)

Total sieving time: 46.23 hours.
Total relation processing time: 0.73 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,4400000,4400000,28,28,56,56,2.4,2.4,100000
total time: 46.95 hours.
 --------- CPU info (if available) ----------

May 19, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 19, 2009

2·10¹⁸¹-1 = 1(9)₁₈₁_<182> = 19 · 71 · 7349 · 808897818779368181_<18> · 797129087967153857493783971_<27> · C130

C130 = P46 · P84

P46 = 5050517525163785428349019657192204840675990331_<46>

P84 = 619486140631122497714177220241924734371086778583423922913708782283498388270677109979_<84>

Number: 19999_181
N=3128725609853561538026773920634567520995491992088880828324972714133336327873248318256123375586149260625874239143237635528827613049
  ( 130 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=5050517525163785428349019657192204840675990331
 r2=619486140631122497714177220241924734371086778583423922913708782283498388270677109979
Version: 
Total time: 68.24 hours.
Scaled time: 162.76 units (timescale=2.385).
Factorization parameters were as follows:
n: 3128725609853561538026773920634567520995491992088880828324972714133336327873248318256123375586149260625874239143237635528827613049
m: 1000000000000000000000000000000000000
deg: 5
c5: 20
c0: -1
skew: 0.55
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [2900000, 4800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 17839570
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1166869 x 1167117
Total sieving time: 62.68 hours.
Total relation processing time: 1.76 hours.
Matrix solve time: 3.07 hours.
Time per square root: 0.73 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,53,53,2.5,2.5,100000
total time: 68.24 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 18, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / May 18, 2009

(55·10¹⁶⁷+53)/9 = 6(1)₁₆₆7_<168> = 13 · C167

C167 = P51 · P117

P51 = 413253709863765149819165994687158966560294819480339_<51>

P117 = 113752268610108864645974297516771880453518903037560549478996788182332828844323184288710023807427966999107247784733531_<117>

Number: n
N=47008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547009
  ( 167 digits)
SNFS difficulty: 170 digits.
Divisors found:

Mon May 18 20:45:42 2009  prp51 factor: 413253709863765149819165994687158966560294819480339
Mon May 18 20:45:42 2009  prp117 factor: 113752268610108864645974297516771880453518903037560549478996788182332828844323184288710023807427966999107247784733531
Mon May 18 20:45:42 2009  elapsed time 01:47:01 (Msieve 1.39 - dependency 5)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 46.69 hours.
Scaled time: 123.67 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_6_1_166_7
n: 47008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547008547009
m: 5000000000000000000000000000000000
deg: 5
c5: 44
c0: 1325
skew: 1.98
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2400000, 5036893)
Primes: RFBsize:335439, AFBsize:335533, largePrimes:16351362 encountered
Relations: rels:15644308, finalFF:647400
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1750957 hash collisions in 17268406 relations
Msieve: matrix is 861002 x 861250 (230.9 MB)

Total sieving time: 46.06 hours.
Total relation processing time: 0.63 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,56,56,2.4,2.4,100000
total time: 46.69 hours.
 --------- CPU info (if available) ----------

May 18, 2009 (3rd)

By Dmitry Domanov / GMP-ECM 6.2.3, GGNFS, Msieve 1.41 / May 18, 2009

2·10²³²-1 = 1(9)₂₃₂_<233> = 7 · 173137 · 42049591 · C219

C219 = P38 · P182

P38 = 34613759961280378907193267864768175303_<38>

P182 = 11337871068816284810015281720676567521820709766247790016536458359116649482490012289408508986811315047442941807203647099955100565546682002698657209705791404051679009408588287240060857_<182>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1689352593
Step 1 took 410609ms
Step 2 took 104703ms
********** Factor found in step 2: 34613759961280378907193267864768175303
Found probable prime factor of 38 digits: 34613759961280378907193267864768175303
Probable prime cofactor 11337871068816284810015281720676567521820709766247790016536458359116649482490012289408508986811315047442941807203647099955100565546682002698657209705791404051679009408588287240060857 has 182 digits

(7·10¹⁷⁹-43)/9 = (7)₁₇₈3_<179> = 29 · 74139184723_<11> · 5678444893385647_<16> · 64191352839380917_<17> · C134

C134 = P53 · P82

P53 = 59768195256934827918992906434416007822747135583378717_<53>

P82 = 1660479967082549350076027500591027695979166379603958880084664687018341548117976293_<82>

Number: 2
N=99243890892818525257757099486749168779709129287517878619947908485429606390314043914415323816305774703347821779218335872529329446756081
  ( 134 digits)
SNFS difficulty: 180 digits.
Divisors found:
r1=59768195256934827918992906434416007822747135583378717 (pp53)
r2=1660479967082549350076027500591027695979166379603958880084664687018341548117976293 (pp82)
Version: Msieve v. 1.41
Total time: 142.93 hours.
Scaled time: 284.15 units (timescale=1.988).
Factorization parameters were as follows:
n: 99243890892818525257757099486749168779709129287517878619947908485429606390314043914415323816305774703347821779218335872529329446756081
m: 500000000000000000000000000000000000
deg: 5
c5: 112
c0: -215
skew: 1.14
type: snfs
lss: 1
rlim: 7100000
alim: 7100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7100000/7100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3550000, 5650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1233288 x 1233536
Total sieving time: 140.43 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 2.09 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,180.000,5,0,0,0,0,0,0,0,0,7100000,7100000,28,28,53,53,2.5,2.5,100000
total time: 142.93 hours.
 --------- CPU info (if available) ----------

May 18, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.3 / May 18, 2009

2·10²⁴⁵-1 = 1(9)₂₄₅_<246> = 240139 · C240

C240 = P35 · P206

P35 = 11646344158366741257794536820925991_<35>

P206 = 71511794816116647592466076649315262164366978239860741017711346458660357589133354997489778453665412237637499789509689866120922247059753039227205632490112635124358150084519402014002012700683540453240769740251_<206>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4173179287
Step 1 took 6145ms
Step 2 took 3728ms
********** Factor found in step 2: 11646344158366741257794536820925991
Found probable prime factor of 35 digits: 11646344158366741257794536820925991
Probable prime cofactor has 206 digits

May 18, 2009

By Erik Branger / GGNFS, Msieve / May 18, 2009

(53·10¹⁷⁹-17)/9 = 5(8)₁₇₈7_<180> = 13 · 8609 · 2466439 · 1905016558247958781387_<22> · 8442905563306619451552613_<25> · C123

C123 = P49 · P75

P49 = 1267882575806183686123062369811279771630970712791_<49>

P75 = 104615780893553633888163173944050869226186736163185458497293997297646226469_<75>

Number: 58887_179
N=132640525749294118102139295123428335192313886562409838069300157486717226157984219970666790975658435729365925900696341064979
  ( 123 digits)
Divisors found:
 r1=1267882575806183686123062369811279771630970712791 (pp49)
 r2=104615780893553633888163173944050869226186736163185458497293997297646226469 (pp75)
Version: Msieve v. 1.41
Total time: 103.57 hours.
Scaled time: 81.20 units (timescale=0.784).
Factorization parameters were as follows:
# Murphy_E = 2.204181e-10, selected by Jeff Gilchrist
n: 132640525749294118102139295123428335192313886562409838069300157486717226157984219970666790975658435729365925900696341064979
Y0: -360317732448563326023454
Y1: 19879181277307
c0: 171606085697399885470075292375
c1: -919211884570549739620675
c2: 6162561620072014696
c3: -1776083482988118
c4: -4172818468
c5: 21840
skew: 146902.99
type: gnfs
# selected mechanically
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3000000, 5500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 812357 x 812605
Total sieving time: 97.10 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 4.27 hours.
Time per square root: 1.93 hours.
Prototype def-par.txt line would be:
gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6000000,6000000,27,27,52,52,2.5,2.5,100000
total time: 103.57 hours.
 --------- CPU info (if available) ----------

May 17, 2009 (7th)

By Dmitry Domanov / Msieve v. 1.41, GMP-ECM 6.2.3 / May 17, 2009

2·10¹⁷⁷-3 = 1(9)₁₇₆7_<178> = 17 · 66090659226826860491_<20> · 314129679887073807583524645188651_<33> · C124

C124 = P57 · P68

P57 = 129436443535881527128893364288064480493161761142268211249_<57>

P68 = 43779968748061432046513482796553162771143586000974553425324771322949_<68>

Number: 1
N=5666723452861111419953301719983874645151689206796263127100108210064996380732130563446722510620008860655369666194925533653301
  ( 124 digits)
Divisors found:
r1=129436443535881527128893364288064480493161761142268211249 (pp57)
r2=43779968748061432046513482796553162771143586000974553425324771322949 (pp68)
Version: Msieve v. 1.41
Total time: 64.89 hours.
Scaled time: 129.00 units (timescale=1.988).
Factorization parameters were as follows:
n: 5666723452861111419953301719983874645151689206796263127100108210064996380732130563446722510620008860655369666194925533653301
Y0: -790479467134143134043274
Y1: 32457700167143
c0: -16608921037930062398718064421235
c1: 204502172404307051875471623
c2: -475301048895667076195
c3: -3826111044588199
c4: 6563015646
c5: 18360
skew: 335696.21
type: gnfs
# selected mechanically
rlim: 6600000
alim: 6600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6600000/6600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3300000, 6200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 853192 x 853440
Total sieving time: 63.48 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.94 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6600000,6600000,27,27,52,52,2.5,2.5,100000
total time: 64.89 hours.
 --------- CPU info (if available) ----------

(8·10¹⁷³-17)/9 = (8)₁₇₂7_<173> = 3 · 19 · 238591 · 266183 · 6010441682603_<13> · 812262305277809501754934760781703_<33> · C115

C115 = P49 · P67

P49 = 2611259137894710237293454858163599958892111103623_<49>

P67 = 1926129971804758511475517763482213919232130440459976838959776938821_<67>

N=5029624489648056247300436114909387948363823244892596172024214674079949553164223403365426542863909717715506862448483
  ( 115 digits)
Divisors found:
r1=2611259137894710237293454858163599958892111103623 (pp49)
r2=1926129971804758511475517763482213919232130440459976838959776938821 (pp67)
Version: Msieve v. 1.41
Total time: 22.88 hours.
Scaled time: 45.48 units (timescale=1.988).
Factorization parameters were as follows:
name: 0
n: 5029624489648056247300436114909387948363823244892596172024214674079949553164223403365426542863909717715506862448483
skew: 36469.77
# norm 1.93e+016
c5: 170100
c4: -10736202576
c3: -1186048453213825
c2: 14042271287297154850
c1: 548613656918148741678540
c0: 1532467212163374559964486256
# alpha -7.17
Y1: 2806801040923
Y0: -7837331434948602045395
# Murphy_E 5.77e-010
# M 4373931990339949704516262703984833457081464005125254720617819565817044248881822484578247306882686022685927858970917
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 453024 x 453272
Total sieving time: 22.44 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 22.88 hours.
 --------- CPU info (if available) ----------

2·10²⁰⁶-1 = 1(9)₂₀₆_<207> = 11887 · C203

C203 = P32 · C171

P32 = 25251681423007905250365508795903_<32>

C171 = [666296345653486704742396440597318758413330523030411841134328740685319859888372657484412271028953068923412326473632165793283237236740121087632239829994708821140851105993359_<171>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1034025118
Step 1 took 365484ms
Step 2 took 91844ms
********** Factor found in step 2: 25251681423007905250365508795903
Found probable prime factor of 32 digits: 25251681423007905250365508795903
Composite cofactor 666296345653486704742396440597318758413330523030411841134328740685319859888372657484412271028953068923412326473632165793283237236740121087632239829994708821140851105993359 has 171 digits

May 17, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / May 17, 2009

(55·10¹⁵⁶+71)/9 = 6(1)₁₅₅9_<157> = 7 · 19 · 89 · 18371 · 171079 · C144

C144 = P55 · P89

P55 = 4370158092582282757313947484456642816270989901770322191_<55>

P89 = 37588230741138358916968159138254050527582219668790482732985280376540552048714496247601473_<89>

Number: n
N=164266510759235935151091684199368678071275955875794973838775544060115590128095146270263568553806905435199397302142613446385652138637818176187343
  ( 144 digits)
SNFS difficulty: 157 digits.
Divisors found:

Sun May 17 13:36:38 2009  prp55 factor: 4370158092582282757313947484456642816270989901770322191
Sun May 17 13:36:38 2009  prp89 factor: 37588230741138358916968159138254050527582219668790482732985280376540552048714496247601473
Sun May 17 13:36:38 2009  elapsed time 00:38:11 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 18.14 hours.
Scaled time: 48.25 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_1_155_9
n: 164266510759235935151091684199368678071275955875794973838775544060115590128095146270263568553806905435199397302142613446385652138637818176187343
m: 10000000000000000000000000000000
deg: 5
c5: 550
c0: 71
skew: 0.66
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1500000, 2621263)
Primes: RFBsize:216816, AFBsize:216593, largePrimes:12448399 encountered
Relations: rels:11358348, finalFF:405451
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 973747 hash collisions in 12361528 relations
Msieve: matrix is 559501 x 559749 (151.1 MB)

Total sieving time: 17.86 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000
total time: 18.14 hours.
 --------- CPU info (if available) ----------

(55·10¹⁵⁷+71)/9 = 6(1)₁₅₆9_<158> = 3² · 1471403 · 802664521 · C142

C142 = P58 · P85

P58 = 1686182319884758962774964750881255991601351889743917277737_<58>

P85 = 3409631426198123185000501403935973337864779640058934109973986572635032460917715202261_<85>

Number: n
N=5749260228178730669619786717761222950011415158355549533147526451268751883270957466810123899031638901689018728723513873259203959052863467363357
  ( 142 digits)
SNFS difficulty: 159 digits.
Divisors found:

Sun May 17 18:57:23 2009  prp58 factor: 1686182319884758962774964750881255991601351889743917277737
Sun May 17 18:57:23 2009  prp85 factor: 3409631426198123185000501403935973337864779640058934109973986572635032460917715202261
Sun May 17 18:57:23 2009  elapsed time 00:42:44 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 23.25 hours.
Scaled time: 61.08 units (timescale=2.627).
Factorization parameters were as follows:
name: KA_6_1_156_9
n: 5749260228178730669619786717761222950011415158355549533147526451268751883270957466810123899031638901689018728723513873259203959052863467363357
m: 20000000000000000000000000000000
deg: 5
c5: 1375
c0: 568
skew: 0.84
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1600000, 3000103)
Primes: RFBsize:230209, AFBsize:230864, largePrimes:13258094 encountered
Relations: rels:12352354, finalFF:499172
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1168747 hash collisions in 13306719 relations
Msieve: matrix is 600048 x 600296 (161.2 MB)

Total sieving time: 22.97 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,56,56,2.4,2.4,100000
total time: 23.25 hours.
 --------- CPU info (if available) ----------

May 17, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.3 / May 17, 2009

2·10²⁴⁷-1 = 1(9)₂₄₇_<248> = 5711 · 5137651 · C237

C237 = P33 · P205

P33 = 109424217918630909136935706451429_<33>

P205 = 6229307717727602487152483306982713621811871446270813768407187294030930000936284989180582851699942671495245102701667423676129508232560794431964653471639690945651238874214201094168491986383412060065017416271_<205>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1912754877
Step 1 took 18573ms
Step 2 took 14897ms
********** Factor found in step 2: 109424217918630909136935706451429
Found probable prime factor of 33 digits: 109424217918630909136935706451429
Probable prime cofactor has 205 digits
Done!

2·10²⁴⁰-1 = 1(9)₂₄₀_<241> = 30977 · C236

C236 = P29 · C208

P29 = 12900409695855239366375680297_<29>

C208 = [5004804723284328509504727413794179674007575588977579484001085955783285781518184216385475235750566319669217329827167346224955993379403688987397077202076056166105889455325049497934984058409692206566091055812071_<208>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3362628703
Step 1 took 18557ms
Step 2 took 14457ms
********** Factor found in step 2: 12900409695855239366375680297
Found probable prime factor of 29 digits: 12900409695855239366375680297
Composite cofactor has 208 digits

2·10²⁰⁵-1 = 1(9)₂₀₅_<206> = 4871 · 2292880818603421_<16> · C187

C187 = P31 · C157

P31 = 1129082288029883803778855245661_<31>

C157 = [1586005869640370385835630004795171489748136970111735468000037034576203712150943132322655517008937091427800298435286635359428161072876813941823046361696157249_<157>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3975420477
Step 1 took 12357ms
Step 2 took 11288ms
********** Factor found in step 2: 1129082288029883803778855245661
Found probable prime factor of 31 digits: 1129082288029883803778855245661
Composite cofactor has 157 digits

May 17, 2009 (4th)

By matsui / Msieve / May 17, 2009

7·10¹⁷⁰-3 = 6(9)₁₆₉7_<171> = 1429327603703_<13> · 28390070271134877038117841913_<29> · C131

C131 = P53 · P79

P53 = 10977412137489495157200178568512469140915422117788701_<53>

P79 = 1571447302297785507555396244163363334714959786940690062024588758974391266160223_<79>

N=17250424689668834463131362979763025513450745051057365655701643284974919725337463089471895545976264413296899763464783165863925040323
  ( 131 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=10977412137489495157200178568512469140915422117788701 (pp53)
 r2=1571447302297785507555396244163363334714959786940690062024588758974391266160223 (pp79)
Version: Msieve v. 1.41
Total time: 43.50 hours.
Scaled time: 95.83 units (timescale=2.203).
Factorization parameters were as follows:
n: 17250424689668834463131362979763025513450745051057365655701643284974919725337463089471895545976264413296899763464783165863925040323
m: 10000000000000000000000000000000000
deg: 5
c5: 7
c0: -3
skew: 0.84
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4

Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 4550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 925874 x 926122
Total sieving time: 41.19 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 2.10 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 43.50 hours.

May 17, 2009 (3rd)

By Markus Tervooren / ggnfs/msieve / May 17, 2009

(55·10¹⁶⁰+71)/9 = 6(1)₁₅₉9_<161> = 3 · 149 · 21107 · 1084075229719_<13> · C142

C142 = P38 · P104

P38 = 88539989319060976418882479999944058891_<38>

P104 = 67481893525870289348177804373535358169251913889732089510397032622620280152860264580806539879951990357159_<104>

Msieve v. 1.41
Sat May 16 23:48:25 2009
random seeds: 1adbc9bd 4cfcd870
factoring 5974846132010565473273718653317702536894929614781964497842106328436804159921963100290714032559044192138130940159247390971510433112663219450669 (142 digits)
searching for 15-digit factors
commencing number field sieve (142-digit input)
R0: -100000000000000000000000000000000
R1:  1
A0:  71
A1:  0
A2:  0
A3:  0
A4:  0
A5:  55
skew 1.05, size 1.984130e-11, alpha 1.074395, combined = 4.937228e-10

commencing square root phase
reading relations for dependency 1
read 278577 cycles
cycles contain 1059584 unique relations
read 1059584 relations
multiplying 848856 relations
multiply complete, coefficients have about 23.21 million bits
initial square root is modulo 4621231
sqrtTime: 135
prp38 factor: 88539989319060976418882479999944058891
prp104 factor: 67481893525870289348177804373535358169251913889732089510397032622620280152860264580806539879951990357159
elapsed time 00:02:16

Total sieving time: 18:12:01

May 17, 2009 (2nd)

Factorizations of 199...99 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 17, 2009

By Serge Batalov / PFGW / Mar 16, 2009

(16·10⁵⁶⁰⁸²-61)/9 = 1(7)₅₆₀₈₁1_<56083> is PRP.

May 16, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / May 16, 2009

(55·10¹⁷³+53)/9 = 6(1)₁₇₂7_<174> = 13 · 29 · 107 · C170

C170 = P77 · P94

P77 = 12576082971806871968069729416319272329315487489596105277919238868516031336329_<77>

P94 = 1204618859405030553363698323853833563350237788260488026770597375925396803921048656034405570407_<94>

Number: n
N=15149386725281021123753962941845636012571236548033196437966015793924269592977295200949728825977617469721884804063340963115374974865790205783760408317288755574285706415903
  ( 170 digits)
SNFS difficulty: 175 digits.
Divisors found:

Sat May 16 20:13:23 2009  prp77 factor: 12576082971806871968069729416319272329315487489596105277919238868516031336329
Sat May 16 20:13:23 2009  prp94 factor: 1204618859405030553363698323853833563350237788260488026770597375925396803921048656034405570407
Sat May 16 20:13:23 2009  elapsed time 01:57:04 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 92.51 hours.
Scaled time: 246.07 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_1_172_7
n: 15149386725281021123753962941845636012571236548033196437966015793924269592977295200949728825977617469721884804063340963115374974865790205783760408317288755574285706415903
m: 50000000000000000000000000000000000
deg: 5
c5: 88
c0: 265
skew: 1.25
type: snfs
lss: 1
rlim: 5900000
alim: 5900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2950000, 7750001)
Primes: RFBsize:406429, AFBsize:406189, largePrimes:21211462 encountered
Relations: rels:21323565, finalFF:723633
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2986877 hash collisions in 24112465 relations
Msieve: matrix is 1043634 x 1043882 (273.1 MB)

Total sieving time: 90.86 hours.
Total relation processing time: 1.64 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,5900000,5900000,28,28,56,56,2.5,2.5,100000
total time: 92.51 hours.
 --------- CPU info (if available) ----------

May 16, 2009 (5th)

By Sinkiti Sibata / GGNFS / May 16, 2009

(55·10¹⁴³+71)/9 = 6(1)₁₄₂9_<144> = 17 · 29 · 991 · 4457 · 6493441453_<10> · 2838678287817353_<16> · C110

C110 = P41 · P69

P41 = 27019354239685156397295913693344519066703_<41>

P69 = 563496083463933782315403603663316451548918552533691438676317697210167_<69>

Number: 61119_143
N=15225300291787219991255509950617093567241683938470837984337757123021294767004829225327161644868299881682769401
  ( 110 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=27019354239685156397295913693344519066703 (pp41)
 r2=563496083463933782315403603663316451548918552533691438676317697210167 (pp69)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 17.08 hours.
Scaled time: 8.08 units (timescale=0.473).
Factorization parameters were as follows:
name: 61119_143
n: 15225300291787219991255509950617093567241683938470837984337757123021294767004829225327161644868299881682769401
m: 50000000000000000000000000000
deg: 5
c5: 88
c0: 355
skew: 1.32
type: snfs
lss: 1
rlim: 1860000
alim: 1860000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1860000/1860000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [930000, 2230001)
Primes: RFBsize:139249, AFBsize:139185, largePrimes:3996264 encountered
Relations: rels:4113629, finalFF:376850
Max relations in full relation-set: 28
Initial matrix: 278500 x 376850 with sparse part having weight 36482233.
Pruned matrix : 244485 x 245941 with weight 20666563.
Total sieving time: 15.21 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.59 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1860000,1860000,26,26,49,49,2.3,2.3,100000
total time: 17.08 hours.
 --------- CPU info (if available) ----------

May 16, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 16, 2009

(53·10¹⁹⁸-17)/9 = 5(8)₁₉₇7_<199> = C199

C199 = P52 · P148

P52 = 3105261215890219980188797697842256974579853865273347_<52>

P148 = 1896423031580824744009636372699045793880183375458593621015135886801884722666025272281158636589101925037831403331081551847068185738937524060810693821_<148>

Number: 58887_198
N=5888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
  ( 199 digits)
SNFS difficulty: 199 digits.
Divisors found:
 r1=3105261215890219980188797697842256974579853865273347
 r2=1896423031580824744009636372699045793880183375458593621015135886801884722666025272281158636589101925037831403331081551847068185738937524060810693821
Version: 
Total time: 495.00 hours.
Scaled time: 1183.05 units (timescale=2.390).
Factorization parameters were as follows:
n: 5888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
m: 1000000000000000000000000000000000
deg: 6
c6: 53
c0: -17
skew: 0.83
type: snfs
lss: 1
rlim: 20000000
alim: 20000000
lpbr: 29
lpba: 29
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6
Factor base limits: 20000000/20000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 55/55
Sieved rational special-q in [10000000, 20700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 35575862
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3176756 x 3177003
Total sieving time: 445.27 hours.
Total relation processing time: 22.31 hours.
Matrix solve time: 26.88 hours.
Time per square root: 0.54 hours.
Prototype def-par.txt line would be:
snfs,199,6,0,0,0,0,0,0,0,0,20000000,20000000,29,29,55,55,2.6,2.6,100000
total time: 495.00 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 16, 2009 (3rd)

By Dmitry Domanov / Msieve / May 16, 2009

(55·10¹⁶²+71)/9 = 6(1)₁₆₁9_<163> = 7 · C162

C162 = P41 · P58 · P64

P41 = 27343748654766962023770897524061237446659_<41>

P58 = 5056764184952869943581882885968674046825445552654199267029_<58>

P64 = 6313808207126857150929194815143949309287693135354451798881427847_<64>

N=873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873017
  ( 162 digits)
SNFS difficulty: 164 digits.
Divisors found:
r1=27343748654766962023770897524061237446659 (pp41)
r2=5056764184952869943581882885968674046825445552654199267029 (pp58)
r3=6313808207126857150929194815143949309287693135354451798881427847 (pp64)
Version: Msieve v. 1.41
Total time: 41.38 hours.
Scaled time: 36.42 units (timescale=0.880).
Factorization parameters were as follows:
n: 873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873017
m: 200000000000000000000000000000000
deg: 5
c5: 1375
c0: 568
skew: 0.84
type: snfs
lss: 1
rlim: 3900000
alim: 3900000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3900000/3900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1950000, 4050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 712923 x 713171
Total sieving time: 39.93 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.91 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,164.000,5,0,0,0,0,0,0,0,0,3900000,3900000,27,27,51,51,2.4,2.4,100000
total time: 41.38 hours.
 --------- CPU info (if available) ----------

May 16, 2009 (2nd)

By matsui / GGNFS / May 16, 2009

8·10¹⁷⁸+3 = 8(0)₁₇₇3_<179> = 7 · 11 · 73 · 120504276263123_<15> · C162

C162 = P46 · P116

P46 = 1521121596498992083430684328800554217699357191_<46>

P116 = 77644377170813478936009808463885244242858683928639274087657213019286395263296774458233906745544656020639399572401451_<116>

N=118106538961237693228597702847944467131004093955164231095291492466633604287488596160101615398988803382502945819721906856579471463533012033849514923850146895684141
  ( 162 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=1521121596498992083430684328800554217699357191 (pp46)
 r2=77644377170813478936009808463885244242858683928639274087657213019286395263296774458233906745544656020639399572401451 (pp116)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 118.65 hours.
Scaled time: 259.61 units (timescale=2.188).
Factorization parameters were as follows:
n: 118106538961237693228597702847944467131004093955164231095291492466633604287488596160101615398988803382502945819721906856579471463533012033849514923850146895684141
m: 1000000000000000000000000000000000000
deg: 5
c5: 2
c0: 75
skew: 2.06
type: snfs
lss: 1
rlim: 7100000
alim: 7100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

Factor base limits: 7100000/7100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3550000, 5250001)
Primes: RFBsize:483015, AFBsize:482366, largePrimes:17442103 encountered
Relations: rels:17732404, finalFF:1229549
Max relations in full relation-set: 32
Initial matrix: 965446 x 1229548 with sparse part having weight 148799596.
Pruned matrix : 762190 x 767081 with weight 115818416.
Total sieving time: 108.34 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 9.76 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7100000,7100000,28,28,53,53,2.5,2.5,100000
total time: 118.65 hours.

Mar 16, 2009

By Serge Batalov / PFGW / Mar 15, 2009

(5·10⁶⁶³⁹⁴-17)/3 = 1(6)₆₆₃₉₃1_<66395> is PRP.

May 15, 2009 (3rd)

By Dmitry Domanov / GMP-ECM 6.2.3, Msieve v. 1.41, GGNFS-0.77.1-VC8 / May 15, 2009

(55·10¹⁹²+71)/9 = 6(1)₁₉₁9_<193> = 7² · 19 · 28211 · C186

C186 = P33 · P153

P33 = 287860258795288440499702779905657_<33>

P153 = 808295771108102506695396656539593972616330973723038986708273430564327994343724988972906260199977808554283757311321321457279161095184020165058222553689087_<153>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=989525659
Step 1 took 91250ms
********** Factor found in step 1: 287860258795288440499702779905657
Found probable prime factor of 33 digits: 287860258795288440499702779905657
Probable prime cofactor 808295771108102506695396656539593972616330973723038986708273430564327994343724988972906260199977808554283757311321321457279161095184020165058222553689087 has 153 digits

(49·10¹⁷⁰-13)/9 = 5(4)₁₆₉3_<171> = 3³ · 17 · 53 · 5027117 · C160

C160 = P61 · P100

P61 = 2692212159653272355339435109096075286883559301953867086090461_<61>

P100 = 1653623901550726337767533156447700441142090917636728902297814526133953699616039119659459695609726357_<100>

Number: 6
N=4451906375248151182830922835284818657113863806841579312202067690879499966017767766632869279766525410733659197053565189224887023373656337781407513933537157980577
  ( 160 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=2692212159653272355339435109096075286883559301953867086090461 (pp61)
 r2=1653623901550726337767533156447700441142090917636728902297814526133953699616039119659459695609726357 (pp100)
Version: Msieve v. 1.41
Total time: 79.84 hours.
Scaled time: 156.25 units (timescale=1.957).
Factorization parameters were as follows:
n: 4451906375248151182830922835284818657113863806841579312202067690879499966017767766632869279766525410733659197053565189224887023373656337781407513933537157980577
m: 10000000000000000000000000000000000
deg: 5
c5: 49
c0: -13
skew: 0.77
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 4950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 756235 x 756483
Total sieving time: 77.49 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.08 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 79.84 hours.
 --------- CPU info (if available) ----------

(55·10¹⁶⁵+71)/9 = 6(1)₁₆₄9_<166> = 809 · 3691 · 108263 · C155

C155 = P35 · P120

P35 = 24335341153262737407629933896579409_<35>

P120 = 776801609907481825359557101187910185903023150073711522354469400696299227987950943173477493221818097747365114068869669603_<120>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3179055233
Step 1 took 68563ms
Step 2 took 22078ms
********** Factor found in step 2: 24335341153262737407629933896579409
Found probable prime factor of 35 digits: 24335341153262737407629933896579409
Probable prime cofactor 776801609907481825359557101187910185903023150073711522354469400696299227987950943173477493221818097747365114068869669603 has 120 digits

(55·10¹⁹⁷+71)/9 = 6(1)₁₉₆9_<198> = 18642536789_<11> · C188

C188 = P35 · P153

P35 = 57547309236684489528941761046601613_<35>

P153 = 569626452891159171398342923688370533308071766262310180490302207470807685125526248239176720252301776078743824072951071192362669399076391681375266653470367_<153>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=389729675
Step 1 took 332672ms
********** Factor found in step 1: 57547309236684489528941761046601613
Found probable prime factor of 35 digits: 57547309236684489528941761046601613
Probable prime cofactor 569626452891159171398342923688370533308071766262310180490302207470807685125526248239176720252301776078743824072951071192362669399076391681375266653470367 has 153 digits

5·10¹⁶⁸-9 = 4(9)₁₆₇1_<169> = 31 · 29150029 · 97690322401972470211_<20> · C140

C140 = P63 · P78

P63 = 285672459115302906984888083354597717349768178359030194770540009_<63>

P78 = 198266528819518056600744503449893297480133294347181748253063893651091266424791_<78>

Number: 1
N=56639286848126797554729386539227574885723785334536125536236873465330483256275559559736715759646622674484365026756974688483306430233854963119
  ( 140 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=285672459115302906984888083354597717349768178359030194770540009 (pp63)
 r2=198266528819518056600744503449893297480133294347181748253063893651091266424791 (pp78)
Version: GGNFS-0.77.1-VC8
Total time: 52.63 hours.
Scaled time: 50.58 units (timescale=0.961).
Factorization parameters were as follows:
n: 56639286848126797554729386539227574885723785334536125536236873465330483256275559559736715759646622674484365026756974688483306430233854963119
m: 5000000000000000000000000000000000
deg: 5
c5: 8
c0: -45
skew: 1.41
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 4450001)
Primes: RFBsize:328964, AFBsize:327919, largePrimes:9912007 encountered
Relations: rels:10182561, finalFF:745248
Max relations in full relation-set: 32
Initial matrix: 656948 x 745248 with sparse part having weight 81981595.
Pruned matrix : 605955 x 609303 with weight 63712113.
Total sieving time: 47.58 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 4.17 hours.
Time per square root: 0.48 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000
total time: 52.63 hours.
 --------- CPU info (if available) ----------

(55·10¹⁵⁹+71)/9 = 6(1)₁₅₈9_<160> = 17 · 368130319157_<12> · 123677208423467_<15> · C133

C133 = P36 · P48 · P50

P36 = 140978348475664396838504814127042339_<36>

P48 = 882572282190700517976402060539018250089665494407_<48>

P50 = 63456672439732865549259372993901595965810017344261_<50>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2455922270
Step 1 took 49813ms
Step 2 took 16422ms
********** Factor found in step 2: 140978348475664396838504814127042339
Found probable prime factor of 36 digits: 140978348475664396838504814127042339
Composite cofactor 56005100215362762921524962760356855338997610012921755070987428408384155357213923636656407689048227 has 98 digits

Number: 0
N=56005100215362762921524962760356855338997610012921755070987428408384155357213923636656407689048227
  ( 98 digits)
Divisors found:
 r1=882572282190700517976402060539018250089665494407 (pp48)
 r2=63456672439732865549259372993901595965810017344261 (pp50)
Version: Msieve v. 1.41
Total time: 4.15 hours.
Scaled time: 8.17 units (timescale=1.969).
Factorization parameters were as follows:
name: 0
n: 56005100215362762921524962760356855338997610012921755070987428408384155357213923636656407689048227
skew: 1563.26
# norm 4.73e+012
c5: 54720
c4: 420073014
c3: -981929555154
c2: -902696291016996
c1: 539606548664109961
c0: 133625764604402100645
# alpha -3.85
Y1: 6255630337
Y0: -3999587985258256558
# Murphy_E 4.32e-009
# M 7500094444286231710467509873971966573554565601358545473228276408641175903590409269742379495665611
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 159857 x 160093
Polynomial selection time: 0.29 hours.
Total sieving time: 3.70 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 4.15 hours.
 --------- CPU info (if available) ----------

(55·10¹⁸⁸+71)/9 = 6(1)₁₈₇9_<189> = 21379 · 39133 · 3151970057_<10> · C171

C171 = P35 · C136

P35 = 23808035090930888675002054458419521_<35>

C136 = [9733835730442108411910371839197331283579776706732797283991862852256898234576047790599455636483601588124994915389202362114965362983239361_<136>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=751087292
Step 1 took 75563ms
Step 2 took 22469ms
********** Factor found in step 2: 23808035090930888675002054458419521
Found probable prime factor of 35 digits: 23808035090930888675002054458419521
Composite cofactor 9733835730442108411910371839197331283579776706732797283991862852256898234576047790599455636483601588124994915389202362114965362983239361 has 136 digits

May 15, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 15, 2009

(55·10¹⁸³+71)/9 = 6(1)₁₈₂9_<184> = 211 · 2897 · 14843 · 78504742266311_<14> · 18923252562065045071433_<23> · 1456022502472854275881544383_<28> · C111

C111 = P53 · P59

P53 = 26506006175993381272829828763617837641121116742352467_<53>

P59 = 11747987680181600226218167193411018631966399612495045430693_<59>

Number: n
N=311392234006387651672448081841093655775367230411377420724646687474507875782489096294534955481137814140026069631
  ( 111 digits)
Divisors found:
 r1=26506006175993381272829828763617837641121116742352467 (pp53)
 r2=11747987680181600226218167193411018631966399612495045430693 (pp59)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 15.22 hours.
Scaled time: 40.16 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_6_1_182_9
n: 311392234006387651672448081841093655775367230411377420724646687474507875782489096294534955481137814140026069631
Y0: -2584568069450941420360
Y1:  384958070083
c0: -4059072098339572523025137763
c1:  105158492379506668504759
c2: -2883980861159280569
c3: -33217032757935
c4:  172810416
c5:  2700
skew: 87047.99
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1600000, 2250001)
Primes: RFBsize:230209, AFBsize:230270, largePrimes:16995536 encountered
Relations: rels:15559641, finalFF:665605
Max relations in full relation-set: 28
Initial matrix: 460562 x 665605 with sparse part having weight 65940252.
Pruned matrix : 307315 x 309681 with weight 37286889.
Total sieving time: 13.61 hours.
Total relation processing time: 0.63 hours.
Matrix solve time: 0.50 hours.
Total square root time: 0.48 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000
total time: 15.22 hours.
 --------- CPU info (if available) ----------

(55·10¹⁶⁴+53)/9 = 6(1)₁₆₃7_<165> = 151 · 2449623037_<10> · 13672234223_<11> · 4175286873883_<13> · C131

C131 = P49 · P82

P49 = 4997494605967408149532708505482310328253201826819_<49>

P82 = 5791163563277687995964939570082543825557369323515164525575236980824238068315661321_<82>

Number: n
N=28941308669755240703099761874611761902648796448592435335238186323844236163242374178690923009820090062849191275519712456825298767899
  ( 131 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=4997494605967408149532708505482310328253201826819 (pp49)
 r2=5791163563277687995964939570082543825557369323515164525575236980824238068315661321 (pp82)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 38.21 hours.
Scaled time: 101.65 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_1_163_7
n: 28941308669755240703099761874611761902648796448592435335238186323844236163242374178690923009820090062849191275519712456825298767899
m: 1000000000000000000000000000000000
deg: 5
c5: 11
c0: 106
skew: 1.57
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [2050000, 4150001)
Primes: RFBsize:289774, AFBsize:289728, largePrimes:16159564 encountered
Relations: rels:16219905, finalFF:774173
Max relations in full relation-set: 28
Initial matrix: 579567 x 774173 with sparse part having weight 90821724.
Pruned matrix : 504359 x 507320 with weight 60248084.
Total sieving time: 35.33 hours.
Total relation processing time: 0.60 hours.
Matrix solve time: 2.09 hours.
Total square root time: 0.20 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,28,28,56,56,2.4,2.4,100000
total time: 38.21 hours.
 --------- CPU info (if available) ----------

(16·10¹⁶⁹-7)/9 = 1(7)₁₆₉_<170> = 224494463 · 786434162050807_<15> · C147

C147 = P67 · P80

P67 = 3487303178927087329591975815409665587670114255927538052409984233861_<67>

P80 = 28874851741200275794024069838665289918909310930811410451426125078495030526283477_<80>

Number: n
N=100695362268136064504090189001146777329779870588394993991707548409930165374487468529253744023227795557950486006149084859840889633580942941548214697
  ( 147 digits)
SNFS difficulty: 170 digits.
Divisors found:

Fri May 15 18:14:48 2009  prp67 factor: 3487303178927087329591975815409665587670114255927538052409984233861
Fri May 15 18:14:48 2009  prp80 factor: 28874851741200275794024069838665289918909310930811410451426125078495030526283477
Fri May 15 18:14:48 2009  elapsed time 01:16:27 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 44.07 hours.
Scaled time: 115.29 units (timescale=2.616).
Factorization parameters were as follows:
name: KA_1_7_169
n: 100695362268136064504090189001146777329779870588394993991707548409930165374487468529253744023227795557950486006149084859840889633580942941548214697
m: 10000000000000000000000000000000000
deg: 5
c5: 8
c0: -35
skew: 1.34
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2450000, 4945807)
Primes: RFBsize:341992, AFBsize:342818, largePrimes:16487133 encountered
Relations: rels:15756849, finalFF:691854
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1756427 hash collisions in 17765435 relations
Msieve: matrix is 838205 x 838453 (222.9 MB)

Total sieving time: 43.41 hours.
Total relation processing time: 0.67 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,28,28,56,56,2.4,2.4,100000
total time: 44.07 hours.
 --------- CPU info (if available) ----------

(55·10¹⁵⁵+71)/9 = 6(1)₁₅₄9_<156> = 23 · 58111 · 58519711 · 8773380623124748443600727_<25> · C117

C117 = P36 · P82

P36 = 143979646441272912798751233599595527_<36>

P82 = 6185342438048729794328561855111197190980660408468874396459980926568055950707673417_<82>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 890563417348457120832571640459891732891698128325691856818376277007924756340699090705920238580843477520126626410005759 (117 digits)
Using B1=2812000, B2=4281592780, polynomial Dickson(6), sigma=962927361
Step 1 took 31293ms
Step 2 took 11045ms
********** Factor found in step 2: 143979646441272912798751233599595527
Found probable prime factor of 36 digits: 143979646441272912798751233599595527
Probable prime cofactor 6185342438048729794328561855111197190980660408468874396459980926568055950707673417 has 82 digits

(22·10¹⁹⁸-1)/3 = 7(3)₁₉₈_<199> = 7 · 947 · C196

C196 = P91 · P105

P91 = 2882509691785175067582718426919249615849023053552230314201221226189350602539682348570293787_<91>

P105 = 383780258372884261144561599255815402930959690519198066403669312732520597025168652619394376800947167879971_<105>

Number: n
N=1106250314275657464675416100970483230250917684919796852215014833811032332679639965806808467843314728214411424548700155880726102479006386081359682204455171720219238698647357570272037009101423040177
  ( 196 digits)
SNFS difficulty: 201 digits.
Divisors found:

Sat May 16 00:29:16 2009  prp91 factor: 2882509691785175067582718426919249615849023053552230314201221226189350602539682348570293787
Sat May 16 00:29:16 2009  prp105 factor: 383780258372884261144561599255815402930959690519198066403669312732520597025168652619394376800947167879971
Sat May 16 00:29:16 2009  elapsed time 13:18:45 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 48.70 hours.
Scaled time: 98.07 units (timescale=2.014).
Factorization parameters were as follows:
name: KA_7_3_198
n: 1106250314275657464675416100970483230250917684919796852215014833811032332679639965806808467843314728214411424548700155880726102479006386081359682204455171720219238698647357570272037009101423040177
m: 10000000000000000000000000000000000000000
deg: 5
c5: 11
c0: -50
skew: 1.35
type: snfs
lss: 1
rlim: 15700000
alim: 15700000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 15700000/15700000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved  special-q in [7850000, 18449990)
Primes: RFBsize:1013012, AFBsize:1013131, largePrimes:1338580 encountered
Relations: rels:492627, finalFF:2135
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 4991232 hash collisions in 39498402 relations
Msieve: matrix is 2901304 x 2901551 (788.9 MB)

Total sieving time: 48.29 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,201,5,0,0,0,0,0,0,0,0,15700000,15700000,29,29,56,56,2.6,2.6,100000
total time: 48.70 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.95 BogoMIPS (lpj=2830476)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830448)
Total of 4 processors activated (22643.65 BogoMIPS).

May 15, 2009

By Sinkiti Sibata / GGNFS, Msieve / May 15, 2009

(55·10¹⁴⁷+71)/9 = 6(1)₁₄₆9_<148> = 198049777 · 1191274607893_<13> · 3445375456503515469833_<22> · C106

C106 = P35 · P72

P35 = 38467029705765547003621767930288053_<35>

P72 = 195437873678482374142781791356471424100324561115046333227355307258309471_<72>

Number: 61119_147
N=7517914492421835984058082848772797746445706638101076514609535759322165343395314387564217846404742848049963
  ( 106 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=38467029705765547003621767930288053 (pp35)
 r2=195437873678482374142781791356471424100324561115046333227355307258309471 (pp72)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 30.08 hours.
Scaled time: 14.26 units (timescale=0.474).
Factorization parameters were as follows:
name: 61119_147
n: 7517914492421835984058082848772797746445706638101076514609535759322165343395314387564217846404742848049963
m: 200000000000000000000000000000
deg: 5
c5: 1375
c0: 568
skew: 0.84
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 3300001)
Primes: RFBsize:162662, AFBsize:163732, largePrimes:4529351 encountered
Relations: rels:4808079, finalFF:401513
Max relations in full relation-set: 28
Initial matrix: 326461 x 401513 with sparse part having weight 45599410.
Pruned matrix : 298915 x 300611 with weight 32209704.
Total sieving time: 26.26 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 3.41 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000
total time: 30.08 hours.
 --------- CPU info (if available) ----------

(55·10¹³⁰+71)/9 = 6(1)₁₂₉9_<131> = 3² · 1031 · 931529 · 190631621 · 8946032747_<10> · C103

C103 = P50 · P53

P50 = 57792086304242895797761529441075115537051264545837_<50>

P53 = 71734624341105295983203643470137196510267861291590811_<53>

Number: 61119_130
N=4145693600923600439019225896942391349240772136386757922097820672747695605767505311568861222153157503807
  ( 103 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=57792086304242895797761529441075115537051264545837 (pp50)
 r2=71734624341105295983203643470137196510267861291590811 (pp53)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 4.08 hours.
Scaled time: 8.50 units (timescale=2.085).
Factorization parameters were as follows:
name: 61119_130
n: 4145693600923600439019225896942391349240772136386757922097820672747695605767505311568861222153157503807
m: 100000000000000000000000000
deg: 5
c5: 55
c0: 71
skew: 1.05
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1050001)
Primes: RFBsize:85714, AFBsize:85671, largePrimes:2883022 encountered
Relations: rels:2799303, finalFF:196462
Max relations in full relation-set: 0
Initial matrix: 171451 x 196462 with sparse part having weight 12761126.
Pruned matrix : 162923 x 163844 with weight 9315655.
Total sieving time: 3.59 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 4.08 hours.
 --------- CPU info (if available) ----------

(2·10²⁰⁰+61)/9 = (2)₁₉₉9_<200> = 83 · 2467 · 184979095439_<12> · 5333768258713_<13> · 1512398390473675457_<19> · 26701944159591873857_<20> · C133

C133 = P43 · P91

P43 = 1497861280087620589909136478546959010780631_<43>

P91 = 1818455870333425172805446104788266873468151731202279729908506761054955089871521334546301933_<91>

Number: 22229_200
N=2723794637720472432204933599865783189450593732942352213812665665109521854121902291932603177585967974672262187391031649342980554259723
  ( 133 digits)
Divisors found:
 r1=1497861280087620589909136478546959010780631 (pp43)
 r2=1818455870333425172805446104788266873468151731202279729908506761054955089871521334546301933 (pp91)
Version: Msieve-1.40
Total time: 227.95 hours.
Scaled time: 577.64 units (timescale=2.534).
Factorization parameters were as follows:
name: 22229_200
# Murphy_E = 5.494297e-11, selected by Jeff Gilchrist
n: 2723794637720472432204933599865783189450593732942352213812665665109521854121902291932603177585967974672262187391031649342980554259723
Y0: -34083099048428297234644474
Y1: 489835657370593
c0: -9259140913743911300061266453723475
c1: 62185006038906236125531442825
c2: 5782097466008962033351
c3: -160600625715381517
c4: 100331183196
c5: 59220
skew: 932771.02
type: gnfs
# selected mechanically
rlim: 11400000
alim: 11400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6
Factor base limits: 11400000/11400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved algebraic special-q in [5700000, 12700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1656585 x 1656833
Total sieving time: 227.95 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,132,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,11400000,11400000,28,28,54,54,2.6,2.6,100000
total time: 227.95 hours.
 --------- CPU info (if available) ----------

May 14, 2009 (5th)

By Wataru Sakai / Msieve / May 14, 2009

2·10¹⁹⁷-3 = 1(9)₁₉₆7_<198> = 7 · 229 · C195

C195 = P71 · P124

P71 = 45003138917615480291651707486311828111477830485732830843961796036510537_<71>

P124 = 2772385807556537886278044630282889688258769602192237958344592362510261040148261536809278151720138041797820440202530552797127_<124>

Number: 19997_197
N=124766063630692451653150343106674984404242046163443543356207111665626949469744229569557080474111041796631316281971303805364940736119775421085464753587024329382407985028072364316905801621958827199
  ( 195 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=45003138917615480291651707486311828111477830485732830843961796036510537
 r2=2772385807556537886278044630282889688258769602192237958344592362510261040148261536809278151720138041797820440202530552797127
Version: 
Total time: 744.51 hours.
Scaled time: 1495.72 units (timescale=2.009).
Factorization parameters were as follows:
n: 124766063630692451653150343106674984404242046163443543356207111665626949469744229569557080474111041796631316281971303805364940736119775421085464753587024329382407985028072364316905801621958827199
m: 2000000000000000000000000000000000000000
deg: 5
c5: 25
c0: -12
skew: 0.86
type: snfs
lss: 1
rlim: 13900000
alim: 13900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 13900000/13900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6950000, 14750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2364522 x 2364770
Total sieving time: 744.51 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,13900000,13900000,28,28,55,55,2.5,2.5,100000
total time: 744.51 hours.
 --------- CPU info (if available) ----------

May 14, 2009 (4th)

By Erik Branger / GGNFS, Msieve / May 14, 2009

(55·10¹⁴⁹+71)/9 = 6(1)₁₄₈9_<150> = 1451 · 16735128726520447_<17> · C131

C131 = P56 · P76

P56 = 23212997212751433550558533812477592022876236828704855219_<56>

P76 = 1084157780944424495342154432830333239216149136776625618872855134155864499233_<76>

Number: 61119_149
N=25166551547245705068022667865324015802313222330807856045784508390828702589330659816586726877460696078270591924272438604665201547027
  ( 131 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=23212997212751433550558533812477592022876236828704855219 (pp56)
 r2=1084157780944424495342154432830333239216149136776625618872855134155864499233 (pp76)
Version: Msieve v. 1.41
Total time: 19.18 hours.
Scaled time: 13.08 units (timescale=0.682).
Factorization parameters were as follows:
n: 25166551547245705068022667865324015802313222330807856045784508390828702589330659816586726877460696078270591924272438604665201547027
m: 1000000000000000000000000000000
deg: 5
c5: 11
c0: 142
skew: 1.67
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 429819 x 430067
Total sieving time: 18.45 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 19.18 hours.
 --------- CPU info (if available) ----------

May 14, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 14, 2009

(53·10¹⁶⁶-71)/9 = 5(8)₁₆₅1_<167> = 3 · 19 · 29 · 83 · 240857467 · 11060457607_<11> · 20894699998037_<14> · C130

C130 = P43 · P88

P43 = 5424508418994216438894842882597473125698917_<43>

P88 = 1421519024674072529801317548921990745200160059101495179565493543560830040916204609073619_<88>

Number: 58881_166
N=7711041917104953726782529594857675992009409630005014615924347870515549294274391649540185622317721217959229856759607475749281570623
  ( 130 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=5424508418994216438894842882597473125698917
 r2=1421519024674072529801317548921990745200160059101495179565493543560830040916204609073619
Version: 
Total time: 38.60 hours.
Scaled time: 92.10 units (timescale=2.386).
Factorization parameters were as follows:
n: 7711041917104953726782529594857675992009409630005014615924347870515549294274391649540185622317721217959229856759607475749281570623
m: 1000000000000000000000000000000000
deg: 5
c5: 530
c0: -71
skew: 0.67
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2700000, 5800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10253930
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 927795 x 928043
Total sieving time: 35.06 hours.
Total relation processing time: 1.54 hours.
Matrix solve time: 1.86 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,51,51,2.4,2.4,100000
total time: 38.60 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 14, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / May 14, 2009

(55·10¹³⁸+71)/9 = 6(1)₁₃₇9_<139> = 7 · 19 · 1093 · 12097 · 61109474407_<11> · C119

C119 = P48 · P72

P48 = 289391643646385040320441989989840975406837712761_<48>

P72 = 196506156640222333226584793107921238684003927617477930888307670421176329_<72>

Number: 61119_138
N=56867239656747940880840066906923991757368581244680647382966913848232606251219165722336772704148144736484366229434434369
  ( 119 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=289391643646385040320441989989840975406837712761 (pp48)
 r2=196506156640222333226584793107921238684003927617477930888307670421176329 (pp72)
Version: Msieve-1.40
Total time: 4.20 hours.
Scaled time: 5.04 units (timescale=1.199).
Factorization parameters were as follows:
n: 56867239656747940880840066906923991757368581244680647382966913848232606251219165722336772704148144736484366229434434369
m: 5000000000000000000000000000
deg: 5
c5: 88
c0: 355
skew: 1.32
type: snfs
lss: 1
rlim: 1530000
alim: 1530000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1530000/1530000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [765000, 1515001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 255878 x 256126
Total sieving time: 4.04 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,140.000,5,0,0,0,0,0,0,0,0,1530000,1530000,26,26,48,48,2.3,2.3,75000
total time: 4.20 hours.
 --------- CPU info (if available) ----------

(55·10¹⁴⁵+71)/9 = 6(1)₁₄₄9_<146> = 3 · 59167396759_<11> · C135

C135 = P37 · P45 · P54

P37 = 1570742754374861168243498981181423131_<37>

P45 = 281156538114519295288982577419736057441054869_<45>

P54 = 779584528197470392113982771350216223141302084755533973_<54>

Number: 61119_145
N=344283701602467697819545543720316890177993480146959973341192007240028560242683202522108961092181053589124501883180281265657472736105347
  ( 135 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1570742754374861168243498981181423131 (pp37)
 r2=281156538114519295288982577419736057441054869 (pp45)
 r3=779584528197470392113982771350216223141302084755533973 (pp54)
Version: Msieve-1.40
Total time: 8.17 hours.
Scaled time: 9.79 units (timescale=1.199).
Factorization parameters were as follows:
n: 344283701602467697819545543720316890177993480146959973341192007240028560242683202522108961092181053589124501883180281265657472736105347
m: 100000000000000000000000000000
deg: 5
c5: 55
c0: 71
skew: 1.05
type: snfs
lss: 1
rlim: 1950000
alim: 1950000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1950000/1950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [975000, 2375001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 360259 x 360506
Total sieving time: 7.81 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000
total time: 8.17 hours.
 --------- CPU info (if available) ----------

(47·10¹⁷⁰-11)/9 = 5(2)₁₆₉1_<171> = 9095447 · C164

C164 = P52 · P112

P52 = 8325089385253334517465388703578602396233093909125411_<52>

P112 = 6896716845965064599580999289660546133794620672918628965695890490643567789344672084630394151336043454230418416713_<112>

Number: 52221_170
N=57415784207441615813079029785146592819706631485205974178313855517185930743395263830598124778498761217807351548771844003073430280251451327485303605443715105175394043
  ( 164 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=8325089385253334517465388703578602396233093909125411 (pp52)
 r2=6896716845965064599580999289660546133794620672918628965695890490643567789344672084630394151336043454230418416713 (pp112)
Version: Msieve-1.40
Total time: 52.56 hours.
Scaled time: 91.40 units (timescale=1.739).
Factorization parameters were as follows:
n: 57415784207441615813079029785146592819706631485205974178313855517185930743395263830598124778498761217807351548771844003073430280251451327485303605443715105175394043
m: 10000000000000000000000000000000000
deg: 5
c5: 47
c0: -11
skew: 0.75
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 973380 x 973628
Total sieving time: 51.04 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.23 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 52.56 hours.
 --------- CPU info (if available) ----------

May 14, 2009

By Sinkiti Sibata / Msieve / May 14, 2009

(55·10¹²⁰+71)/9 = 6(1)₁₁₉9_<121> = 7 · 19² · 113 · 5351 · 101641 · 94005377 · C99

C99 = P35 · P65

P35 = 10612628407459289169056826061471913_<35>

P65 = 39441821288257056813672440441195723701568061228860695191005265959_<65>

Wed May 13 18:40:18 2009  Msieve v. 1.41
Wed May 13 18:40:18 2009  random seeds: 299d5308 80c0a959
Wed May 13 18:40:18 2009  factoring 418581393045689377984564463862677455714402642533209998362505773916333663494054907215380225573509567 (99 digits)
Wed May 13 18:40:19 2009  searching for 15-digit factors
Wed May 13 18:40:20 2009  commencing quadratic sieve (99-digit input)
Wed May 13 18:40:20 2009  using multiplier of 43
Wed May 13 18:40:20 2009  using 32kb Intel Core sieve core
Wed May 13 18:40:20 2009  sieve interval: 36 blocks of size 32768
Wed May 13 18:40:20 2009  processing polynomials in batches of 6
Wed May 13 18:40:20 2009  using a sieve bound of 2605661 (95294 primes)
Wed May 13 18:40:20 2009  using large prime bound of 390849150 (28 bits)
Wed May 13 18:40:20 2009  using double large prime bound of 2921571209356950 (43-52 bits)
Wed May 13 18:40:20 2009  using trial factoring cutoff of 52 bits
Wed May 13 18:40:20 2009  polynomial 'A' values have 13 factors
Thu May 14 02:36:01 2009  95402 relations (23456 full + 71946 combined from 1419148 partial), need 95390
Thu May 14 02:36:03 2009  begin with 1442604 relations
Thu May 14 02:36:04 2009  reduce to 248255 relations in 11 passes
Thu May 14 02:36:04 2009  attempting to read 248255 relations
Thu May 14 02:36:08 2009  recovered 248255 relations
Thu May 14 02:36:08 2009  recovered 237014 polynomials
Thu May 14 02:36:09 2009  attempting to build 95402 cycles
Thu May 14 02:36:09 2009  found 95402 cycles in 6 passes
Thu May 14 02:36:09 2009  distribution of cycle lengths:
Thu May 14 02:36:09 2009     length 1 : 23456
Thu May 14 02:36:09 2009     length 2 : 16740
Thu May 14 02:36:09 2009     length 3 : 15775
Thu May 14 02:36:09 2009     length 4 : 13018
Thu May 14 02:36:09 2009     length 5 : 9827
Thu May 14 02:36:09 2009     length 6 : 6604
Thu May 14 02:36:09 2009     length 7 : 4044
Thu May 14 02:36:09 2009     length 9+: 5938
Thu May 14 02:36:09 2009  largest cycle: 21 relations
Thu May 14 02:36:09 2009  matrix is 95294 x 95402 (25.9 MB) with weight 6407269 (67.16/col)
Thu May 14 02:36:09 2009  sparse part has weight 6407269 (67.16/col)
Thu May 14 02:36:11 2009  filtering completed in 3 passes
Thu May 14 02:36:11 2009  matrix is 90901 x 90965 (24.9 MB) with weight 6155977 (67.67/col)
Thu May 14 02:36:11 2009  sparse part has weight 6155977 (67.67/col)
Thu May 14 02:36:11 2009  saving the first 48 matrix rows for later
Thu May 14 02:36:11 2009  matrix is 90853 x 90965 (14.9 MB) with weight 4832527 (53.13/col)
Thu May 14 02:36:11 2009  sparse part has weight 3372544 (37.08/col)
Thu May 14 02:36:11 2009  matrix includes 64 packed rows
Thu May 14 02:36:11 2009  using block size 36386 for processor cache size 1024 kB
Thu May 14 02:36:12 2009  commencing Lanczos iteration
Thu May 14 02:36:12 2009  memory use: 14.7 MB
Thu May 14 02:37:08 2009  lanczos halted after 1438 iterations (dim = 90847)
Thu May 14 02:37:08 2009  recovered 15 nontrivial dependencies
Thu May 14 02:37:10 2009  prp35 factor: 10612628407459289169056826061471913
Thu May 14 02:37:10 2009  prp65 factor: 39441821288257056813672440441195723701568061228860695191005265959
Thu May 14 02:37:10 2009  elapsed time 07:56:52

May 13, 2009 (9th)

By Dmitry Domanov / GGNFS-0.77.1-VC8, Msieve / May 13, 2009

(55·10¹⁰⁸+71)/9 = 6(1)₁₀₇9_<109> = 7³ · 397 · 166507538969_<12> · C93

C93 = P39 · P54

P39 = 795809090623752224301704775278817744859_<39>

P54 = 338682498969665965499901130193421539222442974752330159_<54>

Number: 2
N=269526611515229771672836695269380413385510175130506157107543076549664233927981393987792902581
  ( 93 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=795809090623752224301704775278817744859 (pp39)
 r2=338682498969665965499901130193421539222442974752330159 (pp54)
Version: GGNFS-0.77.1-VC8
Total time: 0.71 hours.
Scaled time: 1.40 units (timescale=1.963).
Factorization parameters were as follows:
n: 269526611515229771672836695269380413385510175130506157107543076549664233927981393987792902581
m: 5000000000000000000000
deg: 5
c5: 88
c0: 355
skew: 1.32
type: snfs
lss: 1
rlim: 490000
alim: 490000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 490000/490000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [245000, 395001)
Primes: RFBsize:40766, AFBsize:40609, largePrimes:1258579 encountered
Relations: rels:1276691, finalFF:183902
Max relations in full relation-set: 32
Initial matrix: 81441 x 183902 with sparse part having weight 8158930.
Pruned matrix : 54054 x 54525 with weight 1896575.
Total sieving time: 0.66 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,490000,490000,25,25,44,44,2.2,2.2,50000
total time: 0.71 hours.
 --------- CPU info (if available) ----------

(55·10¹²⁵+71)/9 = 6(1)₁₂₄9_<126> = 1926187 · 2077388651851_<13> · C108

C108 = P47 · P62

P47 = 13802361609306560051417136173839078839962476523_<47>

P62 = 11064978550966575301700323020187377468908938943339427779145269_<62>

Number: 3
N=152722835159661589179909953116879454214067758007163553303317915183692361104914415723369724182544041419019687
  ( 108 digits)
SNFS difficulty: 126 digits.
Divisors found:
r1=13802361609306560051417136173839078839962476523 (pp47)
r2=11064978550966575301700323020187377468908938943339427779145269 (pp62)
Version: GGNFS-0.77.1-VC8
Total time: 1.93 hours.
Scaled time: 3.81 units (timescale=1.976).
Factorization parameters were as follows:
n: 152722835159661589179909953116879454214067758007163553303317915183692361104914415723369724182544041419019687
m: 10000000000000000000000000
deg: 5
c5: 55
c0: 71
skew: 1.05
type: snfs
lss: 1
rlim: 910000
alim: 910000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 910000/910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [455000, 805001)
Primes: RFBsize:72026, AFBsize:71959, largePrimes:2514719 encountered
Relations: rels:2404279, finalFF:195014
Max relations in full relation-set: 32
Initial matrix: 144051 x 195014 with sparse part having weight 16220392.
Pruned matrix : 128954 x 129738 with weight 7826179.
Total sieving time: 1.75 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000
total time: 1.93 hours.
 --------- CPU info (if available) ----------

(55·10¹²⁷+71)/9 = 6(1)₁₂₆9_<128> = 3 · 17 · 269 · 164411016323_<12> · C113

C113 = P54 · P60

P54 = 147564695883632722993402372598585997374827274660357417_<54>

P60 = 183604931912357354495039990669131942492925879496484038120011_<60>

Number: 4
N=27093605940382105687802024807602056821259075656855857209595838697644304254924346891285469235754267974673999971587
  ( 113 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=147564695883632722993402372598585997374827274660357417 (pp54)
 r2=183604931912357354495039990669131942492925879496484038120011 (pp60)
Version: Msieve v. 1.41
Total time: 2.05 hours.
Scaled time: 2.75 units (timescale=1.339).
Factorization parameters were as follows:
n: 27093605940382105687802024807602056821259075656855857209595838697644304254924346891285469235754267974673999971587
m: 20000000000000000000000000
deg: 5
c5: 1375
c0: 568
skew: 0.84
type: snfs
lss: 1
rlim: 1010000
alim: 1010000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1010000/1010000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [505000, 905001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 150245 x 150479
Total sieving time: 1.95 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,129.000,5,0,0,0,0,0,0,0,0,1010000,1010000,26,26,47,47,2.3,2.3,50000
total time: 2.05 hours.
 --------- CPU info (if available) ----------

(55·10¹³⁴+71)/9 = 6(1)₁₃₃9_<135> = 5425331 · C129

C129 = P56 · P73

P56 = 49822004090217615607527790375081111028061432525658809403_<56>

P73 = 2260855195620981138777563605147208165708944206584407558122279483171277583_<73>

Number: 5
N=112640336803618269762916052700030857308265820299463961021200570271401157111171854972740116890768712749712618660706805006203512949
  ( 129 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=49822004090217615607527790375081111028061432525658809403 (pp56)
r2=2260855195620981138777563605147208165708944206584407558122279483171277583 (pp73)
Version: Msieve v. 1.41
Total time: 3.38 hours.
Scaled time: 6.61 units (timescale=1.957).
Factorization parameters were as follows:
n: 112640336803618269762916052700030857308265820299463961021200570271401157111171854972740116890768712749712618660706805006203512949
m: 1000000000000000000000000000
deg: 5
c5: 11
c0: 142
skew: 1.67
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 196615 x 196847
Total sieving time: 3.22 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 3.38 hours.
 --------- CPU info (if available) ----------

May 13, 2009 (8th)

By Tyler Cadigan / GGNFS, Msieve / May 13, 2009

6·10¹⁹²+1 = 6(0)₁₉₁1_<193> = 7 · 99079 · 687912079 · C179

C179 = P70 · P109

P70 = 2915419952598811618594940160413805922953111384734672751972710929408139_<70>

P109 = 4313576840393877505883357285400035595676725490320331778252232358628296531245916896568438767438261380374823357_<109>

Number: 60001_192
N=12575887987552449949026242858572851364527613573509060923551620410457482729565243389228910414519077788326664190901048863112517318053854082566295455325857182378946464323168683102623
  ( 179 digits)
SNFS difficulty: 193 digits.
Divisors found:
 r1=2915419952598811618594940160413805922953111384734672751972710929408139 (pp70)
 r2=4313576840393877505883357285400035595676725490320331778252232358628296531245916896568438767438261380374823357 (pp109)
Version: Msieve-1.40
Total time: 386.28 hours.
Scaled time: 982.69 units (timescale=2.544).
Factorization parameters were as follows:
n: 12575887987552449949026242858572851364527613573509060923551620410457482729565243389228910414519077788326664190901048863112517318053854082566295455325857182378946464323168683102623
m: 200000000000000000000000000000000000000
deg: 5
c5: 75
c0: 4
skew: 0.56
type: snfs
lss: 1
rlim: 11700000
alim: 11700000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 11700000/11700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [5850000, 10850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1767676 x 1767924
Total sieving time: 378.49 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 7.10 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,193.000,5,0,0,0,0,0,0,0,0,11700000,11700000,28,28,55,55,2.5,2.5,100000
total time: 386.28 hours.
 --------- CPU info (if available) ----------

May 13, 2009 (7th)

By Sinkiti Sibata / Msieve, GGNFS / May 13, 2009

(55·10¹³⁹+71)/9 = 6(1)₁₃₈9_<140> = 3² · 759229 · 105356774741_<12> · 48705511430143_<14> · 1883619831516079_<16> · C93

C93 = P44 · P50

P44 = 86804442778701194714084453798411031294437723_<44>

P50 = 10659310159320433870594507542608353345250244368549_<50>

Wed May 13 14:06:03 2009  Msieve v. 1.41
Wed May 13 14:06:03 2009  random seeds: 34888b00 964c2405
Wed May 13 14:06:03 2009  factoring 925275478785158917225656192117079539340868018513415131273758526283118667747065881088140373927 (93 digits)
Wed May 13 14:06:04 2009  searching for 15-digit factors
Wed May 13 14:06:06 2009  commencing quadratic sieve (93-digit input)
Wed May 13 14:06:06 2009  using multiplier of 15
Wed May 13 14:06:06 2009  using 32kb Intel Core sieve core
Wed May 13 14:06:06 2009  sieve interval: 36 blocks of size 32768
Wed May 13 14:06:06 2009  processing polynomials in batches of 6
Wed May 13 14:06:06 2009  using a sieve bound of 1956901 (72864 primes)
Wed May 13 14:06:06 2009  using large prime bound of 244612625 (27 bits)
Wed May 13 14:06:06 2009  using double large prime bound of 1256787622996125 (42-51 bits)
Wed May 13 14:06:06 2009  using trial factoring cutoff of 51 bits
Wed May 13 14:06:06 2009  polynomial 'A' values have 12 factors
Wed May 13 17:07:46 2009  73280 relations (18342 full + 54938 combined from 1001546 partial), need 72960
Wed May 13 17:07:48 2009  begin with 1019888 relations
Wed May 13 17:07:49 2009  reduce to 189126 relations in 12 passes
Wed May 13 17:07:49 2009  attempting to read 189126 relations
Wed May 13 17:07:52 2009  recovered 189126 relations
Wed May 13 17:07:52 2009  recovered 173044 polynomials
Wed May 13 17:07:52 2009  attempting to build 73280 cycles
Wed May 13 17:07:52 2009  found 73280 cycles in 6 passes
Wed May 13 17:07:52 2009  distribution of cycle lengths:
Wed May 13 17:07:52 2009     length 1 : 18342
Wed May 13 17:07:52 2009     length 2 : 12923
Wed May 13 17:07:52 2009     length 3 : 12297
Wed May 13 17:07:52 2009     length 4 : 9931
Wed May 13 17:07:52 2009     length 5 : 7447
Wed May 13 17:07:52 2009     length 6 : 4947
Wed May 13 17:07:52 2009     length 7 : 3129
Wed May 13 17:07:52 2009     length 9+: 4264
Wed May 13 17:07:52 2009  largest cycle: 18 relations
Wed May 13 17:07:53 2009  matrix is 72864 x 73280 (19.4 MB) with weight 4798388 (65.48/col)
Wed May 13 17:07:53 2009  sparse part has weight 4798388 (65.48/col)
Wed May 13 17:07:54 2009  filtering completed in 3 passes
Wed May 13 17:07:54 2009  matrix is 69225 x 69289 (18.4 MB) with weight 4546351 (65.61/col)
Wed May 13 17:07:54 2009  sparse part has weight 4546351 (65.61/col)
Wed May 13 17:07:54 2009  saving the first 48 matrix rows for later
Wed May 13 17:07:54 2009  matrix is 69177 x 69289 (11.9 MB) with weight 3640733 (52.54/col)
Wed May 13 17:07:54 2009  sparse part has weight 2716755 (39.21/col)
Wed May 13 17:07:54 2009  matrix includes 64 packed rows
Wed May 13 17:07:54 2009  using block size 27715 for processor cache size 1024 kB
Wed May 13 17:07:55 2009  commencing Lanczos iteration
Wed May 13 17:07:55 2009  memory use: 11.3 MB
Wed May 13 17:08:29 2009  lanczos halted after 1096 iterations (dim = 69175)
Wed May 13 17:08:29 2009  recovered 18 nontrivial dependencies
Wed May 13 17:08:29 2009  prp44 factor: 86804442778701194714084453798411031294437723
Wed May 13 17:08:29 2009  prp50 factor: 10659310159320433870594507542608353345250244368549
Wed May 13 17:08:29 2009  elapsed time 03:02:26

(55·10¹²²+71)/9 = 6(1)₁₂₁9_<123> = 2139290106271226863_<19> · C105

C105 = P43 · P62

P43 = 5373828558294265105721640099799107187217633_<43>

P62 = 53157762248322536159642656786976043318598797786328241167792961_<62>

Number: 61119_122
N=285660700865052406937603796147704614656446087367273326746205050617928636405919093004427741173180992481313
  ( 105 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=5373828558294265105721640099799107187217633 (pp43)
 r2=53157762248322536159642656786976043318598797786328241167792961 (pp62)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 4.07 hours.
Scaled time: 1.92 units (timescale=0.473).
Factorization parameters were as follows:
name: 61119_122
n: 285660700865052406937603796147704614656446087367273326746205050617928636405919093004427741173180992481313
m: 2000000000000000000000000
deg: 5
c5: 1375
c0: 568
skew: 0.84
type: snfs
lss: 1
rlim: 840000
alim: 840000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 840000/840000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [420000, 820001)
Primes: RFBsize:66890, AFBsize:67446, largePrimes:1430103 encountered
Relations: rels:1423767, finalFF:171226
Max relations in full relation-set: 28
Initial matrix: 134403 x 171226 with sparse part having weight 8895848.
Pruned matrix : 120784 x 121520 with weight 4851384.
Total sieving time: 3.84 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,840000,840000,25,25,46,46,2.2,2.2,50000
total time: 4.07 hours.
 --------- CPU info (if available) ----------

May 13, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / May 13, 2009

(38·10¹⁹⁶-11)/9 = 4(2)₁₉₅1_<197> = 41 · C196

C196 = P51 · P145

P51 = 838649704654846390758515578850272712034860490204961_<51>

P145 = 1227938545005281377336927487713597735223128756351156783641718045398180364148362046277704501731373166079193454606684278099220646885720543931030821_<145>

Number: n
N=1029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981
  ( 196 digits)
SNFS difficulty: 198 digits.
Divisors found:

Wed May 13 08:29:26 2009  prp51 factor: 838649704654846390758515578850272712034860490204961
Wed May 13 08:29:26 2009  prp145 factor: 1227938545005281377336927487713597735223128756351156783641718045398180364148362046277704501731373166079193454606684278099220646885720543931030821
Wed May 13 08:29:26 2009  elapsed time 07:26:30 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 45.69 hours.
Scaled time: 92.01 units (timescale=2.014).
Factorization parameters were as follows:
name: KA_4_2_195_1
n: 1029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981029810298102981
m: 2000000000000000000000000000000000000000
deg: 5
c5: 95
c0: -88
skew: 0.98
type: snfs
lss: 1
rlim: 14200000
alim: 14200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 14200000/14200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [7100000, 17600069)
Primes: RFBsize:922193, AFBsize:921099, largePrimes:21624209 encountered
Relations: rels:22687579, finalFF:1832439
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 3063498 hash collisions in 25110169 relations
Msieve: matrix is 2255039 x 2255287 (612.2 MB)

Total sieving time: 45.26 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,198,5,0,0,0,0,0,0,0,0,14200000,14200000,28,28,56,56,2.5,2.5,100000
total time: 45.69 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.95 BogoMIPS (lpj=2830476)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830448)
Total of 4 processors activated (22643.65 BogoMIPS).

(55·10¹⁷¹+53)/9 = 6(1)₁₇₀7_<172> = 3 · 10037 · C168

C168 = P46 · P123

P46 = 1564288375667914117144174724299318185064610611_<46>

P123 = 129741281454502009424231502334110360678149501887013003964661212991492932260928953098054019152165699509735690212465942370977_<123>

Number: n
N=202952778423536618216303381193288536120059483614330680187011760190997014749131915615924782010265720537714161306868291026904158317927372425728508223277576670024612636947
  ( 168 digits)
SNFS difficulty: 172 digits.
Divisors found:

Wed May 13 18:27:32 2009  prp46 factor: 1564288375667914117144174724299318185064610611
Wed May 13 18:27:32 2009  prp123 factor: 129741281454502009424231502334110360678149501887013003964661212991492932260928953098054019152165699509735690212465942370977
Wed May 13 18:27:32 2009  elapsed time 01:53:42 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 62.51 hours.
Scaled time: 166.95 units (timescale=2.671).
Factorization parameters were as follows:
name: KA_6_1_170_7
n: 202952778423536618216303381193288536120059483614330680187011760190997014749131915615924782010265720537714161306868291026904158317927372425728508223277576670024612636947
m: 10000000000000000000000000000000000
deg: 5
c5: 550
c0: 53
skew: 0.63
type: snfs
lss: 1
rlim: 5300000
alim: 5300000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2650000, 6195757)
Primes: RFBsize:367900, AFBsize:368503, largePrimes:17829043 encountered
Relations: rels:17580473, finalFF:723415
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2219364 hash collisions in 19608042 relations
Msieve: matrix is 928670 x 928918 (249.1 MB)

Total sieving time: 61.63 hours.
Total relation processing time: 0.87 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5300000,5300000,28,28,56,56,2.4,2.4,100000
total time: 62.51 hours.
 --------- CPU info (if available) ----------

May 13, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / May 13, 2009

(55·10¹³⁶+71)/9 = 6(1)₁₃₅9_<137> = 3 · 317 · 14615383 · 75201397 · C119

C119 = P34 · P86

P34 = 1350876569924994979685157442302889_<34>

P86 = 43280063054364300687962637464433987423404953530263290263897966741530468685681866670571_<86>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3080153974
Step 1 took 7820ms
Step 2 took 8057ms
********** Factor found in step 2: 1350876569924994979685157442302889
Found probable prime factor of 34 digits: 1350876569924994979685157442302889
Probable prime cofactor 43280063054364300687962637464433987423404953530263290263897966741530468685681866670571 has 86 digits

(55·10¹⁴⁶+71)/9 = 6(1)₁₄₅9_<147> = 31 · 639127301537443_<15> · C131

C131 = P37 · P95

P37 = 1202940587193747624789004146323185267_<37>

P95 = 25640526478973531362019019068776774655905775461468850331552024081456281866972753004198890605529_<95>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=129212221
Step 1 took 7868ms
Step 2 took 4637ms
********** Factor found in step 2: 1202940587193747624789004146323185267
Found probable prime factor of 37 digits: 1202940587193747624789004146323185267
Probable prime cofactor has 95 digits

(55·10¹¹¹+71)/9 = 6(1)₁₁₀9_<112> = 17 · 23 · C110

C110 = P52 · P58

P52 = 8496004963601417069043767504345188776275945693950363_<52>

P58 = 1839622298813323932133290065541136712345074736938839826043_<58>

SNFS difficulty: 112 digits.
Divisors found:
 r1=8496004963601417069043767504345188776275945693950363 (pp52)
 r2=1839622298813323932133290065541136712345074736938839826043 (pp58)
Version: Msieve v. 1.41
Total time: 0.58 hours.
Scaled time: 1.58 units (timescale=2.726).
Factorization parameters were as follows:
n: 15629440181869849389030974708724069337880079568059107701051435066780335322534811025859619210002841716396703609
m: 10000000000000000000000
deg: 5
c5: 550
c0: 71
skew: 0.66
type: snfs
lss: 1
rlim: 530000
alim: 530000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 530000/530000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [265000, 465001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 52949 x 53178
Total sieving time: 0.55 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,112.000,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000
total time: 0.58 hours.

(55·10²⁰³+71)/9 = 6(1)₂₀₂9_<204> = 1493 · 50741 · 148669 · C191

C191 = P31 · C161

P31 = 1538483614307183777646719386573_<31>

C161 = [35268586554235955747475441610403345347488406143285663324380184048565519635843557694050030383279827772428163249553044073162469530126538634244471616142594370633599_<161>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3878632275
Step 1 took 12345ms
Step 2 took 6401ms
********** Factor found in step 2: 1538483614307183777646719386573
Found probable prime factor of 31 digits: 1538483614307183777646719386573
Composite cofactor has 161 digits

May 13, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 13, 2009

2·10¹⁷⁶-1 = 1(9)₁₇₆_<177> = 257 · 156577 · 16506330678736007_<17> · 6963592316914968855505993_<25> · C128

C128 = P58 · P71

P58 = 2638173759595778891884183100234637053647717064980325343311_<58>

P71 = 16390100988022968074152500639629002445679211540543545306742330563674831_<71>

Number: 19999_176
N=43239934343727043867038071858195868131316110066819744096987416719312710840761544224861895751661857201711227598866960845844905441
  ( 128 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=2638173759595778891884183100234637053647717064980325343311
 r2=16390100988022968074152500639629002445679211540543545306742330563674831
Version: 
Total time: 43.15 hours.
Scaled time: 103.12 units (timescale=2.390).
Factorization parameters were as follows:
n: 43239934343727043867038071858195868131316110066819744096987416719312710840761544224861895751661857201711227598866960845844905441
m: 100000000000000000000000000000000000
deg: 5
c5: 20
c0: -1
skew: 0.55
type: snfs
lss: 1
rlim: 6800000
alim: 6800000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6800000/6800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3400000, 6300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 17790087
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1183787 x 1184034
Total sieving time: 37.04 hours.
Total relation processing time: 2.59 hours.
Matrix solve time: 3.21 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6800000,6800000,28,28,53,53,2.5,2.5,100000
total time: 43.15 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 13, 2009 (3rd)

By Markus Tervooren / msieve 1.41, ggnfs / May 13, 2009

(53·10¹⁶⁵-17)/9 = 5(8)₁₆₄7_<166> = 7 · 639157301 · 683426917 · 6327944358701217101_<19> · C129

C129 = P48 · P82

P48 = 105286041996195116463905211753052493939462823619_<48>

P82 = 2890693427093959193600294796557751916681459460044103037225919482688402201684641967_<82>

N=304349669563139773775039543739558410678652128462622576347732269179402880997642153306106637637619365345888591599963791904886218573
  ( 129 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=105286041996195116463905211753052493939462823619 (pp48)
 r2=2890693427093959193600294796557751916681459460044103037225919482688402201684641967 (pp82)
Version: Msieve-1.39
Total time: 23.99 hours.
Scaled time: 55.15 units (timescale=2.299).
Factorization parameters were as follows:
n: 304349669563139773775039543739558410678652128462622576347732269179402880997642153306106637637619365345888591599963791904886218573
m: 1000000000000000000000000000000000
deg: 5
c5: 53
c0: -17
skew: 0.80
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 26
lpba: 26
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4

Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 688361 x 688609
Total sieving time: 23.27 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.55 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,26,26,51,51,2.4,2.4,200000
total time: 23.99 hours.
 --------- CPU info (if available) ----------
[    0.144009] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.236014] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.331180] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.428163] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197992k/10485760k available (2226k kernel code, 189844k reserved, 1082k data, 392k init)
[    0.083917] Calibrating delay using timer specific routine.. 6004.15 BogoMIPS (lpj=12008301)
[    0.156009] Calibrating delay using timer specific routine.. 5999.99 BogoMIPS (lpj=11999993)
[    0.248015] Calibrating delay using timer specific routine.. 6000.00 BogoMIPS (lpj=12000012)
[    0.347710] Calibrating delay using timer specific routine.. 6000.00 BogoMIPS (lpj=12000008)
[    0.435711] Total of 4 processors activated (24004.15 BogoMIPS).

May 13, 2009 (2nd)

By Erik Branger / GMP-ECM, Msieve / May 13, 2009

(10²⁴⁵-7)/3 = (3)₂₄₄1_<245> = 97 · 66751 · 3258371 · 1403863703183_<13> · 2249810655289_<13> · 81791825300240873_<17> · 145142221366577384926667_<24> · 31324445949473317700096188175894333_<35> · C133

C133 = P39 · P45 · P50

P39 = 489315672447162785103946339787661019447_<39>

P45 = 222569895610081321713872192753638833118459541_<45>

P50 = 12351940072441846049300946746600885270935752027829_<50>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 
1345211973340636127176790697467331273618032323820765030845459707299234006881987792073875316307596244915355092769177331580459819511583 (133 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3233337030
Step 1 took 61137ms
Step 2 took 34851ms
********** Factor found in step 2: 489315672447162785103946339787661019447
Found probable prime factor of 39 digits: 489315672447162785103946339787661019447
Composite cofactor 2749170012505361993924940218503304494061357616514900432821055688206426386787140909263442566489 
has 94 digits

Tue May 12 16:49:26 2009  Msieve v. 1.41
Tue May 12 16:49:26 2009  random seeds: f1649488 eee56b85
Tue May 12 16:49:26 2009  factoring 2749170012505361993924940218503304494061357616514900432821055688206426386787140909263442566489 (94 digits)
Tue May 12 16:49:27 2009  searching for 15-digit factors
Tue May 12 16:49:28 2009  commencing quadratic sieve (94-digit input)
Tue May 12 16:49:28 2009  using multiplier of 1
Tue May 12 16:49:28 2009  using 32kb Intel Core sieve core
Tue May 12 16:49:28 2009  sieve interval: 36 blocks of size 32768
Tue May 12 16:49:28 2009  processing polynomials in batches of 6
Tue May 12 16:49:28 2009  using a sieve bound of 2018827 (75294 primes)
Tue May 12 16:49:28 2009  using large prime bound of 270522818 (28 bits)
Tue May 12 16:49:28 2009  using double large prime bound of 1506492608811942 (42-51 bits)
Tue May 12 16:49:28 2009  using trial factoring cutoff of 51 bits
Tue May 12 16:49:28 2009  polynomial 'A' values have 12 factors
Tue May 12 19:42:45 2009  75640 relations (18903 full + 56737 combined from 1060241 partial), need 75390
Tue May 12 19:42:48 2009  begin with 1079144 relations
Tue May 12 19:42:49 2009  reduce to 194509 relations in 11 passes
Tue May 12 19:42:49 2009  attempting to read 194509 relations
Tue May 12 19:42:52 2009  recovered 194509 relations
Tue May 12 19:42:52 2009  recovered 174919 polynomials
Tue May 12 19:42:53 2009  attempting to build 75640 cycles
Tue May 12 19:42:53 2009  found 75640 cycles in 6 passes
Tue May 12 19:42:53 2009  distribution of cycle lengths:
Tue May 12 19:42:53 2009     length 1 : 18903
Tue May 12 19:42:53 2009     length 2 : 13565
Tue May 12 19:42:53 2009     length 3 : 12840
Tue May 12 19:42:53 2009     length 4 : 10239
Tue May 12 19:42:53 2009     length 5 : 7608
Tue May 12 19:42:53 2009     length 6 : 5067
Tue May 12 19:42:53 2009     length 7 : 3115
Tue May 12 19:42:53 2009     length 9+: 4303
Tue May 12 19:42:53 2009  largest cycle: 20 relations
Tue May 12 19:42:53 2009  matrix is 75294 x 75640 (18.9 MB) with weight 4642777 (61.38/col)
Tue May 12 19:42:53 2009  sparse part has weight 4642777 (61.38/col)
Tue May 12 19:42:54 2009  filtering completed in 3 passes
Tue May 12 19:42:54 2009  matrix is 71370 x 71434 (17.9 MB) with weight 4398060 (61.57/col)
Tue May 12 19:42:54 2009  sparse part has weight 4398060 (61.57/col)
Tue May 12 19:42:54 2009  saving the first 48 matrix rows for later
Tue May 12 19:42:54 2009  matrix is 71322 x 71434 (10.5 MB) with weight 3349481 (46.89/col)
Tue May 12 19:42:54 2009  sparse part has weight 2318382 (32.45/col)
Tue May 12 19:42:54 2009  matrix includes 64 packed rows
Tue May 12 19:42:54 2009  using block size 28573 for processor cache size 2048 kB
Tue May 12 19:42:55 2009  commencing Lanczos iteration
Tue May 12 19:42:55 2009  memory use: 10.7 MB
Tue May 12 19:43:22 2009  lanczos halted after 1130 iterations (dim = 71320)
Tue May 12 19:43:22 2009  recovered 15 nontrivial dependencies
Tue May 12 19:43:22 2009  prp45 factor: 222569895610081321713872192753638833118459541
Tue May 12 19:43:22 2009  prp50 factor: 12351940072441846049300946746600885270935752027829
Tue May 12 19:43:22 2009  elapsed time 02:53:56

May 13, 2009

Factorizations of 611...119 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 12, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 11, 2009

(55·10¹⁵⁸+53)/9 = 6(1)₁₅₇7_<159> = 17 · 4817497834280673583_<19> · C139

C139 = P56 · P84

P56 = 17845553710717112864759785999618398828238960930529700031_<56>

P84 = 418138062769178038646403383540644184918563093786817713598293397086549042213175848237_<84>

Number: n
N=7461905257642570205274359759519501514193898474760211147148201732868313154587524623931779179230011032717598088072376762527591935829590195347
  ( 139 digits)
SNFS difficulty: 160 digits.
Divisors found:

Mon May 11 01:35:01 2009  prp56 factor: 17845553710717112864759785999618398828238960930529700031
Mon May 11 01:35:01 2009  prp84 factor: 418138062769178038646403383540644184918563093786817713598293397086549042213175848237
Mon May 11 01:35:01 2009  elapsed time 00:43:35 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 26.47 hours.
Scaled time: 68.98 units (timescale=2.606).
Factorization parameters were as follows:
name: KA_6_1_157_7
n: 7461905257642570205274359759519501514193898474760211147148201732868313154587524623931779179230011032717598088072376762527591935829590195347
m: 50000000000000000000000000000000
deg: 5
c5: 88
c0: 265
skew: 1.25
type: snfs
lss: 1
rlim: 3300000
alim: 3300000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1650000, 3231931)
Primes: RFBsize:236900, AFBsize:236768, largePrimes:13344150 encountered
Relations: rels:12314752, finalFF:423174
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1315446 hash collisions in 14066940 relations
Msieve: matrix is 609139 x 609387 (163.0 MB)

Total sieving time: 26.17 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,28,28,56,56,2.4,2.4,100000
total time: 26.47 hours.
 --------- CPU info (if available) ----------

(55·10¹⁵²+53)/9 = 6(1)₁₅₁7_<153> = 19 · 59 · 227 · 659 · 12695518245859_<14> · C132

C132 = P55 · P77

P55 = 7068361314994357655785488053712469413994760160307524653_<55>

P77 = 40610105745920779918481121272161456452030286435210027784502911521712533819907_<77>

Number: n
N=287046900452296523635214596698421367210854311194270084376888166052944430800517935676949223976641000358837008264491447433837664667271
  ( 132 digits)
SNFS difficulty: 155 digits.
Divisors found:

Mon May 11 14:21:24 2009  prp55 factor: 7068361314994357655785488053712469413994760160307524653
Mon May 11 14:21:24 2009  prp77 factor: 40610105745920779918481121272161456452030286435210027784502911521712533819907
Mon May 11 14:21:24 2009  elapsed time 00:25:14 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 14.91 hours.
Scaled time: 38.08 units (timescale=2.554).
Factorization parameters were as follows:
name: KA_6_1_151_7
n: 287046900452296523635214596698421367210854311194270084376888166052944430800517935676949223976641000358837008264491447433837664667271
m: 5000000000000000000000000000000
deg: 5
c5: 44
c0: 1325
skew: 1.98
type: snfs
lss: 1
rlim: 2700000
alim: 2700000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 2700000/2700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1350000, 2250257)
Primes: RFBsize:196645, AFBsize:196816, largePrimes:11996756 encountered
Relations: rels:11284515, finalFF:436714
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 914717 hash collisions in 12009197 relations
Msieve: matrix is 430294 x 430542 (115.0 MB)

Total sieving time: 14.70 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2700000,2700000,28,28,56,56,2.4,2.4,100000
total time: 14.91 hours.
 --------- CPU info (if available) ----------

(55·10¹⁶⁹+53)/9 = 6(1)₁₆₈7_<170> = 21385781 · 1709871325461113_<16> · C148

C148 = P38 · P110

P38 = 31499273936242556516634609465971955509_<38>

P110 = 53055583145099933520947588688085961040800233395621622150497267775458366053416556199130127742788741791063315421_<110>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 1671212347334596219507410428017889758975124908091594236923391998388037186811384996722745868763892908306829644401101534483453918223449576156245604289 (148 digits)
Using B1=1798000, B2=2140281790, polynomial Dickson(6), sigma=2177163353
Step 1 took 27627ms
Step 2 took 8830ms
********** Factor found in step 2: 31499273936242556516634609465971955509
Found probable prime factor of 38 digits: 31499273936242556516634609465971955509
Probable prime cofactor 53055583145099933520947588688085961040800233395621622150497267775458366053416556199130127742788741791063315421 has 110 digits

By Robert Backstrom / GGNFS, Msieve / May 12, 2009

(55·10¹⁶¹+53)/9 = 6(1)₁₆₀7_<162> = 13 · 97 · 113 · 76625767327269088745587943_<26> · C131

C131 = P59 · P73

P59 = 25937588457776918008836386172560311496435019969223053253357_<59>

P73 = 2157854800973617411073781544796855937311836707863709108700798479647760419_<73>

Number: n
N=55969549779291807578331999389155335060385717795888554665336739968324394289490377698401886225152663948359880548781879323856843476583
  ( 131 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=25937588457776918008836386172560311496435019969223053253357 (pp59)
 r2=2157854800973617411073781544796855937311836707863709108700798479647760419 (pp73)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 30.09 hours.
Scaled time: 79.41 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_6_1_160_7
n: 55969549779291807578331999389155335060385717795888554665336739968324394289490377698401886225152663948359880548781879323856843476583
m: 100000000000000000000000000000000
deg: 5
c5: 550
c0: 53
skew: 0.63
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [1800000, 3500001)
Primes: RFBsize:256726, AFBsize:256777, largePrimes:14804714 encountered
Relations: rels:14493415, finalFF:613981
Max relations in full relation-set: 28
Initial matrix: 513570 x 613981 with sparse part having weight 68840197.
Pruned matrix : 472743 x 475374 with weight 50744989.
Total sieving time: 27.82 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 1.59 hours.
Total square root time: 0.20 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,56,56,2.4,2.4,100000
total time: 30.09 hours.
 --------- CPU info (if available) ----------

May 12, 2009 (3rd)

By Markus Tervooren / msieve 1.41, lattice siever (64bit/asm) / May 12, 2009

4·10²¹²+9 = 4(0)₂₁₁9_<213> = 1057477 · 1719841 · 2162154127181111154546903829_<28> · 77175797637606010161708971689_<29> · C145

C145 = P52 · P93

P52 = 1746066645189561080367807342423137376428492594383633_<52>

P93 = 754870008751017698161582119509494539523940082054318759700337322475860229316028590649214989769_<93>

N=1318053343734104086960715457060197971758523491913154564415959276396377517554642471068781120825155195038852382956221675167363777490332564956050777
  ( 145 digits)
Divisors found:
 r1=1746066645189561080367807342423137376428492594383633 (pp52)
 r2=754870008751017698161582119509494539523940082054318759700337322475860229316028590649214989769 (pp93)
Version: Msieve-1.39
Total time: 669.60 hours.
Scaled time: 1536.06 units (timescale=2.294).
Factorization parameters were as follows:
name: k2
n: 1318053343734104086960715457060197971758523491913154564415959276396377517554642471068781120825155195038852382956221675167363777490332564956050777
skew: 605055.65
# norm 5.12e+19
c5: 208980
c4: -133514539821
c3: 487140766392643324
c2: 51625269952217739580169
c1: -93618180336738951476232970236
c0: -5793741626299058757465782496791055
# alpha -5.97
Y1: 75003706647780877
Y0: -5753953870187591385948231242
# Murphy_E 1.08e-11
# M 800290932745809964278718692174746748367343098838672689905478792809784630966191593908087431020740065478694759215807174794065578110867414729744866
type: gnfs
rlim: 22000000
alim: 22000000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 22000000/22000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved algebraic special-q in [11000000, 34000001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 2408276 x 2408524
Total sieving time: 657.69 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 10.99 hours.
Time per square root: 0.44 hours.
Prototype def-par.txt line would be:
gnfs,144,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,22000000,22000000,28,28,52,52,2.6,2.6,200000
total time: 669.60 hours.
 --------- CPU info (if available) ----------
[    0.144009] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.236014] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.331180] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.428163] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8197992k/10485760k available (2226k kernel code, 189844k reserved, 1082k data, 392k init)
[    0.083917] Calibrating delay using timer specific routine.. 6004.15 BogoMIPS (lpj=12008301)
[    0.156009] Calibrating delay using timer specific routine.. 5999.99 BogoMIPS (lpj=11999993)
[    0.248015] Calibrating delay using timer specific routine.. 6000.00 BogoMIPS (lpj=12000012)
[    0.347710] Calibrating delay using timer specific routine.. 6000.00 BogoMIPS (lpj=12000008)
[    0.435711] Total of 4 processors activated (24004.15 BogoMIPS).

May 12, 2009 (2nd)

By Dmitry Domanov / GMP-ECM 6.2.3 / May 11, 2009

10²⁴⁵-9 = (9)₂₄₄1_<245> = 40974399286914864833693_<23> · C223

C223 = P34 · C189

P34 = 5715411392874728022457273897097329_<34>

C189 = [427011831602112740817913621551742021102073286561629462464731021857158629869115131922752233372580108125425120862025257386114216115947550294412616236983597923505019820154999571664743031506003_<189>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1951669128
Step 1 took 441703ms
Step 2 took 107218ms
********** Factor found in step 2: 5715411392874728022457273897097329
Found probable prime factor of 34 digits: 5715411392874728022457273897097329
Composite cofactor 427011831602112740817913621551742021102073286561629462464731021857158629869115131922752233372580108125425120862025257386114216115947550294412616236983597923505019820154999571664743031506003 has 189 digits

By Dmitry Domanov / GGNFS, msieve / May 12, 2009

7·10¹⁸⁷-9 = 6(9)₁₈₆1_<188> = 461 · 923371 · 473554153625182489683337_<24> · 4690476648547345168326374837406127_<34> · C122

C122 = P51 · P72

P51 = 132247220045280786396912011749138627359993288829687_<51>

P72 = 559819090026885770857005522645932550743849730325918357433966783937734297_<72>

Tue May 05 13:21:24 2009  Msieve v. 1.41
Tue May 05 13:21:24 2009  random seeds: 796211e0 c7c337b8
Tue May 05 13:21:24 2009  factoring 74034518384334417089817067969336107865932654799596895823511091185372389129149571176376292605794361402236374912345491675039 (122 digits)
Tue May 05 13:21:24 2009  searching for 15-digit factors
Tue May 05 13:21:26 2009  commencing number field sieve (122-digit input)
Tue May 05 13:21:26 2009  R0: -338415587465557897385425
Tue May 05 13:21:26 2009  R1:  25169084109103
Tue May 05 13:21:26 2009  A0: -19554326764852222388358345552
Tue May 05 13:21:26 2009  A1:  2374031057583121590915716
Tue May 05 13:21:26 2009  A2:  89638104094787780664
Tue May 05 13:21:26 2009  A3: -53426264244359
Tue May 05 13:21:26 2009  A4: -7014396274
Tue May 05 13:21:26 2009  A5:  16680
Tue May 05 13:21:26 2009  skew 105853.63, size 1.087434e-011, alpha -5.584116, combined = 2.285903e-010
Tue May 05 13:21:26 2009  
Tue May 05 13:21:26 2009  commencing relation filtering
Tue May 05 13:21:26 2009  commencing duplicate removal, pass 1
Tue May 05 13:23:26 2009  found 3680062 hash collisions in 14352905 relations
Tue May 05 13:23:49 2009  added 62650 free relations
Tue May 05 13:23:49 2009  commencing duplicate removal, pass 2
Tue May 05 13:24:22 2009  found 4221914 duplicates and 10193640 unique relations
Tue May 05 13:24:22 2009  memory use: 106.6 MB
Tue May 05 13:24:22 2009  reading rational ideals above 7929856
Tue May 05 13:24:22 2009  reading algebraic ideals above 7929856
Tue May 05 13:24:22 2009  commencing singleton removal, pass 1
Tue May 05 13:25:56 2009  relations with 0 large ideals: 319804
Tue May 05 13:25:56 2009  relations with 1 large ideals: 1789543
Tue May 05 13:25:56 2009  relations with 2 large ideals: 3700610
Tue May 05 13:25:56 2009  relations with 3 large ideals: 3267043
Tue May 05 13:25:56 2009  relations with 4 large ideals: 1046919
Tue May 05 13:25:56 2009  relations with 5 large ideals: 11575
Tue May 05 13:25:56 2009  relations with 6 large ideals: 58146
Tue May 05 13:25:56 2009  relations with 7+ large ideals: 0
Tue May 05 13:25:56 2009  10193640 relations and about 9206532 large ideals
Tue May 05 13:25:56 2009  commencing singleton removal, pass 2
Tue May 05 13:27:29 2009  found 3746144 singletons
Tue May 05 13:27:29 2009  current dataset: 6447496 relations and about 4826112 large ideals
Tue May 05 13:27:29 2009  commencing singleton removal, pass 3
Tue May 05 13:28:35 2009  found 907584 singletons
Tue May 05 13:28:35 2009  current dataset: 5539912 relations and about 3868151 large ideals
Tue May 05 13:28:35 2009  commencing singleton removal, pass 4
Tue May 05 13:29:33 2009  found 254745 singletons
Tue May 05 13:29:33 2009  current dataset: 5285167 relations and about 3608888 large ideals
Tue May 05 13:29:33 2009  commencing singleton removal, final pass
Tue May 05 13:30:30 2009  memory use: 81.1 MB
Tue May 05 13:30:30 2009  commencing in-memory singleton removal
Tue May 05 13:30:30 2009  begin with 5285167 relations and 3822070 unique ideals
Tue May 05 13:30:35 2009  reduce to 4716125 relations and 3242297 ideals in 13 passes
Tue May 05 13:30:35 2009  max relations containing the same ideal: 33
Tue May 05 13:30:36 2009  reading rational ideals above 720000
Tue May 05 13:30:36 2009  reading algebraic ideals above 720000
Tue May 05 13:30:36 2009  commencing singleton removal, final pass
Tue May 05 13:31:36 2009  keeping 3940660 ideals with weight <= 20, new excess is 380477
Tue May 05 13:31:40 2009  memory use: 128.6 MB
Tue May 05 13:31:40 2009  commencing in-memory singleton removal
Tue May 05 13:31:41 2009  begin with 4717910 relations and 3940660 unique ideals
Tue May 05 13:31:48 2009  reduce to 4695435 relations and 3909770 ideals in 13 passes
Tue May 05 13:31:48 2009  max relations containing the same ideal: 20
Tue May 05 13:31:51 2009  removing 982639 relations and 810483 ideals in 172156 cliques
Tue May 05 13:31:51 2009  commencing in-memory singleton removal
Tue May 05 13:31:51 2009  begin with 3712796 relations and 3909770 unique ideals
Tue May 05 13:31:55 2009  reduce to 3585555 relations and 2966547 ideals in 9 passes
Tue May 05 13:31:55 2009  max relations containing the same ideal: 20
Tue May 05 13:31:57 2009  removing 740278 relations and 568122 ideals in 172156 cliques
Tue May 05 13:31:58 2009  commencing in-memory singleton removal
Tue May 05 13:31:58 2009  begin with 2845277 relations and 2966547 unique ideals
Tue May 05 13:32:00 2009  reduce to 2743763 relations and 2292206 ideals in 8 passes
Tue May 05 13:32:00 2009  max relations containing the same ideal: 19
Tue May 05 13:32:01 2009  removing 74922 relations and 64719 ideals in 10203 cliques
Tue May 05 13:32:02 2009  commencing in-memory singleton removal
Tue May 05 13:32:02 2009  begin with 2668841 relations and 2292206 unique ideals
Tue May 05 13:32:03 2009  reduce to 2667656 relations and 2226298 ideals in 5 passes
Tue May 05 13:32:03 2009  max relations containing the same ideal: 19
Tue May 05 13:32:03 2009  relations with 0 large ideals: 28132
Tue May 05 13:32:03 2009  relations with 1 large ideals: 191693
Tue May 05 13:32:03 2009  relations with 2 large ideals: 536697
Tue May 05 13:32:03 2009  relations with 3 large ideals: 801502
Tue May 05 13:32:03 2009  relations with 4 large ideals: 682034
Tue May 05 13:32:03 2009  relations with 5 large ideals: 329226
Tue May 05 13:32:03 2009  relations with 6 large ideals: 86297
Tue May 05 13:32:03 2009  relations with 7+ large ideals: 12075
Tue May 05 13:32:03 2009  commencing 2-way merge
Tue May 05 13:32:05 2009  reduce to 1695103 relation sets and 1253745 unique ideals
Tue May 05 13:32:05 2009  commencing full merge
Tue May 05 13:32:27 2009  memory use: 100.0 MB
Tue May 05 13:32:27 2009  found 827118 cycles, need 767945
Tue May 05 13:32:27 2009  weight of 767945 cycles is about 53824455 (70.09/cycle)
Tue May 05 13:32:27 2009  distribution of cycle lengths:
Tue May 05 13:32:27 2009  1 relations: 74022
Tue May 05 13:32:27 2009  2 relations: 78780
Tue May 05 13:32:27 2009  3 relations: 82503
Tue May 05 13:32:27 2009  4 relations: 78536
Tue May 05 13:32:27 2009  5 relations: 74402
Tue May 05 13:32:27 2009  6 relations: 67129
Tue May 05 13:32:27 2009  7 relations: 60620
Tue May 05 13:32:27 2009  8 relations: 53361
Tue May 05 13:32:27 2009  9 relations: 45757
Tue May 05 13:32:27 2009  10+ relations: 152835
Tue May 05 13:32:27 2009  heaviest cycle: 17 relations
Tue May 05 13:32:27 2009  commencing cycle optimization
Tue May 05 13:32:29 2009  start with 4650542 relations
Tue May 05 13:32:39 2009  pruned 148029 relations
Tue May 05 13:32:39 2009  memory use: 118.4 MB
Tue May 05 13:32:39 2009  distribution of cycle lengths:
Tue May 05 13:32:39 2009  1 relations: 74022
Tue May 05 13:32:39 2009  2 relations: 80948
Tue May 05 13:32:39 2009  3 relations: 86351
Tue May 05 13:32:39 2009  4 relations: 81424
Tue May 05 13:32:39 2009  5 relations: 77632
Tue May 05 13:32:39 2009  6 relations: 69023
Tue May 05 13:32:39 2009  7 relations: 62318
Tue May 05 13:32:39 2009  8 relations: 53892
Tue May 05 13:32:39 2009  9 relations: 45856
Tue May 05 13:32:39 2009  10+ relations: 136479
Tue May 05 13:32:39 2009  heaviest cycle: 17 relations
Tue May 05 13:32:41 2009  RelProcTime: 643
Tue May 05 13:32:41 2009  
Tue May 05 13:32:41 2009  commencing linear algebra
Tue May 05 13:32:41 2009  read 767945 cycles
Tue May 05 13:32:43 2009  cycles contain 2401694 unique relations
Tue May 05 13:33:28 2009  read 2401694 relations
Tue May 05 13:33:32 2009  using 20 quadratic characters above 134216802
Tue May 05 13:33:44 2009  building initial matrix
Tue May 05 13:34:13 2009  memory use: 275.5 MB
Tue May 05 13:34:15 2009  read 767945 cycles
Tue May 05 13:34:29 2009  matrix is 767716 x 767945 (216.1 MB) with weight 72678072 (94.64/col)
Tue May 05 13:34:29 2009  sparse part has weight 51274069 (66.77/col)
Tue May 05 13:34:42 2009  filtering completed in 3 passes
Tue May 05 13:34:42 2009  matrix is 765071 x 765271 (215.7 MB) with weight 72511181 (94.75/col)
Tue May 05 13:34:42 2009  sparse part has weight 51186251 (66.89/col)
Tue May 05 13:34:46 2009  read 765271 cycles
Tue May 05 13:36:32 2009  matrix is 765071 x 765271 (215.7 MB) with weight 72511181 (94.75/col)
Tue May 05 13:36:32 2009  sparse part has weight 51186251 (66.89/col)
Tue May 05 13:36:32 2009  saving the first 48 matrix rows for later
Tue May 05 13:36:33 2009  matrix is 765023 x 765271 (208.1 MB) with weight 57393419 (75.00/col)
Tue May 05 13:36:33 2009  sparse part has weight 49962643 (65.29/col)
Tue May 05 13:36:33 2009  matrix includes 64 packed rows
Tue May 05 13:36:33 2009  using block size 65536 for processor cache size 6144 kB
Tue May 05 13:36:38 2009  commencing Lanczos iteration (4 threads)
Tue May 05 13:36:38 2009  memory use: 223.6 MB
Tue May 05 14:19:37 2009  lanczos halted after 12100 iterations (dim = 765022)
Tue May 05 14:19:38 2009  recovered 31 nontrivial dependencies
Tue May 05 14:19:38 2009  BLanczosTime: 2817
Tue May 05 14:19:38 2009  
Tue May 05 14:19:38 2009  commencing square root phase
Tue May 05 14:19:38 2009  reading relations for dependency 1
Tue May 05 14:19:39 2009  read 382671 cycles
Tue May 05 14:19:39 2009  cycles contain 1485452 unique relations
Tue May 05 14:20:40 2009  read 1485452 relations
Tue May 05 14:20:47 2009  multiplying 1199326 relations
Tue May 05 14:23:36 2009  multiply complete, coefficients have about 52.81 million bits
Tue May 05 14:23:38 2009  initial square root is modulo 38250617
Tue May 05 14:27:55 2009  reading relations for dependency 2
Tue May 05 14:27:55 2009  read 382694 cycles
Tue May 05 14:27:56 2009  cycles contain 1487123 unique relations
Tue May 05 14:28:56 2009  read 1487123 relations
Tue May 05 14:29:03 2009  multiplying 1199644 relations
Tue May 05 14:31:51 2009  multiply complete, coefficients have about 52.83 million bits
Tue May 05 14:31:53 2009  initial square root is modulo 38414923
Tue May 05 14:36:09 2009  sqrtTime: 991
Tue May 05 14:36:09 2009  prp51 factor: 132247220045280786396912011749138627359993288829687
Tue May 05 14:36:09 2009  prp72 factor: 559819090026885770857005522645932550743849730325918357433966783937734297
Tue May 05 14:36:09 2009  elapsed time 01:14:45

2·10¹⁷⁰-1 = 1(9)₁₇₀_<171> = 372939703851234256631_<21> · 1476778544474435499113_<22> · C129

C129 = P54 · P75

P54 = 435805161629542059835776832137316524513544223593929263_<54>

P75 = 833265940121934456634651862380154649875027665246097890955759336287836945791_<75>

Wed May 06 23:55:15 2009  Msieve v. 1.41
Wed May 06 23:55:15 2009  random seeds: f3d57740 5a083f78
Wed May 06 23:55:15 2009  factoring 363141597715231961840469669719391341355478061523847951174507517995879853212559878525994104711390336716937987367736368470819582033 (129 digits)
Wed May 06 23:55:16 2009  searching for 15-digit factors
Wed May 06 23:55:18 2009  commencing number field sieve (129-digit input)
Wed May 06 23:55:18 2009  R0: -10000000000000000000000000000000000
Wed May 06 23:55:18 2009  R1:  1
Wed May 06 23:55:18 2009  A0: -1
Wed May 06 23:55:18 2009  A1:  0
Wed May 06 23:55:18 2009  A2:  0
Wed May 06 23:55:18 2009  A3:  0
Wed May 06 23:55:18 2009  A4:  0
Wed May 06 23:55:18 2009  A5:  2
Wed May 06 23:55:18 2009  skew 0.87, size 1.292301e-011, alpha 1.449076, combined = 3.697836e-010
Wed May 06 23:55:18 2009  
Wed May 06 23:55:18 2009  commencing relation filtering
Wed May 06 23:55:18 2009  commencing duplicate removal, pass 1
Wed May 06 23:56:41 2009  found 1638964 hash collisions in 11577617 relations
Wed May 06 23:57:02 2009  added 368119 free relations
Wed May 06 23:57:02 2009  commencing duplicate removal, pass 2
Wed May 06 23:57:21 2009  found 1606009 duplicates and 10339726 unique relations
Wed May 06 23:57:21 2009  memory use: 65.3 MB
Wed May 06 23:57:21 2009  reading rational ideals above 8323072
Wed May 06 23:57:21 2009  reading algebraic ideals above 8323072
Wed May 06 23:57:21 2009  commencing singleton removal, pass 1
Wed May 06 23:58:46 2009  relations with 0 large ideals: 322046
Wed May 06 23:58:46 2009  relations with 1 large ideals: 1627628
Wed May 06 23:58:46 2009  relations with 2 large ideals: 3355941
Wed May 06 23:58:46 2009  relations with 3 large ideals: 3166722
Wed May 06 23:58:46 2009  relations with 4 large ideals: 1327236
Wed May 06 23:58:46 2009  relations with 5 large ideals: 200079
Wed May 06 23:58:46 2009  relations with 6 large ideals: 340074
Wed May 06 23:58:46 2009  relations with 7+ large ideals: 0
Wed May 06 23:58:46 2009  10339726 relations and about 9650898 large ideals
Wed May 06 23:58:46 2009  commencing singleton removal, pass 2
Thu May 07 00:00:11 2009  found 3518074 singletons
Thu May 07 00:00:11 2009  current dataset: 6821652 relations and about 5201006 large ideals
Thu May 07 00:00:11 2009  commencing singleton removal, pass 3
Thu May 07 00:01:08 2009  found 1186005 singletons
Thu May 07 00:01:08 2009  current dataset: 5635647 relations and about 3937334 large ideals
Thu May 07 00:01:08 2009  commencing singleton removal, pass 4
Thu May 07 00:01:56 2009  found 344484 singletons
Thu May 07 00:01:56 2009  current dataset: 5291163 relations and about 3584584 large ideals
Thu May 07 00:01:56 2009  commencing singleton removal, final pass
Thu May 07 00:02:45 2009  memory use: 83.8 MB
Thu May 07 00:02:45 2009  commencing in-memory singleton removal
Thu May 07 00:02:45 2009  begin with 5291163 relations and 3793818 unique ideals
Thu May 07 00:02:50 2009  reduce to 4676325 relations and 3166223 ideals in 14 passes
Thu May 07 00:02:50 2009  max relations containing the same ideal: 30
Thu May 07 00:02:51 2009  reading rational ideals above 720000
Thu May 07 00:02:51 2009  reading algebraic ideals above 720000
Thu May 07 00:02:51 2009  commencing singleton removal, final pass
Thu May 07 00:03:45 2009  keeping 3960255 ideals with weight <= 20, new excess is 329215
Thu May 07 00:03:49 2009  memory use: 128.4 MB
Thu May 07 00:03:49 2009  commencing in-memory singleton removal
Thu May 07 00:03:50 2009  begin with 4677019 relations and 3960255 unique ideals
Thu May 07 00:03:55 2009  reduce to 4662695 relations and 3942575 ideals in 10 passes
Thu May 07 00:03:55 2009  max relations containing the same ideal: 20
Thu May 07 00:03:58 2009  removing 962657 relations and 793542 ideals in 169115 cliques
Thu May 07 00:03:58 2009  commencing in-memory singleton removal
Thu May 07 00:03:58 2009  begin with 3700038 relations and 3942575 unique ideals
Thu May 07 00:04:02 2009  reduce to 3580213 relations and 3023676 ideals in 8 passes
Thu May 07 00:04:02 2009  max relations containing the same ideal: 20
Thu May 07 00:04:04 2009  removing 706590 relations and 537475 ideals in 169115 cliques
Thu May 07 00:04:04 2009  commencing in-memory singleton removal
Thu May 07 00:04:04 2009  begin with 2873623 relations and 3023676 unique ideals
Thu May 07 00:04:06 2009  reduce to 2790515 relations and 2399228 ideals in 7 passes
Thu May 07 00:04:06 2009  max relations containing the same ideal: 20
Thu May 07 00:04:08 2009  removing 62997 relations and 53600 ideals in 9397 cliques
Thu May 07 00:04:08 2009  commencing in-memory singleton removal
Thu May 07 00:04:08 2009  begin with 2727518 relations and 2399228 unique ideals
Thu May 07 00:04:09 2009  reduce to 2726829 relations and 2344936 ideals in 5 passes
Thu May 07 00:04:09 2009  max relations containing the same ideal: 20
Thu May 07 00:04:10 2009  relations with 0 large ideals: 9379
Thu May 07 00:04:10 2009  relations with 1 large ideals: 72170
Thu May 07 00:04:10 2009  relations with 2 large ideals: 332378
Thu May 07 00:04:10 2009  relations with 3 large ideals: 740524
Thu May 07 00:04:10 2009  relations with 4 large ideals: 848156
Thu May 07 00:04:10 2009  relations with 5 large ideals: 512541
Thu May 07 00:04:10 2009  relations with 6 large ideals: 180606
Thu May 07 00:04:10 2009  relations with 7+ large ideals: 31075
Thu May 07 00:04:10 2009  commencing 2-way merge
Thu May 07 00:04:12 2009  reduce to 1798033 relation sets and 1416140 unique ideals
Thu May 07 00:04:12 2009  commencing full merge
Thu May 07 00:04:41 2009  memory use: 127.7 MB
Thu May 07 00:04:41 2009  found 900031 cycles, need 848340
Thu May 07 00:04:41 2009  weight of 848340 cycles is about 59797514 (70.49/cycle)
Thu May 07 00:04:41 2009  distribution of cycle lengths:
Thu May 07 00:04:41 2009  1 relations: 56751
Thu May 07 00:04:41 2009  2 relations: 83118
Thu May 07 00:04:41 2009  3 relations: 96995
Thu May 07 00:04:41 2009  4 relations: 95528
Thu May 07 00:04:41 2009  5 relations: 90120
Thu May 07 00:04:41 2009  6 relations: 80315
Thu May 07 00:04:41 2009  7 relations: 70905
Thu May 07 00:04:41 2009  8 relations: 60666
Thu May 07 00:04:41 2009  9 relations: 51810
Thu May 07 00:04:41 2009  10+ relations: 162132
Thu May 07 00:04:41 2009  heaviest cycle: 18 relations
Thu May 07 00:04:41 2009  commencing cycle optimization
Thu May 07 00:04:43 2009  start with 5196529 relations
Thu May 07 00:04:56 2009  pruned 170872 relations
Thu May 07 00:04:56 2009  memory use: 128.9 MB
Thu May 07 00:04:56 2009  distribution of cycle lengths:
Thu May 07 00:04:56 2009  1 relations: 56751
Thu May 07 00:04:56 2009  2 relations: 85525
Thu May 07 00:04:56 2009  3 relations: 101683
Thu May 07 00:04:56 2009  4 relations: 99412
Thu May 07 00:04:56 2009  5 relations: 93679
Thu May 07 00:04:56 2009  6 relations: 82681
Thu May 07 00:04:56 2009  7 relations: 72480
Thu May 07 00:04:56 2009  8 relations: 61297
Thu May 07 00:04:56 2009  9 relations: 51549
Thu May 07 00:04:56 2009  10+ relations: 143283
Thu May 07 00:04:56 2009  heaviest cycle: 18 relations
Thu May 07 00:04:58 2009  RelProcTime: 568
Thu May 07 00:04:58 2009  
Thu May 07 00:04:58 2009  commencing linear algebra
Thu May 07 00:04:58 2009  read 848340 cycles
Thu May 07 00:05:00 2009  cycles contain 2518833 unique relations
Thu May 07 00:05:56 2009  read 2518833 relations
Thu May 07 00:05:59 2009  using 20 quadratic characters above 134214764
Thu May 07 00:06:12 2009  building initial matrix
Thu May 07 00:06:44 2009  memory use: 275.6 MB
Thu May 07 00:06:45 2009  read 848340 cycles
Thu May 07 00:07:10 2009  matrix is 848136 x 848340 (240.4 MB) with weight 75103459 (88.53/col)
Thu May 07 00:07:10 2009  sparse part has weight 57080382 (67.28/col)
Thu May 07 00:07:20 2009  filtering completed in 2 passes
Thu May 07 00:07:21 2009  matrix is 846914 x 847114 (240.2 MB) with weight 75044918 (88.59/col)
Thu May 07 00:07:21 2009  sparse part has weight 57048622 (67.34/col)
Thu May 07 00:07:24 2009  read 847114 cycles
Thu May 07 00:09:39 2009  matrix is 846914 x 847114 (240.2 MB) with weight 75044918 (88.59/col)
Thu May 07 00:09:39 2009  sparse part has weight 57048622 (67.34/col)
Thu May 07 00:09:39 2009  saving the first 48 matrix rows for later
Thu May 07 00:09:40 2009  matrix is 846866 x 847114 (225.9 MB) with weight 59153206 (69.83/col)
Thu May 07 00:09:40 2009  sparse part has weight 54143775 (63.92/col)
Thu May 07 00:09:40 2009  matrix includes 64 packed rows
Thu May 07 00:09:40 2009  using block size 65536 for processor cache size 6144 kB
Thu May 07 00:09:46 2009  commencing Lanczos iteration (4 threads)
Thu May 07 00:09:46 2009  memory use: 246.5 MB
Thu May 07 01:02:50 2009  lanczos halted after 13391 iterations (dim = 846865)
Thu May 07 01:02:52 2009  recovered 38 nontrivial dependencies
Thu May 07 01:02:52 2009  BLanczosTime: 3474
Thu May 07 01:02:52 2009  
Thu May 07 01:02:52 2009  commencing square root phase
Thu May 07 01:02:52 2009  reading relations for dependency 1
Thu May 07 01:02:52 2009  read 424122 cycles
Thu May 07 01:02:53 2009  cycles contain 1575740 unique relations
Thu May 07 01:03:43 2009  read 1575740 relations
Thu May 07 01:03:50 2009  multiplying 1259664 relations
Thu May 07 01:05:05 2009  multiply complete, coefficients have about 27.90 million bits
Thu May 07 01:05:05 2009  initial square root is modulo 102741601
Thu May 07 01:07:13 2009  reading relations for dependency 2
Thu May 07 01:07:14 2009  read 423170 cycles
Thu May 07 01:07:14 2009  cycles contain 1572373 unique relations
Thu May 07 01:08:03 2009  read 1572373 relations
Thu May 07 01:08:10 2009  multiplying 1257552 relations
Thu May 07 01:09:26 2009  multiply complete, coefficients have about 27.85 million bits
Thu May 07 01:09:26 2009  initial square root is modulo 99755471
Thu May 07 01:11:35 2009  sqrtTime: 523
Thu May 07 01:11:35 2009  prp54 factor: 435805161629542059835776832137316524513544223593929263
Thu May 07 01:11:35 2009  prp75 factor: 833265940121934456634651862380154649875027665246097890955759336287836945791
Thu May 07 01:11:35 2009  elapsed time 01:16:20

(55·10¹⁵⁰+53)/9 = 6(1)₁₄₉7_<151> = 3³ · 1622648257064700037_<19> · C132

C132 = P38 · P94

P38 = 90377613606019928854624782853071442817_<38>

P94 = 1543373924611406170236513127510391203460553114247136700047193975005970719034929975233597849099_<94>

[05/09 03:44:07] GGNFS-0.77.1-VC8(Sat 01/17/2009) : makefb
[05/09 03:44:08] name: 
[05/09 03:44:08] n=139486452208136198228535102355156871796087194235955116983831305936858728587122893524901274783831730324992445526989165162831773471883 (132 digits)
[05/09 03:44:08] c0: 53
[05/09 03:44:08] c1: 0
[05/09 03:44:08] c2: 0
[05/09 03:44:08] c3: 0
[05/09 03:44:08] c4: 0
[05/09 03:44:08] c5: 55
[05/09 03:44:08] RFBsize: 176302 (upto 2399993)
[05/09 03:44:08] AFBsize: 175779 (upto 2399993)
[05/09 03:44:08] maxNumLargeRatPrimes: 3
[05/09 03:44:08] maxLargeRatPrime: 134217728
[05/09 03:44:08] maxNumLargeAlgPrimes: 3
[05/09 03:44:08] maxLargeAlgPrime: 134217728
[05/09 03:45:18] GGNFS-0.77.1-VC8(Sat 01/17/2009) : procrels
[05/09 03:53:30] There were 1093778/8178163 duplicates.
[05/09 03:53:31] RelProcTime: 486.6
[05/09 03:54:06] largePrimes: 7039805 , relations: 7084385
[05/09 03:55:56] GGNFS-0.77.1-VC8(Sat 01/17/2009) : matbuild
[05/09 03:58:53] largePrimes: 7039805 , relations: 7084385
[05/09 04:12:40] reduceRelSets dropped relation-set weight from 14596713 to 11211708.
[05/09 04:19:45] reduceRelSets dropped relation-set weight from 11211708 to 11098389.
[05/09 04:19:45] After removing heavy rel-sets, weight is 9758161.
[05/09 04:28:56] Heap stats for matbuild run.
[05/09 04:28:56] Max heap usage: 0 MB
[05/09 04:28:56] malloc/realloc errors: 0 
[05/09 04:28:56] total malloc's : 598 
[05/09 04:28:56] total realloc's: 318 
[05/09 04:28:56] rels:7084385, initialFF:0, finalFF:508034
[05/09 04:28:56] depinf file written. Run matprune.
[05/09 04:39:15] GGNFS-0.77.1-VC8(Sat 01/17/2009) : matprune
[05/09 04:39:19] Pruning matrix with wt=0.700
[05/09 04:39:19] Initial matrix is 352147 x 508032 with sparse part having weight 83261174.
[05/09 04:39:19] (total weight is 128934569)
[05/09 04:44:09] Matrix pruned to 331118 x 332942 with weight 39049575.
[05/09 04:44:11] Matrix is pruned. Run matsolve.
[05/09 04:44:11] Heap stats for matprune run:
[05/09 04:44:11] Max heap usage: 0 MB
[05/09 04:44:11] malloc/realloc errors: 0 
[05/09 04:44:11] total malloc's : 18 
[05/09 04:44:11] total realloc's: 0 
[05/09 04:44:24] GGNFS-0.77.1-VC8(Sat 01/17/2009) : matsolve (seed=1373339240)
[05/09 05:38:46] BLanczosTime: 3262.1
[05/09 05:38:46] Heap stats for matsolve run:
[05/09 05:38:46] Max heap usage: 0 MB
[05/09 05:38:46] malloc/realloc errors: 0 
[05/09 05:38:46] total malloc's : 16 
[05/09 05:38:46] total realloc's: 0 
[05/09 05:42:19] GGNFS-0.77.1-VC8(Sat 01/17/2009) : sqrt
[05/09 05:42:19] bmultiplier=1
[05/09 05:51:08] From dependence 0, sqrt obtained:
[05/09 05:51:08]   r1=90377613606019928854624782853071442817 (pp38)
[05/09 05:51:08]   r2=1543373924611406170236513127510391203460553114247136700047193975005970719034929975233597849099 (pp94)
[05/09 05:51:08] (pp=probable prime, c=composite)
[05/09 05:51:08] sqrtTime: 529.1

May 12, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 12, 2009

2·10¹⁷⁵-1 = 1(9)₁₇₅_<176> = 28907629 · 2056488191_<10> · 132225919007591_<15> · C145

C145 = P66 · P80

P66 = 252597480480496167240007038032606644816424127704209356727130090671_<66>

P80 = 10072695254702194408495084787330701009705144691937916451329143381917222375956381_<80>

Number: 19999_175
N=2544337442985623921716959902522957528934609642218505078688226925961732275234116485121754486032016850727010696319789948443649436146269366871021651
  ( 145 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=252597480480496167240007038032606644816424127704209356727130090671
 r2=10072695254702194408495084787330701009705144691937916451329143381917222375956381
Version: 
Total time: 38.52 hours.
Scaled time: 91.90 units (timescale=2.386).
Factorization parameters were as follows:
n: 2544337442985623921716959902522957528934609642218505078688226925961732275234116485121754486032016850727010696319789948443649436146269366871021651
m: 100000000000000000000000000000000000
deg: 5
c5: 2
c0: -1
skew: 0.87
type: snfs
lss: 1
rlim: 6400000
alim: 6400000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6400000/6400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [3200000, 5900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 15610896
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1126166 x 1126414
Total sieving time: 33.37 hours.
Total relation processing time: 2.06 hours.
Matrix solve time: 2.96 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,6400000,6400000,28,28,52,52,2.5,2.5,100000
total time: 38.52 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 10, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / May 10, 2009

(55·10¹⁵⁴+53)/9 = 6(1)₁₅₃7_<155> = 7 · 6067 · 2306561 · 74778749 · 2448272317_<10> · C127

C127 = P46 · P81

P46 = 7278517545065402090054562438600913836277499509_<46>

P81 = 468168672925009595606107004497002477134020078039196140371123604319737203741838429_<81>

Number: 61117_154
N=3407573899934668020619771206672862792568146534282880109137450143289303958145920235977066012463975368877788939109996770804831361
  ( 127 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=7278517545065402090054562438600913836277499509 (pp46)
 r2=468168672925009595606107004497002477134020078039196140371123604319737203741838429 (pp81)
Version: Msieve-1.40
Total time: 16.01 hours.
Scaled time: 27.84 units (timescale=1.739).
Factorization parameters were as follows:
n: 3407573899934668020619771206672862792568146534282880109137450143289303958145920235977066012463975368877788939109996770804831361
m: 10000000000000000000000000000000
deg: 5
c5: 11
c0: 106
skew: 1.57
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 513580 x 513828
Total sieving time: 15.52 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 16.01 hours.
 --------- CPU info (if available) ----------

May 10, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / May 10, 2009

(37·10¹⁷⁰+71)/9 = 4(1)₁₆₉9_<171> = 107 · 18401 · 79979 · 1170822842191_<13> · 1196912817460672877848632763_<28> · C121

C121 = P48 · P73

P48 = 721930026682008860612700977009297988939291840349_<48>

P73 = 2580531899054483124131152820897988408963237137415384582028726150021967719_<73>

Number: n
N=1862963462738177997469441912533125084737017632225748137647767328895230043809231081922385833611314256025924897557779693931
  ( 121 digits)
SNFS difficulty: 171 digits.
Divisors found:

Sun May 10 04:20:09 2009  prp48 factor: 721930026682008860612700977009297988939291840349
Sun May 10 04:20:09 2009  prp73 factor: 2580531899054483124131152820897988408963237137415384582028726150021967719
Sun May 10 04:20:09 2009  elapsed time 01:41:26 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 57.52 hours.
Scaled time: 152.36 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_4_1_169_9
n: 1862963462738177997469441912533125084737017632225748137647767328895230043809231081922385833611314256025924897557779693931
m: 10000000000000000000000000000000000
deg: 5
c5: 37
c0: 71
skew: 1.14
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2550000, 5792069)
Primes: RFBsize:354971, AFBsize:354642, largePrimes:17447566 encountered
Relations: rels:17068184, finalFF:682228
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2051048 hash collisions in 18743090 relations
Msieve: matrix is 923424 x 923672 (246.2 MB)

Total sieving time: 56.83 hours.
Total relation processing time: 0.68 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,28,28,56,56,2.4,2.4,100000
total time: 57.52 hours.
 --------- CPU info (if available) ----------

(55·10¹⁵⁵+53)/9 = 6(1)₁₅₄7_<156> = 13 · 5373931 · C148

C148 = P58 · P91

P58 = 4574519951664141163904776330845147834730931008411393678889_<58>

P91 = 1912225986241622695547172120836614414703594235215141036385313882156078530401611682475064651_<91>

Number: n
N=8747515926152942519546407836004408792559589434353922398149240659872076613378278769963181244234164340507350866062207908614198534928815983783008852739
  ( 148 digits)
SNFS difficulty: 156 digits.
Divisors found:

Sun May 10 17:40:49 2009  prp58 factor: 4574519951664141163904776330845147834730931008411393678889
Sun May 10 17:40:49 2009  prp91 factor: 1912225986241622695547172120836614414703594235215141036385313882156078530401611682475064651
Sun May 10 17:40:49 2009  elapsed time 00:41:16 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 18.85 hours.
Scaled time: 50.14 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_1_154_7
n: 8747515926152942519546407836004408792559589434353922398149240659872076613378278769963181244234164340507350866062207908614198534928815983783008852739
m: 10000000000000000000000000000000
deg: 5
c5: 55
c0: 53
skew: 0.99
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1450000, 2565383)
Primes: RFBsize:210109, AFBsize:209530, largePrimes:12305001 encountered
Relations: rels:11297272, finalFF:410773
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1007232 hash collisions in 12272639 relations
Msieve: matrix is 549105 x 549353 (147.2 MB)

Total sieving time: 18.59 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,28,28,56,56,2.4,2.4,100000
total time: 18.85 hours.
 --------- CPU info (if available) ----------

May 10, 2009 (3rd)

By matsui / GGNFS / May 10, 2009

7·10¹⁶⁷+9 = 7(0)₁₆₆9_<168> = 178069 · 501731 · 865342599239164691599085917_<27> · C130

C130 = P49 · P82

P49 = 6790719988452911272645568689691193108538390322657_<49>

P82 = 1333321487905646787354335377158150700210766538153045388940264597308992314691236899_<82>

N=9054212878954652228888100592451098523536681789916597423465588315561167609163922756593556020840808722859548049818240407383034120643
  ( 130 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=6790719988452911272645568689691193108538390322657 (pp49)
 r2=1333321487905646787354335377158150700210766538153045388940264597308992314691236899 (pp82)

Version: GGNFS-0.77.1-20060722-nocona

May 10, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 10, 2009

2·10¹⁷⁴-1 = 1(9)₁₇₄_<175> = 31 · 433 · 432861613054879_<15> · C156

C156 = P69 · P87

P69 = 619180306815359879947719443746703720133427088087349543290858026082921_<69>

P87 = 555922429864657334982749661703084805904449869206638420241546962493043429452142780416407_<87>

Number: 19999_174
N=344216220689138912934454927280358723898655801619893389728782160047005078582797351260752955072440170199771132657212043868893991972544665947669729527490884847
  ( 156 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=619180306815359879947719443746703720133427088087349543290858026082921
 r2=555922429864657334982749661703084805904449869206638420241546962493043429452142780416407
Version: 
Total time: 34.42 hours.
Scaled time: 81.94 units (timescale=2.381).
Factorization parameters were as follows:
n: 344216220689138912934454927280358723898655801619893389728782160047005078582797351260752955072440170199771132657212043868893991972544665947669729527490884847
m: 100000000000000000000000000000000000
deg: 5
c5: 1
c0: -5
skew: 1.38
type: snfs
lss: 1
rlim: 6400000
alim: 6400000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6400000/6400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [3200000, 5600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 15451820
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1063716 x 1063964
Total sieving time: 29.79 hours.
Total relation processing time: 1.82 hours.
Matrix solve time: 2.58 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,6400000,6400000,28,28,52,52,2.5,2.5,100000
total time: 34.42 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 10, 2009

By Andreas Tete / GMP-ECM 6.2.3 / May 10, 2009

(41·10¹⁶⁹+31)/9 = 4(5)₁₆₈9_<170> = 7² · 19 · 5591 · 24897386467_<11> · 1730391568858800137586311395687_<31> · C123

C123 = P41 · P82

P41 = 20857207550458330418500632087634039101377_<41>

P82 = 9739751135380665829409170258234123961386776664737312926522131440681813665950217263_<82>

Input number is 203144010920446719675150985051929266983700872415625718248971422027715628531026178691027602422423959557424751697250432471151 (123 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3267817554
********** Factor found in step 2: 20857207550458330418500632087634039101377
Found probable prime factor of 41 digits: 20857207550458330418500632087634039101377
Probable prime cofactor 9739751135380665829409170258234123961386776664737312926522131440681813665950217263 has 82 digits

May 9, 2009 (6th)

By Erik Branger / GMP-ECM, GGNFS, Msieve / May 9, 2009

(52·10¹⁹⁷+11)/9 = 5(7)₁₉₆9_<198> = 3³ · 17² · 311 · 335154602779_<12> · 331678609200563659_<18> · 854252101696507156593065623_<27> · C136

C136 = P33 · P45 · P59

P33 = 124983585212975494444207599696457_<33>

P45 = 632394553174014976691291963192884507171937573_<45>

P59 = 31721157876312680245539261007036254938393070660760364592661_<59>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 2507206647322814436500135705744273279758691833540728488771499003385289025126313519686362630082299794459178069117751368048682483007039121 (136 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1013880214
Step 1 took 43353ms
Step 2 took 14523ms
********** Factor found in step 2: 124983585212975494444207599696457
Found probable prime factor of 33 digits: 124983585212975494444207599696457
Composite cofactor 20060287461353143260577074732985834740382233133179282303851165223232505606725814342567316225784265951753 has 104 digits

Number: 57779_197
N=20060287461353143260577074732985834740382233133179282303851165223232505606725814342567316225784265951753
  ( 104 digits)
Divisors found:
 r1=632394553174014976691291963192884507171937573 (pp45)
 r2=31721157876312680245539261007036254938393070660760364592661 (pp59)
Version: Msieve v. 1.41
Total time: 9.76 hours.
Scaled time: 8.73 units (timescale=0.895).
Factorization parameters were as follows:
name: 57779_197
n: 20060287461353143260577074732985834740382233133179282303851165223232505606725814342567316225784265951753
skew: 9162.82
# norm 1.56e+014
c5: 37800
c4: -971408292
c3: 5500669569536
c2: 114106733298595240
c1: -205004754396022467272
c0: -1438295962118762891247067
# alpha -5.92
Y1: 136309959109
Y0: -55587167437977075996
# Murphy_E 2.26e-009
# M 5905042831134496601099371153764024483475550021478620361667233147008724041134572060710188437332295219513
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 299270 x 299518
Polynomial selection time: 0.64 hours.
Total sieving time: 8.52 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.33 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 9.76 hours.
 --------- CPU info (if available) ----------

May 9, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / May 9, 2009

5·10¹⁶⁸+9 = 5(0)₁₆₇9_<169> = 7 · 23 · 65990746049957014371607_<23> · C144

C144 = P66 · P78

P66 = 657641273061186958218573106478356106521035023165800368518412163301_<66>

P78 = 715602795845022032566832013234571359667906810279528894626944306683762500542867_<78>

Number: n
N=470609933665664958580762326468921066700739717896012857757398341392913611302788239153743792964744616831365739935156375436723459571584868354723967
  ( 144 digits)
SNFS difficulty: 169 digits.
Divisors found:

Sat May 09 01:47:51 2009  prp66 factor: 657641273061186958218573106478356106521035023165800368518412163301
Sat May 09 01:47:51 2009  prp78 factor: 715602795845022032566832013234571359667906810279528894626944306683762500542867
Sat May 09 01:47:51 2009  elapsed time 01:14:58 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 32.75 hours.
Scaled time: 86.75 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_0_167_9
n: 470609933665664958580762326468921066700739717896012857757398341392913611302788239153743792964744616831365739935156375436723459571584868354723967
m: 5000000000000000000000000000000000
deg: 5
c5: 8
c0: 45
skew: 1.41
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2350000, 4171283)
Primes: RFBsize:328964, AFBsize:327919, largePrimes:15583929 encountered
Relations: rels:14730311, finalFF:685939
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1364602 hash collisions in 15945930 relations
Msieve: matrix is 794020 x 794268 (213.9 MB)

Total sieving time: 32.26 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4700000,4700000,28,28,56,56,2.4,2.4,100000
total time: 32.75 hours.
 --------- CPU info (if available) ----------

(41·10¹⁶⁸-23)/9 = 4(5)₁₆₇3_<169> = 109 · 152429 · 79004407 · 133656977 · C146

C146 = P43 · P50 · P53

P43 = 6007797507796559084764857897605363260004329_<43>

P50 = 56423297165889284989630934090458748431402470802993_<50>

P53 = 76600313933033143492732603924738124493658370144085431_<53>

Number: n
N=25965954814608141429080010895967929274799794171251472540569017121325201896645274787113262664165955396361635456063874183933768769701000624020781407
  ( 146 digits)
SNFS difficulty: 171 digits.
Divisors found:

Sat May 09 23:13:11 2009  prp43 factor: 6007797507796559084764857897605363260004329
Sat May 09 23:13:12 2009  prp50 factor: 56423297165889284989630934090458748431402470802993
Sat May 09 23:13:12 2009  prp53 factor: 76600313933033143492732603924738124493658370144085431
Sat May 09 23:13:12 2009  elapsed time 01:36:25 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 66.59 hours.
Scaled time: 174.53 units (timescale=2.621).
Factorization parameters were as follows:
name: KA_4_5_167_3
n: 25965954814608141429080010895967929274799794171251472540569017121325201896645274787113262664165955396361635456063874183933768769701000624020781407
m: 5000000000000000000000000000000000
deg: 5
c5: 328
c0: -575
skew: 1.12
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 6359039)
Primes: RFBsize:348513, AFBsize:348447, largePrimes:17695033 encountered
Relations: rels:17682863, finalFF:683070
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2408078 hash collisions in 19947869 relations
Msieve: matrix is 875534 x 875782 (231.8 MB)

Total sieving time: 65.68 hours.
Total relation processing time: 0.91 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 66.59 hours.
 --------- CPU info (if available) ----------

May 9, 2009 (4th)

By Sinkiti Sibata / GGNFS / May 9, 2009

(55·10¹⁴⁷+53)/9 = 6(1)₁₄₆7_<148> = 3 · C148

C148 = P43 · P46 · P60

P43 = 1934253706957006579243393144221742149992149_<43>

P46 = 1140583220880797403978091503281085123359628851_<46>

P60 = 923333322179040387392850591047434036029068313871256542661761_<60>

Number: 61117_147
N=2037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037039
  ( 148 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1934253706957006579243393144221742149992149 (pp43)
 r2=1140583220880797403978091503281085123359628851 (pp46)
 r3=923333322179040387392850591047434036029068313871256542661761 (pp60)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 29.48 hours.
Scaled time: 13.94 units (timescale=0.473).
Factorization parameters were as follows:
name: 61117_147
n: 2037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037039
m: 500000000000000000000000000000
deg: 5
c5: 44
c0: 1325
skew: 1.98
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 1800001)
Primes: RFBsize:162662, AFBsize:162806, largePrimes:6688861 encountered
Relations: rels:6491098, finalFF:368269
Max relations in full relation-set: 28
Initial matrix: 325535 x 368269 with sparse part having weight 35663558.
Pruned matrix : 306604 x 308295 with weight 26923864.
Total sieving time: 25.88 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 3.21 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,49,49,2.4,2.4,100000
total time: 29.48 hours.
 --------- CPU info (if available) ----------

May 9, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / May 9, 2009

(47·10¹⁶⁹+7)/9 = 5(2)₁₆₈3_<170> = 3910201 · C164

C164 = P39 · P125

P39 = 794713181149411111682301022055428586693_<39>

P125 = 16805283750075034191479848530740623199369945040294683927031175977873033235337781607162824731136170054236085541647539786898011_<125>

Number: 52223_169
N=13355380509140635538229932993782729384556502906684905001615574806057852837289495405024504423742468027148021859291177671485998346944881406920570636195485148262767623
  ( 164 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=794713181149411111682301022055428586693 (pp39)
 r2=16805283750075034191479848530740623199369945040294683927031175977873033235337781607162824731136170054236085541647539786898011 (pp125)
Version: Msieve-1.40
Total time: 77.13 hours.
Scaled time: 134.12 units (timescale=1.739).
Factorization parameters were as follows:
n: 13355380509140635538229932993782729384556502906684905001615574806057852837289495405024504423742468027148021859291177671485998346944881406920570636195485148262767623
m: 10000000000000000000000000000000000
deg: 5
c5: 47
c0: 70
skew: 1.08
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 6750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1039031 x 1039279
Total sieving time: 75.17 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.40 hours.
Time per square root: 0.37 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 77.13 hours.
 --------- CPU info (if available) ----------

May 9, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / May 9, 2009

(55·10¹⁴⁹+53)/9 = 6(1)₁₄₈7_<150> = 13³ · C147

C147 = P34 · P113

P34 = 9098865678589426948210548308231663_<34>

P113 = 30570523042816547814440813700618361961725138008742239062105098207703222902446606516081094383000429754808066107447_<113>

Number: 61117_149
N=278157082890810701461589035553532594952713295908562180751529863955899458858038739695544429272239923127497091994133414251757447023719213068325494361
  ( 147 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=9098865678589426948210548308231663 (pp34)
 r2=30570523042816547814440813700618361961725138008742239062105098207703222902446606516081094383000429754808066107447 (pp113)
Version: Msieve v. 1.41
Total time: 28.51 hours.
Scaled time: 22.52 units (timescale=0.790).
Factorization parameters were as follows:
n: 278157082890810701461589035553532594952713295908562180751529863955899458858038739695544429272239923127497091994133414251757447023719213068325494361
m: 1000000000000000000000000000000
deg: 5
c5: 11
c0: 106
skew: 1.57
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 349166 x 349414
Total sieving time: 27.59 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.63 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 28.51 hours.
 --------- CPU info (if available) ----------

(17·10¹⁹⁵+7)/3 = 5(6)₁₉₄9_<196> = 29 · 43 · 617 · 2801 · 7549 · 1762637 · 39762250686874433_<17> · 700499502160290798232849_<24> · 335892581501510072078226020862078769_<36> · C101

C101 = P49 · P53

P49 = 1817044992552857656312895051970666530297885113571_<49>

P53 = 11624271617724242080352063449012326368972889922281089_<53>

Number: 56669_195
N=21121824535060140072018908089763071056280643107380669147641248739488560912123500709369953560150558819
  ( 101 digits)
Divisors found:
 r1=1817044992552857656312895051970666530297885113571 (pp49)
 r2=11624271617724242080352063449012326368972889922281089 (pp53)
Version: Msieve v. 1.41
Total time: 6.71 hours.
Scaled time: 5.91 units (timescale=0.881).
Factorization parameters were as follows:
name: 56669_195
n: 21121824535060140072018908089763071056280643107380669147641248739488560912123500709369953560150558819
skew: 2574.59
# norm 1.43e+014
c5: 239400
c4: 1890051466
c3: -14769154005126
c2: -13446007784640866
c1: -22632029745018180231
c0: 93555121878115727758
# alpha -6.36
Y1: 56816630959
Y0: -9752533754254193499
# Murphy_E 3.38e-009
# M 7779123482036425925845383173131339324755063127238206233705787903788991635177672816341387515450557856
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 193882 x 194130
Polynomial selection time: 0.43 hours.
Total sieving time: 5.98 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 6.71 hours.
 --------- CPU info (if available) ----------

May 9, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 9, 2009

2·10¹⁶⁸-1 = 1(9)₁₆₈_<169> = 23 · 1777 · 18839 · 135391 · 364756495659471337_<18> · C137

C137 = P51 · P86

P51 = 636103204077055081116683110150349594823972754883063_<51>

P86 = 82686854649109369630282597434781951218127495551479593262504037019953021599941887782351_<86>

Number: 19999_168
N=52597373177352208060513564077435320881813363520162130791000724022083971317654521522294775353936789042386457644556411844586189315400221113
  ( 137 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=636103204077055081116683110150349594823972754883063
 r2=82686854649109369630282597434781951218127495551479593262504037019953021599941887782351
Version: 
Total time: 24.35 hours.
Scaled time: 58.04 units (timescale=2.384).
Factorization parameters were as follows:
n: 52597373177352208060513564077435320881813363520162130791000724022083971317654521522294775353936789042386457644556411844586189315400221113
m: 10000000000000000000000000000000000
deg: 5
c5: 1
c0: -50
skew: 2.19
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2400000, 4300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10775156
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 762793 x 763040
Total sieving time: 21.95 hours.
Total relation processing time: 1.02 hours.
Matrix solve time: 1.30 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,52,52,2.4,2.4,100000
total time: 24.35 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 8, 2009 (7th)

By Wataru Sakai / Msieve / May 8, 2009

4·10²⁰³+1 = 4(0)₂₀₂1_<204> = 7 · 641 · C200

C200 = P73 · P128

P73 = 3996493212534098134156111341457064136963014957402517508990780184800320983_<73>

P128 = 22306161491827264164393810143013170259394176192731199083359389215809287265225238597639960484443643575958988629141966737446379681_<128>

Number: 40001_203
N=89146422999777133942500557165143748607087140628482282148428794294628928014263427679964341430800089146422999777133942500557165143748607087140628482282148428794294628928014263427679964341430800089146423
  ( 200 digits)
SNFS difficulty: 205 digits.
Divisors found:
 r1=3996493212534098134156111341457064136963014957402517508990780184800320983
 r2=22306161491827264164393810143013170259394176192731199083359389215809287265225238597639960484443643575958988629141966737446379681
Version: 
Total time: 858.79 hours.
Scaled time: 1670.35 units (timescale=1.945).
Factorization parameters were as follows:
n: 89146422999777133942500557165143748607087140628482282148428794294628928014263427679964341430800089146422999777133942500557165143748607087140628482282148428794294628928014263427679964341430800089146423
m: 100000000000000000000000000000000000000000
deg: 5
c5: 1
c0: 25
skew: 1.90
type: snfs
lss: 1
rlim: 18300000
alim: 18300000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 18300000/18300000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [9150000, 17650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2921104 x 2921352
Total sieving time: 858.79 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,205,5,0,0,0,0,0,0,0,0,18300000,18300000,29,29,56,56,2.6,2.6,100000
total time: 858.79 hours.
 --------- CPU info (if available) ----------

May 8, 2009 (6th)

By Ignacio Santos / GGNFS, Msieve / May 8, 2009

(47·10¹⁷⁰+61)/9 = 5(2)₁₆₉9_<171> = 18902371219_<11> · C161

C161 = P35 · P127

P35 = 10510633214327225798229348673064411_<35>

P127 = 2628513304830956602240823352104911960288107310430910800133860524644986354367963340687139457780089343410802616392394992059130581_<127>

Number: 52229_170
N=27627339246057276483234757819207456028441582910075966920529994180420725881958578321909646664114761200120848299705705944861235677662427047598986328119589672852791
  ( 161 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=10510633214327225798229348673064411 (pp35)
 r2=2628513304830956602240823352104911960288107310430910800133860524644986354367963340687139457780089343410802616392394992059130581 (pp127)
Version: Msieve-1.40
Total time: 61.03 hours.
Scaled time: 106.12 units (timescale=1.739).
Factorization parameters were as follows:
n: 27627339246057276483234757819207456028441582910075966920529994180420725881958578321909646664114761200120848299705705944861235677662427047598986328119589672852791
m: 10000000000000000000000000000000000
deg: 5
c5: 47
c0: 61
skew: 1.05
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 966761 x 967009
Total sieving time: 59.53 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.21 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 61.03 hours.
 --------- CPU info (if available) ----------

(55·10¹⁶⁵+53)/9 = 6(1)₁₆₄7_<166> = 3 · 47 · C164

C164 = P30 · P57 · P78

P30 = 434392873792766435314567746253_<30>

P57 = 601015833271961930438381726821925015839283136961619049463_<57>

P78 = 166009316724078941748218206828287356577245780644970974597600113903444595211683_<78>

Number: 61117_165
N=43341213553979511426319936958234830575256107171000788022064617809298660362490149724192277383766745468873128447596532702915681639085894405043341213553979511426319937
  ( 164 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=434392873792766435314567746253 (pp30)
 r2=601015833271961930438381726821925015839283136961619049463 (pp57)
 r3=166009316724078941748218206828287356577245780644970974597600113903444595211683 (pp78)
Version: Msieve-1.40
Total time: 45.17 hours.
Scaled time: 78.55 units (timescale=1.739).
Factorization parameters were as follows:
n: 43341213553979511426319936958234830575256107171000788022064617809298660362490149724192277383766745468873128447596532702915681639085894405043341213553979511426319937
m: 1000000000000000000000000000000000
deg: 5
c5: 55
c0: 53
skew: 0.99
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 798827 x 799075
Total sieving time: 43.98 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.81 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 45.17 hours.
 --------- CPU info (if available) ----------

May 8, 2009 (5th)

By Dmitry Domanov / GMP-ECM 6.2.3 / May 8, 2009

(55·10²⁰¹+53)/9 = 6(1)₂₀₀7_<202> = 3 · 29 · 183770345533477853_<18> · 9930904669574722752815513_<25> · C158

C158 = P34 · C125

P34 = 3182926213879566929452257852809267_<34>

C125 = [12092333369161073721453095497369483934473764519498218736238482790936465340160389049119166372609930051353777385455408331203957_<125>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4133403303
Step 1 took 68140ms
Step 2 took 22047ms
********** Factor found in step 2: 3182926213879566929452257852809267
Found probable prime factor of 34 digits: 3182926213879566929452257852809267
Composite cofactor 12092333369161073721453095497369483934473764519498218736238482790936465340160389049119166372609930051353777385455408331203957 has 125 digits

(8·10¹⁸⁰-17)/9 = (8)₁₇₉7_<180> = 3658268353_<10> · C171

C171 = P29 · C142

P29 = 61758845631466767465271797833_<29>

C142 = [3934347785535229374215233762925850576083625703317757636353808208491422978557394268988530803249245868900196615196404588103179803195501264851263_<142>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1165875092
Step 1 took 45750ms
Step 2 took 13265ms
********** Factor found in step 2: 61758845631466767465271797833
Found probable prime factor of 29 digits: 61758845631466767465271797833
Composite cofactor 3934347785535229374215233762925850576083625703317757636353808208491422978557394268988530803249245868900196615196404588103179803195501264851263 has 142 digits

(55·10²⁰⁰+53)/9 = 6(1)₁₉₉7_<201> = 9884441051_<10> · C191

C191 = P35 · P157

P35 = 23074832604403156003968083678423161_<35>

P157 = 2679350349088988305490403091431348358892120669855456232877078195575641044743881337125955286009460700529432362124348914568981407995940754578885914624269755247_<157>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2828504491
Step 1 took 89687ms
Step 2 took 26641ms
********** Factor found in step 2: 23074832604403156003968083678423161
Found probable prime factor of 35 digits: 23074832604403156003968083678423161
Probable prime cofactor 2679350349088988305490403091431348358892120669855456232877078195575641044743881337125955286009460700529432362124348914568981407995940754578885914624269755247 has 157 digits

May 8, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 8, 2009

(55·10¹⁷²+17)/9 = 6(1)₁₇₁3_<173> = 3² · 13 · C171

C171 = P45 · P127

P45 = 493749677347938526775502150247920833506391063_<45>

P127 = 1057858289223318308788894162344464041259794820007724457791366870178514553961234787544201200451027293578968082744471755879288003_<127>

Number: n
N=522317188983855650522317188983855650522317188983855650522317188983855650522317188983855650522317188983855650522317188983855650522317188983855650522317188983855650522317189
  ( 171 digits)
SNFS difficulty: 175 digits.
Divisors found:

Fri May 08 02:39:21 2009  prp45 factor: 493749677347938526775502150247920833506391063
Fri May 08 02:39:21 2009  prp127 factor: 1057858289223318308788894162344464041259794820007724457791366870178514553961234787544201200451027293578968082744471755879288003
Fri May 08 02:39:21 2009  elapsed time 02:22:25 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 91.95 hours.
Scaled time: 238.60 units (timescale=2.595).
Factorization parameters were as follows:
name: KA_6_1_171_3
n: 522317188983855650522317188983855650522317188983855650522317188983855650522317188983855650522317188983855650522317188983855650522317188983855650522317188983855650522317189
m: 50000000000000000000000000000000000
deg: 5
c5: 44
c0: 425
skew: 1.57
type: snfs
lss: 1
rlim: 5800000
alim: 5800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2900000, 7700001)
Primes: RFBsize:399993, AFBsize:400815, largePrimes:21169931 encountered
Relations: rels:21218933, finalFF:661920
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2987853 hash collisions in 24011991 relations
Msieve: matrix is 1038429 x 1038677 (273.8 MB)

Total sieving time: 90.52 hours.
Total relation processing time: 1.43 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,56,56,2.5,2.5,100000
total time: 91.95 hours.
 --------- CPU info (if available) ----------

(55·10¹⁵⁷+53)/9 = 6(1)₁₅₆7_<158> = 127 · 523 · 2203 · C150

C150 = P32 · P119

P32 = 13817558341465076358377329712261_<32>

P119 = 30225184887059178490293947945272519104526393199396084242282172451085350402214128357155116143842990858452098996661902719_<119>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 417638255558508713627723912352227521132881097469078988057677364814564851991010690402606900421091516458151313767659912418053384947164739954461043537659 (150 digits)
Using B1=918000, B2=871204962, polynomial Dickson(3), sigma=3934766055
Step 1 took 14071ms
Step 2 took 4945ms
********** Factor found in step 2: 13817558341465076358377329712261
Found probable prime factor of 32 digits: 13817558341465076358377329712261
Probable prime cofactor 30225184887059178490293947945272519104526393199396084242282172451085350402214128357155116143842990858452098996661902719 has 119 digits

May 8, 2009 (3rd)

By Erik Branger / GMP-ECM / May 8, 2009

(17·10¹⁹⁵+7)/3 = 5(6)₁₉₄9_<196> = 29 · 43 · 617 · 2801 · 7549 · 1762637 · 39762250686874433_<17> · 700499502160290798232849_<24> · C136

C136 = P36 · C101

P36 = 335892581501510072078226020862078769_<36>

C101 = [21121824535060140072018908089763071056280643107380669147641248739488560912123500709369953560150558819_<101>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 7094664169103283184013610577645367109734157140915973908954192728000319531155523620156101021461377924560117765256610115908031581345613811 (136 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2576663519
Step 1 took 42728ms
Step 2 took 33806ms
********** Factor found in step 2: 335892581501510072078226020862078769
Found probable prime factor of 36 digits: 335892581501510072078226020862078769
Composite cofactor 21121824535060140072018908089763071056280643107380669147641248739488560912123500709369953560150558819 has 101 digits

May 8, 2009 (2nd)

By Sinkiti Sibata / GGNFS, Msieve / May 8, 2009

(55·10¹³⁹+53)/9 = 6(1)₁₃₈7_<140> = C140

C140 = P68 · P73

P68 = 55222676755743811812143735433434316389037947984568052041039337458107_<68>

P73 = 1106630730368477338439401197886469885070910057830214075394122282080081431_<73>

Number: 61117_139
N=61111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
  ( 140 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=55222676755743811812143735433434316389037947984568052041039337458107 (pp68)
 r2=1106630730368477338439401197886469885070910057830214075394122282080081431 (pp73)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 11.75 hours.
Scaled time: 5.56 units (timescale=0.473).
Factorization parameters were as follows:
name: 61117_139
n: 61111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
m: 10000000000000000000000000000
deg: 5
c5: 11
c0: 106
skew: 1.57
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1685001)
Primes: RFBsize:119057, AFBsize:119101, largePrimes:3673934 encountered
Relations: rels:3742209, finalFF:354161
Max relations in full relation-set: 28
Initial matrix: 238223 x 354161 with sparse part having weight 31935230.
Pruned matrix : 203926 x 205181 with weight 15076212.
Total sieving time: 10.62 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.90 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 11.75 hours.
 --------- CPU info (if available) ----------

(55·10¹³⁸+53)/9 = 6(1)₁₃₇7_<139> = 3 · 3163 · 206807 · 2533301 · 54546379 · 600759729280698289_<18> · C98

C98 = P42 · P56

P42 = 626966962998021396827054558842257997237883_<42>

P56 = 59832384146594063198278007871246052814557417692463599223_<56>

Thu May 07 23:48:15 2009  Msieve v. 1.41
Thu May 07 23:48:15 2009  random seeds: 3841bec4 032f2dc8
Thu May 07 23:48:15 2009  factoring 37512928177321042052137087899746731284548448675174485642387833241165805143299523703911054704964909 (98 digits)
Thu May 07 23:48:17 2009  searching for 15-digit factors
Thu May 07 23:48:18 2009  commencing quadratic sieve (98-digit input)

Thu May 07 23:48:18 2009  using multiplier of 29
Thu May 07 23:48:18 2009  using 32kb Intel Core sieve core
Thu May 07 23:48:18 2009  sieve interval: 36 blocks of size 32768
Thu May 07 23:48:18 2009  processing polynomials in batches of 6
Thu May 07 23:48:18 2009  using a sieve bound of 2503477 (91765 primes)
Thu May 07 23:48:18 2009  using large prime bound of 375521550 (28 bits)
Thu May 07 23:48:18 2009  using double large prime bound of 2718583754966400 (43-52 bits)
Thu May 07 23:48:18 2009  using trial factoring cutoff of 52 bits
Thu May 07 23:48:18 2009  polynomial 'A' values have 13 factors
Fri May 08 07:31:56 2009  92187 relations (22218 full + 69969 combined from 1379844 partial), need 91861
Fri May 08 07:31:58 2009  begin with 1402062 relations
Fri May 08 07:31:59 2009  reduce to 241624 relations in 10 passes
Fri May 08 07:31:59 2009  attempting to read 241624 relations
Fri May 08 07:32:03 2009  recovered 241624 relations
Fri May 08 07:32:03 2009  recovered 230814 polynomials
Fri May 08 07:32:04 2009  attempting to build 92187 cycles
Fri May 08 07:32:04 2009  found 92187 cycles in 5 passes
Fri May 08 07:32:04 2009  distribution of cycle lengths:
Fri May 08 07:32:04 2009     length 1 : 22218
Fri May 08 07:32:04 2009     length 2 : 16175
Fri May 08 07:32:04 2009     length 3 : 15495
Fri May 08 07:32:04 2009     length 4 : 12495
Fri May 08 07:32:04 2009     length 5 : 9228
Fri May 08 07:32:04 2009     length 6 : 6453
Fri May 08 07:32:04 2009     length 7 : 4259
Fri May 08 07:32:04 2009     length 9+: 5864
Fri May 08 07:32:04 2009  largest cycle: 21 relations
Fri May 08 07:32:04 2009  matrix is 91765 x 92187 (25.0 MB) with weight 6174509 (66.98/col)
Fri May 08 07:32:04 2009  sparse part has weight 6174509 (66.98/col)
Fri May 08 07:32:06 2009  filtering completed in 3 passes
Fri May 08 07:32:06 2009  matrix is 87829 x 87893 (23.9 MB) with weight 5903463 (67.17/col)
Fri May 08 07:32:06 2009  sparse part has weight 5903463 (67.17/col)
Fri May 08 07:32:06 2009  saving the first 48 matrix rows for later
Fri May 08 07:32:06 2009  matrix is 87781 x 87893 (14.6 MB) with weight 4663415 (53.06/col)
Fri May 08 07:32:06 2009  sparse part has weight 3295555 (37.50/col)
Fri May 08 07:32:06 2009  matrix includes 64 packed rows
Fri May 08 07:32:06 2009  using block size 35157 for processor cache size 1024 kB
Fri May 08 07:32:07 2009  commencing Lanczos iteration
Fri May 08 07:32:07 2009  memory use: 14.3 MB
Fri May 08 07:33:25 2009  lanczos halted after 1390 iterations (dim = 87779)
Fri May 08 07:33:26 2009  recovered 16 nontrivial dependencies
Fri May 08 07:33:26 2009  prp42 factor: 626966962998021396827054558842257997237883
Fri May 08 07:33:26 2009  prp56 factor: 59832384146594063198278007871246052814557417692463599223
Fri May 08 07:33:26 2009  elapsed time 07:45:11

(55·10¹¹⁶+53)/9 = 6(1)₁₁₅7_<117> = 19 · 197 · 1669 · 41309713547_<11> · C100

C100 = P35 · P66

P35 = 17998416975481605047372358908971633_<35>

P66 = 131570196632693976742949748125889936861091146498905961587342674901_<66>

Number: 61117_116
N=2368055260541331981772641117518230248090145004742647628081803500179870429023326186569929893350083333
  ( 100 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=17998416975481605047372358908971633 (pp35)
 r2=131570196632693976742949748125889936861091146498905961587342674901 (pp66)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.07 hours.
Scaled time: 0.98 units (timescale=0.473).
Factorization parameters were as follows:
name: 61117_116
n: 2368055260541331981772641117518230248090145004742647628081803500179870429023326186569929893350083333
m: 100000000000000000000000
deg: 5
c5: 550
c0: 53
skew: 0.63
type: snfs
lss: 1
rlim: 640000
alim: 640000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 640000/640000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [320000, 520001)
Primes: RFBsize:52074, AFBsize:52142, largePrimes:1221081 encountered
Relations: rels:1173572, finalFF:126322
Max relations in full relation-set: 28
Initial matrix: 104283 x 126322 with sparse part having weight 5808007.
Pruned matrix : 93513 x 94098 with weight 3332777.
Total sieving time: 1.93 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,640000,640000,25,25,45,45,2.2,2.2,50000
total time: 2.07 hours.
 --------- CPU info (if available) ----------

(55·10¹⁵⁹+53)/9 = 6(1)₁₅₈7_<160> = 3² · 3257 · 1594625783_<10> · 7249010305101463_<16> · 202207490515382002924235133783767_<33> · C98

C98 = P45 · P54

P45 = 177339214346923928023382818463973318947220121_<45>

P54 = 502944882564508401354967688113709310226342169790528803_<54>

Fri May 08 08:00:46 2009  Msieve v. 1.41
Fri May 08 08:00:46 2009  random seeds: c6c87428 b8cc5b0b
Fri May 08 08:00:46 2009  factoring 89191850333795838431224741678938543992837614421268237563958056735200519236760235158865591431645163 (98 digits)
Fri May 08 08:00:48 2009  searching for 15-digit factors
Fri May 08 08:00:49 2009  commencing quadratic sieve (98-digit input)
Fri May 08 08:00:50 2009  using multiplier of 2
Fri May 08 08:00:50 2009  using 32kb Intel Core sieve core
Fri May 08 08:00:50 2009  sieve interval: 36 blocks of size 32768
Fri May 08 08:00:50 2009  processing polynomials in batches of 6
Fri May 08 08:00:50 2009  using a sieve bound of 2534047 (92941 primes)
Fri May 08 08:00:50 2009  using large prime bound of 380107050 (28 bits)
Fri May 08 08:00:50 2009  using double large prime bound of 2778629288667150 (43-52 bits)
Fri May 08 08:00:50 2009  using trial factoring cutoff of 52 bits
Fri May 08 08:00:50 2009  polynomial 'A' values have 13 factors
Fri May 08 15:14:00 2009  93166 relations (22156 full + 71010 combined from 1397542 partial), need 93037
Fri May 08 15:14:01 2009  begin with 1419698 relations
Fri May 08 15:14:03 2009  reduce to 244999 relations in 12 passes
Fri May 08 15:14:03 2009  attempting to read 244999 relations
Fri May 08 15:14:07 2009  recovered 244999 relations
Fri May 08 15:14:07 2009  recovered 233319 polynomials
Fri May 08 15:14:07 2009  attempting to build 93166 cycles
Fri May 08 15:14:07 2009  found 93166 cycles in 5 passes
Fri May 08 15:14:07 2009  distribution of cycle lengths:
Fri May 08 15:14:07 2009     length 1 : 22156
Fri May 08 15:14:07 2009     length 2 : 15953
Fri May 08 15:14:07 2009     length 3 : 15490
Fri May 08 15:14:07 2009     length 4 : 12846
Fri May 08 15:14:07 2009     length 5 : 9851
Fri May 08 15:14:07 2009     length 6 : 6586
Fri May 08 15:14:07 2009     length 7 : 4342
Fri May 08 15:14:07 2009     length 9+: 5942
Fri May 08 15:14:07 2009  largest cycle: 21 relations
Fri May 08 15:14:08 2009  matrix is 92941 x 93166 (25.1 MB) with weight 6214628 (66.70/col)
Fri May 08 15:14:08 2009  sparse part has weight 6214628 (66.70/col)
Fri May 08 15:14:10 2009  filtering completed in 3 passes
Fri May 08 15:14:10 2009  matrix is 89101 x 89165 (24.2 MB) with weight 5980570 (67.07/col)
Fri May 08 15:14:10 2009  sparse part has weight 5980570 (67.07/col)
Fri May 08 15:14:10 2009  saving the first 48 matrix rows for later
Fri May 08 15:14:10 2009  matrix is 89053 x 89165 (14.4 MB) with weight 4603797 (51.63/col)
Fri May 08 15:14:10 2009  sparse part has weight 3252535 (36.48/col)
Fri May 08 15:14:10 2009  matrix includes 64 packed rows
Fri May 08 15:14:10 2009  using block size 35666 for processor cache size 1024 kB
Fri May 08 15:14:10 2009  commencing Lanczos iteration
Fri May 08 15:14:10 2009  memory use: 14.3 MB
Fri May 08 15:15:05 2009  lanczos halted after 1410 iterations (dim = 89052)
Fri May 08 15:15:06 2009  recovered 17 nontrivial dependencies
Fri May 08 15:15:06 2009  prp45 factor: 177339214346923928023382818463973318947220121
Fri May 08 15:15:06 2009  prp54 factor: 502944882564508401354967688113709310226342169790528803
Fri May 08 15:15:06 2009  elapsed time 07:14:20

May 8, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / May 8, 2009

(8·10¹⁹⁹+1)/9 = (8)₁₉₈9_<199> = 3³ · 141442169327_<12> · C187

C187 = P45 · P70 · P73

P45 = 278473795189238042105936853934504027567029947_<45>

P70 = 1121240111371370740629796346623166506341482028979326158193334831378901_<70>

P73 = 7454557093327744248147966603565393081246214460774357627670416990333845203_<73>

Number: 88889_199
N=2327581007576077147015288016795181679544665102324936432988127419120440012555007949741851791245503580514745708551006880414182023517427243632126415766287037827987344845272029386659222209141
  ( 187 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=278473795189238042105936853934504027567029947
 r2=1121240111371370740629796346623166506341482028979326158193334831378901
 r3=7454557093327744248147966603565393081246214460774357627670416990333845203
Version: 
Total time: 290.34 hours.
Scaled time: 691.87 units (timescale=2.383).
Factorization parameters were as follows:
n: 2327581007576077147015288016795181679544665102324936432988127419120440012555007949741851791245503580514745708551006880414182023517427243632126415766287037827987344845272029386659222209141
m: 10000000000000000000000000000000000000000
deg: 5
c5: 4
c0: 5
skew: 1.05
type: snfs
lss: 1
rlim: 17000000
alim: 17000000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 17000000/17000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [8500000, 14600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 36830304
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3039811 x 3040058
Total sieving time: 247.85 hours.
Total relation processing time: 11.88 hours.
Matrix solve time: 25.60 hours.
Time per square root: 5.01 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,17000000,17000000,29,29,56,56,2.6,2.6,100000
total time: 290.34 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673793)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Calibrating delay using timer specific routine.. 5344.61 BogoMIPS (lpj=2672305)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341)

May 7, 2009 (9th)

By Sinkiti Sibata / Msieve / May 7, 2009

(55·10¹²⁰+53)/9 = 6(1)₁₁₉7_<121> = 3 · 107 · 443 · 590634444379578817_<18> · C98

C98 = P30 · P69

P30 = 680042510639859177559807028099_<30>

P69 = 106993301551788122124887302268157248361593191920096227220300069639133_<69>

Thu May 07 15:09:38 2009  Msieve v. 1.41
Thu May 07 15:09:38 2009  random seeds: 88acf240 678bbede
Thu May 07 15:09:38 2009  factoring 72759993408925535493330467370978862283625781683526187157727925722177408230466738121226784120998167 (98 digits)
Thu May 07 15:09:39 2009  searching for 15-digit factors
Thu May 07 15:09:41 2009  commencing quadratic sieve (98-digit input)
Thu May 07 15:09:41 2009  using multiplier of 3
Thu May 07 15:09:41 2009  using 32kb Intel Core sieve core
Thu May 07 15:09:41 2009  sieve interval: 36 blocks of size 32768
Thu May 07 15:09:41 2009  processing polynomials in batches of 6
Thu May 07 15:09:41 2009  using a sieve bound of 2537681 (92941 primes)
Thu May 07 15:09:41 2009  using large prime bound of 380652150 (28 bits)
Thu May 07 15:09:41 2009  using double large prime bound of 2785806185644350 (43-52 bits)
Thu May 07 15:09:41 2009  using trial factoring cutoff of 52 bits
Thu May 07 15:09:41 2009  polynomial 'A' values have 13 factors
Thu May 07 23:39:27 2009  93118 relations (21874 full + 71244 combined from 1408120 partial), need 93037
Thu May 07 23:39:29 2009  begin with 1429994 relations
Thu May 07 23:39:31 2009  reduce to 246943 relations in 12 passes
Thu May 07 23:39:31 2009  attempting to read 246943 relations
Thu May 07 23:39:35 2009  recovered 246943 relations
Thu May 07 23:39:35 2009  recovered 236821 polynomials
Thu May 07 23:39:35 2009  attempting to build 93118 cycles
Thu May 07 23:39:35 2009  found 93118 cycles in 6 passes
Thu May 07 23:39:35 2009  distribution of cycle lengths:
Thu May 07 23:39:35 2009     length 1 : 21874
Thu May 07 23:39:35 2009     length 2 : 15710
Thu May 07 23:39:35 2009     length 3 : 15751
Thu May 07 23:39:35 2009     length 4 : 12687
Thu May 07 23:39:35 2009     length 5 : 9741
Thu May 07 23:39:35 2009     length 6 : 6695
Thu May 07 23:39:35 2009     length 7 : 4566
Thu May 07 23:39:35 2009     length 9+: 6094
Thu May 07 23:39:35 2009  largest cycle: 20 relations
Thu May 07 23:39:36 2009  matrix is 92941 x 93118 (25.5 MB) with weight 6322870 (67.90/col)
Thu May 07 23:39:36 2009  sparse part has weight 6322870 (67.90/col)
Thu May 07 23:39:37 2009  filtering completed in 3 passes
Thu May 07 23:39:37 2009  matrix is 89226 x 89290 (24.6 MB) with weight 6097753 (68.29/col)
Thu May 07 23:39:37 2009  sparse part has weight 6097753 (68.29/col)
Thu May 07 23:39:37 2009  saving the first 48 matrix rows for later
Thu May 07 23:39:37 2009  matrix is 89178 x 89290 (15.2 MB) with weight 4825176 (54.04/col)
Thu May 07 23:39:37 2009  sparse part has weight 3447920 (38.61/col)
Thu May 07 23:39:37 2009  matrix includes 64 packed rows
Thu May 07 23:39:38 2009  using block size 35716 for processor cache size 1024 kB
Thu May 07 23:39:38 2009  commencing Lanczos iteration
Thu May 07 23:39:38 2009  memory use: 14.8 MB
Thu May 07 23:40:33 2009  lanczos halted after 1411 iterations (dim = 89178)
Thu May 07 23:40:33 2009  recovered 18 nontrivial dependencies
Thu May 07 23:40:34 2009  prp30 factor: 680042510639859177559807028099
Thu May 07 23:40:34 2009  prp69 factor: 106993301551788122124887302268157248361593191920096227220300069639133
Thu May 07 23:40:34 2009  elapsed time 08:30:56

May 7, 2009 (8th)

By Andreas Tete / GMP-ECM 6.2.3 / May 7, 2009

(55·10¹⁵⁶+53)/9 = 6(1)₁₅₅7_<157> = 3 · 25903 · 76037963429_<11> · 13692005771750295853_<20> · C122

C122 = P37 · P86

P37 = 4836686945562780478646372773363953343_<37>

P86 = 15617205724583581065383112857335668159768622684480608510969886639257988319179734009343_<86>

Using B1=3000000, B2=5706890290 , polynomial Dickson(6) , sigma=4078726757
********** Factor found in step 2: 4836686945562780478646372773363953343
Found probable prime factor of 37 digits: 4836686945562780478646372773363953343
Probable prime cofactor 15617205724583581065383112857335668159768622684480608510969886639257988319179734009343 has 86 digits

May 7, 2009 (7th)

By Erik Branger / GGNFS, Msieve / May 7, 2009

(55·10¹³⁴+53)/9 = 6(1)₁₃₃7_<135> = 19 · 229 · 1201 · 36263 · 31930240690605613_<17> · C108

C108 = P45 · P63

P45 = 945452696870843572549900286629024050147201761_<45>

P63 = 106827327092084961430164948683844062392323374336348354303704313_<63>

Number: 61117_134
N=101000184498715458216033484984919119474059656317034752219990764224088721060222146196857219028684853696895193
  ( 108 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=945452696870843572549900286629024050147201761 (pp45)
 r2=106827327092084961430164948683844062392323374336348354303704313 (pp63)
Version: Msieve v. 1.41
Total time: 4.41 hours.
Scaled time: 4.17 units (timescale=0.946).
Factorization parameters were as follows:
n: 101000184498715458216033484984919119474059656317034752219990764224088721060222146196857219028684853696895193
m: 1000000000000000000000000000
deg: 5
c5: 11
c0: 106
skew: 1.57
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1175001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 192081 x 192316
Total sieving time: 4.22 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 4.41 hours.
 --------- CPU info (if available) ----------

(55·10¹²³+53)/9 = 6(1)₁₂₂7_<124> = 3³ · 5879 · C119

C119 = P40 · P80

P40 = 1835681480017495887981204792297553833979_<40>

P80 = 20972762040377847630780707795788880682323092070234749979411237951180413489474931_<80>

Number: 61117_123
N=38499310862335564193400938123207594584056945380677685869422937329421803349720040011283798020015441723593147682656480449
  ( 119 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=1835681480017495887981204792297553833979 (pp40)
 r2=20972762040377847630780707795788880682323092070234749979411237951180413489474931 (pp80)
Version: Msieve v. 1.41
Total time: 6.79 hours.
Scaled time: 5.28 units (timescale=0.777).
Factorization parameters were as follows:
n: 38499310862335564193400938123207594584056945380677685869422937329421803349720040011283798020015441723593147682656480449
m: 5000000000000000000000000
deg: 5
c5: 88
c0: 265
skew: 1.25
type: snfs
lss: 1
rlim: 860000
alim: 860000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 860000/860000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [430000, 780001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 119980 x 120217
Total sieving time: 6.64 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,125.000,5,0,0,0,0,0,0,0,0,860000,860000,26,26,46,46,2.3,2.3,50000
total time: 6.79 hours.
 --------- CPU info (if available) ----------

May 7, 2009 (6th)

By Dmitry Domanov / GMP-ECM 6.2.3

(8·10¹⁷³-17)/9 = (8)₁₇₂7_<173> = 3 · 19 · 238591 · 266183 · 6010441682603_<13> · C148

C148 = P33 · C115

P33 = 812262305277809501754934760781703_<33>

C115 = [5029624489648056247300436114909387948363823244892596172024214674079949553164223403365426542863909717715506862448483_<115>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3181479570
Step 1 took 61625ms
Step 2 took 19516ms
********** Factor found in step 2: 812262305277809501754934760781703
Found probable prime factor of 33 digits: 812262305277809501754934760781703
Composite cofactor 5029624489648056247300436114909387948363823244892596172024214674079949553164223403365426542863909717715506862448483 has 115 digits

May 7, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / May 7, 2009

2·10¹⁹¹+3 = 2(0)₁₉₀3_<192> = 2221 · 283112539 · 5806007837521_<13> · 2980061483271130133454822323000539259581_<40> · C128

C128 = P63 · P66

P63 = 182806214988875869300773608643861228898368769920609146878022777_<63>

P66 = 100560756952935629434227230943212354457451323996998349267619421881_<66>

Number: 20003_191
N=18383131354982444551956076518958438866176346336034655261991448351404481492241607264551622466419738184569706208252244605090183537
  ( 128 digits)
Divisors found:
 r1=182806214988875869300773608643861228898368769920609146878022777 (pp63)
 r2=100560756952935629434227230943212354457451323996998349267619421881 (pp66)
Version: Msieve-1.40
Total time: 93.02 hours.
Scaled time: 161.39 units (timescale=1.735).
Factorization parameters were as follows:
# Murphy_E = 1.111965e-10, selected by Jeff Gilchrist
n: 18383131354982444551956076518958438866176346336034655261991448351404481492241607264551622466419738184569706208252244605090183537
Y0: -3310983359586160356951906
Y1: 106136767483589
c0: 1100376690755724515179049294969755
c1: 9384585766997979918145923803
c2: 12785932205895746598243
c3: -47932562596126499
c4: -24806057326
c5: 46200
skew: 654762.88
type: gnfs
# selected mechanically
rlim: 8300000
alim: 8300000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 8300000/8300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved algebraic special-q in [4150000, 8350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1229067 x 1229315
Total sieving time: 89.81 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 2.09 hours.
Time per square root: 0.83 hours.
Prototype def-par.txt line would be:
gnfs,127,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8300000,8300000,28,28,53,53,2.5,2.5,100000
total time: 93.02 hours.
 --------- CPU info (if available) ----------

(55·10¹¹⁰+53)/9 = 6(1)₁₀₉7_<111> = 17 · 953 · 25471 · C103

C103 = P35 · P68

P35 = 56266204953522059398999379228885593_<35>

P68 = 26319930513343521868798396749101678517827230791954269804012507624339_<68>

Number: 61117_110
N=1480922604626245669870149709177536326917729699905447588314159170033824910432676717318422872494853248027
  ( 103 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=56266204953522059398999379228885593 (pp35)
 r2=26319930513343521868798396749101678517827230791954269804012507624339 (pp68)
Version: Msieve-1.40
Total time: 0.78 hours.
Scaled time: 0.94 units (timescale=1.198).
Factorization parameters were as follows:
n: 1480922604626245669870149709177536326917729699905447588314159170033824910432676717318422872494853248027
m: 10000000000000000000000
deg: 5
c5: 55
c0: 53
skew: 0.99
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [255000, 405001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 55362 x 55588
Total sieving time: 0.76 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.78 hours.
 --------- CPU info (if available) ----------

(55·10¹¹³+53)/9 = 6(1)₁₁₂7_<114> = 13 · 4255561 · C107

C107 = P52 · P55

P52 = 3415409239210053907032628591575013137983727665864557_<52>

P55 = 3234277344906079783535156666366066863128489133806494717_<55>

Number: 61117_113
N=11046380725959987072681732680731637625922539239490870544919588042222167311667849904759210018845587458045369
  ( 107 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=3415409239210053907032628591575013137983727665864557 (pp52)
 r2=3234277344906079783535156666366066863128489133806494717 (pp55)
Version: Msieve-1.40
Total time: 0.99 hours.
Scaled time: 1.18 units (timescale=1.198).
Factorization parameters were as follows:
n: 11046380725959987072681732680731637625922539239490870544919588042222167311667849904759210018845587458045369
m: 50000000000000000000000
deg: 5
c5: 88
c0: 265
skew: 1.25
type: snfs
lss: 1
rlim: 590000
alim: 590000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 590000/590000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [295000, 495001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 69333 x 69581
Total sieving time: 0.96 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115.000,5,0,0,0,0,0,0,0,0,590000,590000,25,25,45,45,2.2,2.2,50000
total time: 0.99 hours.
 --------- CPU info (if available) ----------

(55·10¹¹⁹+53)/9 = 6(1)₁₁₈7_<120> = 13 · 47 · 199 · 182050237 · C107

C107 = P53 · P55

P53 = 22563214542059659537989039551101003220252654467441801_<53>

P55 = 1223583668904998755960382454300969162560941781733059269_<55>

Number: 61117_119
N=27607980831663979583355016734159768783013700914780195183979590633553478110498617963490229246000051941103469
  ( 107 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=22563214542059659537989039551101003220252654467441801 (pp53)
 r2=1223583668904998755960382454300969162560941781733059269 (pp55)
Version: Msieve-1.40
Total time: 1.33 hours.
Scaled time: 1.60 units (timescale=1.203).
Factorization parameters were as follows:
n: 27607980831663979583355016734159768783013700914780195183979590633553478110498617963490229246000051941103469
m: 1000000000000000000000000
deg: 5
c5: 11
c0: 106
skew: 1.57
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 615001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 73911 x 74139
Total sieving time: 1.29 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.33 hours.
 --------- CPU info (if available) ----------

(55·10¹²⁸+53)/9 = 6(1)₁₂₇7_<129> = 773231 · 179130185803892047_<18> · C106

C106 = P29 · P78

P29 = 28387544830117222306493512799_<29>

P78 = 155422651376388126156321417359485103331166545348719964250814055488446526704019_<78>

Number: 61117_128
N=4412067483562898136417947180989349016200511211292870274945580118260308530454298344442350244203342661239181
  ( 106 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=28387544830117222306493512799 (pp29)
 r2=155422651376388126156321417359485103331166545348719964250814055488446526704019 (pp78)
Version: Msieve-1.40
Total time: 2.97 hours.
Scaled time: 3.57 units (timescale=1.200).
Factorization parameters were as follows:
n: 4412067483562898136417947180989349016200511211292870274945580118260308530454298344442350244203342661239181
m: 50000000000000000000000000
deg: 5
c5: 88
c0: 265
skew: 1.25
type: snfs
lss: 1
rlim: 1040000
alim: 1040000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1040000/1040000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [520000, 1020001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 153557 x 153791
Total sieving time: 2.86 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,130.000,5,0,0,0,0,0,0,0,0,1040000,1040000,26,26,47,47,2.3,2.3,50000
total time: 2.97 hours.
 --------- CPU info (if available) ----------

May 7, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.3, Msieve / May 7, 2009

(55·10¹²⁵+53)/9 = 6(1)₁₂₄7_<126> = 13 · 27327743 · 35592483890950561_<17> · C101

C101 = P32 · P69

P32 = 49438205682481110643925421520349_<32>

P69 = 977579455083906759296235116370906001403373620855265425236407586719467_<69>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=951753314
Step 1 took 7056ms
Step 2 took 7421ms
********** Factor found in step 2: 49438205682481110643925421520349
Found probable prime factor of 32 digits: 49438205682481110643925421520349
Probable prime cofactor has 69 digits

(55·10¹⁶¹+53)/9 = 6(1)₁₆₀7_<162> = 13 · 97 · 113 · C157

C157 = P26 · C131

P26 = 76625767327269088745587943_<26>

C131 = [55969549779291807578331999389155335060385717795888554665336739968324394289490377698401886225152663948359880548781879323856843476583_<131>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=544097540
Step 1 took 8980ms
Step 2 took 7861ms
********** Factor found in step 2: 76625767327269088745587943
Found probable prime factor of 26 digits: 76625767327269088745587943
Composite cofactor has 131 digits

(55·10¹⁰³+53)/9 = 6(1)₁₀₂7_<104> = 1667 · C101

C101 = P37 · P64

P37 = 7805333240474970433386479163342277351_<37>

P64 = 4696703352729105271957469089746813401400588494288776527114451001_<64>

SNFS difficulty: 104 digits.
Divisors found:
 r1=7805333240474970433386479163342277351 (pp37)
 r2=4696703352729105271957469089746813401400588494288776527114451001 (pp64)
Version: Msieve v. 1.41
Total time: 0.37 hours.
Scaled time: 1.00 units (timescale=2.718).
Factorization parameters were as follows:
n: 36659334799706725321602346197427181230420582550156635339598746917283210024661734319802706125441578351
m: 50000000000000000000000000
deg: 4
c4: 88
c0: 53
skew: 0.88
type: snfs
lss: 1
rlim: 390000
alim: 390000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 390000/390000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [195000, 315001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 35868 x 36095
Total sieving time: 0.35 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,104.000,4,0,0,0,0,0,0,0,0,390000,390000,25,25,44,44,2.2,2.2,10000
total time: 0.37 hours.

(55·10¹⁰⁹+53)/9 = 6(1)₁₀₈7_<110> = C110

C110 = P43 · P68

P43 = 2001279481780336558695312744101134869291031_<43>

P68 = 30536020414673275723489592051637855902564714744776865441185463166907_<68>

SNFS difficulty: 111 digits.
Divisors found:
 r1=2001279481780336558695312744101134869291031 (pp43)
 r2=30536020414673275723489592051637855902564714744776865441185463166907 (pp68)
Version: Msieve v. 1.41
Total time: 0.43 hours.
Scaled time: 1.17 units (timescale=2.728).
Factorization parameters were as follows:
n: 61111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
m: 10000000000000000000000
deg: 5
c5: 11
c0: 106
skew: 1.57
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [250000, 400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 47091 x 47322
Total sieving time: 0.40 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 0.43 hours.

(55·10¹¹²+53)/9 = 6(1)₁₁₁7_<113> = 7 · 1567 · C109

C109 = P39 · P70

P39 = 570070518907964516234430912852482459059_<39>

P70 = 9772924899942846008737812129553836846959336000821691794249026431285527_<70>

SNFS difficulty: 115 digits.
Divisors found:
 r1=570070518907964516234430912852482459059 (pp39)
 r2=9772924899942846008737812129553836846959336000821691794249026431285527 (pp70)
Version: Msieve v. 1.36
Total time: 0.40 hours.
Scaled time: 1.10 units (timescale=2.718).
Factorization parameters were as follows:
n: 5571256368958985423567427396399955429949048328116611460580828800356560407613375067108315353369597147516739093
m: 50000000000000000000000
deg: 5
c5: 44
c0: 1325
skew: 1.98
type: snfs
lss: 1
rlim: 580000
alim: 580000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 580000/580000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [290000, 290000)
Primes: rational ideals filtering, algebraic ideals filtering,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 63814 x 64046
Total sieving time: 0.40 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,115.000,5,0,0,0,0,0,0,0,0,580000,580000,25,25,45,45,2.2,2.2,50000
total time: 0.40 hours.

May 7, 2009 (3rd)

By matsui / GGNFS / May 7, 2009

9·10¹⁸¹+7 = 9(0)₁₈₀7_<182> = 79 · 257 · 244637 · C173

C173 = P52 · P121

P52 = 8512657957698933206364996840866746830424447731789547_<52>

P121 = 2128604465477319399779522456754361848962080507428346805103942531536208640072972366805607636173490224009642228179113256471_<121>

N=18120081741838987135702528960878175958142624061743400579806899044392007938948997541016521900397586625693782117566794488427863577386037399597852690665766112563271351607908637
  ( 173 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=8512657957698933206364996840866746830424447731789547 (pp52)
 r2=2128604465477319399779522456754361848962080507428346805103942531536208640072972366805607636173490224009642228179113256471 (pp121)
Version: GGNFS-0.77.1-20060722-nocona

May 7, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 7, 2009

(14·10¹⁶⁷-11)/3 = 4(6)₁₆₆3_<168> = 19011604170792844575925477496114081_<35> · C134

C134 = P47 · P87

P47 = 93578664829015994605866131061111227599540334869_<47>

P87 = 262307780677246760482479379009707031071807635692941044199126071101861313229393119295467_<87>

Number: n
N=24546411890039112735283532246090593965242266454661597228757806133149530566680832089355587701794240785601818656426814464057750533738823
  ( 134 digits)
SNFS difficulty: 168 digits.
Divisors found:

Thu May 07 01:23:09 2009  prp47 factor: 93578664829015994605866131061111227599540334869
Thu May 07 01:23:09 2009  prp87 factor: 262307780677246760482479379009707031071807635692941044199126071101861313229393119295467
Thu May 07 01:23:09 2009  elapsed time 01:28:44 (Msieve 1.39 - dependency 5)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 54.29 hours.
Scaled time: 142.63 units (timescale=2.627).
Factorization parameters were as follows:
name: KA_4_6_166_3
n: 24546411890039112735283532246090593965242266454661597228757806133149530566680832089355587701794240785601818656426814464057750533738823
m: 2000000000000000000000000000000000
deg: 5
c5: 175
c0: -44
skew: 0.76
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2250000, 5450801)
Primes: RFBsize:315948, AFBsize:315477, largePrimes:17159269 encountered
Relations: rels:17269830, finalFF:509829
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2218141 hash collisions in 19121788 relations
Msieve: matrix is 780536 x 780784 (206.2 MB)

Total sieving time: 53.44 hours.
Total relation processing time: 0.85 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000
total time: 54.29 hours.
 --------- CPU info (if available) ----------

(49·10¹⁹⁷+23)/9 = 5(4)₁₉₆7_<198> = 71 · C196

C196 = P39 · P158

P39 = 471125349006422505303273967001963468167_<39>

P158 = 16276414818403346757892574329473798763642640177996620325409012137632722283621382376422821727629443629996696237888324842707436215660648855822906485305396297871_<158>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 7668231611893583724569640062597809076682316118935837245696400625978090766823161189358372456964006259780907668231611893583724569640062597809076682316118935837245696400625978090766823161189358372457 (196 digits)
Using B1=3454000, B2=5707365310, polynomial Dickson(6), sigma=884789642
Step 1 took 62282ms
Step 2 took 19812ms
********** Factor found in step 2: 471125349006422505303273967001963468167
Found probable prime factor of 39 digits: 471125349006422505303273967001963468167
Probable prime cofactor 16276414818403346757892574329473798763642640177996620325409012137632722283621382376422821727629443629996696237888324842707436215660648855822906485305396297871 has 158 digits

May 7, 2009

Factorizations of 611...117 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 6, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / May 6, 2009

8·10¹⁹⁶+3 = 8(0)₁₉₅3_<197> = 7² · 11 · C195

C195 = P55 · P140

P55 = 3621665081282620076674432630274353389234788872072180469_<55>

P140 = 40981979900057019772289486633568158426513623345700595433142245023700808306621864377405722307822200045704430796237062488553288170254983146933_<140>

Number: n
N=148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423005565862708719851577
  ( 195 digits)
SNFS difficulty: 197 digits.
Divisors found:

Wed May  6 22:18:43 2009  prp55 factor: 3621665081282620076674432630274353389234788872072180469
Wed May  6 22:18:43 2009  prp140 factor: 40981979900057019772289486633568158426513623345700595433142245023700808306621864377405722307822200045704430796237062488553288170254983146933
Wed May  6 22:18:43 2009  elapsed time 03:51:22 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 38.35 hours.
Scaled time: 77.31 units (timescale=2.016).
Factorization parameters were as follows:
name: KA_8_0_195_3
n: 148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423005565862708719851576994434137291280148423005565862708719851577
m: 2000000000000000000000000000000000000000
deg: 5
c5: 5
c0: 6
skew: 1.04
type: snfs
lss: 1
rlim: 13500000
alim: 13500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 13500000/13500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [6750000, 17349990)
Primes: RFBsize:879640, AFBsize:878569, largePrimes:22008942 encountered
Relations: rels:24644624, finalFF:2697963
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2853378 hash collisions in 26648513 relations
Msieve: matrix is 1672355 x 1672603 (447.0 MB)

Total sieving time: 37.86 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,13500000,13500000,28,28,56,56,2.4,2.4,100000
total time: 38.35 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830496)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830453)
Total of 4 processors activated (22643.70 BogoMIPS).

May 6, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / May 6, 2009

(44·10¹⁷⁰-53)/9 = 4(8)₁₆₉3_<171> = 3² · 7 · 9437 · 15530941453_<11> · C155

C155 = P37 · P54 · P65

P37 = 2292642669168448055304163075564111519_<37>

P54 = 309383401453904318103572359005677794938603540643389041_<54>

P65 = 74645649139320830256619174883931685521648798111908759101775184539_<65>

Number: 48883_170
N=52946576002580636960528842851208189219741647489968588151776737420461266890367768097054339727229323615058818228881279646734337015730796232832869667532043381
  ( 155 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=2292642669168448055304163075564111519 (pp37)
 r2=309383401453904318103572359005677794938603540643389041 (pp54)
 r3=74645649139320830256619174883931685521648798111908759101775184539 (pp65)
Version: Msieve-1.40
Total time: 56.02 hours.
Scaled time: 97.42 units (timescale=1.739).
Factorization parameters were as follows:
n: 52946576002580636960528842851208189219741647489968588151776737420461266890367768097054339727229323615058818228881279646734337015730796232832869667532043381
m: 10000000000000000000000000000000000
deg: 5
c5: 44
c0: -53
skew: 1.04
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 948199 x 948447
Total sieving time: 54.23 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.15 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 56.02 hours.
 --------- CPU info (if available) ----------

(73·10¹⁹¹-1)/9 = 8(1)₁₉₁_<192> = 7² · 2957 · 28391329 · 81902647 · 1197538717_<10> · 4210320749_<10> · 281150019363827276479091879_<27> · C127

C127 = P43 · P84

P43 = 8296219599240900750125751408687469456539629_<43>

P84 = 204703931305234648694421978445780610066516435471243580233881603596753881664430161943_<84>

Number: 81111_191
N=1698268766936150674397664693080209666761726866084951569803456920236110045824863664598013300791554963893047144133640896867139147
  ( 127 digits)
Divisors found:
 r1=8296219599240900750125751408687469456539629 (pp43)
 r2=204703931305234648694421978445780610066516435471243580233881603596753881664430161943 (pp84)
Version: Msieve-1.40
Total time: 82.49 hours.
Scaled time: 98.90 units (timescale=1.199).
Factorization parameters were as follows:
# Murphy_E = 1.198987e-10, selected by Jeff Gilchrist
n: 1698268766936150674397664693080209666761726866084951569803456920236110045824863664598013300791554963893047144133640896867139147
Y0: -2261958667367251197875751
Y1: 60001258322377
c0: 2341962305287791279333259678400
c1: 122080630732525840746583134
c2: -86882576737734041865
c3: -5644408174244182
c4: 9837347148
c5: 28680
skew: 232490.02
type: gnfs
# selected mechanically
rlim: 7700000
alim: 7700000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7700000/7700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved algebraic special-q in [3850000, 7750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1177977 x 1178225
Total sieving time: 80.03 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 1.90 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
gnfs,126,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,7700000,7700000,28,28,53,53,2.5,2.5,100000
total time: 82.49 hours.
 --------- CPU info (if available) ----------

May 6, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / May 6, 2009

(31·10¹⁷⁰+23)/9 = 3(4)₁₆₉7_<171> = 17 · 67 · 88327 · 9440546194507_<13> · C150

C150 = P73 · P78

P73 = 1552639791119087352981288123002496139672359803957855921458315665885581003_<73>

P78 = 233579189183869137992954603034611668015422286381180706109516775369226985993419_<78>

Number: 34447_170
N=362664343504208366336153695212934878904723612806464270452574090561920145914063070976459250001943725687749819858052981635954436582224244199353949419257
  ( 150 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=1552639791119087352981288123002496139672359803957855921458315665885581003
 r2=233579189183869137992954603034611668015422286381180706109516775369226985993419
Version: 
Total time: 117.52 hours.
Scaled time: 92.25 units (timescale=0.785).
Factorization parameters were as follows:
n: 362664343504208366336153695212934878904723612806464270452574090561920145914063070976459250001943725687749819858052981635954436582224244199353949419257
m: 10000000000000000000000000000000000
deg: 5
c5: 31
c0: 23
skew: 0.94
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 942515 x 942763
Total sieving time: 117.52 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 117.52 hours.
 --------- CPU info (if available) ----------

May 6, 2009

By Dmitry Domanov / GMP-ECM 6.2.3 / May 6, 2009

(10²⁰⁰+11)/3 = (3)₁₉₉7_<200> = 37 · 53 · 89 · 191 · 7901 · 10433 · 2293803373_<10> · C175

C175 = P35 · P141

P35 = 24305944786595346457197985558606247_<35>

P141 = 217579419882633107192464536745298503242371606246427979750790355132326139358855442920849549924732845182258526980489528858407285267069566255721_<141>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2283099834
Step 1 took 80313ms
Step 2 took 24562ms
********** Factor found in step 2: 24305944786595346457197985558606247
Found probable prime factor of 35 digits: 24305944786595346457197985558606247
Probable prime cofactor 217579419882633107192464536745298503242371606246427979750790355132326139358855442920849549924732845182258526980489528858407285267069566255721 has 141 digits

May 5, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / May 5, 2009

(47·10¹⁹⁵+7)/9 = 5(2)₁₉₄3_<196> = 3² · C195

C195 = P44 · P151

P44 = 88041672141117563537626490623780021076406241_<44>

P151 = 6590593970661965054169564166971283042690684645871625375519446864980216578639928402046295639701137885292568800820435274199357754149064405001068545418167_<151>

Number: n
N=580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247
  ( 195 digits)
SNFS difficulty: 196 digits.
Divisors found:

Tue May  5 01:08:55 2009  prp44 factor: 88041672141117563537626490623780021076406241
Tue May  5 01:08:55 2009  prp151 factor: 6590593970661965054169564166971283042690684645871625375519446864980216578639928402046295639701137885292568800820435274199357754149064405001068545418167
Tue May  5 01:08:55 2009  elapsed time 04:52:50 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 50.12 hours.
Scaled time: 82.75 units (timescale=1.651).
Factorization parameters were as follows:
name: KA_5_2_194_3
n: 580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247
m: 1000000000000000000000000000000000000000
deg: 5
c5: 47
c0: 7
skew: 0.68
type: snfs
lss: 1
rlim: 13000000
alim: 13000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 13000000/13000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [6500000, 17049990)
Primes: RFBsize:849252, AFBsize:848943, largePrimes:22498256 encountered
Relations: rels:25266265, finalFF:1943483
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 3587386 hash collisions in 28065747 relations
Msieve: matrix is 1867365 x 1867613 (493.1 MB)

Total sieving time: 49.56 hours.
Total relation processing time: 0.56 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,56,56,2.5,2.5,100000
total time: 50.12 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830496)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830453)
Total of 4 processors activated (22643.70 BogoMIPS).

(55·10¹⁶⁸+17)/9 = 6(1)₁₆₇3_<169> = 109 · 663028897 · 185562242057_<12> · C147

C147 = P62 · P85

P62 = 96341799290463865188662743214896995784016161192590672095139619_<62>

P85 = 4729953389395374818079029796745396474394029557670207973418519714975101293655196577207_<85>

Number: n
N=455692220094378475899028019297894009795617089865204368694899943284127257853245517194919666672096984551704299608853985767015618988158532829578064133
  ( 147 digits)
SNFS difficulty: 170 digits.
Divisors found:

Tue May 05 13:44:14 2009  prp62 factor: 96341799290463865188662743214896995784016161192590672095139619
Tue May 05 13:44:14 2009  prp85 factor: 4729953389395374818079029796745396474394029557670207973418519714975101293655196577207
Tue May 05 13:44:14 2009  elapsed time 01:23:46 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 54.51 hours.
Scaled time: 144.41 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_6_1_167_3
n: 455692220094378475899028019297894009795617089865204368694899943284127257853245517194919666672096984551704299608853985767015618988158532829578064133
m: 5000000000000000000000000000000000
deg: 5
c5: 88
c0: 85
skew: 0.99
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2450000, 5522809)
Primes: RFBsize:341992, AFBsize:342599, largePrimes:17230416 encountered
Relations: rels:16855884, finalFF:673202
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2033482 hash collisions in 18633936 relations
Msieve: matrix is 876911 x 877159 (232.8 MB)

Total sieving time: 53.25 hours.
Total relation processing time: 1.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,28,28,56,56,2.4,2.4,100000
total time: 54.51 hours.
 --------- CPU info (if available) ----------

(53·10¹⁶³+1)/9 = 5(8)₁₆₂9_<164> = 71 · 125441 · 543667994926069758106471_<24> · C134

C134 = P48 · P86

P48 = 141981755621425466912511299686577381546348961449_<48>

P86 = 85658249428232845412735044023039818341069505361385323720612300437103972695570075959681_<86>

Number: n
N=12161908637278463586191770932142068551815467037940016086673733871817193261682243790326920124709539972049718217444606619034756347337769
  ( 134 digits)
SNFS difficulty: 166 digits.
Divisors found:

Tue May 05 14:56:16 2009  prp48 factor: 141981755621425466912511299686577381546348961449
Tue May 05 14:56:16 2009  prp86 factor: 85658249428232845412735044023039818341069505361385323720612300437103972695570075959681
Tue May 05 14:56:16 2009  elapsed time 01:04:16 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 34.15 hours.
Scaled time: 90.84 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_8_162_9
n: 12161908637278463586191770932142068551815467037940016086673733871817193261682243790326920124709539972049718217444606619034756347337769
m: 1000000000000000000000000000000000
deg: 5
c5: 53
c0: 100
skew: 1.14
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2100000, 4096021)
Primes: RFBsize:296314, AFBsize:295946, largePrimes:14876015 encountered
Relations: rels:13777731, finalFF:487605
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1469947 hash collisions in 15637895 relations
Msieve: matrix is 764135 x 764383 (205.4 MB)

Total sieving time: 33.65 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,56,56,2.4,2.4,100000
total time: 34.15 hours.
 --------- CPU info (if available) ----------

May 5, 2009 (3rd)

By Sinkiti Sibata / Msieve / May 5, 2009

(4·10²⁰³-1)/3 = 1(3)₂₀₃_<204> = 1296951005067479_<16> · 3007224097573595988541199_<25> · 22202898588664747899239883251976133_<35> · C130

C130 = P46 · P84

P46 = 1726411804572458190640150953379052709293364521_<46>

P84 = 891857156466058895139365384393907771800510613597214769971080414959609408393708727761_<84>

Number: 13333_203
N=1539712722915429936027828705221199253961258103511550016874758536693107690174955859182188496690238915491251386488264294882125167481
  ( 130 digits)
Divisors found:
 r1=1726411804572458190640150953379052709293364521 (pp46)
 r2=891857156466058895139365384393907771800510613597214769971080414959609408393708727761 (pp84)
Version: Msieve-1.40
Total time: 195.64 hours.
Scaled time: 384.83 units (timescale=1.967).
Factorization parameters were as follows:
name: 13333_203
# Murphy_E = 8.524581e-11, selected by Jeff Gilchrist
n: 1539712722915429936027828705221199253961258103511550016874758536693107690174955859182188496690238915491251386488264294882125167481
Y0: -7873691196556497306899818
Y1: 169828156742951
c0: -842825461261952705427719662183065
c1: 14038004824796602827276678198
c2: -2692645004606180414079
c3: -56623236251566918
c4: 3837349864
c5: 50880
skew: 687088.58
type: gnfs
# selected mechanically
rlim: 9300000
alim: 9300000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 9300000/9300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved algebraic special-q in [4650000, 9750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1307656 x 1307904
Total sieving time: 195.64 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,129,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,9300000,9300000,28,28,53,53,2.5,2.5,100000
total time: 195.64 hours.
 --------- CPU info (if available) ----------

May 5, 2009 (2nd)

By Andreas Tete / Msieve v1.41 / May 5, 2009

(28·10¹⁹³+17)/9 = 3(1)₁₉₂3_<194> = 3² · 11 · 227 · 17366063534386433_<17> · 424822017456266239_<18> · 5924630108759666362363_<22> · C134

C134 = P50 · P84

P50 = 99382683945977500334658873808598740778689620049967_<50>

P84 = 318694159844854605120879425181906886865805348896942492740283709980063920024563256003_<84>

Mon May 04 17:39:46 2009  
Mon May 04 17:39:46 2009  
Mon May 04 17:39:46 2009  Msieve v. 1.41
Mon May 04 17:39:46 2009  random seeds: 6c343098 f895ee55
Mon May 04 17:39:46 2009  factoring 31672680963290019103108312432868979250603919225165327006653437736262170957787856296821147332483321273817020069534642594806141072701901 (134 digits)
Mon May 04 17:39:48 2009  searching for 15-digit factors
Mon May 04 17:39:50 2009  commencing number field sieve (134-digit input)
Mon May 04 17:39:50 2009  R0: -56411713256521487888728554
Mon May 04 17:39:50 2009  R1:  614927434103333
Mon May 04 17:39:50 2009  A0:  4820545946029657007435914785021859
Mon May 04 17:39:50 2009  A1: -3560072597077147464000211347
Mon May 04 17:39:50 2009  A2: -133972022385765948615479
Mon May 04 17:39:50 2009  A3: -316325078052222669
Mon May 04 17:39:50 2009  A4:  177495376228
Mon May 04 17:39:50 2009  A5:  55440
Mon May 04 17:39:50 2009  skew 909388.56, size 5.929278e-013, alpha -7.937906, combined = 4.367942e-011
Mon May 04 17:39:50 2009  
Mon May 04 17:39:50 2009  commencing relation filtering
Mon May 04 17:39:50 2009  commencing duplicate removal, pass 1
Mon May 04 17:43:08 2009  found 4390910 hash collisions in 17620569 relations
Mon May 04 17:43:51 2009  added 107571 free relations
Mon May 04 17:43:51 2009  commencing duplicate removal, pass 2
Mon May 04 17:45:09 2009  found 4773785 duplicates and 12954354 unique relations
Mon May 04 17:45:09 2009  memory use: 106.6 MB
Mon May 04 17:45:09 2009  reading rational ideals above 11862016
Mon May 04 17:45:09 2009  reading algebraic ideals above 11862016
Mon May 04 17:45:09 2009  commencing singleton removal, pass 1
Mon May 04 17:47:47 2009  relations with 0 large ideals: 378556
Mon May 04 17:47:47 2009  relations with 1 large ideals: 2514711
Mon May 04 17:47:47 2009  relations with 2 large ideals: 5111991
Mon May 04 17:47:47 2009  relations with 3 large ideals: 3647510
Mon May 04 17:47:47 2009  relations with 4 large ideals: 1077514
Mon May 04 17:47:47 2009  relations with 5 large ideals: 122319
Mon May 04 17:47:47 2009  relations with 6 large ideals: 101751
Mon May 04 17:47:47 2009  relations with 7+ large ideals: 2
Mon May 04 17:47:47 2009  12954354 relations and about 12248867 large ideals
Mon May 04 17:47:47 2009  commencing singleton removal, pass 2
Mon May 04 17:50:41 2009  found 6014564 singletons
Mon May 04 17:50:41 2009  current dataset: 6939790 relations and about 5014552 large ideals
Mon May 04 17:50:41 2009  commencing singleton removal, pass 3
Mon May 04 17:52:47 2009  found 1113533 singletons
Mon May 04 17:52:47 2009  current dataset: 5826257 relations and about 3839423 large ideals
Mon May 04 17:52:47 2009  commencing singleton removal, pass 4
Mon May 04 17:54:34 2009  found 260096 singletons
Mon May 04 17:54:34 2009  current dataset: 5566161 relations and about 3575226 large ideals
Mon May 04 17:54:35 2009  commencing singleton removal, final pass
Mon May 04 17:56:32 2009  memory use: 84.4 MB
Mon May 04 17:56:32 2009  commencing in-memory singleton removal
Mon May 04 17:56:32 2009  begin with 5566161 relations and 3905421 unique ideals
Mon May 04 17:56:37 2009  reduce to 4752218 relations and 3071387 ideals in 12 passes
Mon May 04 17:56:37 2009  max relations containing the same ideal: 22
Mon May 04 17:56:39 2009  reading rational ideals above 720000
Mon May 04 17:56:39 2009  reading algebraic ideals above 720000
Mon May 04 17:56:39 2009  commencing singleton removal, final pass
Mon May 04 17:58:43 2009  keeping 4547511 ideals with weight <= 20, new excess is 360797
Mon May 04 17:58:49 2009  memory use: 130.8 MB
Mon May 04 17:58:49 2009  commencing in-memory singleton removal
Mon May 04 17:58:50 2009  begin with 4801193 relations and 4547511 unique ideals
Mon May 04 17:58:58 2009  reduce to 4673110 relations and 4180471 ideals in 12 passes
Mon May 04 17:58:58 2009  max relations containing the same ideal: 20
Mon May 04 17:59:01 2009  removing 323163 relations and 286106 ideals in 37057 cliques
Mon May 04 17:59:01 2009  commencing in-memory singleton removal
Mon May 04 17:59:02 2009  begin with 4349947 relations and 4180471 unique ideals
Mon May 04 17:59:06 2009  reduce to 4337433 relations and 3881733 ideals in 7 passes
Mon May 04 17:59:06 2009  max relations containing the same ideal: 20
Mon May 04 17:59:09 2009  removing 240023 relations and 202966 ideals in 37057 cliques
Mon May 04 17:59:10 2009  commencing in-memory singleton removal
Mon May 04 17:59:10 2009  begin with 4097410 relations and 3881733 unique ideals
Mon May 04 17:59:14 2009  reduce to 4089606 relations and 3670897 ideals in 7 passes
Mon May 04 17:59:14 2009  max relations containing the same ideal: 20
Mon May 04 17:59:18 2009  relations with 0 large ideals: 7573
Mon May 04 17:59:18 2009  relations with 1 large ideals: 79833
Mon May 04 17:59:18 2009  relations with 2 large ideals: 375915
Mon May 04 17:59:18 2009  relations with 3 large ideals: 925180
Mon May 04 17:59:18 2009  relations with 4 large ideals: 1267395
Mon May 04 17:59:18 2009  relations with 5 large ideals: 955897
Mon May 04 17:59:18 2009  relations with 6 large ideals: 387327
Mon May 04 17:59:18 2009  relations with 7+ large ideals: 90486
Mon May 04 17:59:18 2009  commencing 2-way merge
Mon May 04 17:59:22 2009  reduce to 2551084 relation sets and 2132375 unique ideals
Mon May 04 17:59:22 2009  commencing full merge
Mon May 04 18:00:04 2009  memory use: 193.4 MB
Mon May 04 18:00:05 2009  found 1311357 cycles, need 1254575
Mon May 04 18:00:05 2009  weight of 1254575 cycles is about 87944184 (70.10/cycle)
Mon May 04 18:00:05 2009  distribution of cycle lengths:
Mon May 04 18:00:05 2009  1 relations: 117849
Mon May 04 18:00:05 2009  2 relations: 150312
Mon May 04 18:00:05 2009  3 relations: 158711
Mon May 04 18:00:05 2009  4 relations: 146449
Mon May 04 18:00:05 2009  5 relations: 130443
Mon May 04 18:00:05 2009  6 relations: 111940
Mon May 04 18:00:05 2009  7 relations: 94429
Mon May 04 18:00:05 2009  8 relations: 78994
Mon May 04 18:00:05 2009  9 relations: 65647
Mon May 04 18:00:05 2009  10+ relations: 199801
Mon May 04 18:00:05 2009  heaviest cycle: 17 relations
Mon May 04 18:00:05 2009  commencing cycle optimization
Mon May 04 18:00:08 2009  start with 7055729 relations
Mon May 04 18:00:27 2009  pruned 186556 relations
Mon May 04 18:00:27 2009  memory use: 185.4 MB
Mon May 04 18:00:27 2009  distribution of cycle lengths:
Mon May 04 18:00:27 2009  1 relations: 117849
Mon May 04 18:00:27 2009  2 relations: 154178
Mon May 04 18:00:27 2009  3 relations: 165233
Mon May 04 18:00:27 2009  4 relations: 150588
Mon May 04 18:00:27 2009  5 relations: 133901
Mon May 04 18:00:27 2009  6 relations: 113637
Mon May 04 18:00:27 2009  7 relations: 95275
Mon May 04 18:00:27 2009  8 relations: 78523
Mon May 04 18:00:27 2009  9 relations: 64337
Mon May 04 18:00:27 2009  10+ relations: 181054
Mon May 04 18:00:27 2009  heaviest cycle: 17 relations
Mon May 04 18:00:29 2009  RelProcTime: 845
Mon May 04 18:00:29 2009  
Mon May 04 18:00:29 2009  commencing linear algebra
Mon May 04 18:00:30 2009  read 1254575 cycles
Mon May 04 18:00:33 2009  cycles contain 3807029 unique relations
Mon May 04 18:01:54 2009  read 3807029 relations
Mon May 04 18:02:01 2009  using 20 quadratic characters above 268433534
Mon May 04 18:02:26 2009  building initial matrix
Mon May 04 18:03:30 2009  memory use: 443.3 MB
Mon May 04 18:03:37 2009  read 1254575 cycles
Mon May 04 18:03:53 2009  matrix is 1254364 x 1254575 (361.8 MB) with weight 120703793 (96.21/col)
Mon May 04 18:03:53 2009  sparse part has weight 84812850 (67.60/col)
Mon May 04 18:04:14 2009  filtering completed in 2 passes
Mon May 04 18:04:14 2009  matrix is 1250862 x 1251062 (361.4 MB) with weight 120513377 (96.33/col)
Mon May 04 18:04:14 2009  sparse part has weight 84728033 (67.72/col)
Mon May 04 18:04:19 2009  read 1251062 cycles
Mon May 04 18:04:22 2009  matrix is 1250862 x 1251062 (361.4 MB) with weight 120513377 (96.33/col)
Mon May 04 18:04:22 2009  sparse part has weight 84728033 (67.72/col)
Mon May 04 18:04:22 2009  saving the first 48 matrix rows for later
Mon May 04 18:04:23 2009  matrix is 1250814 x 1251062 (349.0 MB) with weight 96938267 (77.48/col)
Mon May 04 18:04:23 2009  sparse part has weight 83977886 (67.13/col)
Mon May 04 18:04:23 2009  matrix includes 64 packed rows
Mon May 04 18:04:23 2009  using block size 65536 for processor cache size 3072 kB
Mon May 04 18:04:34 2009  commencing Lanczos iteration
Mon May 04 18:04:34 2009  memory use: 344.1 MB
Mon May 04 22:18:31 2009  lanczos halted after 19783 iterations (dim = 1250813)
Mon May 04 22:18:35 2009  recovered 30 nontrivial dependencies
Mon May 04 22:18:36 2009  BLanczosTime: 15487
Mon May 04 22:18:36 2009  
Mon May 04 22:18:36 2009  commencing square root phase
Mon May 04 22:18:36 2009  reading relations for dependency 1
Mon May 04 22:18:37 2009  read 626185 cycles
Mon May 04 22:18:38 2009  cycles contain 2333553 unique relations
Mon May 04 22:19:51 2009  read 2333553 relations
Mon May 04 22:20:07 2009  multiplying 1903340 relations
Mon May 04 22:27:41 2009  multiply complete, coefficients have about 93.37 million bits
Mon May 04 22:27:45 2009  initial square root is modulo 5035379
Mon May 04 22:37:34 2009  sqrtTime: 1138
Mon May 04 22:37:34 2009  prp50 factor: 99382683945977500334658873808598740778689620049967
Mon May 04 22:37:34 2009  prp84 factor: 318694159844854605120879425181906886865805348896942492740283709980063920024563256003
Mon May 04 22:37:34 2009  elapsed time 04:57:48

polynomial selection 44:35:57
sieving time 425,55 hours
total time ~ 475,1 hours

May 5, 2009

The graphs of successful SNFS/GNFS in the last 90 days are available. Jeff Gilchrist's efforts of polynomial selections can be perceived in the graph.

May 4, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / May 4, 2009

(49·10¹⁸¹+23)/9 = 5(4)₁₈₀7_<182> = 3 · 19 · 25343 · 4898143973671943075533_<22> · 165703440094533134905772423687_<30> · C125

C125 = P57 · P68

P57 = 573071120607499390267914716161347198804297974326389017377_<57>

P68 = 81030607905776436620401921258086197513441643061834954467157233238891_<68>

Number: 54447_181
N=46436301276070201899460398906248605364338025400814138874003744066901307471773211792610214257185020149990475282233636591208907
  ( 125 digits)
Divisors found:
 r1=573071120607499390267914716161347198804297974326389017377 (pp57)
 r2=81030607905776436620401921258086197513441643061834954467157233238891 (pp68)
Version: Msieve-1.39
Total time: 57.71 hours.
Scaled time: 100.37 units (timescale=1.739).
Factorization parameters were as follows:
# Murphy_E = 1.659559e-10, selected by Jeff Gilchrist
n: 46436301276070201899460398906248605364338025400814138874003744066901307471773211792610214257185020149990475282233636591208907
Y0: -1170658117194019606887157
Y1: 41250645704533
c0: -35661712940272039086308650299876
c1: 1117646923046976003357556634
c2: -3036075700561948116834
c3: -7710223859788701
c4: 18358949432
c5: 21120
skew: 438909.1
type: gnfs
# selected mechanically
rlim: 7000000
alim: 7000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3500000, 6300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 887735 x 887983
Total sieving time: 57.71 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,124,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,7000000,7000000,27,27,52,52,2.5,2.5,100000
total time: 57.71 hours.
 --------- CPU info (if available) ----------

May 4, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 4, 2009

(53·10¹⁶⁸-71)/9 = 5(8)₁₆₇1_<169> = 593 · 17404799 · 2547335314631_<13> · C147

C147 = P45 · P103

P45 = 169017775524223519035278966544358165435527479_<45>

P103 = 1325229688509753839571072379572594850333978022743803818791211312741515576887190505144667080147934159967_<103>

Number: n
N=223987374010578230602619365407550244395618807812115773382000910093930361470571571495008898858070692217063327571950687456345105693573292303410233193
  ( 147 digits)
SNFS difficulty: 171 digits.
Divisors found:

Mon May 04 02:27:53 2009  prp45 factor: 169017775524223519035278966544358165435527479
Mon May 04 02:27:53 2009  prp103 factor: 1325229688509753839571072379572594850333978022743803818791211312741515576887190505144667080147934159967
Mon May 04 02:27:53 2009  elapsed time 01:38:50 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 77.13 hours.
Scaled time: 200.15 units (timescale=2.595).
Factorization parameters were as follows:
name: KA_5_8_167_1
n: 223987374010578230602619365407550244395618807812115773382000910093930361470571571495008898858070692217063327571950687456345105693573292303410233193
m: 5000000000000000000000000000000000
deg: 5
c5: 424
c0: -1775
skew: 1.33
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 7100131)
Primes: RFBsize:348513, AFBsize:349532, largePrimes:18200592 encountered
Relations: rels:18635149, finalFF:670254
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2751633 hash collisions in 21005685 relations
Msieve: matrix is 899202 x 899450 (237.1 MB)

Total sieving time: 76.26 hours.
Total relation processing time: 0.87 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 77.13 hours.
 --------- CPU info (if available) ----------

(46·10¹⁶⁶+53)/9 = 5(1)₁₆₅7_<167> = 3 · 11 · 2929337 · 16036699817919812260473949319_<29> · C131

C131 = P31 · P101

P31 = 1630468449953094566378736443083_<31>

P101 = 20221093893458760666893128729053370437177862662501618757770239518723565275843344695057556709203292201_<101>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 32969855616823691466101238160783310004651583931458204036145062340110338667916054195949780242413798330360782553087497224960254295683 (131 digits)
Using B1=460000, B2=347971482, polynomial Dickson(3), sigma=2688550002
Step 1 took 5725ms
Step 2 took 2293ms
********** Factor found in step 2: 1630468449953094566378736443083
Found probable prime factor of 31 digits: 1630468449953094566378736443083
Probable prime cofactor 20221093893458760666893128729053370437177862662501618757770239518723565275843344695057556709203292201 has 101 digits

(55·10¹⁵⁷+17)/9 = 6(1)₁₅₆3_<158> = 3 · 7 · 233 · 91073945081747118493_<20> · C135

C135 = P50 · P86

P50 = 12124727791377638326845253721179147109990591753399_<50>

P86 = 11310422223706317727474682057533510318275643666078995018519442259981719412163525709063_<86>

Number: n
N=137135790667987258497062069606788365533877730492617388925132440398292490112752801128294151957777779325427769881630714049121531915355137
  ( 135 digits)
SNFS difficulty: 160 digits.
Divisors found:

Mon May 04 12:12:16 2009  prp50 factor: 12124727791377638326845253721179147109990591753399
Mon May 04 12:12:16 2009  prp86 factor: 11310422223706317727474682057533510318275643666078995018519442259981719412163525709063
Mon May 04 12:12:16 2009  elapsed time 02:17:24 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 39.62 hours.
Scaled time: 52.02 units (timescale=1.313).
Factorization parameters were as follows:
name: KA_6_1_156_3
n: 137135790667987258497062069606788365533877730492617388925132440398292490112752801128294151957777779325427769881630714049121531915355137
m: 50000000000000000000000000000000
deg: 5
c5: 44
c0: 425
skew: 1.57
type: snfs
lss: 1
rlim: 3300000
alim: 3300000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1650000, 3210121)
Primes: RFBsize:236900, AFBsize:237488, largePrimes:13811646 encountered
Relations: rels:13142029, finalFF:416258
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1330848 hash collisions in 14317622 relations
Msieve: matrix is 578036 x 578284 (153.5 MB)

Total sieving time: 39.12 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,28,28,56,56,2.4,2.4,100000
total time: 39.62 hours.
 --------- CPU info (if available) ----------

May 4, 2009

By Sinkiti Sibata / Msieve / May 4, 2009

(55·10¹⁹⁸+17)/9 = 6(1)₁₉₇3_<199> = 263 · 1283 · 5147 · 13457053507_<11> · 21070739383_<11> · 26850591611_<11> · 1699893553753500635791_<22> · 24196957677695274336113_<23> · C116

C116 = P45 · P71

P45 = 746799927063051765367184540694213571283990251_<45>

P71 = 15045728972784379234711971257195171910039681620386470902747042503219717_<71>

Number: 61113_198
N=11236149299485819172193467158358845712816422607187364966823244656600967795679114846372943980099447926176442738978967
  ( 116 digits)
Divisors found:
 r1=746799927063051765367184540694213571283990251 (pp45)
 r2=15045728972784379234711971257195171910039681620386470902747042503219717 (pp71)
Version: Msieve-1.40
Total time: 24.09 hours.
Scaled time: 61.77 units (timescale=2.564).
Factorization parameters were as follows:
name: 61113_198
# Murphy_E = 6.103973e-10, selected by Jeff Gilchrist
n: 11236149299485819172193467158358845712816422607187364966823244656600967795679114846372943980099447926176442738978967
Y0: -15107092040465287704648
Y1: 2323038215251
c0: -686769523076129772705030731
c1: 114042434326443914589151
c2: 9623962751739062717
c3: -19077419576851
c4: -3224939526
c5: 14280
skew: 51529.25
type: gnfs
# selected mechanically
rlim: 3900000
alim: 3900000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
Factor base limits: 3900000/3900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1950000, 2950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 510153 x 510401
Total sieving time: 24.09 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3900000,3900000,27,27,51,51,2.5,2.5,100000
total time: 24.09 hours.
 --------- CPU info (if available) ----------

May 3, 2009

By Sinkiti Sibata / Msieve / May 3, 2009

(55·10²⁰⁰+17)/9 = 6(1)₁₉₉3_<201> = 61 · 1057641511_<10> · 151120135181_<12> · 41111111601181_<14> · 85073303235678488039_<20> · 10002437630258266227332161_<26> · C121

C121 = P40 · P81

P40 = 7969824024706850311637866653194343659977_<40>

P81 = 224813519012018880758200954355240402897525050961812494056620389047570537939602381_<81>

Number: 61113_200
N=1791724184900878326582352306606968086033777211959517288152525947796636786189303669848348229317960681422557856295643605237
  ( 121 digits)
Divisors found:
 r1=7969824024706850311637866653194343659977 (pp40)
 r2=224813519012018880758200954355240402897525050961812494056620389047570537939602381 (pp81)
Version: Msieve-1.40
Total time: 50.53 hours.
Scaled time: 130.10 units (timescale=2.575).
Factorization parameters were as follows:
name: 61113_200
# Murphy_E = 2.721748e-10, selected by Jeff Gilchrist
n: 1791724184900878326582352306606968086033777211959517288152525947796636786189303669848348229317960681422557856295643605237
Y0: -176569456505448007089270
Y1: 7053922909259
c0: 692473754981649357842549234393
c1: 21424563729501290145330269
c2: 167347493654071875953
c3: -1379857106816429
c4: -4358776066
c5: 10440
skew: 217623.68
type: gnfs
# selected mechanically
rlim: 5300000
alim: 5300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2650000, 4650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 748338 x 748586
Total sieving time: 50.53 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5300000,5300000,27,27,52,52,2.5,2.5,100000
total time: 50.53 hours.
 --------- CPU info (if available) ----------

May 2, 2009 (5th)

By Jo Yeong Uk / GMP-ECM / May 2, 2009

(55·10¹⁸⁵+17)/9 = 6(1)₁₈₄3_<186> = C186

C186 = P43 · C144

P43 = 1096040361315018452438210082225829075210151_<43>

C144 = [557562597765930815412243176953401553071377242201602332140988914411667452895150577949126139543829258917591831711208244743857512136813261667131663_<144>]

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM]
Input number is 611111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113 (186 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2707379689
Step 1 took 29921ms
Step 2 took 19500ms
********** Factor found in step 2: 1096040361315018452438210082225829075210151
Found probable prime factor of 43 digits: 1096040361315018452438210082225829075210151
Composite cofactor 557562597765930815412243176953401553071377242201602332140988914411667452895150577949126139543829258917591831711208244743857512136813261667131663 has 144 digits

May 2, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / May 1, 2009

(55·10¹³¹+17)/9 = 6(1)₁₃₀3_<132> = 181 · C130

C130 = P64 · P67

P64 = 2959810039062819990859007912121336939581988177042521633010731909_<64>

P67 = 1140716612457302757427878310231801315808493275159253651509479151297_<67>

Number: 61113_131
N=3376304481276856967464702271332105586249232658072437077961939840392879066912216083486801718845917740945365254757519950890116635973
  ( 130 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=2959810039062819990859007912121336939581988177042521633010731909 (pp64)
 r2=1140716612457302757427878310231801315808493275159253651509479151297 (pp67)
Version: Msieve-1.39
Total time: 2.67 hours.
Scaled time: 6.87 units (timescale=2.577).
Factorization parameters were as follows:
n: 3376304481276856967464702271332105586249232658072437077961939840392879066912216083486801718845917740945365254757519950890116635973
m: 200000000000000000000000000
deg: 5
c5: 275
c0: 272
skew: 1.00
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [600000, 1050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 152852 x 153094
Total sieving time: 2.67 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000
total time: 2.67 hours.
 --------- CPU info (if available) ----------

(55·10¹⁴⁶+17)/9 = 6(1)₁₄₅3_<147> = 29077 · 27684913 · 8904218509_<10> · C125

C125 = P60 · P66

P60 = 160965543312759353198552642730359050359052328137190922370513_<60>

P66 = 529661848281448338885793967808712449857065677368809581586525810489_<66>

Number: 61113_146
N=85257307180663645777655545117027633679803372464365020456848138665445440598020230260861824971246596997401711612151618479710857
  ( 125 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=160965543312759353198552642730359050359052328137190922370513 (pp60)
 r2=529661848281448338885793967808712449857065677368809581586525810489 (pp66)
Version: Msieve-1.39
Total time: 7.58 hours.
Scaled time: 13.18 units (timescale=1.739).
Factorization parameters were as follows:
n: 85257307180663645777655545117027633679803372464365020456848138665445440598020230260861824971246596997401711612151618479710857
m: 200000000000000000000000000000
deg: 5
c5: 275
c0: 272
skew: 1.00
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 331424 x 331672
Total sieving time: 7.58 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 7.58 hours.
 --------- CPU info (if available) ----------

By Ignacio Santos / GGNFS, Msieve / May 2, 2009

(55·10¹⁷⁹+17)/9 = 6(1)₁₇₈3_<180> = C180

C180 = P44 · P44 · P93

P44 = 12377994530432761028221676774712257063726401_<44>

P44 = 73269204460209175829580074342407808171006969_<44>

P93 = 673827013176111083910624677558147698900308166031355405696528671720862868315586604941485397777_<93>

Number: 61113_179
N=611111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
  ( 180 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=12377994530432761028221676774712257063726401 (pp44)
 r2=73269204460209175829580074342407808171006969 (pp44)
 r3=673827013176111083910624677558147698900308166031355405696528671720862868315586604941485397777 (pp93)
Version: Msieve-1.39
Total time: 137.25 hours.
Scaled time: 238.68 units (timescale=1.739).
Factorization parameters were as follows:
n: 611111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
m: 1000000000000000000000000000000000000
deg: 5
c5: 11
c0: 34
skew: 1.25
type: snfs
lss: 1
rlim: 7300000
alim: 7300000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7300000/7300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3650000, 5950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1290361 x 1290609
Total sieving time: 137.25 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7300000,7300000,28,28,53,53,2.5,2.5,100000
total time: 137.25 hours.
 --------- CPU info (if available) ----------

May 2, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 1, 2009

(55·10¹⁴⁴+17)/9 = 6(1)₁₄₃3_<145> = 113 · 54559 · C138

C138 = P68 · P71

P68 = 62047967175543760816542807092147978147061016750701197820446736461993_<68>

P71 = 15975254194946695413822386088009888763248723626869235808879754858431023_<71>

Number: n
N=991232047909020325177097572719621562742925067741248714124225850023383164010173789470927731740455872665105602348016057166190487802051608839
  ( 138 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=62047967175543760816542807092147978147061016750701197820446736461993 (pp68)
 r2=15975254194946695413822386088009888763248723626869235808879754858431023 (pp71)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 6.15 hours.
Scaled time: 16.36 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_1_143_3
n: 991232047909020325177097572719621562742925067741248714124225850023383164010173789470927731740455872665105602348016057166190487802051608839
m: 100000000000000000000000000000
deg: 5
c5: 11
c0: 34
skew: 1.25
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 100000
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [950000, 2050001)
Primes: RFBsize:142029, AFBsize:142593, largePrimes:6880110 encountered
Relations: rels:6253829, finalFF:326860
Max relations in full relation-set: 28
Initial matrix: 284687 x 326860 with sparse part having weight 29127953.
Pruned matrix : 268932 x 270419 with weight 21137673.
Total sieving time: 5.74 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.24 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1900000,1900000,28,28,56,56,2.3,2.3,100000
total time: 6.15 hours.
 --------- CPU info (if available) ----------

(55·10¹⁴⁵+17)/9 = 6(1)₁₄₄3_<146> = 3² · 7 · 15313 · 27269897 · C133

C133 = P39 · P95

P39 = 107016565731908504231459299776275005741_<39>

P95 = 21706251995039129583953685992479342156376606649272283107467957832369820404585460036933394617451_<95>

Number: n
N=2322928543420475118824821236796569054213102688127694063920166482940863388996539736729948247430475893861048264045178605545393523786191
  ( 133 digits)
SNFS difficulty: 146 digits.
Divisors found:

Fri May 01 18:04:23 2009  prp39 factor: 107016565731908504231459299776275005741
Fri May 01 18:04:23 2009  prp95 factor: 21706251995039129583953685992479342156376606649272283107467957832369820404585460036933394617451
Fri May 01 18:04:23 2009  elapsed time 00:17:55 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 6.00 hours.
Scaled time: 15.95 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_6_1_144_3
n: 2322928543420475118824821236796569054213102688127694063920166482940863388996539736729948247430475893861048264045178605545393523786191
m: 100000000000000000000000000000
deg: 5
c5: 55
c0: 17
skew: 0.79
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1000000, 1999567)
Primes: RFBsize:148933, AFBsize:148321, largePrimes:9515026 encountered
Relations: rels:8485513, finalFF:307147
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 859106 hash collisions in 9671035 relations
Msieve: matrix is 341182 x 341430 (91.2 MB)

Total sieving time: 5.80 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,56,56,2.4,2.4,100000
total time: 6.00 hours.
 --------- CPU info (if available) ----------

(55·10¹⁹³+17)/9 = 6(1)₁₉₂3_<194> = 3 · 7 · 18665929 · 2338111244797_<13> · 11951408653733_<14> · 471202058198062313251681_<24> · 350428336880383894300155304441_<30> · C107

C107 = P48 · P59

P48 = 384765495832116367237778956105135383415129352909_<48>

P59 = 87814148208409307707864677216212472091320723207070971272713_<59>

Number: n
N=33787854276483560442085336393221876130796021891636512609086462515490869394140277080699950221758475858872117
  ( 107 digits)
Divisors found:

Fri May 01 18:47:23 2009  prp48 factor: 384765495832116367237778956105135383415129352909
Fri May 01 18:47:23 2009  prp59 factor: 87814148208409307707864677216212472091320723207070971272713
Fri May 01 18:47:23 2009  elapsed time 00:46:39 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 13.43 hours.
Scaled time: 17.72 units (timescale=1.319).
Factorization parameters were as follows:
name: KA_6_1_192_3_Jeff_Gilchrist
# Murphy_E = 1.564195e-09, selected by Jeff Gilchrist
n: 33787854276483560442085336393221876130796021891636512609086462515490869394140277080699950221758475858872117
Y0: -394413411388729801681
Y1: 148581631799
c0: -25649377604197306364870640
c1: 10507065941092396630478
c2: -10142164446033363
c3: -19061095063357
c4: -22053853
c5: 3540
skew: 38283.63
type: gnfs
# selected mechanically
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [1150000, 2153159)
Primes: RFBsize:169511, AFBsize:170117, largePrimes:4322460 encountered
Relations: rels:4223392, finalFF:359082
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 401952 hash collisions in 4637187 relations
Msieve: matrix is 329174 x 329422 (90.2 MB)

Total sieving time: 13.26 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.5,2.5,150000
total time: 13.43 hours.
 --------- CPU info (if available) ----------

4·10²¹⁹-9 = 3(9)₂₁₈1_<220> = 13 · 839 · C216

C216 = P77 · P139

P77 = 82467488022247679727947415497469791627336296247529111727738703553530989716089_<77>

P139 = 4447048973020707963671116712924416171932599147193348095813779150964307930192515153073852957342284283845468243469970491789991587228466841917_<139>

Number: n
N=366736957916934079031814431099294031356009901897863757220133858989639680938846612267351242321444943614192720271385348858531218483542679013477583203447327404419180342899055652333363894746493077839919317869258274502613
  ( 216 digits)
SNFS difficulty: 219 digits.
Divisors found:

Fri May  1 20:07:25 2009  prp77 factor: 82467488022247679727947415497469791627336296247529111727738703553530989716089
Fri May  1 20:07:25 2009  prp139 factor: 4447048973020707963671116712924416171932599147193348095813779150964307930192515153073852957342284283845468243469970491789991587228466841917
Fri May  1 20:07:25 2009  elapsed time 69:52:28 (Msieve 1.39 - dependency 5)

Version: GGNFS-0.77.1-20050930-k8
Total time: 250.14 hours.
Scaled time: 503.78 units (timescale=2.014).
Factorization parameters were as follows:
name: KA_3_9_218_1
n: 366736957916934079031814431099294031356009901897863757220133858989639680938846612267351242321444943614192720271385348858531218483542679013477583203447327404419180342899055652333363894746493077839919317869258274502613
m: 2000000000000000000000000000000000000
deg: 6
c6: 125
c0: -18
skew: 0.72
type: snfs
lss: 1
rlim: 32000000
alim: 32000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 32000000/32000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [16000000, 59599990)
Primes: RFBsize:1973815, AFBsize:1973593, largePrimes:37417691 encountered
Relations: rels:33415433, finalFF:949809
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 10597697 hash collisions in 53759234 relations
Msieve: matrix is 5611290 x 5611538 (1524.9 MB)

Total sieving time: 248.31 hours.
Total relation processing time: 1.83 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,219,6,0,0,0,0,0,0,0,0,32000000,32000000,29,29,58,58,2.6,2.6,100000
total time: 250.14 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830496)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830453)
Total of 4 processors activated (22643.70 BogoMIPS).

(55·10¹⁶³+17)/9 = 6(1)₁₆₂3_<164> = 3² · 7² · 2143 · 236254343371_<12> · C147

C147 = P39 · P108

P39 = 988927876452064515740826404730390842363_<39>

P108 = 276767441399096380316151693006323720191422239464515146167317202352562731456327706585980600161679177720537687_<108>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 273703038093879591074250157422546137883823419528662340911505327987668867536699780839613305549266028283942751636145364283724805214548251413217634381 (147 digits)
Using B1=2428000, B2=3567796060, polynomial Dickson(6), sigma=1970218074
Step 1 took 37377ms
Step 2 took 12590ms
********** Factor found in step 2: 988927876452064515740826404730390842363
Found probable prime factor of 39 digits: 988927876452064515740826404730390842363
Probable prime cofactor 276767441399096380316151693006323720191422239464515146167317202352562731456327706585980600161679177720537687 has 108 digits

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / May 2, 2009

(55·10¹⁶⁴+17)/9 = 6(1)₁₆₃3_<165> = 23 · 16298621366653_<14> · C151

C151 = P39 · P45 · P67

P39 = 282451979306041155940265917052798974301_<39>

P45 = 644722799675175966492607182499443099118039843_<45>

P67 = 8952077269999371031550399889027325040511664465137117896843843554189_<67>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 1630202193882551104644598265925382882273090792872901616189458196053098853630152192869885169100062147087738877976546460977103393162871641515066409748427 (151 digits)
Using B1=2830000, B2=4281592780, polynomial Dickson(6), sigma=2000062157
Step 1 took 43743ms
Step 2 took 9375ms
********** Factor found in step 2: 282451979306041155940265917052798974301
Found probable prime factor of 39 digits: 282451979306041155940265917052798974301
Composite cofactor 5771608320422500642589016843134140631258908662565308929895490414334452685237669024313423499189266080364031552327 has 112 digits

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 5771608320422500642589016843134140631258908662565308929895490414334452685237669024313423499189266080364031552327 (112 digits)
Using B1=4640000, B2=8562235510, polynomial Dickson(6), sigma=1859142445
Step 1 took 45879ms
********** Factor found in step 1: 644722799675175966492607182499443099118039843
Found probable prime factor of 45 digits: 644722799675175966492607182499443099118039843
Probable prime cofactor 8952077269999371031550399889027325040511664465137117896843843554189 has 67 digits

(26·10¹⁹⁵-17)/9 = 2(8)₁₉₄7_<196> = 23 · C195

C195 = P74 · P121

P74 = 16387913092815080088799706325752575559733136683692971560249525931029829007_<74>

P121 = 7664420968242000729840063963573618783981209238122361233171156686202207659037578930162203115556226303477752467991137793167_<121>

Number: n
N=125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647342995169
  ( 195 digits)
SNFS difficulty: 196 digits.
Divisors found:

Sat May  2 15:22:30 2009  prp74 factor: 16387913092815080088799706325752575559733136683692971560249525931029829007
Sat May  2 15:22:30 2009  prp121 factor: 7664420968242000729840063963573618783981209238122361233171156686202207659037578930162203115556226303477752467991137793167
Sat May  2 15:22:30 2009  elapsed time 06:44:20 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 10.92 hours.
Scaled time: 15.98 units (timescale=1.464).
Factorization parameters were as follows:
name: KA_2_8_194_7
n: 125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647342995169082125603864734299516908212560386473429951690821256038647342995169
m: 1000000000000000000000000000000000000000
deg: 5
c5: 26
c0: -17
skew: 0.92
type: snfs
lss: 1
rlim: 13100000
alim: 13100000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 13100000/13100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [6550000, 8109131)
Primes: RFBsize:855281, AFBsize:853884, largePrimes:21946999 encountered
Relations: rels:23351118, finalFF:1445023
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 3003984 hash collisions in 25646907 relations
Msieve: matrix is 2161958 x 2162206 (577.1 MB)

Total sieving time: 10.47 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,13100000,13100000,28,28,56,56,2.5,2.5,100000
total time: 10.92 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830496)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830453)
Total of 4 processors activated (22643.70 BogoMIPS).

May 2, 2009 (2nd)

By Sinkiti Sibata / Msieve, GGNFS / May 1, 2009

(55·10¹⁶⁵+17)/9 = 6(1)₁₆₄3_<166> = 4673 · 30557 · 91757 · 3130253801_<10> · 5878154375683_<13> · 57335812309613_<14> · 56460022325299969_<17> · C100

C100 = P34 · P67

P34 = 5465358655311332029004825867899211_<34>

P67 = 1432742875035547153933750660830179143999140191987535372145307749229_<67>

Number: 61113_165
N=7830453672911169816739466041188016318913244857508424008110812471942050633932960185035002833034958319
  ( 100 digits)
Divisors found:
 r1=5465358655311332029004825867899211 (pp34)
 r2=1432742875035547153933750660830179143999140191987535372145307749229 (pp67)
Version: Msieve-1.40
Total time: 4.52 hours.
Scaled time: 11.59 units (timescale=2.564).
Factorization parameters were as follows:
name: 61113_165
# Murphy_E = 3.280698e-09, selected by Jeff Gilchrist
n: 7830453672911169816739466041188016318913244857508424008110812471942050633932960185035002833034958319
Y0: -23554394723977259197
Y1: 6482663053
c0: 626424900598470617370720
c1: 408296215573260026130
c2: -14200135718664369
c3: -3571120408384
c4: 30953858
c5: 1080
skew: 22078.27
type: gnfs
# selected mechanically
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.4
alambda: 2.4
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 206809 x 207057
Total sieving time: 4.52 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,47,47,2.4,2.4,100000
total time: 4.52 hours.
 --------- CPU info (if available) ----------

6·10²²¹+1 = 6(0)₂₂₀1_<222> = 19 · 13547461 · 16726782991_<11> · 3349384721392093940733381409_<28> · 3849322964951777452392095093_<28> · 694683008640191018051495572579_<30> · C119

C119 = P49 · P70

P49 = 2106663983424484976725368044339228518607232620507_<49>

P70 = 7385773499148755352472981597178105724655405297506528416547206510108989_<70>

Number: 60001_221
N=15559343020387713952218299826631328238166893662896524746348459508722856699246398061388342322531961826952273576646437423
  ( 119 digits)
Divisors found:
 r1=2106663983424484976725368044339228518607232620507 (pp49)
 r2=7385773499148755352472981597178105724655405297506528416547206510108989 (pp70)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 88.83 hours.
Scaled time: 39.53 units (timescale=0.445).
Factorization parameters were as follows:
name: 60001_221
n: 15559343020387713952218299826631328238166893662896524746348459508722856699246398061388342322531961826952273576646437423
skew: 47990.39
# norm 2.62e+16
c5: 16560
c4: -4985358464
c3: 805612048914044
c2: 8728007815337305705
c1: -411350596078124939640396
c0: -4656088059625115819178313041
# alpha -6.23
Y1: 4091161783709
Y0: -62314325905034135682686
# Murphy_E 3.66e-10
# M 11870999316973983964274864036355129279554903974482653755267250922085510449071424316612954275416595953497035109209784499
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4110001)
Primes: RFBsize:315948, AFBsize:315821, largePrimes:7697648 encountered
Relations: rels:7814114, finalFF:784249
Max relations in full relation-set: 28
Initial matrix: 631851 x 784249 with sparse part having weight 67572986.
Pruned matrix : 504602 x 507825 with weight 41609053.
Total sieving time: 75.34 hours.
Total relation processing time: 0.91 hours.
Matrix solve time: 12.09 hours.
Time per square root: 0.49 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 88.83 hours.
 --------- CPU info (if available) ----------

May 2, 2009

By Andreas Tete / Msieve v1.41 / May 1, 2009

(55·10¹¹⁹+17)/9 = 6(1)₁₁₈3_<120> = 1619798646167707926668253111679_<31> · C90

C90 = P37 · P54

P37 = 3053270289500435018012281274941085711_<37>

P54 = 123564551359888218602782071126087431100945294762281177_<54>

Thu Apr 30 18:48:20 2009  Msieve v. 1.41
Thu Apr 30 18:48:20 2009  random seeds: f3b53190 42af96b3
Thu Apr 30 18:48:20 2009  factoring 377275973502597272706476705893861400303860757026705314272481031102839141493245455438961847 (90 digits)
Thu Apr 30 18:48:21 2009  searching for 15-digit factors
Thu Apr 30 18:48:22 2009  searching for 20-digit factors
Thu Apr 30 18:48:39 2009  searching for 25-digit factors
Thu Apr 30 18:51:51 2009  commencing quadratic sieve (90-digit input)
Thu Apr 30 18:51:51 2009  using multiplier of 1
Thu Apr 30 18:51:51 2009  using 32kb Intel Core sieve core
Thu Apr 30 18:51:51 2009  sieve interval: 36 blocks of size 32768
Thu Apr 30 18:51:51 2009  processing polynomials in batches of 6
Thu Apr 30 18:51:51 2009  using a sieve bound of 1584943 (59903 primes)
Thu Apr 30 18:51:51 2009  using large prime bound of 126795440 (26 bits)
Thu Apr 30 18:51:51 2009  using double large prime bound of 385111478867040 (42-49 bits)
Thu Apr 30 18:51:51 2009  using trial factoring cutoff of 49 bits
Thu Apr 30 18:51:51 2009  polynomial 'A' values have 11 factors
Thu Apr 30 20:33:03 2009  60071 relations (15333 full + 44738 combined from 648878 partial), need 59999
Thu Apr 30 20:33:04 2009  begin with 664211 relations
Thu Apr 30 20:33:05 2009  reduce to 149145 relations in 10 passes
Thu Apr 30 20:33:05 2009  attempting to read 149145 relations
Thu Apr 30 20:33:08 2009  recovered 149145 relations
Thu Apr 30 20:33:08 2009  recovered 131153 polynomials
Thu Apr 30 20:33:08 2009  attempting to build 60071 cycles
Thu Apr 30 20:33:08 2009  found 60071 cycles in 6 passes
Thu Apr 30 20:33:08 2009  distribution of cycle lengths:
Thu Apr 30 20:33:08 2009     length 1 : 15333
Thu Apr 30 20:33:08 2009     length 2 : 11124
Thu Apr 30 20:33:08 2009     length 3 : 10506
Thu Apr 30 20:33:08 2009     length 4 : 8198
Thu Apr 30 20:33:08 2009     length 5 : 5846
Thu Apr 30 20:33:08 2009     length 6 : 3861
Thu Apr 30 20:33:08 2009     length 7 : 2355
Thu Apr 30 20:33:08 2009     length 9+: 2848
Thu Apr 30 20:33:08 2009  largest cycle: 19 relations
Thu Apr 30 20:33:08 2009  matrix is 59903 x 60071 (15.2 MB) with weight 3744595 (62.34/col)
Thu Apr 30 20:33:08 2009  sparse part has weight 3744595 (62.34/col)
Thu Apr 30 20:33:10 2009  filtering completed in 3 passes
Thu Apr 30 20:33:10 2009  matrix is 56440 x 56503 (14.4 MB) with weight 3555074 (62.92/col)
Thu Apr 30 20:33:10 2009  sparse part has weight 3555074 (62.92/col)
Thu Apr 30 20:33:10 2009  saving the first 48 matrix rows for later
Thu Apr 30 20:33:10 2009  matrix is 56392 x 56503 (10.8 MB) with weight 2995473 (53.01/col)
Thu Apr 30 20:33:10 2009  sparse part has weight 2504930 (44.33/col)
Thu Apr 30 20:33:10 2009  matrix includes 64 packed rows
Thu Apr 30 20:33:10 2009  using block size 22601 for processor cache size 3072 kB
Thu Apr 30 20:33:11 2009  commencing Lanczos iteration
Thu Apr 30 20:33:11 2009  memory use: 9.6 MB
Thu Apr 30 20:33:34 2009  lanczos halted after 893 iterations (dim = 56391)
Thu Apr 30 20:33:34 2009  recovered 17 nontrivial dependencies
Thu Apr 30 20:33:34 2009  prp37 factor: 3053270289500435018012281274941085711
Thu Apr 30 20:33:34 2009  prp54 factor: 123564551359888218602782071126087431100945294762281177
Thu Apr 30 20:33:34 2009  elapsed time 01:45:14

April 2009

Apr 30, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Apr 30, 2009

(53·10¹⁶³-17)/9 = 5(8)₁₆₂7_<164> = 3 · 19 · 34765350967304163312833_<23> · C140

C140 = P53 · P87

P53 = 62622882318570911412650973707031773485945464667516361_<53>

P87 = 474546564403968967469298671548430514892021736391287023805749850667560421046179684788407_<87>

Number: 58887_163
N=29717473657351880511406397184182422265767672183342114852866813048791098856416018648200989323953206454366254829764036411860857577932495626927
  ( 140 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=62622882318570911412650973707031773485945464667516361 (pp53)
 r2=474546564403968967469298671548430514892021736391287023805749850667560421046179684788407 (pp87)
Version: Msieve-1.39
Total time: 50.02 hours.
Scaled time: 128.54 units (timescale=2.570).
Factorization parameters were as follows:
n: 29717473657351880511406397184182422265767672183342114852866813048791098856416018648200989323953206454366254829764036411860857577932495626927
m: 500000000000000000000000000000000
deg: 5
c5: 424
c0: -425
skew: 1.00
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 766824 x 767072
Total sieving time: 50.02 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 50.02 hours.
 --------- CPU info (if available) ----------

(55·10¹⁵⁴+17)/9 = 6(1)₁₅₃3_<155> = 3³ · 13 · C153

C153 = P58 · P96

P58 = 1232654391467284570396223070468890151373701148611847251467_<58>

P96 = 141244562033352471422960766465762608824220881553425132457487800547462661060496451035078688975589_<96>

Number: 61113_154
N=174105729661285216840772396327951883507439062994618550174105729661285216840772396327951883507439062994618550174105729661285216840772396327951883507439063
  ( 153 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=1232654391467284570396223070468890151373701148611847251467 (pp58)
 r2=141244562033352471422960766465762608824220881553425132457487800547462661060496451035078688975589 (pp96)
Version: Msieve-1.39
Total time: 17.35 hours.
Scaled time: 44.60 units (timescale=2.571).
Factorization parameters were as follows:
n: 174105729661285216840772396327951883507439062994618550174105729661285216840772396327951883507439062994618550174105729661285216840772396327951883507439063
m: 10000000000000000000000000000000
deg: 5
c5: 11
c0: 34
skew: 1.25
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 445869 x 446117
Total sieving time: 17.35 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 17.35 hours.
 --------- CPU info (if available) ----------

(55·10¹²⁷+17)/9 = 6(1)₁₂₆3_<128> = 3³ · 7 · 191599 · C121

C121 = P40 · P81

P40 = 4682653728534234711143308235969476153633_<40>

P81 = 360390300507760405496205851150786683695433826066308510126793078082183441435140851_<81>

Number: 61113_127
N=1687582984400237563818213450460429248882679688106067622082261453494543901533963532663363502192978802402071254669070361683
  ( 121 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=4682653728534234711143308235969476153633 (pp40)
 r2=360390300507760405496205851150786683695433826066308510126793078082183441435140851 (pp81)
Version: Msieve-1.39
Total time: 2.48 hours.
Scaled time: 6.39 units (timescale=2.571).
Factorization parameters were as follows:
n: 1687582984400237563818213450460429248882679688106067622082261453494543901533963532663363502192978802402071254669070361683
m: 50000000000000000000000000
deg: 5
c5: 44
c0: 425
skew: 1.57
type: snfs
lss: 1
rlim: 1030000
alim: 1030000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1030000/1030000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [515000, 965001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 155761 x 155992
Total sieving time: 2.48 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1030000,1030000,26,26,47,47,2.3,2.3,50000
total time: 2.48 hours.
 --------- CPU info (if available) ----------

(55·10¹⁵⁸+17)/9 = 6(1)₁₅₇3_<159> = 331 · C157

C157 = P51 · P106

P51 = 473827959932100290692183934041550493799062394539511_<51>

P106 = 3896471482034884541768779423085832074586818741605048169360830630153978031461284856168107994452562187584093_<106>

Number: 61113_158
N=1846257133266196710305471634776770728432359852299429338704263175562269217858341725411211816045652903658945955018462571332661967103054716347767707284323598523
  ( 157 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=473827959932100290692183934041550493799062394539511 (pp51)
 r2=3896471482034884541768779423085832074586818741605048169360830630153978031461284856168107994452562187584093 (pp106)
Version: Msieve-1.39
Total time: 28.19 hours.
Scaled time: 49.02 units (timescale=1.739).
Factorization parameters were as follows:
n: 1846257133266196710305471634776770728432359852299429338704263175562269217858341725411211816045652903658945955018462571332661967103054716347767707284323598523
m: 50000000000000000000000000000000
deg: 5
c5: 88
c0: 85
skew: 0.99
type: snfs
lss: 1
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1650000, 3150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 608868 x 609116
Total sieving time: 28.19 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000
total time: 28.19 hours.
 --------- CPU info (if available) ----------

(55·10¹³⁸+17)/9 = 6(1)₁₃₇3_<139> = 59 · 1657 · 37137218441_<11> · 15147010896290711_<17> · C108

C108 = P43 · P65

P43 = 1187288381940462130868009909981206026936967_<43>

P65 = 93595104147558747071446841923837021201891200362881632886909849003_<65>

Number: 61113_118
N=111124379760904060998273023772063612247139489669364432832383286955350483631183018958061606008642952568793901
  ( 108 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=1187288381940462130868009909981206026936967 (pp43)
 r2=93595104147558747071446841923837021201891200362881632886909849003 (pp65)
Version: Msieve-1.39
Total time: 5.36 hours.
Scaled time: 13.78 units (timescale=2.571).
Factorization parameters were as follows:
n: 111124379760904060998273023772063612247139489669364432832383286955350483631183018958061606008642952568793901
m: 5000000000000000000000000000
deg: 5
c5: 88
c0: 85
skew: 0.99
type: snfs
lss: 1
rlim: 1530000
alim: 1530000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1530000/1530000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [765000, 1665001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 239127 x 239362
Total sieving time: 5.36 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1530000,1530000,26,26,48,48,2.3,2.3,75000
total time: 5.36 hours.
 --------- CPU info (if available) ----------

(55·10¹⁴⁰+17)/9 = 6(1)₁₃₉3_<141> = 61 · 89 · 30738941020813527919_<20> · C118

C118 = P44 · P75

P44 = 10615121701713873642054896444448927095209397_<44>

P75 = 344974075185369880980187433999848289501839524696372984170815766498887686079_<75>

Number: 61113_140
N=3661941792028893320771674453906461398736845292068741409358102612764247173984037287722223413240085681776284995306884363
  ( 118 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=10615121701713873642054896444448927095209397 (pp44)
 r2=344974075185369880980187433999848289501839524696372984170815766498887686079 (pp75)
Version: Msieve-1.39
Total time: 4.88 hours.
Scaled time: 12.50 units (timescale=2.560).
Factorization parameters were as follows:
n: 3661941792028893320771674453906461398736845292068741409358102612764247173984037287722223413240085681776284995306884363
m: 10000000000000000000000000000
deg: 5
c5: 55
c0: 17
skew: 0.79
type: snfs
lss: 1
rlim: 1610000
alim: 1610000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1610000/1610000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [805000, 1605001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 248771 x 249007
Total sieving time: 4.88 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000
total time: 4.88 hours.
 --------- CPU info (if available) ----------

(55·10¹⁴³+17)/9 = 6(1)₁₄₂3_<144> = 10273 · 397115083203972041_<18> · C123

C123 = P53 · P70

P53 = 60340823343326933516766372625551502784610350942842391_<53>

P70 = 2482534413113388832724548281270442360749001612536624017335879644836551_<70>

Number: 61113_143
N=149798170465404801889673648353571477390630741370430580041195733866328662659834965071847732868899781815670187328774549033441
  ( 123 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=60340823343326933516766372625551502784610350942842391 (pp53)
 r2=2482534413113388832724548281270442360749001612536624017335879644836551 (pp70)
Version: Msieve-1.39
Total time: 8.00 hours.
Scaled time: 20.60 units (timescale=2.576).
Factorization parameters were as follows:
n: 149798170465404801889673648353571477390630741370430580041195733866328662659834965071847732868899781815670187328774549033441
m: 50000000000000000000000000000
deg: 5
c5: 88
c0: 85
skew: 0.99
type: snfs
lss: 1
rlim: 1860000
alim: 1860000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1860000/1860000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [930000, 2230001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 318333 x 318562
Total sieving time: 8.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1860000,1860000,26,26,49,49,2.3,2.3,100000
total time: 8.00 hours.
 --------- CPU info (if available) ----------

Apr 30, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 30, 2009

(53·10¹⁶⁷+1)/9 = 5(8)₁₆₆9_<168> = 7 · 31 · 5801 · 2171422861_<10> · C153

C153 = P42 · P112

P42 = 135266161385821144300657096869448610669383_<42>

P112 = 1592711769493037551738175961976900809985538358919210031942464262455167074834538118938696628704611091433213992059_<112>

Number: n
N=215440007253341983299390084531258679074808434912488229449321198057364616718462923193195079761680811761040513937707338780162671744395500109087669636429597
  ( 153 digits)
SNFS difficulty: 170 digits.
Divisors found:

Thu Apr 30 12:02:04 2009  prp42 factor: 135266161385821144300657096869448610669383
Thu Apr 30 12:02:04 2009  prp112 factor: 1592711769493037551738175961976900809985538358919210031942464262455167074834538118938696628704611091433213992059
Thu Apr 30 12:02:04 2009  elapsed time 01:21:52 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 43.70 hours.
Scaled time: 116.72 units (timescale=2.671).
Factorization parameters were as follows:
name: KA_5_8_166_9
n: 215440007253341983299390084531258679074808434912488229449321198057364616718462923193195079761680811761040513937707338780162671744395500109087669636429597
m: 5000000000000000000000000000000000
deg: 5
c5: 212
c0: 125
skew: 0.90
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2450000, 4902193)
Primes: RFBsize:341992, AFBsize:341903, largePrimes:16344668 encountered
Relations: rels:15617764, finalFF:725294
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1679045 hash collisions in 17282749 relations
Msieve: matrix is 834325 x 834573 (223.6 MB)

Total sieving time: 43.13 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,28,28,56,56,2.4,2.4,100000
total time: 43.70 hours.
 --------- CPU info (if available) ----------

(55·10¹⁰²+17)/9 = 6(1)₁₀₁3_<103> = 411583 · C98

C98 = P35 · P63

P35 = 32358778405965305440492935854465363_<35>

P63 = 458849891881505688703834082750529184484557904436360837193089997_<63>

Number: n
N=14847821972994781395517091597833513801860405097176295209255754273405634127529832648848740378273911
  ( 98 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=32358778405965305440492935854465363 (pp35)
 r2=458849891881505688703834082750529184484557904436360837193089997 (pp63)
Version: GGNFS-0.77.1-VC8(Wed
Total time: 0.79 hours.
Scaled time: 0.98 units (timescale=1.243).
Factorization parameters were as follows:
name: KA_6_1_101_3
n: 14847821972994781395517091597833513801860405097176295209255754273405634127529832648848740378273911
m:  100000000000000000000
deg: 5
c5:5500
c0: 17
skew: 0.18
type: snfs
rlim: 400000
alim: 400000
lpbr: 26
lpba: 26
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 10000
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 52/52
Sieved algebraic special-q in [200000, 260001)
Primes: RFBsize:33860, AFBsize:33824, largePrimes:1890853 encountered
Relations: rels:1727952, finalFF:90219
Max relations in full relation-set: 28
Initial matrix: 67751 x 90219 with sparse part having weight 7022083.
Pruned matrix : 61776 x 62178 with weight 3504147.
Total sieving time: 0.68 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,400000,400000,26,26,52,52,2.4,2.4,20000
total time: 0.79 hours.
 --------- CPU info (if available) ----------

(55·10¹³⁹+17)/9 = 6(1)₁₃₈3_<140> = 3 · 7 · 43 · 383833 · 144778732945720361_<18> · C115

C115 = P32 · P40 · P43

P32 = 81763899605527921358782677567481_<32>

P40 = 4069370006867177330397707858452514611997_<40>

P43 = 3660130512500783146450462819085092132451731_<43>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 1217826297265224073102082739938273395751150789544672150731742120357286571820237935321180590087550810674361752653167 (115 digits)
Using B1=1372000, B2=1426564240, polynomial Dickson(6), sigma=3773204362
Step 1 took 13509ms
Step 2 took 5117ms
********** Factor found in step 2: 81763899605527921358782677567481
Found probable prime factor of 32 digits: 81763899605527921358782677567481
Composite cofactor 14894425328790077194413442180434380837484123126965525964547625497245590385796016807 has 83 digits

Thu Apr 30 19:21:58 2009  
Thu Apr 30 19:21:58 2009  
Thu Apr 30 19:21:58 2009  Msieve v. 1.39
Thu Apr 30 19:21:58 2009  random seeds: 891a2560 10e6359e
Thu Apr 30 19:21:58 2009  factoring 14894425328790077194413442180434380837484123126965525964547625497245590385796016807 (83 digits)
Thu Apr 30 19:21:58 2009  searching for 15-digit factors
Thu Apr 30 19:21:59 2009  commencing quadratic sieve (83-digit input)
Thu Apr 30 19:21:59 2009  using multiplier of 3
Thu Apr 30 19:21:59 2009  using 32kb Intel Core sieve core
Thu Apr 30 19:21:59 2009  sieve interval: 12 blocks of size 32768
Thu Apr 30 19:21:59 2009  processing polynomials in batches of 17
Thu Apr 30 19:21:59 2009  using a sieve bound of 1355089 (52059 primes)
Thu Apr 30 19:21:59 2009  using large prime bound of 124668188 (26 bits)
Thu Apr 30 19:21:59 2009  using trial factoring cutoff of 27 bits
Thu Apr 30 19:21:59 2009  polynomial 'A' values have 11 factors
Thu Apr 30 19:39:42 2009  52241 relations (26351 full + 25890 combined from 281262 partial), need 52155
Thu Apr 30 19:39:42 2009  begin with 307613 relations
Thu Apr 30 19:39:42 2009  reduce to 74928 relations in 2 passes
Thu Apr 30 19:39:42 2009  attempting to read 74928 relations
Thu Apr 30 19:39:43 2009  recovered 74928 relations
Thu Apr 30 19:39:43 2009  recovered 68440 polynomials
Thu Apr 30 19:39:43 2009  attempting to build 52241 cycles
Thu Apr 30 19:39:43 2009  found 52241 cycles in 1 passes
Thu Apr 30 19:39:43 2009  distribution of cycle lengths:
Thu Apr 30 19:39:43 2009     length 1 : 26351
Thu Apr 30 19:39:43 2009     length 2 : 25890
Thu Apr 30 19:39:43 2009  largest cycle: 2 relations
Thu Apr 30 19:39:43 2009  matrix is 52059 x 52241 (7.1 MB) with weight 1660494 (31.79/col)
Thu Apr 30 19:39:43 2009  sparse part has weight 1660494 (31.79/col)
Thu Apr 30 19:39:43 2009  filtering completed in 3 passes
Thu Apr 30 19:39:43 2009  matrix is 38003 x 38067 (5.7 MB) with weight 1338402 (35.16/col)
Thu Apr 30 19:39:43 2009  sparse part has weight 1338402 (35.16/col)
Thu Apr 30 19:39:43 2009  saving the first 48 matrix rows for later
Thu Apr 30 19:39:43 2009  matrix is 37955 x 38067 (3.6 MB) with weight 1010804 (26.55/col)
Thu Apr 30 19:39:43 2009  sparse part has weight 719314 (18.90/col)
Thu Apr 30 19:39:43 2009  matrix includes 64 packed rows
Thu Apr 30 19:39:43 2009  using block size 15226 for processor cache size 6144 kB
Thu Apr 30 19:39:44 2009  commencing Lanczos iteration
Thu Apr 30 19:39:44 2009  memory use: 4.2 MB
Thu Apr 30 19:39:47 2009  lanczos halted after 602 iterations (dim = 37953)
Thu Apr 30 19:39:47 2009  recovered 17 nontrivial dependencies
Thu Apr 30 19:39:47 2009  prp40 factor: 4069370006867177330397707858452514611997
Thu Apr 30 19:39:47 2009  prp43 factor: 3660130512500783146450462819085092132451731
Thu Apr 30 19:39:47 2009  elapsed time 00:17:49

Apr 30, 2009 (3rd)

By Sinkiti Sibata / Msieve / Apr 30, 2009

(55·10¹²⁰+17)/9 = 6(1)₁₁₉3_<121> = 23² · 29 · 14885411 · 4444147626799_<13> · C97

C97 = P38 · P59

P38 = 98307462555318089826526950770199792763_<38>

P59 = 61253472778706241794870926147499037925858616278305839202899_<59>

Thu Apr 30 07:44:49 2009  Msieve v. 1.41
Thu Apr 30 07:44:49 2009  random seeds: bf780874 d93eee60
Thu Apr 30 07:44:49 2009  factoring 6021673481575859773124401532919227792673004029510249607602079740999815999962637314855610908819937 (97 digits)
Thu Apr 30 07:44:51 2009  searching for 15-digit factors
Thu Apr 30 07:44:52 2009  commencing quadratic sieve (97-digit input)
Thu Apr 30 07:44:53 2009  using multiplier of 17
Thu Apr 30 07:44:53 2009  using 32kb Intel Core sieve core
Thu Apr 30 07:44:53 2009  sieve interval: 36 blocks of size 32768
Thu Apr 30 07:44:53 2009  processing polynomials in batches of 6
Thu Apr 30 07:44:53 2009  using a sieve bound of 2404033 (88123 primes)
Thu Apr 30 07:44:53 2009  using large prime bound of 360604950 (28 bits)
Thu Apr 30 07:44:53 2009  using double large prime bound of 2527301234494800 (43-52 bits)
Thu Apr 30 07:44:53 2009  using trial factoring cutoff of 52 bits
Thu Apr 30 07:44:53 2009  polynomial 'A' values have 13 factors
Thu Apr 30 13:48:31 2009  88458 relations (21528 full + 66930 combined from 1321428 partial), need 88219
Thu Apr 30 13:48:35 2009  begin with 1342956 relations
Thu Apr 30 13:48:36 2009  reduce to 231324 relations in 11 passes
Thu Apr 30 13:48:36 2009  attempting to read 231324 relations
Thu Apr 30 13:48:40 2009  recovered 231324 relations
Thu Apr 30 13:48:40 2009  recovered 218564 polynomials
Thu Apr 30 13:48:41 2009  attempting to build 88458 cycles
Thu Apr 30 13:48:41 2009  found 88458 cycles in 6 passes
Thu Apr 30 13:48:41 2009  distribution of cycle lengths:
Thu Apr 30 13:48:41 2009     length 1 : 21528
Thu Apr 30 13:48:41 2009     length 2 : 15366
Thu Apr 30 13:48:41 2009     length 3 : 14830
Thu Apr 30 13:48:41 2009     length 4 : 12274
Thu Apr 30 13:48:41 2009     length 5 : 8982
Thu Apr 30 13:48:41 2009     length 6 : 6220
Thu Apr 30 13:48:41 2009     length 7 : 3944
Thu Apr 30 13:48:41 2009     length 9+: 5314
Thu Apr 30 13:48:41 2009  largest cycle: 22 relations
Thu Apr 30 13:48:41 2009  matrix is 88123 x 88458 (23.7 MB) with weight 5867152 (66.33/col)
Thu Apr 30 13:48:41 2009  sparse part has weight 5867152 (66.33/col)
Thu Apr 30 13:48:43 2009  filtering completed in 3 passes
Thu Apr 30 13:48:43 2009  matrix is 84104 x 84167 (22.7 MB) with weight 5602479 (66.56/col)
Thu Apr 30 13:48:43 2009  sparse part has weight 5602479 (66.56/col)
Thu Apr 30 13:48:43 2009  saving the first 48 matrix rows for later
Thu Apr 30 13:48:43 2009  matrix is 84056 x 84167 (13.7 MB) with weight 4362940 (51.84/col)
Thu Apr 30 13:48:43 2009  sparse part has weight 3088177 (36.69/col)
Thu Apr 30 13:48:43 2009  matrix includes 64 packed rows
Thu Apr 30 13:48:43 2009  using block size 33666 for processor cache size 1024 kB
Thu Apr 30 13:48:44 2009  commencing Lanczos iteration
Thu Apr 30 13:48:44 2009  memory use: 13.5 MB
Thu Apr 30 13:49:34 2009  lanczos halted after 1331 iterations (dim = 84054)
Thu Apr 30 13:49:34 2009  recovered 17 nontrivial dependencies
Thu Apr 30 13:49:35 2009  prp38 factor: 98307462555318089826526950770199792763
Thu Apr 30 13:49:35 2009  prp59 factor: 61253472778706241794870926147499037925858616278305839202899
Thu Apr 30 13:49:35 2009  elapsed time 06:04:46

(55·10¹³⁵+17)/9 = 6(1)₁₃₄3_<136> = 19 · 3638454243911_<13> · 342126911555309500721535304267_<30> · C93

C93 = P47 · P47

P47 = 13042718211587829831766097413915690329339148483_<47>

P47 = 19810448732557328228341823177874542870780022037_<47>

Thu Apr 30 14:57:37 2009  Msieve v. 1.41
Thu Apr 30 14:57:37 2009  random seeds: 9171f740 959a443a
Thu Apr 30 14:57:37 2009  factoring 258382100463852506230968335487805430257100969220134618900431126539928243525631289673555119871 (93 digits)
Thu Apr 30 14:57:37 2009  searching for 15-digit factors
Thu Apr 30 14:57:39 2009  commencing quadratic sieve (93-digit input)
Thu Apr 30 14:57:39 2009  using multiplier of 1
Thu Apr 30 14:57:39 2009  using 32kb Intel Core sieve core
Thu Apr 30 14:57:39 2009  sieve interval: 36 blocks of size 32768
Thu Apr 30 14:57:39 2009  processing polynomials in batches of 6
Thu Apr 30 14:57:39 2009  using a sieve bound of 1889131 (70449 primes)
Thu Apr 30 14:57:39 2009  using large prime bound of 221028327 (27 bits)
Thu Apr 30 14:57:39 2009  using double large prime bound of 1047143580966873 (42-50 bits)
Thu Apr 30 14:57:39 2009  using trial factoring cutoff of 50 bits
Thu Apr 30 14:57:39 2009  polynomial 'A' values have 12 factors
Thu Apr 30 16:54:56 2009  70670 relations (18405 full + 52265 combined from 916226 partial), need 70545
Thu Apr 30 16:54:57 2009  begin with 934631 relations
Thu Apr 30 16:54:58 2009  reduce to 177805 relations in 13 passes
Thu Apr 30 16:54:58 2009  attempting to read 177805 relations
Thu Apr 30 16:55:00 2009  recovered 177805 relations
Thu Apr 30 16:55:00 2009  recovered 156794 polynomials
Thu Apr 30 16:55:01 2009  attempting to build 70670 cycles
Thu Apr 30 16:55:01 2009  found 70670 cycles in 6 passes
Thu Apr 30 16:55:01 2009  distribution of cycle lengths:
Thu Apr 30 16:55:01 2009     length 1 : 18405
Thu Apr 30 16:55:01 2009     length 2 : 13040
Thu Apr 30 16:55:01 2009     length 3 : 12090
Thu Apr 30 16:55:01 2009     length 4 : 9445
Thu Apr 30 16:55:01 2009     length 5 : 6860
Thu Apr 30 16:55:01 2009     length 6 : 4372
Thu Apr 30 16:55:01 2009     length 7 : 2799
Thu Apr 30 16:55:01 2009     length 9+: 3659
Thu Apr 30 16:55:01 2009  largest cycle: 18 relations
Thu Apr 30 16:55:01 2009  matrix is 70449 x 70670 (17.6 MB) with weight 4333606 (61.32/col)
Thu Apr 30 16:55:01 2009  sparse part has weight 4333606 (61.32/col)
Thu Apr 30 16:55:02 2009  filtering completed in 3 passes
Thu Apr 30 16:55:02 2009  matrix is 66349 x 66413 (16.7 MB) with weight 4101622 (61.76/col)
Thu Apr 30 16:55:02 2009  sparse part has weight 4101622 (61.76/col)
Thu Apr 30 16:55:02 2009  saving the first 48 matrix rows for later
Thu Apr 30 16:55:02 2009  matrix is 66301 x 66413 (10.0 MB) with weight 3166149 (47.67/col)
Thu Apr 30 16:55:02 2009  sparse part has weight 2210961 (33.29/col)
Thu Apr 30 16:55:02 2009  matrix includes 64 packed rows
Thu Apr 30 16:55:02 2009  using block size 26565 for processor cache size 1024 kB
Thu Apr 30 16:55:03 2009  commencing Lanczos iteration
Thu Apr 30 16:55:03 2009  memory use: 10.0 MB
Thu Apr 30 16:55:30 2009  lanczos halted after 1050 iterations (dim = 66297)
Thu Apr 30 16:55:30 2009  recovered 15 nontrivial dependencies
Thu Apr 30 16:55:31 2009  prp47 factor: 13042718211587829831766097413915690329339148483
Thu Apr 30 16:55:31 2009  prp47 factor: 19810448732557328228341823177874542870780022037
Thu Apr 30 16:55:31 2009  elapsed time 01:57:54

(55·10¹⁵⁰+17)/9 = 6(1)₁₄₉3_<151> = 19690979640099324919_<20> · 860104955775585341543623128989_<30> · C102

C102 = P43 · P59

P43 = 8420887143370657565490007495995287668142801_<43>

P59 = 42849283068676424463551912087229682013357069256594047052443_<59>

Number: 61113_150
N=360828976895667299737562769774660717483559074368529041201510988550692299042274113620704153686059912843
  ( 102 digits)
Divisors found:
 r1=8420887143370657565490007495995287668142801 (pp43)
 r2=42849283068676424463551912087229682013357069256594047052443 (pp59)
Version: Msieve-1.40
Total time: 4.78 hours.
Scaled time: 12.22 units (timescale=2.554).
Factorization parameters were as follows:
name: 61113_150
# Murphy_E = 3.043745e-09, selected by Jeff Gilchrist
n: 360828976895667299737562769774660717483559074368529041201510988550692299042274113620704153686059912843
Y0: -44113535318694843826
Y1: 24303255677
c0: 465157296557827797222705
c1: 268644217472380387089
c2: 16241102223304477
c3: -1397388248401
c4: -105304494
c5: 2160
skew: 16337.53
type: gnfs
# selected mechanically
rlim: 1670000
alim: 1670000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.4
alambda: 2.4
Factor base limits: 1670000/1670000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [835000, 1435001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 220727 x 220975
Total sieving time: 4.78 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1670000,1670000,26,26,48,48,2.4,2.4,100000
total time: 4.78 hours.
 --------- CPU info (if available) ----------

Apr 30, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.2 / Apr 30, 2009

(55·10¹⁵¹+17)/9 = 6(1)₁₅₀3_<152> = 3 · 7 · 83 · 1429 · 2417 · C143

C143 = P31 · P112

P31 = 3308092725448856055133083186613_<31>

P112 = 3068571445944642173555566328749439194505144924727462058149060519333716290496346376102747785291468715529594477999_<112>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1070043456
Step 1 took 7665ms
Step 2 took 8164ms
********** Factor found in step 2: 3308092725448856055133083186613
Found probable prime factor of 31 digits: 3308092725448856055133083186613
Probable prime cofactor has 112 digits

(55·10¹¹⁹+17)/9 = 6(1)₁₁₈3_<120> = C120

C120 = P31 · C90

P31 = 1619798646167707926668253111679_<31>

C90 = [377275973502597272706476705893861400303860757026705314272481031102839141493245455438961847_<90>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=905747387
Step 1 took 6385ms
Step 2 took 7264ms
********** Factor found in step 2: 1619798646167707926668253111679
Found probable prime factor of 31 digits: 1619798646167707926668253111679
Composite cofactor has 90 digits

Apr 30, 2009

By Markus Tervooren / Ggnfs (64bit/asm). msieve 1.41 for postprocessing / Apr 30, 2009

(5·10¹⁹⁰+31)/9 = (5)₁₈₉9_<190> = 3² · 19 · 1289 · C185

C185 = P63 · P122

P63 = 596490706585371570344324760800537294958709584946084830273397247_<63>

P122 = 42254676923334035495094749677381553294665771130138374934168106601251727561083274480199497819607561303592623938582818320563_<122>

Msieve v. 1.41
Wed Apr 29 14:52:14 2009
random seeds: edf8ec04 782fc9ce
factoring 25204522094536113291302272288484910808757664065055896068649052738446121049254172986700581871597074460711443004258051962650930979432605880416640832031519767150543081837570969633087690061 (185 digits)
searching for 15-digit factors
commencing number field sieve (185-digit input)
R0: -100000000000000000000000000000000000000
R1:  1
A0:  31
A1:  0
A2:  0
A3:  0
A4:  0
A5:  5
skew 1.44, size 3.598405e-13, alpha 1.058678, combined = 4.358459e-11

commencing relation filtering
commencing duplicate removal, pass 1
found 2765388 hash collisions in 21909200 relations
added 2008 free relations
commencing duplicate removal, pass 2
found 2395885 duplicates and 19515323 unique relations
memory use: 98.6 MB
reading rational ideals above 10551296
reading algebraic ideals above 10551296
commencing singleton removal, pass 1
relations with 0 large ideals: 276562
relations with 1 large ideals: 1803867
relations with 2 large ideals: 5315527
relations with 3 large ideals: 7329666
relations with 4 large ideals: 4050810
relations with 5 large ideals: 56111
relations with 6 large ideals: 682780
relations with 7+ large ideals: 0
19515323 relations and about 18790045 large ideals
commencing singleton removal, pass 2
found 6777251 singletons
current dataset: 12738072 relations and about 10470759 large ideals
commencing singleton removal, pass 3
found 1852958 singletons
current dataset: 10885114 relations and about 8502586 large ideals
commencing singleton removal, pass 4
found 526086 singletons
current dataset: 10359028 relations and about 7965610 large ideals
commencing singleton removal, pass 5
found 160949 singletons
current dataset: 10198079 relations and about 7803602 large ideals
commencing singleton removal, final pass
memory use: 176.4 MB
commencing in-memory singleton removal
begin with 10198079 relations and 8686922 unique ideals
reduce to 8126643 relations and 6547174 ideals in 20 passes
max relations containing the same ideal: 52
reading rational ideals above 720000
reading algebraic ideals above 720000
commencing singleton removal, final pass
keeping 7164674 ideals with weight <= 20, new excess is 791838
memory use: 250.5 MB
commencing in-memory singleton removal
begin with 8128654 relations and 7164674 unique ideals
reduce to 8125274 relations and 7151386 ideals in 9 passes
max relations containing the same ideal: 20
removing 402438 relations and 374760 ideals in 27678 cliques
commencing in-memory singleton removal
begin with 7722836 relations and 7151386 unique ideals
reduce to 7706040 relations and 6759735 ideals in 8 passes
max relations containing the same ideal: 20
removing 289505 relations and 261827 ideals in 27678 cliques
commencing in-memory singleton removal
begin with 7416535 relations and 6759735 unique ideals
reduce to 7407787 relations and 6489121 ideals in 8 passes
max relations containing the same ideal: 20
relations with 0 large ideals: 63990
relations with 1 large ideals: 431150
relations with 2 large ideals: 1396533
relations with 3 large ideals: 2324416
relations with 4 large ideals: 2038853
relations with 5 large ideals: 878401
relations with 6 large ideals: 252051
relations with 7+ large ideals: 22393
commencing 2-way merge
reduce to 4358946 relation sets and 3440280 unique ideals
commencing full merge
memory use: 311.5 MB
found 2107420 cycles, need 1990480
weight of 1990480 cycles is about 139461325 (70.06/cycle)
distribution of cycle lengths:
1 relations: 259851
2 relations: 243805
3 relations: 238556
4 relations: 210119
5 relations: 188648
6 relations: 157800
7 relations: 135361
8 relations: 114188
9 relations: 95544
10+ relations: 346608
heaviest cycle: 20 relations
commencing cycle optimization
start with 11200236 relations
pruned 262711 relations
memory use: 383.6 MB
distribution of cycle lengths:
1 relations: 259851
2 relations: 249376
3 relations: 247493
4 relations: 215226
5 relations: 192636
6 relations: 159411
7 relations: 136102
8 relations: 113416
9 relations: 94468
10+ relations: 322501
heaviest cycle: 20 relations
RelProcTime: 875

commencing linear algebra
read 1990480 cycles
cycles contain 6522097 unique relations
read 6522097 relations
using 20 quadratic characters above 268435034
building initial matrix
memory use: 797.2 MB
read 1990480 cycles
matrix is 1989699 x 1990480 (596.7 MB) with weight 176041428 (88.44/col)
sparse part has weight 134521867 (67.58/col)
filtering completed in 3 passes
matrix is 1962834 x 1963034 (591.7 MB) with weight 174425357 (88.85/col)
sparse part has weight 133519598 (68.02/col)
read 1963034 cycles
matrix is 1962834 x 1963034 (591.7 MB) with weight 174425357 (88.85/col)
sparse part has weight 133519598 (68.02/col)
saving the first 48 matrix rows for later
matrix is 1962786 x 1963034 (560.2 MB) with weight 138173302 (70.39/col)
sparse part has weight 127216851 (64.81/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (4 threads)
memory use: 585.2 MB
linear algebra completed 1962681 of 1963034 dimensions (100.0%, ETA 0h 0m)
lanczos halted after 31043 iterations (dim = 1962785)
recovered 35 nontrivial dependencies
BLanczosTime: 18268

commencing square root phase
reading relations for dependency 1
read 981558 cycles
cycles contain 3931062 unique relations
read 3931062 relations
multiplying 3243788 relations
multiply complete, coefficients have about 84.11 million bits
initial square root is modulo 1090381
reading relations for dependency 2
read 982286 cycles
cycles contain 3935792 unique relations
read 3935792 relations
multiplying 3247420 relations
multiply complete, coefficients have about 84.21 million bits
initial square root is modulo 1107721
sqrtTime: 1133
prp63 factor: 596490706585371570344324760800537294958709584946084830273397247
prp122 factor: 42254676923334035495094749677381553294665771130138374934168106601251727561083274480199497819607561303592623938582818320563
elapsed time 05:38:12

Sieving took ~ 151hours on one core (Q6700@3.3Ghz)

(55·10¹⁰⁵+17)/9 = 6(1)₁₀₄3_<106> = 683 · 1445241877_<10> · C94

C94 = P38 · P56

P38 = 81029967971957752955713055836047647693_<38>

P56 = 76403503205391551231527775810749279533656827067863897451_<56>

Number: k1
N=6190973417678248911826496973321001897506450037367806314609001941975686201499624743187528730543
  ( 94 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=81029967971957752955713055836047647693 (pp38)
 r2=76403503205391551231527775810749279533656827067863897451 (pp56)
Version: Msieve-1.39
Total time: 0.20 hours.
Scaled time: 0.50 units (timescale=2.472).
Factorization parameters were as follows:
n: 6190973417678248911826496973321001897506450037367806314609001941975686201499624743187528730543
m: 200000000000000000000000000
deg: 4
c4: 275
c0: 136
skew: 0.84
type: snfs
lss: 1
rlim: 440000
alim: 440000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2

Factor base limits: 440000/440000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [220000, 300001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 38956 x 39183
Total sieving time: 0.19 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107,4,0,0,0,0,0,0,0,0,440000,440000,25,25,44,44,2.2,2.2,40000
total time: 0.20 hours.
 --------- CPU info (if available) ----------
[    0.140008] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.232014] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.327367] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.424240] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8198000k/10485760k available (2226k kernel code, 189836k reserved, 1082k data, 392k init)
[    0.083992] Calibrating delay using timer specific routine.. 6404.32 BogoMIPS (lpj=12808640)
[    0.152009] Calibrating delay using timer specific routine.. 6400.07 BogoMIPS (lpj=12800150)
[    0.244015] Calibrating delay using timer specific routine.. 6400.09 BogoMIPS (lpj=12800199)
[    0.343793] Calibrating delay using timer specific routine.. 6400.09 BogoMIPS (lpj=12800187)
[    0.428765] Total of 4 processors activated (25604.58 BogoMIPS).

Apr 29, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Apr 29, 2009

(53·10¹⁷⁰+1)/9 = 5(8)₁₆₉9_<171> = 1559 · 2903 · 370723 · 33658580232709090033_<20> · 67871489825328151030318753_<26> · C114

C114 = P50 · P64

P50 = 15878422731457635314161599067107119872220986892417_<50>

P64 = 9676095432618857994298840083734799477765342988159463785324899923_<64>

Number: n
N=153641133669048676609099915708201614219856303269170854973086875495889780066889209852193311327532571098675292583891
  ( 114 digits)
Divisors found:

Wed Apr 29 23:25:18 2009  prp50 factor: 15878422731457635314161599067107119872220986892417
Wed Apr 29 23:25:18 2009  prp64 factor: 9676095432618857994298840083734799477765342988159463785324899923
Wed Apr 29 23:25:18 2009  elapsed time 00:59:50 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 18.46 hours.
Scaled time: 49.31 units (timescale=2.671).
Factorization parameters were as follows:
name: KA_5_8_169_9
n: 153641133669048676609099915708201614219856303269170854973086875495889780066889209852193311327532571098675292583891
Y0: -8973732757865968818489
Y1:  1655113373459
c0:  6530038059463148739514985720
c1: -505049272014818434778864
c2: -6938797053941142849
c3:  242228848255076
c4:  1249680886
c5:  2640
skew: 50592.33
type: gnfs
rlim: 3500000
alim: 3500080
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3500000/3500080
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1750040, 2600177)
Primes: RFBsize:250150, AFBsize:249214, largePrimes:16960803 encountered
Relations: rels:14902027, finalFF:531448
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 952641 hash collisions in 15494590 relations
Msieve: matrix is 583643 x 583891 (164.2 MB)

Total sieving time: 17.90 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500080,28,28,56,56,2.6,2.6,100000
total time: 18.46 hours.
 --------- CPU info (if available) ----------

Apr 29, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Apr 29, 2009

(32·10¹⁸¹+13)/9 = 3(5)₁₈₀7_<182> = 23² · 37 · 97 · C176

C176 = P66 · P110

P66 = 187800281843242246319283489339418659405151754020076889041478011149_<66>

P110 = 99719960730962349469939681299619260059373306342828270295826680925337086911707248717062806086045272017174413653_<110>

Number: 35557_181
N=18727436730671778320522303528559253229414786914835635432755071053358037163310680742910392316975444058249585114122365890923566366436594254106385535068325004598463565976671817297
  ( 176 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=187800281843242246319283489339418659405151754020076889041478011149 (pp66)
 r2=99719960730962349469939681299619260059373306342828270295826680925337086911707248717062806086045272017174413653 (pp110)
Version: Msieve-1.39
Total time: 137.88 hours.
Scaled time: 239.22 units (timescale=1.735).
Factorization parameters were as follows:
n: 18727436730671778320522303528559253229414786914835635432755071053358037163310680742910392316975444058249585114122365890923566366436594254106385535068325004598463565976671817297
m: 2000000000000000000000000000000000000
deg: 5
c5: 10
c0: 13
skew: 1.05
type: snfs
lss: 1
rlim: 7700000
alim: 7700000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7700000/7700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3850000, 6150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1475073 x 1475319
Total sieving time: 137.88 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,7700000,7700000,28,28,53,53,2.5,2.5,100000
total time: 137.88 hours.
 --------- CPU info (if available) ----------

(38·10¹⁷⁰+43)/9 = 4(2)₁₆₉7_<171> = 7 · 17 · 2895407 · 52481041 · C155

C155 = P51 · P105

P51 = 159420766227975595294803856574498124726059142719287_<51>

P105 = 146466118542925818385076619853708085471450289535066254778571014685940595834245664133461216599012397408957_<105>

Number: 42227_170
N=23349740844550738413468620796920875678681831018675493539509566502420110283104445553529638281716803731915120107180379989058300534100274710632172829990453659
  ( 155 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=159420766227975595294803856574498124726059142719287 (pp51)
 r2=146466118542925818385076619853708085471450289535066254778571014685940595834245664133461216599012397408957 (pp105)
Version: Msieve-1.39
Total time: 72.39 hours.
Scaled time: 185.32 units (timescale=2.560).
Factorization parameters were as follows:
n: 23349740844550738413468620796920875678681831018675493539509566502420110283104445553529638281716803731915120107180379989058300534100274710632172829990453659
m: 10000000000000000000000000000000000
deg: 5
c5: 38
c0: 43
skew: 1.03
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 6150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1013018 x 1013266
Total sieving time: 72.39 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 72.39 hours.
 --------- CPU info (if available) ----------

Apr 29, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Apr 29, 2009

6·10²⁰²+1 = 6(0)₂₀₁1_<203> = 113761 · 244393 · 660429923798209_<15> · 135180804513951511904761_<24> · 5164634473621039289825138497_<28> · C127

C127 = P40 · P88

P40 = 1664792180982452240067957261454638056603_<40>

P88 = 2811432753405739343413857814027793980466733704390188713337746638191403396481943299125843_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2090088941
Step 1 took 39950ms
Step 2 took 13878ms
********** Factor found in step 2: 1664792180982452240067957261454638056603
Found probable prime factor of 40 digits: 1664792180982452240067957261454638056603
Probable prime cofactor 2811432753405739343413857814027793980466733704390188713337746638191403396481943299125843 has 88 digits

Apr 29, 2009 (2nd)

By matsui / GGNFS / Apr 29, 2009

6·10¹⁷³-7 = 5(9)₁₇₂3_<174> = 13413022373_<11> · C164

C164 = P63 · P102

P63 = 254106107960663411887642298189807618950496854389331792179242251_<63>

P102 = 176039244907150995933870857374771574815002400239328663586454894500763717483116064141859499252833070191_<102>

N=44732647371690177676556686975116849751041565641321994088050866177437636038751129875566338175972264890219757780761885559854944409552577729082119380134429900275839941
  ( 164 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=254106107960663411887642298189807618950496854389331792179242251 (pp63)
 r2=176039244907150995933870857374771574815002400239328663586454894500763717483116064141859499252833070191 (pp102)
Version: GGNFS-0.77.1-20060722-nocona

Apr 29, 2009

Factorizations of 611...113 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 28, 2009 (4th)

By Robert Backstrom / GMP-ECM / Apr 28, 2009

(17·10¹⁹⁵-11)/3 = 5(6)₁₉₄3_<196> = 7² · C195

C195 = P30 · P31 · P135

P30 = 414958074700194542917848678779_<30>

P31 = 2262764706204964092765220058089_<31>

P135 = 123165186981656208756429892828244296154398570791072162187495203445595219090684605813054472085211731050735511770532990502679306295915277_<135>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 115646258503401360544217687074829931972789115646258503401360544217687074829931972789115646258503401360544217687074829931972789115646258503401360544217687074829931972789115646258503401360544217687 (195 digits)
Using B1=256000, B2=128992510, polynomial Dickson(3), sigma=2791982785
Step 1 took 4578ms
Step 2 took 1922ms
********** Factor found in step 2: 414958074700194542917848678779
Found probable prime factor of 30 digits: 414958074700194542917848678779
Composite cofactor 278693838135226779409771569075683326071205809800631128168413521983821959681026143781812575882484316995296990661338781612806612800609366574896864133131995689362525653 has 165 digits

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 278693838135226779409771569075683326071205809800631128168413521983821959681026143781812575882484316995296990661338781612806612800609366574896864133131995689362525653 (165 digits)
Using B1=582000, B2=522330282, polynomial Dickson(3), sigma=2912169454
Step 1 took 8203ms
Step 2 took 3687ms
********** Factor found in step 2: 2262764706204964092765220058089
Found probable prime factor of 31 digits: 2262764706204964092765220058089
Probable prime cofactor 123165186981656208756429892828244296154398570791072162187495203445595219090684605813054472085211731050735511770532990502679306295915277 has 135 digits

Apr 28, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 28, 2009

(37·10¹⁹⁴+71)/9 = 4(1)₁₉₃9_<195> = 116269 · 575551 · 474471463 · 16349135082988589810249_<23> · 7590690876337436335686621759791_<31> · C123

C123 = P50 · P73

P50 = 12689133514263467130577716351690146927441657627153_<50>

P73 = 8222299893729791483441854911572970421842011419673633184844616755425556501_<73>

Number: 41119_194
N=104333861145851641332524267483514811395721107982807617312384858364100696592011759800416745004248697924636939449966193271653
  ( 123 digits)
Divisors found:
 r1=12689133514263467130577716351690146927441657627153 (pp50)
 r2=8222299893729791483441854911572970421842011419673633184844616755425556501 (pp73)
Version: Msieve-1.39
Total time: 52.43 hours.
Scaled time: 134.81 units (timescale=2.571).
Factorization parameters were as follows:
# Murphy_E = 2.261027e-10, selected by Jeff Gilchrist
n: 104333861145851641332524267483514811395721107982807617312384858364100696592011759800416745004248697924636939449966193271653
Y0: -358902855847175299483599
Y1: 12722330017853
c0: -67487540322810138587241212720
c1: -1928877254811875151103060
c2: 9917690775179473736
c3: -365384477507579
c4: 7519778430
c5: 17520
skew: 108467.52
type: gnfs
# selected mechanically
rlim: 6000000
alim: 6000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3000000, 5460001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 872357 x 872605
Total sieving time: 52.43 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6000000,6000000,27,27,52,52,2.5,2.5,60000
total time: 52.43 hours.
 --------- CPU info (if available) ----------

Apr 28, 2009 (2nd)

By Sinkiti Sibata / Msieve / Apr 28, 2009

(53·10¹⁵¹+1)/9 = 5(8)₁₅₀9_<152> = C152

C152 = P41 · P112

P41 = 11005133755709399739846139646663420523079_<41>

P112 = 5351037997001869599349449652602850650625326819936478162439626755570976783012160572839424777050332270827075435391_<112>

Number: 58889_151
N=58888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
  ( 152 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=11005133755709399739846139646663420523079 (pp41)
 r2=5351037997001869599349449652602850650625326819936478162439626755570976783012160572839424777050332270827075435391 (pp112)
Version: Msieve-1.40
Total time: 17.28 hours.
Scaled time: 44.13 units (timescale=2.554).
Factorization parameters were as follows:
name: 58889_151
n: 58888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
m: 2000000000000000000000000000000
deg: 5
c5: 265
c0: 16
skew: 0.57
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 417672 x 417920
Total sieving time: 17.28 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,153.000,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 17.28 hours.
 --------- CPU info (if available) ----------

Apr 28, 2009

By Erik Branger / GGNFS, Msieve / Apr 28, 2009

(53·10¹⁵⁹+1)/9 = 5(8)₁₅₈9_<160> = 3² · 13 · 47 · 61 · 543172787 · 146740646009623_<15> · C132

C132 = P35 · P98

P35 = 10377904187206720222921982134102753_<35>

P98 = 21223730306600451520506577284963975239844497432815229537295512873899546101677447590414810139556667_<98>

Number: 58889_159
N=220257839617014993830972198331986848532988764441820703907772064964369436808103896076625018003186857576871201553751260640857244204251
  ( 132 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=10377904187206720222921982134102753
 r2=21223730306600451520506577284963975239844497432815229537295512873899546101677447590414810139556667
Version: 
Total time: 35.62 hours.
Scaled time: 13.04 units (timescale=0.366).
Factorization parameters were as follows:
n: 220257839617014993830972198331986848532988764441820703907772064964369436808103896076625018003186857576871201553751260640857244204251
m: 100000000000000000000000000000000
deg: 5
c5: 53
c0: 10
skew: 0.72
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 2950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 552981 x 553229
Total sieving time: 35.62 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 35.62 hours.
 --------- CPU info (if available) ----------

(53·10¹⁵⁸+1)/9 = 5(8)₁₅₇9_<159> = 17 · 89803869709_<11> · C147

C147 = P44 · P104

P44 = 19946527811963839934482153629736138114375201_<44>

P104 = 19338468652164063844346333500613745540736302026055121157305398505959820677361605766269700887682845416813_<104>

Number: 58889_158
N=385735302811181373164720709392959043285994687825358692003531655890684490008848014445034506438029630727378434344317104001017539262422756993915654413
  ( 147 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=19946527811963839934482153629736138114375201 r2=19338468652164063844346333500613745540736302026055121157305398505959820677361605766269700887682845416813
Version: 
Total time: 49.58 hours.
Scaled time: 38.92 units (timescale=0.785).
Factorization parameters were as follows:
n: 385735302811181373164720709392959043285994687825358692003531655890684490008848014445034506438029630727378434344317104001017539262422756993915654413
m: 100000000000000000000000000000000
deg: 5
c5: 53
c0: 100
skew: 1.14
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 652164 x 652412
Total sieving time: 49.58 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 49.58 hours.
 --------- CPU info (if available) ----------

Apr 27, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 27, 2009

(8·10¹⁹⁶+1)/9 = (8)₁₉₅9_<196> = 3 · 1049 · 19963 · 41551177 · 17551912671521_<14> · C168

C168 = P84 · P84

P84 = 421129308634456116834768473972139562323863312499765456942425930345152305882854016787_<84>

P84 = 460682463707263415511160506455196986916514178796229063957358489523887114186474351731_<84>

Number: 88889_196
N=194006887441057763765515995169149538695667950334540943575287725969382691109491784798555200805367453309820823386266387230890825153146947270793405098814003126465216508297
  ( 168 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=421129308634456116834768473972139562323863312499765456942425930345152305882854016787
 r2=460682463707263415511160506455196986916514178796229063957358489523887114186474351731
Version: 
Total time: 229.06 hours.
Scaled time: 547.23 units (timescale=2.389).
Factorization parameters were as follows:
n: 194006887441057763765515995169149538695667950334540943575287725969382691109491784798555200805367453309820823386266387230890825153146947270793405098814003126465216508297
m: 2000000000000000000000000000000000000000
deg: 5
c5: 5
c0: 2
skew: 0.83
type: snfs
lss: 1
rlim: 14000000
alim: 14000000
lpbr: 29
lpba: 29
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 14000000/14000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 55/55
Sieved rational special-q in [7000000, 12300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 33667751
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2463371 x 2463619
Total sieving time: 202.13 hours.
Total relation processing time: 9.13 hours.
Matrix solve time: 17.44 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,14000000,14000000,29,29,55,55,2.5,2.5,100000
total time: 229.06 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673787)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

Apr 27, 2009 (6th)

By Ignacio Santos / GGNFS, Msieve / Apr 27, 2009

(53·10¹⁵³-17)/9 = 5(8)₁₅₂7_<154> = 7³ · 523 · 23831 · 229108109084325281_<18> · C127

C127 = P37 · P91

P37 = 1259429971180200006189700716076596071_<37>

P91 = 4773982244934065198215618554300837516932709210804279640544817629668719303310081359797913443_<91>

Number: 58887_153
N=6012496321152096259587445596313959195882890027045872444206377914501626152518858072335323398759172848423407980293982711731882453
  ( 127 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=1259429971180200006189700716076596071 (pp37)
 r2=4773982244934065198215618554300837516932709210804279640544817629668719303310081359797913443 (pp91)
Version: Msieve-1.39
Total time: 22.23 hours.
Scaled time: 57.14 units (timescale=2.571).
Factorization parameters were as follows:
n: 6012496321152096259587445596313959195882890027045872444206377914501626152518858072335323398759172848423407980293982711731882453
m: 5000000000000000000000000000000
deg: 5
c5: 424
c0: -425
skew: 1.00
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 520131 x 520379
Total sieving time: 22.23 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 22.23 hours.
 --------- CPU info (if available) ----------

(53·10¹⁵⁴+1)/9 = 5(8)₁₅₃9_<155> = 37971697959006556067063120880293_<32> · C124

C124 = P56 · P68

P56 = 26750290160545884056238066771927664782732542089391686301_<56>

P68 = 57975545719181940975342922884870737353678736928569607670017493537673_<68>

Number: 58889_154
N=1550862670204110724982219118634479678512243171560765368957625011087319684805930920674488261437103400564207360267959541517573
  ( 124 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=26750290160545884056238066771927664782732542089391686301 (pp56)
 r2=57975545719181940975342922884870737353678736928569607670017493537673 (pp68)
Version: Msieve-1.39
Total time: 15.78 hours.
Scaled time: 27.44 units (timescale=1.739).
Factorization parameters were as follows:
n: 1550862670204110724982219118634479678512243171560765368957625011087319684805930920674488261437103400564207360267959541517573
m: 10000000000000000000000000000000
deg: 5
c5: 53
c0: 10
skew: 0.72
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1450000, 2350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 450588 x 450836
Total sieving time: 15.78 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000
total time: 15.78 hours.
 --------- CPU info (if available) ----------

(53·10¹⁶⁹-17)/9 = 5(8)₁₆₈7_<170> = 3 · 10289 · C166

C166 = P53 · P114

P53 = 10349469969241347631837446124602660629190655792332907_<53>

P114 = 184340529031864544303987400282044404412493423618646133662587944074027945204887635621848468895056963952913120131623_<114>

Number: 58887_169
N=1907826769329344895483490099099001810635594288038646090934943107165869339064012987620724038257326234777882168299118440045643855537917157122133310295425175394074218061
  ( 166 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=10349469969241347631837446124602660629190655792332907 (pp53)
 r2=184340529031864544303987400282044404412493423618646133662587944074027945204887635621848468895056963952913120131623 (pp114)
Version: Msieve-1.39
Total time: 72.50 hours.
Scaled time: 186.41 units (timescale=2.571).
Factorization parameters were as follows:
n: 1907826769329344895483490099099001810635594288038646090934943107165869339064012987620724038257326234777882168299118440045643855537917157122133310295425175394074218061
m: 10000000000000000000000000000000000
deg: 5
c5: 53
c0: -170
skew: 1.26
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 6150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1038042 x 1038289
Total sieving time: 72.50 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 72.50 hours.
 --------- CPU info (if available) ----------

Apr 27, 2009 (5th)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve / Apr 27, 2009

(10²¹²-7)/3 = (3)₂₁₁1_<212> = 31 · 1093 · 100741 · 10606483 · 31419071 · 50412367 · 160369474887919636204031018406084819503_<39> · C142

C142 = P44 · P99

P44 = 25944778565180928052792910166261047114212759_<44>

P99 = 139706665555714048450456121278199435970156709083690111782361972187434491639694660431695110194802271_<99>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=4244805371
Step 1 took 162657ms
Step 2 took 52038ms
********** Factor found in step 2: 25944778565180928052792910166261047114212759
Found probable prime factor of 44 digits: 25944778565180928052792910166261047114212759
Probable prime cofactor 139706665555714048450456121278199435970156709083690111782361972187434491639694660431695110194802271 has 99 digits

(14·10¹⁹⁴-11)/3 = 4(6)₁₉₃3_<195> = 23 · 1487 · C191

C191 = P44 · P68 · P80

P44 = 19918602523557170046661811204547110828816287_<44>

P68 = 38002400406508649071698524483443108152436953406221425871715619951251_<68>

P80 = 18025946657480442016359745430074112476927580274403990407522607197025714289498299_<80>

Number: 46663_194
N=13644825200042883736342991920314220831749558979756927185364950342582575558219545237468689999317758739997855813182850403984288958412522051012153640731752482870871222089022738126565500034112063
  ( 191 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=19918602523557170046661811204547110828816287
 r2=38002400406508649071698524483443108152436953406221425871715619951251
 r3=18025946657480442016359745430074112476927580274403990407522607197025714289498299
Version: 
Total time: 581.92 hours.
Scaled time: 1161.52 units (timescale=1.996).
Factorization parameters were as follows:
n: 13644825200042883736342991920314220831749558979756927185364950342582575558219545237468689999317758739997855813182850403984288958412522051012153640731752482870871222089022738126565500034112063
m: 1000000000000000000000000000000000000000
deg: 5
c5: 7
c0: -55
skew: 1.51
type: snfs
lss: 1
rlim: 12900000
alim: 12900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 12900000/12900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6450000, 12150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1950698 x 1950946
Total sieving time: 581.92 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,12900000,12900000,28,28,55,55,2.5,2.5,100000
total time: 581.92 hours.
 --------- CPU info (if available) ----------

Apr 27, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 27, 2009

(53·10¹⁵⁵-17)/9 = 5(8)₁₅₄7_<156> = 13 · 12659042761_<11> · C145

C145 = P67 · P78

P67 = 4922032361863921654624733150235114276655806509234915061421645406483_<67>

P78 = 727017184113077927619676603072589808158867829035481257917742796614728442684473_<78>

Number: n
N=3578402107835750531698448482643947610984702739732320519120106422645908869862545312176728426906934381208959970689773175902877349108209185797638459
  ( 145 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=4922032361863921654624733150235114276655806509234915061421645406483 (pp67)
 r2=727017184113077927619676603072589808158867829035481257917742796614728442684473 (pp78)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 19.09 hours.
Scaled time: 48.76 units (timescale=2.554).
Factorization parameters were as follows:
name: KA_5_8_154_7
n: 3578402107835750531698448482643947610984702739732320519120106422645908869862545312176728426906934381208959970689773175902877349108209185797638459
m: 10000000000000000000000000000000
deg: 5
c5: 53
c0: -17
skew: 0.80
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [1450000, 2550001)
Primes: RFBsize:210109, AFBsize:209174, largePrimes:13191696 encountered
Relations: rels:12964330, finalFF:660670
Max relations in full relation-set: 28
Initial matrix: 419348 x 660670 with sparse part having weight 77279116.
Pruned matrix : 341602 x 343762 with weight 40442152.
Total sieving time: 17.68 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.70 hours.
Total square root time: 0.44 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,28,28,56,56,2.4,2.4,100000
total time: 19.09 hours.
 --------- CPU info (if available) ----------

(53·10¹⁵⁵+1)/9 = 5(8)₁₅₄9_<156> = 7 · 1792927 · 3543577 · C143

C143 = P67 · P76

P67 = 2443577634254454687137637845111973397935401399897115454809979896223_<67>

P76 = 5418819651805614652357594463326606111851486150836128615586608425053563039831_<76>

Number: n
N=13241306505210711739279184521760332252149425240510002368729844950310950047876697791013586060711032376595753767593684056758030112492701795458313
  ( 143 digits)
SNFS difficulty: 156 digits.
Divisors found:

Mon Apr 27 18:10:44 2009  prp67 factor: 2443577634254454687137637845111973397935401399897115454809979896223
Mon Apr 27 18:10:44 2009  prp76 factor: 5418819651805614652357594463326606111851486150836128615586608425053563039831
Mon Apr 27 18:10:44 2009  elapsed time 00:34:11 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 15.04 hours.
Scaled time: 39.84 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_8_154_9
n: 13241306505210711739279184521760332252149425240510002368729844950310950047876697791013586060711032376595753767593684056758030112492701795458313
m: 10000000000000000000000000000000
deg: 5
c5: 53
c0: 1
skew: 0.45
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1450000, 2361467)
Primes: RFBsize:210109, AFBsize:210189, largePrimes:12185451 encountered
Relations: rels:11340683, finalFF:370663
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 907702 hash collisions in 12192549 relations
Msieve: matrix is 486333 x 486581 (129.7 MB)

Total sieving time: 14.81 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,28,28,56,56,2.4,2.4,100000
total time: 15.04 hours.
 --------- CPU info (if available) ----------

(53·10¹⁶¹-17)/9 = 5(8)₁₆₀7_<162> = 13 · 301013 · C156

C156 = P38 · P55 · P63

P38 = 40079032860800981034271182219977895493_<38>

P55 = 3845042550038572909061181163224247339297802581922082119_<55>

P63 = 976531759921969567716202456727446938275394815869598707738421069_<63>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 150488999807799992509622990698558863388953783720787139244149406501198616489318219808265088701481814071635773688508952434430736032327990150409780126769094023 (156 digits)
Using B1=1398000, B2=2139965110, polynomial Dickson(6), sigma=2643783734
Step 1 took 23821ms
Step 2 took 9563ms
********** Factor found in step 2: 40079032860800981034271182219977895493
Found probable prime factor of 38 digits: 40079032860800981034271182219977895493
Composite cofactor 3754806168364025338444730098765301182030827656499506159990711901017869567305316246258327391762206262324084086017765211 has 118 digits

Number: n
N=3754806168364025338444730098765301182030827656499506159990711901017869567305316246258327391762206262324084086017765211
  ( 118 digits)
Divisors found:

Mon Apr 27 18:53:56 2009  prp55 factor: 3845042550038572909061181163224247339297802581922082119
Mon Apr 27 18:53:56 2009  prp63 factor: 976531759921969567716202456727446938275394815869598707738421069
Mon Apr 27 18:53:56 2009  elapsed time 00:56:10 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 27.34 hours.
Scaled time: 72.15 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_5_8_160_7
n: 3754806168364025338444730098765301182030827656499506159990711901017869567305316246258327391762206262324084086017765211
Y0: -46560131168840686478827
Y1:  3378042388439
c0:  81517691767964263443146531760
c1:  2433157487496539211369302
c2: -4257028842031457161
c3: -501233010921252
c4: -401084884
c5:  17160
skew: 94782.03
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2250000, 3750001)
Primes: RFBsize:315948, AFBsize:316419, largePrimes:14325298 encountered
Relations: rels:13552992, finalFF:777281
Max relations in full relation-set: 28
Initial matrix: 632452 x 777281 with sparse part having weight 74821822.
Pruned matrix : 

Msieve: found 1227986 hash collisions in 14513606 relations
Msieve: matrix is 580380 x 580628 (160.7 MB)

Total sieving time: 26.66 hours.
Total relation processing time: 0.68 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,56,56,2.4,2.4,60000
total time: 27.34 hours.
 --------- CPU info (if available) ----------

(53·10¹⁷²+1)/9 = 5(8)₁₇₁9_<173> = 807379 · 603812754341_<12> · 28759572858649_<14> · 9993027152629419597904559069_<28> · C114

C114 = P38 · P77

P38 = 35301764274656969995635746440541350381_<38>

P77 = 11906324612627081905737388568432204863860375854067088525617352372196014894391_<77>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 420314264852507707333627373820020436227707521394433722129394296927603797534587440177074834216240620687800242612971 (114 digits)
Using B1=1172000, B2=1426247560, polynomial Dickson(6), sigma=1695054277
Step 1 took 11700ms
Step 2 took 5070ms
********** Factor found in step 2: 35301764274656969995635746440541350381
Found probable prime factor of 38 digits: 35301764274656969995635746440541350381
Probable prime cofactor 11906324612627081905737388568432204863860375854067088525617352372196014894391 has 77 digits

Apr 27, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.2 / Apr 27, 2009

6·10²¹⁶+1 = 6(0)₂₁₅1_<217> = 7³ · 3559 · 4057 · 18461 · 8865690481_<10> · C193

C193 = P35 · C158

P35 = 75489457323208605217787830670233307_<35>

C158 = [98055067697465091816689131698585149675657995487502821941906044701157348721437441754279639798790119281752053294533196233210198961184141683435508604336743525047_<158>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1144671962
Step 1 took 16225ms
********** Factor found in step 1: 75489457323208605217787830670233307
Found probable prime factor of 35 digits: 75489457323208605217787830670233307
Composite cofactor has 158 digits

6·10²³³+1 = 6(0)₂₃₂1_<234> = 294510113 · 1778348809_<10> · 778008505367081881201_<21> · C196

C196 = P31 · C165

P31 = 2561616974580876396755878639763_<31>

C165 = [574824873435899378320065034350864626543502944955975704501487535802286423132854167632694971627309959241359282121449541103533943009375174285144531117192634556032152531_<165>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2878558676
Step 1 took 15537ms
Step 2 took 15985ms
********** Factor found in step 2: 2561616974580876396755878639763
Found probable prime factor of 31 digits: 2561616974580876396755878639763
Composite cofactor has 165 digits

Apr 27, 2009 (2nd)

By Tyler Cadigan / ggnfs, msieve / Apr 27, 2009

6·10¹⁹⁴+1 = 6(0)₁₉₃1_<195> = 153817 · 33881245227068299278185531_<26> · 901361069267656452128353133474957_<33> · C132

C132 = P51 · P81

P51 = 266634767326292612283152421868647275640368024889323_<51>

P81 = 479040217579134298529209937599938953347103505261874490787658533513714122044192133_<81>

Number: 60001_194
N=127728776954149061732629779151943546510736581677373866290113899810994265965188567884730521444012921154476658141238516044262272295959
  ( 132 digits)
Divisors found:
 r1=266634767326292612283152421868647275640368024889323 (pp51)
 r2=479040217579134298529209937599938953347103505261874490787658533513714122044192133 (pp81)
Version: Msieve-1.40
Total time: 172.66 hours.
Scaled time: 437.34 units (timescale=2.533).
Factorization parameters were as follows:
name: 60001_194
n: 127728776954149061732629779151943546510736581677373866290113899810994265965188567884730521444012921154476658141238516044262272295959
skew: 135621.62
# norm 3.35e+18
c5: 118440
c4: -198636398962
c3: -14944684265948103
c2: -3350417460951912749221
c1: 53455124993580901826489895
c0: 1773295866630335112183564218255
# alpha -6.78
Y1: 439575619875863
Y0: -16090222539693828700212894
# Murphy_E 6.47e-11
# M 59533760174489839394087245664387266171938052700247014464675137044353023313433652697868784876534862498628846968815646467114351145795
type: gnfs
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved algebraic special-q in [4000000, 11000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1368948 x 1369196
Total sieving time: 166.98 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 3.76 hours.
Time per square root: 1.54 hours.
Prototype def-par.txt line would be:
gnfs,131,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,28,28,55,55,2.5,2.5,100000
total time: 172.66 hours.
 --------- CPU info (if available) ----------

Apr 27, 2009

Factorizations of 600...001 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 26, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 26, 2009

(53·10¹⁴⁹+1)/9 = 5(8)₁₄₈9_<150> = 7 · 89 · 181 · 13860095467_<11> · 127907351040860227747_<21> · C115

C115 = P36 · P79

P36 = 298749405551037697759977109415955797_<36>

P79 = 9860477861640212173667954263879056032708182342505378235882532507138565347054351_<79>

Number: 58889_149
N=2945811899614180730648502625419787915632663325606645886918019990610313348603055671902651871116824477221833172522747
  ( 115 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=298749405551037697759977109415955797 (pp36)
 r2=9860477861640212173667954263879056032708182342505378235882532507138565347054351 (pp79)
Version: Msieve-1.39
Total time: 11.63 hours.
Scaled time: 29.90 units (timescale=2.571).
Factorization parameters were as follows:
n: 2945811899614180730648502625419787915632663325606645886918019990610313348603055671902651871116824477221833172522747
m: 1000000000000000000000000000000
deg: 5
c5: 53
c0: 10
skew: 0.72
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 361280 x 361528
Total sieving time: 11.63 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 11.63 hours.
 --------- CPU info (if available) ----------

(53·10¹⁵⁰-17)/9 = 5(8)₁₄₉7_<151> = 23 · 853 · 1003753 · 816312569 · 3680454677_<10> · C122

C122 = P42 · P81

P42 = 646588374346983737232638435333887307048501_<42>

P81 = 153937272537308898972231509958686605521190984086624596387981731443058693734868357_<81>

Number: 58887_150
N=99534050801307145446580083087138050744490378834399385389609897359260896132388374257778620864667781554294052423079449182857
  ( 122 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=646588374346983737232638435333887307048501 (pp42)
 r2=153937272537308898972231509958686605521190984086624596387981731443058693734868357 (pp81)
Version: Msieve-1.39
Total time: 13.05 hours.
Scaled time: 33.54 units (timescale=2.571).
Factorization parameters were as follows:
n: 99534050801307145446580083087138050744490378834399385389609897359260896132388374257778620864667781554294052423079449182857
m: 1000000000000000000000000000000
deg: 5
c5: 53
c0: -17
skew: 0.80
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 410988 x 411236
Total sieving time: 13.05 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 13.05 hours.
 --------- CPU info (if available) ----------

(85·10¹⁸⁰+41)/9 = 9(4)₁₇₉9_<181> = 7 · 127 · 2011 · C175

C175 = P81 · P95

P81 = 414375958481886884185001240050648075749952502026192245534940573345783519916635579_<81>

P95 = 12748762611266692012282983698888185917241129880100555296765430261008552339575567088257949707889_<95>

Number: 94449_180
N=5282780726501678588038255536307588602642968982432640972091318023337585039562744860771070945818495711407531045193194709438048239991880676775174361285396262314550313234714382731
  ( 175 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=414375958481886884185001240050648075749952502026192245534940573345783519916635579 (pp81)
 r2=12748762611266692012282983698888185917241129880100555296765430261008552339575567088257949707889 (pp95)
Version: Msieve-1.39
Total time: 128.77 hours.
Scaled time: 223.92 units (timescale=1.739).
Factorization parameters were as follows:
n: 5282780726501678588038255536307588602642968982432640972091318023337585039562744860771070945818495711407531045193194709438048239991880676775174361285396262314550313234714382731
m: 1000000000000000000000000000000000000
deg: 5
c5: 85
c0: 41
skew: 0.86
type: snfs
lss: 1
rlim: 7500000
alim: 7500000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7500000/7500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3750000, 5850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1247569 x 1247817
Total sieving time: 128.77 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,53,53,2.5,2.5,100000
total time: 128.77 hours.
 --------- CPU info (if available) ----------

(53·10¹⁶²+1)/9 = 5(8)₁₆₁9_<163> = 3 · 1723 · 2655315417745817_<16> · 171350162476640484283_<21> · C124

C124 = P47 · P77

P47 = 26342549352212524177658708353759886900127603649_<47>

P77 = 95053560209664005393787353568489591164108220293809699182000297998744547765379_<77>

Number: 58889_162
N=2503953100926578709140928919928972652459114083988579647062913004484757863174594928313473290166903382947849977348817156267971
  ( 124 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=26342549352212524177658708353759886900127603649 (pp47)
 r2=95053560209664005393787353568489591164108220293809699182000297998744547765379 (pp77)
Version: Msieve-1.39
Total time: 35.93 hours.
Scaled time: 91.98 units (timescale=2.560).
Factorization parameters were as follows:
n: 2503953100926578709140928919928972652459114083988579647062913004484757863174594928313473290166903382947849977348817156267971
m: 500000000000000000000000000000000
deg: 5
c5: 212
c0: 125
skew: 0.90
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 3850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 724072 x 724320
Total sieving time: 35.93 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 35.93 hours.
 --------- CPU info (if available) ----------

Apr 26, 2009 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Apr 26, 2009

(53·10¹⁴⁰+1)/9 = 5(8)₁₃₉9_<141> = 577153 · 11923297 · C128

C128 = P34 · P45 · P50

P34 = 3492350119576818700587648285417907_<34>

P45 = 626497419541031597886693211292085596727199999_<45>

P50 = 39111905731165024668312789845345170825587785659453_<50>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 85574829142419551318043870019681831105246990546938000717559749678652140035247595216207608491893437943546231263497379972501175129 (128 digits)
Using B1=882000, B2=871165692, polynomial Dickson(3), sigma=3328769994
Step 1 took 10904ms
Step 2 took 4243ms
********** Factor found in step 2: 3492350119576818700587648285417907
Found probable prime factor of 34 digits: 3492350119576818700587648285417907
Composite cofactor 24503508013906972671895221182159865490563135055105532257550937518736971877266849444954435940547 has 95 digits

Number: n
N=24503508013906972671895221182159865490563135055105532257550937518736971877266849444954435940547
  ( 95 digits)
Divisors found:
 r1=626497419541031597886693211292085596727199999 (pp45)
 r2=39111905731165024668312789845345170825587785659453 (pp50)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 3.36 hours.
Scaled time: 8.94 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_8_139_9
n:  24503508013906972671895221182159865490563135055105532257550937518736971877266849444954435940547
m:  4878869189112173983388
deg: 4
c4: 43246560
c3: 243773149584
c2: 347355289183340212
c1: -1107047333699642379
c0: -74718258204081308948937
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.819
# E(F1,F2) = 4.143619e-05
# GGNFS version 0.77.1-20060513-pentium-m polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1240667234.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1440001)
Primes: RFBsize:92938, AFBsize:92998, largePrimes:1843462 encountered
Relations: rels:1887158, finalFF:211814
Max relations in full relation-set: 28
Initial matrix: 186017 x 211814 with sparse part having weight 16131864.
Pruned matrix : 174225 x 175219 with weight 11184565.
Total sieving time: 3.17 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Total square root time: 0.07 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 3.36 hours.
 --------- CPU info (if available) ----------

(53·10¹⁴²+1)/9 = 5(8)₁₄₁9_<143> = 17² · 6379 · 2008796784103_<13> · 24838614894526801_<17> · C108

C108 = P43 · P66

P43 = 2068776505732953917580438564404929945073177_<43>

P66 = 309461026129065613336287718747252395686825797638200927646978423349_<66>

Number: n
N=640205700295822709913287799054834670776087148367279389602473482798865277861406545945488212501320225890409773
  ( 108 digits)
Divisors found:

Sun Apr 26 14:28:43 2009  prp43 factor: 2068776505732953917580438564404929945073177
Sun Apr 26 14:28:43 2009  prp66 factor: 309461026129065613336287718747252395686825797638200927646978423349
Sun Apr 26 14:28:43 2009  elapsed time 00:27:26 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 9.15 hours.
Scaled time: 23.74 units (timescale=2.595).
Factorization parameters were as follows:
name: KA_5_8_141_9
n: 640205700295822709913287799054834670776087148367279389602473482798865277861406545945488212501320225890409773
Y0: -715245836271708223585
Y1:  146694848041
c0:  286853924357173847644917408
c1:  9917237000351373716964
c2: -1001623086484141097
c3: -14504523771059
c4:  642729609
c5:  3420
skew: 32438.62
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1250000, 2346959)
Primes: RFBsize:183072, AFBsize:182762, largePrimes:15313352 encountered
Relations: rels:13294024, finalFF:336894
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1147672 hash collisions in 14735925 relations
Msieve: matrix is 368338 x 368586 (100.7 MB)

Total sieving time: 8.61 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000
total time: 9.15 hours.
 --------- CPU info (if available) ----------

Apr 26, 2009

By matsui / GGNFS / Apr 26, 2009

4·10¹⁷⁷-9 = 3(9)₁₇₆1_<178> = 13 · 227 · 385001 · 5083123 · 1162925053_<10> · 332230023790700823439_<21> · C133

C133 = P41 · P92

P41 = 64657499314578118063033769725403663002679_<41>

P92 = 27726100791358863600050685537869345949466612785403199549604397338078169719410730274414575719_<92>

N=1792700342913209540033076226702597938072348072879606518518071854016188520494872504571755209446502225955209177348084664558615345351201
  ( 133 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=64657499314578118063033769725403663002679 (pp41)
 r2=27726100791358863600050685537869345949466612785403199549604397338078169719410730274414575719 (pp92)
Version: GGNFS-0.77.1-20060722-nocona

Apr 25, 2009 (7th)

By Ignacio Santos / GGNFS, Msieve / Apr 25, 2009

(53·10¹¹³+1)/9 = 5(8)₁₁₂9_<114> = 7 · 47 · C112

C112 = P39 · P73

P39 = 289531175486154600675813449406456787961_<39>

P73 = 6182186873256482269014449455225313046649108060530092150465438847951149881_<73>

Number: 58889_113
N=1789935832489023978385680513340087808172914555893279297534616683552853765619723066531577169875042215467747382641
  ( 112 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=289531175486154600675813449406456787961 (pp39)
 r2=6182186873256482269014449455225313046649108060530092150465438847951149881 (pp73)
Version: Msieve-1.39
Total time: 1.06 hours.
Scaled time: 1.28 units (timescale=1.203).
Factorization parameters were as follows:
n: 1789935832489023978385680513340087808172914555893279297534616683552853765619723066531577169875042215467747382641
m: 100000000000000000000000
deg: 5
c5: 53
c0: 100
skew: 1.14
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 510001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 59612 x 59838
Total sieving time: 1.03 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 1.06 hours.
 --------- CPU info (if available) ----------

(53·10¹²⁸+1)/9 = 5(8)₁₂₇9_<129> = 19 · 71 · 673 · 941 · 5903 · 921784063808351_<15> · C102

C102 = P29 · P74

P29 = 12421340045339931728781770009_<29>

P74 = 10198734659319124820400947026165352095142553000316341381362596248248760401_<74>

Number: 58889_128
N=126681951235596951070128622542082458491076664658048307858846714431283866232339985443226702580928613609
  ( 102 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=12421340045339931728781770009 (pp29)
 r2=10198734659319124820400947026165352095142553000316341381362596248248760401 (pp74)
Version: Msieve-1.39
Total time: 2.59 hours.
Scaled time: 3.08 units (timescale=1.186).
Factorization parameters were as follows:
n: 126681951235596951070128622542082458491076664658048307858846714431283866232339985443226702580928613609
m: 100000000000000000000000000
deg: 5
c5: 53
c0: 100
skew: 1.14
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 148952 x 149186
Total sieving time: 2.48 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.59 hours.
 --------- CPU info (if available) ----------

(53·10¹³³+1)/9 = 5(8)₁₃₂9_<134> = 262918391 · C126

C126 = P58 · P68

P58 = 6902507297954552900544343980154530186562139765296085565049_<58>

P68 = 32449313991032259990721014237413613972619180694610646930008757342471_<68>

Number: 58889_133
N=223981626636718953939166959563847661341001013842690406883286034140110377021472373489798546990533229335367752531578853640896079
  ( 126 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=6902507297954552900544343980154530186562139765296085565049 (pp58)
 r2=32449313991032259990721014237413613972619180694610646930008757342471 (pp68)
Version: Msieve-1.39
Total time: 4.06 hours.
Scaled time: 4.83 units (timescale=1.189).
Factorization parameters were as follows:
n: 223981626636718953939166959563847661341001013842690406883286034140110377021472373489798546990533229335367752531578853640896079
m: 1000000000000000000000000000
deg: 5
c5: 53
c0: 100
skew: 1.14
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1265001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 197595 x 197831
Total sieving time: 3.86 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 4.06 hours.
 --------- CPU info (if available) ----------

(53·10¹³⁸+1)/9 = 5(8)₁₃₇9_<139> = 3 · 568606156271_<12> · 421748910868721_<15> · C112

C112 = P42 · P71

P42 = 633237938276842858605725159374066027361003_<42>

P71 = 12926461350690842029880554414352022638905256637045133099332495876548231_<71>

Number: 58889_138
N=8185525734926762194466972507409641598365163339665518849949331023072147151841412623469926862436337252969778035693
  ( 112 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=633237938276842858605725159374066027361003 (pp42)
 r2=12926461350690842029880554414352022638905256637045133099332495876548231 (pp71)
Version: Msieve-1.39
Total time: 5.99 hours.
Scaled time: 7.06 units (timescale=1.178).
Factorization parameters were as follows:
n: 8185525734926762194466972507409641598365163339665518849949331023072147151841412623469926862436337252969778035693
m: 10000000000000000000000000000
deg: 5
c5: 53
c0: 100
skew: 1.14
type: snfs
lss: 1
rlim: 1610000
alim: 1610000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1610000/1610000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [805000, 1705001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 238513 x 238750
Total sieving time: 5.82 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000
total time: 5.99 hours.
 --------- CPU info (if available) ----------

(53·10¹⁴⁶+1)/9 = 5(8)₁₄₅9_<147> = 19 · 541 · 1172317 · 235060575725579_<15> · C123

C123 = P34 · P89

P34 = 9237495928744902899345213964123421_<34>

P89 = 22506262284520226043638845786993481451478146780791861537970684431898609724245820689195797_<89>

Number: 58889_146
N=207901506224520545540916343484854785474436665052904598304605157182071243981211522776531317754495948145242139489790542461537
  ( 123 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=9237495928744902899345213964123421 (pp34)
 r2=22506262284520226043638845786993481451478146780791861537970684431898609724245820689195797 (pp89)
Version: Msieve-1.39
Total time: 8.46 hours.
Scaled time: 21.74 units (timescale=2.571).
Factorization parameters were as follows:
n: 207901506224520545540916343484854785474436665052904598304605157182071243981211522776531317754495948145242139489790542461537
m: 200000000000000000000000000000
deg: 5
c5: 265
c0: 16
skew: 0.57
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 347190 x 347428
Total sieving time: 8.46 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 8.46 hours.
 --------- CPU info (if available) ----------

Apr 25, 2009 (6th)

By Sinkiti Sibata / Msieve / Apr 25, 2009

(53·10¹²⁵-17)/9 = 5(8)₁₂₄7_<126> = 13 · 339749 · 35535200978096463458378999_<26> · C94

C94 = P36 · P59

P36 = 333310210633105268385300246208958849_<36>

P59 = 11257045633707776513130579531935967239498275141186226824801_<59>

Sat Apr 25 07:11:07 2009  Msieve v. 1.41
Sat Apr 25 07:11:07 2009  random seeds: 54733750 bd397ade
Sat Apr 25 07:11:07 2009  factoring 3752088251277616965378755358494011502094212586258828900203423274576430990063210653009341614049 (94 digits)
Sat Apr 25 07:11:08 2009  searching for 15-digit factors
Sat Apr 25 07:11:09 2009  commencing quadratic sieve (94-digit input)
Sat Apr 25 07:11:10 2009  using multiplier of 1
Sat Apr 25 07:11:10 2009  using 32kb Intel Core sieve core
Sat Apr 25 07:11:10 2009  sieve interval: 36 blocks of size 32768
Sat Apr 25 07:11:10 2009  processing polynomials in batches of 6
Sat Apr 25 07:11:10 2009  using a sieve bound of 2023667 (75294 primes)
Sat Apr 25 07:11:10 2009  using large prime bound of 271171378 (28 bits)
Sat Apr 25 07:11:10 2009  using double large prime bound of 1512999890036866 (42-51 bits)
Sat Apr 25 07:11:10 2009  using trial factoring cutoff of 51 bits
Sat Apr 25 07:11:10 2009  polynomial 'A' values have 12 factors
Sat Apr 25 10:02:45 2009  75406 relations (18873 full + 56533 combined from 1065411 partial), need 75390
Sat Apr 25 10:02:47 2009  begin with 1084284 relations
Sat Apr 25 10:02:48 2009  reduce to 194604 relations in 11 passes
Sat Apr 25 10:02:48 2009  attempting to read 194604 relations
Sat Apr 25 10:02:51 2009  recovered 194604 relations
Sat Apr 25 10:02:51 2009  recovered 177197 polynomials
Sat Apr 25 10:02:51 2009  attempting to build 75406 cycles
Sat Apr 25 10:02:51 2009  found 75406 cycles in 6 passes
Sat Apr 25 10:02:51 2009  distribution of cycle lengths:
Sat Apr 25 10:02:51 2009     length 1 : 18873
Sat Apr 25 10:02:51 2009     length 2 : 13359
Sat Apr 25 10:02:51 2009     length 3 : 12926
Sat Apr 25 10:02:51 2009     length 4 : 10168
Sat Apr 25 10:02:51 2009     length 5 : 7471
Sat Apr 25 10:02:51 2009     length 6 : 5003
Sat Apr 25 10:02:51 2009     length 7 : 3191
Sat Apr 25 10:02:51 2009     length 9+: 4415
Sat Apr 25 10:02:51 2009  largest cycle: 21 relations
Sat Apr 25 10:02:51 2009  matrix is 75294 x 75406 (19.0 MB) with weight 4689045 (62.18/col)
Sat Apr 25 10:02:51 2009  sparse part has weight 4689045 (62.18/col)
Sat Apr 25 10:02:53 2009  filtering completed in 3 passes
Sat Apr 25 10:02:53 2009  matrix is 71416 x 71480 (18.2 MB) with weight 4481400 (62.69/col)
Sat Apr 25 10:02:53 2009  sparse part has weight 4481400 (62.69/col)
Sat Apr 25 10:02:53 2009  saving the first 48 matrix rows for later
Sat Apr 25 10:02:53 2009  matrix is 71368 x 71480 (10.9 MB) with weight 3486418 (48.77/col)
Sat Apr 25 10:02:53 2009  sparse part has weight 2428371 (33.97/col)
Sat Apr 25 10:02:53 2009  matrix includes 64 packed rows
Sat Apr 25 10:02:53 2009  using block size 28592 for processor cache size 1024 kB
Sat Apr 25 10:02:53 2009  commencing Lanczos iteration
Sat Apr 25 10:02:53 2009  memory use: 10.9 MB
Sat Apr 25 10:03:25 2009  lanczos halted after 1130 iterations (dim = 71366)
Sat Apr 25 10:03:25 2009  recovered 16 nontrivial dependencies
Sat Apr 25 10:03:26 2009  prp36 factor: 333310210633105268385300246208958849
Sat Apr 25 10:03:26 2009  prp59 factor: 11257045633707776513130579531935967239498275141186226824801
Sat Apr 25 10:03:26 2009  elapsed time 02:52:19

(44·10²⁰⁰-53)/9 = 4(8)₁₉₉3_<201> = 3 · 7 · 23 · 490151 · 603522709 · 12983684697563_<14> · 485460576989519_<15> · 7046882295480502467634870497200027_<34> · C122

C122 = P41 · P82

P41 = 17093319897861558819189989484935430767783_<41>

P82 = 4506757199284748937489169617028628948676844119512148373046760090531769332278731307_<82>

Number: 48883_200
N=77035442509364829592824984655079160994427570285601319384761126720874299891224577489225266938170642713438522459468169082381
  ( 122 digits)
Divisors found:
 r1=17093319897861558819189989484935430767783 (pp41)
 r2=4506757199284748937489169617028628948676844119512148373046760090531769332278731307 (pp82)
Version: Msieve-1.40
Total time: 79.27 hours.
Scaled time: 154.97 units (timescale=1.955).
Factorization parameters were as follows:
name: 48883_200
# Murphy_E = 2.266954e-10, selected by Jeff Gilchrist
n: 77035442509364829592824984655079160994427570285601319384761126720874299891224577489225266938170642713438522459468169082381
Y0: -368091799120498919063005
Y1: 12847974784117
c0: 109359585716408333906284552008
c1: 3405141569669740082931020
c2: -37901142473314887746
c3: -844999055076687
c4: 3776565670
c5: 11400
skew: 118654.68
type: gnfs
# selected mechanically
rlim: 5900000
alim: 5900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2950000, 5350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 810955 x 811203
Total sieving time: 79.27 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5900000,5900000,27,27,52,52,2.5,2.5,100000
total time: 79.27 hours.
 --------- CPU info (if available) ----------

Apr 25, 2009 (5th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Apr 25, 2009

(53·10¹³⁷+1)/9 = 5(8)₁₃₆9_<138> = 7 · 31 · 83 · 563 · C131

C131 = P35 · P97

P35 = 36467916497685454043561178729676819_<35>

P97 = 1592488069431850510302639201300386274192150371140061427937716746570830122530356070413043274127267_<97>

GMP-ECM 6.2.1 [powered by GMP 4.1.4] [ECM]
Input number is 58074721939601040028418481668829073459340358599573882754390265440597520075691743627452543446548688855220890656508104815055185723673 (131 digits)
Using B1=2328000, B2=3567716890, polynomial Dickson(6), sigma=2561432034
Step 1 took 30984ms
Step 2 took 14000ms
********** Factor found in step 2: 36467916497685454043561178729676819
Found probable prime factor of 35 digits: 36467916497685454043561178729676819
Probable prime cofactor 1592488069431850510302639201300386274192150371140061427937716746570830122530356070413043274127267 has 97 digits

(53·10¹⁴⁹-17)/9 = 5(8)₁₄₈7_<150> = 13 · 71 · 103 · 349 · 45001306334623_<14> · C129

C129 = P60 · P70

P60 = 131330752110030357457784241422186029366093966226597288556911_<60>

P70 = 3003152975980207409359615676165557286711523353567898461432663515019759_<70>

Number: n
N=394406339036956571634680918351574479618516919731322456206028760825031051850575746378939836515426834482961187849144726626761004449
  ( 129 digits)
SNFS difficulty: 151 digits.
Divisors found:

Sat Apr 25 14:53:44 2009  prp60 factor: 131330752110030357457784241422186029366093966226597288556911
Sat Apr 25 14:53:44 2009  prp70 factor: 3003152975980207409359615676165557286711523353567898461432663515019759
Sat Apr 25 14:53:44 2009  elapsed time 00:30:53 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 14.25 hours.
Scaled time: 23.12 units (timescale=1.623).
Factorization parameters were as follows:
name: KA_5_8_148_7
n: 394406339036956571634680918351574479618516919731322456206028760825031051850575746378939836515426834482961187849144726626761004449
m: 1000000000000000000000000000000
deg: 5
c5: 53
c0: -170
skew: 1.26
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1200000, 2100000)
Primes: RFBsize:176302, AFBsize:177593, largePrimes:12023284 encountered
Relations: rels:11768502, finalFF:640523
Max relations in full relation-set: 28
Initial matrix: 353960 x 640523 with sparse part having weight 76137185.
Pruned matrix : 278048 x 279881 with weight 34253707.

Msieve: found 1026664 hash collisions in 12593327 relations
Msieve: matrix is 353458 x 353706 (92.8 MB)

Total sieving time: 13.96 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,56,56,2.4,2.4,100000
total time: 14.25 hours.
 --------- CPU info (if available) ----------

(17·10¹⁶⁸+7)/3 = 5(6)₁₆₇9_<169> = 739 · 857 · 4229411 · 851745859 · C148

C148 = P62 · P87

P62 = 17750314911886256685469328373006864448252907163669091067552591_<62>

P87 = 139928578638319314678328668947574395690000477539047365624769415108634425048302841672417_<87>

Number: n
N=2483776336002808045620469682926685372479589939012661589982962543702359427428652288125288118566905146030280923577515033415821039268567270581541582447
  ( 148 digits)
SNFS difficulty: 170 digits.
Divisors found:

Sat Apr 25 15:59:55 2009  prp62 factor: 17750314911886256685469328373006864448252907163669091067552591
Sat Apr 25 15:59:55 2009  prp87 factor: 139928578638319314678328668947574395690000477539047365624769415108634425048302841672417
Sat Apr 25 15:59:55 2009  elapsed time 01:36:27 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 60.77 hours.
Scaled time: 160.36 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_5_6_167_9
n: 2483776336002808045620469682926685372479589939012661589982962543702359427428652288125288118566905146030280923577515033415821039268567270581541582447
m: 5000000000000000000000000000000000
deg: 5
c5: 136
c0: 175
skew: 1.05
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2450000, 5951689)
Primes: RFBsize:341992, AFBsize:341883, largePrimes:17859820 encountered
Relations: rels:18199396, finalFF:629046
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2359672 hash collisions in 20150521 relations
Msieve: matrix is 817865 x 818113 (216.9 MB)

Total sieving time: 59.83 hours.
Total relation processing time: 0.94 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,28,28,56,56,2.4,2.4,100000
total time: 60.77 hours.
 --------- CPU info (if available) ----------

Apr 25, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.41 / Apr 25, 2009

(53·10¹⁸⁸+1)/9 = 5(8)₁₈₇9_<189> = 23 · 149 · 9133 · 1021637597731_<13> · C170

C170 = P35 · C135

P35 = 29078929780665430520713512844261283_<35>

C135 = [633330658677630357428348768527318821653634753038708389251181720953905597265954465448747588805040851833232202227201717842921321235662823_<135>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1241649351
Step 1 took 11620ms
Step 2 took 13245ms
********** Factor found in step 2: 29078929780665430520713512844261283
Found probable prime factor of 35 digits: 29078929780665430520713512844261283
Composite cofactor has 135 digits

(53·10¹⁷⁸+1)/9 = 5(8)₁₇₇9_<179> = 29 · 83 · 56671 · 397302042061058419_<18> · C154

C154 = P30 · C124

P30 = 764648480363550491427385880911_<30>

C124 = [1421064422676721817294303535151760278742043022221943758499295816466638534361724872580455743508352819227160020715265251355093_<124>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3079772143
Step 1 took 9764ms
Step 2 took 11665ms
********** Factor found in step 2: 764648480363550491427385880911
Found probable prime factor of 30 digits: 764648480363550491427385880911
Composite cofactor has 124 digits

(53·10¹⁴³+1)/9 = 5(8)₁₄₂9_<144> = 7³ · C142

C142 = P53 · P89

P53 = 79473050106862706275240784169605362262487122995225933_<53>

P89 = 21603263304638811935007782608993962985407454791157017884866832547047245476678698092370731_<89>

SNFS difficulty: 146 digits.
Divisors found:
 r1=79473050106862706275240784169605362262487122995225933 (pp53)
 r2=21603263304638811935007782608993962985407454791157017884866832547047245476678698092370731 (pp89)
Version: Msieve-1.41
Total time: 6.28 hours.
Factorization parameters were as follows:
n: 1716877227081308713961775186264982183349530288305798509880142533203757693553611920958859734369938451571104632329122125040492387431162941367023
m: 100000000000000000000000000000
deg: 5
c5: 53
c0: 100
skew: 1.14
type: snfs
lss: 1
rlim: 1950000
alim: 1950000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1950000/1950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [975000, 2175001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 319085 x 319317
Total sieving time: 6.00 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,146.000,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000
total time: 6.28 hours.

Apr 25, 2009 (3rd)

By Wataru Sakai / Msieve / Apr 25, 2009

(7·10²⁰⁰+11)/9 = (7)₁₉₉9_<200> = 31 · C199

C199 = P46 · P154

P46 = 1224138868623984405220163344723881547828209211_<46>

P154 = 2049571856416049713388251526936262340434423910767572808137910239843291577199511366868089995800953673223303727077940898700883017337359301880186873070702519_<154>

Number: 77779_200
N=2508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702509
  ( 199 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=1224138868623984405220163344723881547828209211
 r2=2049571856416049713388251526936262340434423910767572808137910239843291577199511366868089995800953673223303727077940898700883017337359301880186873070702519
Version: 
Total time: 659.25 hours.
Scaled time: 1318.50 units (timescale=2.000).
Factorization parameters were as follows:
n: 2508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702509
m: 10000000000000000000000000000000000000000
deg: 5
c5: 7
c0: 11
skew: 1.09
type: snfs
lss: 1
rlim: 15600000
alim: 15600000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 15600000/15600000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7800000, 14200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2392576 x 2392824
Total sieving time: 659.25 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15600000,15600000,29,29,56,56,2.6,2.6,100000
total time: 659.25 hours.
 --------- CPU info (if available) ----------

Apr 25, 2009 (2nd)

By Max Dettweiler / GGNFS via factLat.pl / Apr 25, 2009

(53·10¹⁰³+1)/9 = 5(8)₁₀₂9_<104> = 17597 · 35327 · C95

C95 = P30 · P66

P30 = 660234879222823531615373589467_<30>

P66 = 143479384203030468046198093958135532280512482215395035709729983593_<66>

Number: c95
N=94730093900252915605913258436650410862800245694330855242156893772095109619833510783979427614931
  ( 95 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=660234879222823531615373589467 (pp30)
 r2=143479384203030468046198093958135532280512482215395035709729983593 (pp66)
Version: GGNFS-0.77.1-VC8(Sat
Total time: 0.35 hours.
Scaled time: 0.38 units (timescale=1.083).
Factorization parameters were as follows:
n: 94730093900252915605913258436650410862800245694330855242156893772095109619833510783979427614931
m: 100000000000000000000000000
deg: 4
c4: 53
c0: 10
skew: 0.66
type: snfs
lss: 1
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [200000, 260001)
Primes: RFBsize:33860, AFBsize:33767, largePrimes:1130050 encountered
Relations: rels:1106897, finalFF:145363
Max relations in full relation-set: 32
Initial matrix: 67692 x 145363 with sparse part having weight 5316144.
Pruned matrix : 41195 x 41597 with weight 1145405.
Total sieving time: 0.32 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,105,4,0,0,0,0,0,0,0,0,400000,400000,25,25,44,44,2.2,2.2,20000
total time: 0.35 hours.
 --------- CPU info (if available) ----------

Apr 25, 2009

Factorizations of 588...889 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 24, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Apr 24, 2009

(53·10¹⁶⁵-71)/9 = 5(8)₁₆₄1_<166> = 367 · 1942027 · 1371144007102407524796878911_<28> · C130

C130 = P37 · P93

P37 = 7456075032830949289097809630839141133_<37>

P93 = 808199714463033799839895000646180717663570250954579698107795831316200571506223546388577376143_<93>

Number: 58881_165
N=6025997712548928580140437380295469588477406790695466700698973804134750409989600365698409400134707346602045944981706534764804190019
  ( 130 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=7456075032830949289097809630839141133
 r2=808199714463033799839895000646180717663570250954579698107795831316200571506223546388577376143
Version: 
Total time: 24.84 hours.
Scaled time: 59.16 units (timescale=2.382).
Factorization parameters were as follows:
n: 6025997712548928580140437380295469588477406790695466700698973804134750409989600365698409400134707346602045944981706534764804190019
m: 1000000000000000000000000000000000
deg: 5
c5: 53
c0: -71
skew: 1.06
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2400000, 4400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9904777
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 778856 x 779104
Total sieving time: 22.38 hours.
Total relation processing time: 0.97 hours.
Matrix solve time: 1.39 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000
total time: 24.84 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init)
Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672387)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)

2·10¹⁹¹-1 = 1(9)₁₉₁_<192> = 2749 · 218227091623637911_<18> · 1634251873308525786539681_<25> · C147

C147 = P39 · P108

P39 = 374917624436804778786980691929301633251_<39>

P108 = 544116308602057079193319001051462073305059198331631713353356980808064530293851666207891990993563912562753711_<108>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 203998793838406605456849058402298086054508973666863581672079665320253658796228665748890577906627191442159765577090127199451780519415081662361244461 (147 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2535079878
Step 1 took 13915ms
Step 2 took 6304ms
********** Factor found in step 2: 374917624436804778786980691929301633251
Found probable prime factor of 39 digits: 374917624436804778786980691929301633251
Probable prime cofactor 544116308602057079193319001051462073305059198331631713353356980808064530293851666207891990993563912562753711 has 108 digits

2·10¹⁸⁰-1 = 1(9)₁₈₀_<181> = 2089 · 25247 · 906097649 · 2812810690923703_<16> · C149

C149 = P37 · P112

P37 = 3646742702319169110919751900918642423_<37>

P112 = 4080009229030868132507753050857621102187848916600309751871730009887972204041194243916993303782420351451924397113_<112>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 14878743881363177813121181985179871892369482209890801997246302818188423938858501010328725657818896907386546241733098581247875698793343660876700524799 (149 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=386652535
Step 1 took 13915ms
Step 2 took 6364ms
********** Factor found in step 2: 3646742702319169110919751900918642423
Found probable prime factor of 37 digits: 3646742702319169110919751900918642423
Probable prime cofactor 4080009229030868132507753050857621102187848916600309751871730009887972204041194243916993303782420351451924397113 has 112 digits

Apr 24, 2009 (4th)

By Sinkiti Sibata / Msieve / Apr 24, 2009

(53·10¹¹³-17)/9 = 5(8)₁₁₂7_<114> = 13 · 2963 · 255383398285427_<15> · C95

C95 = P34 · P62

P34 = 5067488575798423942258912441786211_<34>

P62 = 11813345789802296777872794313744435491728937700087705183033609_<62>

Fri Apr 24 06:48:16 2009  Msieve v. 1.41
Fri Apr 24 06:48:16 2009  random seeds: 4fb1af00 b2fd5f23
Fri Apr 24 06:48:16 2009  factoring 59863994831779548547391373386370555107607649273242788480501437709143034117417916270887605765499 (95 digits)
Fri Apr 24 06:48:17 2009  searching for 15-digit factors
Fri Apr 24 06:48:19 2009  commencing quadratic sieve (95-digit input)
Fri Apr 24 06:48:19 2009  using multiplier of 3
Fri Apr 24 06:48:19 2009  using 32kb Intel Core sieve core
Fri Apr 24 06:48:19 2009  sieve interval: 36 blocks of size 32768
Fri Apr 24 06:48:19 2009  processing polynomials in batches of 6
Fri Apr 24 06:48:19 2009  using a sieve bound of 2150039 (80000 primes)
Fri Apr 24 06:48:19 2009  using large prime bound of 322505850 (28 bits)
Fri Apr 24 06:48:19 2009  using double large prime bound of 2067129303583950 (43-51 bits)
Fri Apr 24 06:48:19 2009  using trial factoring cutoff of 51 bits
Fri Apr 24 06:48:19 2009  polynomial 'A' values have 12 factors
Fri Apr 24 06:48:19 2009  restarting with 1761 full and 115577 partial relations
Fri Apr 24 11:14:39 2009  80263 relations (18873 full + 61390 combined from 1218465 partial), need 80096
Fri Apr 24 11:14:40 2009  begin with 1237338 relations
Fri Apr 24 11:14:42 2009  reduce to 213249 relations in 11 passes
Fri Apr 24 11:14:42 2009  attempting to read 213249 relations
Fri Apr 24 11:14:46 2009  recovered 213249 relations
Fri Apr 24 11:14:46 2009  recovered 200611 polynomials
Fri Apr 24 11:14:46 2009  attempting to build 80263 cycles
Fri Apr 24 11:14:46 2009  found 80263 cycles in 6 passes
Fri Apr 24 11:14:46 2009  distribution of cycle lengths:
Fri Apr 24 11:14:46 2009     length 1 : 18873
Fri Apr 24 11:14:46 2009     length 2 : 13543
Fri Apr 24 11:14:46 2009     length 3 : 13334
Fri Apr 24 11:14:46 2009     length 4 : 11007
Fri Apr 24 11:14:46 2009     length 5 : 8458
Fri Apr 24 11:14:46 2009     length 6 : 5909
Fri Apr 24 11:14:46 2009     length 7 : 3736
Fri Apr 24 11:14:46 2009     length 9+: 5403
Fri Apr 24 11:14:46 2009  largest cycle: 21 relations
Fri Apr 24 11:14:46 2009  matrix is 80000 x 80263 (22.1 MB) with weight 5481572 (68.30/col)
Fri Apr 24 11:14:46 2009  sparse part has weight 5481572 (68.30/col)
Fri Apr 24 11:14:48 2009  filtering completed in 3 passes
Fri Apr 24 11:14:48 2009  matrix is 76727 x 76791 (21.3 MB) with weight 5264271 (68.55/col)
Fri Apr 24 11:14:48 2009  sparse part has weight 5264271 (68.55/col)
Fri Apr 24 11:14:48 2009  saving the first 48 matrix rows for later
Fri Apr 24 11:14:48 2009  matrix is 76679 x 76791 (14.7 MB) with weight 4313718 (56.17/col)
Fri Apr 24 11:14:48 2009  sparse part has weight 3380078 (44.02/col)
Fri Apr 24 11:14:48 2009  matrix includes 64 packed rows
Fri Apr 24 11:14:48 2009  using block size 30716 for processor cache size 1024 kB
Fri Apr 24 11:14:49 2009  commencing Lanczos iteration
Fri Apr 24 11:14:49 2009  memory use: 13.4 MB
Fri Apr 24 11:15:34 2009  lanczos halted after 1214 iterations (dim = 76677)
Fri Apr 24 11:15:35 2009  recovered 16 nontrivial dependencies
Fri Apr 24 11:15:37 2009  prp34 factor: 5067488575798423942258912441786211
Fri Apr 24 11:15:37 2009  prp62 factor: 11813345789802296777872794313744435491728937700087705183033609
Fri Apr 24 11:15:37 2009  elapsed time 04:27:21

(53·10¹¹⁴-17)/9 = 5(8)₁₁₃7_<115> = 71 · 181 · 277 · 10789 · 18899 · 68813 · C96

C96 = P36 · P60

P36 = 167266927763015205609857861924093563_<36>

P60 = 704881442955466017239089882681824408103143399235767556204409_<60>

Fri Apr 24 12:54:32 2009  Msieve v. 1.41
Fri Apr 24 12:54:32 2009  random seeds: 59d15950 4f27dd33
Fri Apr 24 12:54:32 2009  factoring 117903353400321857683749787677987415989823219588292979192960515969393246858575069561884069119267 (96 digits)
Fri Apr 24 12:54:33 2009  searching for 15-digit factors
Fri Apr 24 12:54:34 2009  commencing quadratic sieve (96-digit input)
Fri Apr 24 12:54:34 2009  using multiplier of 3
Fri Apr 24 12:54:34 2009  using 32kb Intel Core sieve core
Fri Apr 24 12:54:34 2009  sieve interval: 36 blocks of size 32768
Fri Apr 24 12:54:34 2009  processing polynomials in batches of 6
Fri Apr 24 12:54:34 2009  using a sieve bound of 2191457 (81176 primes)
Fri Apr 24 12:54:34 2009  using large prime bound of 328718550 (28 bits)
Fri Apr 24 12:54:34 2009  using double large prime bound of 2139358506583350 (43-51 bits)
Fri Apr 24 12:54:34 2009  using trial factoring cutoff of 51 bits
Fri Apr 24 12:54:34 2009  polynomial 'A' values have 12 factors
Fri Apr 24 17:40:31 2009  81350 relations (19358 full + 61992 combined from 1224123 partial), need 81272
Fri Apr 24 17:40:33 2009  begin with 1243481 relations
Fri Apr 24 17:40:34 2009  reduce to 214446 relations in 11 passes
Fri Apr 24 17:40:34 2009  attempting to read 214446 relations
Fri Apr 24 17:40:37 2009  recovered 214446 relations
Fri Apr 24 17:40:37 2009  recovered 201995 polynomials
Fri Apr 24 17:40:38 2009  attempting to build 81350 cycles
Fri Apr 24 17:40:38 2009  found 81350 cycles in 5 passes
Fri Apr 24 17:40:38 2009  distribution of cycle lengths:
Fri Apr 24 17:40:38 2009     length 1 : 19358
Fri Apr 24 17:40:38 2009     length 2 : 13809
Fri Apr 24 17:40:38 2009     length 3 : 13726
Fri Apr 24 17:40:38 2009     length 4 : 11158
Fri Apr 24 17:40:38 2009     length 5 : 8472
Fri Apr 24 17:40:38 2009     length 6 : 5816
Fri Apr 24 17:40:38 2009     length 7 : 3810
Fri Apr 24 17:40:38 2009     length 9+: 5201
Fri Apr 24 17:40:38 2009  largest cycle: 20 relations
Fri Apr 24 17:40:38 2009  matrix is 81176 x 81350 (22.6 MB) with weight 5591847 (68.74/col)
Fri Apr 24 17:40:38 2009  sparse part has weight 5591847 (68.74/col)
Fri Apr 24 17:40:40 2009  filtering completed in 3 passes
Fri Apr 24 17:40:40 2009  matrix is 77874 x 77938 (21.8 MB) with weight 5392030 (69.18/col)
Fri Apr 24 17:40:40 2009  sparse part has weight 5392030 (69.18/col)
Fri Apr 24 17:40:40 2009  saving the first 48 matrix rows for later
Fri Apr 24 17:40:40 2009  matrix is 77826 x 77938 (15.6 MB) with weight 4492035 (57.64/col)
Fri Apr 24 17:40:40 2009  sparse part has weight 3631965 (46.60/col)
Fri Apr 24 17:40:40 2009  matrix includes 64 packed rows
Fri Apr 24 17:40:40 2009  using block size 31175 for processor cache size 1024 kB
Fri Apr 24 17:40:41 2009  commencing Lanczos iteration
Fri Apr 24 17:40:41 2009  memory use: 14.0 MB
Fri Apr 24 17:41:26 2009  lanczos halted after 1233 iterations (dim = 77826)
Fri Apr 24 17:41:26 2009  recovered 18 nontrivial dependencies
Fri Apr 24 17:41:27 2009  prp36 factor: 167266927763015205609857861924093563
Fri Apr 24 17:41:27 2009  prp60 factor: 704881442955466017239089882681824408103143399235767556204409
Fri Apr 24 17:41:27 2009  elapsed time 04:46:55

(53·10¹²¹-17)/9 = 5(8)₁₂₀7_<122> = 3² · 21211 · 620505581 · 136569534114199_<15> · C94

C94 = P37 · P58

P37 = 3631090387354731446722862437746442697_<37>

P58 = 1002520188473252584276320790788755291702994964270538468591_<58>

Fri Apr 24 18:28:38 2009  Msieve v. 1.41
Fri Apr 24 18:28:38 2009  random seeds: 752e6e18 d6e9ebde
Fri Apr 24 18:28:38 2009  factoring 3640241419494281102214649384034662170741936618630879393491492058162045661401457588404315829927 (94 digits)
Fri Apr 24 18:28:39 2009  searching for 15-digit factors
Fri Apr 24 18:28:41 2009  commencing quadratic sieve (94-digit input)
Fri Apr 24 18:28:41 2009  using multiplier of 3
Fri Apr 24 18:28:41 2009  using 32kb Intel Core sieve core
Fri Apr 24 18:28:41 2009  sieve interval: 36 blocks of size 32768
Fri Apr 24 18:28:41 2009  processing polynomials in batches of 6
Fri Apr 24 18:28:41 2009  using a sieve bound of 2024387 (75294 primes)
Fri Apr 24 18:28:41 2009  using large prime bound of 271267858 (28 bits)
Fri Apr 24 18:28:41 2009  using double large prime bound of 1513968973265930 (42-51 bits)
Fri Apr 24 18:28:41 2009  using trial factoring cutoff of 51 bits
Fri Apr 24 18:28:41 2009  polynomial 'A' values have 12 factors
Fri Apr 24 21:36:38 2009  75663 relations (18586 full + 57077 combined from 1073486 partial), need 75390
Fri Apr 24 21:36:39 2009  begin with 1092072 relations
Fri Apr 24 21:36:40 2009  reduce to 196620 relations in 11 passes
Fri Apr 24 21:36:40 2009  attempting to read 196620 relations
Fri Apr 24 21:36:43 2009  recovered 196620 relations
Fri Apr 24 21:36:43 2009  recovered 180006 polynomials
Fri Apr 24 21:36:43 2009  attempting to build 75663 cycles
Fri Apr 24 21:36:44 2009  found 75663 cycles in 5 passes
Fri Apr 24 21:36:44 2009  distribution of cycle lengths:
Fri Apr 24 21:36:44 2009     length 1 : 18586
Fri Apr 24 21:36:44 2009     length 2 : 13344
Fri Apr 24 21:36:44 2009     length 3 : 12710
Fri Apr 24 21:36:44 2009     length 4 : 10087
Fri Apr 24 21:36:44 2009     length 5 : 7735
Fri Apr 24 21:36:44 2009     length 6 : 5214
Fri Apr 24 21:36:44 2009     length 7 : 3265
Fri Apr 24 21:36:44 2009     length 9+: 4722
Fri Apr 24 21:36:44 2009  largest cycle: 20 relations
Fri Apr 24 21:36:44 2009  matrix is 75294 x 75663 (19.9 MB) with weight 4913605 (64.94/col)
Fri Apr 24 21:36:44 2009  sparse part has weight 4913605 (64.94/col)
Fri Apr 24 21:36:45 2009  filtering completed in 4 passes
Fri Apr 24 21:36:45 2009  matrix is 71656 x 71720 (18.9 MB) with weight 4671198 (65.13/col)
Fri Apr 24 21:36:45 2009  sparse part has weight 4671198 (65.13/col)
Fri Apr 24 21:36:45 2009  saving the first 48 matrix rows for later
Fri Apr 24 21:36:46 2009  matrix is 71608 x 71720 (12.0 MB) with weight 3712909 (51.77/col)
Fri Apr 24 21:36:46 2009  sparse part has weight 2707303 (37.75/col)
Fri Apr 24 21:36:46 2009  matrix includes 64 packed rows
Fri Apr 24 21:36:46 2009  using block size 28688 for processor cache size 1024 kB
Fri Apr 24 21:36:46 2009  commencing Lanczos iteration
Fri Apr 24 21:36:46 2009  memory use: 11.5 MB
Fri Apr 24 21:37:20 2009  lanczos halted after 1134 iterations (dim = 71607)
Fri Apr 24 21:37:20 2009  recovered 17 nontrivial dependencies
Fri Apr 24 21:37:21 2009  prp37 factor: 3631090387354731446722862437746442697
Fri Apr 24 21:37:21 2009  prp58 factor: 1002520188473252584276320790788755291702994964270538468591
Fri Apr 24 21:37:21 2009  elapsed time 03:08:43

Apr 24, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 24, 2009

(52·10¹⁸⁰+11)/9 = 5(7)₁₇₉9_<181> = 7 · C180

C180 = P83 · P97

P83 = 85953570641100435302364859126378100802894940416504268380526330442075309405460436217_<83>

P97 = 9602821840215038595051714729650614572066911996666266197149048428837644236481298696881375472096541_<97>

Number: 57779_180
N=825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825397
  ( 180 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=85953570641100435302364859126378100802894940416504268380526330442075309405460436217 (pp83)
 r2=9602821840215038595051714729650614572066911996666266197149048428837644236481298696881375472096541 (pp97)
Version: Msieve-1.39
Total time: 110.43 hours.
Scaled time: 192.03 units (timescale=1.739).
Factorization parameters were as follows:
n: 825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825397
m: 1000000000000000000000000000000000000
deg: 5
c5: 52
c0: 11
skew: 0.73
type: snfs
lss: 1
rlim: 7500000
alim: 7500000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7500000/7500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3750000, 5550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1404538 x 1404784
Total sieving time: 110.43 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,53,53,2.5,2.5,100000
total time: 110.43 hours.
 --------- CPU info (if available) ----------

(53·10¹⁴⁷-17)/9 = 5(8)₁₄₆7_<148> = 7 · 157090823 · 108192642452257497081257210337049_<33> · C107

C107 = P52 · P56

P52 = 2579775523673369950784734958514551180203035362426083_<52>

P56 = 19186902085390185374523921439602412837798066940823099701_<56>

Number: 58887_147
N=49497900375007139446580117975996554390248271087641053217622845679414045570759456353804961562101355551901183
  ( 107 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=2579775523673369950784734958514551180203035362426083 (pp52)
 r2=19186902085390185374523921439602412837798066940823099701 (pp56)
Version: Msieve-1.39
Total time: 12.45 hours.
Scaled time: 32.15 units (timescale=2.583).
Factorization parameters were as follows:
n: 49497900375007139446580117975996554390248271087641053217622845679414045570759456353804961562101355551901183
m: 200000000000000000000000000000
deg: 5
c5: 1325
c0: -136
skew: 0.63
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 3100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 402501 x 402749
Total sieving time: 12.45 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000
total time: 12.45 hours.
 --------- CPU info (if available) ----------

(53·10¹⁴³-17)/9 = 5(8)₁₄₂7_<144> = 13² · 29 · 127 · 268114348509373801_<18> · C121

C121 = P52 · P70

P52 = 3197499649810280310555966924736478732434405762799143_<52>

P70 = 1103606817437336719982382319701730917790387846170402709338588861412267_<70>

Number: 58887_143
N=3528782412284122116403286244880646943846723460132929373308594335392789097445085449072815348528186472100920160758037287181
  ( 121 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=3197499649810280310555966924736478732434405762799143 (pp52)
 r2=1103606817437336719982382319701730917790387846170402709338588861412267 (pp70)
Version: Msieve-1.39
Total time: 9.26 hours.
Scaled time: 23.82 units (timescale=2.571).
Factorization parameters were as follows:
n: 3528782412284122116403286244880646943846723460132929373308594335392789097445085449072815348528186472100920160758037287181
m: 50000000000000000000000000000
deg: 5
c5: 424
c0: -425
skew: 1.00
type: snfs
lss: 1
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [955000, 2455001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 319640 x 319868
Total sieving time: 9.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 9.26 hours.
 --------- CPU info (if available) ----------

(53·10¹⁶⁴-17)/9 = 5(8)₁₆₃7_<165> = 800977 · C159

C159 = P35 · P43 · P83

P35 = 26420433379971578160086373777968563_<35>

P43 = 1931614398915714664197849198169905631094719_<43>

P83 = 14406316220093108541547534674609427084176701563508733048745187396069463990428743523_<83>

Number: 58887_164
N=735213231951590231540841857992038334295352911368102815547623575819141983963196057925369753299893616032531382160647420448887906754986583745711660745425759901831
  ( 159 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=26420433379971578160086373777968563 (pp35)
 r2=1931614398915714664197849198169905631094719 (pp43)
 r3=14406316220093108541547534674609427084176701563508733048745187396069463990428743523 (pp83)
Version: Msieve-1.39
Total time: 44.59 hours.
Scaled time: 77.54 units (timescale=1.739).
Factorization parameters were as follows:
n: 735213231951590231540841857992038334295352911368102815547623575819141983963196057925369753299893616032531382160647420448887906754986583745711660745425759901831
m: 1000000000000000000000000000000000
deg: 5
c5: 53
c0: -170
skew: 1.26
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 784296 x 784544
Total sieving time: 44.59 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 44.59 hours.
 --------- CPU info (if available) ----------

Apr 24, 2009 (2nd)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve / Apr 24, 2009

(53·10¹²⁸-17)/9 = 5(8)₁₂₇7_<129> = 23 · 63691 · 4788800872882184084781263_<25> · C98

C98 = P48 · P51

P48 = 112604159725354687671910018636786167653258924591_<48>

P51 = 745497589659523189147719856571126344213064487387523_<51>

Number: n
N=83946129660887876362622100012087832005382299917977951928607011873563078474950417997646958051278093
  ( 98 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=112604159725354687671910018636786167653258924591 (pp48)
 r2=745497589659523189147719856571126344213064487387523 (pp51)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 2.60 hours.
Scaled time: 6.88 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_8_127_7
n: 83946129660887876362622100012087832005382299917977951928607011873563078474950417997646958051278093
m: 50000000000000000000000000
deg: 5
c5: 424
c0: -425
skew: 1.00
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 1055001)
Primes: RFBsize:83548, AFBsize:84061, largePrimes:2777007 encountered
Relations: rels:2655347, finalFF:192381
Max relations in full relation-set: 28
Initial matrix: 167676 x 192381 with sparse part having weight 15348036.
Pruned matrix : 160977 x 161879 with weight 10790182.
Total sieving time: 2.33 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.06 hours.
Total square root time: 0.14 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 2.60 hours.
 --------- CPU info (if available) ----------

(53·10¹⁴⁴-17)/9 = 5(8)₁₄₃7_<145> = 17519 · 106957 · 6636577684770897967_<19> · C117

C117 = P36 · P81

P36 = 493043766422451686167629421455051011_<36>

P81 = 960473041699645228846742337228722619911387336255548265515490052356974875912822097_<81>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 473555246026821580479096651610338154141012072413920587982512535283509902483472861171889354142003106781845080102990067 (117 digits)
Using B1=2400000, B2=3567796060, polynomial Dickson(6), sigma=4105013632
Step 1 took 26785ms
Step 2 took 9594ms
********** Factor found in step 2: 493043766422451686167629421455051011
Found probable prime factor of 36 digits: 493043766422451686167629421455051011
Probable prime cofactor 960473041699645228846742337228722619911387336255548265515490052356974875912822097 has 81 digits

(17·10¹⁶⁷-53)/9 = 1(8)₁₆₆3_<168> = 3² · 2842894383216641696187208791071_<31> · C136

C136 = P48 · P88

P48 = 823828965221082614714987491762129205824830523981_<48>

P88 = 8961198957496977939253687411601927777122185598907503134441460972542651247105156582110937_<88>

Number: n
N=7382495264294979622827850118446254916311984354166976601889891234115975629567482988730135681174541273056980748634482050644700216780880197
  ( 136 digits)
SNFS difficulty: 169 digits.
Divisors found:

Fri Apr 24 20:49:26 2009  prp48 factor: 823828965221082614714987491762129205824830523981
Fri Apr 24 20:49:26 2009  prp88 factor: 8961198957496977939253687411601927777122185598907503134441460972542651247105156582110937
Fri Apr 24 20:49:26 2009  elapsed time 01:44:44 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 56.29 hours.
Scaled time: 149.11 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_1_8_166_3
n: 7382495264294979622827850118446254916311984354166976601889891234115975629567482988730135681174541273056980748634482050644700216780880197
m: 2000000000000000000000000000000000
deg: 5
c5: 425
c0: -424
skew: 1.00
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2300000, 5636291)
Primes: RFBsize:322441, AFBsize:322881, largePrimes:16952467 encountered
Relations: rels:16721012, finalFF:607071
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2174169 hash collisions in 18710656 relations
Msieve: matrix is 829496 x 829744 (220.4 MB)

Total sieving time: 55.50 hours.
Total relation processing time: 0.79 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,56,56,2.4,2.4,100000
total time: 56.29 hours.
 --------- CPU info (if available) ----------

Apr 24, 2009

By Erik Branger / GGNFS, Msieve / Apr 24, 2009

(53·10¹³⁷-17)/9 = 5(8)₁₃₆7_<138> = 13 · 257 · 1187573234723866457_<19> · C117

C117 = P49 · P68

P49 = 5584838927938453061724271226184215519985376889149_<49>

P68 = 26575768460269751918333188566808886042747046132589556424376472164199_<68>

Number: 58887_137
N=148421386236793474713355586446923384287979293005900666819660923606388680051470227246194467606188867817466602149376651
  ( 117 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=5584838927938453061724271226184215519985376889149
 r2=26575768460269751918333188566808886042747046132589556424376472164199
Version: 
Total time: 7.27 hours.
Scaled time: 7.31 units (timescale=1.005).
Factorization parameters were as follows:
n: 148421386236793474713355586446923384287979293005900666819660923606388680051470227246194467606188867817466602149376651
m: 2000000000000000000000000000
deg: 5
c5: 1325
c0: -136
skew: 0.63
type: snfs
lss: 1
rlim: 1490000
alim: 1490000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1490000/1490000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [745000, 1645001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 265186 x 265427
Total sieving time: 7.27 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1490000,1490000,26,26,48,48,2.3,2.3,75000
total time: 7.27 hours.
 --------- CPU info (if available) ----------

(53·10¹²⁶-17)/9 = 5(8)₁₂₅7_<127> = 139 · 2152525333033_<13> · C113

C113 = P49 · P64

P49 = 4186857306152507699817842593643290853547861453707_<49>

P64 = 4700912079944416830169055586945991616973525269591821004558075543_<64>

Number: 58887_126
N=19682048087495862967660904785941718578127783173067256935609610238613756161755275463953558441169432519094303387901
  ( 113 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=4186857306152507699817842593643290853547861453707
 r2=4700912079944416830169055586945991616973525269591821004558075543
Version: 
Total time: 3.85 hours.
Scaled time: 3.00 units (timescale=0.779).
Factorization parameters were as follows:
n: 19682048087495862967660904785941718578127783173067256935609610238613756161755275463953558441169432519094303387901
m: 20000000000000000000000000
deg: 5
c5: 265
c0: -272
skew: 1.01
type: snfs
lss: 1
rlim: 990000
alim: 990000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 990000/990000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [495000, 895001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 157081 x 157329
Total sieving time: 3.85 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,990000,990000,26,26,47,47,2.3,2.3,50000
total time: 3.85 hours.
 --------- CPU info (if available) ----------

Apr 23, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Apr 23, 2009

(35·10¹⁷⁶-71)/9 = 3(8)₁₇₅1_<177> = 3² · 367 · 232568767 · 60323230600525753781_<20> · 8193256915460198815721_<22> · C124

C124 = P61 · P63

P61 = 1320105305128237839759047437665736026132731396793537417927679_<61>

P63 = 775918004093695593851387986591834584873455900442876905422417139_<63>

Number: 38881_176
N=1024293473548601319173469912038505104746286056967893105461707929204618101281103354521416633306699402398601839123952472090381
  ( 124 digits)
Divisors found:
 r1=1320105305128237839759047437665736026132731396793537417927679 (pp61)
 r2=775918004093695593851387986591834584873455900442876905422417139 (pp63)
Version: Msieve-1.39
Total time: 61.25 hours.
Scaled time: 156.80 units (timescale=2.560).
Factorization parameters were as follows:
# Murphy_E = 1.931282e-10, selected by Jeff Gilchrist
n: 1024293473548601319173469912038505104746286056967893105461707929204618101281103354521416633306699402398601839123952472090381
Y0: -520935780629937847389521
Y1: 22406701384781
c0: -94888778317472415354353368632
c1: 14232405039257419376998134
c2: -339826485793637340641
c3: -3544791087233806
c4: -11143299794
c5: 26700
skew: 129910.61
type: gnfs
# selected mechanically
rlim: 6300000
alim: 6300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 6300000/6300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [3150000, 5970001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 917653 x 917901
Total sieving time: 61.25 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6300000,6300000,27,27,52,52,2.5,2.5,60000
total time: 61.25 hours.
 --------- CPU info (if available) ----------

(53·10¹²⁹-17)/9 = 5(8)₁₂₈7_<130> = 7 · 4623547 · 5222837 · C116

C116 = P35 · P81

P35 = 57168349928028616133688579199585387_<35>

P81 = 609393635442267750361101031452473824611828346367866478338485749744303280641982437_<81>

Number: 58887_129
N=34838028594877064284253557354927967622169804547748141483986966848529666618721039767304379796183953057786696135848119
  ( 116 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=57168349928028616133688579199585387 (pp35)
 r2=609393635442267750361101031452473824611828346367866478338485749744303280641982437 (pp81)
Version: Msieve-1.39
Total time: 2.82 hours.
Scaled time: 7.26 units (timescale=2.571).
Factorization parameters were as follows:
n: 34838028594877064284253557354927967622169804547748141483986966848529666618721039767304379796183953057786696135848119
m: 100000000000000000000000000
deg: 5
c5: 53
c0: -170
skew: 1.26
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 160216 x 160464
Total sieving time: 2.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.82 hours.
 --------- CPU info (if available) ----------

Apr 23, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Apr 23, 2009

(53·10¹⁶⁷-71)/9 = 5(8)₁₆₆1_<168> = 73 · 769 · 66501587107_<11> · 353614322081_<12> · C141

C141 = P41 · P101

P41 = 15289508170453564157615559715265886034189_<41>

P101 = 29176204089714079058424787149185032695439825811546932354672800303249154820310505588922930701582824751_<101>

Number: n
N=446089810812504105158182504969145136704663270654799288006352123575641893590592744605656997178397333941887287764109361491827634663159581411939
  ( 141 digits)
SNFS difficulty: 169 digits.
Divisors found:

Thu Apr 23 06:30:42 2009  prp41 factor: 15289508170453564157615559715265886034189
Thu Apr 23 06:30:42 2009  prp101 factor: 29176204089714079058424787149185032695439825811546932354672800303249154820310505588922930701582824751
Thu Apr 23 06:30:42 2009  elapsed time 01:28:32 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 61.86 hours.
Scaled time: 164.56 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_8_166_1
n: 446089810812504105158182504969145136704663270654799288006352123575641893590592744605656997178397333941887287764109361491827634663159581411939
m: 2000000000000000000000000000000000
deg: 5
c5: 1325
c0: -568
skew: 0.84
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2350000, 6054613)
Primes: RFBsize:328964, AFBsize:327815, largePrimes:17382610 encountered
Relations: rels:17432208, finalFF:658654
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2355284 hash collisions in 19429834 relations
Msieve: matrix is 837045 x 837293 (221.6 MB)

Total sieving time: 60.95 hours.
Total relation processing time: 0.91 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4700000,4700000,28,28,56,56,2.4,2.4,100000
total time: 61.86 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶⁴-43)/9 = 5(7)₁₆₃3_<165> = 3 · 241 · 107897 · 36883061 · 6612904342793249107_<19> · C131

C131 = P57 · P74

P57 = 428137267533980125175224262378383639832168779350627365977_<57>

P74 = 70926893194183362183806185858869881540459489448292533660130576984615410977_<74>

Number: n
N=30366446246832116288365725625880877232177375057371824681954491156869978949948474947696757112176249442217908790306207886226842129529
  ( 131 digits)
SNFS difficulty: 166 digits.
Divisors found:

Thu Apr 23 22:54:37 2009  prp57 factor: 428137267533980125175224262378383639832168779350627365977
Thu Apr 23 22:54:37 2009  prp74 factor: 70926893194183362183806185858869881540459489448292533660130576984615410977
Thu Apr 23 22:54:37 2009  elapsed time 01:04:41 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 36.73 hours.
Scaled time: 97.29 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_7_163_3
n: 30366446246832116288365725625880877232177375057371824681954491156869978949948474947696757112176249442217908790306207886226842129529
m: 1000000000000000000000000000000000
deg: 5
c5: 26
c0: -215
skew: 1.53
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2100000, 4258643)
Primes: RFBsize:296314, AFBsize:296491, largePrimes:15450463 encountered
Relations: rels:14663369, finalFF:610735
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1605925 hash collisions in 16362314 relations
Msieve: matrix is 745844 x 746092 (199.0 MB)

Total sieving time: 36.28 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,56,56,2.4,2.4,100000
total time: 36.73 hours.
 --------- CPU info (if available) ----------

(53·10¹⁰⁹-17)/9 = 5(8)₁₀₈7_<110> = 3 · 19 · 479 · 34483 · 62171 · C97

C97 = P43 · P54

P43 = 1184825813345484206359746383415693747268967_<43>

P54 = 849132744499225818718955971430604327755370155419332359_<54>

Number: n
N=1006074394639578460861665960829727793726759540115934699440062720584295891926720766143730739603153
  ( 97 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=1184825813345484206359746383415693747268967 (pp43)
 r2=849132744499225818718955971430604327755370155419332359 (pp54)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 0.60 hours.
Scaled time: 1.56 units (timescale=2.627).
Factorization parameters were as follows:
name: KA_5_8_108_7
n: 1006074394639578460861665960829727793726759540115934699440062720584295891926720766143730739603153
m: 10000000000000000000000
deg: 5
c5: 53
c0: -170
skew: 1.26
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
qintsize: 20000
Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [255000, 395001)
Primes: RFBsize:42291, AFBsize:42411, largePrimes:1076456 encountered
Relations: rels:1001878, finalFF:95374
Max relations in full relation-set: 28
Initial matrix: 84767 x 95374 with sparse part having weight 4131287.
Pruned matrix : 78247 x 78734 with weight 2783143.
Total sieving time: 0.55 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.60 hours.
 --------- CPU info (if available) ----------

Apr 23, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.41 / Apr 23, 2009

(53·10¹²⁴-17)/9 = 5(8)₁₂₃7_<125> = 3 · 89 · 1191809 · 4836787 · C110

C110 = P33 · P78

P33 = 162409129263521507054727247357759_<33>

P78 = 235585218437968568279588300257584868514845787402833345248144612223210092321113_<78>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1932810670
Step 1 took 7136ms
Step 2 took 9389ms
********** Factor found in step 2: 162409129263521507054727247357759
Found probable prime factor of 33 digits: 162409129263521507054727247357759
Probable prime cofactor has 78 digits

(53·10¹⁰²-17)/9 = 5(8)₁₀₁7_<103> = 59 · 1399 · C98

C98 = P49 · P50

P49 = 3536462375192796870546965456753026665578804701991_<49>

P50 = 20174119642955981100844036468742758967519435241877_<50>

SNFS difficulty: 105 digits.
Divisors found:
 r1=3536462375192796870546965456753026665578804701991 (pp49)
 r2=20174119642955981100844036468742758967519435241877 (pp50)
Version: Msieve-1.40
Total time: 0.42 hours.
Scaled time: 0.84 units (timescale=2.015).
Factorization parameters were as follows:
n: 71345015069951768077547992983958140668139335468299255992644732785995915834420335213880239988477107
m: 50000000000000000000000000
deg: 4
c4: 212
c0: -425
skew: 1.19
type: snfs
lss: 1
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [200000, 320001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 34633 x 34864
Total sieving time: 0.40 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105.000,4,0,0,0,0,0,0,0,0,400000,400000,25,25,44,44,2.2,2.2,20000
total time: 0.42 hours.

(53·10¹⁰⁴-17)/9 = 5(8)₁₀₃7_<105> = 409 · 34159 · C98

C98 = P38 · P60

P38 = 66094496635789648498726769864747288141_<38>

P60 = 637734048402595454621522275124133541105908678950119792488997_<60>

SNFS difficulty: 105 digits.
Divisors found:
 r1=66094496635789648498726769864747288141 (pp38)
 r2=637734048402595454621522275124133541105908678950119792488997 (pp60)
Version: Msieve-1.41
Total time: 0.42 hours.
Scaled time: 0.84 units (timescale=1.848).
Factorization parameters were as follows:
n: 42150710916673858134656553899915395570225911665995794361124020760449882967755843422642816331084577
m: 100000000000000000000000000
deg: 4
c4: 53
c0: -17
skew: 0.75
type: snfs
lss: 1
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [200000, 260001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 39510 x 39752
Total sieving time: 0.40 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,105,4,0,0,0,0,0,0,0,0,400000,400000,25,25,44,44,2.2,2.2,20000
total time: 0.42 hours.

(53·10¹⁹³-17)/9 = 5(8)₁₉₂7_<194> = 3³ · 7018213 · 17851313 · 679746483103291781_<18> · C161

C161 = P32 · C130

P32 = 20572446508725500234225553940201_<32>

C130 = [1244915789843555096011732458304270596627375015872090006518666492540398283834017403659916118975910672983647063299114503997601252229_<130>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=376038659
Step 1 took 11933ms
Step 2 took 12688ms
********** Factor found in step 2: 20572446508725500234225553940201
Found probable prime factor of 32 digits: 20572446508725500234225553940201
Composite cofactor has 130 digits

(53·10²⁰¹-17)/9 = 5(8)₂₀₀7_<202> = 7 · 941 · 5749 · 33767 · 276508825669_<12> · 296805472688401_<15> · C164

C164 = P31 · P133

P31 = 7137096825470911352763152350693_<31>

P133 = 7862459463037571684520567683265681573742169480804138362430647497393328622184882892466314752452755748772299349279963553756975752154591_<133>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1668989920
Step 1 took 11501ms
Step 2 took 12549ms
********** Factor found in step 2: 7137096825470911352763152350693
Found probable prime factor of 31 digits: 7137096825470911352763152350693
Probable prime cofactor has 133 digits

(53·10¹⁹⁷-17)/9 = 5(8)₁₉₆7_<198> = 13 · 97 · 1381 · 8093 · 199895588321879_<15> · C174

C174 = P33 · P142

P33 = 124131209152910945615138358610613_<33>

P142 = 1683956464285538192987701175282364657277752256350514234040551728309986650671586386857006585378655255901615254486990382871923560979892400767137_<142>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3750431010
Step 1 took 12365ms
Step 2 took 12241ms
********** Factor found in step 2: 124131209152910945615138358610613
Found probable prime factor of 33 digits: 124131209152910945615138358610613
Probable prime cofactor has 142 digits

(53·10¹³⁰-17)/9 = 5(8)₁₂₉7_<131> = 3² · 31 · 1787 · 689561 · 1251681026599_<13> · C108

C108 = P34 · P74

P34 = 2684522574849883505513247949489097_<34>

P74 = 50976637352551995002585907351700594122427409787504925659946717615102657493_<74>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2846608915
Step 1 took 7404ms
Step 2 took 5757ms
********** Factor found in step 2: 2684522574849883505513247949489097
Found probable prime factor of 34 digits: 2684522574849883505513247949489097
Probable prime cofactor has 74 digits

(53·10¹⁴⁸-17)/9 = 5(8)₁₄₇7_<149> = 3² · 1669 · 27337 · 218487524683_<12> · 66654703895377530032933214908629_<32> · C97

C97 = P49 · P49

P49 = 1293513234549944335404040049217391458765838967629_<49>

P49 = 7612991358325177921065847363673485843300748322977_<49>

N=9847505076507975189294121039002185454967285936943322205169240479190597831569216491897858739911533
  ( 97 digits)
Divisors found:
 r1=1293513234549944335404040049217391458765838967629 (pp49)
 r2=7612991358325177921065847363673485843300748322977 (pp49)
Version: Msieve-1.40
Total time: 2.08 hours.
Factorization parameters were as follows:
n: 9847505076507975189294121039002185454967285936943322205169240479190597831569216491897858739911533
skew: 3372.48
# norm 5.25e+13
c5: 140400
c4: -913012644
c3: -6915870530610
c2: 2736702776419444
c1: 6677853531088220367
c0: 9789361965300509717732
# alpha -6.05
Y1: 1013445211
Y0: -2339871812921506437
# Murphy_E 4.64e-09
# M 1911477931379528567900052509646008537492807656147084893400253968977167626506619701535654175781347
type: gnfs
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1020001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 137001 x 137249
Polynomial selection time: 0.26 hours.
Total sieving time: 1.60 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,96,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 2.08 hours.

(53·10¹³⁸-17)/9 = 5(8)₁₃₇7_<139> = C139

C139 = P50 · P90

P50 = 14212328108433255333011168440885868143857201519173_<50>

P90 = 414350755482105931010853345568490156490520800534066379136735288507168858874680066897030219_<90>

SNFS difficulty: 141 digits.
Divisors found:
 r1=14212328108433255333011168440885868143857201519173 (pp50)
 r2=414350755482105931010853345568490156490520800534066379136735288507168858874680066897030219 (pp90)
Version: Msieve-1.40
Total time: 6.39 hours.
Factorization parameters were as follows:
n: 5888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
m: 5000000000000000000000000000
deg: 5
c5: 424
c0: -425
skew: 1.00
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1885001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 260637 x 260870
Total sieving time: 6.00 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,141.000,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 6.39 hours.

Apr 23, 2009 (2nd)

By matsui / GGNFS / Apr 23, 2009

5·10¹⁶⁹+3 = 5(0)₁₆₈3_<170> = 31 · 16244243 · 29298332253113065055747_<23> · C139

C139 = P63 · P77

P63 = 219470599991522042446043080605252718567618567796903842516245509_<63>

P77 = 15441503431769976028446348762595181204879730780351588237227771804855548607617_<77>

N=3388956022941703290284911268189108916185410146351262338185883006343651520714919578492806480155277094510806544535131569600239126927479442053
  ( 139 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=219470599991522042446043080605252718567618567796903842516245509 (pp63)
 r2=15441503431769976028446348762595181204879730780351588237227771804855548607617 (pp77)
Version: GGNFS-0.77.1-20060722-nocona

Apr 23, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 23, 2009

(52·10¹⁶⁵-43)/9 = 5(7)₁₆₄3_<166> = 2132023 · 139451311 · 41362644195312023971_<20> · C132

C132 = P43 · P90

P43 = 2212108396188581657218483107142706525530369_<43>

P90 = 212388818457277709952441788024194276072656999962330691651813192423763170730676394041761159_<90>

Number: 57773_165
N=469827088565916424848798223220483523992904480604340677368464169830717413232119283714579864983812929914816116960729561312397299137671
  ( 132 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=2212108396188581657218483107142706525530369
 r2=212388818457277709952441788024194276072656999962330691651813192423763170730676394041761159
Version: 
Total time: 24.79 hours.
Scaled time: 58.87 units (timescale=2.375).
Factorization parameters were as follows:
n: 469827088565916424848798223220483523992904480604340677368464169830717413232119283714579864983812929914816116960729561312397299137671
m: 1000000000000000000000000000000000
deg: 5
c5: 52
c0: -43
skew: 0.96
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2400000, 4400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9737720
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 825721 x 825969
Total sieving time: 22.27 hours.
Total relation processing time: 0.94 hours.
Matrix solve time: 1.48 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000
total time: 24.79 hours.
 --------- CPU info (if available) ----------

Apr 22, 2009 (6th)

By Ignacio Santos / GGNFS, Msieve / Apr 22, 2009

(4·10¹⁸¹+17)/3 = 1(3)₁₈₀9_<182> = 19 · 199 · 1453 · C175

C175 = P56 · P57 · P63

P56 = 22309717107372494315385593361862526662022588401333102253_<56>

P57 = 156122557936970418953523058188454015963068329714979720107_<57>

P63 = 696797723896822116787571000843431402872490055258855522222137813_<63>

Number: 13339_181
N=2426981383050532361400098863086638563435741633027187834221881554935421362496427028345140294389201291954999639289891944114627786910306473748343509362899791334208138772853897723
  ( 175 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=22309717107372494315385593361862526662022588401333102253 (pp56)
 r2=156122557936970418953523058188454015963068329714979720107 (pp57)
 r3=696797723896822116787571000843431402872490055258855522222137813 (pp63)
Version: Msieve-1.39
Total time: 131.58 hours.
Scaled time: 228.81 units (timescale=1.739).
Factorization parameters were as follows:
n: 2426981383050532361400098863086638563435741633027187834221881554935421362496427028345140294389201291954999639289891944114627786910306473748343509362899791334208138772853897723
m: 1000000000000000000000000000000000000
deg: 5
c5: 40
c0: 17
skew: 0.84
type: snfs
lss: 1
rlim: 7400000
alim: 7400000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3700000, 5900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1446798 x 1447043
Total sieving time: 131.58 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,53,53,2.5,2.5,100000
total time: 131.58 hours.
 --------- CPU info (if available) ----------

(8·10¹⁷³-11)/3 = 2(6)₁₇₂3_<174> = 26026517172463_<14> · 835337687643105193_<18> · 133430923595218323637_<21> · C122

C122 = P40 · P83

P40 = 2420995607054671044108003821518248239767_<40>

P83 = 37969957194046514176647750464622844630717776681886775745942777306692010895939678283_<83>

Number: 26663_173
N=91925099566840514579862159855723574163615261031069756391977117342379508653758020321481439131791263848497042220577026880061
  ( 122 digits)
Divisors found:
 r1=2420995607054671044108003821518248239767 (pp40)
 r2=37969957194046514176647750464622844630717776681886775745942777306692010895939678283 (pp83)
Version: Msieve-1.39
Total time: 54.53 hours.
Scaled time: 140.20 units (timescale=2.571).
Factorization parameters were as follows:
# Murphy_E = 2.150701e-10, selected by Jeff Gilchrist
n: 91925099566840514579862159855723574163615261031069756391977117342379508653758020321481439131791263848497042220577026880061
Y0: -349452957735598923964078
Y1: 10362996766331
c0: -1062632721513365353062035043615
c1: 316697255897387397597827777
c2: 1563572907539943899645
c3: -3712873729966849
c4: -11060071302
c5: 17640
skew: 347138.3
type: gnfs
# selected mechanically
rlim: 5900000
alim: 5900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2950000, 5470001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 809289 x 809537
Total sieving time: 54.53 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5900000,5900000,27,27,52,52,2.5,2.5,60000
total time: 54.53 hours.
 --------- CPU info (if available) ----------

Apr 22, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 21, 2009

(17·10¹⁶⁴+7)/3 = 5(6)₁₆₃9_<165> = 631 · 20411 · 546745561 · 36771006513555924569_<20> · C130

C130 = P53 · P77

P53 = 24684467871388862668725282027781049084155761016849459_<53>

P77 = 88658314742674979794126359600408571068896112076998888313552681943961026591339_<77>

Number: 56669_164
N=2188483321797042080199208926466285626226356003556927267628384147997644819195672652362693649569098240692076340501181169127676235601
  ( 130 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=24684467871388862668725282027781049084155761016849459
 r2=88658314742674979794126359600408571068896112076998888313552681943961026591339
Version: 
Total time: 21.83 hours.
Scaled time: 52.00 units (timescale=2.382).
Factorization parameters were as follows:
n: 2188483321797042080199208926466285626226356003556927267628384147997644819195672652362693649569098240692076340501181169127676235601
m: 1000000000000000000000000000000000
deg: 5
c5: 17
c0: 70
skew: 1.33
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 4000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9658440
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 757735 x 757983
Total sieving time: 19.70 hours.
Total relation processing time: 0.84 hours.
Matrix solve time: 1.21 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 21.83 hours.
 --------- CPU info (if available) ----------

By Jo Yeong Uk / GMP-ECM / Apr 22, 2009

2·10¹⁸³-1 = 1(9)₁₈₃_<184> = 298385575419109_<15> · C169

C169 = P39 · P131

P39 = 138315648629492573181397043870991531509_<39>

P131 = 48459714744214666303053112592352799187563839995254738535415184574936072669072865614713121962535167281027204906904020713946527407079_<131>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 6702736877246236350782731803505581851819006651598315170749396069506347157382739930428866242940491670173578185223001548816068081968260436967719825339733369220980898152211 (169 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3048775659
Step 1 took 16609ms
Step 2 took 7140ms
********** Factor found in step 2: 138315648629492573181397043870991531509
Found probable prime factor of 39 digits: 138315648629492573181397043870991531509
Probable prime cofactor 48459714744214666303053112592352799187563839995254738535415184574936072669072865614713121962535167281027204906904020713946527407079 has 131 digits

Apr 22, 2009 (4th)

By matsui / GGNFS / Apr 22, 2009

7·10¹⁷⁵+1 = 7(0)₁₇₄1_<176> = 17 · 43 · 16106554067_<11> · C163

C163 = P42 · P50 · P72

P42 = 546424038802294846052914856058998495168369_<42>

P50 = 50847756028512910420533268455094582971422236487293_<50>

P72 = 213981604431953258247908719407251822585834319843385691315588724389559589_<72>

N=5945358239123625634011428660866607620137468294219930437924782752600840851464522625179701735071778160104909516766334428716890094478708550908337237518092811760086913
  ( 163 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=546424038802294846052914856058998495168369 (pp42)
 r2=50847756028512910420533268455094582971422236487293 (pp50)
 r3=213981604431953258247908719407251822585834319843385691315588724389559589 (pp72)
Version: GGNFS-0.77.1-20060722-nocona

Apr 22, 2009 (3rd)

By Sinkiti Sibata / GGNFS / Apr 22, 2009

5·10¹⁸⁸+9 = 5(0)₁₈₇9_<189> = 89 · 20644698707_<11> · 2095779451075181845289_<22> · 17069365974029360492115172688628301_<35> · C121

C121 = P54 · P68

P54 = 112851366896191612350337923343819108022586261622918801_<54>

P68 = 67406481306382958257320834957187828313474877802170323638967682116047_<68>

Number: 50009_188
N=7606913553087904523289891655928436341384431709516903459521491661869372564112334503851881776661479063881775251744140099647
  ( 121 digits)
Divisors found:
 r1=112851366896191612350337923343819108022586261622918801 (pp54)
 r2=67406481306382958257320834957187828313474877802170323638967682116047 (pp68)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 140.12 hours.
Scaled time: 62.64 units (timescale=0.447).
Factorization parameters were as follows:
name: 50009_188
n: 7606913553087904523289891655928436341384431709516903459521491661869372564112334503851881776661479063881775251744140099647
skew: 109016.74
# norm 2.11e+16
c5: 5700
c4: 4393438342
c3: -159644453182350
c2: -66523826013641583182
c1: -1678125279183183409996345
c0: 13790779317453160370267289525
# alpha -5.21
Y1: 9695498203633
Y0: -266111893921478002019566
# Murphy_E 2.41e-10
# M 5755240981910880162683132603904024483240966666901395640250549525151778137375628477746712617517491336934374610157755148949
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5380001)
Primes: RFBsize:348513, AFBsize:347346, largePrimes:7784026 encountered
Relations: rels:7980316, finalFF:810325
Max relations in full relation-set: 28
Initial matrix: 695939 x 810325 with sparse part having weight 73710325.
Pruned matrix : 602700 x 606243 with weight 51408708.
Total sieving time: 117.79 hours.
Total relation processing time: 1.23 hours.
Matrix solve time: 20.51 hours.
Time per square root: 0.59 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 140.12 hours.
 --------- CPU info (if available) ----------

Apr 22, 2009 (2nd)

By Robert Backstrom / GGNFS / Apr 22, 2009

(53·10¹⁶²-71)/9 = 5(8)₁₆₁1_<163> = 70679701 · 44026722517_<11> · 1236279080219216121922252206884753_<34> · C112

C112 = P42 · P70

P42 = 443544821402465146063268358238856200246841_<42>

P70 = 3451185210796963823875477889316547070862232437023870711320410226459441_<70>

Number: KA_5_8_161_1
N=1530755327949768346559116010704472935748277600679650175511082917507123042329452736442582425054160912093674875881
  ( 112 digits)
Divisors found:
 r1=443544821402465146063268358238856200246841 (pp42)
 r2=3451185210796963823875477889316547070862232437023870711320410226459441 (pp70)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 15.86 hours.
Scaled time: 42.37 units (timescale=2.671).
Factorization parameters were as follows:
n: 1530755327949768346559116010704472935748277600679650175511082917507123042329452736442582425054160912093674875881
Y0: -2793386256401126466886
Y1:  580659604429
c0:  1249418291818091229406104855
c1:  87816497597904215717963
c2: -2303223579921404027
c3: -109127595890605
c4:  828480114
c5:  9000
skew: 36890.51
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1750000, 2400001)
Primes: RFBsize:250150, AFBsize:250833, largePrimes:16869364 encountered
Relations: rels:15156758, finalFF:588554
Max relations in full relation-set: 28
Initial matrix: 501060 x 588554 with sparse part having weight 51733363.
Pruned matrix : 430049 x 432618 with weight 33187546.
Total sieving time: 14.33 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 0.80 hours.
Total square root time: 0.25 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,28,28,56,56,2.6,2.6,100000
total time: 15.86 hours.
 --------- CPU info (if available) ----------

Apr 22, 2009

Factorizations of 588...887 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 21, 2009 (5th)

By Wataru Sakai / GMP-ECM / Apr 21, 2009

8·10¹⁹⁰-9 = 7(9)₁₈₉1_<191> = 31 · 257 · 30319 · 2445649 · 568034078420777_<15> · 1118584622077795641597568510231_<31> · C132

C132 = P46 · P86

P46 = 5956694674603727915072852316779388032674317487_<46>

P86 = 35779774073720156830334101164802233650029559245191540826257705794588243741259881976407_<86>

Apr 21, 2009 (4th)

By Sinkiti Sibata / Msieve / Apr 21, 2009

(13·10¹⁹⁵-1)/3 = 4(3)₁₉₅_<196> = 7 · C195

C195 = P55 · P141

P55 = 4108959678924632386368511921044689765845824495413027737_<55>

P141 = 150657993122393397191374958950288699170836432534995369715829292300612307048500313165210751477061418430213152010301608423612711599020092518587_<141>

Number: 43333_195
N=619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619
  ( 195 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=4108959678924632386368511921044689765845824495413027737
 r2=150657993122393397191374958950288699170836432534995369715829292300612307048500313165210751477061418430213152010301608423612711599020092518587
Version: 
Total time: 441.44 hours.
Scaled time: 1473.97 units (timescale=3.339).
Factorization parameters were as follows:
name: 43333_195
n: 619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619
m: 1000000000000000000000000000000000000000
deg: 5
c5: 13
c0: -1
skew: 0.60
type: snfs
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 9500000/9500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved algebraic special-q in [4750000, 12750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1926738 x 1926986
Total sieving time: 441.44 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,55,55,2.5,2.5,100000
total time: 441.44 hours.
 --------- CPU info (if available) ----------

Apr 21, 2009 (3rd)

By Andreas Tete / Msieve v1.41, GGNFS / Apr 21, 2009

(52·10¹⁸⁸+11)/9 = 5(7)₁₈₇9_<189> = 3² · 1093 · 5081 · 64231 · 11552017 · 14214270311_<11> · 96882854526001774645678465981_<29> · C131

C131 = P44 · P87

P44 = 81794757600323035554827444059633541274214747_<44>

P87 = 138308699903585154803319669716002943598265094204006724265991671763585624304306433563833_<87>

Mon Apr 20 19:08:11 2009  
Mon Apr 20 19:08:11 2009  
Mon Apr 20 19:08:11 2009  Msieve v. 1.41
Mon Apr 20 19:08:11 2009  random seeds: 87569ffc 473e86b3
Mon Apr 20 19:08:11 2009  factoring 11312926582629569735706825148931447422166875763212917695378460963807918703953528423373129743219702130852404196787051012831774445251 (131 digits)
Mon Apr 20 19:08:12 2009  searching for 15-digit factors
Mon Apr 20 19:08:14 2009  commencing number field sieve (131-digit input)
Mon Apr 20 19:08:14 2009  R0: -12083212830902574969747860
Mon Apr 20 19:08:14 2009  R1:  213108260669881
Mon Apr 20 19:08:14 2009  A0:  56090967640472498013392023696851
Mon Apr 20 19:08:14 2009  A1:  332754979081695566842805070
Mon Apr 20 19:08:14 2009  A2: -1465196442719012042647
Mon Apr 20 19:08:14 2009  A3: -25753535061241090
Mon Apr 20 19:08:14 2009  A4:  2934479696
Mon Apr 20 19:08:14 2009  A5:  43920
Mon Apr 20 19:08:14 2009  skew 392473.78, size 1.303298e-012, alpha -6.358696, combined = 6.937147e-011
Mon Apr 20 19:08:14 2009  
Mon Apr 20 19:08:14 2009  commencing relation filtering
Mon Apr 20 19:08:14 2009  commencing duplicate removal, pass 1
Mon Apr 20 19:10:10 2009  error -15 reading relation 9581126
Mon Apr 20 19:10:11 2009  error -15 reading relation 9725613
Mon Apr 20 19:11:18 2009  found 3444048 hash collisions in 15840366 relations
Mon Apr 20 19:11:59 2009  added 104414 free relations
Mon Apr 20 19:11:59 2009  commencing duplicate removal, pass 2
Mon Apr 20 19:13:09 2009  found 3625670 duplicates and 12319109 unique relations
Mon Apr 20 19:13:09 2009  memory use: 106.6 MB
Mon Apr 20 19:13:09 2009  reading rational ideals above 10420224
Mon Apr 20 19:13:09 2009  reading algebraic ideals above 10420224
Mon Apr 20 19:13:09 2009  commencing singleton removal, pass 1
Mon Apr 20 19:16:02 2009  relations with 0 large ideals: 374026
Mon Apr 20 19:16:02 2009  relations with 1 large ideals: 2578236
Mon Apr 20 19:16:02 2009  relations with 2 large ideals: 5243824
Mon Apr 20 19:16:02 2009  relations with 3 large ideals: 3361638
Mon Apr 20 19:16:02 2009  relations with 4 large ideals: 647320
Mon Apr 20 19:16:02 2009  relations with 5 large ideals: 15067
Mon Apr 20 19:16:02 2009  relations with 6 large ideals: 98994
Mon Apr 20 19:16:02 2009  relations with 7+ large ideals: 4
Mon Apr 20 19:16:02 2009  12319109 relations and about 11869560 large ideals
Mon Apr 20 19:16:02 2009  commencing singleton removal, pass 2
Mon Apr 20 19:18:33 2009  found 5868335 singletons
Mon Apr 20 19:18:33 2009  current dataset: 6450774 relations and about 4791520 large ideals
Mon Apr 20 19:18:33 2009  commencing singleton removal, pass 3
Mon Apr 20 19:20:20 2009  found 1098994 singletons
Mon Apr 20 19:20:20 2009  current dataset: 5351780 relations and about 3626493 large ideals
Mon Apr 20 19:20:20 2009  commencing singleton removal, pass 4
Mon Apr 20 19:21:59 2009  found 274520 singletons
Mon Apr 20 19:21:59 2009  current dataset: 5077260 relations and about 3346643 large ideals
Mon Apr 20 19:21:59 2009  commencing singleton removal, final pass
Mon Apr 20 19:23:46 2009  memory use: 74.7 MB
Mon Apr 20 19:23:46 2009  commencing in-memory singleton removal
Mon Apr 20 19:23:46 2009  begin with 5077260 relations and 3647012 unique ideals
Mon Apr 20 19:23:52 2009  reduce to 4263128 relations and 2811805 ideals in 14 passes
Mon Apr 20 19:23:52 2009  max relations containing the same ideal: 23
Mon Apr 20 19:23:53 2009  reading rational ideals above 720000
Mon Apr 20 19:23:53 2009  reading algebraic ideals above 720000
Mon Apr 20 19:23:53 2009  commencing singleton removal, final pass
Mon Apr 20 19:25:41 2009  keeping 4000705 ideals with weight <= 20, new excess is 343752
Mon Apr 20 19:25:46 2009  memory use: 128.7 MB
Mon Apr 20 19:25:46 2009  commencing in-memory singleton removal
Mon Apr 20 19:25:47 2009  begin with 4290130 relations and 4000705 unique ideals
Mon Apr 20 19:25:54 2009  reduce to 4190944 relations and 3768298 ideals in 12 passes
Mon Apr 20 19:25:54 2009  max relations containing the same ideal: 20
Mon Apr 20 19:25:57 2009  removing 149756 relations and 137809 ideals in 11947 cliques
Mon Apr 20 19:25:57 2009  commencing in-memory singleton removal
Mon Apr 20 19:25:58 2009  begin with 4041188 relations and 3768298 unique ideals
Mon Apr 20 19:26:02 2009  reduce to 4037824 relations and 3627111 ideals in 8 passes
Mon Apr 20 19:26:02 2009  max relations containing the same ideal: 20
Mon Apr 20 19:26:05 2009  removing 110736 relations and 98789 ideals in 11947 cliques
Mon Apr 20 19:26:05 2009  commencing in-memory singleton removal
Mon Apr 20 19:26:06 2009  begin with 3927088 relations and 3627111 unique ideals
Mon Apr 20 19:26:10 2009  reduce to 3925129 relations and 3526358 ideals in 7 passes
Mon Apr 20 19:26:10 2009  max relations containing the same ideal: 20
Mon Apr 20 19:26:11 2009  relations with 0 large ideals: 8781
Mon Apr 20 19:26:11 2009  relations with 1 large ideals: 84877
Mon Apr 20 19:26:11 2009  relations with 2 large ideals: 374180
Mon Apr 20 19:26:11 2009  relations with 3 large ideals: 893493
Mon Apr 20 19:26:11 2009  relations with 4 large ideals: 1203750
Mon Apr 20 19:26:11 2009  relations with 5 large ideals: 907674
Mon Apr 20 19:26:11 2009  relations with 6 large ideals: 366841
Mon Apr 20 19:26:11 2009  relations with 7+ large ideals: 85533
Mon Apr 20 19:26:11 2009  commencing 2-way merge
Mon Apr 20 19:26:15 2009  reduce to 2337038 relation sets and 1938267 unique ideals
Mon Apr 20 19:26:15 2009  commencing full merge
Mon Apr 20 19:26:54 2009  memory use: 175.7 MB
Mon Apr 20 19:26:55 2009  found 1180571 cycles, need 1128467
Mon Apr 20 19:26:55 2009  weight of 1128467 cycles is about 79026752 (70.03/cycle)
Mon Apr 20 19:26:55 2009  distribution of cycle lengths:
Mon Apr 20 19:26:55 2009  1 relations: 128978
Mon Apr 20 19:26:55 2009  2 relations: 137710
Mon Apr 20 19:26:55 2009  3 relations: 137141
Mon Apr 20 19:26:55 2009  4 relations: 123799
Mon Apr 20 19:26:55 2009  5 relations: 109162
Mon Apr 20 19:26:55 2009  6 relations: 93570
Mon Apr 20 19:26:55 2009  7 relations: 78142
Mon Apr 20 19:26:55 2009  8 relations: 66063
Mon Apr 20 19:26:55 2009  9 relations: 55092
Mon Apr 20 19:26:55 2009  10+ relations: 198810
Mon Apr 20 19:26:55 2009  heaviest cycle: 19 relations
Mon Apr 20 19:26:55 2009  commencing cycle optimization
Mon Apr 20 19:26:58 2009  start with 6454929 relations
Mon Apr 20 19:27:15 2009  pruned 170048 relations
Mon Apr 20 19:27:15 2009  memory use: 171.3 MB
Mon Apr 20 19:27:15 2009  distribution of cycle lengths:
Mon Apr 20 19:27:15 2009  1 relations: 128978
Mon Apr 20 19:27:15 2009  2 relations: 141126
Mon Apr 20 19:27:15 2009  3 relations: 142718
Mon Apr 20 19:27:15 2009  4 relations: 126930
Mon Apr 20 19:27:15 2009  5 relations: 112065
Mon Apr 20 19:27:15 2009  6 relations: 94751
Mon Apr 20 19:27:15 2009  7 relations: 78734
Mon Apr 20 19:27:15 2009  8 relations: 65542
Mon Apr 20 19:27:15 2009  9 relations: 54402
Mon Apr 20 19:27:15 2009  10+ relations: 183221
Mon Apr 20 19:27:15 2009  heaviest cycle: 19 relations
Mon Apr 20 19:27:17 2009  RelProcTime: 895
Mon Apr 20 19:27:17 2009  
Mon Apr 20 19:27:17 2009  commencing linear algebra
Mon Apr 20 19:27:17 2009  read 1128467 cycles
Mon Apr 20 19:27:20 2009  cycles contain 3583964 unique relations
Mon Apr 20 19:28:27 2009  read 3583964 relations
Mon Apr 20 19:28:33 2009  using 20 quadratic characters above 268430840
Mon Apr 20 19:28:56 2009  building initial matrix
Mon Apr 20 19:29:53 2009  memory use: 407.2 MB
Mon Apr 20 19:30:05 2009  read 1128467 cycles
Mon Apr 20 19:30:25 2009  matrix is 1128216 x 1128467 (323.7 MB) with weight 105969391 (93.91/col)
Mon Apr 20 19:30:25 2009  sparse part has weight 75825912 (67.19/col)
Mon Apr 20 19:30:49 2009  filtering completed in 3 passes
Mon Apr 20 19:30:49 2009  matrix is 1122687 x 1122887 (322.9 MB) with weight 105636528 (94.08/col)
Mon Apr 20 19:30:49 2009  sparse part has weight 75655471 (67.38/col)
Mon Apr 20 19:30:55 2009  read 1122887 cycles
Mon Apr 20 19:30:56 2009  matrix is 1122687 x 1122887 (322.9 MB) with weight 105636528 (94.08/col)
Mon Apr 20 19:30:56 2009  sparse part has weight 75655471 (67.38/col)
Mon Apr 20 19:30:56 2009  saving the first 48 matrix rows for later
Mon Apr 20 19:30:57 2009  matrix is 1122639 x 1122887 (309.2 MB) with weight 84191763 (74.98/col)
Mon Apr 20 19:30:57 2009  sparse part has weight 74309659 (66.18/col)
Mon Apr 20 19:30:57 2009  matrix includes 64 packed rows
Mon Apr 20 19:30:57 2009  using block size 65536 for processor cache size 3072 kB
Mon Apr 20 19:31:07 2009  commencing Lanczos iteration
Mon Apr 20 19:31:07 2009  memory use: 307.1 MB
Mon Apr 20 22:47:31 2009  lanczos halted after 17753 iterations (dim = 1122639)
Mon Apr 20 22:47:34 2009  recovered 30 nontrivial dependencies
Mon Apr 20 22:47:34 2009  BLanczosTime: 12017
Mon Apr 20 22:47:34 2009  
Mon Apr 20 22:47:34 2009  commencing square root phase
Mon Apr 20 22:47:34 2009  reading relations for dependency 1
Mon Apr 20 22:47:35 2009  read 560536 cycles
Mon Apr 20 22:47:36 2009  cycles contain 2179676 unique relations
Mon Apr 20 22:48:35 2009  read 2179676 relations
Mon Apr 20 22:48:49 2009  multiplying 1789248 relations
Mon Apr 20 22:55:12 2009  multiply complete, coefficients have about 83.73 million bits
Mon Apr 20 22:55:16 2009  initial square root is modulo 1023313
Mon Apr 20 23:03:42 2009  reading relations for dependency 2
Mon Apr 20 23:03:43 2009  read 562605 cycles
Mon Apr 20 23:03:44 2009  cycles contain 2184477 unique relations
Mon Apr 20 23:04:41 2009  read 2184477 relations
Mon Apr 20 23:04:55 2009  multiplying 1793096 relations
Mon Apr 20 23:11:28 2009  multiply complete, coefficients have about 83.91 million bits
Mon Apr 20 23:11:31 2009  initial square root is modulo 1054013
Mon Apr 20 23:20:00 2009  reading relations for dependency 3
Mon Apr 20 23:20:01 2009  read 561085 cycles
Mon Apr 20 23:20:02 2009  cycles contain 2178671 unique relations
Mon Apr 20 23:20:59 2009  read 2178671 relations
Mon Apr 20 23:21:13 2009  multiplying 1788758 relations
Mon Apr 20 23:27:36 2009  multiply complete, coefficients have about 83.70 million bits
Mon Apr 20 23:27:40 2009  initial square root is modulo 1017953
Mon Apr 20 23:36:06 2009  sqrtTime: 2912
Mon Apr 20 23:36:06 2009  prp44 factor: 81794757600323035554827444059633541274214747
Mon Apr 20 23:36:06 2009  prp87 factor: 138308699903585154803319669716002943598265094204006724265991671763585624304306433563833
Mon Apr 20 23:36:06 2009  elapsed time 04:27:55
total time 191,26 hours

Apr 21, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Apr 21, 2009

(53·10¹⁵⁴-71)/9 = 5(8)₁₅₃1_<155> = 3 · 229 · 784913 · C147

C147 = P44 · P49 · P54

P44 = 58432003235623530165281017016867956379005573_<44>

P49 = 1909904305005828208979377889723705736501215261699_<49>

P54 = 978571848436525753147014195992938337808040799827522913_<54>

Number: n
N=109208162789513448702851703858513074211371194492462397897159818344452513876803589060910022195654513695691535571956886639124083657821847491431599151
  ( 147 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=58432003235623530165281017016867956379005573 (pp44)
 r2=1909904305005828208979377889723705736501215261699 (pp49)
 r3=978571848436525753147014195992938337808040799827522913 (pp54)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 24.35 hours.
Scaled time: 35.09 units (timescale=1.441).
Factorization parameters were as follows:
name: KA_5_8_153_1
n: 109208162789513448702851703858513074211371194492462397897159818344452513876803589060910022195654513695691535571956886639124083657821847491431599151
m: 10000000000000000000000000000000
deg: 5
c5: 53
c0: -710
skew: 1.68
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 20000
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [1450000, 2950001)
Primes: RFBsize:210109, AFBsize:209895, largePrimes:13516363 encountered
Relations: rels:13120834, finalFF:478919
Max relations in full relation-set: 28
Initial matrix: 420069 x 478918 with sparse part having weight 55190721.
Pruned matrix : 400471 x 402635 with weight 43607320.
Total sieving time: 22.43 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 0.94 hours.
Total square root time: 0.45 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,28,28,56,56,2.4,2.4,100000
total time: 24.35 hours.
 --------- CPU info (if available) ----------

2·10¹⁸⁹-1 = 1(9)₁₈₉_<190> = 31 · 5439829 · 2720009561_<10> · 13767101225803399878919_<23> · 317174697888724493139312350540581_<33> · C117

C117 = P54 · P64

P54 = 513218192797005307893534212745911015541469979463052889_<54>

P64 = 1945671599615643697213895686057854815110769046170890008443525071_<64>

Number: n
N=998554062131199145511682309200429404184445404728977563784886142161737708964524438853301713011987413991352186470480119
  ( 117 digits)
Divisors found:

Tue Apr 21 14:48:53 2009  prp54 factor: 513218192797005307893534212745911015541469979463052889
Tue Apr 21 14:48:53 2009  prp64 factor: 1945671599615643697213895686057854815110769046170890008443525071
Tue Apr 21 14:48:53 2009  elapsed time 00:56:00 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 21.19 hours.
Scaled time: 56.37 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_1_9_189
n: 998554062131199145511682309200429404184445404728977563784886142161737708964524438853301713011987413991352186470480119
Y0: -39549417387425509027250
Y1:  1988506022909
c0:  2486995315355389860517375156431
c1:  58401840270545545618714084
c2:  125760847171208808779
c3: -1783059507957566
c4: -4048042212
c5:  10320
skew: 217819.22
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2250000, 3451699)
Primes: RFBsize:315948, AFBsize:315612, largePrimes:13634890 encountered
Relations: rels:12392196, finalFF:666830
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 934308 hash collisions in 13111368 relations
Msieve: matrix is 654514 x 654762 (184.4 MB)

Total sieving time: 20.61 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,56,56,2.4,2.4,60000
total time: 21.19 hours.
 --------- CPU info (if available) ----------

Apr 21, 2009

By Ignacio Santos / GGNFS, Msieve / Apr 21, 2009

(25·10¹⁷³+11)/9 = 2(7)₁₇₂9_<174> = 3² · 19 · 67 · 941 · 15161 · 10094239 · 34387963 · 92007751184296289889437071_<26> · C122

C122 = P39 · P84

P39 = 309663452002993767114281190640908937591_<39>

P84 = 171836221375684041886673540732326857211429098070211664166511506444287611655348677411_<84>

Number: 27779_173
N=53211397490344946900536786881309863034780265482886037675997088339278604798975900411608112094043137173327508782150990456901
  ( 122 digits)
Divisors found:
 r1=309663452002993767114281190640908937591 (pp39)
 r2=171836221375684041886673540732326857211429098070211664166511506444287611655348677411 (pp84)
Version: Msieve-1.39
Total time: 45.64 hours.
Scaled time: 117.34 units (timescale=2.571).
Factorization parameters were as follows:
# Murphy_E = 2.358547e-10, selected by Jeff Gilchrist
n: 53211397490344946900536786881309863034780265482886037675997088339278604798975900411608112094043137173327508782150990456901
Y0: -348709088850161602305536
Y1: 11955423470957
c0: 21632123064086795098280205422505
c1: 296416490313361015058593979
c2: -1664067767180628526287
c3: -3283788797457339
c4: 5983105142
c5: 10320
skew: 411539.22
type: gnfs
# selected mechanically
rlim: 5800000
alim: 5800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2900000, 5000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 792665 x 792913
Total sieving time: 45.64 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5800000,5800000,27,27,52,52,2.5,2.5,60000
total time: 45.64 hours.
 --------- CPU info (if available) ----------

(49·10¹⁷³-31)/9 = 5(4)₁₇₂1_<174> = 2741 · 807085684543_<12> · 15477414385463353_<17> · 294569208541863507869_<21> · C122

C122 = P40 · P82

P40 = 5931851484368810751905079921740369165257_<40>

P82 = 9100156549889364411984182615500796454801011418152264037858984439499480211034026343_<82>

Number: 54441_173
N=53980777138449781902663795465980934453425776747350796708496115707652003245333207846637476138009335666563011187390658365151
  ( 122 digits)
Divisors found:
 r1=5931851484368810751905079921740369165257 (pp40)
 r2=9100156549889364411984182615500796454801011418152264037858984439499480211034026343 (pp82)
Version: Msieve-1.39
Total time: 49.31 hours.
Scaled time: 130.12 units (timescale=2.639).
Factorization parameters were as follows:
# Murphy_E = 2.256858e-10, selected by Jeff Gilchrist
n: 53980777138449781902663795465980934453425776747350796708496115707652003245333207846637476138009335666563011187390658365151
Y0: -323737180325506520777503
Y1: 16149092889517
c0: 427754643269965365750037883136
c1: 71856727713288899503966296
c2: -221173711071066753176
c3: -1988180336202337
c4: 3126697882
c5: 15180
skew: 249593.92
type: gnfs
# selected mechanically
rlim: 5900000
alim: 5900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2950000, 5230001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 804752 x 805000
Total sieving time: 49.31 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5900000,5900000,27,27,52,52,2.5,2.5,60000
total time: 49.31 hours.
 --------- CPU info (if available) ----------

Apr 20, 2009 (5th)

By Wataru Sakai / Msieve / Apr 20, 2009

2·10¹⁸³-9 = 1(9)₁₈₂1_<184> = 11 · 29 · 89 · 181 · C177

C177 = P60 · P118

P60 = 199744837434442791340990120371036864210437097079699444679911_<60>

P118 = 1948476479308863608330608439312461206938858412379710908007928999570893351886680145473233888864975347874868634937712811_<118>

Number: 19991_183
N=389198117604384394634436911082435858690725856435322764917915198011353298288637497175881159133185736433867163958074800375420504241189187064377844430117629293074161117512339039821
  ( 177 digits)
SNFS difficulty: 183 digits.
Divisors found:
 r1=199744837434442791340990120371036864210437097079699444679911
 r2=1948476479308863608330608439312461206938858412379710908007928999570893351886680145473233888864975347874868634937712811
Version: 
Total time: 168.64 hours.
Scaled time: 317.05 units (timescale=1.880).
Factorization parameters were as follows:
n: 389198117604384394634436911082435858690725856435322764917915198011353298288637497175881159133185736433867163958074800375420504241189187064377844430117629293074161117512339039821
m: 2000000000000000000000000000000000000
deg: 5
c5: 125
c0: -18
skew: 0.68
type: snfs
lss: 1
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [4000000, 5500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1426873 x 1427120
Total sieving time: 168.64 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,183,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,53,53,2.5,2.5,100000
total time: 168.64 hours.
 --------- CPU info (if available) ----------

2·10¹⁹¹-7 = 1(9)₁₉₀3_<192> = 17 · 31 · 389 · C186

C186 = P75 · P112

P75 = 128310718329815993931447087546082492234669614032972499261568404331467602141_<75>

P112 = 7603382568421390295289669853703818922067601220779471394301400646577106498502213407372609170471837455808074363591_<112>

Number: 19993_191
N=975595479090549894391789388447973932088798700506821851387540670136534587298722457720130924913293951795827378135929718101686316785608015492456207957932322941615488553826041570123364048331
  ( 186 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=128310718329815993931447087546082492234669614032972499261568404331467602141
 r2=7603382568421390295289669853703818922067601220779471394301400646577106498502213407372609170471837455808074363591
Version: 
Total time: 339.94 hours.
Scaled time: 675.12 units (timescale=1.986).
Factorization parameters were as follows:
n: 975595479090549894391789388447973932088798700506821851387540670136534587298722457720130924913293951795827378135929718101686316785608015492456207957932322941615488553826041570123364048331
m: 100000000000000000000000000000000000000
deg: 5
c5: 20
c0: -7
skew: 0.81
type: snfs
lss: 1
rlim: 10800000
alim: 10800000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 10800000/10800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5400000, 9000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1393898 x 1394146
Total sieving time: 339.94 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,10800000,10800000,28,28,54,54,2.5,2.5,100000
total time: 339.94 hours.
 --------- CPU info (if available) ----------

Apr 20, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 20, 2009

(53·10¹⁶³-71)/9 = 5(8)₁₆₂1_<164> = 3 · 23 · 2389 · 96513550638754153673_<20> · C139

C139 = P57 · P82

P57 = 377498624063625239463952264309281335010127635110927025061_<57>

P82 = 9805380550742964674231939389316251929069674579746840643746394494793350010716857197_<82>

Number: 58881_163
N=3701517666325701027779366640216236218837963742983531931726635303099814464739514466644120549856564034083324033280638783693272531866777214017
  ( 139 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=377498624063625239463952264309281335010127635110927025061
 r2=9805380550742964674231939389316251929069674579746840643746394494793350010716857197
Version: 
Total time: 34.87 hours.
Scaled time: 83.23 units (timescale=2.387).
Factorization parameters were as follows:
n: 3701517666325701027779366640216236218837963742983531931726635303099814464739514466644120549856564034083324033280638783693272531866777214017
m: 1000000000000000000000000000000000
deg: 5
c5: 53
c0: -7100
skew: 2.66
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2400000, 5300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 10183017
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 870654 x 870902
Total sieving time: 31.70 hours.
Total relation processing time: 1.43 hours.
Matrix solve time: 1.63 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000
total time: 34.87 hours.
 --------- CPU info (if available) ----------

Apr 20, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 20, 2009

(52·10¹⁸³+11)/9 = 5(7)₁₈₂9_<184> = 199 · 229 · 1381 · 27093641 · 3271989401_<10> · 75894316021_<11> · 13201833342001_<14> · 25458040823627_<14> · C122

C122 = P51 · P71

P51 = 760709516823435322284803971154506765518059289320909_<51>

P71 = 53371819833679274984631391612038926591773108484753524753906129523475223_<71>

Number: 57779_183
N=40600451277665603438462039829671810932492997712468478849840455596499272861676146916196939261839959572308339955745357337707
  ( 122 digits)
Divisors found:
 r1=760709516823435322284803971154506765518059289320909 (pp51)
 r2=53371819833679274984631391612038926591773108484753524753906129523475223 (pp71)
Version: Msieve-1.39
Total time: 51.53 hours.
Scaled time: 132.99 units (timescale=2.581).
Factorization parameters were as follows:
# Murphy_E = 2.262445e-10, selected by Jeff Gilchrist
n: 40600451277665603438462039829671810932492997712468478849840455596499272861676146916196939261839959572308339955745357337707
Y0: -293254863654452879987050
Y1: 12192311360713
c0: -63029949335627363746734079251
c1: -30365307533505781597878895
c2: -1310763885392580973715
c3: -1061241013495825
c4: -1142314074
c5: 18720
skew: 203548.67
type: gnfs
rlim: 5800000
alim: 5800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 5800000/5800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2900000, 5300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 818639 x 818887
Total sieving time: 51.53 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5800000,5800000,27,27,52,52,2.5,2.5,60000
total time: 51.53 hours.
 --------- CPU info (if available) ----------

(17·10¹⁸⁰-11)/3 = 5(6)₁₇₉3_<181> = 4423 · C178

C178 = P42 · P136

P42 = 175738775151637385522300574841309392108541_<42>

P136 = 7290261927712186063891569599218901948236195147537934711419522834797162143981560091333540946292921842334124888216342937023769847028282741_<136>

Number: 56663_180
N=1281181701710754389931419097143718441480141683623483306956063003994272364157057803903836008742181023438088778355565604039490541864496194136709623935488733137387896601100308990881
  ( 178 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=175738775151637385522300574841309392108541 (pp42)
 r2=7290261927712186063891569599218901948236195147537934711419522834797162143981560091333540946292921842334124888216342937023769847028282741 (pp136)
Version: Msieve-1.39
Total time: 131.06 hours.
Scaled time: 227.92 units (timescale=1.739).
Factorization parameters were as follows:
n: 1281181701710754389931419097143718441480141683623483306956063003994272364157057803903836008742181023438088778355565604039490541864496194136709623935488733137387896601100308990881
m: 1000000000000000000000000000000000000
deg: 5
c5: 17
c0: -11
skew: 0.92
type: snfs
lss: 1
rlim: 7300000
alim: 7300000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7300000/7300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3650000, 5850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1378758 x 1379006
Total sieving time: 131.06 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7300000,7300000,28,28,53,53,2.5,2.5,100000
total time: 131.06 hours.
 --------- CPU info (if available) ----------

Apr 20, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Apr 20, 2009

(13·10¹⁶⁷+17)/3 = 4(3)₁₆₆9_<168> = 263 · 341569 · 7993784054790885255053_<22> · C138

C138 = P49 · P90

P49 = 1846311335649698654729517594024921557409680683367_<49>

P90 = 326836501228653793160065539312213663723576161842178591891017245168156703068080309956568087_<90>

Number: n
N=603441937122550160266933168238968012391700013260122407056599572853112687366988676069682707100660537151260148591255804012395446972223908929
  ( 138 digits)
SNFS difficulty: 169 digits.
Divisors found:

Mon Apr 20 10:46:06 2009  prp49 factor: 1846311335649698654729517594024921557409680683367
Mon Apr 20 10:46:06 2009  prp90 factor: 326836501228653793160065539312213663723576161842178591891017245168156703068080309956568087
Mon Apr 20 10:46:06 2009  elapsed time 00:58:38 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 61.67 hours.
Scaled time: 164.72 units (timescale=2.671).
Factorization parameters were as follows:
name: KA_4_3_166_9
n: 603441937122550160266933168238968012391700013260122407056599572853112687366988676069682707100660537151260148591255804012395446972223908929
m: 2000000000000000000000000000000000
deg: 5
c5: 325
c0: 136
skew: 0.84
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved  special-q in [2300000, 6034741)
Primes: RFBsize:322441, AFBsize:321816, largePrimes:10466991 encountered
Relations: rels:11329164, finalFF:647785
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1597998 hash collisions in 12898935 relations
Msieve: matrix is 739632 x 739880 (193.8 MB)

Total sieving time: 61.26 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000
total time: 61.67 hours.
 --------- CPU info (if available) ----------

Apr 20, 2009

By Markus Tervooren / Msieve, ggnfs, factMsieve.pl / Apr 20, 2009

(53·10¹⁸³-71)/9 = 5(8)₁₈₂1_<184> = 73 · 113 · 5779 · 80273 · 543483353732909_<15> · 1633503274622224469_<19> · 9329922208436263697241721_<25> · C114

C114 = P43 · P72

P43 = 1099460710064905094872964317328985126416851_<43>

P72 = 168984112509748557056357145099368984533273143568828753891708684224898777_<72>

Sun Apr 19 18:52:26 2009
random seeds: 83640b58 38b2f3fd
factoring 185791392329655960317126843193149532656075039568978618086291692551310739540908266190324079981475502216424182091227 (114 digits)
searching for 15-digit factors
commencing number field sieve (114-digit input)
R0: -5971029592928472269554
R1:  2129960935729
A0:  862370790294329460331503539
A1: -10194782863141842356898
A2:  1238072463545608887
A3: -92182453340548
A4: -5047177812
A5:  24480
skew 39869.06, size 7.804671e-11, alpha -6.508276, combined = 6.655291e-10

commencing relation filtering
commencing duplicate removal, pass 1
error -5 reading relation 5820643
error -5 reading relation 7796563
found 689413 hash collisions in 7929051 relations
added 509 free relations
commencing duplicate removal, pass 2
found 775167 duplicates and 7154393 unique relations
memory use: 48.6 MB
reading rational ideals above 2686976
reading algebraic ideals above 2686976
commencing singleton removal, pass 1
relations with 0 large ideals: 73324
relations with 1 large ideals: 655600
relations with 2 large ideals: 2115377
relations with 3 large ideals: 2828898
relations with 4 large ideals: 1334809
relations with 5 large ideals: 88476
relations with 6 large ideals: 57908
relations with 7+ large ideals: 1
7154393 relations and about 7393740 large ideals
commencing singleton removal, pass 2
found 3488166 singletons
current dataset: 3666227 relations and about 3152132 large ideals
commencing singleton removal, pass 3
found 720586 singletons
current dataset: 2945641 relations and about 2375343 large ideals
commencing singleton removal, pass 4
found 217203 singletons
current dataset: 2728438 relations and about 2151780 large ideals
commencing singleton removal, final pass
memory use: 46.1 MB
commencing in-memory singleton removal
begin with 2728438 relations and 2260018 unique ideals
reduce to 2313233 relations and 1835471 ideals in 16 passes
max relations containing the same ideal: 65
reading rational ideals above 720000
reading algebraic ideals above 720000
commencing singleton removal, final pass
keeping 2011906 ideals with weight <= 20, new excess is 218763
memory use: 65.5 MB
commencing in-memory singleton removal
begin with 2313746 relations and 2011906 unique ideals
reduce to 2311378 relations and 2007004 ideals in 9 passes
max relations containing the same ideal: 20
removing 254221 relations and 228917 ideals in 25304 cliques
commencing in-memory singleton removal
begin with 2057157 relations and 2007004 unique ideals
reduce to 2037641 relations and 1758296 ideals in 8 passes
max relations containing the same ideal: 20
removing 188091 relations and 162787 ideals in 25304 cliques
commencing in-memory singleton removal
begin with 1849550 relations and 1758296 unique ideals
reduce to 1836735 relations and 1582524 ideals in 8 passes
max relations containing the same ideal: 20
relations with 0 large ideals: 18963
relations with 1 large ideals: 140280
relations with 2 large ideals: 422112
relations with 3 large ideals: 621928
relations with 4 large ideals: 452573
relations with 5 large ideals: 152546
relations with 6 large ideals: 26344
relations with 7+ large ideals: 1989
commencing 2-way merge
reduce to 1057712 relation sets and 803500 unique ideals
commencing full merge
memory use: 71.5 MB
found 498479 cycles, need 465700
weight of 465700 cycles is about 32909516 (70.67/cycle)
distribution of cycle lengths:
1 relations: 51136
2 relations: 49656
3 relations: 50299
4 relations: 45791
5 relations: 42157
6 relations: 37795
7 relations: 33099
8 relations: 28795
9 relations: 25932
10+ relations: 101040
heaviest cycle: 18 relations
commencing cycle optimization
start with 2870886 relations
pruned 70362 relations
memory use: 96.4 MB
distribution of cycle lengths:
1 relations: 51136
2 relations: 50814
3 relations: 52098
4 relations: 47102
5 relations: 43351
6 relations: 38370
7 relations: 33575
8 relations: 29072
9 relations: 25739
10+ relations: 94443
heaviest cycle: 18 relations
RelProcTime: 275

commencing linear algebra
read 465700 cycles
cycles contain 1621811 unique relations
read 1621811 relations
using 20 quadratic characters above 134217404
building initial matrix
memory use: 198.4 MB
read 465700 cycles
matrix is 465414 x 465700 (140.0 MB) with weight 43993893 (94.47/col)
sparse part has weight 31572525 (67.80/col)
filtering completed in 3 passes
matrix is 460957 x 461157 (139.2 MB) with weight 43699323 (94.76/col)
sparse part has weight 31410540 (68.11/col)
read 461157 cycles
matrix is 460957 x 461157 (139.2 MB) with weight 43699323 (94.76/col)
sparse part has weight 31410540 (68.11/col)
saving the first 48 matrix rows for later
matrix is 460909 x 461157 (133.7 MB) with weight 34683440 (75.21/col)
sparse part has weight 30448887 (66.03/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (4 threads)
memory use: 134.9 MB
linear algebra completed 459370 of 461157 dimensions (99.6%, ETA 0h 0m)
lanczos halted after 7290 iterations (dim = 460906)
recovered 27 nontrivial dependencies
BLanczosTime: 1632

commencing square root phase
reading relations for dependency 1
read 230605 cycles
cycles contain 985785 unique relations
read 985785 relations
multiplying 807772 relations
multiply complete, coefficients have about 36.24 million bits
initial square root is modulo 159773
sqrtTime: 209
prp43 factor: 1099460710064905094872964317328985126416851
prp72 factor: 168984112509748557056357145099368984533273143568828753891708684224898777
elapsed time 00:32:31

Total Sieving time: 08:11:12

Apr 19, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Apr 19, 2009

(53·10¹⁴⁸-71)/9 = 5(8)₁₄₇1_<149> = 3 · 19 · 2381 · 5711 · 13834209197_<11> · C130

C130 = P41 · P89

P41 = 82385359894943408004943162699533169281913_<41>

P89 = 66662648941747010745791795419173523195324651729972252459647715337503778584049915638822583_<89>

Number: 58881_148
N=5492026324616095798033102395215615366695629783537974299978961263104321958528283500871403176146355042788370590000930782242917841279
  ( 130 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=82385359894943408004943162699533169281913
 r2=66662648941747010745791795419173523195324651729972252459647715337503778584049915638822583
Version: 
Total time: 9.99 hours.
Scaled time: 23.83 units (timescale=2.386).
Factorization parameters were as follows:
n: 5492026324616095798033102395215615366695629783537974299978961263104321958528283500871403176146355042788370590000930782242917841279
m: 1000000000000000000000000000000
deg: 5
c5: 53
c0: -7100
skew: 2.66
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6910517
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 436261 x 436509
Total sieving time: 9.21 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.39 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000
total time: 9.99 hours.
 --------- CPU info (if available) ----------

2·10¹⁹⁹-1 = 1(9)₁₉₉_<200> = 19 · 17339562682791539_<17> · 7572092218037286911_<19> · C163

C163 = P35 · P129

P35 = 15088679290694653491630959079652649_<35>

P129 = 531338312951247025629014580036481987176765320031147478358915519016343794161299690194525950929141452320767635858987664888979395601_<129>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 8017193398980115789611498508984984667086036428422295572972632192194297168351927795512719154924815800899613373920817281990053320592884375557748210291511125038597049 (163 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1624952013
Step 1 took 5507ms
********** Factor found in step 1: 15088679290694653491630959079652649
Found probable prime factor of 35 digits: 15088679290694653491630959079652649
Probable prime cofactor 531338312951247025629014580036481987176765320031147478358915519016343794161299690194525950929141452320767635858987664888979395601 has 129 digits

Apr 19, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Apr 19, 2009

(53·10¹⁵⁰-71)/9 = 5(8)₁₄₉1_<151> = 248747801 · 11462866529_<11> · C133

C133 = P61 · P73

P61 = 1006667291845049530667097296308918344203566521580425950778739_<61>

P73 = 2051610515873675499019042734361944316125748570732769002787444070163735651_<73>

Number: 58881_150
N=2065289201935377916361303754850202748421005648580776733236968519814503971051359873268351261206738974803314183796084499535780787124089
  ( 133 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=1006667291845049530667097296308918344203566521580425950778739 (pp61)
 r2=2051610515873675499019042734361944316125748570732769002787444070163735651 (pp73)
Version: Msieve-1.39
Total time: 13.07 hours.
Scaled time: 33.81 units (timescale=2.587).
Factorization parameters were as follows:
n: 2065289201935377916361303754850202748421005648580776733236968519814503971051359873268351261206738974803314183796084499535780787124089
m: 1000000000000000000000000000000
deg: 5
c5: 53
c0: -71
skew: 1.06
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 388006 x 388254
Total sieving time: 13.07 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 13.07 hours.
 --------- CPU info (if available) ----------

(37·10¹⁸⁶+17)/9 = 4(1)₁₈₅3_<187> = 3 · 5431 · 48847 · 118529 · 20791445904137_<14> · 6636802404266483_<16> · 8319806456856435884237_<22> · C122

C122 = P54 · P68

P54 = 936611623971359060206147696654335999846721752617956297_<54>

P68 = 40530251017074094158289636271902336998641296433950350474105003157453_<68>

Number: 41113_186
N=37961104225068594578714829076645712945921588378067673385352537851945754998378505684467544660269645616821258158008963831541
  ( 122 digits)
Divisors found:
 r1=936611623971359060206147696654335999846721752617956297 (pp54)
 r2=40530251017074094158289636271902336998641296433950350474105003157453 (pp68)
Version: Msieve-1.39
Total time: 49.82 hours.
Scaled time: 128.79 units (timescale=2.585).
Factorization parameters were as follows:
n: 37961104225068594578714829076645712945921588378067673385352537851945754998378505684467544660269645616821258158008963831541
Y0: -318842747860980647659276
Y1:  12477258589133
c0:  182009490340765499157220857085
c1:  2767449488789833424934041
c2: -35423532070220414210
c3: -462278175788232
c4:  2468121056
c5:  11520
skew: 131899.69
type: gnfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5020001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 678008 x 678256
Total sieving time: 49.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 49.82 hours.
 --------- CPU info (if available) ----------

Apr 19, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 19, 2009

(53·10¹⁵⁹-71)/9 = 5(8)₁₅₈1_<160> = 73 · 5966567237_<10> · 4981932222649_<13> · 26273193042133_<14> · 2062452635612297_<16> · C107

C107 = P52 · P55

P52 = 6078143242188653953677512610851837554339876404942979_<52>

P55 = 8239870283677649983233243756347853355656983261837612011_<55>

Number: n
N=50083111881246415258836189923446650619873710853182232529963769466745141613279822608636885515510257980520769
  ( 107 digits)
Divisors found:
 r1=6078143242188653953677512610851837554339876404942979 (pp52)
 r2=8239870283677649983233243756347853355656983261837612011 (pp55)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 8.87 hours.
Scaled time: 23.49 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_8_158_1
n: 50083111881246415258836189923446650619873710853182232529963769466745141613279822608636885515510257980520769
Y0: -476444653022084686012
Y1:  101590671413
c0: -176302300640800173013419063
c1:  18648490637306616368999
c2:  138703903042426525
c3: -19244747603213
c4: -25299728
c5:  2040
skew: 40590.29
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1250000, 2200001)
Primes: RFBsize:183072, AFBsize:182873, largePrimes:15737194 encountered
Relations: rels:14081049, finalFF:507587
Max relations in full relation-set: 28
Initial matrix: 366022 x 507587 with sparse part having weight 47260200.
Pruned matrix : 271239 x 273133 with weight 27017065.
Total sieving time: 7.88 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 0.30 hours.
Total square root time: 0.18 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000
total time: 8.87 hours.
 --------- CPU info (if available) ----------

2·10¹⁹³-1 = 1(9)₁₉₃_<194> = 61 · 3011 · 3019 · 2630399 · 1921011481_<10> · 5467489597378404813936108409_<28> · 394666621455911984281003929471901_<33> · C109

C109 = P50 · P60

P50 = 27527725817981321521808835728186950658541825851539_<50>

P60 = 120167217091555354429467632255431770850693114035283138229779_<60>

Number: n
N=3307930204406174659160459281208577919156483154925588805331903346568937950394323661593005058106900251722779881
  ( 109 digits)
Divisors found:
 r1=27527725817981321521808835728186950658541825851539 (pp50)
 r2=120167217091555354429467632255431770850693114035283138229779 (pp60)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 11.32 hours.
Scaled time: 30.11 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_1_9_193
n: 3307930204406174659160459281208577919156483154925588805331903346568937950394323661593005058106900251722779881
Y0: -839776940653718696932
Y1:  114057450119
c0: -1649652311583314793830770533
c1:  216144923746544112026007
c2: -3923772748444895801
c3: -94689262172047
c4:  1534734054
c5:  7920
skew: 54002.35
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1600000, 2700001)
Primes: RFBsize:230209, AFBsize:230226, largePrimes:16506913 encountered
Relations: rels:14758898, finalFF:602642
Max relations in full relation-set: 28
Initial matrix: 460518 x 602642 with sparse part having weight 53211012.
Pruned matrix : 348381 x 350747 with weight 29897839.
Total sieving time: 9.85 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 0.54 hours.
Total square root time: 0.21 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000
total time: 11.32 hours.
 --------- CPU info (if available) ----------

(53·10¹⁴⁹-71)/9 = 5(8)₁₄₈1_<150> = 65563 · 1815347719_<10> · 321073852383149036798633_<24> · C113

C113 = P57 · P57

P57 = 106800209355250487145003373704765155010615558207705547567_<57>

P57 = 144290479211011391034524051927928805222760474712705729043_<57>

Number: n
N=15410253387705434693965673668065684984653498882240991066120364949759038956067606885783711480075651457014249888381
  ( 113 digits)
SNFS difficulty: 151 digits.
Divisors found:

Sun Apr 19 10:39:07 2009  prp57 factor: 106800209355250487145003373704765155010615558207705547567
Sun Apr 19 10:39:07 2009  prp57 factor: 144290479211011391034524051927928805222760474712705729043
Sun Apr 19 10:39:07 2009  elapsed time 00:25:17 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 15.47 hours.
Scaled time: 40.98 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_8_148_1
n: 15410253387705434693965673668065684984653498882240991066120364949759038956067606885783711480075651457014249888381
m: 1000000000000000000000000000000
deg: 5
c5: 53
c0: -710
skew: 1.68
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1200000, 2207143)
Primes: RFBsize:176302, AFBsize:176159, largePrimes:11666723 encountered
Relations: rels:11027980, finalFF:373357
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1019499 hash collisions in 11953025 relations
Msieve: matrix is 406774 x 407022 (108.2 MB)

Total sieving time: 15.20 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,56,56,2.4,2.4,100000
total time: 15.47 hours.
 --------- CPU info (if available) ----------

(53·10¹⁵⁶-71)/9 = 5(8)₁₅₅1_<157> = 21893 · 414036871 · 5097582013_<10> · C135

C135 = P33 · P102

P33 = 458737405579699161469808051148151_<33>

P102 = 277818197649398752305269669956120329087419350051266481378494174971171347683342879820983467197939102529_<102>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 127445599212513259661167031097844600127945207600601649714644003218328810348288025994342263956141841235757118525999000793680536957773879 (135 digits)
Using B1=2072000, B2=2854078510, polynomial Dickson(6), sigma=272239408
Step 1 took 25849ms
Step 2 took 9266ms
********** Factor found in step 2: 458737405579699161469808051148151
Found probable prime factor of 33 digits: 458737405579699161469808051148151
Probable prime cofactor 277818197649398752305269669956120329087419350051266481378494174971171347683342879820983467197939102529 has 102 digits

Apr 19, 2009 (2nd)

By Markus Tervooren / Lattice siever (64bit/asm), msieve 1.40, factMsieve.pl / Apr 19, 2009

(53·10¹⁵²-71)/9 = 5(8)₁₅₁1_<153> = 7 · 47 · 132859 · C146

C146 = P39 · P107

P39 = 358120980514725128858958545331653679533_<39>

P107 = 37619820414914044458839692273435650922151956137997093517622555060481625863874724410536072161511382815906487_<107>

N=13472446973776891128080751122167770404510906719855480603757492405880322489403977649474835501358900905981133251349172146984833702939748174393830571
  ( 146 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=358120980514725128858958545331653679533 (pp39)
 r2=37619820414914044458839692273435650922151956137997093517622555060481625863874724410536072161511382815906487 (pp107)
Version: Msieve-1.39
Total time: 11.66 hours.
Scaled time: 26.15 units (timescale=2.243).
Factorization parameters were as follows:
n: 13472446973776891128080751122167770404510906719855480603757492405880322489403977649474835501358900905981133251349172146984833702939748174393830571
m: 2000000000000000000000000000000
deg: 5
c5: 1325
c0: -568
skew: 0.84
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4

Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 479562 x 479810
Total sieving time: 10.80 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.73 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 11.66 hours.
 --------- CPU info (if available) ----------
[    0.144009] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.238418] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.335353] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.432195] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
[    0.004000] Memory: 8198000k/10485760k available (2226k kernel code, 189836k reserved, 1082k data, 392k init)
[    0.083969] Calibrating delay using timer specific routine.. 5804.04 BogoMIPS (lpj=11608082)
[    0.160010] Calibrating delay using timer specific routine.. 8120.06 BogoMIPS (lpj=16240129)
[    0.252015] Calibrating delay using timer specific routine.. 5800.09 BogoMIPS (lpj=11600186)
[    0.351781] Calibrating delay using timer specific routine.. 5800.09 BogoMIPS (lpj=11600195)
[    0.439785] Total of 4 processors activated (25524.29 BogoMIPS).

Apr 19, 2009

By Serge Batalov / GMP-ECM 6.2.2 / Apr 19, 2009

(53·10¹⁹⁵-71)/9 = 5(8)₁₉₄1_<196> = 1319 · 33857 · C189

C189 = P34 · P155

P34 = 6522546262176896794087564739115713_<34>

P155 = 20217289175101472176634624589120256959714664779605055451404756357758626997987860981678743694952263411707665143615277807384449498161455207993683372278411239_<155>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3935644505
Step 1 took 11044ms
Step 2 took 11361ms
********** Factor found in step 2: 6522546262176896794087564739115713
Found probable prime factor of 34 digits: 6522546262176896794087564739115713
Probable prime cofactor  has 155 digits

(53·10²⁰¹-71)/9 = 5(8)₂₀₀1_<202> = 845726166293_<12> · C190

C190 = P32 · C159

P32 = 26614080411265630091650323405683_<32>

C159 = [261632763104934685678706508770395191162055898507905747696347081652713863042849725984808309953127668896691497252042853273203709573229850203050723384365743227999_<159>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1279820415
Step 1 took 11153ms
Step 2 took 11248ms
********** Factor found in step 2: 26614080411265630091650323405683
Found probable prime factor of 32 digits: 26614080411265630091650323405683
Composite cofactor  has 159 digits

(53·10¹⁶²-71)/9 = 5(8)₁₆₁1_<163> = 70679701 · 44026722517_<11> · C145

C145 = P34 · C112

P34 = 1236279080219216121922252206884753_<34>

C112 = [1530755327949768346559116010704472935748277600679650175511082917507123042329452736442582425054160912093674875881_<112>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3167953602
Step 1 took 8465ms
Step 2 took 8816ms
********** Factor found in step 2: 1236279080219216121922252206884753
Found probable prime factor of 34 digits: 1236279080219216121922252206884753
Composite cofactor has 112 digits

(53·10¹⁶⁹-71)/9 = 5(8)₁₆₈1_<170> = 3² · 55619 · C165

C165 = P33 · C132

P33 = 268408781245025917238865818507107_<33>

C132 = [438299479011775469486372343095698175154784520161586980563186912608598242291187115880197057529976739290204068936254644363207769097473_<132>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=504785334
Step 1 took 9505ms
Step 2 took 9856ms
********** Factor found in step 2: 268408781245025917238865818507107
Found probable prime factor of 33 digits: 268408781245025917238865818507107
Composite cofactor has 132 digits

(53·10¹⁷⁵-71)/9 = 5(8)₁₇₄1_<176> = 3 · 73 · 1024183 · C168

C168 = P40 · P129

P40 = 2158548290899707807210634246105330347041_<40>

P129 = 121632578456805687673146582029186126326283394657268436697370779282164748561294068326344587870149269097387136954490861643986922133_<129>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2926320089
Step 1 took 9548ms
Step 2 took 4621ms
********** Factor found in step 2: 2158548290899707807210634246105330347041
Found probable prime factor of 40 digits: 2158548290899707807210634246105330347041
Probable prime cofactor has 129 digits

Apr 18, 2009 (8th)

By Ignacio Santos / GGNFS, Msieve / Apr 17, 2009

(53·10¹⁰⁷-71)/9 = 5(8)₁₀₆1_<108> = 97 · 269 · 461 · C101

C101 = P40 · P62

P40 = 1384979565662153197387040503504412975669_<40>

P62 = 35348016964029802824250185131245245092377627875980924329954213_<62>

Number: 58881_107
N=48956281181860419416589475081239022881768631931593997948842662890271506639806479700042463569853043497
  ( 101 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=1384979565662153197387040503504412975669 (pp40)
 r2=35348016964029802824250185131245245092377627875980924329954213 (pp62)
Version: Msieve-1.39
Total time: 0.76 hours.
Scaled time: 0.84 units (timescale=1.095).
Factorization parameters were as follows:
n: 48956281181860419416589475081239022881768631931593997948842662890271506639806479700042463569853043497
m: 2000000000000000000000
deg: 5
c5: 1325
c0: -568
skew: 0.84
type: snfs
lss: 1
rlim: 470000
alim: 470000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2Factor base limits: 470000/470000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [235000, 385001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 52946 x 53184
Total sieving time: 0.72 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,109,5,0,0,0,0,0,0,0,0,470000,470000,25,25,44,44,2.2,2.2,50000
total time: 0.76 hours.
 --------- CPU info (if available) ----------

(53·10¹¹¹-71)/9 = 5(8)₁₁₀1_<112> = 73 · 73751 · 106363 · C101

C101 = P50 · P51

P50 = 14493900658606329765271121197487209608426062754421_<50>

P51 = 709523408350170592136127179652066112526467686866489_<51>

Number: 58881_111
N=10283761795583145401413388163687678748300979703369701831666106090610374480536842407958300829821497869
  ( 101 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=14493900658606329765271121197487209608426062754421 (pp50)
 r2=709523408350170592136127179652066112526467686866489 (pp51)
Version: Msieve-1.39
Total time: 0.96 hours.
Scaled time: 1.15 units (timescale=1.194).
Factorization parameters were as follows:
n: 10283761795583145401413388163687678748300979703369701831666106090610374480536842407958300829821497869
m: 10000000000000000000000
deg: 5
c5: 530
c0: -71
skew: 0.67
type: snfs
lss: 1
rlim: 530000
alim: 530000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 530000/530000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [265000, 465001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 67516 x 67760
Total sieving time: 0.93 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000
total time: 0.96 hours.
 --------- CPU info (if available) ----------

(53·10¹¹⁵-71)/9 = 5(8)₁₁₄1_<116> = 3² · 223 · 5273 · C109

C109 = P51 · P59

P51 = 258714152872988458408233821774037897987784234433911_<51>

P59 = 21508396256747219765998592929869798919896339768469661174761_<59>

Number: 58881_115
N=5564526517220912931129146686473021353849511621980841461190488031968603807486322892528236218644273668075720271
  ( 109 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=258714152872988458408233821774037897987784234433911 (pp51)
 r2=21508396256747219765998592929869798919896339768469661174761 (pp59)
Version: Msieve-1.39
Total time: 1.34 hours.
Scaled time: 1.60 units (timescale=1.188).
Factorization parameters were as follows:
n: 5564526517220912931129146686473021353849511621980841461190488031968603807486322892528236218644273668075720271
m: 100000000000000000000000
deg: 5
c5: 53
c0: -71
skew: 1.06
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 510001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 59467 x 59698
Total sieving time: 1.30 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 1.34 hours.
 --------- CPU info (if available) ----------

(53·10¹²⁰-71)/9 = 5(8)₁₁₉1_<121> = 331 · 43613 · 3706627 · C108

C108 = P50 · P58

P50 = 26786575570913598534091002158361449653541557924127_<50>

P58 = 4108594908349800945919523446359933990845020074836239443163_<58>

Number: 58881_120
N=110055188002782773317772931442183797479669644135257477753433827406525740778348919818614135594749472682893701
  ( 108 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=26786575570913598534091002158361449653541557924127 (pp50)
 r2=4108594908349800945919523446359933990845020074836239443163 (pp58)
Version: Msieve-1.39
Total time: 1.36 hours.
Scaled time: 1.63 units (timescale=1.196).
Factorization parameters were as follows:
n: 110055188002782773317772931442183797479669644135257477753433827406525740778348919818614135594749472682893701
m: 1000000000000000000000000
deg: 5
c5: 53
c0: -71
skew: 1.06
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 625001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 80948 x 81174
Total sieving time: 1.32 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 1.36 hours.
 --------- CPU info (if available) ----------

(53·10¹¹⁹-71)/9 = 5(8)₁₁₈1_<120> = 23 · 73 · 3137 · C114

C114 = P36 · P78

P36 = 247302525192062034320407341931514849_<36>

P78 = 452105295957014023819909058843366067525219824276276508453661905503232282583903_<78>

Number: 58881_119
N=111806781342874122419607601654461901702135891354354991213991070266617193220703400932346201808666658354992732875647
  ( 114 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=247302525192062034320407341931514849 (pp36)
 r2=452105295957014023819909058843366067525219824276276508453661905503232282583903 (pp78)
Version: Msieve-1.39
Total time: 1.79 hours.
Scaled time: 2.10 units (timescale=1.175).
Factorization parameters were as follows:
n: 111806781342874122419607601654461901702135891354354991213991070266617193220703400932346201808666658354992732875647
m: 1000000000000000000000000
deg: 5
c5: 53
c0: -710
skew: 1.68
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 725001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 91225 x 91452
Total sieving time: 1.74 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 1.79 hours.
 --------- CPU info (if available) ----------

(53·10¹²⁴-71)/9 = 5(8)₁₂₃1_<125> = 3² · 103 · 10391 · 313517 · 1925993 · C107

C107 = P42 · P65

P42 = 645449533165367934958837365343863903897071_<42>

P65 = 15686216002025477513604797878670354464346679288472277430682098283_<65>

Number: 58881_124
N=10124660795638468662831440992732320261481090609423641679678285332988429044938130752945016949841399137829093
  ( 107 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=645449533165367934958837365343863903897071 (pp42)
 r2=15686216002025477513604797878670354464346679288472277430682098283 (pp65)
Version: Msieve-1.39
Total time: 2.33 hours.
Scaled time: 2.75 units (timescale=1.178).
Factorization parameters were as follows:
n: 10124660795638468662831440992732320261481090609423641679678285332988429044938130752945016949841399137829093
m: 10000000000000000000000000
deg: 5
c5: 53
c0: -710
skew: 1.68
type: snfs
lss: 1
rlim: 910000
alim: 910000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 910000/910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [455000, 855001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 135894 x 136122
Total sieving time: 2.21 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000
total time: 2.33 hours.
 --------- CPU info (if available) ----------

(53·10¹²⁸-71)/9 = 5(8)₁₂₇1_<129> = 7 · 167 · C126

C126 = P53 · P74

P53 = 24969206764244227895770332415233048905828749459976209_<53>

P74 = 20175026012093362314000182915103646299439827080940433333601709650431305361_<74>

Number: 58881_128
N=503754395969964832240281342077749263378005892975952856192377150460982796312137629502898963976808288185533694515730443874156449
  ( 126 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=24969206764244227895770332415233048905828749459976209 (pp53)
 r2=20175026012093362314000182915103646299439827080940433333601709650431305361 (pp74)
Version: Msieve-1.39
Total time: 3.22 hours.
Scaled time: 3.79 units (timescale=1.176).
Factorization parameters were as follows:
n: 503754395969964832240281342077749263378005892975952856192377150460982796312137629502898963976808288185533694515730443874156449
m: 50000000000000000000000000
deg: 5
c5: 424
c0: -1775
skew: 1.33
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 1085001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 182936 x 183184
Total sieving time: 3.05 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 3.22 hours.
 --------- CPU info (if available) ----------

(53·10¹²⁹-71)/9 = 5(8)₁₂₈1_<130> = 17 · 21589 · C125

C125 = P56 · P69

P56 = 25322624759976549455734598285790216107772481213399224703_<56>

P69 = 633640886576731402778133093433220256786188375338961718270777059934179_<69>

Number: 58881_129
N=16045450403361431036200049831719554590406576576003817000729916621179328494873175851778789549386231247636701939410562810823837
  ( 125 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=25322624759976549455734598285790216107772481213399224703 (pp56)
 r2=633640886576731402778133093433220256786188375338961718270777059934179 (pp69)
Version: Msieve-1.39
Total time: 3.29 hours.
Scaled time: 3.90 units (timescale=1.183).
Factorization parameters were as follows:
n: 16045450403361431036200049831719554590406576576003817000729916621179328494873175851778789549386231247636701939410562810823837
m: 100000000000000000000000000
deg: 5
c5: 53
c0: -710
skew: 1.68
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 178470 x 178705
Total sieving time: 3.15 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 3.29 hours.
 --------- CPU info (if available) ----------

(28·10¹⁷⁶+71)/9 = 3(1)₁₇₅9_<177> = 11 · 4177 · 334891 · 78854016401726471_<17> · 20922377657995813028793412603_<29> · C122

C122 = P44 · P78

P44 = 17523944894902605507691685863551313076801221_<44>

P78 = 699339647751129622336695924473895312705541651662527802496178396153595100045639_<78>

Number: 31119_176
N=12255189450011394345886624005277270545972982902709668725171403353927774914407355488728521798333587784910725597129230925219
  ( 122 digits)
Divisors found:
 r1=17523944894902605507691685863551313076801221 (pp44)
 r2=699339647751129622336695924473895312705541651662527802496178396153595100045639 (pp78)
Version: Msieve-1.39
Total time: 42.01 hours.
Scaled time: 73.06 units (timescale=1.739).
Factorization parameters were as follows:
n: 12255189450011394345886624005277270545972982902709668725171403353927774914407355488728521798333587784910725597129230925219
Y0: -244870820893368151508838
Y1:  12427739286793
c0: -163742196505265923710132207365
c1:  65321964375096181901087226
c2:  197404084512766770793
c3: -2347860226599054
c4: -2773401392
c5:  13920
skew: 246057.74
type: gnfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [3000000, 5220001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 704331 x 704579
Total sieving time: 42.01 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6000000,6000000,27,27,50,50,2.4,2.4,60000
total time: 42.01 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶⁷-43)/9 = 5(7)₁₆₆3_<168> = 3⁴ · 7 · 61 · 129913170341_<12> · 867242538361868937630981343_<27> · C126

C126 = P44 · P82

P44 = 49637779755040036765627367016478664200260103_<44>

P82 = 2987045509611890878333062958493333869323375170995634475635740926374588918561839811_<82>

Number: 57773_167
N=148270307124396366588776691013993480723011390291670678142012858099810032240249803524315671307492094495902151881145156420360533
  ( 126 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=49637779755040036765627367016478664200260103 (pp44)
 r2=2987045509611890878333062958493333869323375170995634475635740926374588918561839811 (pp82)
Version: Msieve-1.39
Total time: 52.12 hours.
Scaled time: 134.21 units (timescale=2.575).
Factorization parameters were as follows:
n: 148270307124396366588776691013993480723011390291670678142012858099810032240249803524315671307492094495902151881145156420360533
m: 2000000000000000000000000000000000
deg: 5
c5: 325
c0: -86
skew: 0.77
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2300000, 4900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 877895 x 878143
Total sieving time: 52.12 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000
total time: 52.12 hours.
 --------- CPU info (if available) ----------

(53·10¹³⁵-71)/9 = 5(8)₁₃₄1_<136> = 73 · 17971 · C130

C130 = P39 · P42 · P50

P39 = 208950478073359106691735508553258069951_<39>

P42 = 238220374772566897555570835368515940408729_<42>

P50 = 90181194435531348598364513854322550480408866621333_<50>

Number: 58881_135
N=4488882689149023875520064585705347876974462576989631612642963502758164324782689377702804967279009552596450208508600910972159017907
  ( 130 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=208950478073359106691735508553258069951 (pp39)
 r2=238220374772566897555570835368515940408729 (pp42)
 r3=90181194435531348598364513854322550480408866621333 (pp50)
Version: Msieve-1.39
Total time: 3.61 hours.
Scaled time: 9.32 units (timescale=2.585).
Factorization parameters were as follows:
n: 4488882689149023875520064585705347876974462576989631612642963502758164324782689377702804967279009552596450208508600910972159017907
m: 1000000000000000000000000000
deg: 5
c5: 53
c0: -71
skew: 1.06
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1265001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 180652 x 180900
Total sieving time: 3.61 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 3.61 hours.
 --------- CPU info (if available) ----------

(53·10¹⁴²-71)/9 = 5(8)₁₄₁1_<143> = 3² · 1709 · 278909 · 76152539500821414403933627_<26> · C108

C108 = P53 · P55

P53 = 71133922634174006030717975784795514715709640159273987_<53>

P55 = 2534107945612965006523312677086987427729240908255143361_<55>

Number: 58881_142
N=180261038549878282546405625387619251986666046371548632232487890600553463920445113493554792990997936363050307
  ( 108 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=71133922634174006030717975784795514715709640159273987 (pp53)
 r2=2534107945612965006523312677086987427729240908255143361 (pp55)
Version: Msieve-1.39
Total time: 9.02 hours.
Scaled time: 23.19 units (timescale=2.570).
Factorization parameters were as follows:
n: 180261038549878282546405625387619251986666046371548632232487890600553463920445113493554792990997936363050307
m: 20000000000000000000000000000
deg: 5
c5: 1325
c0: -568
skew: 0.84
type: snfs
lss: 1
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [900000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 323665 x 323913
Total sieving time: 9.02 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,49,49,2.3,2.3,100000
total time: 9.02 hours.
 --------- CPU info (if available) ----------

(53·10¹⁵⁸-71)/9 = 5(8)₁₅₇1_<159> = 7 · 103² · 36843969518977_<14> · C141

C141 = P54 · P87

P54 = 590800533267749425396799989726967304158855580389298407_<54>

P87 = 364295308035138105843948238320786618697318570121178416315717666433432812884446432322033_<87>

Number: 58881_158
N=215225862254098635062373516145563229858180884948610690716839884723050559871095844778820344045193448097260622781286766391923370173940757901431
  ( 141 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=590800533267749425396799989726967304158855580389298407 (pp54)
 r2=364295308035138105843948238320786618697318570121178416315717666433432812884446432322033 (pp87)
Version: Msieve-1.39
Total time: 36.12 hours.
Scaled time: 62.82 units (timescale=1.739).
Factorization parameters were as follows:
n: 215225862254098635062373516145563229858180884948610690716839884723050559871095844778820344045193448097260622781286766391923370173940757901431
m: 50000000000000000000000000000000
deg: 5
c5: 424
c0: -1775
skew: 1.33
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 710549 x 710797
Total sieving time: 36.12 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 36.12 hours.
 --------- CPU info (if available) ----------

By Ignacio Santos / GGNFS, Msieve / Apr 18, 2009

(53·10¹⁴⁷-71)/9 = 5(8)₁₄₆1_<148> = 173 · 911 · 1864678338609841_<16> · C128

C128 = P40 · P88

P40 = 8841650303160994912744847210119857502267_<40>

P88 = 2266374213407869403317452567641879525824318358979772631723729317593675170965387268563441_<88>

Number: 58881_147
N=20038488251053949891160955364517975958712532523335809074228319663764962729976432022531272278261934548560037253969985567490820747
  ( 128 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=8841650303160994912744847210119857502267 (pp40)
 r2=2266374213407869403317452567641879525824318358979772631723729317593675170965387268563441 (pp88)
Version: Msieve-1.39
Total time: 13.69 hours.
Scaled time: 35.28 units (timescale=2.577).
Factorization parameters were as follows:
n: 20038488251053949891160955364517975958712532523335809074228319663764962729976432022531272278261934548560037253969985567490820747
m: 200000000000000000000000000000
deg: 5
c5: 1325
c0: -568
skew: 0.84
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 3300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 406122 x 406370
Total sieving time: 13.69 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000
total time: 13.69 hours.
 --------- CPU info (if available) ----------

(32·10¹⁹⁴+13)/9 = 3(5)₁₉₃7_<195> = 3 · 7 · 17 · 167 · 166186338707_<12> · 494623864127202459693037_<24> · 3118053696717644861370191005951739_<34> · C122

C122 = P44 · P79

P44 = 19474818079230790147783809942972607846336609_<44>

P79 = 1194800501768501725770690816539500998982141406904802206750689178224457211794067_<79>

Number: 35557_194
N=23268522412915237066157072508677930272386856866646539514759309590878493431200958246887248353476180538089263618054471098803
  ( 122 digits)
Divisors found:
 r1=19474818079230790147783809942972607846336609 (pp44)
 r2=1194800501768501725770690816539500998982141406904802206750689178224457211794067 (pp79)
Version: Msieve-1.39
Total time: 50.89 hours.
Scaled time: 131.26 units (timescale=2.579).
Factorization parameters were as follows:
n: 23268522412915237066157072508677930272386856866646539514759309590878493431200958246887248353476180538089263618054471098803
Y0: -279098707443920442464360
Y1:  10054681781741
c0:  794709234251163174045516183
c1: -1662989921838592892427253
c2:  9037051214934208389
c3: -32437449469927
c4: -6193801292
c5:  13740
skew: 95344.69
type: gnfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5080001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 686177 x 686425
Total sieving time: 50.89 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 50.89 hours.
 --------- CPU info (if available) ----------

(52·10¹⁷⁵+11)/9 = 5(7)₁₇₄9_<176> = 59 · C174

C174 = P84 · P91

P84 = 221396733866059271753457736994463053326306135043477879714218658472367433821816422859_<84>

P91 = 4423210550645817710188763098309667499105730033402825302895493919405103994634059074107437659_<91>

Number: 57779_175
N=979284369114877589453860640301318267419962335216572504708097928436911487758945386064030131826741996233521657250470809792843691148775894538606403013182674199623352165725047081
  ( 174 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=221396733866059271753457736994463053326306135043477879714218658472367433821816422859 (pp84)
 r2=4423210550645817710188763098309667499105730033402825302895493919405103994634059074107437659 (pp91)
Version: Msieve-1.39
Total time: 59.74 hours.
Scaled time: 103.90 units (timescale=1.739).
Factorization parameters were as follows:
n: 979284369114877589453860640301318267419962335216572504708097928436911487758945386064030131826741996233521657250470809792843691148775894538606403013182674199623352165725047081
m: 100000000000000000000000000000000000
deg: 5
c5: 52
c0: 11
skew: 0.73
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3100000, 6000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1140797 x 1141045
Total sieving time: 59.74 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,53,53,2.5,2.5,100000
total time: 59.74 hours.
 --------- CPU info (if available) ----------

Apr 18, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Apr 17, 2009

(47·10¹⁹⁶+61)/9 = 5(2)₁₉₅9_<197> = C197

C197 = P76 · P122

P76 = 1579229435921678256326591199705715594120801084508283699645866680988859851099_<76>

P122 = 33068166685826757029330791732171671095878658225580448280795059966475529175322301526715686040210443228306558116508701585871_<122>

Number: 52229_196
N=52222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
  ( 197 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=1579229435921678256326591199705715594120801084508283699645866680988859851099
 r2=33068166685826757029330791732171671095878658225580448280795059966475529175322301526715686040210443228306558116508701585871
Version: 
Total time: 419.87 hours.
Scaled time: 1003.49 units (timescale=2.390).
Factorization parameters were as follows:
n: 52222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
m: 1000000000000000000000000000000000000000
deg: 5
c5: 470
c0: 61
skew: 0.66
type: snfs
lss: 1
rlim: 18000000
alim: 18000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 18000000/18000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [9000000, 18400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 24409029
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2823593 x 2823841
Total sieving time: 384.51 hours.
Total relation processing time: 12.75 hours.
Matrix solve time: 21.79 hours.
Time per square root: 0.82 hours.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,18000000,18000000,28,28,55,55,2.5,2.5,100000
total time: 419.87 hours.
 --------- CPU info (if available) ----------

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Apr 18, 2009

2·10¹⁸⁹-1 = 1(9)₁₈₉_<190> = 31 · 5439829 · 2720009561_<10> · 13767101225803399878919_<23> · C150

C150 = P33 · C117

P33 = 317174697888724493139312350540581_<33>

C117 = [998554062131199145511682309200429404184445404728977563784886142161737708964524438853301713011987413991352186470480119_<117>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 316716082982021715964078119995152309103483041202058322413122073625672839431656295396252831115566430331967060364389847629059167242554614320568263209139 (150 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3783356541
Step 1 took 4615ms
Step 2 took 2683ms
********** Factor found in step 2: 317174697888724493139312350540581
Found probable prime factor of 33 digits: 317174697888724493139312350540581
Composite cofactor 998554062131199145511682309200429404184445404728977563784886142161737708964524438853301713011987413991352186470480119 has 117 digits

Apr 18, 2009 (6th)

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.41 / Apr 17, 2009

(53·10¹³⁹-71)/9 = 5(8)₁₃₈1_<140> = 3 · 751 · 2415546311873706757_<19> · C119

C119 = P35 · P37 · P48

P35 = 19628836388346054508128484997147281_<35>

P37 = 1950538446329560608415371227959497329_<37>

P48 = 282623148366498362008930795950925297690193155889_<48>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2883563787
Step 1 took 6925ms
********** Factor found in step 1: 1950538446329560608415371227959497329
Found probable prime factor of 37 digits: 1950538446329560608415371227959497329
Composite cofactor has 82 digits

Thu Apr 16 11:00:26 2009  Msieve v. 1.41
Thu Apr 16 11:00:26 2009  random seeds: 06ab07b0 44c37f3d
Thu Apr 16 11:00:26 2009  factoring 5547563538845248822936990017294757100627630247645492603497532000944928035525487809 (82 digits)
Thu Apr 16 11:00:26 2009  searching for 15-digit factors
Thu Apr 16 11:00:27 2009  commencing quadratic sieve (82-digit input)
Thu Apr 16 11:00:27 2009  using multiplier of 1
Thu Apr 16 11:00:27 2009  using 64kb Opteron sieve core
Thu Apr 16 11:00:27 2009  sieve interval: 6 blocks of size 65536
Thu Apr 16 11:00:27 2009  processing polynomials in batches of 17
Thu Apr 16 11:00:27 2009  using a sieve bound of 1348597 (51765 primes)
Thu Apr 16 11:00:27 2009  using large prime bound of 125419521 (26 bits)
Thu Apr 16 11:00:27 2009  using trial factoring cutoff of 27 bits
Thu Apr 16 11:00:27 2009  polynomial 'A' values have 10 factors
Thu Apr 16 11:13:18 2009  51987 relations (27028 full + 24959 combined from 270581 partial), need 51861
Thu Apr 16 11:13:18 2009  begin with 297609 relations
Thu Apr 16 11:13:18 2009  reduce to 73841 relations in 2 passes
Thu Apr 16 11:13:18 2009  attempting to read 73841 relations
Thu Apr 16 11:13:18 2009  recovered 73841 relations
Thu Apr 16 11:13:18 2009  recovered 64025 polynomials
Thu Apr 16 11:13:18 2009  attempting to build 51987 cycles
Thu Apr 16 11:13:18 2009  found 51987 cycles in 1 passes
Thu Apr 16 11:13:18 2009  distribution of cycle lengths:
Thu Apr 16 11:13:18 2009     length 1 : 27028
Thu Apr 16 11:13:18 2009     length 2 : 24959
Thu Apr 16 11:13:18 2009  largest cycle: 2 relations
Thu Apr 16 11:13:18 2009  matrix is 51765 x 51987 (7.6 MB) with weight 1583604 (30.46/col)
Thu Apr 16 11:13:18 2009  sparse part has weight 1583604 (30.46/col)
Thu Apr 16 11:13:19 2009  filtering completed in 3 passes
Thu Apr 16 11:13:19 2009  matrix is 36391 x 36453 (5.9 MB) with weight 1254865 (34.42/col)
Thu Apr 16 11:13:19 2009  sparse part has weight 1254865 (34.42/col)
Thu Apr 16 11:13:19 2009  saving the first 48 matrix rows for later
Thu Apr 16 11:13:19 2009  matrix is 36343 x 36453 (4.6 MB) with weight 1009631 (27.70/col)
Thu Apr 16 11:13:19 2009  sparse part has weight 832049 (22.83/col)
Thu Apr 16 11:13:19 2009  matrix includes 64 packed rows
Thu Apr 16 11:13:19 2009  using block size 14581 for processor cache size 6144 kB
Thu Apr 16 11:13:19 2009  commencing Lanczos iteration
Thu Apr 16 11:13:19 2009  memory use: 4.3 MB
Thu Apr 16 11:13:25 2009  lanczos halted after 576 iterations (dim = 36339)
Thu Apr 16 11:13:25 2009  recovered 15 nontrivial dependencies
Thu Apr 16 11:13:25 2009  prp35 factor: 19628836388346054508128484997147281
Thu Apr 16 11:13:25 2009  prp48 factor: 282623148366498362008930795950925297690193155889
Thu Apr 16 11:13:25 2009  elapsed time 00:12:59

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.41 / Apr 18, 2009

(53·10¹³⁸-71)/9 = 5(8)₁₃₇1_<139> = 29 · 647951 · 358891536869_<12> · 207918343886153_<15> · 6192700806701161_<16> · C90

C90 = P42 · P49

P42 = 343285591799040843138102857725593336454477_<42>

P49 = 1975611290293895905492495874305707347552169153691_<49>

Fri Apr 17 16:08:56 2009  Msieve v. 1.41
Fri Apr 17 16:08:56 2009  random seeds: c0d9302b 3e47c1e3
Fri Apr 17 16:08:56 2009  factoring 678198890953406730719061459299602476927341145140434803371927643801924003643416583638024607 (90 digits)
Fri Apr 17 16:08:56 2009  searching for 15-digit factors
Fri Apr 17 16:08:57 2009  commencing quadratic sieve (90-digit input)
Fri Apr 17 16:08:57 2009  using multiplier of 15
Fri Apr 17 16:08:57 2009  using 64kb Opteron sieve core
Fri Apr 17 16:08:57 2009  sieve interval: 18 blocks of size 65536
Fri Apr 17 16:08:57 2009  processing polynomials in batches of 6
Fri Apr 17 16:08:57 2009  using a sieve bound of 1618739 (61134 primes)
Fri Apr 17 16:08:57 2009  using large prime bound of 135974076 (27 bits)
Fri Apr 17 16:08:57 2009  using double large prime bound of 436737990159996 (42-49 bits)
Fri Apr 17 16:08:57 2009  using trial factoring cutoff of 49 bits
Fri Apr 17 16:08:57 2009  polynomial 'A' values have 12 factors
Fri Apr 17 17:01:51 2009  61570 relations (16202 full + 45368 combined from 667867 partial), need 61230
Fri Apr 17 17:01:51 2009  begin with 684069 relations
Fri Apr 17 17:01:51 2009  reduce to 150644 relations in 10 passes
Fri Apr 17 17:01:51 2009  attempting to read 150644 relations
Fri Apr 17 17:01:52 2009  recovered 150644 relations
Fri Apr 17 17:01:52 2009  recovered 130162 polynomials
Fri Apr 17 17:01:52 2009  attempting to build 61570 cycles
Fri Apr 17 17:01:52 2009  found 61570 cycles in 5 passes
Fri Apr 17 17:01:52 2009  distribution of cycle lengths:
Fri Apr 17 17:01:52 2009     length 1 : 16202
Fri Apr 17 17:01:52 2009     length 2 : 11713
Fri Apr 17 17:01:52 2009     length 3 : 10999
Fri Apr 17 17:01:52 2009     length 4 : 8245
Fri Apr 17 17:01:52 2009     length 5 : 5920
Fri Apr 17 17:01:52 2009     length 6 : 3701
Fri Apr 17 17:01:52 2009     length 7 : 2252
Fri Apr 17 17:01:52 2009     length 9+: 2538
Fri Apr 17 17:01:52 2009  largest cycle: 16 relations
Fri Apr 17 17:01:53 2009  matrix is 61134 x 61570 (16.2 MB) with weight 3746682 (60.85/col)
Fri Apr 17 17:01:53 2009  sparse part has weight 3746682 (60.85/col)
Fri Apr 17 17:01:53 2009  filtering completed in 3 passes
Fri Apr 17 17:01:53 2009  matrix is 57223 x 57287 (15.1 MB) with weight 3493687 (60.99/col)
Fri Apr 17 17:01:53 2009  sparse part has weight 3493687 (60.99/col)
Fri Apr 17 17:01:53 2009  saving the first 48 matrix rows for later
Fri Apr 17 17:01:53 2009  matrix is 57175 x 57287 (9.8 MB) with weight 2739358 (47.82/col)
Fri Apr 17 17:01:53 2009  sparse part has weight 2003525 (34.97/col)
Fri Apr 17 17:01:53 2009  matrix includes 64 packed rows
Fri Apr 17 17:01:53 2009  using block size 22914 for processor cache size 6144 kB
Fri Apr 17 17:01:53 2009  commencing Lanczos iteration
Fri Apr 17 17:01:53 2009  memory use: 8.7 MB
Fri Apr 17 17:02:08 2009  lanczos halted after 905 iterations (dim = 57171)
Fri Apr 17 17:02:08 2009  recovered 15 nontrivial dependencies
Fri Apr 17 17:02:09 2009  prp42 factor: 343285591799040843138102857725593336454477
Fri Apr 17 17:02:09 2009  prp49 factor: 1975611290293895905492495874305707347552169153691
Fri Apr 17 17:02:09 2009  elapsed time 00:53:13

(53·10¹³³-71)/9 = 5(8)₁₃₂1_<134> = 3³ · C133

C133 = P49 · P85

P49 = 1736132214682934259760138027279169156218659023617_<49>

P85 = 1256281025374591242622665628469340154953343169071606736108858272346763080946503313059_<85>

SNFS difficulty: 136 digits.
Divisors found:
 r1=1736132214682934259760138027279169156218659023617 (pp49)
 r2=1256281025374591242622665628469340154953343169071606736108858272346763080946503313059 (pp85)
Version: Msieve-1.41
Total time: 2.32 hours.
Scaled time: 6.60 units (timescale=2.846).
Factorization parameters were as follows:
n: 2181069958847736625514403292181069958847736625514403292181069958847736625514403292181069958847736625514403292181069958847736625514403
m: 500000000000000000000000000
deg: 5
c5: 424
c0: -1775
skew: 1.33
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1475001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 230935 x 231183
Total sieving time: 2.06 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,136.000,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 2.32 hours.

Apr 18, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Apr 17, 2009

(89·10¹⁶⁷+1)/9 = 9(8)₁₆₆9_<168> = 11 · 47 · 247241048054093075068483_<24> · C142

C142 = P53 · P90

P53 = 11735515965675694227339384230495652756357364865648203_<53>

P90 = 659225790392093267074705101810375554863868616091506172922557608512373829311495920690579333_<90>

Number: n
N=7736354788131589206605390894565669193375418184832672785771192551985407171377229803380722616315685306413508395609143695564930928388730640388599
  ( 142 digits)
SNFS difficulty: 171 digits.
Divisors found:

Fri Apr 17 03:58:58 2009  prp53 factor: 11735515965675694227339384230495652756357364865648203
Fri Apr 17 03:58:58 2009  prp90 factor: 659225790392093267074705101810375554863868616091506172922557608512373829311495920690579333
Fri Apr 17 03:58:58 2009  elapsed time 01:46:12 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 38.58 hours.
Scaled time: 102.19 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_9_8_166_9
n: 7736354788131589206605390894565669193375418184832672785771192551985407171377229803380722616315685306413508395609143695564930928388730640388599
m: 5000000000000000000000000000000000
deg: 5
c5: 356
c0: 125
skew: 0.81
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 4700557)
Primes: RFBsize:348513, AFBsize:349036, largePrimes:16214116 encountered
Relations: rels:15325613, finalFF:700471
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1460658 hash collisions in 16448507 relations
Msieve: matrix is 883293 x 883541 (238.8 MB)

Total sieving time: 38.03 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 38.58 hours.
 --------- CPU info (if available) ----------

(82·10¹⁶⁷-1)/9 = 9(1)₁₆₇_<168> = 6136826462026924582665204373_<28> · C141

C141 = P52 · P89

P52 = 9296318818779243323402076699581821393618881424501441_<52>

P89 = 15970425640509844064334216093304767762181621347681644889750865211008039470305029735475627_<89>

Number: n
N=148466168425786214041772406044824270769076040264514519242184892190960766848593410970947645326074786069119538379819788655771134770639481878507
  ( 141 digits)
SNFS difficulty: 171 digits.
Divisors found:

Fri Apr 17 19:21:19 2009  prp52 factor: 9296318818779243323402076699581821393618881424501441
Fri Apr 17 19:21:19 2009  prp89 factor: 15970425640509844064334216093304767762181621347681644889750865211008039470305029735475627
Fri Apr 17 19:21:19 2009  elapsed time 01:21:04 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 52.39 hours.
Scaled time: 139.35 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_9_1_167
n: 148466168425786214041772406044824270769076040264514519242184892190960766848593410970947645326074786069119538379819788655771134770639481878507
m: 5000000000000000000000000000000000
deg: 5
c5: 328
c0: -125
skew: 0.82
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 5581229)
Primes: RFBsize:348513, AFBsize:348767, largePrimes:17098512 encountered
Relations: rels:16600199, finalFF:677269
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2019117 hash collisions in 18657465 relations
Msieve: matrix is 870062 x 870310 (231.6 MB)

Total sieving time: 51.69 hours.
Total relation processing time: 0.70 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 52.39 hours.
 --------- CPU info (if available) ----------

4·10²¹⁷+1 = 4(0)₂₁₆1_<218> = 18686807 · C211

C211 = P57 · P154

P57 = 578022421484392833484314349887736849483921909178334750733_<57>

P154 = 3703225908027418809075172754492065279505406206615636647652312656725745127646139680370212557167658670799266733808441570447351849092965953387204337084674371_<154>

Number: n
N=2140547606661748045024492413283874553849675870254345753129467222516934005900526505143441573512264561837664401414324020149616785789032872229054433965096337753153869465232877933613805718654877743426150866758563943
  ( 211 digits)
SNFS difficulty: 218 digits.
Divisors found:

Sat Apr 18 00:43:41 2009  prp57 factor: 578022421484392833484314349887736849483921909178334750733
Sat Apr 18 00:43:41 2009  prp154 factor: 3703225908027418809075172754492065279505406206615636647652312656725745127646139680370212557167658670799266733808441570447351849092965953387204337084674371
Sat Apr 18 00:43:41 2009  elapsed time 56:50:02 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 174.05 hours.
Scaled time: 350.71 units (timescale=2.015).
Factorization parameters were as follows:
name: KA_4_0_216_1
n: 2140547606661748045024492413283874553849675870254345753129467222516934005900526505143441573512264561837664401414324020149616785789032872229054433965096337753153869465232877933613805718654877743426150866758563943
m: 2000000000000000000000000000000000000
deg: 6
c6: 5
c0: 8
skew: 1.08
type: snfs
lss: 1
rlim: 31000000
alim: 31000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 31000000/31000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [15500000, 45599990)
Primes: RFBsize:1915979, AFBsize:1916784, largePrimes:34927111 encountered
Relations: rels:29018997, finalFF:841025
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 8207149 hash collisions in 48938562 relations
Msieve: matrix is 5272052 x 5272300 (1428.4 MB)

Total sieving time: 173.00 hours.
Total relation processing time: 1.05 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,218,6,0,0,0,0,0,0,0,0,31000000,31000000,29,29,58,58,2.6,2.6,100000
total time: 174.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.97 BogoMIPS (lpj=2830489)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830455)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22643.69 BogoMIPS).

By Robert Backstrom / GGNFS, Msieve / Apr 18, 2009

(53·10¹⁴⁵-71)/9 = 5(8)₁₄₄1_<146> = 3 · 17 · 929 · 485499853 · 850230413 · 1274328443_<10> · 4221790879_<10> · C105

C105 = P43 · P63

P43 = 3316688302115642889056012400773516430032419_<43>

P63 = 168748133784761883638959898979058638917739521572854314854336157_<63>

Number: n
N=559684961327765247034503844891371736894556026815844268035413780122864846810001043646439238215822233873783
  ( 105 digits)
Divisors found:

Sat Apr 18 02:54:26 2009  prp43 factor: 3316688302115642889056012400773516430032419
Sat Apr 18 02:54:26 2009  prp63 factor: 168748133784761883638959898979058638917739521572854314854336157
Sat Apr 18 02:54:26 2009  elapsed time 00:38:14 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 5.68 hours.
Scaled time: 15.10 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_8_144_1
n: 559684961327765247034503844891371736894556026815844268035413780122864846810001043646439238215822233873783
Y0: -176799813543897703182
Y1:  72476416319
c0: -10442345234358626558524313
c1:  19040482229417220485271
c2:  581533457134543607
c3: -10679814889731
c4: -189005634
c5:  3240
skew: 43207.82
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1250000, 1851097)
Primes: RFBsize:183072, AFBsize:183757, largePrimes:14104467 encountered
Relations: rels:11862900, finalFF:384598
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 684206 hash collisions in 12317492 relations
Msieve: matrix is 376672 x 376920 (104.9 MB)

Total sieving time: 5.43 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000
total time: 5.68 hours.
 --------- CPU info (if available) ----------

(46·10¹⁶⁵+71)/9 = 5(1)₁₆₄9_<166> = 181 · 191 · 1361 · 23993 · 25637611 · 1804773857_<10> · C137

C137 = P57 · P81

P57 = 694575844284880677867191247137091366345427839339582636913_<57>

P81 = 140877189974738893565168112114361733965740981505111702335142003362792062349532543_<81>

Number: n
N=97849893167185795053681505438158227359229056175828170023743411900227181839092558179099204573640195680027563053318468911424344244846559759
  ( 137 digits)
SNFS difficulty: 166 digits.
Divisors found:

Sat Apr 18 05:42:10 2009  prp57 factor: 694575844284880677867191247137091366345427839339582636913
Sat Apr 18 05:42:10 2009  prp81 factor: 140877189974738893565168112114361733965740981505111702335142003362792062349532543
Sat Apr 18 05:42:10 2009  elapsed time 00:59:04 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 34.25 hours.
Scaled time: 91.11 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_1_164_9
n: 97849893167185795053681505438158227359229056175828170023743411900227181839092558179099204573640195680027563053318468911424344244846559759
m: 1000000000000000000000000000000000
deg: 5
c5: 46
c0: 71
skew: 1.09
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved  special-q in [2100000, 4073129)
Primes: RFBsize:296314, AFBsize:296472, largePrimes:8717814 encountered
Relations: rels:8479753, finalFF:538519
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 872510 hash collisions in 9552985 relations
Msieve: matrix is 720695 x 720943 (193.3 MB)

Total sieving time: 33.98 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 34.25 hours.
 --------- CPU info (if available) ----------

Apr 18, 2009 (4th)

By Sinkiti Sibata / Msieve, GGNFS / Apr 17, 2009

(53·10¹³⁰-71)/9 = 5(8)₁₂₉1_<131> = 3 · 19 · 61 · 577 · 2927 · 7382416109_<10> · 1369886219328469_<16> · C96

C96 = P38 · P59

P38 = 37956724012464402598129885947865441919_<38>

P59 = 26125126047863880080771368057462882723263924827439187557293_<59>

Fri Apr 17 08:04:56 2009  Msieve v. 1.41
Fri Apr 17 08:04:56 2009  random seeds: 8d9111a4 23cf54e5
Fri Apr 17 08:04:56 2009  factoring 991624199189614174782401830448492816243117370394794813266981352510574370554134332396855576365267 (96 digits)
Fri Apr 17 08:04:57 2009  searching for 15-digit factors
Fri Apr 17 08:04:59 2009  commencing quadratic sieve (96-digit input)
Fri Apr 17 08:04:59 2009  using multiplier of 67
Fri Apr 17 08:04:59 2009  using 32kb Intel Core sieve core
Fri Apr 17 08:04:59 2009  sieve interval: 36 blocks of size 32768
Fri Apr 17 08:04:59 2009  processing polynomials in batches of 6
Fri Apr 17 08:04:59 2009  using a sieve bound of 2299963 (84681 primes)
Fri Apr 17 08:04:59 2009  using large prime bound of 344994450 (28 bits)
Fri Apr 17 08:04:59 2009  using double large prime bound of 2333789820820650 (43-52 bits)
Fri Apr 17 08:04:59 2009  using trial factoring cutoff of 52 bits
Fri Apr 17 08:04:59 2009  polynomial 'A' values have 13 factors
Fri Apr 17 12:43:45 2009  85035 relations (21540 full + 63495 combined from 1262176 partial), need 84777
Fri Apr 17 12:43:47 2009  begin with 1283716 relations
Fri Apr 17 12:43:48 2009  reduce to 219055 relations in 12 passes
Fri Apr 17 12:43:48 2009  attempting to read 219055 relations
Fri Apr 17 12:43:52 2009  recovered 219055 relations
Fri Apr 17 12:43:52 2009  recovered 204927 polynomials
Fri Apr 17 12:43:52 2009  attempting to build 85035 cycles
Fri Apr 17 12:43:52 2009  found 85035 cycles in 6 passes
Fri Apr 17 12:43:52 2009  distribution of cycle lengths:
Fri Apr 17 12:43:52 2009     length 1 : 21540
Fri Apr 17 12:43:52 2009     length 2 : 15038
Fri Apr 17 12:43:52 2009     length 3 : 14584
Fri Apr 17 12:43:52 2009     length 4 : 11363
Fri Apr 17 12:43:52 2009     length 5 : 8571
Fri Apr 17 12:43:52 2009     length 6 : 5599
Fri Apr 17 12:43:52 2009     length 7 : 3502
Fri Apr 17 12:43:52 2009     length 9+: 4838
Fri Apr 17 12:43:52 2009  largest cycle: 21 relations
Fri Apr 17 12:43:53 2009  matrix is 84681 x 85035 (22.9 MB) with weight 5657471 (66.53/col)
Fri Apr 17 12:43:53 2009  sparse part has weight 5657471 (66.53/col)
Fri Apr 17 12:43:54 2009  filtering completed in 3 passes
Fri Apr 17 12:43:54 2009  matrix is 80389 x 80453 (21.7 MB) with weight 5370825 (66.76/col)
Fri Apr 17 12:43:54 2009  sparse part has weight 5370825 (66.76/col)
Fri Apr 17 12:43:54 2009  saving the first 48 matrix rows for later
Fri Apr 17 12:43:54 2009  matrix is 80341 x 80453 (13.9 MB) with weight 4286515 (53.28/col)
Fri Apr 17 12:43:54 2009  sparse part has weight 3167151 (39.37/col)
Fri Apr 17 12:43:54 2009  matrix includes 64 packed rows
Fri Apr 17 12:43:54 2009  using block size 32181 for processor cache size 1024 kB
Fri Apr 17 12:43:55 2009  commencing Lanczos iteration
Fri Apr 17 12:43:55 2009  memory use: 13.2 MB
Fri Apr 17 12:44:38 2009  lanczos halted after 1272 iterations (dim = 80340)
Fri Apr 17 12:44:38 2009  recovered 17 nontrivial dependencies
Fri Apr 17 12:44:40 2009  prp38 factor: 37956724012464402598129885947865441919
Fri Apr 17 12:44:40 2009  prp59 factor: 26125126047863880080771368057462882723263924827439187557293
Fri Apr 17 12:44:40 2009  elapsed time 04:39:44

(44·10¹⁸⁵+1)/9 = 4(8)₁₈₄9_<186> = 3² · 19 · C184

C184 = P33 · P46 · P106

P33 = 301279492672528356310887081620281_<33>

P46 = 2007681696397209428158663231335805768631686309_<46>

P106 = 4726608434867671415692354975353016939132883160285222480786726238803221676691996179230672373731698457768071_<106>

Number: 48889_185
N=2858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402859
  ( 184 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=301279492672528356310887081620281 (pp33)
 r2=2007681696397209428158663231335805768631686309 (pp46)
 r3=4726608434867671415692354975353016939132883160285222480786726238803221676691996179230672373731698457768071 (pp106)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 342.67 hours.
Scaled time: 871.76 units (timescale=2.544).
Factorization parameters were as follows:
name: 48889_185
n: 2858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402859
m: 20000000000000000000000000000000000000
deg: 5
c5: 11
c0: 8
skew: 0.94
type: snfs
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved algebraic special-q in [4000000, 8100001)
Primes: RFBsize:539777, AFBsize:539726, largePrimes:19572351 encountered
Relations: rels:20827886, finalFF:1635103
Max relations in full relation-set: 28
Initial matrix: 1079569 x 1635103 with sparse part having weight 203875562.
Pruned matrix : 801126 x 806587 with weight 198989218.
Total sieving time: 323.10 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 18.63 hours.
Time per square root: 0.37 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,54,54,2.5,2.5,100000
total time: 342.67 hours.
 --------- CPU info (if available) ----------

By Sinkiti Sibata / Msieve, GGNFS / Apr 18, 2009

(53·10¹⁵¹-71)/9 = 5(8)₁₅₀1_<152> = 3² · 73 · 601 · 3067 · 8360509 · 50792883547972719649_<20> · 542501417551026748883_<21> · C96

C96 = P47 · P49

P47 = 42936148687473484273728024786408390015437208617_<47>

P49 = 4916094149477628730365878389162042910302106837749_<49>

Fri Apr 17 22:03:47 2009  Msieve v. 1.41
Fri Apr 17 22:03:47 2009  random seeds: e488b000 c6788c06
Fri Apr 17 22:03:47 2009  factoring 211078149363589963815116393190719711120312274320994824021579216883462998082421755858953483683133 (96 digits)
Fri Apr 17 22:03:48 2009  searching for 15-digit factors
Fri Apr 17 22:03:50 2009  commencing quadratic sieve (96-digit input)
Fri Apr 17 22:03:50 2009  using multiplier of 3
Fri Apr 17 22:03:50 2009  using 32kb Intel Core sieve core
Fri Apr 17 22:03:50 2009  sieve interval: 36 blocks of size 32768
Fri Apr 17 22:03:50 2009  processing polynomials in batches of 6
Fri Apr 17 22:03:50 2009  using a sieve bound of 2221733 (82353 primes)
Fri Apr 17 22:03:50 2009  using large prime bound of 333259950 (28 bits)
Fri Apr 17 22:03:50 2009  using double large prime bound of 2192853470339550 (43-51 bits)
Fri Apr 17 22:03:50 2009  using trial factoring cutoff of 51 bits
Fri Apr 17 22:03:50 2009  polynomial 'A' values have 12 factors
Sat Apr 18 02:35:33 2009  82536 relations (20005 full + 62531 combined from 1235511 partial), need 82449
Sat Apr 18 02:35:35 2009  begin with 1255516 relations
Sat Apr 18 02:35:36 2009  reduce to 216093 relations in 10 passes
Sat Apr 18 02:35:36 2009  attempting to read 216093 relations
Sat Apr 18 02:35:39 2009  recovered 216093 relations
Sat Apr 18 02:35:39 2009  recovered 202007 polynomials
Sat Apr 18 02:35:40 2009  attempting to build 82536 cycles
Sat Apr 18 02:35:40 2009  found 82536 cycles in 6 passes
Sat Apr 18 02:35:40 2009  distribution of cycle lengths:
Sat Apr 18 02:35:40 2009     length 1 : 20005
Sat Apr 18 02:35:40 2009     length 2 : 14414
Sat Apr 18 02:35:40 2009     length 3 : 13967
Sat Apr 18 02:35:40 2009     length 4 : 11178
Sat Apr 18 02:35:40 2009     length 5 : 8393
Sat Apr 18 02:35:40 2009     length 6 : 5707
Sat Apr 18 02:35:40 2009     length 7 : 3677
Sat Apr 18 02:35:40 2009     length 9+: 5195
Sat Apr 18 02:35:40 2009  largest cycle: 20 relations
Sat Apr 18 02:35:40 2009  matrix is 82353 x 82536 (23.0 MB) with weight 5698494 (69.04/col)
Sat Apr 18 02:35:40 2009  sparse part has weight 5698494 (69.04/col)
Sat Apr 18 02:35:42 2009  filtering completed in 3 passes
Sat Apr 18 02:35:42 2009  matrix is 78705 x 78769 (22.1 MB) with weight 5470954 (69.46/col)
Sat Apr 18 02:35:42 2009  sparse part has weight 5470954 (69.46/col)
Sat Apr 18 02:35:42 2009  saving the first 48 matrix rows for later
Sat Apr 18 02:35:42 2009  matrix is 78657 x 78769 (15.6 MB) with weight 4510774 (57.27/col)
Sat Apr 18 02:35:42 2009  sparse part has weight 3628703 (46.07/col)
Sat Apr 18 02:35:42 2009  matrix includes 64 packed rows
Sat Apr 18 02:35:42 2009  using block size 31507 for processor cache size 1024 kB
Sat Apr 18 02:35:43 2009  commencing Lanczos iteration
Sat Apr 18 02:35:43 2009  memory use: 14.0 MB
Sat Apr 18 02:36:32 2009  lanczos halted after 1245 iterations (dim = 78657)
Sat Apr 18 02:36:32 2009  recovered 19 nontrivial dependencies
Sat Apr 18 02:36:33 2009  prp47 factor: 42936148687473484273728024786408390015437208617
Sat Apr 18 02:36:33 2009  prp49 factor: 4916094149477628730365878389162042910302106837749
Sat Apr 18 02:36:33 2009  elapsed time 04:32:46

Apr 18, 2009 (3rd)

By Jeff Gilchrist / GGNFS, Msieve 1.41 / Apr 18, 2009

(32·10¹⁷⁰+31)/9 = 3(5)₁₆₉9_<171> = 3449 · 15128611 · 23008033 · C153

C153 = P52 · P102

P52 = 1528216471097860021313334111063020163874176813026371_<52>

P102 = 193798696059930635413390537724663298714890396659618435429067607489207334036908047360384278676186052967_<102>

Number: 35559_170
N=296166359396073944683160485101585851681443934301671987655522323564543253916503976987487165849021699261332677580008470890265619918699850211710956573792757
  ( 153 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=1528216471097860021313334111063020163874176813026371 (pp52)
 r2=193798696059930635413390537724663298714890396659618435429067607489207334036908047360384278676186052967 (pp102)
Version: Msieve-1.41
Total time: 90.66 hours.
Scaled time: 68.27 units (timescale=0.753).
Factorization parameters were as follows:
n: 296166359396073944683160485101585851681443934301671987655522323564543253916503976987487165849021699261332677580008470890265619918699850211710956573792757
m: 20000000000000000000000000000000000
deg: 5
c5: 1
c0: 31
skew: 1.99
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 794466 x 794714
Total sieving time: 90.66 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 90.66 hours.
 --------- CPU info (if available) ----------

Apr 18, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Apr 17, 2009

(17·10¹⁹⁰+1)/9 = 1(8)₁₈₉9_<191> = 13 · 649123 · 707912267722698978623_<21> · 24592951456281913764228758669239_<32> · C132

C132 = P37 · P95

P37 = 7213700843439887344632470841269291957_<37>

P95 = 17823288757233023573682324129309601544137069773637839144377564166930756298795605248649159083659_<95>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=87697117
Step 1 took 38211ms
Step 2 took 13867ms
********** Factor found in step 2: 7213700843439887344632470841269291957
Found probable prime factor of 37 digits: 7213700843439887344632470841269291957
Probable prime cofactor 17823288757233023573682324129309601544137069773637839144377564166930756298795605248649159083659 has 95 digits

(49·10¹⁹⁷+41)/9 = 5(4)₁₉₆9_<198> = 3 · 103 · 229 · 693483587 · 106035242108839020242123_<24> · 2001264824074391733510725271041_<31> · C131

C131 = P40 · P91

P40 = 7753115765111063522021142552571754477947_<40>

P91 = 6743608649761494883582317379979859049540910030066178214889108592918675243582982981900750267_<91>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2900669674
Step 1 took 41286ms
Step 2 took 15713ms
********** Factor found in step 2: 7753115765111063522021142552571754477947
Found probable prime factor of 40 digits: 7753115765111063522021142552571754477947
Probable prime cofactor 6743608649761494883582317379979859049540910030066178214889108592918675243582982981900750267 has 91 digits

Apr 18, 2009

By Max Dettweiler / GMP-ECM, YAFU v1.10, Msieve / Apr 17, 2009

(34·10¹⁷⁰-7)/9 = 3(7)₁₇₀_<171> = 13 · 29 · 33490275305670749792334851887141_<32> · C137

C137 = P41 · P96

P41 = 34681276407981177103088346208185521753173_<41>

P96 = 862742647641399005036569351298107041173106291055284796151924344953422830786304949874008936124657_<96>

P41=34681276407981177103088346208185521753173
P96=862742647641399005036569351298107041173106291055284796151924344953422830786304949874008936124657

B1=3000000
B2=(unknown--might be 760000000?)
Method=ECM

Found by the ECM "workers" at http://factorization.ath.cx

(53·10¹²³-71)/9 = 5(8)₁₂₂1_<124> = 90943231 · 77869883783146913142335509_<26> · C90

C90 = P36 · P55

P36 = 202264546609434854254852740781297727_<36>

P55 = 4111248127642512233539893307565579092523923938001118957_<55>

04/16/09 16:34:17 v1.10 @ Core2Duo, starting SIQS on c90: 831559738536500690691743153345461801909511644511260916432349884974767033138555344560710739
04/16/09 16:34:17 v1.10 @ Core2Duo, random seeds: 597820055, 1786273408
04/16/09 16:34:18 v1.10 @ Core2Duo, ==== sieve params ====
04/16/09 16:34:18 v1.10 @ Core2Duo, n = 90 digits, 299 bits
04/16/09 16:34:18 v1.10 @ Core2Duo, factor base: 66328 primes (max prime = 1764199)
04/16/09 16:34:18 v1.10 @ Core2Duo, single large prime cutoff: 211703880 (120 * pmax)
04/16/09 16:34:18 v1.10 @ Core2Duo, double large prime range from 43 to 50 bits
04/16/09 16:34:18 v1.10 @ Core2Duo, double large prime cutoff: 968973437116546
04/16/09 16:34:18 v1.10 @ Core2Duo, using 10 large prime slices of factor base
04/16/09 16:34:18 v1.10 @ Core2Duo, buckets hold 1024 elements
04/16/09 16:34:18 v1.10 @ Core2Duo, sieve interval: 22 blocks of size 32768
04/16/09 16:34:18 v1.10 @ Core2Duo, polynomial A has ~ 12 factors
04/16/09 16:34:18 v1.10 @ Core2Duo, using multiplier of 1
04/16/09 16:34:18 v1.10 @ Core2Duo, using small prime variation correction of 20 bits
04/16/09 16:34:18 v1.10 @ Core2Duo, using SSE2 for trial division and x128 sieve scanning
04/16/09 16:34:18 v1.10 @ Core2Duo, trial factoring cutoff at 97 bits
04/16/09 16:34:18 v1.10 @ Core2Duo, ==== sieving started ====
04/16/09 17:40:00 v1.10 @ Core2Duo, sieve time = 1211.2770, relation time = 637.2920, poly_time = 2089.8140
04/16/09 17:40:00 v1.10 @ Core2Duo, 66408 relations found: 18863 full + 47545 from 811249 partial, using 443534 polys (223 A polys)
04/16/09 17:40:00 v1.10 @ Core2Duo, on average, sieving found 1.87 rels/poly and 210.54 rels/sec
04/16/09 17:40:00 v1.10 @ Core2Duo, trial division touched 26209823 sieve locations out of 639483772928
04/16/09 17:40:00 v1.10 @ Core2Duo, ==== post processing stage (msieve-1.38) ====
04/16/09 17:40:00 v1.10 @ Core2Duo, begin with 830112 relations
04/16/09 17:40:01 v1.10 @ Core2Duo, reduce to 156592 relations in 9 passes
04/16/09 17:40:03 v1.10 @ Core2Duo, recovered 156592 relations
04/16/09 17:40:03 v1.10 @ Core2Duo, recovered 132068 polynomials
04/16/09 17:40:04 v1.10 @ Core2Duo, attempting to build 66408 cycles
04/16/09 17:40:04 v1.10 @ Core2Duo, found 66408 cycles in 5 passes
04/16/09 17:40:04 v1.10 @ Core2Duo, distribution of cycle lengths:
04/16/09 17:40:04 v1.10 @ Core2Duo,    length 1 : 18863
04/16/09 17:40:04 v1.10 @ Core2Duo,    length 2 : 14095
04/16/09 17:40:04 v1.10 @ Core2Duo,    length 3 : 11947
04/16/09 17:40:04 v1.10 @ Core2Duo,    length 4 : 8470
04/16/09 17:40:04 v1.10 @ Core2Duo,    length 5 : 5531
04/16/09 17:40:04 v1.10 @ Core2Duo,    length 6 : 3328
04/16/09 17:40:04 v1.10 @ Core2Duo,    length 7 : 2009
04/16/09 17:40:04 v1.10 @ Core2Duo,    length 9+: 2165
04/16/09 17:40:04 v1.10 @ Core2Duo, largest cycle: 19 relations
04/16/09 17:40:04 v1.10 @ Core2Duo, matrix is 66328 x 66408 (15.3 MB) with weight 3748888 (56.45/col)
04/16/09 17:40:04 v1.10 @ Core2Duo, sparse part has weight 3748888 (56.45/col)
04/16/09 17:40:04 v1.10 @ Core2Duo, filtering completed in 3 passes
04/16/09 17:40:04 v1.10 @ Core2Duo, matrix is 61551 x 61614 (14.4 MB) with weight 3515995 (57.06/col)
04/16/09 17:40:04 v1.10 @ Core2Duo, sparse part has weight 3515995 (57.06/col)
04/16/09 17:40:04 v1.10 @ Core2Duo, saving the first 48 matrix rows for later
04/16/09 17:40:04 v1.10 @ Core2Duo, matrix is 61503 x 61614 (9.0 MB) with weight 2658612 (43.15/col)
04/16/09 17:40:04 v1.10 @ Core2Duo, sparse part has weight 1991948 (32.33/col)
04/16/09 17:40:04 v1.10 @ Core2Duo, matrix includes 64 packed rows
04/16/09 17:40:04 v1.10 @ Core2Duo, using block size 24645 for processor cache size 2048 kB
04/16/09 17:40:05 v1.10 @ Core2Duo, commencing Lanczos iteration
04/16/09 17:40:05 v1.10 @ Core2Duo, memory use: 9.0 MB
04/16/09 17:40:23 v1.10 @ Core2Duo, lanczos halted after 974 iterations (dim = 61500)
04/16/09 17:40:23 v1.10 @ Core2Duo, recovered 16 nontrivial dependencies
04/16/09 17:40:24 v1.10 @ Core2Duo, prp36 = 202264546609434854254852740781297727
04/16/09 17:40:28 v1.10 @ Core2Duo, prp55 = 4111248127642512233539893307565579092523923938001118957
04/16/09 17:40:28 v1.10 @ Core2Duo, Lanczos elapsed time = 22.7030 seconds.
04/16/09 17:40:28 v1.10 @ Core2Duo, Sqrt elapsed time = 4.9220 seconds.
04/16/09 17:40:28 v1.10 @ Core2Duo, SIQS elapsed time = 3970.3590 seconds.

(53·10¹²¹-71)/9 = 5(8)₁₂₀1_<122> = 3 · 194659 · 384621067 · 207102242897777867_<18> · C91

C91 = P34 · P58

P34 = 1133539780530774666049337268862213_<34>

P58 = 1116819481169900334059112170711297777323250963240946700829_<58>

04/16/09 16:35:26 v1.10 @ Core2Duo, starting SIQS on c91: 1265959309577822454446640479059957214320018167680776045410923986160203316835382572933874577
04/16/09 16:35:26 v1.10 @ Core2Duo, random seeds: 1414385627, 1486820648
04/16/09 16:35:27 v1.10 @ Core2Duo, ==== sieve params ====
04/16/09 16:35:27 v1.10 @ Core2Duo, n = 91 digits, 305 bits
04/16/09 16:35:27 v1.10 @ Core2Duo, factor base: 67412 primes (max prime = 1799261)
04/16/09 16:35:27 v1.10 @ Core2Duo, single large prime cutoff: 215911320 (120 * pmax)
04/16/09 16:35:27 v1.10 @ Core2Duo, double large prime range from 43 to 50 bits
04/16/09 16:35:27 v1.10 @ Core2Duo, double large prime cutoff: 1003912224363295
04/16/09 16:35:27 v1.10 @ Core2Duo, using 10 large prime slices of factor base
04/16/09 16:35:27 v1.10 @ Core2Duo, buckets hold 1024 elements
04/16/09 16:35:27 v1.10 @ Core2Duo, sieve interval: 22 blocks of size 32768
04/16/09 16:35:27 v1.10 @ Core2Duo, polynomial A has ~ 12 factors
04/16/09 16:35:27 v1.10 @ Core2Duo, using multiplier of 29
04/16/09 16:35:27 v1.10 @ Core2Duo, using small prime variation correction of 23 bits
04/16/09 16:35:27 v1.10 @ Core2Duo, using SSE2 for trial division and x128 sieve scanning
04/16/09 16:35:27 v1.10 @ Core2Duo, trial factoring cutoff at 96 bits
04/16/09 16:35:27 v1.10 @ Core2Duo, ==== sieving started ====
04/16/09 17:38:42 v1.10 @ Core2Duo, sieve time = 1146.0730, relation time = 650.4160, poly_time = 1994.7900
04/16/09 17:38:42 v1.10 @ Core2Duo, 67497 relations found: 19809 full + 47688 from 813125 partial, using 414687 polys (202 A polys)
04/16/09 17:38:42 v1.10 @ Core2Duo, on average, sieving found 2.01 rels/poly and 219.41 rels/sec
04/16/09 17:38:42 v1.10 @ Core2Duo, trial division touched 29489564 sieve locations out of 597892399104
04/16/09 17:38:42 v1.10 @ Core2Duo, ==== post processing stage (msieve-1.38) ====
04/16/09 17:38:44 v1.10 @ Core2Duo, begin with 832934 relations
04/16/09 17:38:45 v1.10 @ Core2Duo, reduce to 156443 relations in 10 passes
04/16/09 17:38:47 v1.10 @ Core2Duo, recovered 156443 relations
04/16/09 17:38:47 v1.10 @ Core2Duo, recovered 130277 polynomials
04/16/09 17:38:48 v1.10 @ Core2Duo, attempting to build 67497 cycles
04/16/09 17:38:48 v1.10 @ Core2Duo, found 67497 cycles in 5 passes
04/16/09 17:38:48 v1.10 @ Core2Duo, distribution of cycle lengths:
04/16/09 17:38:48 v1.10 @ Core2Duo,    length 1 : 19809
04/16/09 17:38:48 v1.10 @ Core2Duo,    length 2 : 14671
04/16/09 17:38:48 v1.10 @ Core2Duo,    length 3 : 12452
04/16/09 17:38:48 v1.10 @ Core2Duo,    length 4 : 8410
04/16/09 17:38:48 v1.10 @ Core2Duo,    length 5 : 5369
04/16/09 17:38:48 v1.10 @ Core2Duo,    length 6 : 3216
04/16/09 17:38:48 v1.10 @ Core2Duo,    length 7 : 1758
04/16/09 17:38:48 v1.10 @ Core2Duo,    length 9+: 1812
04/16/09 17:38:48 v1.10 @ Core2Duo, largest cycle: 19 relations
04/16/09 17:38:48 v1.10 @ Core2Duo, matrix is 67412 x 67497 (15.8 MB) with weight 3859261 (57.18/col)
04/16/09 17:38:48 v1.10 @ Core2Duo, sparse part has weight 3859261 (57.18/col)
04/16/09 17:38:48 v1.10 @ Core2Duo, filtering completed in 3 passes
04/16/09 17:38:48 v1.10 @ Core2Duo, matrix is 62004 x 62068 (14.7 MB) with weight 3599837 (58.00/col)
04/16/09 17:38:48 v1.10 @ Core2Duo, sparse part has weight 3599837 (58.00/col)
04/16/09 17:38:49 v1.10 @ Core2Duo, saving the first 48 matrix rows for later
04/16/09 17:38:49 v1.10 @ Core2Duo, matrix is 61956 x 62068 (9.8 MB) with weight 2860904 (46.09/col)
04/16/09 17:38:49 v1.10 @ Core2Duo, sparse part has weight 2204854 (35.52/col)
04/16/09 17:38:49 v1.10 @ Core2Duo, matrix includes 64 packed rows
04/16/09 17:38:49 v1.10 @ Core2Duo, using block size 24827 for processor cache size 2048 kB
04/16/09 17:38:49 v1.10 @ Core2Duo, commencing Lanczos iteration
04/16/09 17:38:49 v1.10 @ Core2Duo, memory use: 9.4 MB
04/16/09 17:39:10 v1.10 @ Core2Duo, lanczos halted after 982 iterations (dim = 61955)
04/16/09 17:39:10 v1.10 @ Core2Duo, recovered 17 nontrivial dependencies
04/16/09 17:39:11 v1.10 @ Core2Duo, prp58 = 1116819481169900334059112170711297777323250963240946700829
04/16/09 17:39:12 v1.10 @ Core2Duo, prp34 = 1133539780530774666049337268862213
04/16/09 17:39:12 v1.10 @ Core2Duo, Lanczos elapsed time = 27.3910 seconds.
04/16/09 17:39:12 v1.10 @ Core2Duo, Sqrt elapsed time = 2.2500 seconds.
04/16/09 17:39:12 v1.10 @ Core2Duo, SIQS elapsed time = 3825.8750 seconds.

Apr 16, 2009 (4th)

Factorizations of 588...881 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 16, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 16, 2009

(52·10¹⁷⁴-61)/9 = 5(7)₁₇₃1_<175> = 15749 · C171

C171 = P34 · P51 · P87

P34 = 4456418495820421423482950428914067_<34>

P51 = 586089258996949155306651521414790973265453349486223_<51>

P87 = 140461764836441451075909139943636759414509330131265327498354115378476241498359801842619_<87>

Number: 57771_174
N=366866326609802386042147296830133835657995922139677298735016685362739080435442109199173139740794830006843468015605929124247747652408265780543385470682441918710888169266479
  ( 171 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=4456418495820421423482950428914067 (pp34)
 r2=586089258996949155306651521414790973265453349486223 (pp51)
 r3=140461764836441451075909139943636759414509330131265327498354115378476241498359801842619 (pp87)
Version: Msieve-1.39
Total time: 81.98 hours.
Scaled time: 142.24 units (timescale=1.735).
Factorization parameters were as follows:
n: 366866326609802386042147296830133835657995922139677298735016685362739080435442109199173139740794830006843468015605929124247747652408265780543385470682441918710888169266479
m: 100000000000000000000000000000000000
deg: 5
c5: 26
c0: -305
skew: 1.64
type: snfs
lss: 1
rlim: 6100000
alim: 6100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6100000/6100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3050000, 7050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1314040 x 1314288
Total sieving time: 81.98 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6100000,6100000,28,28,53,53,2.5,2.5,100000
total time: 81.98 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶⁸-61)/9 = 5(7)₁₆₇1_<169> = 113 · C167

C167 = P47 · P51 · P71

P47 = 19594909439998386601697728948481069367588129493_<47>

P51 = 227202190339783073222336540223881606408474505882161_<51>

P71 = 11484884081582197425900107097665164509550167084613358848553590701850079_<71>

Number: 57771_168
N=51130776794493608652900688298918387413962635201573254670599803343166175024582104228121927236971484759095378564405113077679449360865290068829891838741396263520157325467
  ( 167 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=19594909439998386601697728948481069367588129493 (pp47)
 r2=227202190339783073222336540223881606408474505882161 (pp51)
 r3=11484884081582197425900107097665164509550167084613358848553590701850079 (pp71)
Version: Msieve-1.39
Total time: 70.05 hours.
Scaled time: 180.81 units (timescale=2.581).
Factorization parameters were as follows:
n: 51130776794493608652900688298918387413962635201573254670599803343166175024582104228121927236971484759095378564405113077679449360865290068829891838741396263520157325467
m: 10000000000000000000000000000000000
deg: 5
c5: 13
c0: -1525
skew: 2.59
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 6100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1040706 x 1040954
Total sieving time: 70.05 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 70.05 hours.
 --------- CPU info (if available) ----------

(37·10¹⁷⁸+17)/9 = 4(1)₁₇₇3_<179> = 13752402607_<11> · 4488398865557_<13> · 10792876087603367_<17> · 7049599458449368393_<19> · C121

C121 = P57 · P64

P57 = 901053580759546473335733195289088783980467426146667758137_<57>

P64 = 9714868865503115801159431371805518306707962321967502211308133021_<64>

Number: 41113_178
N=8753617377871015379501280731640734720391420036927883299454746453053412071345125172976838459344035255267627866305051141877
  ( 121 digits)
Divisors found:
 r1=901053580759546473335733195289088783980467426146667758137 (pp57)
 r2=9714868865503115801159431371805518306707962321967502211308133021 (pp64)
Version: Msieve-1.39
Total time: 42.93 hours.
Scaled time: 74.87 units (timescale=1.744).
Factorization parameters were as follows:
n: 8753617377871015379501280731640734720391420036927883299454746453053412071345125172976838459344035255267627866305051141877
Y0: -232444750578107045732042
Y1:  18042078346271
c0: -88669467322140490833982108215
c1: -3045316310392554112648423
c2:  33782754219691244909
c3: -10726229016841
c4: -330767170
c5:  12900
skew: 121095.13
type: gnfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [3000000, 5280001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 713270 x 713518
Total sieving time: 42.93 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6000000,6000000,27,27,50,50,2.4,2.4,60000
total time: 42.93 hours.
 --------- CPU info (if available) ----------

(47·10¹⁸⁷+61)/9 = 5(2)₁₈₆9_<188> = 472333 · 17123431378539583_<17> · 3005422296029909783_<19> · 229120334047763623675514957_<27> · C121

C121 = P33 · P45 · P45

P33 = 418959790849984109280420085898543_<33>

P45 = 130459351366153640145461498845742658269799017_<45>

P45 = 171553492944694353363214986772791976579824851_<45>

Number: 52229_187
N=9376637445301894692630526042340308089577381927812760651326578892014175084978443337190895669157712510157322717408832872581
  ( 121 digits)
Divisors found:
 r1=418959790849984109280420085898543 (pp33)
 r2=130459351366153640145461498845742658269799017 (pp45)
 r3=171553492944694353363214986772791976579824851 (pp45)
Version: Msieve-1.39
Total time: 44.72 hours.
Scaled time: 115.52 units (timescale=2.583).
Factorization parameters were as follows:
n: 9376637445301894692630526042340308089577381927812760651326578892014175084978443337190895669157712510157322717408832872581
Y0: -235662499711423574126299
Y1:  7140679275653
c0:  3616806725893284226991581464
c1:  3136244370186715815288714
c2: -77509608345842470109
c3: -1117609557837509
c4:  4914956575
c5:  12900
skew: 113010.98
type: gnfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 4720001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 640055 x 640303
Total sieving time: 44.72 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 44.72 hours.
 --------- CPU info (if available) ----------

Apr 16, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Apr 16, 2009

(29·10¹⁶⁹+43)/9 = 3(2)₁₆₈7_<170> = 37 · 67 · 89 · 219274245089_<12> · 7009215964631_<13> · 11889948082870718027_<20> · C121

C121 = P50 · P72

P50 = 32583084617094617615042603090346568972351851388073_<50>

P72 = 245278642849600244520859043647749948902552614694651833843364433822233153_<72>

Number: n
N=7991934774734654452054356447725718770084016035191644948179308728459372861636901877233956143656618879080281199811689384169
  ( 121 digits)
SNFS difficulty: 171 digits.
Divisors found:

Thu Apr 16 21:15:03 2009  prp50 factor: 32583084617094617615042603090346568972351851388073
Thu Apr 16 21:15:03 2009  prp72 factor: 245278642849600244520859043647749948902552614694651833843364433822233153
Thu Apr 16 21:15:03 2009  elapsed time 01:37:35 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 65.88 hours.
Scaled time: 175.23 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_3_2_168_7
n: 7991934774734654452054356447725718770084016035191644948179308728459372861636901877233956143656618879080281199811689384169
m: 10000000000000000000000000000000000
deg: 5
c5: 29
c0: 430
skew: 1.71
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 6403351)
Primes: RFBsize:348513, AFBsize:348691, largePrimes:18018717 encountered
Relations: rels:18137376, finalFF:707077
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2444613 hash collisions in 20202113 relations
Msieve: matrix is 880336 x 880584 (232.9 MB)

Total sieving time: 64.94 hours.
Total relation processing time: 0.94 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 65.88 hours.
 --------- CPU info (if available) ----------

Apr 16, 2009

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Apr 16, 2009

2·10¹⁹³-1 = 1(9)₁₉₃_<194> = 61 · 3011 · 3019 · 2630399 · 1921011481_<10> · 5467489597378404813936108409_<28> · C142

C142 = P33 · C109

P33 = 394666621455911984281003929471901_<33>

C109 = [3307930204406174659160459281208577919156483154925588805331903346568937950394323661593005058106900251722779881_<109>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 1305529637784949287620571177887970771289520181235731640907698902880282231900498703097479220981210951629363692688397047212888405051383997623781 (142 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1344099513
Step 1 took 4654ms
Step 2 took 2600ms
********** Factor found in step 2: 394666621455911984281003929471901
Found probable prime factor of 33 digits: 394666621455911984281003929471901
Composite cofactor 3307930204406174659160459281208577919156483154925588805331903346568937950394323661593005058106900251722779881 has 109 digits

(8·10¹⁹³+1)/9 = (8)₁₉₂9_<193> = 3 · 2418067 · C187

C187 = P58 · P59 · P71

P58 = 1681578303467735333201104967483311312998583427691180027389_<58>

P59 = 35884535642448250237342854660843058641051045981390093667103_<59>

P71 = 20306424780177190474846958704671361567809643262574547068456307082537867_<71>

Number: 88889_193
N=1225343616600765389446596377587123501111823188920308230898053264431036428255694719361772425231791742314403597155481201704900221111723936087363568901508090124451871252104661683469880265089
  ( 187 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=1681578303467735333201104967483311312998583427691180027389
 r2=35884535642448250237342854660843058641051045981390093667103
 r3=20306424780177190474846958704671361567809643262574547068456307082537867
Version: 
Total time: 208.79 hours.
Scaled time: 499.02 units (timescale=2.390).
Factorization parameters were as follows:
n: 1225343616600765389446596377587123501111823188920308230898053264431036428255694719361772425231791742314403597155481201704900221111723936087363568901508090124451871252104661683469880265089
m: 1000000000000000000000000000000000000000
deg: 5
c5: 2
c0: 25
skew: 1.66
type: snfs
lss: 1
rlim: 12000000
alim: 12000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6000000, 11100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 22616652
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2153331 x 2153578
Total sieving time: 188.60 hours.
Total relation processing time: 6.21 hours.
Matrix solve time: 12.83 hours.
Time per square root: 1.16 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,55,55,2.5,2.5,100000
total time: 208.79 hours.
 --------- CPU info (if available) ----------

Apr 15, 2009 (2nd)

By Jeff Gilchrist / GGNFS, Msieve 1.41 / Apr 15, 2009

(47·10¹⁸²+61)/9 = 5(2)₁₈₁9_<183> = 613 · 3677 · 5851441249_<10> · 530965497313_<12> · 10585881510667_<14> · 2179431821107410771893_<22> · C121

C121 = P44 · P78

P44 = 17506708982877796590471231654665554196604017_<44>

P78 = 184627872613379352806475438960335967278715754772741368162582062046769524215971_<78>

Number: 52229_182
N=3232226435970265846236451757188221400714438709580553767065174279795300964396998306487207820154993202004200696972674155507
  ( 121 digits)
Divisors found:
 r1=17506708982877796590471231654665554196604017 (pp44)
 r2=184627872613379352806475438960335967278715754772741368162582062046769524215971 (pp78)
Version: Msieve-1.41
Total time: 24.87 hours.
Scaled time: 92.16 units (timescale=3.706).
Factorization parameters were as follows:
n: 3232226435970265846236451757188221400714438709580553767065174279795300964396998306487207820154993202004200696972674155507
Y0: -185237779331646459172495
Y1:  7107011474677
c0:  55561197852791414195499475416
c1: -4782340600789847977395504
c2: -149176072421321140560
c3:  896428011026213
c4:  5109382940
c5:  14820
skew: 114386.69
type: gnfs
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved algebraic special-q in [2200000, 4000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 721051 x 721299
Total sieving time: 24.28 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4400000,4400000,27,27,53,53,2.5,2.5,100000
total time: 24.87 hours.
 --------- CPU info (if available) ----------

(43·10¹⁸⁰+11)/9 = 4(7)₁₇₉9_<181> = 3 · 123341 · 44408731 · 85698463 · 4608479822817881_<16> · 101634239042663041733027_<24> · C121

C121 = P59 · P63

P59 = 18676433807687590180365272544953252176843032508168358289251_<59>

P63 = 387850313579850484085035039843960807035642431536398508046292593_<63>

Number: 47779_180
N=7243660708864952842040160790748686888826709453225422267548583677017716601532894954117510926890870537131075823270472817843
  ( 121 digits)
Divisors found:
 r1=18676433807687590180365272544953252176843032508168358289251 (pp59)
 r2=387850313579850484085035039843960807035642431536398508046292593 (pp63)
Version: Msieve-1.41
Total time: 27.88 hours.
Scaled time: 99.14 units (timescale=3.556).
Factorization parameters were as follows:
n: 7243660708864952842040160790748686888826709453225422267548583677017716601532894954117510926890870537131075823270472817843
Y0: -238635564021888899190086
Y1:  10660975489501
c0:  3060659713647717335169676087065
c1:  77381263460365481918711579
c2: -243420606357591876439
c3: -1951509855053695
c4:  3094543218
c5:  9360
skew: 286689.37
type: gnfs
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved algebraic special-q in [2200000, 4200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 733879 x 734127
Total sieving time: 26.99 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.50 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4400000,4400000,27,27,53,53,2.5,2.5,100000
total time: 27.88 hours.
 --------- CPU info (if available) ----------

Apr 15, 2009

By Robert Backstrom / GGNFS, Msieve / Apr 15, 2009

(46·10¹⁶⁴+53)/9 = 5(1)₁₆₃7_<165> = 11² · 9511 · 1759886443463004645030568229_<28> · C132

C132 = P44 · P89

P44 = 11285753184776442856762752555140164277069129_<44>

P89 = 22360863791807806952061637322870117280197298346250658978177527581370911848085145743419727_<89>

Number: n
N=252359189752747203387481007806132642014097328260445368426717671665279502548365537787656106881257387644151261259364816582589241307783
  ( 132 digits)
SNFS difficulty: 166 digits.
Divisors found:

Wed Apr 15 16:30:13 2009  prp44 factor: 11285753184776442856762752555140164277069129
Wed Apr 15 16:30:13 2009  prp89 factor: 22360863791807806952061637322870117280197298346250658978177527581370911848085145743419727
Wed Apr 15 16:30:13 2009  elapsed time 00:57:06 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 28.65 hours.
Scaled time: 74.34 units (timescale=2.595).
Factorization parameters were as follows:
name: KA_5_1_163_7
n: 252359189752747203387481007806132642014097328260445368426717671665279502548365537787656106881257387644151261259364816582589241307783
m: 1000000000000000000000000000000000
deg: 5
c5: 23
c0: 265
skew: 1.63
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2050000, 3645899)
Primes: RFBsize:289774, AFBsize:289682, largePrimes:14524305 encountered
Relations: rels:13480818, finalFF:556526
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1314584 hash collisions in 15355401 relations
Msieve: matrix is 675331 x 675579 (181.4 MB)

Total sieving time: 28.29 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,28,28,56,56,2.4,2.4,100000
total time: 28.65 hours.
 --------- CPU info (if available) ----------

Apr 14, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Apr 14, 2009

(2·10¹⁷¹+7)/9 = (2)₁₇₀3_<171> = 151 · 599 · 4139 · 147729150559_<12> · C151

C151 = P65 · P87

P65 = 25253094403184544346171495882979001456863037424443302102508569041_<65>

P87 = 159113667900210245746532907667701881096819030984060918003028803426828497942798849216147_<87>

Number: n
N=4018112476320963647194617559312925511372532354290249565022495815523720386385026834556628042670177642790261114138766659873405014576266701042753481505027
  ( 151 digits)
SNFS difficulty: 171 digits.
Divisors found:

Tue Apr 14 12:01:12 2009  prp65 factor: 25253094403184544346171495882979001456863037424443302102508569041
Tue Apr 14 12:01:12 2009  prp87 factor: 159113667900210245746532907667701881096819030984060918003028803426828497942798849216147
Tue Apr 14 12:01:12 2009  elapsed time 01:23:33 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 35.03 hours.
Scaled time: 91.29 units (timescale=2.606).
Factorization parameters were as follows:
name: KA_2_170_3
n: 4018112476320963647194617559312925511372532354290249565022495815523720386385026834556628042670177642790261114138766659873405014576266701042753481505027
m: 10000000000000000000000000000000000
deg: 5
c5: 20
c0: 7
skew: 0.81
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 4422959)
Primes: RFBsize:348513, AFBsize:347941, largePrimes:15922524 encountered
Relations: rels:14992231, finalFF:680601
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1379854 hash collisions in 16218455 relations
Msieve: matrix is 860413 x 860661 (232.8 MB)

Total sieving time: 34.59 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 35.03 hours.
 --------- CPU info (if available) ----------

(47·10¹⁶⁴+7)/9 = 5(2)₁₆₃3_<165> = 23 · 43 · 21759131 · 3120834083_<10> · 3374993773673_<13> · C133

C133 = P65 · P69

P65 = 20398266286980159421404905123974135815941181589412331885179004209_<65>

P69 = 112948533588779377061204194941043083851885494268137274349596053865987_<69>

Number: n
N=2303954264867844524330553774540163037301266630240816352596872696898564697965909487259971496062975076341497274290832388187297394939283
  ( 133 digits)
SNFS difficulty: 166 digits.
Divisors found:

Wed Apr 15 00:44:52 2009  prp65 factor: 20398266286980159421404905123974135815941181589412331885179004209
Wed Apr 15 00:44:52 2009  prp69 factor: 112948533588779377061204194941043083851885494268137274349596053865987
Wed Apr 15 00:44:52 2009  elapsed time 01:02:06 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 46.09 hours.
Scaled time: 122.59 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_2_163_3
n: 2303954264867844524330553774540163037301266630240816352596872696898564697965909487259971496062975076341497274290832388187297394939283
m: 1000000000000000000000000000000000
deg: 5
c5: 47
c0: 70
skew: 1.08
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2100000, 4872583)
Primes: RFBsize:296314, AFBsize:296696, largePrimes:16186740 encountered
Relations: rels:15719737, finalFF:550036
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1974808 hash collisions in 17758903 relations
Msieve: matrix is 759246 x 759494 (201.2 MB)

Total sieving time: 45.52 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,56,56,2.4,2.4,100000
total time: 46.09 hours.
 --------- CPU info (if available) ----------

Apr 14, 2009 (4th)

By Wataru Sakai / Msieve / Apr 14, 2009

(82·10¹⁹⁵+71)/9 = 9(1)₁₉₄9_<196> = 11 · C195

C195 = P44 · P53 · P99

P44 = 26817179798988518160368430220371768368944123_<44>

P53 = 41336149253678642884740626247977819067177540825049981_<53>

P99 = 747197718833206552292925059686568743196749345648134372526995569692687022286641164505132635390259683_<99>

Number: 91119_195
N=828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282829
  ( 195 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=26817179798988518160368430220371768368944123
 r2=41336149253678642884740626247977819067177540825049981
 r3=747197718833206552292925059686568743196749345648134372526995569692687022286641164505132635390259683
Version: 
Total time: 729.76 hours.
Scaled time: 1444.92 units (timescale=1.980).
Factorization parameters were as follows:
n: 828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282829
m: 1000000000000000000000000000000000000000
deg: 5
c5: 82
c0: 71
skew: 0.97
type: snfs
lss: 1
rlim: 13400000
alim: 13400000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 13400000/13400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6700000, 15200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2253396 x 2253644
Total sieving time: 729.76 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,13400000,13400000,28,28,55,55,2.5,2.5,100000
total time: 729.76 hours.
 --------- CPU info (if available) ----------

(52·10¹⁸⁶-61)/9 = 5(7)₁₈₅1_<187> = C187

C187 = P52 · P54 · P83

P52 = 1482475847766385096562505037464122985100924080834529_<52>

P54 = 192860932423855597241429916466095224241530870434302299_<54>

P83 = 20208261142197016589293170339084167717687793242636949187506813175574959234255083601_<83>

Number: 57771_186
N=5777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
  ( 187 digits)
SNFS difficulty: 188 digits.
Divisors found:
 r1=1482475847766385096562505037464122985100924080834529
 r2=192860932423855597241429916466095224241530870434302299
 r3=20208261142197016589293170339084167717687793242636949187506813175574959234255083601
Version: 
Total time: 393.88 hours.
Scaled time: 684.17 units (timescale=1.737).
Factorization parameters were as follows:
n: 5777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
m: 20000000000000000000000000000000000000
deg: 5
c5: 65
c0: -244
skew: 1.30
type: snfs
lss: 1
rlim: 9600000
alim: 9600000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 9600000/9600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4800000, 9100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1926902 x 1927149
Total sieving time: 393.88 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,188,5,0,0,0,0,0,0,0,0,9600000,9600000,28,28,54,54,2.5,2.5,100000
total time: 393.88 hours.
 --------- CPU info (if available) ----------

Apr 14, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 14, 2009

(7·10¹⁹⁴+17)/3 = 2(3)₁₉₃9_<195> = 1709 · C192

C192 = P63 · P129

P63 = 346829221976324092618801102438231038737439780793265937700693079_<63>

P129 = 393657963022806093903868529787748043691165968836977987683147655420299632252039577434692218103776328441087411740739267406602236849_<129>

Number: 23339_194
N=136532085039984396333138287497561927052857421494051102008972108445484688901891944606982640920616344841037643846303881412131850984981470645601716403354788375268188024185683635654378779013068071
  ( 192 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=346829221976324092618801102438231038737439780793265937700693079 (pp63)
 r2=393657963022806093903868529787748043691165968836977987683147655420299632252039577434692218103776328441087411740739267406602236849 (pp129)
Version: Msieve-1.39
Total time: 525.40 hours.
Scaled time: 916.30 units (timescale=1.744).
Factorization parameters were as follows:
n: 136532085039984396333138287497561927052857421494051102008972108445484688901891944606982640920616344841037643846303881412131850984981470645601716403354788375268188024185683635654378779013068071
m: 500000000000000000000000000000000000000
deg: 5
c5: 112
c0: 85
skew: 0.95
type: snfs
lss: 1
rlim: 12700000
alim: 12700000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 12700000/12700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6350000, 14950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2537985 x 2538232
Total sieving time: 525.40 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,12700000,12700000,28,28,55,55,2.5,2.5,100000
total time: 525.40 hours.
 --------- CPU info (if available) ----------

(29·10¹⁶⁷+43)/9 = 3(2)₁₆₆7_<168> = 3² · 9067 · 55143554263432152331343_<23> · C140

C140 = P37 · P104

P37 = 4800573794884051481511926497391306549_<37>

P104 = 14916311979172569492728684520219784207270861744830265394871640637715056063809315699069363930229167578787_<104>

Number: 32227_167
N=71606856403530898614318803019976572490320678307484085258590318918033797130638183025963493447882757092868811532376557010544452763536826576063
  ( 140 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=4800573794884051481511926497391306549 (pp37)
 r2=14916311979172569492728684520219784207270861744830265394871640637715056063809315699069363930229167578787 (pp104)
Version: Msieve-1.39
Total time: 59.66 hours.
Scaled time: 103.75 units (timescale=1.739).
Factorization parameters were as follows:
n: 71606856403530898614318803019976572490320678307484085258590318918033797130638183025963493447882757092868811532376557010544452763536826576063
m: 2000000000000000000000000000000000
deg: 5
c5: 725
c0: 344
skew: 0.86
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 5750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 974006 x 974254
Total sieving time: 59.66 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000
total time: 59.66 hours.
 --------- CPU info (if available) ----------

Apr 14, 2009 (2nd)

By Jeff Gilchrist / GGNFS & Msieve 1.41 / Apr 14, 2009

(29·10¹⁷⁰-11)/9 = 3(2)₁₆₉1_<171> = 3² · 257 · 3307 · 22121849 · C157

C157 = P50 · P108

P50 = 12128123182634994286036427814173335412207095123621_<50>

P108 = 157011201819375816815738752111265025210257283065238438120187834665257869938723695758458452814451628310344539_<108>

Number: 32221_170
N=1904251196718953636692162604583969903297314220743772932280383376864559932289145597338154925039823123268209183786578507255925998331853435869770613657307255719
  ( 157 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=12128123182634994286036427814173335412207095123621 (pp50)
 r2=157011201819375816815738752111265025210257283065238438120187834665257869938723695758458452814451628310344539 (pp108)
Version: Msieve-1.41
Total time: 34.88 hours.
Scaled time: 129.51 units (timescale=3.713).
Factorization parameters were as follows:
n: 1904251196718953636692162604583969903297314220743772932280383376864559932289145597338154925039823123268209183786578507255925998331853435869770613657307255719
m: 10000000000000000000000000000000000
deg: 5
c5: 29
c0: -11
skew: 0.82
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 805085 x 805333
Total sieving time: 34.08 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.53 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 34.88 hours.
 --------- CPU info (if available) ----------

(43·10¹⁷⁷-61)/9 = 4(7)₁₇₆1_<178> = 13 · 2593 · 357583 · 127558727 · 458872771789_<12> · 2367916363141745435233386787_<28> · C121

C121 = P44 · P78

P44 = 23458394311309179842266062524539260421928509_<44>

P78 = 121909095092311908628611882099805127119896107845918011449043507752877570553757_<78>

Number: 47771_177
N=2859791622810339532002420199806141256086331750290755724214138455762859858329326969029525125381588126101060803108995358313
  ( 121 digits)
Divisors found:
 r1=23458394311309179842266062524539260421928509 (pp44)
 r2=121909095092311908628611882099805127119896107845918011449043507752877570553757 (pp78)
Version: Msieve-1.41
Total time: 29.33 hours.
Scaled time: 108.98 units (timescale=3.716).
Factorization parameters were as follows:
n: 2859791622810339532002420199806141256086331750290755724214138455762859858329326969029525125381588126101060803108995358313
Y0: -174568903292024692763149
Y1:  10713486627859
c0:  3999749289757025257324102518
c1: -90701164448737131225067
c2: -14051139356920072819
c3: -43072998826651
c4:  920786306
c5:  17640
skew: 58874.87
type: gnfs
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 53/53
Sieved algebraic special-q in [2200000, 4300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 766054 x 766302
Total sieving time: 28.49 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.49 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4400000,4400000,27,27,53,53,2.5,2.5,100000
total time: 29.33 hours.
 --------- CPU info (if available) ----------

Apr 14, 2009

By Andreas Tete / GMP-ECM 6.2.1 / Apr 14, 2009

(46·10¹⁶⁴+71)/9 = 5(1)₁₆₃9_<165> = 3 · 17 · 79 · 179 · 233 · 41244039563019883_<17> · 38761045063606867373_<20> · C121

C121 = P37 · P84

P37 = 2085491164318326769316061631065415687_<37>

P84 = 912313446682833428261016780631623637749006006146390104272853716796969509502773150281_<84>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=983803196
********** Factor found in step 2: 2085491164318326769316061631065415687
Found probable prime factor of 37 digits: 2085491164318326769316061631065415687
Probable prime cofactor 912313446682833428261016780631623637749006006146390104272853716796969509502773150281 has 84 digits

Apr 13, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Apr 13, 2009

(32·10¹⁶⁷+31)/9 = 3(5)₁₆₆9_<168> = 983 · 9337 · 1179789025019489_<16> · C146

C146 = P61 · P85

P61 = 5463215511259409267862691359715547396629804846074347587647637_<61>

P85 = 6010268966830633552407442674646264717255365729873344812447062941431439165340265027253_<85>

Number: n
N=32835394646430181205812761282197698125513991593693821482034452227895325294651015157181683388666833151226627373344575666356437173478223009966051161
  ( 146 digits)
SNFS difficulty: 168 digits.
Divisors found:

Mon Apr 13 20:51:07 2009  prp61 factor: 5463215511259409267862691359715547396629804846074347587647637
Mon Apr 13 20:51:07 2009  prp85 factor: 6010268966830633552407442674646264717255365729873344812447062941431439165340265027253
Mon Apr 13 20:51:07 2009  elapsed time 01:21:47 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 38.37 hours.
Scaled time: 97.99 units (timescale=2.554).
Factorization parameters were as follows:
name: KA_3_5_166_9
n: 32835394646430181205812761282197698125513991593693821482034452227895325294651015157181683388666833151226627373344575666356437173478223009966051161
m: 2000000000000000000000000000000000
deg: 5
c5: 100
c0: 31
skew: 0.79
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2250000, 4453171)
Primes: RFBsize:315948, AFBsize:316592, largePrimes:15819911 encountered
Relations: rels:15045685, finalFF:641270
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1549571 hash collisions in 16281834 relations
Msieve: matrix is 826261 x 826509 (221.8 MB)

Total sieving time: 37.90 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000
total time: 38.37 hours.
 --------- CPU info (if available) ----------

Apr 13, 2009 (2nd)

By Jeff Gilchrist / GGNFS, Msieve 1.41 / Apr 13, 2009

5·10¹⁷⁰-7 = 4(9)₁₆₉3_<171> = 29 · 371840101717736949659_<21> · C149

C149 = P47 · P103

P47 = 36186346361901794734149614174823118926381921601_<47>

P103 = 1281359654549060281898606138184287341774636409267856035278076719876171866019239509683237360176741662263_<103>

Number: 49993_170
N=46367724273679128016875371673688962314473643710346808216784893586777456121488913841522626515505467594301778975907422007305297498445090108152886243063
  ( 149 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=36186346361901794734149614174823118926381921601 (pp47)
 r2=1281359654549060281898606138184287341774636409267856035278076719876171866019239509683237360176741662263 (pp103)
Version: Msieve-1.41
Total time: 33.32 hours.
Scaled time: 122.77 units (timescale=3.685).
Factorization parameters were as follows:
n: 46367724273679128016875371673688962314473643710346808216784893586777456121488913841522626515505467594301778975907422007305297498445090108152886243063
m: 10000000000000000000000000000000000
deg: 5
c5: 5
c0: -7
skew: 1.07
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 5250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 860100 x 860348
Total sieving time: 32.47 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.63 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 33.32 hours.
 --------- CPU info (if available) ----------

3·10¹⁷¹+7 = 3(0)₁₇₀7_<172> = 31620332097111024989233352721851562907652707_<44> · C128

C128 = P54 · P75

P54 = 119542069001731768208656345412449977669924073427695871_<54>

P75 = 793659208661801859516537543036477671956372358203480550399351605739016658931_<75>

Number: 30007_171
N=94875663885708949340722098875716958576811202800602452263648706419261724778781975587671373398601569684090092604704674588003973901
  ( 128 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=119542069001731768208656345412449977669924073427695871 (pp54)
 r2=793659208661801859516537543036477671956372358203480550399351605739016658931 (pp75)
Version: Msieve-1.41
Total time: 44.42 hours.
Scaled time: 163.50 units (timescale=3.681).
Factorization parameters were as follows:
n: 94875663885708949340722098875716958576811202800602452263648706419261724778781975587671373398601569684090092604704674588003973901
m: 10000000000000000000000000000000000
deg: 5
c5: 30
c0: 7
skew: 0.75
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 982062 x 982310
Total sieving time: 43.42 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.84 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 44.42 hours.
 --------- CPU info (if available) ----------

Apr 13, 2009

By Sinkiti Sibata / GGNFS / Apr 13, 2009

(17·10¹⁸⁰+7)/3 = 5(6)₁₇₉9_<181> = 239 · C179

C179 = P48 · P49 · P83

P48 = 554926436167528943257699327435205874475108632793_<48>

P49 = 3523835766306910904207910803375786328587724571921_<49>

P83 = 12124914694059309969702016472528715477560656576791053322559643089873095090003003307_<83>

Number: 56669_180
N=23709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902371
  ( 179 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=554926436167528943257699327435205874475108632793 (pp48)
 r2=3523835766306910904207910803375786328587724571921 (pp49)
 r3=12124914694059309969702016472528715477560656576791053322559643089873095090003003307 (pp83)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 266.79 hours.
Scaled time: 678.70 units (timescale=2.544).
Factorization parameters were as follows:
name: 56669_180
n: 23709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902371
m: 1000000000000000000000000000000000000
deg: 5
c5: 17
c0: 7
skew: 0.84
type: snfs
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved algebraic special-q in [3000000, 6300001)
Primes: RFBsize:412849, AFBsize:413446, largePrimes:18103909 encountered
Relations: rels:19163581, finalFF:1171199
Max relations in full relation-set: 28
Initial matrix: 826360 x 1171199 with sparse part having weight 155619666.
Pruned matrix : 656224 x 660419 with weight 152393023.
Total sieving time: 254.35 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 11.67 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,53,53,2.5,2.5,100000
total time: 266.79 hours.
 --------- CPU info (if available) ----------

Apr 12, 2009 (2nd)

By Jeff Gilchrist / GGNFS & Msieve 1.41 / Apr 12, 2009

(17·10¹⁶⁴-11)/3 = 5(6)₁₆₃3_<165> = 31 · 383069 · 1593268421_<10> · 12235022127066387424376957_<26> · C124

C124 = P42 · P82

P42 = 450081134598038991950517876062431432323767_<42>

P82 = 5438817017371359971306142994586362267552757887934854040958910381842538227187462283_<82>

Number: 56663_164
N=2447908934049624041479766689351333818597811560902790473946582004995814104101521660195361352308148553703338584975482356980061
  ( 124 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=450081134598038991950517876062431432323767 (pp42)
 r2=5438817017371359971306142994586362267552757887934854040958910381842538227187462283 (pp82)
Version: Msieve-1.41
Total time: 21.95 hours.
Scaled time: 80.85 units (timescale=3.683).
Factorization parameters were as follows:
n: 2447908934049624041479766689351333818597811560902790473946582004995814104101521660195361352308148553703338584975482356980061
m: 1000000000000000000000000000000000
deg: 5
c5: 17
c0: -110
skew: 1.45
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 3850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 753801 x 754049
Total sieving time: 21.38 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.46 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,166.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 21.95 hours.
 --------- CPU info (if available) ----------

Apr 12, 2009

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 12, 2009

(52·10¹⁶¹+11)/9 = 5(7)₁₆₀9_<162> = 3² · 8664553 · C154

C154 = P47 · P108

P47 = 18928489948339749847018632028593340878665991563_<47>

P108 = 391431879723808945338088267301885408398292615483568378380918267204298704333073286676905854436479613341848329_<108>

Number: n
N=7409214400811851559358864890571681062392662479437488681089206894365760226084084298889686619055539375683607782674712805634350769647035555578866083939648227
  ( 154 digits)
SNFS difficulty: 163 digits.
Divisors found:

Sun Apr 12 04:53:40 2009  prp47 factor: 18928489948339749847018632028593340878665991563
Sun Apr 12 04:53:40 2009  prp108 factor: 391431879723808945338088267301885408398292615483568378380918267204298704333073286676905854436479613341848329
Sun Apr 12 04:53:40 2009  elapsed time 00:55:48 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 22.58 hours.
Scaled time: 59.57 units (timescale=2.638).
Factorization parameters were as follows:
name: KA_5_7_160_9
n: 7409214400811851559358864890571681062392662479437488681089206894365760226084084298889686619055539375683607782674712805634350769647035555578866083939648227
m: 200000000000000000000000000000000
deg: 5
c5: 65
c0: 44
skew: 0.92
type: snfs
lss: 1
rlim: 3700000
alim: 3700000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3700000/3700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1850000, 3250123)
Primes: RFBsize:263397, AFBsize:263373, largePrimes:13742240 encountered
Relations: rels:12753845, finalFF:533425
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1099106 hash collisions in 13613282 relations
Msieve: matrix is 678552 x 678800 (183.0 MB)

Total sieving time: 22.26 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3700000,3700000,28,28,56,56,2.4,2.4,100000
total time: 22.58 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶²+11)/9 = 5(7)₁₆₁9_<163> = 7 · 23 · C161

C161 = P42 · P120

P42 = 321519970820085608181037744328588516697743_<42>

P120 = 111616141305248804803400290837173564328599235003578090047986807312818902456903064735501933589562639357218054538297354173_<120>

Number: n
N=35886818495514147688060731538992408557625948930296756383712905452035886818495514147688060731538992408557625948930296756383712905452035886818495514147688060731539
  ( 161 digits)
SNFS difficulty: 164 digits.
Divisors found:

Sun Apr 12 06:15:36 2009  prp42 factor: 321519970820085608181037744328588516697743
Sun Apr 12 06:15:36 2009  prp120 factor: 111616141305248804803400290837173564328599235003578090047986807312818902456903064735501933589562639357218054538297354173
Sun Apr 12 06:15:36 2009  elapsed time 00:52:55 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 30.70 hours.
Scaled time: 81.32 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_7_161_9
n: 35886818495514147688060731538992408557625948930296756383712905452035886818495514147688060731538992408557625948930296756383712905452035886818495514147688060731539
m: 200000000000000000000000000000000
deg: 5
c5: 325
c0: 22
skew: 0.58
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved  special-q in [1900000, 3800113)
Primes: RFBsize:269987, AFBsize:269688, largePrimes:8808225 encountered
Relations: rels:8644280, finalFF:545089
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 881198 hash collisions in 9436045 relations
Msieve: matrix is 699430 x 699678 (186.3 MB)

Total sieving time: 30.47 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 30.70 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶³+11)/9 = 5(7)₁₆₂9_<164> = 97 · 87931 · 876568187833930289_<18> · C139

C139 = P54 · P86

P54 = 285499687981964450229006620431228817065494664829635261_<54>

P86 = 27067973613206102904512248875476135325093088787990227833361756111499707732578188978893_<86>

Number: n
N=7727898020874389273633226675969318827671185863144042247840595857996178908012693244379155722125782899946146998056281826623324143363217546073
  ( 139 digits)
SNFS difficulty: 166 digits.
Divisors found:

Sun Apr 12 13:31:34 2009  prp54 factor: 285499687981964450229006620431228817065494664829635261
Sun Apr 12 13:31:34 2009  prp86 factor: 27067973613206102904512248875476135325093088787990227833361756111499707732578188978893
Sun Apr 12 13:31:34 2009  elapsed time 01:05:41 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 30.87 hours.
Scaled time: 82.12 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_7_162_9
n: 7727898020874389273633226675969318827671185863144042247840595857996178908012693244379155722125782899946146998056281826623324143363217546073
m: 1000000000000000000000000000000000
deg: 5
c5: 13
c0: 275
skew: 1.84
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2050000, 3861203)
Primes: RFBsize:289774, AFBsize:290078, largePrimes:14963521 encountered
Relations: rels:14071940, finalFF:586784
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1356936 hash collisions in 15148444 relations
Msieve: matrix is 754434 x 754682 (201.5 MB)

Total sieving time: 30.49 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,28,28,56,56,2.4,2.4,100000
total time: 30.87 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶⁵+11)/9 = 5(7)₁₆₄9_<166> = 17 · 86761097 · 592224781 · 124457150677_<12> · 190862997763738379_<18> · C120

C120 = P39 · P81

P39 = 947603373792569765729573937197287389869_<39>

P81 = 293854339940673288307735977122722469845978112409126167654289550189645063181598133_<81>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 278457363931370693256810083723809311549125447635796682650235234084816134689205258661992118672738189311298709411653514577 (120 digits)
Using B1=2136000, B2=2854078510, polynomial Dickson(6), sigma=2890840773
Step 1 took 23758ms
********** Factor found in step 1: 947603373792569765729573937197287389869
Found probable prime factor of 39 digits: 947603373792569765729573937197287389869
Probable prime cofactor 293854339940673288307735977122722469845978112409126167654289550189645063181598133 has 81 digits

Apr 11, 2009 (2nd)

By Andreas Tete / GMP-ECM 6.2.2 / Apr 11, 2009

(47·10¹⁶⁴+43)/9 = 5(2)₁₆₃7_<165> = 21031 · 56099 · 9480603531462587241575906463236513_<34> · C122

C122 = P37 · P86

P37 = 1925457966905235846156525388783627303_<37>

P86 = 24247684792636549715927770946748662555654899363148036016451038975272737398252341068097_<86>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=17151464
********** Factor found in step 2: 1925457966905235846156525388783627303
Found probable prime factor of 37 digits: 1925457966905235846156525388783627303
Probable prime cofactor 24247684792636549715927770946748662555654899363148036016451038975272737398252341068097 has 86 digits

(49·10¹⁶⁶+23)/9 = 5(4)₁₆₅7_<167> = 3 · 29 · 193 · 955469 · 4188451 · 622422253 · 1830545011_<10> · 15678994369_<11> · C122

C122 = P32 · P91

P32 = 29197910954985748593465543486977_<32>

P91 = 1553357653460083080407321738143405658573231909383968797372397037983792553040705001133212217_<91>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=15830070
********** Factor found in step 2: 29197910954985748593465543486977
Found probable prime factor of 32 digits: 29197910954985748593465543486977
Probable prime cofactor 1553357653460083080407321738143405658573231909383968797372397037983792553040705001133212217 has 91 digits

Apr 11, 2009

By Robert Backstrom / GGNFS / Apr 11, 2009

(52·10¹⁶⁰+11)/9 = 5(7)₁₅₉9_<161> = 3331 · C158

C158 = P40 · P52 · P66

P40 = 1984602862159222328197712995842323139233_<40>

P52 = 8995729372655953524904434979327475766365640628552961_<52>

P66 = 971574720881561621643707317580907592723358162775265761540357497393_<66>

Number: n
N=17345475165949497981920677807798792488074985823409720137429534007138330164448447246405817405517195370092398011941692518096000533706928183061476366790086393809
  ( 158 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=1984602862159222328197712995842323139233 (pp40)
 r2=8995729372655953524904434979327475766365640628552961 (pp52)
 r3=971574720881561621643707317580907592723358162775265761540357497393 (pp66)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 20.60 hours.
Scaled time: 54.79 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_7_159_9
n: 17345475165949497981920677807798792488074985823409720137429534007138330164448447246405817405517195370092398011941692518096000533706928183061476366790086393809
m: 100000000000000000000000000000000
deg: 5
c5: 52
c0: 11
skew: 0.73
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [1750000, 2850001)
Primes: RFBsize:250150, AFBsize:249882, largePrimes:13781805 encountered
Relations: rels:13310814, finalFF:645052
Max relations in full relation-set: 28
Initial matrix: 500100 x 645052 with sparse part having weight 68070186.
Pruned matrix : 420473 x 423037 with weight 45366021.
Total sieving time: 18.84 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 1.15 hours.
Total square root time: 0.31 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,56,56,2.4,2.4,100000
total time: 20.60 hours.
 --------- CPU info (if available) ----------

Apr 10, 2009 (4th)

By Sinkiti Sibata / Msieve / Apr 10, 2009

(52·10¹⁵¹+11)/9 = 5(7)₁₅₀9_<152> = C152

C152 = P64 · P89

P64 = 3953535681244358031390387279802526646473653843971170017410808979_<64>

P89 = 14614204205080672347139781653275652403689134613732690915539647764779044145671465056087201_<89>

Number: 57779_151
N=57777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
  ( 152 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=3953535681244358031390387279802526646473653843971170017410808979 (pp64)
 r2=14614204205080672347139781653275652403689134613732690915539647764779044145671465056087201 (pp89)
Version: Msieve-1.40
Total time: 15.17 hours.
Scaled time: 39.07 units (timescale=2.575).
Factorization parameters were as follows:
name: 57779_151
n: 57777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
m: 2000000000000000000000000000000
deg: 5
c5: 65
c0: 44
skew: 0.92
type: snfs
lss: 1
rlim: 2500000
alim: 2500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1250000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 416304 x 416552
Total sieving time: 15.17 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,153.000,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000
total time: 15.17 hours.
 --------- CPU info (if available) ----------

Apr 10, 2009 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Apr 10, 2009

(52·10¹⁵⁴+11)/9 = 5(7)₁₅₃9_<155> = 1009 · 1873 · 1780071853727_<13> · C137

C137 = P41 · P96

P41 = 93050385464681516500046281914738043499239_<41>

P96 = 184576404077904571046705571397602099672425078097604346576358124523939748687222923404111884169099_<96>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 17174905547133833686201829165853188941164294376020559094629779979976178551279987548468323356118519181871603715021418206048713273953815661 (137 digits)
Using B1=1262000, B2=1426326730, polynomial Dickson(6), sigma=2614469203
Step 1 took 17378ms
Step 2 took 6412ms
********** Factor found in step 2: 93050385464681516500046281914738043499239
Found probable prime factor of 41 digits: 93050385464681516500046281914738043499239
Probable prime cofactor 184576404077904571046705571397602099672425078097604346576358124523939748687222923404111884169099 has 96 digits

(52·10¹⁶⁶+11)/9 = 5(7)₁₆₅9_<167> = 19 · 313 · 1543 · 83115250284832640411_<20> · 12632594670057892169047869846613_<32> · C109

C109 = P47 · P63

P47 = 42691128655357150982468169102793571554807074883_<47>

P63 = 140470799532314444373497792586935413113578875626021083297673571_<63>

Number: n
N=5996856975154919058724890468413883408998447325094790249647861377749782830297948367090644019881202485487017193
  ( 109 digits)
Divisors found:
 r1=42691128655357150982468169102793571554807074883 (pp47)
 r2=140470799532314444373497792586935413113578875626021083297673571 (pp63)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 13.47 hours.
Scaled time: 35.25 units (timescale=2.616).
Factorization parameters were as follows:
name: KA_5_7_165_9
n:5996856975154919058724890468413883408998447325094790249647861377749782830297948367090644019881202485487017193
Y0: -1067795297988797501616
Y1:  164264666753
c0:  8530558915607398247347346489
c1:  242316730277730117495673
c2: -1667914485931205175
c3: -70391702544601
c4: -4927106
c5:  4320
skew: 77192.47
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1600000, 2900001)
Primes: RFBsize:230209, AFBsize:230575, largePrimes:16977985 encountered
Relations: rels:15492064, finalFF:690402
Max relations in full relation-set: 28
Initial matrix: 460861 x 690402 with sparse part having weight 64012452.
Pruned matrix : 306082 x 308450 with weight 37318507.
Total sieving time: 11.29 hours.
Total relation processing time: 0.51 hours.
Matrix solve time: 0.52 hours.
Total square root time: 1.16 hours, sqrts: 5.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000
total time: 13.47 hours.
 --------- CPU info (if available) ----------

(41·10¹⁶⁶-23)/9 = 4(5)₁₆₅3_<167> = 439 · 2586919225049507147_<19> · C146

C146 = P52 · P95

P52 = 1065505954138455564238719164964882682924840493039843_<52>

P95 = 37647667807395859819607873997112941704493623479901923145975021806996208571696732038445830885287_<95>

Number: n
N=40113814208206942961286412653651200042765317891904117999505219090653791939685124936497665627919725179282174773415014399429404984085252766453489941
  ( 146 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Apr 10 12:32:01 2009  prp52 factor: 1065505954138455564238719164964882682924840493039843
Fri Apr 10 12:32:01 2009  prp95 factor: 37647667807395859819607873997112941704493623479901923145975021806996208571696732038445830885287
Fri Apr 10 12:32:01 2009  elapsed time 01:07:27 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 44.86 hours.
Scaled time: 115.97 units (timescale=2.585).
Factorization parameters were as follows:
name: KA_4_5_165_3
n: 40113814208206942961286412653651200042765317891904117999505219090653791939685124936497665627919725179282174773415014399429404984085252766453489941
m: 1000000000000000000000000000000000
deg: 5
c5: 410
c0: -23
skew: 0.56
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2200000, 4801133)
Primes: RFBsize:309335, AFBsize:309429, largePrimes:16673429 encountered
Relations: rels:16590378, finalFF:596243
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1931330 hash collisions in 18160482 relations
Msieve: matrix is 738140 x 738388 (196.1 MB)

Total sieving time: 44.21 hours.
Total relation processing time: 0.65 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,4400000,4400000,28,28,56,56,2.4,2.4,100000
total time: 44.86 hours.
 --------- CPU info (if available) ----------

Apr 10, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 10, 2009

(52·10¹⁵³+11)/9 = 5(7)₁₅₂9_<154> = 29 · 40543 · 710027 · 470818507 · C134

C134 = P35 · P99

P35 = 19627040332408708604436682113596563_<35>

P99 = 748968841027261409761188316700947313844944317053127062144103065053216914230007485726769694669513251_<99>

Number: 57779_153
N=14700041650559466010672832813381002063469358855134283947591049880295228687855696994256445000105441634400101420815978396489308196556313
  ( 134 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=19627040332408708604436682113596563
 r2=748968841027261409761188316700947313844944317053127062144103065053216914230007485726769694669513251
Version: 
Total time: 9.99 hours.
Scaled time: 23.80 units (timescale=2.383).
Factorization parameters were as follows:
n: 14700041650559466010672832813381002063469358855134283947591049880295228687855696994256445000105441634400101420815978396489308196556313
m: 10000000000000000000000000000000
deg: 5
c5: 13
c0: 275
skew: 1.84
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7814054
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 480721 x 480969
Total sieving time: 9.06 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.51 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 9.99 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 10, 2009

By Andreas Tete / Msieve v1.41, GGNFS / Apr 10, 2009

(52·10¹⁷²+11)/9 = 5(7)₁₇₁9_<173> = 3951719 · 13380499109519_<14> · 36282474114511_<14> · 309043953890409714925505897364313_<33> · C107

C107 = P51 · P57

P51 = 118145920262199525963524190015546715838352113676563_<51>

P57 = 824834068673450927934822305182677949265824343092447793071_<57>

Thu Apr 09 17:24:45 2009  Msieve v. 1.41
Thu Apr 09 17:24:45 2009  random seeds: ae9280b0 10196da0
Thu Apr 09 17:24:45 2009  factoring 97450780107039141260457072613462534480633327041513829548037360610763669539962170088778288463915365246494973 (107 digits)
Thu Apr 09 17:24:47 2009  searching for 15-digit factors
Thu Apr 09 17:24:49 2009  commencing number field sieve (107-digit input)
Thu Apr 09 17:24:49 2009  R0: -583560684231641996834
Thu Apr 09 17:24:49 2009  R1:  78488406179
Thu Apr 09 17:24:49 2009  A0: -27278358361861303319170275
Thu Apr 09 17:24:50 2009  A1:  3917602922717724100809
Thu Apr 09 17:24:50 2009  A2:  311529443604860231
Thu Apr 09 17:24:50 2009  A3: -1660678779952
Thu Apr 09 17:24:50 2009  A4: -179866821
Thu Apr 09 17:24:50 2009  A5:  1440
Thu Apr 09 17:24:50 2009  skew 39860.96, size 3.272186e-010, alpha -4.805594, combined = 1.441065e-009
Thu Apr 09 17:24:50 2009  
Thu Apr 09 17:24:50 2009  commencing relation filtering
Thu Apr 09 17:24:50 2009  commencing duplicate removal, pass 1
Thu Apr 09 17:26:03 2009  found 423914 hash collisions in 5084040 relations
Thu Apr 09 17:26:30 2009  added 34695 free relations
Thu Apr 09 17:26:30 2009  commencing duplicate removal, pass 2
Thu Apr 09 17:26:42 2009  found 407648 duplicates and 4711086 unique relations
Thu Apr 09 17:26:42 2009  memory use: 41.3 MB
Thu Apr 09 17:26:42 2009  reading rational ideals above 2949120
Thu Apr 09 17:26:42 2009  reading algebraic ideals above 2949120
Thu Apr 09 17:26:42 2009  commencing singleton removal, pass 1
Thu Apr 09 17:27:46 2009  relations with 0 large ideals: 116858
Thu Apr 09 17:27:46 2009  relations with 1 large ideals: 738043
Thu Apr 09 17:27:46 2009  relations with 2 large ideals: 1692634
Thu Apr 09 17:27:46 2009  relations with 3 large ideals: 1613036
Thu Apr 09 17:27:46 2009  relations with 4 large ideals: 515175
Thu Apr 09 17:27:46 2009  relations with 5 large ideals: 2472
Thu Apr 09 17:27:46 2009  relations with 6 large ideals: 32868
Thu Apr 09 17:27:46 2009  relations with 7+ large ideals: 0
Thu Apr 09 17:27:46 2009  4711086 relations and about 4612394 large ideals
Thu Apr 09 17:27:46 2009  commencing singleton removal, pass 2
Thu Apr 09 17:28:51 2009  found 2070067 singletons
Thu Apr 09 17:28:51 2009  current dataset: 2641019 relations and about 2113480 large ideals
Thu Apr 09 17:28:51 2009  commencing singleton removal, pass 3
Thu Apr 09 17:29:29 2009  found 489447 singletons
Thu Apr 09 17:29:29 2009  current dataset: 2151572 relations and about 1588891 large ideals
Thu Apr 09 17:29:29 2009  commencing singleton removal, final pass
Thu Apr 09 17:30:04 2009  memory use: 33.4 MB
Thu Apr 09 17:30:04 2009  commencing in-memory singleton removal
Thu Apr 09 17:30:04 2009  begin with 2151572 relations and 1635870 unique ideals
Thu Apr 09 17:30:08 2009  reduce to 1811566 relations and 1286231 ideals in 14 passes
Thu Apr 09 17:30:08 2009  max relations containing the same ideal: 42
Thu Apr 09 17:30:08 2009  reading rational ideals above 100000
Thu Apr 09 17:30:08 2009  reading algebraic ideals above 100000
Thu Apr 09 17:30:08 2009  commencing singleton removal, final pass
Thu Apr 09 17:30:48 2009  keeping 1637389 ideals with weight <= 25, new excess is 128075
Thu Apr 09 17:30:52 2009  memory use: 47.7 MB
Thu Apr 09 17:30:52 2009  commencing in-memory singleton removal
Thu Apr 09 17:30:53 2009  begin with 1820656 relations and 1637389 unique ideals
Thu Apr 09 17:30:56 2009  reduce to 1801170 relations and 1573710 ideals in 11 passes
Thu Apr 09 17:30:56 2009  max relations containing the same ideal: 25
Thu Apr 09 17:30:58 2009  removing 290398 relations and 250951 ideals in 39447 cliques
Thu Apr 09 17:30:58 2009  commencing in-memory singleton removal
Thu Apr 09 17:30:58 2009  begin with 1510772 relations and 1573710 unique ideals
Thu Apr 09 17:31:01 2009  reduce to 1480022 relations and 1291204 ideals in 9 passes
Thu Apr 09 17:31:01 2009  max relations containing the same ideal: 25
Thu Apr 09 17:31:02 2009  removing 217191 relations and 177744 ideals in 39447 cliques
Thu Apr 09 17:31:02 2009  commencing in-memory singleton removal
Thu Apr 09 17:31:02 2009  begin with 1262831 relations and 1291204 unique ideals
Thu Apr 09 17:31:04 2009  reduce to 1240337 relations and 1090388 ideals in 8 passes
Thu Apr 09 17:31:04 2009  max relations containing the same ideal: 25
Thu Apr 09 17:31:05 2009  relations with 0 large ideals: 5419
Thu Apr 09 17:31:05 2009  relations with 1 large ideals: 46967
Thu Apr 09 17:31:05 2009  relations with 2 large ideals: 172417
Thu Apr 09 17:31:05 2009  relations with 3 large ideals: 329391
Thu Apr 09 17:31:05 2009  relations with 4 large ideals: 356668
Thu Apr 09 17:31:05 2009  relations with 5 large ideals: 223079
Thu Apr 09 17:31:05 2009  relations with 6 large ideals: 85257
Thu Apr 09 17:31:05 2009  relations with 7+ large ideals: 21139
Thu Apr 09 17:31:05 2009  commencing 2-way merge
Thu Apr 09 17:31:07 2009  reduce to 751009 relation sets and 601060 unique ideals
Thu Apr 09 17:31:07 2009  commencing full merge
Thu Apr 09 17:31:23 2009  memory use: 50.7 MB
Thu Apr 09 17:31:24 2009  found 355008 cycles, need 335260
Thu Apr 09 17:31:24 2009  weight of 335260 cycles is about 23712374 (70.73/cycle)
Thu Apr 09 17:31:24 2009  distribution of cycle lengths:
Thu Apr 09 17:31:24 2009  1 relations: 32881
Thu Apr 09 17:31:24 2009  2 relations: 33611
Thu Apr 09 17:31:24 2009  3 relations: 33970
Thu Apr 09 17:31:24 2009  4 relations: 31832
Thu Apr 09 17:31:24 2009  5 relations: 30348
Thu Apr 09 17:31:24 2009  6 relations: 26986
Thu Apr 09 17:31:24 2009  7 relations: 24661
Thu Apr 09 17:31:24 2009  8 relations: 21895
Thu Apr 09 17:31:24 2009  9 relations: 19028
Thu Apr 09 17:31:24 2009  10+ relations: 80048
Thu Apr 09 17:31:24 2009  heaviest cycle: 19 relations
Thu Apr 09 17:31:24 2009  commencing cycle optimization
Thu Apr 09 17:31:25 2009  start with 2173536 relations
Thu Apr 09 17:31:35 2009  pruned 66094 relations
Thu Apr 09 17:31:35 2009  memory use: 55.2 MB
Thu Apr 09 17:31:35 2009  distribution of cycle lengths:
Thu Apr 09 17:31:35 2009  1 relations: 32881
Thu Apr 09 17:31:35 2009  2 relations: 34444
Thu Apr 09 17:31:35 2009  3 relations: 35444
Thu Apr 09 17:31:35 2009  4 relations: 32852
Thu Apr 09 17:31:35 2009  5 relations: 31506
Thu Apr 09 17:31:35 2009  6 relations: 27645
Thu Apr 09 17:31:35 2009  7 relations: 25198
Thu Apr 09 17:31:35 2009  8 relations: 22193
Thu Apr 09 17:31:35 2009  9 relations: 19286
Thu Apr 09 17:31:35 2009  10+ relations: 73811
Thu Apr 09 17:31:35 2009  heaviest cycle: 19 relations
Thu Apr 09 17:31:36 2009  RelProcTime: 305
Thu Apr 09 17:31:36 2009  
Thu Apr 09 17:31:36 2009  commencing linear algebra
Thu Apr 09 17:31:36 2009  read 335260 cycles
Thu Apr 09 17:31:37 2009  cycles contain 1123030 unique relations
Thu Apr 09 17:31:54 2009  read 1123030 relations
Thu Apr 09 17:31:57 2009  using 20 quadratic characters above 87500574
Thu Apr 09 17:32:07 2009  building initial matrix
Thu Apr 09 17:32:32 2009  memory use: 125.5 MB
Thu Apr 09 17:32:33 2009  read 335260 cycles
Thu Apr 09 17:32:34 2009  matrix is 335062 x 335260 (94.9 MB) with weight 31928740 (95.24/col)
Thu Apr 09 17:32:34 2009  sparse part has weight 22524397 (67.18/col)
Thu Apr 09 17:32:41 2009  filtering completed in 2 passes
Thu Apr 09 17:32:41 2009  matrix is 333741 x 333937 (94.7 MB) with weight 31851832 (95.38/col)
Thu Apr 09 17:32:41 2009  sparse part has weight 22487289 (67.34/col)
Thu Apr 09 17:32:42 2009  read 333937 cycles
Thu Apr 09 17:32:43 2009  matrix is 333741 x 333937 (94.7 MB) with weight 31851832 (95.38/col)
Thu Apr 09 17:32:43 2009  sparse part has weight 22487289 (67.34/col)
Thu Apr 09 17:32:43 2009  saving the first 48 matrix rows for later
Thu Apr 09 17:32:44 2009  matrix is 333693 x 333937 (91.4 MB) with weight 25249537 (75.61/col)
Thu Apr 09 17:32:44 2009  sparse part has weight 21955093 (65.75/col)
Thu Apr 09 17:32:44 2009  matrix includes 64 packed rows
Thu Apr 09 17:32:44 2009  using block size 65536 for processor cache size 3072 kB
Thu Apr 09 17:32:49 2009  commencing Lanczos iteration
Thu Apr 09 17:32:49 2009  memory use: 88.4 MB
Thu Apr 09 17:49:15 2009  lanczos halted after 5279 iterations (dim = 333693)
Thu Apr 09 17:49:16 2009  recovered 33 nontrivial dependencies
Thu Apr 09 17:49:16 2009  BLanczosTime: 1060
Thu Apr 09 17:49:16 2009  
Thu Apr 09 17:49:16 2009  commencing square root phase
Thu Apr 09 17:49:16 2009  reading relations for dependency 1
Thu Apr 09 17:49:17 2009  read 166851 cycles
Thu Apr 09 17:49:17 2009  cycles contain 696453 unique relations
Thu Apr 09 17:49:26 2009  read 696453 relations
Thu Apr 09 17:49:29 2009  multiplying 561498 relations
Thu Apr 09 17:50:54 2009  multiply complete, coefficients have about 21.70 million bits
Thu Apr 09 17:50:55 2009  initial square root is modulo 1709443
Thu Apr 09 17:52:58 2009  reading relations for dependency 2
Thu Apr 09 17:52:58 2009  read 167207 cycles
Thu Apr 09 17:52:59 2009  cycles contain 697067 unique relations
Thu Apr 09 17:53:07 2009  read 697067 relations
Thu Apr 09 17:53:11 2009  multiplying 561526 relations
Thu Apr 09 17:54:35 2009  multiply complete, coefficients have about 21.70 million bits
Thu Apr 09 17:54:36 2009  initial square root is modulo 1712237
Thu Apr 09 17:56:39 2009  sqrtTime: 443
Thu Apr 09 17:56:39 2009  prp51 factor: 118145920262199525963524190015546715838352113676563
Thu Apr 09 17:56:39 2009  prp57 factor: 824834068673450927934822305182677949265824343092447793071
Thu Apr 09 17:56:39 2009  elapsed time 00:31:54
total time for Polysearch + Sieving + factorization ~ 10 hours

Apr 9, 2009 (4th)

By Robert Backstrom / GGNFS / Apr 9, 2009

(52·10¹⁴⁰+11)/9 = 5(7)₁₃₉9_<141> = 3 · 23 · 113 · 1439 · 2821728461_<10> · C125

C125 = P43 · P82

P43 = 1858703100709054768133619754033983334336277_<43>

P82 = 9818547917634304819287024108448651704534852780908499389251702140960977795402014729_<82>

Number: n
N=18249765458967315251100758570354262987161550021582943083881949385207687813350351661755670150068944041437021726912929793023933
  ( 125 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=1858703100709054768133619754033983334336277 (pp43)
 r2=9818547917634304819287024108448651704534852780908499389251702140960977795402014729 (pp82)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 3.60 hours.
Scaled time: 9.55 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_7_139_9
n: 18249765458967315251100758570354262987161550021582943083881949385207687813350351661755670150068944041437021726912929793023933
m: 10000000000000000000000000000
deg: 5
c5: 52
c0: 11
skew: 0.73
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 100000
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [800000, 1400001)
Primes: RFBsize:121127, AFBsize:120941, largePrimes:5917320 encountered
Relations: rels:5319702, finalFF:317067
Max relations in full relation-set: 28
Initial matrix: 242136 x 317067 with sparse part having weight 24371004.
Pruned matrix : 208945 x 210219 with weight 12742149.
Total sieving time: 3.16 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.11 hours.
Total square root time: 0.24 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,56,56,2.3,2.3,100000
total time: 3.60 hours.
 --------- CPU info (if available) ----------

(52·10¹³⁹+11)/9 = 5(7)₁₃₈9_<140> = 353 · 2894867749_<10> · C128

C128 = P60 · P69

P60 = 106562174939360003911367421423355456729232756135646331248841_<60>

P69 = 530584214402232516348340135462445847762080807588416523417975808079327_<69>

Number: n
N=56540207875193597111760613217706491076129293855908752726056959507882390115350784593308042957937614467659848751785382557504810007
  ( 128 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=106562174939360003911367421423355456729232756135646331248841 (pp60)
 r2=530584214402232516348340135462445847762080807588416523417975808079327 (pp69)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 4.78 hours.
Scaled time: 12.72 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_7_138_9
n: 56540207875193597111760613217706491076129293855908752726056959507882390115350784593308042957937614467659848751785382557504810007
m: 10000000000000000000000000000
deg: 5
c5: 26
c0: 55
skew: 1.16
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.3
alambda: 2.3
qintsize: 100000
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved rational special-q in [800000, 1700001)
Primes: RFBsize:121127, AFBsize:121466, largePrimes:6325858 encountered
Relations: rels:5753045, finalFF:323128
Max relations in full relation-set: 28
Initial matrix: 242659 x 323128 with sparse part having weight 28887173.
Pruned matrix : 217171 x 218448 with weight 16093286.
Total sieving time: 4.48 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.15 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,56,56,2.3,2.3,100000
total time: 4.78 hours.
 --------- CPU info (if available) ----------

Apr 9, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 9, 2009

(52·10¹⁴⁴+11)/9 = 5(7)₁₄₃9_<145> = 7 · 103 · 167 · 653 · 2954611865092757_<16> · C122

C122 = P39 · P83

P39 = 724290725579767305836091030202155649537_<39>

P83 = 34338597671396579436444177778028131407510991420689462672723960428011307199603139061_<83>

Number: 57779_144
N=24871127822807536540677308893737853256793987719707497098779318903928078213373681114319761189526515069860939915500591264757
  ( 122 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=724290725579767305836091030202155649537
 r2=34338597671396579436444177778028131407510991420689462672723960428011307199603139061
Version: 
Total time: 5.51 hours.
Scaled time: 13.14 units (timescale=2.384).
Factorization parameters were as follows:
n: 24871127822807536540677308893737853256793987719707497098779318903928078213373681114319761189526515069860939915500591264757
m: 100000000000000000000000000000
deg: 5
c5: 26
c0: 55
skew: 1.16
type: snfs
lss: 1
rlim: 1350000
alim: 1350000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1350000/1350000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [675000, 1275001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4442108
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 236109 x 236357
Total sieving time: 5.21 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1350000,1350000,27,27,49,49,2.3,2.3,75000
total time: 5.51 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(52·10¹⁴⁵+11)/9 = 5(7)₁₄₄9_<146> = 223 · 145617467609_<12> · C133

C133 = P35 · P45 · P53

P35 = 56954380313470557383476264133069369_<35>

P45 = 877944135394782865480706076381912796258246379_<45>

P53 = 35583485323197678203373839989701525841764457126274647_<53>

Number: 57779_145
N=1779272625363021460612243496577185608423839199881627329550077736603303475175902484372231463577430300728043315288438234114262937132597
  ( 133 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=56954380313470557383476264133069369
 r2=877944135394782865480706076381912796258246379
 r3=35583485323197678203373839989701525841764457126274647
Version: 
Total time: 4.23 hours.
Scaled time: 10.09 units (timescale=2.384).
Factorization parameters were as follows:
n: 1779272625363021460612243496577185608423839199881627329550077736603303475175902484372231463577430300728043315288438234114262937132597
m: 100000000000000000000000000000
deg: 5
c5: 52
c0: 11
skew: 0.73
type: snfs
lss: 1
rlim: 1350000
alim: 1350000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1350000/1350000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [675000, 1125001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4184175
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 215777 x 216025
Total sieving time: 3.95 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1350000,1350000,27,27,49,49,2.3,2.3,75000
total time: 4.23 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 9, 2009 (2nd)

By Andreas Tete / Msieve v1.41, GGNFS / Apr 9, 2009

(52·10¹⁴²+11)/9 = 5(7)₁₄₁9_<143> = 33937 · 58603297 · 850234538894121437711_<21> · C110

C110 = P31 · P80

P31 = 3343047086365563711398608131791_<31>

P80 = 10220781380272666838366366338702762386870049984758453088533674483692999433547011_<80>

Thu Apr 09 03:03:15 2009  Msieve v. 1.41
Thu Apr 09 03:03:15 2009  random seeds: 0244d728 35297466
Thu Apr 09 03:03:15 2009  factoring 34168553413699943534215778841743330944560565854995941012155248657561572877659329534745682232709216307282126701 (110 digits)
Thu Apr 09 03:03:16 2009  searching for 15-digit factors
Thu Apr 09 03:03:18 2009  commencing number field sieve (110-digit input)
Thu Apr 09 03:03:18 2009  R0: -1700913657140603924940
Thu Apr 09 03:03:18 2009  R1:  198739532677
Thu Apr 09 03:03:18 2009  A0:  2785491139512664258540157293
Thu Apr 09 03:03:18 2009  A1:  403368444129627968520825
Thu Apr 09 03:03:18 2009  A2:  728029085584517419
Thu Apr 09 03:03:18 2009  A3: -89078160501357
Thu Apr 09 03:03:18 2009  A4:  189651940
Thu Apr 09 03:03:18 2009  A5:  2400
Thu Apr 09 03:03:18 2009  skew 104086.27, size 1.972286e-010, alpha -6.860694, combined = 1.100483e-009
Thu Apr 09 03:03:19 2009  
Thu Apr 09 03:03:19 2009  commencing relation filtering
Thu Apr 09 03:03:19 2009  commencing duplicate removal, pass 1
Thu Apr 09 03:04:30 2009  found 550305 hash collisions in 5661426 relations
Thu Apr 09 03:04:47 2009  added 42618 free relations
Thu Apr 09 03:04:47 2009  commencing duplicate removal, pass 2
Thu Apr 09 03:05:13 2009  found 539667 duplicates and 5164376 unique relations
Thu Apr 09 03:05:13 2009  memory use: 41.3 MB
Thu Apr 09 03:05:13 2009  reading rational ideals above 3080192
Thu Apr 09 03:05:13 2009  reading algebraic ideals above 3080192
Thu Apr 09 03:05:13 2009  commencing singleton removal, pass 1
Thu Apr 09 03:06:09 2009  relations with 0 large ideals: 111892
Thu Apr 09 03:06:09 2009  relations with 1 large ideals: 725947
Thu Apr 09 03:06:09 2009  relations with 2 large ideals: 1725109
Thu Apr 09 03:06:09 2009  relations with 3 large ideals: 1771461
Thu Apr 09 03:06:09 2009  relations with 4 large ideals: 711542
Thu Apr 09 03:06:09 2009  relations with 5 large ideals: 76946
Thu Apr 09 03:06:09 2009  relations with 6 large ideals: 41477
Thu Apr 09 03:06:09 2009  relations with 7+ large ideals: 2
Thu Apr 09 03:06:09 2009  5164376 relations and about 5234055 large ideals
Thu Apr 09 03:06:09 2009  commencing singleton removal, pass 2
Thu Apr 09 03:07:05 2009  found 2269372 singletons
Thu Apr 09 03:07:05 2009  current dataset: 2895004 relations and about 2370513 large ideals
Thu Apr 09 03:07:05 2009  commencing singleton removal, pass 3
Thu Apr 09 03:07:46 2009  found 592847 singletons
Thu Apr 09 03:07:46 2009  current dataset: 2302157 relations and about 1730815 large ideals
Thu Apr 09 03:07:46 2009  commencing singleton removal, pass 4
Thu Apr 09 03:08:23 2009  found 185711 singletons
Thu Apr 09 03:08:23 2009  current dataset: 2116446 relations and about 1539384 large ideals
Thu Apr 09 03:08:23 2009  commencing singleton removal, final pass
Thu Apr 09 03:09:01 2009  memory use: 33.3 MB
Thu Apr 09 03:09:01 2009  commencing in-memory singleton removal
Thu Apr 09 03:09:01 2009  begin with 2116446 relations and 1590336 unique ideals
Thu Apr 09 03:09:03 2009  reduce to 1885716 relations and 1355557 ideals in 14 passes
Thu Apr 09 03:09:03 2009  max relations containing the same ideal: 39
Thu Apr 09 03:09:03 2009  reading rational ideals above 720000
Thu Apr 09 03:09:03 2009  reading algebraic ideals above 720000
Thu Apr 09 03:09:03 2009  commencing singleton removal, final pass
Thu Apr 09 03:09:43 2009  keeping 1723978 ideals with weight <= 20, new excess is 193681
Thu Apr 09 03:09:45 2009  memory use: 47.9 MB
Thu Apr 09 03:09:45 2009  commencing in-memory singleton removal
Thu Apr 09 03:09:45 2009  begin with 1905859 relations and 1723978 unique ideals
Thu Apr 09 03:09:47 2009  reduce to 1875377 relations and 1595193 ideals in 11 passes
Thu Apr 09 03:09:47 2009  max relations containing the same ideal: 20
Thu Apr 09 03:09:48 2009  removing 235209 relations and 207452 ideals in 27757 cliques
Thu Apr 09 03:09:48 2009  commencing in-memory singleton removal
Thu Apr 09 03:09:48 2009  begin with 1640168 relations and 1595193 unique ideals
Thu Apr 09 03:09:50 2009  reduce to 1620757 relations and 1367935 ideals in 8 passes
Thu Apr 09 03:09:50 2009  max relations containing the same ideal: 20
Thu Apr 09 03:09:51 2009  removing 174444 relations and 146687 ideals in 27757 cliques
Thu Apr 09 03:09:51 2009  commencing in-memory singleton removal
Thu Apr 09 03:09:51 2009  begin with 1446313 relations and 1367935 unique ideals
Thu Apr 09 03:09:52 2009  reduce to 1432880 relations and 1207596 ideals in 7 passes
Thu Apr 09 03:09:52 2009  max relations containing the same ideal: 20
Thu Apr 09 03:09:53 2009  relations with 0 large ideals: 15040
Thu Apr 09 03:09:53 2009  relations with 1 large ideals: 103426
Thu Apr 09 03:09:53 2009  relations with 2 large ideals: 299605
Thu Apr 09 03:09:53 2009  relations with 3 large ideals: 441521
Thu Apr 09 03:09:53 2009  relations with 4 large ideals: 358753
Thu Apr 09 03:09:53 2009  relations with 5 large ideals: 163345
Thu Apr 09 03:09:53 2009  relations with 6 large ideals: 44150
Thu Apr 09 03:09:53 2009  relations with 7+ large ideals: 7040
Thu Apr 09 03:09:53 2009  commencing 2-way merge
Thu Apr 09 03:09:54 2009  reduce to 864816 relation sets and 639532 unique ideals
Thu Apr 09 03:09:54 2009  commencing full merge
Thu Apr 09 03:10:04 2009  memory use: 49.4 MB
Thu Apr 09 03:10:05 2009  found 403958 cycles, need 375732
Thu Apr 09 03:10:05 2009  weight of 375732 cycles is about 26631272 (70.88/cycle)
Thu Apr 09 03:10:05 2009  distribution of cycle lengths:
Thu Apr 09 03:10:05 2009  1 relations: 40847
Thu Apr 09 03:10:05 2009  2 relations: 37918
Thu Apr 09 03:10:05 2009  3 relations: 37801
Thu Apr 09 03:10:05 2009  4 relations: 35042
Thu Apr 09 03:10:05 2009  5 relations: 32630
Thu Apr 09 03:10:05 2009  6 relations: 29567
Thu Apr 09 03:10:05 2009  7 relations: 26654
Thu Apr 09 03:10:05 2009  8 relations: 23522
Thu Apr 09 03:10:05 2009  9 relations: 20609
Thu Apr 09 03:10:05 2009  10+ relations: 91142
Thu Apr 09 03:10:05 2009  heaviest cycle: 20 relations
Thu Apr 09 03:10:05 2009  commencing cycle optimization
Thu Apr 09 03:10:05 2009  start with 2428548 relations
Thu Apr 09 03:10:12 2009  pruned 77505 relations
Thu Apr 09 03:10:12 2009  memory use: 61.7 MB
Thu Apr 09 03:10:12 2009  distribution of cycle lengths:
Thu Apr 09 03:10:12 2009  1 relations: 40847
Thu Apr 09 03:10:12 2009  2 relations: 39017
Thu Apr 09 03:10:12 2009  3 relations: 39486
Thu Apr 09 03:10:12 2009  4 relations: 36367
Thu Apr 09 03:10:12 2009  5 relations: 33787
Thu Apr 09 03:10:12 2009  6 relations: 30392
Thu Apr 09 03:10:12 2009  7 relations: 27261
Thu Apr 09 03:10:12 2009  8 relations: 23779
Thu Apr 09 03:10:12 2009  9 relations: 20663
Thu Apr 09 03:10:12 2009  10+ relations: 84133
Thu Apr 09 03:10:12 2009  heaviest cycle: 20 relations
Thu Apr 09 03:10:13 2009  RelProcTime: 321
Thu Apr 09 03:10:13 2009  
Thu Apr 09 03:10:13 2009  commencing linear algebra
Thu Apr 09 03:10:13 2009  read 375732 cycles
Thu Apr 09 03:10:14 2009  cycles contain 1262361 unique relations
Thu Apr 09 03:10:36 2009  read 1262361 relations
Thu Apr 09 03:10:38 2009  using 20 quadratic characters above 129051674
Thu Apr 09 03:10:46 2009  building initial matrix
Thu Apr 09 03:11:03 2009  memory use: 140.2 MB
Thu Apr 09 03:11:03 2009  read 375732 cycles
Thu Apr 09 03:11:04 2009  matrix is 375495 x 375732 (108.0 MB) with weight 35920809 (95.60/col)
Thu Apr 09 03:11:04 2009  sparse part has weight 25294481 (67.32/col)
Thu Apr 09 03:11:09 2009  filtering completed in 3 passes
Thu Apr 09 03:11:10 2009  matrix is 373450 x 373650 (107.6 MB) with weight 35776280 (95.75/col)
Thu Apr 09 03:11:10 2009  sparse part has weight 25215452 (67.48/col)
Thu Apr 09 03:11:11 2009  read 373650 cycles
Thu Apr 09 03:11:11 2009  matrix is 373450 x 373650 (107.6 MB) with weight 35776280 (95.75/col)
Thu Apr 09 03:11:11 2009  sparse part has weight 25215452 (67.48/col)
Thu Apr 09 03:11:11 2009  saving the first 48 matrix rows for later
Thu Apr 09 03:11:12 2009  matrix is 373402 x 373650 (102.5 MB) with weight 28487580 (76.24/col)
Thu Apr 09 03:11:12 2009  sparse part has weight 24633976 (65.93/col)
Thu Apr 09 03:11:12 2009  matrix includes 64 packed rows
Thu Apr 09 03:11:12 2009  using block size 65536 for processor cache size 3072 kB
Thu Apr 09 03:11:15 2009  commencing Lanczos iteration
Thu Apr 09 03:11:15 2009  memory use: 99.6 MB
Thu Apr 09 03:30:38 2009  lanczos halted after 5906 iterations (dim = 373402)
Thu Apr 09 03:30:39 2009  recovered 31 nontrivial dependencies
Thu Apr 09 03:30:39 2009  BLanczosTime: 1226
Thu Apr 09 03:30:39 2009  
Thu Apr 09 03:30:39 2009  commencing square root phase
Thu Apr 09 03:30:39 2009  reading relations for dependency 1
Thu Apr 09 03:30:39 2009  read 186146 cycles
Thu Apr 09 03:30:40 2009  cycles contain 777166 unique relations
Thu Apr 09 03:30:58 2009  read 777166 relations
Thu Apr 09 03:31:03 2009  multiplying 628388 relations
Thu Apr 09 03:32:32 2009  multiply complete, coefficients have about 25.11 million bits
Thu Apr 09 03:32:33 2009  initial square root is modulo 16293239
Thu Apr 09 03:34:38 2009  sqrtTime: 239
Thu Apr 09 03:34:38 2009  prp31 factor: 3343047086365563711398608131791
Thu Apr 09 03:34:38 2009  prp80 factor: 10220781380272666838366366338702762386870049984758453088533674483692999433547011
Thu Apr 09 03:34:38 2009  elapsed time 00:31:23

Apr 9, 2009

By Sinkiti Sibata / GGNFS, Msieve / Apr 9, 2009

(52·10¹⁵⁷-43)/9 = 5(7)₁₅₆3_<158> = 23 · 53 · 1213 · 29567 · 12658876837_<11> · 135348159141181289_<18> · C120

C120 = P34 · P87

P34 = 1563245310616346305114141976356471_<34>

P87 = 493417335839288436508758464426809943832532907598333625203510886400945640369114348815759_<87>

Number: 57773_157
N=771332336427578513933358574990653834345535965729313032742009229397885912124919989008537968701911759932297553236486426489
  ( 120 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=1563245310616346305114141976356471 (pp34)
 r2=493417335839288436508758464426809943832532907598333625203510886400945640369114348815759 (pp87)
Version: GGNFS-0.77.1-20060513-k8
Total time: 65.25 hours.
Scaled time: 129.14 units (timescale=1.979).
Factorization parameters were as follows:
name: 57773_157
n: 771332336427578513933358574990653834345535965729313032742009229397885912124919989008537968701911759932297553236486426489
m: 20000000000000000000000000000000
deg: 5
c5: 325
c0: -86
skew: 0.77
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1000000, 3500001)
Primes: RFBsize:148933, AFBsize:148895, largePrimes:8955379 encountered
Relations: rels:10119563, finalFF:424072
Max relations in full relation-set: 28
Initial matrix: 297894 x 424072 with sparse part having weight 61358057.
Pruned matrix : 267588 x 269141 with weight 42138672.
Total sieving time: 63.24 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 1.54 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,50,50,2.4,2.4,100000
total time: 65.25 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶⁹-43)/9 = 5(7)₁₆₈3_<170> = 5153 · C167

C167 = P30 · P137

P30 = 141123905140081748758439889157_<30>

P137 = 79451135073637208062710826844545700257591647268293500083720115297127311011627099148183218921499931962868099751915326230940533150055049513_<137>

Number: 57773_169
N=11212454449403799297065355671992582530133471332772710610863143368480065549733704206826659766694697802790176164909330055846648122992000344998598443193824525087866830541
  ( 167 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=141123905140081748758439889157 (pp30)
 r2=79451135073637208062710826844545700257591647268293500083720115297127311011627099148183218921499931962868099751915326230940533150055049513 (pp137)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 129.59 hours.
Scaled time: 329.68 units (timescale=2.544).
Factorization parameters were as follows:
name: 57773_169
n: 11212454449403799297065355671992582530133471332772710610863143368480065549733704206826659766694697802790176164909330055846648122992000344998598443193824525087866830541
m: 10000000000000000000000000000000000
deg: 5
c5: 26
c0: -215
skew: 1.53
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2500000, 7400001)
Primes: RFBsize:348513, AFBsize:348441, largePrimes:10507710 encountered
Relations: rels:11670776, finalFF:884620
Max relations in full relation-set: 28
Initial matrix: 697020 x 884620 with sparse part having weight 117081634.
Pruned matrix : 600360 x 603909 with weight 99044012.
Total sieving time: 122.70 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 6.37 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 129.59 hours.
 --------- CPU info (if available) ----------

(52·10¹³⁶+11)/9 = 5(7)₁₃₅9_<137> = C137

C137 = P39 · P42 · P58

P39 = 162327654977075883402432607143510339247_<39>

P42 = 225516353255079604804093456753934845067833_<42>

P58 = 1578302626785572386446896929818689186951420900821885917029_<58>

Number: 57779_136
N=57777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
  ( 137 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=162327654977075883402432607143510339247 (pp39)
 r2=225516353255079604804093456753934845067833 (pp42)
 r3=1578302626785572386446896929818689186951420900821885917029 (pp58)
Version: Msieve-1.40
Total time: 5.82 hours.
Scaled time: 11.40 units (timescale=1.960).
Factorization parameters were as follows:
name: 57779_136
n: 57777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
m: 2000000000000000000000000000
deg: 5
c5: 65
c0: 44
skew: 0.92
type: snfs
lss: 1
rlim: 1410000
alim: 1410000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1410000/1410000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [705000, 1305001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 195509 x 195757
Total sieving time: 5.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,138.000,5,0,0,0,0,0,0,0,0,1410000,1410000,26,26,48,48,2.3,2.3,75000
total time: 5.82 hours.
 --------- CPU info (if available) ----------

Apr 8, 2009 (5th)

By Andreas Tete / Msieve, GGNFS / Apr 8, 2009

(52·10¹⁴⁹+11)/9 = 5(7)₁₄₈9_<150> = 3 · 17 · 1783 · 628363 · 8825785487_<10> · 213641945483460762505333_<24> · C106

C106 = P48 · P59

P48 = 449254024867847727675909476262097732256487477847_<48>

P59 = 11937045302486433091318474345081585284330222063528243378473_<59>

Wed Apr 08 15:53:47 2009  Msieve v. 1.41
Wed Apr 08 15:53:47 2009  random seeds: 55fce73c e1f53e2b
Wed Apr 08 15:53:47 2009  factoring 5362765647171864912608824510227527182258184685704261834523201022179084754944556645341581873430918024187631 (106 digits)
Wed Apr 08 15:53:49 2009  searching for 15-digit factors
Wed Apr 08 15:53:52 2009  commencing number field sieve (106-digit input)
Wed Apr 08 15:53:52 2009  R0: -271133063771250244924
Wed Apr 08 15:53:52 2009  R1:  100195085147
Wed Apr 08 15:53:52 2009  A0: -59425125008032265936367375
Wed Apr 08 15:53:52 2009  A1:  5255982720263690813535
Wed Apr 08 15:53:52 2009  A2:  111647876233073929
Wed Apr 08 15:53:52 2009  A3: -15196907018525
Wed Apr 08 15:53:52 2009  A4: -106597328
Wed Apr 08 15:53:52 2009  A5:  3660
Wed Apr 08 15:53:52 2009  skew 36177.73, size 5.317563e-010, alpha -6.255835, combined = 1.903280e-009
Wed Apr 08 15:53:52 2009  
Wed Apr 08 15:53:52 2009  commencing relation filtering
Wed Apr 08 15:53:52 2009  commencing duplicate removal, pass 1
Wed Apr 08 15:54:41 2009  found 351678 hash collisions in 4591979 relations
Wed Apr 08 15:55:04 2009  added 31407 free relations
Wed Apr 08 15:55:04 2009  commencing duplicate removal, pass 2
Wed Apr 08 15:55:11 2009  found 335788 duplicates and 4287597 unique relations
Wed Apr 08 15:55:11 2009  memory use: 40.3 MB
Wed Apr 08 15:55:11 2009  reading rational ideals above 2555904
Wed Apr 08 15:55:11 2009  reading algebraic ideals above 2555904
Wed Apr 08 15:55:11 2009  commencing singleton removal, pass 1
Wed Apr 08 15:55:58 2009  relations with 0 large ideals: 94646
Wed Apr 08 15:55:58 2009  relations with 1 large ideals: 617918
Wed Apr 08 15:55:58 2009  relations with 2 large ideals: 1486882
Wed Apr 08 15:55:58 2009  relations with 3 large ideals: 1505950
Wed Apr 08 15:55:58 2009  relations with 4 large ideals: 534854
Wed Apr 08 15:55:58 2009  relations with 5 large ideals: 17526
Wed Apr 08 15:55:58 2009  relations with 6 large ideals: 29821
Wed Apr 08 15:55:58 2009  relations with 7+ large ideals: 0
Wed Apr 08 15:55:58 2009  4287597 relations and about 4323015 large ideals
Wed Apr 08 15:55:58 2009  commencing singleton removal, pass 2
Wed Apr 08 15:56:45 2009  found 1956078 singletons
Wed Apr 08 15:56:45 2009  current dataset: 2331519 relations and about 1946125 large ideals
Wed Apr 08 15:56:45 2009  commencing singleton removal, pass 3
Wed Apr 08 15:57:13 2009  found 481565 singletons
Wed Apr 08 15:57:13 2009  current dataset: 1849954 relations and about 1424840 large ideals
Wed Apr 08 15:57:13 2009  commencing singleton removal, final pass
Wed Apr 08 15:57:38 2009  memory use: 33.3 MB
Wed Apr 08 15:57:38 2009  commencing in-memory singleton removal
Wed Apr 08 15:57:38 2009  begin with 1849954 relations and 1464090 unique ideals
Wed Apr 08 15:57:43 2009  reduce to 1493132 relations and 1095577 ideals in 17 passes
Wed Apr 08 15:57:43 2009  max relations containing the same ideal: 15
Wed Apr 08 15:57:43 2009  reading rational ideals above 100000
Wed Apr 08 15:57:43 2009  reading algebraic ideals above 100000
Wed Apr 08 15:57:43 2009  commencing singleton removal, final pass
Wed Apr 08 15:58:20 2009  keeping 1381232 ideals with weight <= 25, new excess is 104356
Wed Apr 08 15:58:23 2009  memory use: 46.6 MB
Wed Apr 08 15:58:23 2009  commencing in-memory singleton removal
Wed Apr 08 15:58:23 2009  begin with 1496135 relations and 1381232 unique ideals
Wed Apr 08 15:58:27 2009  reduce to 1480368 relations and 1350857 ideals in 12 passes
Wed Apr 08 15:58:27 2009  max relations containing the same ideal: 25
Wed Apr 08 15:58:29 2009  relations with 0 large ideals: 3762
Wed Apr 08 15:58:29 2009  relations with 1 large ideals: 37480
Wed Apr 08 15:58:29 2009  relations with 2 large ideals: 160886
Wed Apr 08 15:58:29 2009  relations with 3 large ideals: 359726
Wed Apr 08 15:58:29 2009  relations with 4 large ideals: 446278
Wed Apr 08 15:58:29 2009  relations with 5 large ideals: 312236
Wed Apr 08 15:58:29 2009  relations with 6 large ideals: 127460
Wed Apr 08 15:58:29 2009  relations with 7+ large ideals: 32540
Wed Apr 08 15:58:29 2009  commencing 2-way merge
Wed Apr 08 15:58:32 2009  reduce to 831906 relation sets and 702521 unique ideals
Wed Apr 08 15:58:32 2009  ignored 126 oversize relation sets
Wed Apr 08 15:58:32 2009  commencing full merge
Wed Apr 08 15:58:48 2009  memory use: 53.8 MB
Wed Apr 08 15:58:49 2009  found 362928 cycles, need 348721
Wed Apr 08 15:58:49 2009  weight of 348721 cycles is about 24522820 (70.32/cycle)
Wed Apr 08 15:58:49 2009  distribution of cycle lengths:
Wed Apr 08 15:58:49 2009  1 relations: 38690
Wed Apr 08 15:58:49 2009  2 relations: 37640
Wed Apr 08 15:58:49 2009  3 relations: 37108
Wed Apr 08 15:58:49 2009  4 relations: 33406
Wed Apr 08 15:58:49 2009  5 relations: 30118
Wed Apr 08 15:58:49 2009  6 relations: 26528
Wed Apr 08 15:58:49 2009  7 relations: 23071
Wed Apr 08 15:58:49 2009  8 relations: 19577
Wed Apr 08 15:58:49 2009  9 relations: 16983
Wed Apr 08 15:58:49 2009  10+ relations: 85600
Wed Apr 08 15:58:49 2009  heaviest cycle: 23 relations
Wed Apr 08 15:58:49 2009  commencing cycle optimization
Wed Apr 08 15:58:50 2009  start with 2308529 relations
Wed Apr 08 15:59:03 2009  pruned 63973 relations
Wed Apr 08 15:59:03 2009  memory use: 59.7 MB
Wed Apr 08 15:59:03 2009  distribution of cycle lengths:
Wed Apr 08 15:59:03 2009  1 relations: 38690
Wed Apr 08 15:59:03 2009  2 relations: 38619
Wed Apr 08 15:59:03 2009  3 relations: 38562
Wed Apr 08 15:59:03 2009  4 relations: 34268
Wed Apr 08 15:59:03 2009  5 relations: 31073
Wed Apr 08 15:59:03 2009  6 relations: 26924
Wed Apr 08 15:59:03 2009  7 relations: 23273
Wed Apr 08 15:59:03 2009  8 relations: 19526
Wed Apr 08 15:59:03 2009  9 relations: 17009
Wed Apr 08 15:59:03 2009  10+ relations: 80777
Wed Apr 08 15:59:03 2009  heaviest cycle: 23 relations
Wed Apr 08 15:59:04 2009  RelProcTime: 258
Wed Apr 08 15:59:05 2009  
Wed Apr 08 15:59:05 2009  commencing linear algebra
Wed Apr 08 15:59:05 2009  read 348721 cycles
Wed Apr 08 15:59:07 2009  cycles contain 1241197 unique relations
Wed Apr 08 15:59:29 2009  read 1241197 relations
Wed Apr 08 15:59:33 2009  using 20 quadratic characters above 67107102
Wed Apr 08 15:59:44 2009  building initial matrix
Wed Apr 08 16:00:16 2009  memory use: 133.6 MB
Wed Apr 08 16:00:16 2009  read 348721 cycles
Wed Apr 08 16:00:18 2009  matrix is 348372 x 348721 (98.2 MB) with weight 32653745 (93.64/col)
Wed Apr 08 16:00:18 2009  sparse part has weight 23311371 (66.85/col)
Wed Apr 08 16:00:25 2009  filtering completed in 3 passes
Wed Apr 08 16:00:25 2009  matrix is 345226 x 345426 (97.5 MB) with weight 32393005 (93.78/col)
Wed Apr 08 16:00:25 2009  sparse part has weight 23152847 (67.03/col)
Wed Apr 08 16:00:27 2009  read 345426 cycles
Wed Apr 08 16:00:28 2009  matrix is 345226 x 345426 (97.5 MB) with weight 32393005 (93.78/col)
Wed Apr 08 16:00:28 2009  sparse part has weight 23152847 (67.03/col)
Wed Apr 08 16:00:28 2009  saving the first 48 matrix rows for later
Wed Apr 08 16:00:28 2009  matrix is 345178 x 345426 (93.6 MB) with weight 25761950 (74.58/col)
Wed Apr 08 16:00:28 2009  sparse part has weight 22474477 (65.06/col)
Wed Apr 08 16:00:28 2009  matrix includes 64 packed rows
Wed Apr 08 16:00:28 2009  using block size 65536 for processor cache size 3072 kB
Wed Apr 08 16:00:33 2009  commencing Lanczos iteration
Wed Apr 08 16:00:33 2009  memory use: 91.0 MB
Wed Apr 08 16:20:55 2009  lanczos halted after 5461 iterations (dim = 345178)
Wed Apr 08 16:20:56 2009  recovered 30 nontrivial dependencies
Wed Apr 08 16:20:56 2009  BLanczosTime: 1311
Wed Apr 08 16:20:56 2009  
Wed Apr 08 16:20:56 2009  commencing square root phase
Wed Apr 08 16:20:56 2009  reading relations for dependency 1
Wed Apr 08 16:20:56 2009  read 172900 cycles
Wed Apr 08 16:20:57 2009  cycles contain 761657 unique relations
Wed Apr 08 16:21:06 2009  read 761657 relations
Wed Apr 08 16:21:10 2009  multiplying 618710 relations
Wed Apr 08 16:22:39 2009  multiply complete, coefficients have about 24.39 million bits
Wed Apr 08 16:22:40 2009  initial square root is modulo 10105189
Wed Apr 08 16:24:44 2009  sqrtTime: 228
Wed Apr 08 16:24:44 2009  prp48 factor: 449254024867847727675909476262097732256487477847
Wed Apr 08 16:24:44 2009  prp59 factor: 11937045302486433091318474345081585284330222063528243378473
Wed Apr 08 16:24:44 2009  elapsed time 00:30:57

Apr 8, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 8, 2009

(8·10¹⁸⁴+1)/9 = (8)₁₈₃9_<184> = 3 · 19603 · 172173708801163613627_<21> · 27179099398845119796776615939_<29> · C131

C131 = P54 · P77

P54 = 655200614742021634033184493527939976327840479083596331_<54>

P77 = 49297794490247366498009769287197835197566546266043480968889690856371958296947_<77>

Number: 88889_184
N=32299945255435921563264500910223759473383544543244622969530356135443820563047187110300569176110925997216606362828072402522777701457
  ( 131 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=655200614742021634033184493527939976327840479083596331
 r2=49297794490247366498009769287197835197566546266043480968889690856371958296947
Version: 
Total time: 90.35 hours.
Scaled time: 215.67 units (timescale=2.387).
Factorization parameters were as follows:
n: 32299945255435921563264500910223759473383544543244622969530356135443820563047187110300569176110925997216606362828072402522777701457
m: 10000000000000000000000000000000000000
deg: 5
c5: 4
c0: 5
skew: 1.05
type: snfs
lss: 1
rlim: 7400000
alim: 7400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [3700000, 6100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 19738380
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1439655 x 1439903
Total sieving time: 82.17 hours.
Total relation processing time: 2.51 hours.
Matrix solve time: 5.15 hours.
Time per square root: 0.52 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,54,54,2.5,2.5,100000
total time: 90.35 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 8, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 8, 2009

(64·10³²¹-1)/9 = 7(1)₃₂₁_<322> = 13 · 557 · 3163 · 48947 · 10809769 · 1731548410507_<13> · 261280146756814062538507318913686335068158574151673052598829302142577942835385969_<81> · C211

C211 = P57 · P154

P57 = 136920528458324437784046746620817633432816773555317196129_<57>

P154 = 9473001739252911590386140919918219522378832016848880341270650479366213030853894032663349942975658310158914485340068110000467344258703110989631095198989717_<154>

Number: n
N=1297048404225135176763377838306703308284086026735410232090598831035125692096921942005723226083643408967468407954149338910641471501414593415858038052157558954903248295597331322908306784373809350097683957943205493
  ( 211 digits)
SNFS difficulty: 216 digits.
Divisors found:

Wed Apr  8 03:01:28 2009  prp57 factor: 136920528458324437784046746620817633432816773555317196129
Wed Apr  8 03:01:28 2009  prp154 factor: 9473001739252911590386140919918219522378832016848880341270650479366213030853894032663349942975658310158914485340068110000467344258703110989631095198989717
Wed Apr  8 03:01:28 2009  elapsed time 37:00:40 (Msieve 1.40 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 164.17 hours.
Scaled time: 330.47 units (timescale=2.013).
Factorization parameters were as follows:
name: KA_7_1_321
n: 1297048404225135176763377838306703308284086026735410232090598831035125692096921942005723226083643408967468407954149338910641471501414593415858038052157558954903248295597331322908306784373809350097683957943205493
m: 1000000000000000000000000000000000000
deg: 6
c6: 4
c3: 10
c0: 25
skew: 1.36
type: snfs
lss: 1
rlim: 29000000
alim: 29000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
Factor base limits: 29000000/29000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [14500000, 43099990)
Primes: RFBsize:1799676, AFBsize:1800414, largePrimes:38190043 encountered
Relations: rels:35567012, finalFF:1582831
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 10222882 hash collisions in 53039926 relations
Msieve: matrix is 4419521 x 4419769 (1191.6 MB)

Total sieving time: 162.85 hours.
Total relation processing time: 1.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,216,6,0,0,0,0,0,0,0,0,29000000,29000000,29,29,58,58,2.6,2.6,100000
total time: 164.17 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368972k/3407296k available (2746k kernel code, 36964k reserved, 1423k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.94 BogoMIPS (lpj=2830471)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830448)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22643.66 BogoMIPS).

(52·10¹²¹+11)/9 = 5(7)₁₂₀9_<122> = 2131 · 364423 · 26234906906371_<14> · C100

C100 = P30 · P70

P30 = 364380770250394223205085702913_<30>

P70 = 7782813588336038236590157745377257175997742877047838277174240662961821_<70>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 2835907610033120194199551806236055848179990717764081780027871686218836290400926117700635184267484573 (100 digits)
Using B1=410000, B2=258309880, polynomial Dickson(3), sigma=1875643875
Step 1 took 2844ms
Step 2 took 1547ms
********** Factor found in step 2: 364380770250394223205085702913
Found probable prime factor of 30 digits: 364380770250394223205085702913
Probable prime cofactor 7782813588336038236590157745377257175997742877047838277174240662961821 has 70 digits

(52·10¹³¹+11)/9 = 5(7)₁₃₀9_<132> = 3 · 156615616223844733_<18> · C115

C115 = P43 · P72

P43 = 7763687498449931812059462700396020833572123_<43>

P72 = 158393177019022554878786757562711332700651832607685626917554728976969727_<72>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 1229715128262352446646479717712916921331965604795480595127657762873153975570827675722018351807183853308813442120421 (115 digits)
Using B1=3016000, B2=5707048630, polynomial Dickson(6), sigma=776505955
Step 1 took 23656ms
Step 2 took 10813ms
********** Factor found in step 2: 7763687498449931812059462700396020833572123
Found probable prime factor of 43 digits: 7763687498449931812059462700396020833572123
Probable prime cofactor 158393177019022554878786757562711332700651832607685626917554728976969727 has 72 digits

(52·10¹⁶³-43)/9 = 5(7)₁₆₂3_<164> = 68227 · 1064333 · 10051697 · C146

C146 = P50 · P97

P50 = 11345284585959792348128719462608562601664887183003_<50>

P97 = 6977056631564364741721701334882809627921614120837450546938867006111665296912706481813926549424033_<97>

Number: n
N=79156693057455737307008940043409821123504830816174226754932381838488471827986295021737720124311306762782216540492587282060531047450730353517311099
  ( 146 digits)
SNFS difficulty: 166 digits.
Divisors found:

Wed Apr 08 12:35:24 2009  prp50 factor: 11345284585959792348128719462608562601664887183003
Wed Apr 08 12:35:24 2009  prp97 factor: 6977056631564364741721701334882809627921614120837450546938867006111665296912706481813926549424033
Wed Apr 08 12:35:24 2009  elapsed time 00:49:52 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 38.25 hours.
Scaled time: 100.47 units (timescale=2.627).
Factorization parameters were as follows:
name: KA_5_7_162_3
n: 79156693057455737307008940043409821123504830816174226754932381838488471827986295021737720124311306762782216540492587282060531047450730353517311099
m: 1000000000000000000000000000000000
deg: 5
c5: 13
c0: -1075
skew: 2.42
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved  special-q in [2050000, 4350000)
Primes: RFBsize:289774, AFBsize:289152, largePrimes:9241359 encountered
Relations: rels:9588942, finalFF:654042
Max relations in full relation-set: 28
Initial matrix: 578992 x 654042 with sparse part having weight 71044949.
Pruned matrix : 543963 x 546921 with weight 56786987.

Msieve: found 1073917 hash collisions in 10559866 relations
Msieve: matrix is 634107 x 634355 (168.3 MB)

Total sieving time: 37.64 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.33 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 38.25 hours.
 --------- CPU info (if available) ----------

(52·10¹⁵²+11)/9 = 5(7)₁₅₁9_<153> = 3² · 757 · C149

C149 = P38 · P111

P38 = 93808864550850625172985855237704776067_<38>

P111 = 904021097507399866702195420272204652716997344737015447439748923511012042343544803174140630732101383321666439749_<111>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 84805192687182999820604400084805192687182999820604400084805192687182999820604400084805192687182999820604400084805192687182999820604400084805192687183 (149 digits)
Using B1=2012000, B2=2853999340, polynomial Dickson(6), sigma=853283790
Step 1 took 23687ms
Step 2 took 9922ms
********** Factor found in step 2: 93808864550850625172985855237704776067
Found probable prime factor of 38 digits: 93808864550850625172985855237704776067
Probable prime cofactor 904021097507399866702195420272204652716997344737015447439748923511012042343544803174140630732101383321666439749 has 111 digits

(52·10¹⁶³-61)/9 = 5(7)₁₆₂1_<164> = 3 · 281 · 49559 · 154452407 · C148

C148 = P72 · P76

P72 = 985599952264306027024189286435490320222399984074792036487401000273442791_<72>

P76 = 9084799990658051214181652821663796864828696072835756124477903941113082320359_<76>

Number: n
N=8953978437123343116951200201478548849810829379828748970302581367078882584804549791697998382013828361531770509760399305306292768437157835291721081969
  ( 148 digits)
SNFS difficulty: 166 digits.
Divisors found:

Wed Apr 08 16:56:58 2009  prp72 factor: 985599952264306027024189286435490320222399984074792036487401000273442791
Wed Apr 08 16:56:58 2009  prp76 factor: 9084799990658051214181652821663796864828696072835756124477903941113082320359
Wed Apr 08 16:56:58 2009  elapsed time 00:55:33 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 42.65 hours.
Scaled time: 112.98 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_7_162_1
n: 8953978437123343116951200201478548849810829379828748970302581367078882584804549791697998382013828361531770509760399305306292768437157835291721081969
m: 1000000000000000000000000000000000
deg: 5
c5: 13
c0: -1525
skew: 2.59
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved  special-q in [2050000, 4750091)
Primes: RFBsize:289774, AFBsize:290733, largePrimes:9093056 encountered
Relations: rels:9165804, finalFF:598084
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1115970 hash collisions in 10198363 relations
Msieve: matrix is 725226 x 725474 (192.8 MB)

Total sieving time: 42.35 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 42.65 hours.
 --------- CPU info (if available) ----------

(52·10¹⁵⁶-61)/9 = 5(7)₁₅₅1_<157> = 4937 · 114370423 · 18365093151893_<14> · C132

C132 = P50 · P83

P50 = 24695978014100333072677731977278205511815080160837_<50>

P83 = 22561325654314430046535809389320157194646910045717054254420912038014349179571854781_<83>

Number: n
N=557174002327906975798769654208559431606013104752429834529952087837656117353644842339464494240064263927360215844965204480695887411697
  ( 132 digits)
SNFS difficulty: 158 digits.
Divisors found:

Wed Apr 08 21:24:46 2009  prp50 factor: 24695978014100333072677731977278205511815080160837
Wed Apr 08 21:24:46 2009  prp83 factor: 22561325654314430046535809389320157194646910045717054254420912038014349179571854781
Wed Apr 08 21:24:46 2009  elapsed time 00:52:14 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 21.26 hours.
Scaled time: 55.86 units (timescale=2.627).
Factorization parameters were as follows:
name: KA_5_7_155_1
n: 557174002327906975798769654208559431606013104752429834529952087837656117353644842339464494240064263927360215844965204480695887411697
m: 20000000000000000000000000000000
deg: 5
c5: 65
c0: -244
skew: 1.30
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1500000, 2900083)
Primes: RFBsize:216816, AFBsize:216527, largePrimes:12681842 encountered
Relations: rels:11727577, finalFF:433586
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1107459 hash collisions in 12643471 relations
Msieve: matrix is 588100 x 588348 (157.8 MB)

Total sieving time: 20.97 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000
total time: 21.26 hours.
 --------- CPU info (if available) ----------

Apr 8, 2009 (2nd)

By Max Dettweiler / GMP-ECM, msieve v1.40beta2, GGNFS, msieve v1.41, msieve v1.39 / Apr 8, 2009

(49·10¹⁹⁰-13)/9 = 5(4)₁₈₉3_<191> = 23 · 56783 · 3577949592990109125475959133_<28> · 10560005477046551407109442082543_<32> · C127

C127 = P36 · P41 · P51

P36 = 151384963804792601957076838327835443_<36>

P41 = 27247030603187965412926575051567284862283_<41>

P51 = 267489733874812578723107950256592587386798727120657_<51>

---------------------------------
P36=151384963804792601957076838327835443
B1=1000000
B2=900000000
Method=ECM

Found by the ECM "workers" at http://factorization.ath.cx
---------------------------------
Tue Apr 07 03:16:09 2009  Msieve v. 1.40
Tue Apr 07 03:16:09 2009  random seeds: 28de34d8 8bda56ae
Tue Apr 07 03:16:09 2009  factoring 7288300964925622921639267800655225120410607285033175107865679394472800601695388603369479931 (91 digits)
Tue Apr 07 03:16:10 2009  searching for 15-digit factors
Tue Apr 07 03:16:11 2009  commencing quadratic sieve (91-digit input)
Tue Apr 07 03:16:11 2009  using multiplier of 3
Tue Apr 07 03:16:11 2009  using 32kb Intel Core sieve core
Tue Apr 07 03:16:11 2009  sieve interval: 36 blocks of size 32768
Tue Apr 07 03:16:11 2009  processing polynomials in batches of 6
Tue Apr 07 03:16:11 2009  using a sieve bound of 1713449 (64706 primes)
Tue Apr 07 03:16:11 2009  using large prime bound of 164491104 (27 bits)
Tue Apr 07 03:16:11 2009  using double large prime bound of 615256603721856 (42-50 bits)
Tue Apr 07 03:16:11 2009  using trial factoring cutoff of 50 bits
Tue Apr 07 03:16:11 2009  polynomial 'A' values have 12 factors
Tue Apr 07 04:37:43 2009  64819 relations (16665 full + 48154 combined from 762683 partial), need 64802
Tue Apr 07 04:37:43 2009  begin with 779348 relations
Tue Apr 07 04:37:44 2009  reduce to 162308 relations in 11 passes
Tue Apr 07 04:37:44 2009  attempting to read 162308 relations
Tue Apr 07 04:37:46 2009  recovered 162308 relations
Tue Apr 07 04:37:46 2009  recovered 142998 polynomials
Tue Apr 07 04:37:46 2009  attempting to build 64819 cycles
Tue Apr 07 04:37:46 2009  found 64819 cycles in 5 passes
Tue Apr 07 04:37:46 2009  distribution of cycle lengths:
Tue Apr 07 04:37:46 2009     length 1 : 16665
Tue Apr 07 04:37:46 2009     length 2 : 11914
Tue Apr 07 04:37:46 2009     length 3 : 11364
Tue Apr 07 04:37:46 2009     length 4 : 8678
Tue Apr 07 04:37:46 2009     length 5 : 6457
Tue Apr 07 04:37:46 2009     length 6 : 4061
Tue Apr 07 04:37:46 2009     length 7 : 2502
Tue Apr 07 04:37:46 2009     length 9+: 3178
Tue Apr 07 04:37:46 2009  largest cycle: 22 relations
Tue Apr 07 04:37:46 2009  matrix is 64706 x 64819 (16.1 MB) with weight 3957333 (61.05/col)
Tue Apr 07 04:37:46 2009  sparse part has weight 3957333 (61.05/col)
Tue Apr 07 04:37:47 2009  filtering completed in 3 passes
Tue Apr 07 04:37:47 2009  matrix is 60951 x 61015 (15.3 MB) with weight 3763741 (61.69/col)
Tue Apr 07 04:37:47 2009  sparse part has weight 3763741 (61.69/col)
Tue Apr 07 04:37:47 2009  saving the first 48 matrix rows for later
Tue Apr 07 04:37:47 2009  matrix is 60903 x 61015 (9.4 MB) with weight 2929803 (48.02/col)
Tue Apr 07 04:37:47 2009  sparse part has weight 2100869 (34.43/col)
Tue Apr 07 04:37:47 2009  matrix includes 64 packed rows
Tue Apr 07 04:37:47 2009  using block size 24406 for processor cache size 2048 kB
Tue Apr 07 04:37:47 2009  commencing Lanczos iteration
Tue Apr 07 04:37:47 2009  memory use: 9.3 MB
Tue Apr 07 04:38:04 2009  lanczos halted after 965 iterations (dim = 60897)
Tue Apr 07 04:38:04 2009  recovered 14 nontrivial dependencies
Tue Apr 07 04:38:04 2009  prp41 factor: 27247030603187965412926575051567284862283
Tue Apr 07 04:38:04 2009  prp51 factor: 267489733874812578723107950256592587386798727120657
Tue Apr 07 04:38:04 2009  elapsed time 01:21:55

(52·10¹¹²+11)/9 = 5(7)₁₁₁9_<113> = 19 · 1471 · 6203 · 244561123 · C97

C97 = P39 · P58

P39 = 342635300376985740079889564063862325331_<39>

P58 = 3977161757490024436199522761739823455145947091623722643189_<58>

Number: 57779_112
N=1362716013425455038269365465041655392090464515205357520408224328485283338132684220072647149320559
  ( 97 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=342635300376985740079889564063862325331
 (pp40)
 r2=3977161757490024436199522761739823455145947091623722643189
 (pp59)
Version: Msieve-1.41
Total time: 0.95 hours.
Scaled time: 1.03 units (timescale=1.088).
Factorization parameters were as follows:
n: 1362716013425455038269365465041655392090464515205357520408224328485283338132684220072647149320559
m: 20000000000000000000000
deg: 5
c5: 325
c0: 22
skew: 0.58
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [280000, 480001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 56708 x 56935
Total sieving time: 0.95 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,114,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000
total time: 0.95 hours.
 --------- CPU info (if available) ----------

(52·10¹¹³+11)/9 = 5(7)₁₁₂9_<114> = 3 · 797 · C111

C111 = P32 · P80

P32 = 21191076950997992778938517729283_<32>

P80 = 11403239072609000017840567548152233635496296586350682597719486296171078116689943_<80>

Number: 57779_113
N=241646916678284306891584181421069752311910404758585436126214043403503880291835122449927970630605511408522700869
  ( 111 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=21191076950997992778938517729283
 (pp33)
 r2=11403239072609000017840567548152233635496296586350682597719486296171078116689943
 (pp81)
Version: Msieve-1.39
Total time: 1.01 hours.
Scaled time: 1.09 units (timescale=1.085).
Factorization parameters were as follows:
n: 241646916678284306891584181421069752311910404758585436126214043403503880291835122449927970630605511408522700869
m: 100000000000000000000000
deg: 5
c5: 13
c0: 275
skew: 1.84
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [300000, 500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 59957 x 60198
Total sieving time: 1.01 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000
total time: 1.01 hours.
 --------- CPU info (if available) ----------

(52·10¹¹⁴+11)/9 = 5(7)₁₁₃9_<115> = 7 · 419 · 36721 · C107

C107 = P42 · P66

P42 = 156191211927687234042225904227266197684409_<42>

P66 = 343461195244667387875682227644599921552361260327667052031805907567_<66>

Number: 57779_114
N=53645620335396606821871926431568222512112838049256370755536983441795441250273823494624946636921862091022903
  ( 107 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=156191211927687234042225904227266197684409
 (pp43)
 r2=343461195244667387875682227644599921552361260327667052031805907567
 (pp67)
Version: Msieve-1.39
Total time: 1.01 hours.
Scaled time: 1.10 units (timescale=1.090).
Factorization parameters were as follows:
n: 53645620335396606821871926431568222512112838049256370755536983441795441250273823494624946636921862091022903
m: 100000000000000000000000
deg: 5
c5: 26
c0: 55
skew: 1.16
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [305000, 505001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 62274 x 62507
Total sieving time: 1.01 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000
total time: 1.01 hours.
 --------- CPU info (if available) ----------

(52·10¹⁰⁴+11)/9 = 5(7)₁₀₃9_<105> = 3 · 27103 · 997052731 · C91

C91 = P29 · P63

P29 = 19220610958847864530012111841_<29>

P63 = 370797586486105227102882427553203663841628754066639649741320861_<63>

Number: 57779_104
N=7126956154329172964190407581733579595542753084022720093873577878288167714232922899398415101
  ( 91 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=19220610958847864530012111841 (pp29)
 r2=370797586486105227102882427553203663841628754066639649741320861 (pp63)
Version: GGNFS-0.77.1-VC8(Sat
Total time: 0.35 hours.
Scaled time: 0.38 units (timescale=1.092).
Factorization parameters were as follows:
n: 7126956154329172964190407581733579595542753084022720093873577878288167714232922899398415101
m: 200000000000000000000000000
deg: 4
c4: 13
c0: 44
skew: 1.36
type: snfs
lss: 1
rlim: 410000
alim: 410000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2Factor base limits: 410000/410000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [205000, 265001)
Primes: RFBsize:34614, AFBsize:34155, largePrimes:979903 encountered
Relations: rels:899445, finalFF:86300
Max relations in full relation-set: 32
Initial matrix: 68836 x 86300 with sparse part having weight 3259399.
Pruned matrix : 57430 x 57838 with weight 1677024.
Total sieving time: 0.31 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,106,4,0,0,0,0,0,0,0,0,410000,410000,25,25,44,44,2.2,2.2,20000
total time: 0.35 hours.
 --------- CPU info (if available) ----------

(52·10¹¹⁷+11)/9 = 5(7)₁₁₆9_<118> = 17 · 59 · 10956842667605569320979_<23> · C93

C93 = P38 · P55

P38 = 71924007866618544951803639781410382773_<38>

P55 = 7309717546312534089494372288483167098053407071733225079_<55>

Number: 57779_117
N=525744182303742310034568486879758102100680007383383575604620876268515086518106958523153164067
  ( 93 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=71924007866618544951803639781410382773
 (pp39)
 r2=7309717546312534089494372288483167098053407071733225079
 (pp56)
Version: Msieve-1.41
Total time: 1.23 hours.
Scaled time: 1.34 units (timescale=1.088).
Factorization parameters were as follows:
n: 525744182303742310034568486879758102100680007383383575604620876268515086518106958523153164067
m: 200000000000000000000000
deg: 5
c5: 325
c0: 22
skew: 0.58
type: snfs
lss: 1
rlim: 670000
alim: 670000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 670000/670000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [335000, 585001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 73690 x 73919
Total sieving time: 1.23 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,670000,670000,25,25,45,45,2.2,2.2,50000
total time: 1.23 hours.
 --------- CPU info (if available) ----------

(52·10¹¹⁹+11)/9 = 5(7)₁₁₈9_<120> = 3 · 1069 · 25044948075953116163_<20> · C97

C97 = P47 · P51

P47 = 65362022175359856796126919799848878544914687343_<47>

P51 = 110056642251239621825067197259113037041248732781833_<51>

Number: 57779_119
N=7193524691371170713641673802460032864647362592976192622799232625333131233825174851481483825439719
  ( 97 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=65362022175359856796126919799848878544914687343
 (pp48)
 r2=110056642251239621825067197259113037041248732781833
 (pp52)
Version: Msieve-1.41
Total time: 1.25 hours.
Scaled time: 1.35 units (timescale=1.081).
Factorization parameters were as follows:
n: 7193524691371170713641673802460032864647362592976192622799232625333131233825174851481483825439719
m: 1000000000000000000000000
deg: 5
c5: 26
c0: 55
skew: 1.16
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 620001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 83078 x 83303
Total sieving time: 1.25 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 1.25 hours.
 --------- CPU info (if available) ----------

(52·10¹³³+11)/9 = 5(7)₁₃₂9_<134> = 17 · 5372303 · C126

C126 = P45 · P82

P45 = 552786152596759621451787350162034188925429337_<45>

P82 = 1144443240550567536987813732224100088589848122719187256363678808463144355031420117_<82>

Number: 57779_133
N=632632375809316105191624717695862274880643287462266870057488849072710396462327540718929685197421552487417492556979729043772429
  ( 126 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=552786152596759621451787350162034188925429337
 (pp46)
 r2=1144443240550567536987813732224100088589848122719187256363678808463144355031420117
 (pp83)
Version: Msieve-1.39
Total time: 3.25 hours.
Scaled time: 3.54 units (timescale=1.090).
Factorization parameters were as follows:
n: 632632375809316105191624717695862274880643287462266870057488849072710396462327540718929685197421552487417492556979729043772429
m: 1000000000000000000000000000
deg: 5
c5: 13
c0: 275
skew: 1.84
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1175001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 182164 x 182412
Total sieving time: 3.25 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 3.25 hours.
 --------- CPU info (if available) ----------

Apr 8, 2009

By Serge Batalov / GMP-ECM 6.2.2 / Apr 8, 2009

(52·10¹¹⁶+11)/9 = 5(7)₁₁₅9_<117> = 3³ · 162618791 · C108

C108 = P37 · P71

P37 = 2645715604664475548380977250122717151_<37>

P71 = 49737411941327305141315767551566392120952692721970711669814872930052497_<71>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2645698852
Step 1 took 6533ms
Step 2 took 7036ms
********** Factor found in step 2: 2645715604664475548380977250122717151
Found probable prime factor of 37 digits: 2645715604664475548380977250122717151
Probable prime cofactor has 71 digits

(52·10¹⁴³+11)/9 = 5(7)₁₄₂9_<144> = 3³ · 83 · 357347 · C135

C135 = P31 · P105

P31 = 2627625558851476694029546636907_<31>

P105 = 274577761184714753670872305144563611669505000759721875940972634740657525851157819603161894138821807409811_<105>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4099621279
Step 1 took 8108ms
Step 2 took 7905ms
********** Factor found in step 2: 2627625558851476694029546636907
Found probable prime factor of 31 digits: 2627625558851476694029546636907
Probable prime cofactor has 105 digits

Apr 7, 2009 (6th)

Factorizations of 577...779 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 7, 2009 (5th)

By Wataru Sakai / Msieve / Apr 7, 2009

(17·10¹⁸⁵-11)/3 = 5(6)₁₈₄3_<186> = C186

C186 = P70 · P117

P70 = 4925952720289718922267290651764752755426360242050366403515405657991967_<70>

P117 = 115036968246284402056838380084523901776546762863252344722745402064736836757750211510628015588193248445323115293824889_<117>

Number: 56663_185
N=566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
  ( 186 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=4925952720289718922267290651764752755426360242050366403515405657991967
 r2=115036968246284402056838380084523901776546762863252344722745402064736836757750211510628015588193248445323115293824889
Version: 
Total time: 295.50 hours.
Scaled time: 576.22 units (timescale=1.950).
Factorization parameters were as follows:
n: 566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
m: 10000000000000000000000000000000000000
deg: 5
c5: 17
c0: -11
skew: 0.92
type: snfs
lss: 1
rlim: 8900000
alim: 8900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8900000/8900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4450000, 7350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1351725 x 1351973
Total sieving time: 295.50 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,8900000,8900000,28,28,54,54,2.5,2.5,100000
total time: 295.50 hours.
 --------- CPU info (if available) ----------

Apr 7, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 7, 2009

(52·10¹⁵⁶-43)/9 = 5(7)₁₅₅3_<157> = 67 · 2539 · 12377 · 7507813 · 152592998381199941_<18> · C124

C124 = P56 · P68

P56 = 42324712149887703249058741715715368573418753560232777947_<56>

P68 = 56593411293658825684156944002955180765863478393823025834036693149223_<68>

Number: 57773_156
N=2395299842584313661176009271399515634228386385781040937035513146893887555216345156622566136206011349430618766637825094585181
  ( 124 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=42324712149887703249058741715715368573418753560232777947
 r2=56593411293658825684156944002955180765863478393823025834036693149223
Version: 
Total time: 12.70 hours.
Scaled time: 30.37 units (timescale=2.391).
Factorization parameters were as follows:
n: 2395299842584313661176009271399515634228386385781040937035513146893887555216345156622566136206011349430618766637825094585181
m: 20000000000000000000000000000000
deg: 5
c5: 65
c0: -172
skew: 1.21
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8058475
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 577122 x 577370
Total sieving time: 11.43 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.75 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 12.70 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 7, 2009 (3rd)

By Sinkiti Sibata / Msieve / Apr 7, 2009

(49·10¹⁶³-13)/9 = 5(4)₁₆₂3_<164> = 22877 · 1141039 · 712917216005380730823319_<24> · C130

C130 = P43 · P88

P43 = 1838559489041997202537670965985653716498713_<43>

P88 = 1591245618155628933095288983361565267658381139712189781371408687414923895947384324120423_<88>

Number: 54443_163
N=2925599730656530118218153085930991963465403815206131233254026841784401287021285104721191904053437108456642251087246239876936515599
  ( 130 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=1838559489041997202537670965985653716498713
 r2=1591245618155628933095288983361565267658381139712189781371408687414923895947384324120423
Version: 
Total time: 55.29 hours.
Scaled time: 141.76 units (timescale=2.564).
Factorization parameters were as follows:
name: 54443_163
n: 2925599730656530118218153085930991963465403815206131233254026841784401287021285104721191904053437108456642251087246239876936515599
m: 500000000000000000000000000000000
deg: 5
c5: 392
c0: -325
skew: 0.96
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 784249 x 784497
Total sieving time: 55.29 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 55.29 hours.
 --------- CPU info (if available) ----------

Apr 7, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Apr 7, 2009

(52·10¹⁵³-43)/9 = 5(7)₁₅₂3_<154> = 19 · 251 · 3217 · 21637541 · C140

C140 = P43 · P97

P43 = 5226656307048277075739951443464065439796783_<43>

P97 = 3330048848530137402109121586611241776634331048046456390576341906231093818995585219392171771569367_<97>

Number: n
N=17405020816948895352788462978289144993085486311485555507689951772738726034033330243643593383421865564930217703918043370446279816473467946361
  ( 140 digits)
SNFS difficulty: 156 digits.
Divisors found:

Tue Apr 07 04:13:58 2009  prp43 factor: 5226656307048277075739951443464065439796783
Tue Apr 07 04:13:58 2009  prp97 factor: 3330048848530137402109121586611241776634331048046456390576341906231093818995585219392171771569367
Tue Apr 07 04:13:58 2009  elapsed time 00:25:53 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 16.44 hours.
Scaled time: 43.74 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_7_152_3
n: 17405020816948895352788462978289144993085486311485555507689951772738726034033330243643593383421865564930217703918043370446279816473467946361
m: 10000000000000000000000000000000
deg: 5
c5: 13
c0: -1075
skew: 2.42
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [1400000, 2437891)
Primes: RFBsize:203362, AFBsize:203212, largePrimes:7790060 encountered
Relations: rels:7668575, finalFF:424928
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 658674 hash collisions in 8502371 relations
Msieve: matrix is 424079 x 424327 (112.4 MB)

Total sieving time: 16.30 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 16.44 hours.
 --------- CPU info (if available) ----------

(52·10¹⁵³-61)/9 = 5(7)₁₅₂1_<154> = 109 · 10654546681733_<14> · C139

C139 = P65 · P75

P65 = 21877636042769256562956587384071382231100312437993942946107314253_<65>

P75 = 227404453978194883205305035375145786814416581210812947786666686879475096631_<75>

Number: n
N=4975071878639619027580647578105061421944161740530495775744169980983929912826073249348360403185875188699533329276365263088506585953058581643
  ( 139 digits)
SNFS difficulty: 156 digits.
Divisors found:

Tue Apr 07 16:01:50 2009  prp65 factor: 21877636042769256562956587384071382231100312437993942946107314253
Tue Apr 07 16:01:50 2009  prp75 factor: 227404453978194883205305035375145786814416581210812947786666686879475096631
Tue Apr 07 16:01:50 2009  elapsed time 01:33:48 (Msieve 1.39 - dependency 5)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.53 hours.
Scaled time: 48.37 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_5_7_152_1
n: 4975071878639619027580647578105061421944161740530495775744169980983929912826073249348360403185875188699533329276365263088506585953058581643
m: 10000000000000000000000000000000
deg: 5
c5: 13
c0: -1525
skew: 2.59
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1400000, 2550059)
Primes: RFBsize:203362, AFBsize:203673, largePrimes:12268068 encountered
Relations: rels:11304635, finalFF:423323
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1009925 hash collisions in 12132181 relations
Msieve: matrix is 540033 x 540281 (144.2 MB)

Total sieving time: 26.17 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,56,56,2.4,2.4,100000
total time: 26.53 hours.
 --------- CPU info (if available) ----------

(52·10¹⁵⁹-43)/9 = 5(7)₁₅₈3_<160> = 332623 · 6508577549_<10> · C145

C145 = P45 · P101

P45 = 255158710652956081464085443158694106632566387_<45>

P101 = 10459527719841289135517282631223674345622062975143907800726130556696015686727283793221178817377069877_<101>

Number: n
N=2668839607033556974468153671896871207588601016196528363541022727523800195201718900138212731528155645460355752215651205000868056419190870740424399
  ( 145 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Apr 07 17:36:05 2009  prp45 factor: 255158710652956081464085443158694106632566387
Tue Apr 07 17:36:05 2009  prp101 factor: 10459527719841289135517282631223674345622062975143907800726130556696015686727283793221178817377069877
Tue Apr 07 17:36:05 2009  elapsed time 00:34:01 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 26.54 hours.
Scaled time: 70.60 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_7_158_3
n: 2668839607033556974468153671896871207588601016196528363541022727523800195201718900138212731528155645460355752215651205000868056419190870740424399
m: 100000000000000000000000000000000
deg: 5
c5: 26
c0: -215
skew: 1.53
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved  special-q in [1700000, 3353351)
Primes: RFBsize:243539, AFBsize:243539, largePrimes:8794996 encountered
Relations: rels:8707881, finalFF:419993
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 891260 hash collisions in 9762998 relations
Msieve: matrix is 566469 x 566717 (150.8 MB)

Total sieving time: 26.37 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 26.54 hours.
 --------- CPU info (if available) ----------

Apr 7, 2009

By Max Dettweiler / GMP-ECM / Apr 7, 2009

(17·10²⁰⁰+7)/3 = 5(6)₁₉₉9_<201> = 139 · 1319 · 4091 · 5953 · 4583407129440823_<16> · 1454913548016373279_<19> · 16235484672840827305747235427721_<32> · C124

C124 = P39 · P86

P39 = 100034433648149700990445975108099542857_<39>

P86 = 11718237858780679052337995092680150045988631324939268850238847645056920552478961481867_<86>

P39=100034433648149700990445975108099542857
P86=11718237858780679052337995092680150045988631324939268850238847645056920552478961481867

B1=1000000
B2=900000000
Method=ECM

Found by the ECM "workers" at http://factorization.ath.cx/

Apr 6, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 6, 2009

(52·10¹⁵⁴-43)/9 = 5(7)₁₅₃3_<155> = 149 · 43869806235097027_<17> · C136

C136 = P45 · P92

P45 = 644362268145717611996869352240115972961249339_<45>

P92 = 13717619367664715143177371786799265045598831380451245098960355618867000486046534325108460809_<92>

Number: 57773_154
N=8839116329308060449769823283800910310769081476155727628618745501770973967180392667477101570262093537763612128214917683828260403958655251
  ( 136 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=644362268145717611996869352240115972961249339
 r2=13717619367664715143177371786799265045598831380451245098960355618867000486046534325108460809
Version: 
Total time: 12.25 hours.
Scaled time: 29.19 units (timescale=2.383).
Factorization parameters were as follows:
n: 8839116329308060449769823283800910310769081476155727628618745501770973967180392667477101570262093537763612128214917683828260403958655251
m: 10000000000000000000000000000000
deg: 5
c5: 26
c0: -215
skew: 1.53
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8347585
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 476289 x 476537
Total sieving time: 11.17 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 12.25 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 6, 2009 (3rd)

By Andreas Tete / Msieve v1.41, GGNFS / Apr 6, 2009

(52·10¹⁶⁴-61)/9 = 5(7)₁₆₃1_<165> = 31 · 331 · 25913 · 157931 · 87326546699387_<14> · 3012754065006304230901_<22> · C116

C116 = P58 · P59

P58 = 1685645882744324078184380208870777133400255977328802807319_<58>

P59 = 31024854582650382849964071719783112624254304541889736365429_<59>

Mon Apr 06 12:28:44 2009  Msieve v. 1.41
Mon Apr 06 12:28:44 2009  random seeds: d61ac388 89579085
Mon Apr 06 12:28:44 2009  factoring 52296918389985992784801051521686146462966025183955903334306486053990434106755070365178483332617530969438858859774851 (116 digits)
Mon Apr 06 12:28:45 2009  searching for 15-digit factors
Mon Apr 06 12:28:47 2009  commencing number field sieve (116-digit input)
Mon Apr 06 12:28:47 2009  R0: -22847768657417603897317
Mon Apr 06 12:28:47 2009  R1:  2527396540427
Mon Apr 06 12:28:47 2009  A0:  898990150492261702300858080
Mon Apr 06 12:28:47 2009  A1:  215800709421276599729876
Mon Apr 06 12:28:47 2009  A2:  12656715388262471695
Mon Apr 06 12:28:47 2009  A3:  171570845453858
Mon Apr 06 12:28:47 2009  A4: -3873010736
Mon Apr 06 12:28:47 2009  A5:  8400
Mon Apr 06 12:28:47 2009  skew 58360.61, size 4.912365e-011, alpha -6.153610, combined = 5.160237e-010
Mon Apr 06 12:28:47 2009  
Mon Apr 06 12:28:47 2009  commencing relation filtering
Mon Apr 06 12:28:47 2009  commencing duplicate removal, pass 1
Mon Apr 06 12:30:20 2009  found 636778 hash collisions in 8155392 relations
Mon Apr 06 12:30:45 2009  added 59663 free relations
Mon Apr 06 12:30:45 2009  commencing duplicate removal, pass 2
Mon Apr 06 12:31:05 2009  found 565861 duplicates and 7649193 unique relations
Mon Apr 06 12:31:05 2009  memory use: 48.6 MB
Mon Apr 06 12:31:05 2009  reading rational ideals above 3997696
Mon Apr 06 12:31:05 2009  reading algebraic ideals above 3997696
Mon Apr 06 12:31:05 2009  commencing singleton removal, pass 1
Mon Apr 06 12:32:27 2009  relations with 0 large ideals: 128553
Mon Apr 06 12:32:27 2009  relations with 1 large ideals: 967018
Mon Apr 06 12:32:27 2009  relations with 2 large ideals: 2568517
Mon Apr 06 12:32:27 2009  relations with 3 large ideals: 2794911
Mon Apr 06 12:32:27 2009  relations with 4 large ideals: 1068979
Mon Apr 06 12:32:27 2009  relations with 5 large ideals: 62451
Mon Apr 06 12:32:27 2009  relations with 6 large ideals: 58745
Mon Apr 06 12:32:27 2009  relations with 7+ large ideals: 19
Mon Apr 06 12:32:27 2009  7649193 relations and about 7686588 large ideals
Mon Apr 06 12:32:27 2009  commencing singleton removal, pass 2
Mon Apr 06 12:33:51 2009  found 3501835 singletons
Mon Apr 06 12:33:51 2009  current dataset: 4147358 relations and about 3436549 large ideals
Mon Apr 06 12:33:51 2009  commencing singleton removal, pass 3
Mon Apr 06 12:34:46 2009  found 796417 singletons
Mon Apr 06 12:34:46 2009  current dataset: 3350941 relations and about 2582397 large ideals
Mon Apr 06 12:34:46 2009  commencing singleton removal, pass 4
Mon Apr 06 12:35:36 2009  found 238513 singletons
Mon Apr 06 12:35:36 2009  current dataset: 3112428 relations and about 2337330 large ideals
Mon Apr 06 12:35:36 2009  commencing singleton removal, final pass
Mon Apr 06 12:36:31 2009  memory use: 50.1 MB
Mon Apr 06 12:36:31 2009  commencing in-memory singleton removal
Mon Apr 06 12:36:31 2009  begin with 3112428 relations and 2459063 unique ideals
Mon Apr 06 12:36:35 2009  reduce to 2672100 relations and 2009098 ideals in 14 passes
Mon Apr 06 12:36:35 2009  max relations containing the same ideal: 19
Mon Apr 06 12:36:36 2009  reading rational ideals above 720000
Mon Apr 06 12:36:36 2009  reading algebraic ideals above 720000
Mon Apr 06 12:36:36 2009  commencing singleton removal, final pass
Mon Apr 06 12:37:29 2009  keeping 2395199 ideals with weight <= 20, new excess is 241096
Mon Apr 06 12:37:33 2009  memory use: 67.0 MB
Mon Apr 06 12:37:33 2009  commencing in-memory singleton removal
Mon Apr 06 12:37:33 2009  begin with 2682564 relations and 2395199 unique ideals
Mon Apr 06 12:37:36 2009  reduce to 2663888 relations and 2325325 ideals in 9 passes
Mon Apr 06 12:37:36 2009  max relations containing the same ideal: 20
Mon Apr 06 12:37:38 2009  removing 283257 relations and 253811 ideals in 29446 cliques
Mon Apr 06 12:37:38 2009  commencing in-memory singleton removal
Mon Apr 06 12:37:39 2009  begin with 2380631 relations and 2325325 unique ideals
Mon Apr 06 12:37:41 2009  reduce to 2359480 relations and 2050072 ideals in 7 passes
Mon Apr 06 12:37:41 2009  max relations containing the same ideal: 20
Mon Apr 06 12:37:42 2009  removing 209956 relations and 180510 ideals in 29446 cliques
Mon Apr 06 12:37:42 2009  commencing in-memory singleton removal
Mon Apr 06 12:37:43 2009  begin with 2149524 relations and 2050072 unique ideals
Mon Apr 06 12:37:45 2009  reduce to 2136134 relations and 1855986 ideals in 7 passes
Mon Apr 06 12:37:45 2009  max relations containing the same ideal: 20
Mon Apr 06 12:37:46 2009  relations with 0 large ideals: 16774
Mon Apr 06 12:37:46 2009  relations with 1 large ideals: 130730
Mon Apr 06 12:37:46 2009  relations with 2 large ideals: 416239
Mon Apr 06 12:37:46 2009  relations with 3 large ideals: 668603
Mon Apr 06 12:37:46 2009  relations with 4 large ideals: 570245
Mon Apr 06 12:37:46 2009  relations with 5 large ideals: 257488
Mon Apr 06 12:37:46 2009  relations with 6 large ideals: 66509
Mon Apr 06 12:37:46 2009  relations with 7+ large ideals: 9546
Mon Apr 06 12:37:46 2009  commencing 2-way merge
Mon Apr 06 12:37:48 2009  reduce to 1255153 relation sets and 975005 unique ideals
Mon Apr 06 12:37:48 2009  commencing full merge
Mon Apr 06 12:38:04 2009  memory use: 75.0 MB
Mon Apr 06 12:38:05 2009  found 599605 cycles, need 563205
Mon Apr 06 12:38:05 2009  weight of 563205 cycles is about 39603761 (70.32/cycle)
Mon Apr 06 12:38:05 2009  distribution of cycle lengths:
Mon Apr 06 12:38:05 2009  1 relations: 61811
Mon Apr 06 12:38:05 2009  2 relations: 61616
Mon Apr 06 12:38:05 2009  3 relations: 61256
Mon Apr 06 12:38:05 2009  4 relations: 56642
Mon Apr 06 12:38:05 2009  5 relations: 51364
Mon Apr 06 12:38:05 2009  6 relations: 45948
Mon Apr 06 12:38:05 2009  7 relations: 40047
Mon Apr 06 12:38:05 2009  8 relations: 34563
Mon Apr 06 12:38:05 2009  9 relations: 30620
Mon Apr 06 12:38:05 2009  10+ relations: 119338
Mon Apr 06 12:38:05 2009  heaviest cycle: 18 relations
Mon Apr 06 12:38:05 2009  commencing cycle optimization
Mon Apr 06 12:38:06 2009  start with 3440975 relations
Mon Apr 06 12:38:15 2009  pruned 88888 relations
Mon Apr 06 12:38:15 2009  memory use: 91.0 MB
Mon Apr 06 12:38:15 2009  distribution of cycle lengths:
Mon Apr 06 12:38:15 2009  1 relations: 61811
Mon Apr 06 12:38:15 2009  2 relations: 63169
Mon Apr 06 12:38:15 2009  3 relations: 63625
Mon Apr 06 12:38:15 2009  4 relations: 58170
Mon Apr 06 12:38:15 2009  5 relations: 52951
Mon Apr 06 12:38:15 2009  6 relations: 46648
Mon Apr 06 12:38:15 2009  7 relations: 40611
Mon Apr 06 12:38:15 2009  8 relations: 34684
Mon Apr 06 12:38:15 2009  9 relations: 30566
Mon Apr 06 12:38:15 2009  10+ relations: 110970
Mon Apr 06 12:38:15 2009  heaviest cycle: 18 relations
Mon Apr 06 12:38:16 2009  RelProcTime: 488
Mon Apr 06 12:38:16 2009  
Mon Apr 06 12:38:16 2009  commencing linear algebra
Mon Apr 06 12:38:17 2009  read 563205 cycles
Mon Apr 06 12:38:18 2009  cycles contain 1908962 unique relations
Mon Apr 06 12:38:41 2009  read 1908962 relations
Mon Apr 06 12:38:44 2009  using 20 quadratic characters above 134215308
Mon Apr 06 12:38:57 2009  building initial matrix
Mon Apr 06 12:39:25 2009  memory use: 211.0 MB
Mon Apr 06 12:39:30 2009  read 563205 cycles
Mon Apr 06 12:39:31 2009  matrix is 562965 x 563205 (159.4 MB) with weight 53088746 (94.26/col)
Mon Apr 06 12:39:31 2009  sparse part has weight 37833274 (67.17/col)
Mon Apr 06 12:39:41 2009  filtering completed in 3 passes
Mon Apr 06 12:39:41 2009  matrix is 558794 x 558994 (158.7 MB) with weight 52833426 (94.52/col)
Mon Apr 06 12:39:41 2009  sparse part has weight 37701662 (67.45/col)
Mon Apr 06 12:39:43 2009  read 558994 cycles
Mon Apr 06 12:39:45 2009  matrix is 558794 x 558994 (158.7 MB) with weight 52833426 (94.52/col)
Mon Apr 06 12:39:45 2009  sparse part has weight 37701662 (67.45/col)
Mon Apr 06 12:39:45 2009  saving the first 48 matrix rows for later
Mon Apr 06 12:39:45 2009  matrix is 558746 x 558994 (152.4 MB) with weight 41872936 (74.91/col)
Mon Apr 06 12:39:45 2009  sparse part has weight 36594739 (65.47/col)
Mon Apr 06 12:39:45 2009  matrix includes 64 packed rows
Mon Apr 06 12:39:45 2009  using block size 65536 for processor cache size 3072 kB
Mon Apr 06 12:39:50 2009  commencing Lanczos iteration
Mon Apr 06 12:39:50 2009  memory use: 150.0 MB
Mon Apr 06 13:26:56 2009  lanczos halted after 8838 iterations (dim = 558743)
Mon Apr 06 13:26:58 2009  recovered 28 nontrivial dependencies
Mon Apr 06 13:26:58 2009  BLanczosTime: 2922
Mon Apr 06 13:26:58 2009  
Mon Apr 06 13:26:58 2009  commencing square root phase
Mon Apr 06 13:26:58 2009  reading relations for dependency 1
Mon Apr 06 13:26:58 2009  read 279405 cycles
Mon Apr 06 13:26:59 2009  cycles contain 1164385 unique relations
Mon Apr 06 13:27:16 2009  read 1164385 relations
Mon Apr 06 13:27:23 2009  multiplying 951528 relations
Mon Apr 06 13:30:28 2009  multiply complete, coefficients have about 41.70 million bits
Mon Apr 06 13:30:29 2009  initial square root is modulo 972337
Mon Apr 06 13:34:46 2009  sqrtTime: 468
Mon Apr 06 13:34:46 2009  prp58 factor: 1685645882744324078184380208870777133400255977328802807319
Mon Apr 06 13:34:46 2009  prp59 factor: 31024854582650382849964071719783112624254304541889736365429
Mon Apr 06 13:34:46 2009  elapsed time 01:06:02

Apr 6, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Apr 6, 2009

(17·10¹⁶⁷-11)/3 = 5(6)₁₆₆3_<168> = 457 · 33995374298549333_<17> · C149

C149 = P66 · P84

P66 = 211948524783140872523869494554357501250761114692475486316231413047_<66>

P84 = 172092221659899480381622501487547441908021614419060870914312272506350998473867118309_<84>

Number: n
N=36474692507468977480556677591592218144617617675625929624485770122373994931696435310509024634439460262095368089707082829808131805594612499364995177523
  ( 149 digits)
SNFS difficulty: 168 digits.
Divisors found:

Mon Apr 06 02:28:48 2009  prp66 factor: 211948524783140872523869494554357501250761114692475486316231413047
Mon Apr 06 02:28:48 2009  prp84 factor: 172092221659899480381622501487547441908021614419060870914312272506350998473867118309
Mon Apr 06 02:28:48 2009  elapsed time 01:58:21 (Msieve 1.40 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 55.83 hours.
Scaled time: 147.35 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_5_6_166_3
n: 36474692507468977480556677591592218144617617675625929624485770122373994931696435310509024634439460262095368089707082829808131805594612499364995177523
skew: 0.36
deg: 5
c5: 1700
c0: -11
m: 1000000000000000000000000000000000
type: snfs
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [3000000, 6267913)
Primes: RFBsize:412849, AFBsize:413992, largePrimes:17364952 encountered
Relations: rels:16491595, finalFF:741470
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1772352 hash collisions in 18183333 relations
Msieve: matrix is 1054088 x 1054336 (282.2 MB)

Total sieving time: 54.69 hours.
Total relation processing time: 1.15 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,56,56,2.4,2.4,100000
total time: 55.83 hours.
 --------- CPU info (if available) ----------

(49·10¹⁶⁴-31)/9 = 5(4)₁₆₃1_<165> = 523 · 1637 · 454200427 · 18266240106599_<14> · C137

C137 = P56 · P81

P56 = 97242893951521724288182917546832140952424722461682859509_<56>

P81 = 788222135806169106863746019469358535526566092827867970024563598445394794227816063_<81>

Number: n
N=76649001562441256983057132920583752272727540399996815081522836182540755572653972704335494117436254992778464429440434061430253553922493067
  ( 137 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Apr 06 04:07:25 2009  prp56 factor: 97242893951521724288182917546832140952424722461682859509
Mon Apr 06 04:07:25 2009  prp81 factor: 788222135806169106863746019469358535526566092827867970024563598445394794227816063
Mon Apr 06 04:07:25 2009  elapsed time 01:20:18 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 45.90 hours.
Scaled time: 122.08 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_4_163_1
n: 76649001562441256983057132920583752272727540399996815081522836182540755572653972704335494117436254992778464429440434061430253553922493067
skew: 1.45
deg: 5
c5: 49
c0: -310
m: 1000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 5304371)
Primes: RFBsize:348513, AFBsize:348872, largePrimes:16463712 encountered
Relations: rels:15664570, finalFF:702248
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1652819 hash collisions in 17291763 relations
Msieve: matrix is 857577 x 857825 (228.7 MB)

Total sieving time: 45.07 hours.
Total relation processing time: 0.83 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 45.90 hours.
 --------- CPU info (if available) ----------

Apr 6, 2009

By Serge Batalov / Msieve-1.41 / Apr 6, 2009

(34·10¹⁹¹+11)/9 = 3(7)₁₉₀9_<192> = 113 · 1013 · 1367 · 2387502161115178976633_<22> · 1337145504619678888281505265819_<31> · 120026378003113347218196971409257395549_<39> · C94

C94 = P46 · P49

P46 = 5576459049616245331794588700591305015687512059_<46>

P49 = 1129854043384976187722965516017107068808930983589_<49>

N=6300584804979656332522486024330108364763076187442062528945022670680294571785341216951168599751
  ( 94 digits)
Divisors found:
 r1=5576459049616245331794588700591305015687512059 (pp46)
 r2=1129854043384976187722965516017107068808930983589 (pp49)
Version: Msieve-1.41
Total time: 1.82 hours.
Scaled time: 5.19 units (timescale=2.847).
Factorization parameters were as follows:
name: t
n:  6300584804979656332522486024330108364763076187442062528945022670680294571785341216951168599751
m:  2977730393083962263171
deg: 4
c4: 80138160
c3: 449063211
c2: -104636056272405988
c1: 116041174740284550030
c0: -88597242062159449752
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.529
# E(F1,F2) = 5.303132e-05
# GGNFS version 0.77.1-20060722-k8 polyselect.
# Options were:
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1238954774.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 158994 x 159221
Polynomial selection time: 0.17 hours.
Total sieving time: 1.55 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 1.82 hours.

Apr 5, 2009 (7th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 5, 2009

(52·10¹⁷³-61)/9 = 5(7)₁₇₂1_<174> = 487 · 3887741496601493354323269097_<28> · 90653296002215312383583343122057_<32> · C112

C112 = P56 · P57

P56 = 11358246151509454265298361082211131044094523460551505429_<56>

P57 = 296373669679166061270584211220807804253893546318858753913_<57>

Number: n
N=3366285093042122150456621987002021960445506732334155592635888015253782697409856377749511153026058866847194493677
  ( 112 digits)
Divisors found:

Sun Apr 05 12:27:26 2009  prp56 factor: 11358246151509454265298361082211131044094523460551505429
Sun Apr 05 12:27:26 2009  prp57 factor: 296373669679166061270584211220807804253893546318858753913
Sun Apr 05 12:27:26 2009  elapsed time 00:41:20 (Msieve 1.40 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 16.14 hours.
Scaled time: 42.23 units (timescale=2.616).
Factorization parameters were as follows:
name: KA_5_7_172_1
n: 3366285093042122150456621987002021960445506732334155592635888015253782697409856377749511153026058866847194493677
Y0: -3622036013363435736377
Y1:  481341996359
c0: -1520636057258479594764414408
c1:  196038286467304068605146
c2: -187469281259963629
c3: -111326065901342
c4: -625599852
c5:  5400
skew: 68735.52
type: gnfs
rlim: 3500000
alim: 3500080
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
q0: 1750001
qintsize: 99999
Factor base limits: 3500000/3500080
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1750001, 2518163)
Primes: RFBsize:250150, AFBsize:250369, largePrimes:16373806 encountered
Relations: rels:14214082, finalFF:505175
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 969515 hash collisions in 16139625 relations
Msieve: matrix is 450646 x 450894 (124.0 MB)

Total sieving time: 15.77 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500080,28,28,56,56,2.6,2.6,100000
total time: 16.14 hours.
 --------- CPU info (if available) ----------

(52·10¹⁵¹-61)/9 = 5(7)₁₅₀1_<152> = 3 · 167 · C150

C150 = P71 · P79

P71 = 94351484168597880784045155675864400216052806712470671801849481953624839_<71>

P79 = 1222290319651907786823602119359510097400460955121974664647743836225572719664489_<79>

Number: n
N=115324905744067420714127300953648259037480594366821911732091372809935684187181193169217121312929696163229097360833887779995564426702151253049456642271
  ( 150 digits)
SNFS difficulty: 153 digits.
Divisors found:

Sun Apr 05 16:18:40 2009  prp71 factor: 94351484168597880784045155675864400216052806712470671801849481953624839
Sun Apr 05 16:18:40 2009  prp79 factor: 1222290319651907786823602119359510097400460955121974664647743836225572719664489
Sun Apr 05 16:18:40 2009  elapsed time 00:59:05 (Msieve 1.40 - dependency 2)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 21.37 hours.
Scaled time: 38.95 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_5_7_150_1
n: 115324905744067420714127300953648259037480594366821911732091372809935684187181193169217121312929696163229097360833887779995564426702151253049456642271
skew: 1.30
deg: 5
c5: 65
c0: -244
type: snfs
m: 2000000000000000000000000000000
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1000000, 2000000
)
Primes: RFBsize:148933, AFBsize:148971, largePrimes:17723461 encountered
Relations: rels:17159742, finalFF:364288
Max relations in full relation-set: 28
Initial matrix: 297971 x 364287 with sparse part having weight 64131147.
Pruned matrix : 285825 x 287378 with weight 44814466.

Msieve: found 1569893 hash collisions in 18295843 relations
Msieve: matrix is 399889 x 400137 (105.8 MB)

Total sieving time: 20.97 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,56,56,2.6,2.6,100000
total time: 21.37 hours.
 --------- CPU info (if available) ----------

(37·10¹⁶⁷+17)/9 = 4(1)₁₆₆3_<168> = 157 · 76919 · 4887648636361_<13> · C148

C148 = P57 · P92

P57 = 173207329770929129788153516150523370482395041926341393891_<57>

P92 = 40212371719260342715433361435253229581586380261851521721210578233067994371204047342065429361_<92>

Number: n
N=6965077529249110553611950308829260280080127396948883048161401576107756620314473740991982962973447965340956826328069876057159678111842314192137433651
  ( 148 digits)
SNFS difficulty: 168 digits.
Divisors found:

Sun Apr 05 23:04:03 2009  prp57 factor: 173207329770929129788153516150523370482395041926341393891
Sun Apr 05 23:04:03 2009  prp92 factor: 40212371719260342715433361435253229581586380261851521721210578233067994371204047342065429361
Sun Apr 05 23:04:03 2009  elapsed time 01:51:37 (Msieve 1.40 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 49.39 hours.
Scaled time: 130.35 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_4_1_166_3
n: 6965077529249110553611950308829260280080127396948883048161401576107756620314473740991982962973447965340956826328069876057159678111842314192137433651
skew: 0.34
deg: 5
c5: 3700
c0: 17
m: 1000000000000000000000000000000000
type: snfs
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [3000000, 5916623)
Primes: RFBsize:412849, AFBsize:411316, largePrimes:17134015 encountered
Relations: rels:16290176, finalFF:820249
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1583804 hash collisions in 17495448 relations
Msieve: matrix is 1034114 x 1034362 (277.9 MB)

Total sieving time: 48.45 hours.
Total relation processing time: 0.95 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,56,56,2.4,2.4,100000
total time: 49.39 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶⁰-61)/9 = 5(7)₁₅₉1_<161> = 3 · 7 · 67 · 439 · 217720831 · C147

C147 = P39 · P109

P39 = 149008281078740942531313177231564940583_<39>

P109 = 2883313254510041458866821834674195828764042985699917059832669638957731959328453054117719731853150688457037899_<109>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 429637551866091578297626068655909887684954878631681645707893117502917598671280423538565206659975600988026257343457552634828423780994648030114155117 (147 digits)
Using B1=634000, B2=522408822, polynomial Dickson(3), sigma=4032056949
Step 1 took 9703ms
********** Factor found in step 1: 149008281078740942531313177231564940583
Found probable prime factor of 39 digits: 149008281078740942531313177231564940583
Probable prime cofactor 2883313254510041458866821834674195828764042985699917059832669638957731959328453054117719731853150688457037899 has 109 digits

Apr 5, 2009 (6th)

By Andreas Tete / Msieve v1.40, GGNFS, Msieve v1.41 / Apr 5, 2009

(49·10¹⁶¹-31)/9 = 5(4)₁₆₀1_<162> = 17 · 99928195881605184721_<20> · 954328629156044847391_<21> · C120

C120 = P59 · P61

P59 = 42332905570352079910250248491152463870303006578684797037033_<59>

P61 = 7933056952978764392358391566405953858218810888756092478579471_<61>

Sun Apr 05 09:14:00 2009  
Sun Apr 05 09:14:00 2009  
Sun Apr 05 09:14:00 2009  Msieve v. 1.41
Sun Apr 05 09:14:00 2009  random seeds: 4dfce958 7c71a87e
Sun Apr 05 09:14:00 2009  factoring 335829350874675033217001092909629874466816595322856380608747420361731618351359657712279857781403403313118396761620549543 (120 digits)
Sun Apr 05 09:14:01 2009  searching for 15-digit factors
Sun Apr 05 09:14:03 2009  commencing number field sieve (120-digit input)
Sun Apr 05 09:14:03 2009  R0: -124649807631972485453326
Sun Apr 05 09:14:03 2009  R1:  6091932872993
Sun Apr 05 09:14:03 2009  A0: -3902837875525956067279602109515
Sun Apr 05 09:14:03 2009  A1:  281787695888883644122412193
Sun Apr 05 09:14:03 2009  A2:  298129955431666715375
Sun Apr 05 09:14:03 2009  A3: -3716331300607841
Sun Apr 05 09:14:03 2009  A4: -1896684492
Sun Apr 05 09:14:03 2009  A5:  11160
Sun Apr 05 09:14:03 2009  skew 377391.63, size 1.615448e-011, alpha -7.252922, combined = 2.729843e-010
Sun Apr 05 09:14:04 2009  
Sun Apr 05 09:14:04 2009  commencing relation filtering
Sun Apr 05 09:14:04 2009  commencing duplicate removal, pass 1
Sun Apr 05 09:15:44 2009  found 822477 hash collisions in 8818929 relations
Sun Apr 05 09:16:08 2009  added 58983 free relations
Sun Apr 05 09:16:08 2009  commencing duplicate removal, pass 2
Sun Apr 05 09:16:46 2009  found 747915 duplicates and 8129996 unique relations
Sun Apr 05 09:16:46 2009  memory use: 48.6 MB
Sun Apr 05 09:16:46 2009  reading rational ideals above 5570560
Sun Apr 05 09:16:46 2009  reading algebraic ideals above 5570560
Sun Apr 05 09:16:46 2009  commencing singleton removal, pass 1
Sun Apr 05 09:18:19 2009  relations with 0 large ideals: 216641
Sun Apr 05 09:18:19 2009  relations with 1 large ideals: 1421092
Sun Apr 05 09:18:19 2009  relations with 2 large ideals: 3105061
Sun Apr 05 09:18:19 2009  relations with 3 large ideals: 2621118
Sun Apr 05 09:18:19 2009  relations with 4 large ideals: 704509
Sun Apr 05 09:18:19 2009  relations with 5 large ideals: 5859
Sun Apr 05 09:18:19 2009  relations with 6 large ideals: 55716
Sun Apr 05 09:18:19 2009  relations with 7+ large ideals: 0
Sun Apr 05 09:18:19 2009  8129996 relations and about 7649754 large ideals
Sun Apr 05 09:18:19 2009  commencing singleton removal, pass 2
Sun Apr 05 09:19:53 2009  found 3539625 singletons
Sun Apr 05 09:19:53 2009  current dataset: 4590371 relations and about 3452788 large ideals
Sun Apr 05 09:19:53 2009  commencing singleton removal, pass 3
Sun Apr 05 09:20:57 2009  found 702710 singletons
Sun Apr 05 09:20:57 2009  current dataset: 3887661 relations and about 2711027 large ideals
Sun Apr 05 09:20:57 2009  commencing singleton removal, pass 4
Sun Apr 05 09:21:56 2009  found 179345 singletons
Sun Apr 05 09:21:56 2009  current dataset: 3708316 relations and about 2528624 large ideals
Sun Apr 05 09:21:56 2009  commencing singleton removal, final pass
Sun Apr 05 09:22:57 2009  memory use: 66.6 MB
Sun Apr 05 09:22:57 2009  commencing in-memory singleton removal
Sun Apr 05 09:22:58 2009  begin with 3708316 relations and 2663753 unique ideals
Sun Apr 05 09:23:01 2009  reduce to 3341110 relations and 2290421 ideals in 12 passes
Sun Apr 05 09:23:01 2009  max relations containing the same ideal: 19
Sun Apr 05 09:23:02 2009  reading rational ideals above 720000
Sun Apr 05 09:23:02 2009  reading algebraic ideals above 720000
Sun Apr 05 09:23:02 2009  commencing singleton removal, final pass
Sun Apr 05 09:24:08 2009  keeping 2824055 ideals with weight <= 20, new excess is 334702
Sun Apr 05 09:24:13 2009  memory use: 92.0 MB
Sun Apr 05 09:24:13 2009  commencing in-memory singleton removal
Sun Apr 05 09:24:13 2009  begin with 3357964 relations and 2824055 unique ideals
Sun Apr 05 09:24:17 2009  reduce to 3327759 relations and 2712302 ideals in 10 passes
Sun Apr 05 09:24:17 2009  max relations containing the same ideal: 20
Sun Apr 05 09:24:20 2009  removing 636215 relations and 522614 ideals in 113601 cliques
Sun Apr 05 09:24:20 2009  commencing in-memory singleton removal
Sun Apr 05 09:24:20 2009  begin with 2691544 relations and 2712302 unique ideals
Sun Apr 05 09:24:23 2009  reduce to 2620186 relations and 2115568 ideals in 8 passes
Sun Apr 05 09:24:23 2009  max relations containing the same ideal: 20
Sun Apr 05 09:24:25 2009  removing 487715 relations and 374114 ideals in 113601 cliques
Sun Apr 05 09:24:25 2009  commencing in-memory singleton removal
Sun Apr 05 09:24:25 2009  begin with 2132471 relations and 2115568 unique ideals
Sun Apr 05 09:24:27 2009  reduce to 2073625 relations and 1680289 ideals in 8 passes
Sun Apr 05 09:24:27 2009  max relations containing the same ideal: 20
Sun Apr 05 09:24:29 2009  relations with 0 large ideals: 27264
Sun Apr 05 09:24:29 2009  relations with 1 large ideals: 183328
Sun Apr 05 09:24:29 2009  relations with 2 large ideals: 488627
Sun Apr 05 09:24:29 2009  relations with 3 large ideals: 655097
Sun Apr 05 09:24:29 2009  relations with 4 large ideals: 474809
Sun Apr 05 09:24:29 2009  relations with 5 large ideals: 191787
Sun Apr 05 09:24:29 2009  relations with 6 large ideals: 46151
Sun Apr 05 09:24:29 2009  relations with 7+ large ideals: 6562
Sun Apr 05 09:24:29 2009  commencing 2-way merge
Sun Apr 05 09:24:30 2009  reduce to 1314049 relation sets and 920713 unique ideals
Sun Apr 05 09:24:30 2009  commencing full merge
Sun Apr 05 09:24:45 2009  memory use: 71.9 MB
Sun Apr 05 09:24:46 2009  found 643030 cycles, need 586913
Sun Apr 05 09:24:46 2009  weight of 586913 cycles is about 41219723 (70.23/cycle)
Sun Apr 05 09:24:46 2009  distribution of cycle lengths:
Sun Apr 05 09:24:46 2009  1 relations: 61391
Sun Apr 05 09:24:46 2009  2 relations: 61235
Sun Apr 05 09:24:46 2009  3 relations: 63460
Sun Apr 05 09:24:46 2009  4 relations: 60361
Sun Apr 05 09:24:46 2009  5 relations: 57898
Sun Apr 05 09:24:46 2009  6 relations: 51907
Sun Apr 05 09:24:46 2009  7 relations: 47009
Sun Apr 05 09:24:46 2009  8 relations: 41190
Sun Apr 05 09:24:46 2009  9 relations: 35581
Sun Apr 05 09:24:46 2009  10+ relations: 106881
Sun Apr 05 09:24:46 2009  heaviest cycle: 16 relations
Sun Apr 05 09:24:46 2009  commencing cycle optimization
Sun Apr 05 09:24:47 2009  start with 3439931 relations
Sun Apr 05 09:24:56 2009  pruned 115086 relations
Sun Apr 05 09:24:56 2009  memory use: 88.4 MB
Sun Apr 05 09:24:56 2009  distribution of cycle lengths:
Sun Apr 05 09:24:56 2009  1 relations: 61391
Sun Apr 05 09:24:56 2009  2 relations: 63128
Sun Apr 05 09:24:56 2009  3 relations: 66431
Sun Apr 05 09:24:56 2009  4 relations: 62893
Sun Apr 05 09:24:56 2009  5 relations: 60470
Sun Apr 05 09:24:56 2009  6 relations: 53689
Sun Apr 05 09:24:56 2009  7 relations: 48368
Sun Apr 05 09:24:56 2009  8 relations: 41672
Sun Apr 05 09:24:56 2009  9 relations: 35699
Sun Apr 05 09:24:56 2009  10+ relations: 93172
Sun Apr 05 09:24:56 2009  heaviest cycle: 16 relations
Sun Apr 05 09:24:57 2009  RelProcTime: 514
Sun Apr 05 09:24:57 2009  
Sun Apr 05 09:24:57 2009  commencing linear algebra
Sun Apr 05 09:24:57 2009  read 586913 cycles
Sun Apr 05 09:24:58 2009  cycles contain 1811025 unique relations
Sun Apr 05 09:25:25 2009  read 1811025 relations
Sun Apr 05 09:25:28 2009  using 20 quadratic characters above 134212104
Sun Apr 05 09:25:39 2009  building initial matrix
Sun Apr 05 09:26:07 2009  memory use: 208.0 MB
Sun Apr 05 09:26:08 2009  read 586913 cycles
Sun Apr 05 09:26:08 2009  matrix is 586646 x 586913 (167.0 MB) with weight 56007431 (95.43/col)
Sun Apr 05 09:26:08 2009  sparse part has weight 39093231 (66.61/col)
Sun Apr 05 09:26:19 2009  filtering completed in 3 passes
Sun Apr 05 09:26:19 2009  matrix is 584235 x 584435 (166.6 MB) with weight 55838102 (95.54/col)
Sun Apr 05 09:26:19 2009  sparse part has weight 38999914 (66.73/col)
Sun Apr 05 09:26:21 2009  read 584435 cycles
Sun Apr 05 09:26:22 2009  matrix is 584235 x 584435 (166.6 MB) with weight 55838102 (95.54/col)
Sun Apr 05 09:26:22 2009  sparse part has weight 38999914 (66.73/col)
Sun Apr 05 09:26:22 2009  saving the first 48 matrix rows for later
Sun Apr 05 09:26:23 2009  matrix is 584187 x 584435 (159.9 MB) with weight 44285250 (75.77/col)
Sun Apr 05 09:26:23 2009  sparse part has weight 38420102 (65.74/col)
Sun Apr 05 09:26:23 2009  matrix includes 64 packed rows
Sun Apr 05 09:26:23 2009  using block size 65536 for processor cache size 3072 kB
Sun Apr 05 09:26:28 2009  commencing Lanczos iteration
Sun Apr 05 09:26:28 2009  memory use: 156.6 MB
Sun Apr 05 10:16:16 2009  lanczos halted after 9240 iterations (dim = 584187)
Sun Apr 05 10:16:18 2009  recovered 30 nontrivial dependencies
Sun Apr 05 10:16:18 2009  BLanczosTime: 3081
Sun Apr 05 10:16:18 2009  
Sun Apr 05 10:16:18 2009  commencing square root phase
Sun Apr 05 10:16:18 2009  reading relations for dependency 1
Sun Apr 05 10:16:18 2009  read 292523 cycles
Sun Apr 05 10:16:19 2009  cycles contain 1115775 unique relations
Sun Apr 05 10:16:58 2009  read 1115775 relations
Sun Apr 05 10:17:05 2009  multiplying 904932 relations
Sun Apr 05 10:19:17 2009  multiply complete, coefficients have about 39.86 million bits
Sun Apr 05 10:19:18 2009  initial square root is modulo 527981
Sun Apr 05 10:23:19 2009  reading relations for dependency 2
Sun Apr 05 10:23:19 2009  read 292163 cycles
Sun Apr 05 10:23:20 2009  cycles contain 1114875 unique relations
Sun Apr 05 10:23:47 2009  read 1114875 relations
Sun Apr 05 10:23:54 2009  multiplying 903926 relations
Sun Apr 05 10:26:07 2009  multiply complete, coefficients have about 39.81 million bits
Sun Apr 05 10:26:08 2009  initial square root is modulo 519487
Sun Apr 05 10:29:55 2009  sqrtTime: 817
Sun Apr 05 10:29:55 2009  prp59 factor: 42332905570352079910250248491152463870303006578684797037033
Sun Apr 05 10:29:55 2009  prp61 factor: 7933056952978764392358391566405953858218810888756092478579471
Sun Apr 05 10:29:55 2009  elapsed time 01:15:55

Apr 5, 2009 (5th)

By Sinkiti Sibata / GGNFS, Msieve / Apr 5, 2009

(52·10¹⁴³-43)/9 = 5(7)₁₄₂3_<144> = 3 · 7 · C143

C143 = P54 · P89

P54 = 807615122125603613914057337949993440439897588347926777_<54>

P89 = 34067251540330300201992138205970272893273963119767457598149839792467516383883488667168769_<89>

Number: 57773_143
N=27513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513
  ( 143 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=807615122125603613914057337949993440439897588347926777
 r2=34067251540330300201992138205970272893273963119767457598149839792467516383883488667168769
Version: 
Total time: 12.31 hours.
Scaled time: 24.59 units (timescale=1.997).
Factorization parameters were as follows:
name: 57773_143
n: 27513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513227513
m: 100000000000000000000000000000
deg: 5
c5: 13
c0: -1075
skew: 2.42
type: snfs
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [955000, 2255001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 304696 x 304944
Total sieving time: 12.31 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 12.31 hours.
 --------- CPU info (if available) ----------

(52·10¹⁵⁰-43)/9 = 5(7)₁₄₉3_<151> = 17 · 2789 · C147

C147 = P53 · P94

P53 = 83934125900908945406290151909996201257658792803890131_<53>

P94 = 1451860288607149446470241259122719534737861510205531933315916529210374674233815808967348105891_<94>

Number: 57773_150
N=121860624254482479020053103110492434095665276986855456895319380291856195089485537253027181949629379659118338383518819264289915798995587239317861721
  ( 147 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=83934125900908945406290151909996201257658792803890131 (pp53)
 r2=1451860288607149446470241259122719534737861510205531933315916529210374674233815808967348105891 (pp94)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 31.31 hours.
Scaled time: 79.96 units (timescale=2.554).
Factorization parameters were as follows:
name: 57773_150
n: 121860624254482479020053103110492434095665276986855456895319380291856195089485537253027181949629379659118338383518819264289915798995587239317861721
m: 1000000000000000000000000000000
deg: 5
c5: 52
c0: -43
skew: 0.96
type: snfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176638, largePrimes:7741497 encountered
Relations: rels:8627507, finalFF:1294063
Max relations in full relation-set: 28
Initial matrix: 353006 x 1294063 with sparse part having weight 144568564.
Pruned matrix : 225830 x 227659 with weight 57153150.
Total sieving time: 30.27 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.82 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 31.31 hours.
 --------- CPU info (if available) ----------

(52·10¹⁴⁸-43)/9 = 5(7)₁₄₇3_<149> = 3037 · C146

C146 = P36 · P110

P36 = 279391734608130202021631452260130399_<36>

P110 = 68093003102523641973256112661038226007344276787206714553496377637729064483403180969104371107836390478992760271_<110>

Number: 57773_148
N=19024622251490871839900486591299893901145135916291662093440163904437858998280466834961401968316686788863278820473420407565945926169831339406578129
  ( 146 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=279391734608130202021631452260130399 (pp36)
 r2=68093003102523641973256112661038226007344276787206714553496377637729064483403180969104371107836390478992760271 (pp110)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 25.01 hours.
Scaled time: 64.39 units (timescale=2.575).
Factorization parameters were as follows:
name: 57773_148
n: 19024622251490871839900486591299893901145135916291662093440163904437858998280466834961401968316686788863278820473420407565945926169831339406578129
m: 1000000000000000000000000000000
deg: 5
c5: 13
c0: -1075
skew: 2.42
type: snfs
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 2050001)
Primes: RFBsize:169511, AFBsize:169386, largePrimes:7403976 encountered
Relations: rels:7863011, finalFF:884468
Max relations in full relation-set: 28
Initial matrix: 338963 x 884468 with sparse part having weight 100265027.
Pruned matrix : 226894 x 228652 with weight 48084185.
Total sieving time: 24.07 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.72 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 25.01 hours.
 --------- CPU info (if available) ----------

(52·10¹⁴⁴-43)/9 = 5(7)₁₄₃3_<145> = 53 · 234569521 · C135

C135 = P35 · P37 · P64

P35 = 31371138588821349613700530590890927_<35>

P37 = 1982018047701077780509528578676893737_<37>

P64 = 7474385572268945148575813102413960721896402211291117415186582479_<64>

Number: 57773_144
N=464743563390790662302223148122243684524167207021974568049135016313948762126363846796085039585775798660735169198518865155608494645009321
  ( 135 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=31371138588821349613700530590890927 (pp35)
 r2=1982018047701077780509528578676893737 (pp37)
 r3=7474385572268945148575813102413960721896402211291117415186582479 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.48 hours.
Scaled time: 34.81 units (timescale=1.991).
Factorization parameters were as follows:
name: 57773_144
n: 464743563390790662302223148122243684524167207021974568049135016313948762126363846796085039585775798660735169198518865155608494645009321
m: 100000000000000000000000000000
deg: 5
c5: 26
c0: -215
skew: 1.53
type: snfs
rlim: 1930000
alim: 1930000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1930000/1930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [965000, 2465001)
Primes: RFBsize:144125, AFBsize:144102, largePrimes:4071093 encountered
Relations: rels:4146063, finalFF:323236
Max relations in full relation-set: 28
Initial matrix: 288293 x 323236 with sparse part having weight 32977760.
Pruned matrix : 276680 x 278185 with weight 26148654.
Total sieving time: 16.29 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.96 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000
total time: 17.48 hours.
 --------- CPU info (if available) ----------

Apr 5, 2009 (4th)

By Yang Hae Hun / yafu 1.08, Msieve / Apr 5, 2009

(52·10¹²⁵-61)/9 = 5(7)₁₂₄1_<126> = 89 · 406465909 · 13816078758771664430119_<23> · C94

C94 = P38 · P56

P38 = 93345974488586136481557578198948240419_<38>

P56 = 12384152945704090840185713643463307864708033860757696411_<56>

04/04/09 05:55:26 v1.08 @ *-PC, starting SIQS on c94: 1156010824932442916599876024512135484674672743806345713411843319712970870311267513080241436209
04/04/09 05:55:26 v1.08 @ *-PC, random seeds: 422699426, 400398816
04/04/09 05:55:26 v1.08 @ *-PC, ==== sieve params ====
04/04/09 05:55:26 v1.08 @ *-PC, n = 94 digits, 314 bits
04/04/09 05:55:26 v1.08 @ *-PC, factor base: 78247 primes (max prime = 2104337)
04/04/09 05:55:26 v1.08 @ *-PC, single large prime cutoff: 252520440 (120 * pmax)
04/04/09 05:55:26 v1.08 @ *-PC, double large prime range from 44 to 51 bits
04/04/09 05:55:26 v1.08 @ *-PC, double large prime cutoff: 1330864275125599
04/04/09 05:55:26 v1.08 @ *-PC, using 6 large prime slices of factor base
04/04/09 05:55:26 v1.08 @ *-PC, buckets hold 2048 elements
04/04/09 05:55:26 v1.08 @ *-PC, sieve interval: 22 blocks of size 32768
04/04/09 05:55:26 v1.08 @ *-PC, polynomial A has ~ 12 factors
04/04/09 05:55:26 v1.08 @ *-PC, using multiplier of 17
04/04/09 05:55:26 v1.08 @ *-PC, using small prime variation correction of 22 bits
04/04/09 05:55:26 v1.08 @ *-PC, using x128 sieve scanning
04/04/09 05:55:26 v1.08 @ *-PC, trial factoring cutoff at 98 bits
04/04/09 05:55:26 v1.08 @ *-PC, ==== sieving started ====
04/04/09 07:48:48 v1.08 @ *-PC, sieve time = 2093.8070, relation time = 1660.5040, poly_time = 3039.7980
04/04/09 07:48:48 v1.08 @ *-PC, 78347 relations found: 21602 full + 56745 from 987404 partial, using 634518 polys (309 A polys)
04/04/09 07:48:48 v1.08 @ *-PC, trial division touched 55165090 sieve locations out of 914842976256
04/04/09 07:48:48 v1.08 @ *-PC, ==== post processing stage (msieve-1.38) ====
04/04/09 07:48:49 v1.08 @ *-PC, begin with 1009006 relations
04/04/09 07:48:50 v1.08 @ *-PC, reduce to 189007 relations in 9 passes
04/04/09 07:48:52 v1.08 @ *-PC, failed to read relation 115163
04/04/09 07:48:52 v1.08 @ *-PC, failed to read relation 117523
04/04/09 07:48:53 v1.08 @ *-PC, recovered 189005 relations
04/04/09 07:48:53 v1.08 @ *-PC, recovered 163565 polynomials
04/04/09 07:48:53 v1.08 @ *-PC, attempting to build 78345 cycles
04/04/09 07:48:54 v1.08 @ *-PC, found 78345 cycles in 5 passes
04/04/09 07:48:54 v1.08 @ *-PC, distribution of cycle lengths:
04/04/09 07:48:54 v1.08 @ *-PC,    length 1 : 21602
04/04/09 07:48:54 v1.08 @ *-PC,    length 2 : 15679
04/04/09 07:48:54 v1.08 @ *-PC,    length 3 : 13869
04/04/09 07:48:54 v1.08 @ *-PC,    length 4 : 10354
04/04/09 07:48:54 v1.08 @ *-PC,    length 5 : 6936
04/04/09 07:48:54 v1.08 @ *-PC,    length 6 : 4448
04/04/09 07:48:54 v1.08 @ *-PC,    length 7 : 2507
04/04/09 07:48:54 v1.08 @ *-PC,    length 9+: 2950
04/04/09 07:48:54 v1.08 @ *-PC, largest cycle: 18 relations
04/04/09 07:48:54 v1.08 @ *-PC, matrix is 78247 x 78345 (19.5 MB) with weight 4811341 (61.41/col)
04/04/09 07:48:54 v1.08 @ *-PC, sparse part has weight 4811341 (61.41/col)
04/04/09 07:48:54 v1.08 @ *-PC, filtering completed in 3 passes
04/04/09 07:48:54 v1.08 @ *-PC, matrix is 72791 x 72855 (18.4 MB) with weight 4532402 (62.21/col)
04/04/09 07:48:54 v1.08 @ *-PC, sparse part has weight 4532402 (62.21/col)
04/04/09 07:48:55 v1.08 @ *-PC, saving the first 48 matrix rows for later
04/04/09 07:48:55 v1.08 @ *-PC, matrix is 72743 x 72855 (12.7 MB) with weight 3684887 (50.58/col)
04/04/09 07:48:55 v1.08 @ *-PC, sparse part has weight 2890111 (39.67/col)
04/04/09 07:48:55 v1.08 @ *-PC, matrix includes 64 packed rows
04/04/09 07:48:55 v1.08 @ *-PC, using block size 29142 for processor cache size 3072 kB
04/04/09 07:48:55 v1.08 @ *-PC, commencing Lanczos iteration
04/04/09 07:48:55 v1.08 @ *-PC, memory use: 11.8 MB
04/04/09 07:49:27 v1.08 @ *-PC, lanczos halted after 1152 iterations (dim = 72741)
04/04/09 07:49:28 v1.08 @ *-PC, recovered 16 nontrivial dependencies
04/04/09 07:49:34 v1.08 @ *-PC, prp38 = 93345974488586136481557578198948240419
04/04/09 07:49:40 v1.08 @ *-PC, Lanczos elapsed time = 39.7290 seconds.
04/04/09 07:49:40 v1.08 @ *-PC, Sqrt elapsed time = 12.7690 seconds.
04/04/09 07:49:40 v1.08 @ *-PC, SIQS elapsed time = 6855.0230 seconds.

(52·10¹⁰⁸-43)/9 = 5(7)₁₀₇3_<109> = 787 · 27101510437_<11> · C96

C96 = P48 · P49

P48 = 168828879314912911150075820888642221890121755641_<48>

P49 = 1604522709759573928184708173767707806180222246187_<49>

04/04/09 01:21:39 v1.08 @ *-PC, starting SIQS on c96: 270889770924036143349846384565327398000486810407942250817297836462141095614664437154536957990867
04/04/09 01:21:39 v1.08 @ *-PC, random seeds: 422699426, 400398816
04/04/09 01:21:39 v1.08 @ *-PC, ==== sieve params ====
04/04/09 01:21:39 v1.08 @ *-PC, n = 96 digits, 323 bits
04/04/09 01:21:39 v1.08 @ *-PC, factor base: 88192 primes (max prime = 2417741)
04/04/09 01:21:39 v1.08 @ *-PC, single large prime cutoff: 314306330 (130 * pmax)
04/04/09 01:21:39 v1.08 @ *-PC, double large prime range from 44 to 51 bits
04/04/09 01:21:39 v1.08 @ *-PC, double large prime cutoff: 1973493179149929
04/04/09 01:21:39 v1.08 @ *-PC, using 6 large prime slices of factor base
04/04/09 01:21:39 v1.08 @ *-PC, buckets hold 2048 elements
04/04/09 01:21:39 v1.08 @ *-PC, sieve interval: 26 blocks of size 32768
04/04/09 01:21:39 v1.08 @ *-PC, polynomial A has ~ 13 factors
04/04/09 01:21:39 v1.08 @ *-PC, using multiplier of 43
04/04/09 01:21:39 v1.08 @ *-PC, using small prime variation correction of 22 bits
04/04/09 01:21:39 v1.08 @ *-PC, using x128 sieve scanning
04/04/09 01:21:39 v1.08 @ *-PC, trial factoring cutoff at 98 bits
04/04/09 01:21:39 v1.08 @ *-PC, ==== sieving started ====
04/04/09 05:13:03 v1.08 @ *-PC, sieve time = 4487.4190, relation time = 3026.6580, poly_time = 6358.5370
04/04/09 05:13:03 v1.08 @ *-PC, 88261 relations found: 22368 full + 65893 from 1212706 partial, using 1164596 polys (284 A polys)
04/04/09 05:13:03 v1.08 @ *-PC, trial division touched 107331281 sieve locations out of 1984397049856
04/04/09 05:13:03 v1.08 @ *-PC, ==== post processing stage (msieve-1.38) ====
04/04/09 05:13:04 v1.08 @ *-PC, begin with 1235074 relations
04/04/09 05:13:05 v1.08 @ *-PC, reduce to 225380 relations in 10 passes
04/04/09 05:13:09 v1.08 @ *-PC, failed to read relation 173574
04/04/09 05:13:10 v1.08 @ *-PC, recovered 225379 relations
04/04/09 05:13:10 v1.08 @ *-PC, recovered 204955 polynomials
04/04/09 05:13:10 v1.08 @ *-PC, attempting to build 88260 cycles
04/04/09 05:13:10 v1.08 @ *-PC, found 88260 cycles in 6 passes
04/04/09 05:13:10 v1.08 @ *-PC, distribution of cycle lengths:
04/04/09 05:13:10 v1.08 @ *-PC,    length 1 : 22368
04/04/09 05:13:10 v1.08 @ *-PC,    length 2 : 15781
04/04/09 05:13:10 v1.08 @ *-PC,    length 3 : 15116
04/04/09 05:13:10 v1.08 @ *-PC,    length 4 : 11934
04/04/09 05:13:10 v1.08 @ *-PC,    length 5 : 8788
04/04/09 05:13:10 v1.08 @ *-PC,    length 6 : 5766
04/04/09 05:13:10 v1.08 @ *-PC,    length 7 : 3630
04/04/09 05:13:10 v1.08 @ *-PC,    length 9+: 4877
04/04/09 05:13:10 v1.08 @ *-PC, largest cycle: 19 relations
04/04/09 05:13:11 v1.08 @ *-PC, matrix is 88192 x 88260 (23.5 MB) with weight 5803843 (65.76/col)
04/04/09 05:13:11 v1.08 @ *-PC, sparse part has weight 5803843 (65.76/col)
04/04/09 05:13:11 v1.08 @ *-PC, filtering completed in 3 passes
04/04/09 05:13:11 v1.08 @ *-PC, matrix is 83625 x 83689 (22.5 MB) with weight 5553704 (66.36/col)
04/04/09 05:13:11 v1.08 @ *-PC, sparse part has weight 5553704 (66.36/col)
04/04/09 05:13:12 v1.08 @ *-PC, saving the first 48 matrix rows for later
04/04/09 05:13:12 v1.08 @ *-PC, matrix is 83577 x 83689 (14.4 MB) with weight 4333696 (51.78/col)
04/04/09 05:13:12 v1.08 @ *-PC, sparse part has weight 3270621 (39.08/col)
04/04/09 05:13:12 v1.08 @ *-PC, matrix includes 64 packed rows
04/04/09 05:13:12 v1.08 @ *-PC, using block size 33475 for processor cache size 3072 kB
04/04/09 05:13:13 v1.08 @ *-PC, commencing Lanczos iteration
04/04/09 05:13:13 v1.08 @ *-PC, memory use: 13.7 MB
04/04/09 05:13:55 v1.08 @ *-PC, lanczos halted after 1323 iterations (dim = 83573)
04/04/09 05:13:55 v1.08 @ *-PC, recovered 16 nontrivial dependencies
04/04/09 05:13:56 v1.08 @ *-PC, prp48 = 168828879314912911150075820888642221890121755641
04/04/09 05:13:57 v1.08 @ *-PC, prp49 = 1604522709759573928184708173767707806180222246187
04/04/09 05:13:57 v1.08 @ *-PC, Lanczos elapsed time = 52.1000 seconds.
04/04/09 05:13:57 v1.08 @ *-PC, Sqrt elapsed time = 2.1370 seconds.
04/04/09 05:13:57 v1.08 @ *-PC, SIQS elapsed time = 13938.3330 seconds.
04/04/09 05:13:57 v1.08 @ *-PC, 
04/04/09 05:13:57 v1.08 @ *-PC, 
04/04/09 05:13:57 v1.08 @ *-PC, Total factoring time = 13948.1140 seconds

Apr 5, 2009 (3rd)

By Wataru Sakai / GMP-ECM / Apr 5, 2009

(34·10¹⁹¹+11)/9 = 3(7)₁₉₀9_<192> = 113 · 1013 · 1367 · 2387502161115178976633_<22> · 1337145504619678888281505265819_<31> · C132

C132 = P39 · C94

P39 = 120026378003113347218196971409257395549_<39>

C94 = [6300584804979656332522486024330108364763076187442062528945022670680294571785341216951168599751_<94>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=314363672
Step 1 took 40842ms
Step 2 took 15087ms
********** Factor found in step 2: 120026378003113347218196971409257395549
Found probable prime factor of 39 digits: 120026378003113347218196971409257395549
Composite cofactor 6300584804979656332522486024330108364763076187442062528945022670680294571785341216951168599751 has 94 digits

Apr 5, 2009 (2nd)

By Tyler Cadigan / GGNFS, Msieve / Apr 5, 2009

6·10¹⁹⁵+1 = 6(0)₁₉₄1_<196> = 17 · 353 · 421 · 53984968629707_<14> · 5444649381690383_<16> · 450367983155898302933_<21> · C140

C140 = P48 · P93

P48 = 154154162540960500400074342123380051113966965013_<48>

P93 = 116380439153233275654538630432091976492720690680968724771611953842197614880172185920433608769_<93>

Number: 60001_195
N=17940529133815885800153881115863745792404754507504894161833210949988179704602632689155214043439581558442074568668317290243055511365952998997
  ( 140 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=154154162540960500400074342123380051113966965013 (pp48)
 r2=116380439153233275654538630432091976492720690680968724771611953842197614880172185920433608769 (pp93)
Version: Msieve-1.40
Total time: 357.78 hours.
Scaled time: 908.76 units (timescale=2.540).
Factorization parameters were as follows:
n: 17940529133815885800153881115863745792404754507504894161833210949988179704602632689155214043439581558442074568668317290243055511365952998997
m: 1000000000000000000000000000000000000000
deg: 5
c5: 6
c0: 1
skew: 0.70
type: snfs
lss: 1
rlim: 12800000
alim: 12800000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 12800000/12800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6400000, 6400000)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2217430 x 2217678
Total sieving time: 343.89 hours.
Total relation processing time: 1.18 hours.
Matrix solve time: 12.41 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,195.000,5,0,0,0,0,0,0,0,0,12800000,12800000,28,28,55,55,2.5,2.5,100000
total time: 357.78 hours.
 --------- CPU info (if available) ----------

Apr 5, 2009

By Ignacio Santos / GGNFS, Msieve / Apr 5, 2009

(52·10¹⁶⁰-43)/9 = 5(7)₁₅₉3_<161> = 31 · C160

C160 = P68 · P92

P68 = 25077457244459140237993454335905531978093720860626327806488779925969_<68>

P92 = 74321701159152728181638421439507978993647655703021914136648517945051670135068011396281957507_<92>

Number: 57773_160
N=1863799283154121863799283154121863799283154121863799283154121863799283154121863799283154121863799283154121863799283154121863799283154121863799283154121863799283
  ( 160 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=25077457244459140237993454335905531978093720860626327806488779925969 (pp68)
 r2=74321701159152728181638421439507978993647655703021914136648517945051670135068011396281957507 (pp92)
Version: Msieve-1.39
Total time: 27.54 hours.
Scaled time: 70.82 units (timescale=2.571).
Factorization parameters were as follows:
n: 1863799283154121863799283154121863799283154121863799283154121863799283154121863799283154121863799283154121863799283154121863799283154121863799283154121863799283
m: 100000000000000000000000000000000
deg: 5
c5: 52
c0: -43
skew: 0.96
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 603436 x 603684
Total sieving time: 27.54 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 27.54 hours.
 --------- CPU info (if available) ----------

(52·10¹⁵⁸-43)/9 = 5(7)₁₅₇3_<159> = 3² · 47² · C155

C155 = P41 · P115

P41 = 17854761218842140415213502565193224912319_<41>

P115 = 1627678258039001439860605970380250863485153126084028212198178736018092326228243501514019586278029624355784203540507_<115>

Number: 57773_158
N=29061806638387293283928262048074934750655287851605944257219343985603228096060448557807845570030570785059995864281362998731340364055016235490054714439805733
  ( 155 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=17854761218842140415213502565193224912319 (pp41)
 r2=1627678258039001439860605970380250863485153126084028212198178736018092326228243501514019586278029624355784203540507 (pp115)
Version: Msieve-1.39
Total time: 24.46 hours.
Scaled time: 42.54 units (timescale=1.739).
Factorization parameters were as follows:
n: 29061806638387293283928262048074934750655287851605944257219343985603228096060448557807845570030570785059995864281362998731340364055016235490054714439805733
m: 100000000000000000000000000000000
deg: 5
c5: 13
c0: -1075
skew: 2.42
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 576977 x 577225
Total sieving time: 24.46 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 24.46 hours.
 --------- CPU info (if available) ----------

Apr 4, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Apr 4, 2009

(16·10¹⁶⁴+17)/3 = 5(3)₁₆₃9_<165> = 7 · 11 · 31 · 47940839077_<11> · 842314039257867811_<18> · C133

C133 = P37 · P38 · P59

P37 = 2649677219441206617450398015543024233_<37>

P38 = 77491984690871110773116882178649397417_<38>

P59 = 26947400854473157601390674819569193818375636070543656911591_<59>

Number: 53339_164
N=5533076039547277534902686816907006617446562817173649013529351377329245459054776917181026429204484592208927485101171248718472484912151
  ( 133 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=2649677219441206617450398015543024233 (pp37)
 r2=77491984690871110773116882178649397417 (pp38)
 r3=26947400854473157601390674819569193818375636070543656911591 (pp59)
Version: Msieve-1.39
Total time: 27.26 hours.
Scaled time: 70.09 units (timescale=2.571).
Factorization parameters were as follows:
n: 5533076039547277534902686816907006617446562817173649013529351377329245459054776917181026429204484592208927485101171248718472484912151
m: 1000000000000000000000000000000000
deg: 5
c5: 8
c0: 85
skew: 1.60
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 3350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 657083 x 657331
Total sieving time: 27.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 27.26 hours.
 --------- CPU info (if available) ----------

(52·10¹¹¹-43)/9 = 5(7)₁₁₀3_<112> = 83 · 229 · 7223179 · C101

C101 = P36 · P65

P36 = 584863423487287086370090553502096421_<36>

P65 = 71955570365071690112944453052017200142045082048440819573180970021_<65>

Number: 57773_111
N=42084181222696208551145766341065718167394244888696962675813164926208923535971702108149224245852394841
  ( 101 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=584863423487287086370090553502096421 (pp36)
 r2=71955570365071690112944453052017200142045082048440819573180970021 (pp65)
Version: Msieve-1.39
Total time: 0.76 hours.
Scaled time: 1.94 units (timescale=2.571).
Factorization parameters were as follows:
n: 42084181222696208551145766341065718167394244888696962675813164926208923535971702108149224245852394841
m: 20000000000000000000000
deg: 5
c5: 65
c0: -172
skew: 1.21
type: snfs
lss: 1
rlim: 540000
alim: 540000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 540000/540000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [270000, 420001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 55522 x 55767
Total sieving time: 0.76 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,540000,540000,25,25,45,45,2.2,2.2,50000
total time: 0.76 hours.
 --------- CPU info (if available) ----------

(52·10¹¹³-61)/9 = 5(7)₁₁₂1_<114> = 17 · 19 · C112

C112 = P37 · P75

P37 = 6334577555036252676913035833364473701_<37>

P75 = 282384369624194315326280610935163963623341034525658187309847619129846017477_<75>

Number: 57771_113
N=1788785689714482284141726866185070519435844513243894048847609219126246990024079807361541107671138630890952872377
  ( 112 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=6334577555036252676913035833364473701 (pp37)
 r2=282384369624194315326280610935163963623341034525658187309847619129846017477 (pp75)
Version: Msieve-1.39
Total time: 0.96 hours.
Scaled time: 2.46 units (timescale=2.560).
Factorization parameters were as follows:
n: 1788785689714482284141726866185070519435844513243894048847609219126246990024079807361541107671138630890952872377
m: 100000000000000000000000
deg: 5
c5: 13
c0: -1525
skew: 2.59
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [300000, 500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 71901 x 72149
Total sieving time: 0.96 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000
total time: 0.96 hours.
 --------- CPU info (if available) ----------

(52·10¹¹⁵-43)/9 = 5(7)₁₁₄3_<116> = 31 · 17296260017_<11> · C105

C105 = P39 · P66

P39 = 550328367113756181354375808078026537541_<39>

P66 = 195805567121042826972413900256066733405415435163832249084028696839_<66>

Number: 57773_115
N=107757358025506483908409848584543500927131912107158239835226331391898336429932949665089098889429541532899
  ( 105 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=550328367113756181354375808078026537541 (pp39)
 r2=195805567121042826972413900256066733405415435163832249084028696839 (pp66)
Version: Msieve-1.39
Total time: 1.02 hours.
Scaled time: 2.62 units (timescale=2.571).
Factorization parameters were as follows:
n: 107757358025506483908409848584543500927131912107158239835226331391898336429932949665089098889429541532899
m: 100000000000000000000000
deg: 5
c5: 52
c0: -43
skew: 0.96
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 510001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 61620 x 61857
Total sieving time: 1.02 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 1.02 hours.
 --------- CPU info (if available) ----------

(16·10¹⁶⁵+17)/3 = 5(3)₁₆₄9_<166> = 19 · 3527 · 14731 · 415998187758484049_<18> · C140

C140 = P50 · P90

P50 = 17341860308469023779168462781855560492984381719029_<50>

P90 = 748893938640871307834077166117365969021084229218403936692626349730095244157941293835195353_<90>

Number: 53339_165
N=12987214069769162665161528597771091153224110850225315252735583091972876470942161386503929317169635014496235037525504716535947677808172472237
  ( 140 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=17341860308469023779168462781855560492984381719029 (pp50)
 r2=748893938640871307834077166117365969021084229218403936692626349730095244157941293835195353 (pp90)
Version: Msieve-1.39
Total time: 26.23 hours.
Scaled time: 45.62 units (timescale=1.739).
Factorization parameters were as follows:
n: 12987214069769162665161528597771091153224110850225315252735583091972876470942161386503929317169635014496235037525504716535947677808172472237
m: 1000000000000000000000000000000000
deg: 5
c5: 16
c0: 17
skew: 1.01
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 3450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 629722 x 629970
Total sieving time: 26.23 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 26.23 hours.
 --------- CPU info (if available) ----------

(52·10¹¹⁸-61)/9 = 5(7)₁₁₇1_<119> = 3 · 7 · 893573383 · C109

C109 = P47 · P62

P47 = 35469078962720437482623252574943957771679143009_<47>

P62 = 86808330592926759947184437511766974195098122568233928200733033_<62>

Number: 57771_118
N=3079011532422459502412599001197813568660563775233613155587158700454209167901460143786256134210885231037316297
  ( 109 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=35469078962720437482623252574943957771679143009 (pp47)
 r2=86808330592926759947184437511766974195098122568233928200733033 (pp62)
Version: Msieve-1.39
Total time: 1.30 hours.
Scaled time: 2.26 units (timescale=1.735).
Factorization parameters were as follows:
n: 3079011532422459502412599001197813568660563775233613155587158700454209167901460143786256134210885231037316297
m: 1000000000000000000000000
deg: 5
c5: 13
c0: -1525
skew: 2.59
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 665001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 90017 x 90265
Total sieving time: 1.30 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.30 hours.
 --------- CPU info (if available) ----------

(52·10¹²³-43)/9 = 5(7)₁₂₂3_<124> = 67 · 1399 · 1188132191_<10> · C110

C110 = P52 · P59

P52 = 3351093236793991965948846032892508785295368129973073_<52>

P59 = 15481642800218606985702257125585375058473500820560165696967_<59>

Number: 57773_123
N=51880428482272973194192552107268711120003394748027687836359488509276490989788630088265501092903065879987769591
  ( 110 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=3351093236793991965948846032892508785295368129973073 (pp52)
 r2=15481642800218606985702257125585375058473500820560165696967 (pp59)
Version: Msieve-1.39
Total time: 1.72 hours.
Scaled time: 4.42 units (timescale=2.571).
Factorization parameters were as follows:
n: 51880428482272973194192552107268711120003394748027687836359488509276490989788630088265501092903065879987769591
m: 10000000000000000000000000
deg: 5
c5: 13
c0: -1075
skew: 2.42
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 745001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 110711 x 110957
Total sieving time: 1.72 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 1.72 hours.
 --------- CPU info (if available) ----------

(52·10¹²⁵-43)/9 = 5(7)₁₂₄3_<126> = 3 · 7 · 40933 · 79481 · C115

C115 = P41 · P75

P41 = 14055106398571740700573036109279926184137_<41>

P75 = 601686827538001186614971055977599214541821458117175854938872100149974919813_<75>

Number: 57773_125
N=8456772379665691914425816005149003194304336951392330104780408317456651846308656132020957545982902312336505647606381
  ( 115 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=14055106398571740700573036109279926184137 (pp41)
 r2=601686827538001186614971055977599214541821458117175854938872100149974919813 (pp75)
Version: Msieve-1.39
Total time: 1.57 hours.
Scaled time: 2.73 units (timescale=1.739).
Factorization parameters were as follows:
n: 8456772379665691914425816005149003194304336951392330104780408317456651846308656132020957545982902312336505647606381
m: 10000000000000000000000000
deg: 5
c5: 52
c0: -43
skew: 0.96
type: snfs
lss: 1
rlim: 910000
alim: 910000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 910000/910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [455000, 755001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 112107 x 112352
Total sieving time: 1.57 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000
total time: 1.57 hours.
 --------- CPU info (if available) ----------

(52·10¹²⁶-61)/9 = 5(7)₁₂₅1_<127> = 59 · 558718289 · C117

C117 = P34 · P84

P34 = 1079623793866750213337578330763569_<34>

P84 = 162346708300343897190983060524349673701062352373627192853614222738074262254046907409_<84>

Number: 57771_126
N=175273369136995905543707848858571777917934298230314867088250610038095869054135327591545894755333845216855190013382721
  ( 117 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=1079623793866750213337578330763569 (pp34)
 r2=162346708300343897190983060524349673701062352373627192853614222738074262254046907409 (pp84)
Version: Msieve-1.39
Total time: 2.21 hours.
Scaled time: 5.69 units (timescale=2.571).
Factorization parameters were as follows:
n: 175273369136995905543707848858571777917934298230314867088250610038095869054135327591545894755333845216855190013382721
m: 20000000000000000000000000
deg: 5
c5: 65
c0: -244
skew: 1.30
type: snfs
lss: 1
rlim: 960000
alim: 960000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 960000/960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [480000, 880001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 138707 x 138954
Total sieving time: 2.21 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,960000,960000,26,26,47,47,2.3,2.3,50000
total time: 2.21 hours.
 --------- CPU info (if available) ----------

(52·10¹²⁸-43)/9 = 5(7)₁₂₇3_<129> = 3 · 8753 · 556297188168655163_<18> · C107

C107 = P44 · P64

P44 = 22280461524640293696839248296287379439151813_<44>

P64 = 1775217634961080691725523313726899374646671985030998419880422313_<64>

Number: 57773_128
N=39552668213613296251633284908196732545871870203936203625314569956333416616933435735524261822510328959603469
  ( 107 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=22280461524640293696839248296287379439151813 (pp44)
 r2=1775217634961080691725523313726899374646671985030998419880422313 (pp64)
Version: Msieve-1.39
Total time: 2.08 hours.
Scaled time: 3.62 units (timescale=1.739).
Factorization parameters were as follows:
n: 39552668213613296251633284908196732545871870203936203625314569956333416616933435735524261822510328959603469
m: 100000000000000000000000000
deg: 5
c5: 13
c0: -1075
skew: 2.42
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 935001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 148648 x 148888
Total sieving time: 2.08 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 2.08 hours.
 --------- CPU info (if available) ----------

(52·10¹³⁰-43)/9 = 5(7)₁₂₉3_<131> = 31 · 11047 · 1155101 · 7951426453_<10> · C110

C110 = P43 · P67

P43 = 9069319562026888280647856398649591992308737_<43>

P67 = 2025419913187861110709996677032782962657803641003575793894784431349_<67>

Number: 57773_130
N=18369180439993470611356772724825352981162210617425475877591603791499473317466866124191856857952278218189396213
  ( 110 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=9069319562026888280647856398649591992308737 (pp43)
 r2=2025419913187861110709996677032782962657803641003575793894784431349 (pp67)
Version: Msieve-1.39
Total time: 2.36 hours.
Scaled time: 6.06 units (timescale=2.571).
Factorization parameters were as follows:
n: 18369180439993470611356772724825352981162210617425475877591603791499473317466866124191856857952278218189396213
m: 100000000000000000000000000
deg: 5
c5: 52
c0: -43
skew: 0.96
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 149408 x 149656
Total sieving time: 2.36 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.36 hours.
 --------- CPU info (if available) ----------

(52·10¹³⁷-43)/9 = 5(7)₁₃₆3_<138> = 3 · 7 · 367 · 117847184220059599_<18> · C117

C117 = P45 · P73

P45 = 152645919106180786882959648969601199812661693_<45>

P73 = 4167456418324956580495444071727674303785313298397610150851768988491199277_<73>

Number: 57773_137
N=636145215310165239663009084995166438093475786332103850131046358434587007959262497181659221575042494159288643047195961
  ( 117 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=152645919106180786882959648969601199812661693 (pp45)
 r2=4167456418324956580495444071727674303785313298397610150851768988491199277 (pp73)
Version: Msieve-1.39
Total time: 4.01 hours.
Scaled time: 6.97 units (timescale=1.739).
Factorization parameters were as follows:
n: 636145215310165239663009084995166438093475786332103850131046358434587007959262497181659221575042494159288643047195961
m: 2000000000000000000000000000
deg: 5
c5: 325
c0: -86
skew: 0.77
type: snfs
lss: 1
rlim: 1450000
alim: 1450000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1450000/1450000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [725000, 1475001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 226018 x 226266
Total sieving time: 4.01 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000
total time: 4.01 hours.
 --------- CPU info (if available) ----------

(52·10¹³⁹-43)/9 = 5(7)₁₃₈3_<140> = 8117 · 159571 · 1888446894411880963_<19> · C113

C113 = P43 · P70

P43 = 3247662922074435283007291656832063050525993_<43>

P70 = 7273368612241825094697226221211906396160023667985265743758395925654521_<70>

Number: 57773_139
N=23621449560557765908725892838169934193339121800804351781075706927027056750885980500072820603341159937671848464353
  ( 113 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=3247662922074435283007291656832063050525993 (pp43)
 r2=7273368612241825094697226221211906396160023667985265743758395925654521 (pp70)
Version: Msieve-1.39
Total time: 5.46 hours.
Scaled time: 14.04 units (timescale=2.571).
Factorization parameters were as follows:
n: 23621449560557765908725892838169934193339121800804351781075706927027056750885980500072820603341159937671848464353
m: 10000000000000000000000000000
deg: 5
c5: 26
c0: -215
skew: 1.53
type: snfs
lss: 1
rlim: 1590000
alim: 1590000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1590000/1590000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [795000, 1695001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 265096 x 265344
Total sieving time: 5.46 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1590000,1590000,26,26,48,48,2.3,2.3,100000
total time: 5.46 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶²-61)/9 = 5(7)₁₆₁1_<163> = C163

C163 = P71 · P92

P71 = 89078462498074378184875910436072504162314307600547461270396507262562803_<71>

P92 = 64861669316560968069909293449376891140462180764471597340201527070805685962402940951248966057_<92>

Number: 57771_162
N=5777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
  ( 163 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=89078462498074378184875910436072504162314307600547461270396507262562803 (pp71)
 r2=64861669316560968069909293449376891140462180764471597340201527070805685962402940951248966057 (pp92)
Version: Msieve-1.39
Total time: 34.98 hours.
Scaled time: 89.94 units (timescale=2.571).
Factorization parameters were as follows:
n: 5777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771
m: 200000000000000000000000000000000
deg: 5
c5: 325
c0: -122
skew: 0.82
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 3700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 756780 x 757028
Total sieving time: 34.98 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 34.98 hours.
 --------- CPU info (if available) ----------

(52·10¹⁶⁶-43)/9 = 5(7)₁₆₅3_<167> = 17² · C165

C165 = P33 · P54 · P78

P33 = 930690578246037840231253796684173_<33>

P54 = 829470565962315416296810464504282017537683004182518241_<54>

P78 = 258974315881724332250612717573084960788626745202188734295579617407732766967649_<78>

Number: 57773_166
N=199923106497500961168781237985390234525182622068435217224144559784698193002691272587466359092656670511341791618608227604767397154940407535563244905805459438677431757
  ( 165 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=930690578246037840231253796684173 (pp33)
 r2=829470565962315416296810464504282017537683004182518241 (pp54)
 r3=258974315881724332250612717573084960788626745202188734295579617407732766967649 (pp78)
Version: Msieve-1.39
Total time: 41.71 hours.
Scaled time: 72.36 units (timescale=1.735).
Factorization parameters were as follows:
n: 199923106497500961168781237985390234525182622068435217224144559784698193002691272587466359092656670511341791618608227604767397154940407535563244905805459438677431757
m: 2000000000000000000000000000000000
deg: 5
c5: 65
c0: -172
skew: 1.21
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 4550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 835200 x 835448
Total sieving time: 41.71 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000
total time: 41.71 hours.
 --------- CPU info (if available) ----------

Apr 4, 2009 (4th)

By Sinkiti Sibata / Msieve, GGNFS / Apr 4, 2009

(52·10¹³¹-43)/9 = 5(7)₁₃₀3_<132> = 3² · 7 · 53 · 538305143176019_<15> · 1690631556676993027_<19> · C96

C96 = P45 · P52

P45 = 125155891443348836665628058919128450479204023_<45>

P52 = 1519202326823390871867348017285177880865046294224793_<52>

Sat Apr 04 03:56:01 2009  Msieve v. 1.40
Sat Apr 04 03:56:01 2009  random seeds: a1b86020 f9981365
Sat Apr 04 03:56:01 2009  factoring 190137121496391268466690391434700784277022450168414359899204069633799018412216845934612471942239 (96 digits)
Sat Apr 04 03:56:02 2009  searching for 15-digit factors
Sat Apr 04 03:56:03 2009  commencing quadratic sieve (96-digit input)
Sat Apr 04 03:56:03 2009  using multiplier of 11
Sat Apr 04 03:56:03 2009  using 32kb Intel Core sieve core
Sat Apr 04 03:56:03 2009  sieve interval: 36 blocks of size 32768
Sat Apr 04 03:56:03 2009  processing polynomials in batches of 6
Sat Apr 04 03:56:03 2009  using a sieve bound of 2231371 (82052 primes)
Sat Apr 04 03:56:03 2009  using large prime bound of 334705650 (28 bits)
Sat Apr 04 03:56:03 2009  using double large prime bound of 2210005845812100 (43-51 bits)
Sat Apr 04 03:56:03 2009  using trial factoring cutoff of 51 bits
Sat Apr 04 03:56:04 2009  polynomial 'A' values have 12 factors
Sat Apr 04 08:47:03 2009  82295 relations (19804 full + 62491 combined from 1244824 partial), need 82148
Sat Apr 04 08:47:05 2009  begin with 1264628 relations
Sat Apr 04 08:47:06 2009  reduce to 217236 relations in 13 passes
Sat Apr 04 08:47:06 2009  attempting to read 217236 relations
Sat Apr 04 08:47:09 2009  recovered 217236 relations
Sat Apr 04 08:47:09 2009  recovered 203981 polynomials
Sat Apr 04 08:47:10 2009  attempting to build 82295 cycles
Sat Apr 04 08:47:10 2009  found 82295 cycles in 5 passes
Sat Apr 04 08:47:10 2009  distribution of cycle lengths:
Sat Apr 04 08:47:10 2009     length 1 : 19804
Sat Apr 04 08:47:10 2009     length 2 : 13973
Sat Apr 04 08:47:10 2009     length 3 : 13819
Sat Apr 04 08:47:10 2009     length 4 : 11182
Sat Apr 04 08:47:10 2009     length 5 : 8586
Sat Apr 04 08:47:10 2009     length 6 : 5841
Sat Apr 04 08:47:10 2009     length 7 : 3726
Sat Apr 04 08:47:10 2009     length 9+: 5364
Sat Apr 04 08:47:10 2009  largest cycle: 19 relations
Sat Apr 04 08:47:10 2009  matrix is 82052 x 82295 (23.0 MB) with weight 5693962 (69.19/col)
Sat Apr 04 08:47:10 2009  sparse part has weight 5693962 (69.19/col)
Sat Apr 04 08:47:12 2009  filtering completed in 3 passes
Sat Apr 04 08:47:12 2009  matrix is 78662 x 78726 (22.1 MB) with weight 5475579 (69.55/col)
Sat Apr 04 08:47:12 2009  sparse part has weight 5475579 (69.55/col)
Sat Apr 04 08:47:12 2009  saving the first 48 matrix rows for later
Sat Apr 04 08:47:12 2009  matrix is 78614 x 78726 (16.2 MB) with weight 4588936 (58.29/col)
Sat Apr 04 08:47:12 2009  sparse part has weight 3771115 (47.90/col)
Sat Apr 04 08:47:12 2009  matrix includes 64 packed rows
Sat Apr 04 08:47:12 2009  using block size 31490 for processor cache size 1024 kB
Sat Apr 04 08:47:13 2009  commencing Lanczos iteration
Sat Apr 04 08:47:13 2009  memory use: 14.3 MB
Sat Apr 04 08:47:59 2009  lanczos halted after 1244 iterations (dim = 78611)
Sat Apr 04 08:48:00 2009  recovered 15 nontrivial dependencies
Sat Apr 04 08:48:01 2009  prp45 factor: 125155891443348836665628058919128450479204023
Sat Apr 04 08:48:01 2009  prp52 factor: 1519202326823390871867348017285177880865046294224793
Sat Apr 04 08:48:01 2009  elapsed time 04:52:00

(52·10¹³²-43)/9 = 5(7)₁₃₁3_<133> = 16774897 · 177179604623047913_<18> · C109

C109 = P38 · P71

P38 = 58243268431179785212059991498513475671_<38>

P71 = 33376554773954173590238561719317951008512612316705496043260499341740883_<71>

Number: 57773_132
N=1943959639007388070686902824258908750890244729630791609378855341289029354915096807349162275426308192206557493
  ( 109 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=58243268431179785212059991498513475671
 r2=33376554773954173590238561719317951008512612316705496043260499341740883
Version: 
Total time: 4.63 hours.
Scaled time: 9.26 units (timescale=1.997).
Factorization parameters were as follows:
name: 57773_132
n: 1943959639007388070686902824258908750890244729630791609378855341289029354915096807349162275426308192206557493
m: 200000000000000000000000000
deg: 5
c5: 325
c0: -86
skew: 0.77
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [600000, 1125001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 192102 x 192350
Total sieving time: 4.63 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000
total time: 4.63 hours.
 --------- CPU info (if available) ----------

(52·10¹³¹-61)/9 = 5(7)₁₃₀1_<132> = 19 · 1439 · 22790595942931147_<17> · C111

C111 = P45 · P67

P45 = 170734765586832689268962358210656835090378467_<45>

P67 = 5430862347417027425377351447539772306948373514937322866566784004119_<67>

Number: 57771_131
N=927237009820602090854641088217798022236681357650069566783350283991149548339030541083050828802686994777396905573
  ( 111 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=170734765586832689268962358210656835090378467 (pp45)
 r2=5430862347417027425377351447539772306948373514937322866566784004119 (pp67)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 7.08 hours.
Scaled time: 3.35 units (timescale=0.473).
Factorization parameters were as follows:
name: 57771_131
n: 927237009820602090854641088217798022236681357650069566783350283991149548339030541083050828802686994777396905573
m: 200000000000000000000000000
deg: 5
c5: 65
c0: -244
skew: 1.30
type: snfs
lss: 1
rlim: 1170000
alim: 1170000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1170000/1170000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [585000, 1185001)
Primes: RFBsize:90764, AFBsize:90658, largePrimes:3000713 encountered
Relations: rels:2937323, finalFF:244128
Max relations in full relation-set: 28
Initial matrix: 181489 x 244128 with sparse part having weight 20379068.
Pruned matrix : 164404 x 165375 with weight 10687648.
Total sieving time: 6.42 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.46 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1170000,1170000,26,26,47,47,2.3,2.3,50000
total time: 7.08 hours.
 --------- CPU info (if available) ----------

(52·10¹³⁸-61)/9 = 5(7)₁₃₇1_<139> = 193 · 10667 · C133

C133 = P40 · P94

P40 = 1488134143786863459816687408572516745377_<40>

P94 = 1885902120508917874568650234764485594866141066106480990873896225831672478296591657582919019233_<94>

Number: 57771_138
N=2806475337369368692547874286527855158239603803400142018446206803014953278392260949962757532566312829494371910549643337462630026835841
  ( 133 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=1488134143786863459816687408572516745377
 r2=1885902120508917874568650234764485594866141066106480990873896225831672478296591657582919019233
Version: 
Total time: 7.06 hours.
Scaled time: 18.09 units (timescale=2.564).
Factorization parameters were as follows:
name: 57771_138
n: 2806475337369368692547874286527855158239603803400142018446206803014953278392260949962757532566312829494371910549643337462630026835841
m: 10000000000000000000000000000
deg: 5
c5: 13
c0: -1525
skew: 2.59
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1785001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 275592 x 275840
Total sieving time: 7.06 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 7.06 hours.
 --------- CPU info (if available) ----------

(52·10¹³⁵-61)/9 = 5(7)₁₃₄1_<136> = 229 · 281 · 419 · 148781 · 49719491941057866118670558347_<29> · C95

C95 = P30 · P66

P30 = 212622608180129249577618921109_<30>

P66 = 136245263200260621589881241454529097142890857081373341190727226007_<66>

Sat Apr 04 08:56:03 2009  Msieve v. 1.40
Sat Apr 04 08:56:03 2009  random seeds: 7e00eff0 a03e8cf1
Sat Apr 04 08:56:03 2009  factoring 28968823213827596660909780275544464919163711569396466774004831324203409199116588424275746081763 (95 digits)
Sat Apr 04 08:56:04 2009  searching for 15-digit factors
Sat Apr 04 08:56:06 2009  commencing quadratic sieve (95-digit input)
Sat Apr 04 08:56:06 2009  using multiplier of 43
Sat Apr 04 08:56:06 2009  using 32kb Intel Core sieve core
Sat Apr 04 08:56:06 2009  sieve interval: 36 blocks of size 32768
Sat Apr 04 08:56:06 2009  processing polynomials in batches of 6
Sat Apr 04 08:56:06 2009  using a sieve bound of 2128183 (78614 primes)
Sat Apr 04 08:56:06 2009  using large prime bound of 310714718 (28 bits)
Sat Apr 04 08:56:06 2009  using double large prime bound of 1933086450144842 (43-51 bits)
Sat Apr 04 08:56:06 2009  using trial factoring cutoff of 51 bits
Sat Apr 04 08:56:06 2009  polynomial 'A' values have 12 factors
Sat Apr 04 12:02:44 2009  78791 relations (20247 full + 58544 combined from 1150423 partial), need 78710
Sat Apr 04 12:02:45 2009  begin with 1170670 relations
Sat Apr 04 12:02:46 2009  reduce to 201338 relations in 11 passes
Sat Apr 04 12:02:46 2009  attempting to read 201338 relations
Sat Apr 04 12:02:49 2009  recovered 201338 relations
Sat Apr 04 12:02:49 2009  recovered 183647 polynomials
Sat Apr 04 12:02:50 2009  attempting to build 78791 cycles
Sat Apr 04 12:02:50 2009  found 78791 cycles in 5 passes
Sat Apr 04 12:02:50 2009  distribution of cycle lengths:
Sat Apr 04 12:02:50 2009     length 1 : 20247
Sat Apr 04 12:02:50 2009     length 2 : 14054
Sat Apr 04 12:02:50 2009     length 3 : 13555
Sat Apr 04 12:02:50 2009     length 4 : 10496
Sat Apr 04 12:02:50 2009     length 5 : 7683
Sat Apr 04 12:02:50 2009     length 6 : 5176
Sat Apr 04 12:02:50 2009     length 7 : 3289
Sat Apr 04 12:02:50 2009     length 9+: 4291
Sat Apr 04 12:02:50 2009  largest cycle: 17 relations
Sat Apr 04 12:02:50 2009  matrix is 78614 x 78791 (21.4 MB) with weight 5287791 (67.11/col)
Sat Apr 04 12:02:50 2009  sparse part has weight 5287791 (67.11/col)
Sat Apr 04 12:02:51 2009  filtering completed in 3 passes
Sat Apr 04 12:02:51 2009  matrix is 74280 x 74344 (20.3 MB) with weight 5033352 (67.70/col)
Sat Apr 04 12:02:51 2009  sparse part has weight 5033352 (67.70/col)
Sat Apr 04 12:02:51 2009  saving the first 48 matrix rows for later
Sat Apr 04 12:02:52 2009  matrix is 74232 x 74344 (14.7 MB) with weight 4174334 (56.15/col)
Sat Apr 04 12:02:52 2009  sparse part has weight 3395769 (45.68/col)
Sat Apr 04 12:02:52 2009  matrix includes 64 packed rows
Sat Apr 04 12:02:52 2009  using block size 29737 for processor cache size 1024 kB
Sat Apr 04 12:02:52 2009  commencing Lanczos iteration
Sat Apr 04 12:02:52 2009  memory use: 13.0 MB
Sat Apr 04 12:03:33 2009  lanczos halted after 1175 iterations (dim = 74230)
Sat Apr 04 12:03:33 2009  recovered 16 nontrivial dependencies
Sat Apr 04 12:03:35 2009  prp30 factor: 212622608180129249577618921109
Sat Apr 04 12:03:35 2009  prp66 factor: 136245263200260621589881241454529097142890857081373341190727226007
Sat Apr 04 12:03:35 2009  elapsed time 03:07:32

(52·10¹³³-61)/9 = 5(7)₁₃₂1_<134> = 3 · 619 · C131

C131 = P61 · P70

P61 = 3727936761833065162703458001986420391902010444196421633656883_<61>

P70 = 8346038692541827722054963938348693762716229106800612265655725055932841_<70>

SNFS difficulty: 136 digits.
Divisors found:
 r1=3727936761833065162703458001986420391902010444196421633656883 (pp61)
 r2=8346038692541827722054963938348693762716229106800612265655725055932841 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.19 hours.
Scaled time: 14.46 units (timescale=2.010).
Factorization parameters were as follows:
name: 57771_133
n: 31113504457607850176509304134506073116735475378447914796864716089271824328367139352599772632082809788787171662777478609465685394603
m: 1000000000000000000000000000
deg: 5
c5: 13
c0: -1525
skew: 2.59
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1325001)
Primes: RFBsize:100021, AFBsize:100334, largePrimes:3209377 encountered
Relations: rels:3139651, finalFF:235208
Max relations in full relation-set: 28
Initial matrix: 200421 x 235208 with sparse part having weight 20085663.
Pruned matrix : 190225 x 191291 with weight 13896714.
Total sieving time: 6.70 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 7.19 hours.
 --------- CPU info (if available) ----------
リファイル、B1とsigmaを含むGMP-ECMの出力など)

(52·10¹⁴¹-43)/9 = 5(7)₁₄₀3_<142> = 190766010375699666087127_<24> · C119

C119 = P38 · P82

P38 = 20393852617805428554285413653665644021_<38>

P82 = 1485116628074158277002992507452765414963770251509441579656065692357493518700226319_<82>

Number: 57773_141
N=30287249633196543786224687333698870543501346160586480059269536897380902988604308015472103838181959086901590647589188699
  ( 119 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=20393852617805428554285413653665644021 (pp38)
 r2=1485116628074158277002992507452765414963770251509441579656065692357493518700226319 (pp82)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 14.70 hours.
Scaled time: 37.86 units (timescale=2.575).
Factorization parameters were as follows:
name: 57773_141
n: 30287249633196543786224687333698870543501346160586480059269536897380902988604308015472103838181959086901590647589188699
m: 20000000000000000000000000000
deg: 5
c5: 65
c0: -172
skew: 1.21
type: snfs
lss: 1
rlim: 1710000
alim: 1710000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1710000/1710000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [855000, 2155001)
Primes: RFBsize:128837, AFBsize:128081, largePrimes:4479831 encountered
Relations: rels:5338652, finalFF:979480
Max relations in full relation-set: 28
Initial matrix: 256985 x 979480 with sparse part having weight 111332712.
Pruned matrix : 175547 x 176895 with weight 31186762.
Total sieving time: 14.26 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1710000,1710000,26,26,48,48,2.3,2.3,100000
total time: 14.70 hours.
 --------- CPU info (if available) ----------

(52·10¹³⁵-43)/9 = 5(7)₁₃₄3_<136> = 19 · 23 · 578213 · 677027299937_<12> · C116

C116 = P48 · P69

P48 = 121450106747496191455412062850052462583940149739_<48>

P69 = 278091339149783647900019057676926732120133817504646813479559173522831_<69>

Number: 57773_135
N=33774222825295390805722597659168785422704821500943553011801432552753561624812264670904491506852692162555018275191109
  ( 116 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=121450106747496191455412062850052462583940149739 (pp48)
 r2=278091339149783647900019057676926732120133817504646813479559173522831 (pp69)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.01 hours.
Scaled time: 11.85 units (timescale=1.972).
Factorization parameters were as follows:
name: 57773_135
n: 33774222825295390805722597659168785422704821500943553011801432552753561624812264670904491506852692162555018275191109
m: 1000000000000000000000000000
deg: 5
c5: 52
c0: -43
skew: 0.96
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1190001)
Primes: RFBsize:102146, AFBsize:102092, largePrimes:3274557 encountered
Relations: rels:3266462, finalFF:306601
Max relations in full relation-set: 28
Initial matrix: 204304 x 306601 with sparse part having weight 25546728.
Pruned matrix : 173094 x 174179 with weight 10913020.
Total sieving time: 5.66 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 6.01 hours.
 --------- CPU info (if available) ----------

(52·10¹³⁷-61)/9 = 5(7)₁₃₆1_<138> = 809 · 120527697096371_<15> · 7390796411862630909918487_<25> · C96

C96 = P37 · P60

P37 = 7661897610542591853010023137765323993_<37>

P60 = 104640033648984922939572123020578281103707523333533750006079_<60>

Sat Apr 04 12:11:37 2009  Msieve v. 1.40
Sat Apr 04 12:11:37 2009  random seeds: ae493be0 3b80aac3
Sat Apr 04 12:11:37 2009  factoring 801741223782253989753375726173871272236737637575163767113820153002695760206582401004739154553447 (96 digits)
Sat Apr 04 12:11:38 2009  searching for 15-digit factors
Sat Apr 04 12:11:40 2009  commencing quadratic sieve (96-digit input)
Sat Apr 04 12:11:40 2009  using multiplier of 7
Sat Apr 04 12:11:40 2009  using 32kb Intel Core sieve core
Sat Apr 04 12:11:40 2009  sieve interval: 36 blocks of size 32768
Sat Apr 04 12:11:40 2009  processing polynomials in batches of 6
Sat Apr 04 12:11:40 2009  using a sieve bound of 2300003 (84369 primes)
Sat Apr 04 12:11:40 2009  using large prime bound of 345000450 (28 bits)
Sat Apr 04 12:11:40 2009  using double large prime bound of 2333862839164950 (43-52 bits)
Sat Apr 04 12:11:40 2009  using trial factoring cutoff of 52 bits
Sat Apr 04 12:11:40 2009  polynomial 'A' values have 13 factors
Sat Apr 04 17:18:49 2009  84861 relations (20544 full + 64317 combined from 1279231 partial), need 84465
Sat Apr 04 17:18:50 2009  begin with 1299775 relations
Sat Apr 04 17:18:52 2009  reduce to 222805 relations in 10 passes
Sat Apr 04 17:18:52 2009  attempting to read 222805 relations
Sat Apr 04 17:18:55 2009  recovered 222805 relations
Sat Apr 04 17:18:55 2009  recovered 209685 polynomials
Sat Apr 04 17:18:56 2009  attempting to build 84861 cycles
Sat Apr 04 17:18:56 2009  found 84861 cycles in 5 passes
Sat Apr 04 17:18:56 2009  distribution of cycle lengths:
Sat Apr 04 17:18:56 2009     length 1 : 20544
Sat Apr 04 17:18:56 2009     length 2 : 14698
Sat Apr 04 17:18:56 2009     length 3 : 14151
Sat Apr 04 17:18:56 2009     length 4 : 11368
Sat Apr 04 17:18:56 2009     length 5 : 8725
Sat Apr 04 17:18:56 2009     length 6 : 6139
Sat Apr 04 17:18:56 2009     length 7 : 3811
Sat Apr 04 17:18:56 2009     length 9+: 5425
Sat Apr 04 17:18:56 2009  largest cycle: 20 relations
Sat Apr 04 17:18:56 2009  matrix is 84369 x 84861 (23.1 MB) with weight 5723707 (67.45/col)
Sat Apr 04 17:18:56 2009  sparse part has weight 5723707 (67.45/col)
Sat Apr 04 17:18:58 2009  filtering completed in 3 passes
Sat Apr 04 17:18:58 2009  matrix is 80555 x 80619 (22.0 MB) with weight 5443758 (67.52/col)
Sat Apr 04 17:18:58 2009  sparse part has weight 5443758 (67.52/col)
Sat Apr 04 17:18:58 2009  saving the first 48 matrix rows for later
Sat Apr 04 17:18:58 2009  matrix is 80507 x 80619 (14.2 MB) with weight 4370777 (54.22/col)
Sat Apr 04 17:18:58 2009  sparse part has weight 3242834 (40.22/col)
Sat Apr 04 17:18:58 2009  matrix includes 64 packed rows
Sat Apr 04 17:18:58 2009  using block size 32247 for processor cache size 1024 kB
Sat Apr 04 17:18:59 2009  commencing Lanczos iteration
Sat Apr 04 17:18:59 2009  memory use: 13.4 MB
Sat Apr 04 17:19:43 2009  lanczos halted after 1274 iterations (dim = 80501)
Sat Apr 04 17:19:43 2009  recovered 13 nontrivial dependencies
Sat Apr 04 17:19:44 2009  prp37 factor: 7661897610542591853010023137765323993
Sat Apr 04 17:19:44 2009  prp60 factor: 104640033648984922939572123020578281103707523333533750006079
Sat Apr 04 17:19:44 2009  elapsed time 05:08:07

(52·10¹⁴⁵-43)/9 = 5(7)₁₄₄3_<146> = 31 · 89 · 173 · 809 · 1223258461_<10> · C129

C129 = P38 · P41 · P51

P38 = 13419920511365218416841677070162907599_<38>

P41 = 20666737252888646473219963431260187449291_<41>

P51 = 441036384332449093808152402633252549071244128342479_<51>

Number: 57773_145
N=122319664330917094801628691096892538188494950873258729274378802181259935772704253682964589697748126855092868966579095257840524011
  ( 129 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=13419920511365218416841677070162907599 (pp38)
 r2=20666737252888646473219963431260187449291 (pp41)
 r3=441036384332449093808152402633252549071244128342479 (pp51)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 14.81 hours.
Scaled time: 37.97 units (timescale=2.564).
Factorization parameters were as follows:
name: 57773_145
n: 122319664330917094801628691096892538188494950873258729274378802181259935772704253682964589697748126855092868966579095257840524011
m: 100000000000000000000000000000
deg: 5
c5: 52
c0: -43
skew: 0.96
type: snfs
rlim: 1950000
alim: 1950000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1950000/1950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [975000, 2275001)
Primes: RFBsize:145502, AFBsize:145551, largePrimes:4006262 encountered
Relations: rels:4065679, finalFF:342403
Max relations in full relation-set: 28
Initial matrix: 291119 x 342403 with sparse part having weight 31724919.
Pruned matrix : 272864 x 274383 with weight 22738350.
Total sieving time: 14.09 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.57 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000
total time: 14.81 hours.
 --------- CPU info (if available) ----------

Apr 4, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 4, 2009

(37·10¹⁹⁵+53)/9 = 4(1)₁₉₄7_<196> = C196

C196 = P73 · P124

P73 = 4056360560086047507543906248121877688926356700992813898073165645472671699_<73>

P124 = 1013497456701408757672140181978775551363217130114066050778854198003534742597824804711171095712189587253568907167829952469983_<124>

Number: 41117_195
N=4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
  ( 196 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=4056360560086047507543906248121877688926356700992813898073165645472671699
 r2=1013497456701408757672140181978775551363217130114066050778854198003534742597824804711171095712189587253568907167829952469983
Version: 
Total time: 297.67 hours.
Scaled time: 709.65 units (timescale=2.384).
Factorization parameters were as follows:
n: 4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
m: 1000000000000000000000000000000000000000
deg: 5
c5: 37
c0: 53
skew: 1.07
type: snfs
lss: 1
rlim: 16000000
alim: 16000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 16000000/16000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [8000000, 14700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 23311414
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2563890 x 2564137
Total sieving time: 270.08 hours.
Total relation processing time: 8.66 hours.
Matrix solve time: 17.77 hours.
Time per square root: 1.17 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,16000000,16000000,28,28,55,55,2.5,2.5,100000
total time: 297.67 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 4, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.41 / Apr 4, 2009

(52·10¹³⁴-61)/9 = 5(7)₁₃₃1_<135> = 31 · 131 · 151 · 198899 · 1493071 · 3030209714127622153_<19> · C100

C100 = P31 · P69

P31 = 1157114914057201543799531433343_<31>

P69 = 904875147033446577736916556210785819990564089251781354589525835489571_<69>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=175975155
Step 1 took 6637ms
Step 2 took 6012ms
********** Factor found in step 2: 1157114914057201543799531433343
Found probable prime factor of 31 digits: 1157114914057201543799531433343
Probable prime cofactor has 69 digits

(52·10¹⁶⁵-61)/9 = 5(7)₁₆₄1_<166> = 412642667 · 10656471820840239088252079_<26> · 19263288243743295037277268265951_<32> · C101

C101 = P35 · P67

P35 = 26071796022213963116946939411064517_<35>

P67 = 2616205707065874152343040065011215274098234733772473710931790869341_<67>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2576297680
Step 1 took 6720ms
Step 2 took 5984ms
********** Factor found in step 2: 26071796022213963116946939411064517
Found probable prime factor of 35 digits: 26071796022213963116946939411064517
Probable prime cofactor has 67 digits

(52·10¹⁸³-43)/9 = 5(7)₁₈₂3_<184> = 53 · 155534297 · 208302845438646705692873_<24> · 12102717778758856313763816055466931127_<38> · C114

C114 = P28 · P87

P28 = 1927918425418659151712340193_<28>

P87 = 144208889124852107838377556122845331733359677018582379551483368531814341400694406271151_<87>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=827704889
Step 1 took 6520ms
Step 2 took 6257ms
********** Factor found in step 2: 1927918425418659151712340193
Found probable prime factor of 28 digits: 1927918425418659151712340193
Probable prime cofactor has 87 digits

(52·10¹⁷¹-43)/9 = 5(7)₁₇₀3_<172> = 19 · 30158387489_<11> · C161

C161 = P30 · C131

P30 = 570722929894025945844003120791_<30>

C131 = [17667446903780369270027340030229025609340516134487338842476289026281681885771004853140501484263830394674231779800354344547160811833_<131>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1171269362
Step 1 took 10276ms
Step 2 took 8617ms
********** Factor found in step 2: 570722929894025945844003120791
Found probable prime factor of 30 digits: 570722929894025945844003120791
Composite cofactor has 131 digits

(52·10¹¹⁹-43)/9 = 5(7)₁₁₈3_<120> = 3 · 7 · 29 · C117

C117 = P40 · P78

P40 = 1110328809306095270316842029530857139241_<40>

P78 = 854460386205466413815166641841724795646010036397639195420102772004094676165317_<78>

SNFS difficulty: 121 digits.
Divisors found:
 r1=1110328809306095270316842029530857139241 (pp40)
 r2=854460386205466413815166641841724795646010036397639195420102772004094676165317 (pp78)
Version: Msieve-1.41
Total time: 0.68 hours.
Scaled time: 1.95 units (timescale=2.847).
Factorization parameters were as follows:
n: 948731983214741835431490603904397007845283707352672869914249224594052180259076810800948731983214741835431490603904397
m: 1000000000000000000000000
deg: 5
c5: 26
c0: -215
skew: 1.53
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 370000)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 75841 x 76071
Total sieving time: 0.65 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121.000,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 0.68 hours.

Apr 4, 2009

By Robert Backstrom / Msieve, GGNFS / Apr 4, 2009

(52·10¹¹⁴-61)/9 = 5(7)₁₁₃1_<115> = 2009630868555904244621_<22> · C94

C94 = P40 · P54

P40 = 4086170979912939632301607690085835323423_<40>

P54 = 703603524213671653937284467857848873269377644859294537_<54>

Sat Apr 04 05:00:04 2009  
Sat Apr 04 05:00:04 2009  
Sat Apr 04 05:00:04 2009  Msieve v. 1.40
Sat Apr 04 05:00:04 2009  random seeds: 52a843a0 459c56f1
Sat Apr 04 05:00:04 2009  factoring 2875044302006376450035207601416874806511587051887097330162325414618175753882613109911012040151 (94 digits)
Sat Apr 04 05:00:04 2009  searching for 15-digit factors
Sat Apr 04 05:00:05 2009  commencing quadratic sieve (94-digit input)
Sat Apr 04 05:00:05 2009  using multiplier of 1
Sat Apr 04 05:00:05 2009  using 64kb Opteron sieve core
Sat Apr 04 05:00:05 2009  sieve interval: 18 blocks of size 65536
Sat Apr 04 05:00:05 2009  processing polynomials in batches of 6
Sat Apr 04 05:00:05 2009  using a sieve bound of 2022539 (75294 primes)
Sat Apr 04 05:00:05 2009  using large prime bound of 271020226 (28 bits)
Sat Apr 04 05:00:05 2009  using double large prime bound of 1511482239584034 (42-51 bits)
Sat Apr 04 05:00:05 2009  using trial factoring cutoff of 51 bits
Sat Apr 04 05:00:05 2009  polynomial 'A' values have 12 factors
Sat Apr 04 06:55:37 2009  75475 relations (18579 full + 56896 combined from 1070057 partial), need 75390
Sat Apr 04 06:55:40 2009  begin with 1088636 relations
Sat Apr 04 06:55:40 2009  reduce to 195823 relations in 12 passes
Sat Apr 04 06:55:40 2009  attempting to read 195823 relations
Sat Apr 04 06:55:43 2009  recovered 195823 relations
Sat Apr 04 06:55:43 2009  recovered 177830 polynomials
Sat Apr 04 06:55:43 2009  attempting to build 75475 cycles
Sat Apr 04 06:55:43 2009  found 75475 cycles in 5 passes
Sat Apr 04 06:55:43 2009  distribution of cycle lengths:
Sat Apr 04 06:55:43 2009     length 1 : 18579
Sat Apr 04 06:55:43 2009     length 2 : 13293
Sat Apr 04 06:55:43 2009     length 3 : 12866
Sat Apr 04 06:55:43 2009     length 4 : 10164
Sat Apr 04 06:55:43 2009     length 5 : 7653
Sat Apr 04 06:55:43 2009     length 6 : 5192
Sat Apr 04 06:55:43 2009     length 7 : 3227
Sat Apr 04 06:55:43 2009     length 9+: 4501
Sat Apr 04 06:55:43 2009  largest cycle: 20 relations
Sat Apr 04 06:55:43 2009  matrix is 75294 x 75475 (19.1 MB) with weight 4697664 (62.24/col)
Sat Apr 04 06:55:43 2009  sparse part has weight 4697664 (62.24/col)
Sat Apr 04 06:55:45 2009  filtering completed in 3 passes
Sat Apr 04 06:55:45 2009  matrix is 71542 x 71606 (18.2 MB) with weight 4479870 (62.56/col)
Sat Apr 04 06:55:45 2009  sparse part has weight 4479870 (62.56/col)
Sat Apr 04 06:55:45 2009  saving the first 48 matrix rows for later
Sat Apr 04 06:55:45 2009  matrix is 71494 x 71606 (10.6 MB) with weight 3406165 (47.57/col)
Sat Apr 04 06:55:45 2009  sparse part has weight 2353599 (32.87/col)
Sat Apr 04 06:55:45 2009  matrix includes 64 packed rows
Sat Apr 04 06:55:45 2009  using block size 28642 for processor cache size 1024 kB
Sat Apr 04 06:55:45 2009  commencing Lanczos iteration
Sat Apr 04 06:55:45 2009  memory use: 10.8 MB
Sat Apr 04 06:56:16 2009  lanczos halted after 1132 iterations (dim = 71494)
Sat Apr 04 06:56:17 2009  recovered 18 nontrivial dependencies
Sat Apr 04 06:56:18 2009  prp40 factor: 4086170979912939632301607690085835323423
Sat Apr 04 06:56:18 2009  prp54 factor: 703603524213671653937284467857848873269377644859294537
Sat Apr 04 06:56:18 2009  elapsed time 01:56:14

(17·10¹⁶³-11)/3 = 5(6)₁₆₂3_<164> = 43 · 103 · 478309750388080201_<18> · C143

C143 = P55 · P89

P55 = 1581505296155364220086626947364770666501816355519283359_<55>

P89 = 16913835469895485186233099368027408790492129797916749218694546323573961927732707309455733_<89>

Number: n
N=26749320373940163244971032413497287625039267210811665245714874458689143859502033260323866931096097072092563654060575255012266473731240494047147
  ( 143 digits)
SNFS difficulty: 164 digits.
Divisors found:

Sat Apr 04 13:06:14 2009  prp55 factor: 1581505296155364220086626947364770666501816355519283359
Sat Apr 04 13:06:14 2009  prp89 factor: 16913835469895485186233099368027408790492129797916749218694546323573961927732707309455733
Sat Apr 04 13:06:14 2009  elapsed time 01:26:54 (Msieve 1.40 - dependency 4)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 32.70 hours.
Scaled time: 85.91 units (timescale=2.627).
Factorization parameters were as follows:
name: KA_5_6_162_3
n: 26749320373940163244971032413497287625039267210811665245714874458689143859502033260323866931096097072092563654060575255012266473731240494047147
skew: 0.23
deg: 5
c5: 17000
c0: -11
m: 100000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 4435447)
Primes: RFBsize:348513, AFBsize:348762, largePrimes:15989422 encountered
Relations: rels:15347668, finalFF:722034
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1339057 hash collisions in 16592062 relations
Msieve: matrix is 738183 x 738430 (197.4 MB)

Total sieving time: 32.29 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 32.70 hours.
 --------- CPU info (if available) ----------

Apr 3, 2009 (6th)

By Erik Branger / GMP-ECM, Msieve / Apr 3, 2009

(16·10¹⁹³+17)/3 = 5(3)₁₉₂9_<194> = 26513 · 50023 · 2101717849035273779_<19> · 30071047709254340291_<20> · 1967786130729617339487631_<25> · C123

C123 = P35 · P35 · P54

P35 = 28908882578973117144496171187035193_<35>

P35 = 57749307267023763311033988438420401_<35>

P54 = 193682851615402438266837470310134941116692660151926803_<54>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 323347311841892954308216612017508749535509420962094692577376901022301501696811575352725622481922650643907464856537865349579 (123 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1898868028
Step 1 took 37627ms
Step 2 took 12776ms
********** Factor found in step 2: 28908882578973117144496171187035193
Found probable prime factor of 35 digits: 28908882578973117144496171187035193
Composite cofactor 11185050510291245263177482647494883428694317570240480105088214343493952278744833893908003 has 89 digits

Fri Apr 03 07:48:01 2009  Msieve v. 1.40
Fri Apr 03 07:48:01 2009  random seeds: 5ec5ff50 75d6f83e
Fri Apr 03 07:48:01 2009  factoring 11185050510291245263177482647494883428694317570240480105088214343493952278744833893908003 (89 digits)
Fri Apr 03 07:48:02 2009  searching for 15-digit factors
Fri Apr 03 07:48:03 2009  commencing quadratic sieve (89-digit input)
Fri Apr 03 07:48:03 2009  using multiplier of 3
Fri Apr 03 07:48:03 2009  using 32kb Intel Core sieve core
Fri Apr 03 07:48:03 2009  sieve interval: 28 blocks of size 32768
Fri Apr 03 07:48:03 2009  processing polynomials in batches of 8
Fri Apr 03 07:48:03 2009  using a sieve bound of 1531469 (58333 primes)
Fri Apr 03 07:48:03 2009  using large prime bound of 122517520 (26 bits)
Fri Apr 03 07:48:03 2009  using double large prime bound of 362040129222640 (42-49 bits)
Fri Apr 03 07:48:03 2009  using trial factoring cutoff of 49 bits
Fri Apr 03 07:48:03 2009  polynomial 'A' values have 11 factors
Fri Apr 03 08:43:33 2009  58566 relations (15659 full + 42907 combined from 617626 partial), need 58429
Fri Apr 03 08:43:34 2009  begin with 633285 relations
Fri Apr 03 08:43:35 2009  reduce to 142097 relations in 11 passes
Fri Apr 03 08:43:35 2009  attempting to read 142097 relations
Fri Apr 03 08:43:36 2009  recovered 142097 relations
Fri Apr 03 08:43:36 2009  recovered 119810 polynomials
Fri Apr 03 08:43:37 2009  attempting to build 58566 cycles
Fri Apr 03 08:43:37 2009  found 58566 cycles in 6 passes
Fri Apr 03 08:43:37 2009  distribution of cycle lengths:
Fri Apr 03 08:43:37 2009     length 1 : 15659
Fri Apr 03 08:43:37 2009     length 2 : 11326
Fri Apr 03 08:43:37 2009     length 3 : 10358
Fri Apr 03 08:43:37 2009     length 4 : 7828
Fri Apr 03 08:43:37 2009     length 5 : 5459
Fri Apr 03 08:43:37 2009     length 6 : 3414
Fri Apr 03 08:43:37 2009     length 7 : 2156
Fri Apr 03 08:43:37 2009     length 9+: 2366
Fri Apr 03 08:43:37 2009  largest cycle: 17 relations
Fri Apr 03 08:43:37 2009  matrix is 58333 x 58566 (14.2 MB) with weight 3485108 (59.51/col)
Fri Apr 03 08:43:37 2009  sparse part has weight 3485108 (59.51/col)
Fri Apr 03 08:43:37 2009  filtering completed in 3 passes
Fri Apr 03 08:43:38 2009  matrix is 54258 x 54322 (13.3 MB) with weight 3258769 (59.99/col)
Fri Apr 03 08:43:38 2009  sparse part has weight 3258769 (59.99/col)
Fri Apr 03 08:43:38 2009  saving the first 48 matrix rows for later
Fri Apr 03 08:43:38 2009  matrix is 54210 x 54322 (9.2 MB) with weight 2638136 (48.56/col)
Fri Apr 03 08:43:38 2009  sparse part has weight 2091942 (38.51/col)
Fri Apr 03 08:43:38 2009  matrix includes 64 packed rows
Fri Apr 03 08:43:38 2009  using block size 21728 for processor cache size 2048 kB
Fri Apr 03 08:43:38 2009  commencing Lanczos iteration
Fri Apr 03 08:43:38 2009  memory use: 8.6 MB
Fri Apr 03 08:43:57 2009  lanczos halted after 859 iterations (dim = 54209)
Fri Apr 03 08:43:57 2009  recovered 17 nontrivial dependencies
Fri Apr 03 08:43:58 2009  prp35 factor: 57749307267023763311033988438420401
Fri Apr 03 08:43:58 2009  prp54 factor: 193682851615402438266837470310134941116692660151926803
Fri Apr 03 08:43:58 2009  elapsed time 00:55:57

Apr 3, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Apr 3, 2009

(49·10¹⁶⁰-31)/9 = 5(4)₁₅₉1_<161> = 3 · 100483242763_<12> · 17953395062563_<14> · 214735143465929_<15> · C122

C122 = P61 · P62

P61 = 1567737971651068384965094581648394152466087463266918812121997_<61>

P62 = 29882400504340187380633681424970223502423170295790042907585351_<62>

Number: 54441_160
N=46847773954739148293115346008995526360669585899651036428463200421145076006403340307215453801976038064451718542119702065947
  ( 122 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=1567737971651068384965094581648394152466087463266918812121997 (pp61)
 r2=29882400504340187380633681424970223502423170295790042907585351 (pp62)
Version: Msieve-1.39
Total time: 25.51 hours.
Scaled time: 65.15 units (timescale=2.554).
Factorization parameters were as follows:
n: 46847773954739148293115346008995526360669585899651036428463200421145076006403340307215453801976038064451718542119702065947
m: 100000000000000000000000000000000
deg: 5
c5: 49
c0: -31
skew: 0.91
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 682659 x 682906
Total sieving time: 25.51 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 25.51 hours.
 --------- CPU info (if available) ----------

(17·10¹⁶¹-11)/3 = 5(6)₁₆₀3_<162> = 10123777 · 650392879 · 72267019367663_<14> · C133

C133 = P50 · P84

P50 = 10823475366366524674742715673706966151548924932793_<50>

P84 = 110027803460989649627988595282755172401357864566493256317329413217484842292458614079_<84>

Number: 56663_161
N=1190883220375438919605700302393143743902592774522304485685872845482221743405099031895484550773471103314323235837109088713048998592647
  ( 133 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=10823475366366524674742715673706966151548924932793 (pp50)
 r2=110027803460989649627988595282755172401357864566493256317329413217484842292458614079 (pp84)
Version: Msieve-1.39
Total time: 26.02 hours.
Scaled time: 45.25 units (timescale=1.739).
Factorization parameters were as follows:
n: 1190883220375438919605700302393143743902592774522304485685872845482221743405099031895484550773471103314323235837109088713048998592647
m: 100000000000000000000000000000000
deg: 5
c5: 170
c0: -11
skew: 0.58
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 679494 x 679742
Total sieving time: 26.02 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 26.02 hours.
 --------- CPU info (if available) ----------

(16·10¹⁶²+17)/3 = 5(3)₁₆₁9_<163> = 11 · 128934707059768151160147271273_<30> · C133

C133 = P62 · P71

P62 = 88786862660586663244640643872864911682545620326200986806441777_<62>

P71 = 42353323427847191474859755218340012612106669231687179673124239284988569_<71>

Number: 53339_162
N=3760418710407676147088591359768419603013377672839821197966929806224449753101770249904932480950033657688556959993576877288425009047113
  ( 133 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=88786862660586663244640643872864911682545620326200986806441777 (pp62)
 r2=42353323427847191474859755218340012612106669231687179673124239284988569 (pp71)
Version: Msieve-1.39
Total time: 26.45 hours.
Scaled time: 68.01 units (timescale=2.571).
Factorization parameters were as follows:
n: 3760418710407676147088591359768419603013377672839821197966929806224449753101770249904932480950033657688556959993576877288425009047113
m: 200000000000000000000000000000000
deg: 5
c5: 50
c0: 17
skew: 0.81
type: snfs
lss: 1
rlim: 3700000
alim: 3700000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3700000/3700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1850000, 3150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 596624 x 596872
Total sieving time: 26.45 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,51,51,2.4,2.4,100000
total time: 26.45 hours.
 --------- CPU info (if available) ----------

(17·10¹⁶³+7)/3 = 5(6)₁₆₂9_<164> = 487 · 123379 · 28380172528601352066591619_<26> · C131

C131 = P63 · P69

P63 = 148591516859296022679317547384453453317316739620861227614314937_<63>

P69 = 223639448250590176645911909739904742040253594405448053845320498425051_<69>

Number: 56669_163
N=33230924845131230638453045298820336196589723482764603996276526130903891126914846634423420467368882127568945743878401132370804286787
  ( 131 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=148591516859296022679317547384453453317316739620861227614314937 (pp63)
 r2=223639448250590176645911909739904742040253594405448053845320498425051 (pp69)
Version: Msieve-1.39
Total time: 39.44 hours.
Scaled time: 68.59 units (timescale=1.739).
Factorization parameters were as follows:
n: 33230924845131230638453045298820336196589723482764603996276526130903891126914846634423420467368882127568945743878401132370804286787
m: 500000000000000000000000000000000
deg: 5
c5: 136
c0: 175
skew: 1.05
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 4300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 750901 x 751149
Total sieving time: 39.44 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 39.44 hours.
 --------- CPU info (if available) ----------

Apr 3, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 3, 2009

(16·10¹⁶¹+17)/3 = 5(3)₁₆₀9_<162> = 53 · 311 · 4078073 · 270585397 · 1011552929_<10> · 324228801887_<12> · C122

C122 = P49 · P74

P49 = 3163136667118281002802364642599093883066161549419_<49>

P74 = 28264737660333454210808193745298846039677110745960392543532282451321424089_<74>

Number: 53339_161
N=89405228079879721975382948088960952194148538040782131611170920385353678079829242583342250139601121790793716448717830554291
  ( 122 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=3163136667118281002802364642599093883066161549419
 r2=28264737660333454210808193745298846039677110745960392543532282451321424089
Version: 
Total time: 12.35 hours.
Scaled time: 29.54 units (timescale=2.391).
Factorization parameters were as follows:
n: 89405228079879721975382948088960952194148538040782131611170920385353678079829242583342250139601121790793716448717830554291
m: 200000000000000000000000000000000
deg: 5
c5: 5
c0: 17
skew: 1.28
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9090268
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 549032 x 549280
Total sieving time: 11.13 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 0.69 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 12.35 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 3, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 3, 2009

(17·10¹⁶⁵+7)/3 = 5(6)₁₆₄9_<166> = 752287 · 793892455313_<12> · C148

C148 = P52 · P97

P52 = 7257637173651497122210754800561918501478911133555621_<52>

P97 = 1307335884095391993398822026800587406558775089321301467965713560222929048372608055123835019731719_<97>

Number: n
N=9488169510859261975548862126800284710138279837509243307297657669910691674074118310280029600192922952587724790404344825790272107433974239825984442499
  ( 148 digits)
SNFS difficulty: 166 digits.
Divisors found:

Fri Apr 03 07:00:45 2009  prp52 factor: 7257637173651497122210754800561918501478911133555621
Fri Apr 03 07:00:45 2009  prp97 factor: 1307335884095391993398822026800587406558775089321301467965713560222929048372608055123835019731719
Fri Apr 03 07:00:45 2009  elapsed time 01:21:33 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 32.55 hours.
Scaled time: 85.90 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_5_6_164_9
n: 9488169510859261975548862126800284710138279837509243307297657669910691674074118310280029600192922952587724790404344825790272107433974239825984442499
skew: 0.84
deg: 5
c5: 17
c0: 7
m: 1000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2500000, 4500137)
Primes: RFBsize:348513, AFBsize:349046, largePrimes:15772259 encountered
Relations: rels:14854719, finalFF:735109
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1253373 hash collisions in 15777903 relations
Msieve: matrix is 840330 x 840578 (225.3 MB)

Total sieving time: 32.08 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 32.55 hours.
 --------- CPU info (if available) ----------

(49·10¹⁶⁴+23)/9 = 5(4)₁₆₃7_<165> = 31 · 17574544940866361270498281_<26> · C138

C138 = P33 · P106

P33 = 116881026652426546549683929429743_<33>

P106 = 8549953848429424668598583893325141587389629788921750650527504769263938653022826202215204408813818779715639_<106>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 999327383635296506345501756747525298073121935987552909461603917267905674696629019627053241237793565161394081678893939537848872116968850777 (138 digits)
Using B1=412000, B2=258309880, polynomial Dickson(3), sigma=473458618
Step 1 took 5678ms
********** Factor found in step 1: 116881026652426546549683929429743
Found probable prime factor of 33 digits: 116881026652426546549683929429743
Probable prime cofactor 8549953848429424668598583893325141587389629788921750650527504769263938653022826202215204408813818779715639 has 106 digits

Apr 3, 2009 (2nd)

Factorizations of 577...771 and Factorizations of 577...773 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 3, 2009

By mersenneforum,Tom Womack

The first hole of repunit numbers, (10²⁶³-1)/9, was completely factored. Congratulations!

Apr 2, 2009 (6th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 2, 2009

(49·10¹⁵⁹+23)/9 = 5(4)₁₅₈7_<160> = 13 · 12309503347_<11> · 3352290844358539423008099551_<28> · C122

C122 = P46 · P76

P46 = 4541937364441984968505266910447705904637713171_<46>

P76 = 2234533427167717200687940183412832692594637552725928783392672647725505963037_<76>

Number: 54447_159
N=10149110864947657634820731641856022994726723192422012104136400709120522063809365407235470987049813809054869015715734060327
  ( 122 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=4541937364441984968505266910447705904637713171
 r2=2234533427167717200687940183412832692594637552725928783392672647725505963037
Version: 
Total time: 17.99 hours.
Scaled time: 42.98 units (timescale=2.389).
Factorization parameters were as follows:
n: 10149110864947657634820731641856022994726723192422012104136400709120522063809365407235470987049813809054869015715734060327
m: 100000000000000000000000000000000
deg: 5
c5: 49
c0: 230
skew: 1.36
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1800000, 3300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9239528
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 714452 x 714699
Total sieving time: 16.04 hours.
Total relation processing time: 0.68 hours.
Matrix solve time: 1.19 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000
total time: 17.99 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 2, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Apr 2, 2009

(17·10¹⁵⁹-11)/3 = 5(6)₁₅₈3_<160> = 7 · 97 · 37409 · 83351596807_<11> · 788178310186820437_<18> · C124

C124 = P46 · P78

P46 = 5024692703056695669806893926694802530649223503_<46>

P78 = 675824424361780743765679593969457519635514350512020551879532910413503246526229_<78>

Number: 56663_159
N=3395810053638131453696372678482980616610204164219241348030275455590375109043845161436300944878284771737131376771000972760187
  ( 124 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=5024692703056695669806893926694802530649223503 (pp46)
 r2=675824424361780743765679593969457519635514350512020551879532910413503246526229 (pp78)
Version: Msieve-1.39
Total time: 23.83 hours.
Scaled time: 61.26 units (timescale=2.571).
Factorization parameters were as follows:
n: 3395810053638131453696372678482980616610204164219241348030275455590375109043845161436300944878284771737131376771000972760187
m: 100000000000000000000000000000000
deg: 5
c5: 17
c0: -110
skew: 1.45
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 581876 x 582124
Total sieving time: 23.83 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 23.83 hours.
 --------- CPU info (if available) ----------

(49·10¹⁶⁰+23)/9 = 5(4)₁₅₉7_<161> = 3² · 3307 · 31838452761895407829_<20> · C137

C137 = P61 · P76

P61 = 9285683870890698716616456731171714281776817892289149419042703_<61>

P76 = 6187440244467790533181492495760904465444360877468414333345719414889567252687_<76>

Number: 54447_160
N=57454614080154564373390560969099711576819122294811653619347417220368300344461613266527072685189981522380001361300747252253901429244492961
  ( 137 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=9285683870890698716616456731171714281776817892289149419042703 (pp61)
 r2=6187440244467790533181492495760904465444360877468414333345719414889567252687 (pp76)
Version: Msieve-1.39
Total time: 24.37 hours.
Scaled time: 42.37 units (timescale=1.739).
Factorization parameters were as follows:
n: 57454614080154564373390560969099711576819122294811653619347417220368300344461613266527072685189981522380001361300747252253901429244492961
m: 100000000000000000000000000000000
deg: 5
c5: 49
c0: 23
skew: 0.86
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 669295 x 669543
Total sieving time: 24.37 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 24.37 hours.
 --------- CPU info (if available) ----------

(16·10¹⁶³+17)/3 = 5(3)₁₆₂9_<164> = 489977 · 1818023 · 404670141371483587_<18> · C135

C135 = P56 · P79

P56 = 27301446782712309048436486454571303733558437148082226127_<56>

P79 = 5419220686700744836266372750790973569994429238428190314031647706010711660202441_<79>

Number: 53339_163
N=147952565181734040237698809471184003259730494285431717731168000912810184465437822121306390798769757887521596502279744695010454759376007
  ( 135 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=27301446782712309048436486454571303733558437148082226127 (pp56)
 r2=5419220686700744836266372750790973569994429238428190314031647706010711660202441 (pp79)
Version: Msieve-1.39
Total time: 28.82 hours.
Scaled time: 74.08 units (timescale=2.571).
Factorization parameters were as follows:
n: 147952565181734040237698809471184003259730494285431717731168000912810184465437822121306390798769757887521596502279744695010454759376007
m: 400000000000000000000000000000000
deg: 5
c5: 125
c0: 136
skew: 1.02
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 3400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 635590 x 635838
Total sieving time: 28.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 28.82 hours.
 --------- CPU info (if available) ----------

(17·10¹⁶⁰+7)/3 = 5(6)₁₅₉9_<161> = 2347 · 205991 · 14990497243464228674047859_<26> · C127

C127 = P42 · P85

P42 = 989305839297597455448441667592295923732537_<42>

P85 = 7903504770702278656014169956012092871449979941049288506442631913106346161258415273459_<85>

Number: 56669_160
N=7818983420572183313885508354149170315271535459558520090924152834647048606412117555333256200815847360324458229993451556830835483
  ( 127 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=989305839297597455448441667592295923732537 (pp42)
 r2=7903504770702278656014169956012092871449979941049288506442631913106346161258415273459 (pp85)
Version: Msieve-1.39
Total time: 21.08 hours.
Scaled time: 36.66 units (timescale=1.739).
Factorization parameters were as follows:
n: 7818983420572183313885508354149170315271535459558520090924152834647048606412117555333256200815847360324458229993451556830835483
m: 100000000000000000000000000000000
deg: 5
c5: 17
c0: 7
skew: 0.84
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 678821 x 679069
Total sieving time: 21.08 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 21.08 hours.
 --------- CPU info (if available) ----------

Apr 2, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Apr 2, 2009

(49·10¹⁵¹+23)/9 = 5(4)₁₅₀7_<152> = 3² · 35141 · 216023 · 1077539993_<10> · C132

C132 = P42 · P91

P42 = 721551372956281980471202568692439332262527_<42>

P91 = 1024934935996861843669773828940876270110257891172988594032904817298182725911063379309446971_<91>

Number: n
N=739543210259394661443579113437306566244676470411317230428536046709252205643074977157926363275568492588887893658971345668634556955717
  ( 132 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=721551372956281980471202568692439332262527 (pp42)
 r2=1024934935996861843669773828940876270110257891172988594032904817298182725911063379309446971 (pp91)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 16.69 hours.
Scaled time: 44.40 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_4_150_7
n: 739543210259394661443579113437306566244676470411317230428536046709252205643074977157926363275568492588887893658971345668634556955717
skew: 0.54
deg: 5
c5: 490
c0: 23
m: 1000000000000000000000000000000
type: snfs
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176098, largePrimes:12236159 encountered
Relations: rels:12002234, finalFF:607088
Max relations in full relation-set: 28
Initial matrix: 352466 x 607088 with sparse part having weight 72817144.
Pruned matrix : 280201 x 282027 with weight 40961214.
Total sieving time: 15.87 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.46 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,56,56,2.4,2.4,100000
total time: 16.69 hours.
 --------- CPU info (if available) ----------

(17·10¹⁵⁷-11)/3 = 5(6)₁₅₆3_<158> = 53 · 83 · 63541 · 69341 · C145

C145 = P38 · P108

P38 = 26201209266896744637916838325961582561_<38>

P108 = 111585617966479360240182754132847068745709815654221731867966943515303904651729783621338697908163074841361257_<108>

Number: n
N=2923678127515718895502905546363302956334206803471874728800797810382648762181563970508588374406983004178545147309611651741668796899365351232239177
  ( 145 digits)
SNFS difficulty: 158 digits.
Divisors found:

Thu Apr 02 21:23:40 2009  prp38 factor: 26201209266896744637916838325961582561
Thu Apr 02 21:23:40 2009  prp108 factor: 111585617966479360240182754132847068745709815654221731867966943515303904651729783621338697908163074841361257
Thu Apr 02 21:23:40 2009  elapsed time 01:04:52 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 23.56 hours.
Scaled time: 62.30 units (timescale=2.644).
Factorization parameters were as follows:
name: KA_5_6_156_3
n: 2923678127515718895502905546363302956334206803471874728800797810382648762181563970508588374406983004178545147309611651741668796899365351232239177
skew: 0.36
deg: 5
c5: 1700
c0: -11
m: 10000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1750000, 3350261)
Primes: RFBsize:250150, AFBsize:250482, largePrimes:13834293 encountered
Relations: rels:12944590, finalFF:527612
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1178405 hash collisions in 13882782 relations
Msieve: matrix is 640506 x 640754 (171.0 MB)

Total sieving time: 23.21 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,56,56,2.4,2.4,100000
total time: 23.56 hours.
 --------- CPU info (if available) ----------

(47·10¹⁶⁰+61)/9 = 5(2)₁₅₉9_<161> = 602702967978397806981731_<24> · C137

C137 = P39 · P45 · P54

P39 = 149475423087669771725404269873003177613_<39>

P45 = 805851248526890988295119477659282638721085559_<45>

P54 = 719328626510539286405990039328350670878493687056107477_<54>

Number: n
N=86646698285537530193450319277642828024489879500902537700671930529507367477335548923716463218539734619713860135139678033581656660881717159
  ( 137 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu Apr 02 23:59:54 2009  prp39 factor: 149475423087669771725404269873003177613
Thu Apr 02 23:59:54 2009  prp45 factor: 805851248526890988295119477659282638721085559
Thu Apr 02 23:59:54 2009  prp54 factor: 719328626510539286405990039328350670878493687056107477
Thu Apr 02 23:59:54 2009  elapsed time 01:04:50 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 26.06 hours.
Scaled time: 68.45 units (timescale=2.627).
Factorization parameters were as follows:
name: KA_5_2_159_9
n: 86646698285537530193450319277642828024489879500902537700671930529507367477335548923716463218539734619713860135139678033581656660881717159
skew: 1.05
deg: 5
c5: 47
c0: 61
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2250000, 3858307)
Primes: RFBsize:315948, AFBsize:315702, largePrimes:15105273 encountered
Relations: rels:14286619, finalFF:585267
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1139206 hash collisions in 15114291 relations
Msieve: matrix is 721821 x 722069 (193.9 MB)

Total sieving time: 25.67 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000
total time: 26.06 hours.
 --------- CPU info (if available) ----------

Apr 2, 2009 (3rd)

By Wataru Sakai / GMP-ECM / Apr 2, 2009

(10²²⁸-7)/3 = (3)₂₂₇1_<228> = 19 · 169543477479631_<15> · 581348028289141_<15> · 400300190913832630371913_<24> · 231114981863793246629131203527_<30> · C145

C145 = P38 · P107

P38 = 89875252897502081322528223874139578641_<38>

P107 = 21406902544531901415351462430088886680130030138525132686272468825695973807571949096156849738401872062478109_<107>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2832758251
Step 1 took 44394ms
Step 2 took 15690ms
********** Factor found in step 2: 89875252897502081322528223874139578641
Found probable prime factor of 38 digits: 89875252897502081322528223874139578641
Probable prime cofactor 21406902544531901415351462430088886680130030138525132686272468825695973807571949096156849738401872062478109 has 107 digits

(11·10¹⁹⁹+1)/3 = 3(6)₁₉₈7_<200> = 37 · 804767 · 3708220977874028647789423_<25> · 202496992269035712972643097267_<30> · C139

C139 = P36 · P103

P36 = 719085495087018136230487973283012437_<36>

P103 = 2280524986393322347188566632802167131802841297889369062727060879857698833111173208966665751748661072369_<103>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3773404872
Step 1 took 14486ms
Step 2 took 6765ms
********** Factor found in step 2: 719085495087018136230487973283012437
Found probable prime factor of 36 digits: 719085495087018136230487973283012437
Probable prime cofactor 2280524986393322347188566632802167131802841297889369062727060879857698833111173208966665751748661072369 has 103 digits

Apr 2, 2009 (2nd)

By Sinkiti Sibata / Msieve / Apr 2, 2009

(49·10¹⁷³+23)/9 = 5(4)₁₇₂7_<174> = C174

C174 = P59 · P116

P59 = 53213885460303743162383640973716467334882950425261428933189_<59>

P116 = 10231247722938530429684370381649939532547858816450603052160092865623046227263385154146691843887422122878799160699923_<116>

Number: 54447_173
N=544444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447
  ( 174 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=53213885460303743162383640973716467334882950425261428933189
 r2=10231247722938530429684370381649939532547858816450603052160092865623046227263385154146691843887422122878799160699923
Version: 
Total time: 101.87 hours.
Scaled time: 340.14 units (timescale=3.339).
Factorization parameters were as follows:
name: 54447_173
n: 544444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447
m: 50000000000000000000000000000000000
deg: 5
c5: 392
c0: 575
skew: 1.08
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved algebraic special-q in [2500000, 8200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1225107 x 1225354
Total sieving time: 101.87 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,53,53,2.5,2.5,100000
total time: 101.87 hours.
 --------- CPU info (if available) ----------

Apr 2, 2009

By Serge Batalov / Msieve-1.40 / Apr 2, 2009

(64·10²⁹¹-1)/9 = 7(1)₂₉₁_<292> = 13 · 373 · 7963 · 36637 · 8447849 · 118824644683_<12> · 112742918287126625015508954219077_<33> · 1076861795965616779294050545059091493301417539513533599117_<58> · C173

C173 = P71 · P103

P71 = 29526732107423789709510964684168327772183952338581119781372039115193043_<71>

P103 = 1396919461377911767198329585214695926966845728727174158023799620445910709651433967937547618165269580961_<103>

SNFS difficulty: 195 digits.
Divisors found:
 r1=29526732107423789709510964684168327772183952338581119781372039115193043 (pp71)
 r2=1396919461377911767198329585214695926966845728727174158023799620445910709651433967937547618165269580961 (pp103)
Version: Msieve-1.40
Total time: 223.80 hours.
Scaled time: 637.17 units (timescale=2.847).
Factorization parameters were as follows:
n: 41246466711752333929895586078766965786778844173689331039930896474968955906844933773973849869182007627958973707341586225377562029715681445290994676117150913031629425232454323
m: 200000000000000000000000000000000
deg: 6
c6: 25
c3: 5
c0: 1
skew: 0.58
type: snfs
lss: 0
rlim: 12500000
alim: 12500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 12500000/12500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [6250000, 12850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 2288296 x 2288544
Total sieving time: 204.26 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 18.91 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,195,6,0,0,0,0,0,0,0,0,12500000,12500000,28,28,56,56,2.6,2.6,100000
total time: 223.80 hours.

Apr 1, 2009 (6th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 1, 2009

(17·10¹⁵²-11)/3 = 5(6)₁₅₁3_<153> = 51980313113038103168212390459_<29> · C125

C125 = P53 · P72

P53 = 26115174500292589890466940447279158913756606529973591_<53>

P72 = 417441712422809702333784001467203387678858490366427777403814455586698627_<72>

Number: 56663_152
N=10901563163622632381653948387832731890897911637792767943828429248839136551842798610658820914905961307803746277372645185959557
  ( 125 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=26115174500292589890466940447279158913756606529973591
 r2=417441712422809702333784001467203387678858490366427777403814455586698627
Version: 
Total time: 12.47 hours.
Scaled time: 29.80 units (timescale=2.390).
Factorization parameters were as follows:
n: 10901563163622632381653948387832731890897911637792767943828429248839136551842798610658820914905961307803746277372645185959557
m: 1000000000000000000000000000000
deg: 5
c5: 1700
c0: -11
skew: 0.36
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7437194
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 445819 x 446067
Total sieving time: 11.54 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 12.47 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 1, 2009 (5th)

By Andreas Tete / Msieve v1.40, GGNFS / Apr 1, 2009

(29·10¹⁹⁹-11)/9 = 3(2)₁₉₈1_<200> = 12983 · 135123913 · 784830287 · 2800975366074227639275163_<25> · 59042658088541072222079473718797_<32> · C123

C123 = P48 · P75

P48 = 155050675604209896581134157847019089481518228889_<48>

P75 = 912690668714493907373500136316795190459438996987480098514102369812675642763_<75>

Wed Apr 01 09:36:21 2009  Msieve v. 1.40
Wed Apr 01 09:36:21 2009  random seeds: 2f036818 1c9667a9
Wed Apr 01 09:36:21 2009  factoring 141513304801840397176199213853517368373409932385348059248024938365674114582593771384352156694628593078442977112469430380307 (123 digits)
Wed Apr 01 09:36:23 2009  searching for 15-digit factors
Wed Apr 01 09:36:27 2009  commencing number field sieve (123-digit input)
Wed Apr 01 09:36:27 2009  R0: -423073470827005685607315
Wed Apr 01 09:36:27 2009  R1:  13967401442491
Wed Apr 01 09:36:27 2009  A0:  70931679734101278720793471830592
Wed Apr 01 09:36:27 2009  A1:  399817006788178411525051256
Wed Apr 01 09:36:27 2009  A2: -2498575242122106646366
Wed Apr 01 09:36:27 2009  A3: -3509459972756639
Wed Apr 01 09:36:27 2009  A4:  12966908382
Wed Apr 01 09:36:27 2009  A5:  10440
Wed Apr 01 09:36:27 2009  skew 445487.65, size 1.077372e-011, alpha -7.850271, combined = 2.207649e-010
Wed Apr 01 09:36:27 2009  
Wed Apr 01 09:36:27 2009  commencing relation filtering
Wed Apr 01 09:36:27 2009  commencing duplicate removal, pass 1
Wed Apr 01 09:39:09 2009  found 988578 hash collisions in 8803354 relations
Wed Apr 01 09:40:00 2009  added 36113 free relations
Wed Apr 01 09:40:00 2009  commencing duplicate removal, pass 2
Wed Apr 01 09:40:28 2009  found 938588 duplicates and 7900878 unique relations
Wed Apr 01 09:40:29 2009  memory use: 50.6 MB
Wed Apr 01 09:40:29 2009  reading rational ideals above 5963776
Wed Apr 01 09:40:29 2009  reading algebraic ideals above 5963776
Wed Apr 01 09:40:29 2009  commencing singleton removal, pass 1
Wed Apr 01 09:43:04 2009  relations with 0 large ideals: 209492
Wed Apr 01 09:43:04 2009  relations with 1 large ideals: 1364215
Wed Apr 01 09:43:04 2009  relations with 2 large ideals: 2981284
Wed Apr 01 09:43:04 2009  relations with 3 large ideals: 2528208
Wed Apr 01 09:43:04 2009  relations with 4 large ideals: 727713
Wed Apr 01 09:43:04 2009  relations with 5 large ideals: 33577
Wed Apr 01 09:43:04 2009  relations with 6 large ideals: 56384
Wed Apr 01 09:43:04 2009  relations with 7+ large ideals: 5
Wed Apr 01 09:43:04 2009  7900878 relations and about 7583434 large ideals
Wed Apr 01 09:43:04 2009  commencing singleton removal, pass 2
Wed Apr 01 09:46:06 2009  found 3541501 singletons
Wed Apr 01 09:46:06 2009  current dataset: 4359377 relations and about 3355214 large ideals
Wed Apr 01 09:46:06 2009  commencing singleton removal, pass 3
Wed Apr 01 09:47:41 2009  found 714711 singletons
Wed Apr 01 09:47:41 2009  current dataset: 3644666 relations and about 2595898 large ideals
Wed Apr 01 09:47:41 2009  commencing singleton removal, pass 4
Wed Apr 01 09:49:14 2009  found 193202 singletons
Wed Apr 01 09:49:14 2009  current dataset: 3451464 relations and about 2398555 large ideals
Wed Apr 01 09:49:14 2009  commencing singleton removal, final pass
Wed Apr 01 09:50:46 2009  memory use: 52.8 MB
Wed Apr 01 09:50:46 2009  commencing in-memory singleton removal
Wed Apr 01 09:50:46 2009  begin with 3451464 relations and 2525566 unique ideals
Wed Apr 01 09:50:53 2009  reduce to 3066244 relations and 2133375 ideals in 13 passes
Wed Apr 01 09:50:53 2009  max relations containing the same ideal: 34
Wed Apr 01 09:50:55 2009  reading rational ideals above 720000
Wed Apr 01 09:50:55 2009  reading algebraic ideals above 720000
Wed Apr 01 09:50:55 2009  commencing singleton removal, final pass
Wed Apr 01 09:52:34 2009  keeping 2716200 ideals with weight <= 20, new excess is 299435
Wed Apr 01 09:52:43 2009  memory use: 91.4 MB
Wed Apr 01 09:52:43 2009  commencing in-memory singleton removal
Wed Apr 01 09:52:43 2009  begin with 3076966 relations and 2716200 unique ideals
Wed Apr 01 09:52:53 2009  reduce to 3044552 relations and 2631466 ideals in 11 passes
Wed Apr 01 09:52:53 2009  max relations containing the same ideal: 20
Wed Apr 01 09:52:57 2009  removing 287604 relations and 254733 ideals in 32871 cliques
Wed Apr 01 09:52:57 2009  commencing in-memory singleton removal
Wed Apr 01 09:52:58 2009  begin with 2756948 relations and 2631466 unique ideals
Wed Apr 01 09:53:03 2009  reduce to 2739934 relations and 2359481 ideals in 7 passes
Wed Apr 01 09:53:03 2009  max relations containing the same ideal: 20
Wed Apr 01 09:53:07 2009  removing 213938 relations and 181067 ideals in 32871 cliques
Wed Apr 01 09:53:07 2009  commencing in-memory singleton removal
Wed Apr 01 09:53:08 2009  begin with 2525996 relations and 2359481 unique ideals
Wed Apr 01 09:53:12 2009  reduce to 2514692 relations and 2166979 ideals in 7 passes
Wed Apr 01 09:53:12 2009  max relations containing the same ideal: 20
Wed Apr 01 09:53:16 2009  relations with 0 large ideals: 14088
Wed Apr 01 09:53:16 2009  relations with 1 large ideals: 113775
Wed Apr 01 09:53:16 2009  relations with 2 large ideals: 386067
Wed Apr 01 09:53:16 2009  relations with 3 large ideals: 685336
Wed Apr 01 09:53:16 2009  relations with 4 large ideals: 700000
Wed Apr 01 09:53:16 2009  relations with 5 large ideals: 422321
Wed Apr 01 09:53:16 2009  relations with 6 large ideals: 155398
Wed Apr 01 09:53:16 2009  relations with 7+ large ideals: 37707
Wed Apr 01 09:53:16 2009  commencing 2-way merge
Wed Apr 01 09:53:21 2009  reduce to 1535349 relation sets and 1187636 unique ideals
Wed Apr 01 09:53:21 2009  commencing full merge
Wed Apr 01 09:53:46 2009  memory use: 101.8 MB
Wed Apr 01 09:53:47 2009  found 756022 cycles, need 709836
Wed Apr 01 09:53:47 2009  weight of 709836 cycles is about 49793751 (70.15/cycle)
Wed Apr 01 09:53:47 2009  distribution of cycle lengths:
Wed Apr 01 09:53:47 2009  1 relations: 81660
Wed Apr 01 09:53:47 2009  2 relations: 80216
Wed Apr 01 09:53:47 2009  3 relations: 79723
Wed Apr 01 09:53:47 2009  4 relations: 72217
Wed Apr 01 09:53:47 2009  5 relations: 66456
Wed Apr 01 09:53:47 2009  6 relations: 58726
Wed Apr 01 09:53:47 2009  7 relations: 51392
Wed Apr 01 09:53:47 2009  8 relations: 43837
Wed Apr 01 09:53:47 2009  9 relations: 38242
Wed Apr 01 09:53:47 2009  10+ relations: 137367
Wed Apr 01 09:53:47 2009  heaviest cycle: 18 relations
Wed Apr 01 09:53:47 2009  commencing cycle optimization
Wed Apr 01 09:53:50 2009  start with 4180043 relations
Wed Apr 01 09:54:13 2009  pruned 121259 relations
Wed Apr 01 09:54:13 2009  memory use: 109.1 MB
Wed Apr 01 09:54:13 2009  distribution of cycle lengths:
Wed Apr 01 09:54:13 2009  1 relations: 81660
Wed Apr 01 09:54:13 2009  2 relations: 82329
Wed Apr 01 09:54:13 2009  3 relations: 83048
Wed Apr 01 09:54:13 2009  4 relations: 74701
Wed Apr 01 09:54:13 2009  5 relations: 68609
Wed Apr 01 09:54:13 2009  6 relations: 59877
Wed Apr 01 09:54:13 2009  7 relations: 52159
Wed Apr 01 09:54:13 2009  8 relations: 44088
Wed Apr 01 09:54:13 2009  9 relations: 38064
Wed Apr 01 09:54:13 2009  10+ relations: 125301
Wed Apr 01 09:54:13 2009  heaviest cycle: 18 relations
Wed Apr 01 09:54:15 2009  RelProcTime: 566
Wed Apr 01 09:54:15 2009  
Wed Apr 01 09:54:15 2009  commencing linear algebra
Wed Apr 01 09:54:16 2009  read 709836 cycles
Wed Apr 01 09:54:19 2009  cycles contain 2265034 unique relations
Wed Apr 01 09:55:18 2009  read 2265034 relations
Wed Apr 01 09:55:26 2009  using 20 quadratic characters above 134217104
Wed Apr 01 09:55:55 2009  building initial matrix
Wed Apr 01 09:57:11 2009  memory use: 265.2 MB
Wed Apr 01 09:57:13 2009  read 709836 cycles
Wed Apr 01 09:57:15 2009  matrix is 709592 x 709836 (202.6 MB) with weight 67855787 (95.59/col)
Wed Apr 01 09:57:15 2009  sparse part has weight 47435926 (66.83/col)
Wed Apr 01 09:57:42 2009  filtering completed in 3 passes
Wed Apr 01 09:57:43 2009  matrix is 706151 x 706351 (202.1 MB) with weight 67635450 (95.75/col)
Wed Apr 01 09:57:43 2009  sparse part has weight 47325320 (67.00/col)
Wed Apr 01 09:57:48 2009  read 706351 cycles
Wed Apr 01 09:57:50 2009  matrix is 706151 x 706351 (202.1 MB) with weight 67635450 (95.75/col)
Wed Apr 01 09:57:50 2009  sparse part has weight 47325320 (67.00/col)
Wed Apr 01 09:57:50 2009  saving the first 48 matrix rows for later
Wed Apr 01 09:57:52 2009  matrix is 706103 x 706351 (193.9 MB) with weight 53758455 (76.11/col)
Wed Apr 01 09:57:52 2009  sparse part has weight 46585813 (65.95/col)
Wed Apr 01 09:57:52 2009  matrix includes 64 packed rows
Wed Apr 01 09:57:52 2009  using block size 65536 for processor cache size 3072 kB
Wed Apr 01 09:58:05 2009  commencing Lanczos iteration
Wed Apr 01 09:58:05 2009  memory use: 190.9 MB
Wed Apr 01 11:15:28 2009  lanczos halted after 11167 iterations (dim = 706103)
Wed Apr 01 11:15:30 2009  recovered 29 nontrivial dependencies
Wed Apr 01 11:15:30 2009  BLanczosTime: 4699
Wed Apr 01 11:15:30 2009  
Wed Apr 01 11:15:30 2009  commencing square root phase
Wed Apr 01 11:15:30 2009  reading relations for dependency 1
Wed Apr 01 11:15:31 2009  read 353185 cycles
Wed Apr 01 11:15:32 2009  cycles contain 1388016 unique relations
Wed Apr 01 11:15:52 2009  read 1388016 relations
Wed Apr 01 11:16:01 2009  multiplying 1131652 relations
Wed Apr 01 11:19:41 2009  multiply complete, coefficients have about 50.96 million bits
Wed Apr 01 11:19:43 2009  initial square root is modulo 20687743
Wed Apr 01 11:25:15 2009  sqrtTime: 585
Wed Apr 01 11:25:15 2009  prp48 factor: 155050675604209896581134157847019089481518228889
Wed Apr 01 11:25:15 2009  prp75 factor: 912690668714493907373500136316795190459438996987480098514102369812675642763
Wed Apr 01 11:25:15 2009  elapsed time 01:48:54

Apr 1, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Apr 1, 2009

(17·10¹⁵¹-11)/3 = 5(6)₁₅₀3_<152> = 197 · 2549 · 150077 · 64049057277893410133_<20> · C122

C122 = P47 · P75

P47 = 32464004422451646227175787281454353721578743329_<47>

P75 = 361628487228543343997268749954229942453264699691372232919817973583847898639_<75>

Number: 56663_151
N=11739908808671929786042058831125218787662532380612200515342021307743382533901311210652185262270993252909610679206989429231
  ( 122 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=32464004422451646227175787281454353721578743329 (pp47)
 r2=361628487228543343997268749954229942453264699691372232919817973583847898639 (pp75)
Version: Msieve-1.39
Total time: 11.87 hours.
Scaled time: 20.64 units (timescale=1.739).
Factorization parameters were as follows:
n: 11739908808671929786042058831125218787662532380612200515342021307743382533901311210652185262270993252909610679206989429231
m: 1000000000000000000000000000000
deg: 5
c5: 170
c0: -11
skew: 0.58
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 469483 x 469731
Total sieving time: 11.87 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 11.87 hours.
 --------- CPU info (if available) ----------

(17·10¹⁵¹+7)/3 = 5(6)₁₅₀9_<152> = 59513 · 75059999230714943790772542299_<29> · C119

C119 = P35 · P84

P35 = 62238710570922495573366663882681629_<35>

P84 = 203819945539082511597499093572063494216006110047531367428499987663572659507351099803_<84>

Number: 56669_151
N=12685490598988142060189052548698739487943122986927356219830691821817806004377075201132067447650111602237073638053619087
  ( 119 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=62238710570922495573366663882681629 (pp35)
 r2=203819945539082511597499093572063494216006110047531367428499987663572659507351099803 (pp84)
Version: Msieve-1.39
Total time: 18.17 hours.
Scaled time: 46.72 units (timescale=2.571).
Factorization parameters were as follows:
n: 12685490598988142060189052548698739487943122986927356219830691821817806004377075201132067447650111602237073638053619087
m: 2000000000000000000000000000000
deg: 5
c5: 85
c0: 112
skew: 1.06
type: snfs
lss: 1
rlim: 2500000
alim: 2500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1250000, 2250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 455657 x 455905
Total sieving time: 18.17 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000
total time: 18.17 hours.
 --------- CPU info (if available) ----------

(17·10¹⁵⁴-11)/3 = 5(6)₁₅₃3_<155> = 3329 · 39712011226005639096211_<23> · C129

C129 = P33 · P43 · P54

P33 = 198234862416162631936484562619177_<33>

P43 = 2328113640357218004986198980376773869988793_<43>

P54 = 928769146549963888152360439285040769713792736737212157_<54>

Number: 56663_154
N=428639301860656654814110326255012769887434929139487247434823933423336520857476621914409947268509542352591090828640998551880219677
  ( 129 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=198234862416162631936484562619177 (pp33)
 r2=2328113640357218004986198980376773869988793 (pp43)
 r3=928769146549963888152360439285040769713792736737212157 (pp54)
Version: Msieve-1.39
Total time: 15.68 hours.
Scaled time: 27.20 units (timescale=1.735).
Factorization parameters were as follows:
n: 428639301860656654814110326255012769887434929139487247434823933423336520857476621914409947268509542352591090828640998551880219677
m: 10000000000000000000000000000000
deg: 5
c5: 17
c0: -110
skew: 1.45
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 446463 x 446711
Total sieving time: 15.68 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 15.68 hours.
 --------- CPU info (if available) ----------

(47·10¹⁵⁹-11)/9 = 5(2)₁₅₈1_<160> = 149 · 190711 · 834433046171802615899_<21> · C132

C132 = P39 · P93

P39 = 536600157415957928667906809610285118781_<39>

P93 = 410441291752214959587758213627032843532720810198270608605012431607818445610475890040947017281_<93>

Number: 52221_159
N=220242861764247661969571070417579128819047493932409916977507088501723368631731121810801082211846597159340822029796611724062744654461
  ( 132 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=536600157415957928667906809610285118781 (pp39)
 r2=410441291752214959587758213627032843532720810198270608605012431607818445610475890040947017281 (pp93)
Version: Msieve-1.39
Total time: 24.30 hours.
Scaled time: 42.25 units (timescale=1.739).
Factorization parameters were as follows:
n: 220242861764247661969571070417579128819047493932409916977507088501723368631731121810801082211846597159340822029796611724062744654461
m: 100000000000000000000000000000000
deg: 5
c5: 47
c0: -110
skew: 1.19
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 631939 x 632187
Total sieving time: 24.30 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 24.30 hours.
 --------- CPU info (if available) ----------

(47·10¹⁵⁹+7)/9 = 5(2)₁₅₈3_<160> = 3³ · 59927713 · 191530975350692846041_<21> · C131

C131 = P57 · P74

P57 = 511170948529923283034557432633722003404601633248959994471_<57>

P74 = 32965426305433629230190054462246589863807476823608132777661922721319318643_<74>

Number: 52223_159
N=16850968233241792739085910398697245799033831050992627002110908064022523588952110206176397144014275422600148319412030862186767222853
  ( 131 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=511170948529923283034557432633722003404601633248959994471 (pp57)
 r2=32965426305433629230190054462246589863807476823608132777661922721319318643 (pp74)
Version: Msieve-1.39
Total time: 35.25 hours.
Scaled time: 90.23 units (timescale=2.560).
Factorization parameters were as follows:
n: 16850968233241792739085910398697245799033831050992627002110908064022523588952110206176397144014275422600148319412030862186767222853
m: 100000000000000000000000000000000
deg: 5
c5: 47
c0: 70
skew: 1.08
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 725307 x 725555
Total sieving time: 35.25 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 35.25 hours.
 --------- CPU info (if available) ----------

Apr 1, 2009 (3rd)

By Sinkiti Sibata / Msieve / Apr 1, 2009

(17·10¹⁴⁷+7)/3 = 5(6)₁₄₆9_<148> = 23 · 103² · 509 · 3797 · 10174717796583088789_<20> · C118

C118 = P36 · P82

P36 = 129573033117179924588512239938857447_<36>

P82 = 9114440288419780231543146000035797635625289495351245774582669051068725173190763913_<82>

Number: 56669_147
N=1180985673335975127458015295142275435200430185710279701518984234077262189735487732400421632109737794206544658338910111
  ( 118 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=129573033117179924588512239938857447
 r2=9114440288419780231543146000035797635625289495351245774582669051068725173190763913
Version: 
Total time: 11.81 hours.
Scaled time: 30.29 units (timescale=2.564).
Factorization parameters were as follows:
name: 56669_147
n: 1180985673335975127458015295142275435200430185710279701518984234077262189735487732400421632109737794206544658338910111
m: 200000000000000000000000000000
deg: 5
c5: 425
c0: 56
skew: 0.67
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 340985 x 341233
Total sieving time: 11.81 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 11.81 hours.
 --------- CPU info (if available) ----------

Apr 1, 2009 (2nd)

By Robert Backstrom / GGNFS, GMP-ECM / Apr 1, 2009

(17·10¹⁷²-11)/3 = 5(6)₁₇₁3_<173> = 4955881256811199723_<19> · 11290582017638819227_<20> · 11112034900286103762642201273601_<32> · C104

C104 = P50 · P55

P50 = 24347751356528083429704521631474972231425477386529_<50>

P55 = 3743156540295891619951667529358841860694687010479704207_<55>

Number: n
N=91137444731686262774627615616319827328697194596617503688409426242033418216434046022033424397591326427503
  ( 104 digits)
Divisors found:
 r1=24347751356528083429704521631474972231425477386529 (pp50)
 r2=3743156540295891619951667529358841860694687010479704207 (pp55)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 7.24 hours.
Scaled time: 13.21 units (timescale=1.826).
Factorization parameters were as follows:
name: KA_5_6_171_3
n: 91137444731686262774627615616319827328697194596617503688409426242033418216434046022033424397591326427503
skew: 9728.52
# norm 1.89e+14
c5: 35640
c4: 506717856
c3: -4809118050740
c2: -160389437028591787
c1: 49262667408050328184
c0: 855687188550426097738455
# alpha -5.68
Y1: 14927678093
Y0: -76129256497011755726
# Murphy_E 2.02e-09
# M 75295145679565946908817500749177518298741612364355916353443022990180492699640146162695390995764326746603
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1150000, 1900001)
Primes: RFBsize:169511, AFBsize:169665, largePrimes:14693412 encountered
Relations: rels:12787035, finalFF:387064
Max relations in full relation-set: 28
Initial matrix: 339260 x 387064 with sparse part having weight 32969349.
Pruned matrix : 304212 x 305972 with weight 22888041.
Total sieving time: 6.35 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.35 hours.
Total square root time: 0.17 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,28,28,56,56,2.6,2.6,100000
total time: 7.24 hours.
 --------- CPU info (if available) ----------

(17·10¹⁷⁷-11)/3 = 5(6)₁₇₆3_<178> = 7 · 1110019 · 24634710995869151_<17> · 220512259049881369_<18> · 4111560817269325357643_<22> · C116

C116 = P37 · P80

P37 = 1473812243093126799020140728678603053_<37>

P80 = 22154916899888862927394726868174094819291933894082264587057091242978910569170611_<80>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 32652187771767028015187037982311727388503491875203013336891204030571771264825654590531346637599232988597952302475383 (116 digits)
Using B1=3130000, B2=5707048630, polynomial Dickson(6), sigma=2678381111
Step 1 took 31871ms
Step 2 took 11122ms
********** Factor found in step 2: 1473812243093126799020140728678603053
Found probable prime factor of 37 digits: 1473812243093126799020140728678603053
Probable prime cofactor 22154916899888862927394726868174094819291933894082264587057091242978910569170611 has 80 digits

(17·10¹⁵⁷+7)/3 = 5(6)₁₅₆9_<158> = 19 · 47 · 24481189 · 151014727 · 1992059893701340537_<19> · C121

C121 = P31 · P91

P31 = 1082985503619346698482704731511_<31>

P91 = 7956084075679697378771476734726063706643361276396233640080959594833325824674938385234259973_<91>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 8616323719537841537759651358421384010839230693036831137814836804107326568016821978024742706935361081846090501105739109203 (121 digits)
Using B1=694000, B2=696689082, polynomial Dickson(3), sigma=3423227726
Step 1 took 7675ms
Step 2 took 3276ms
********** Factor found in step 2: 1082985503619346698482704731511
Found probable prime factor of 31 digits: 1082985503619346698482704731511
Probable prime cofactor 7956084075679697378771476734726063706643361276396233640080959594833325824674938385234259973 has 91 digits

Apr 1, 2009

Jason Papadopoulos's Msieve Version 1.40 was released.

March 2009

Mar 31, 2009 (6th)

By Sinkiti Sibata / GGNFS / Mar 31, 2009

(17·10¹⁴³+7)/3 = 5(6)₁₄₂9_<144> = C144

C144 = P50 · P95

P50 = 27982756612723364391161873357402661413921623326919_<50>

P95 = 20250566250825028908340470371472117580789090434207731128039313703339686354231140442904863190251_<95>

Number: 56669_143
N=566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 144 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=27982756612723364391161873357402661413921623326919 (pp50)
 r2=20250566250825028908340470371472117580789090434207731128039313703339686354231140442904863190251 (pp95)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.71 hours.
Scaled time: 35.25 units (timescale=1.991).
Factorization parameters were as follows:
name: 56669_143
n: 566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 50000000000000000000000000000
deg: 5
c5: 136
c0: 175
skew: 1.05
type: snfs
lss: 1
rlim: 1870000
alim: 1870000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3

Factor base limits: 1870000/1870000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [935000, 2435001)
Primes: RFBsize:139952, AFBsize:140182, largePrimes:4117559 encountered
Relations: rels:4277564, finalFF:355683
Max relations in full relation-set: 28
Initial matrix: 280201 x 355683 with sparse part having weight 38073609.
Pruned matrix : 254929 x 256394 with weight 25011096.
Total sieving time: 16.72 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.74 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1870000,1870000,26,26,49,49,2.3,2.3,100000
total time: 17.71 hours.
 --------- CPU info (if available) ----------

(17·10¹³²-11)/3 = 5(6)₁₃₁3_<133> = 11927 · 12241 · C125

C125 = P59 · P66

P59 = 52284820891276381659708546870688803399267075582265861157609_<59>

P66 = 742341815766471509352216623789785937342597231924390451309162340601_<66>

Number: 56663_132
N=38813208877454852412647671331555464620012372235449573546831005263411310143039209096758615090003459192994254154202289800783009
  ( 125 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=52284820891276381659708546870688803399267075582265861157609 (pp59)
 r2=742341815766471509352216623789785937342597231924390451309162340601 (pp66)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 8.62 hours.
Scaled time: 4.08 units (timescale=0.473).
Factorization parameters were as follows:
name: 56663_132
n: 38813208877454852412647671331555464620012372235449573546831005263411310143039209096758615090003459192994254154202289800783009
m: 200000000000000000000000000
deg: 5
c5: 425
c0: -88
skew: 0.73
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [600000, 1350001)
Primes: RFBsize:92938, AFBsize:92785, largePrimes:3089925 encountered
Relations: rels:3013509, finalFF:213784
Max relations in full relation-set: 28
Initial matrix: 185790 x 213784 with sparse part having weight 19355847.
Pruned matrix : 178577 x 179569 with weight 14186814.
Total sieving time: 7.78 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.64 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000
total time: 8.62 hours.
 --------- CPU info (if available) ----------

(17·10¹³³+7)/3 = 5(6)₁₃₂9_<134> = 1585523 · C128

C128 = P61 · P67

P61 = 6354900264814491244184743748128071268238350143265482183046067_<61>

P67 = 5624013846139737478130811647155975800741681473273243786489905382309_<67>

Number: 56669_133
N=35740047080153783115518769936901998057843794550231479875515313664113776127288387911538758294056072770099624330058073371793828703
  ( 128 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=6354900264814491244184743748128071268238350143265482183046067 (pp61)
 r2=5624013846139737478130811647155975800741681473273243786489905382309 (pp67)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 6.47 hours.
Scaled time: 16.65 units (timescale=2.575).
Factorization parameters were as follows:
name: 56669_133
n: 35740047080153783115518769936901998057843794550231479875515313664113776127288387911538758294056072770099624330058073371793828703
m: 500000000000000000000000000
deg: 5
c5: 136
c0: 175
skew: 1.05
type: snfs
lss: 1
rlim: 1280000
alim: 1280000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1280000/1280000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [640000, 1315001)
Primes: RFBsize:98610, AFBsize:98755, largePrimes:3463453 encountered
Relations: rels:3624793, finalFF:411535
Max relations in full relation-set: 28
Initial matrix: 197432 x 411535 with sparse part having weight 40428850.
Pruned matrix : 153381 x 154432 with weight 13499290.
Total sieving time: 6.23 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1280000,1280000,26,26,47,47,2.3,2.3,75000
total time: 6.47 hours.
 --------- CPU info (if available) ----------

(17·10¹³⁴+7)/3 = 5(6)₁₃₃9_<135> = 3187 · 1526387 · 124908761 · C117

C117 = P39 · P79

P39 = 177690045721539954255192188637430523827_<39>

P79 = 5248376050110084584175551640517401731912747171702980190279975114064593981426783_<79>

Number: 56669_134
N=932584180307896199826436755725362816413786179614293760112655727894376981585212686153454842386632332266149796537458541
  ( 117 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=177690045721539954255192188637430523827 (pp39)
 r2=5248376050110084584175551640517401731912747171702980190279975114064593981426783 (pp79)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 10.06 hours.
Scaled time: 25.81 units (timescale=2.564).
Factorization parameters were as follows:
name: 56669_134
n: 932584180307896199826436755725362816413786179614293760112655727894376981585212686153454842386632332266149796537458541
m: 1000000000000000000000000000
deg: 5
c5: 17
c0: 70
skew: 1.33
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1325001)
Primes: RFBsize:100021, AFBsize:100398, largePrimes:4120790 encountered
Relations: rels:5006144, finalFF:1098798
Max relations in full relation-set: 28
Initial matrix: 200484 x 1098798 with sparse part having weight 104332057.
Pruned matrix : 130458 x 131524 with weight 15361620.
Total sieving time: 9.84 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 10.06 hours.
 --------- CPU info (if available) ----------

(17·10¹⁴⁷-11)/3 = 5(6)₁₄₆3_<148> = 7 · 59 · 14797 · 65029 · 332207 · 171783755123_<12> · C120

C120 = P35 · P85

P35 = 86544108390160860576618609111824549_<35>

P85 = 2887144271562123331708866792687322803919554408546240280625249905275715279143834477443_<85>

Number: 56663_147
N=249865326776104423930264688962865431115384646336343536218983974506030500463312084659865793670525610032092933357714148207
  ( 120 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=86544108390160860576618609111824549 (pp35)
 r2=2887144271562123331708866792687322803919554408546240280625249905275715279143834477443 (pp85)
Version: GGNFS-0.77.1-20060513-k8
Total time: 28.69 hours.
Scaled time: 55.23 units (timescale=1.925).
Factorization parameters were as follows:
name: 56663_147
n: 249865326776104423930264688962865431115384646336343536218983974506030500463312084659865793670525610032092933357714148207
m: 200000000000000000000000000000
deg: 5
c5: 425
c0: -88
skew: 0.73
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 3550001)
Primes: RFBsize:155805, AFBsize:156018, largePrimes:4577116 encountered
Relations: rels:4946005, finalFF:377828
Max relations in full relation-set: 28
Initial matrix: 311890 x 377828 with sparse part having weight 46231365.
Pruned matrix : 289754 x 291377 with weight 34207449.
Total sieving time: 27.11 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.28 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 28.69 hours.
 --------- CPU info (if available) ----------

Mar 31, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Mar 31, 2009

(17·10¹⁴⁶+7)/3 = 5(6)₁₄₅9_<147> = 2753 · 191602500378467_<15> · 348303469429687_<15> · C115

C115 = P43 · P73

P43 = 3057392239329248851492355041710477577863419_<43>

P73 = 1008814518216364144881525304100909685341593542436645633932512347413758923_<73>

Number: 56669_146
N=3084341678917386880850198417534629193145857975643907546729705176891505592880992672853761482215266377566809886537737
  ( 115 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=3057392239329248851492355041710477577863419 (pp43)
 r2=1008814518216364144881525304100909685341593542436645633932512347413758923 (pp73)
Version: Msieve-1.39
Total time: 10.06 hours.
Scaled time: 17.50 units (timescale=1.739).
Factorization parameters were as follows:
n: 3084341678917386880850198417534629193145857975643907546729705176891505592880992672853761482215266377566809886537737
m: 200000000000000000000000000000
deg: 5
c5: 85
c0: 112
skew: 1.06
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 373222 x 373467
Total sieving time: 10.06 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 10.06 hours.
 --------- CPU info (if available) ----------

(17·10¹⁵⁶+7)/3 = 5(6)₁₅₅9_<157> = 15870103 · C150

C150 = P40 · P111

P40 = 2367635701915964097724774454907252952361_<40>

P111 = 150811007437796566561181108281747578101194546138167998981260017491864192266868547474304779267945342162030780643_<111>

Number: 56669_156
N=357065525451641156120200774164267658922356500563774958906483887764727592925305315703790118228386209381669839613937393264975448909604850495719319948123
  ( 150 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=2367635701915964097724774454907252952361 (pp40)
 r2=150811007437796566561181108281747578101194546138167998981260017491864192266868547474304779267945342162030780643 (pp111)
Version: Msieve-1.39
Total time: 25.77 hours.
Scaled time: 66.27 units (timescale=2.571).
Factorization parameters were as follows:
n: 357065525451641156120200774164267658922356500563774958906483887764727592925305315703790118228386209381669839613937393264975448909604850495719319948123
m: 20000000000000000000000000000000
deg: 5
c5: 85
c0: 112
skew: 1.06
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1550000, 2950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 606794 x 607042
Total sieving time: 25.77 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000
total time: 25.77 hours.
 --------- CPU info (if available) ----------

(17·10¹⁶²+7)/3 = 5(6)₁₆₁9_<163> = 151 · 883 · C158

C158 = P60 · P98

P60 = 938555543805634759258867025023469462009038450912147151697593_<60>

P98 = 45282462535927402072019537780515353914840639175316981835821290735171335483580567771222872954596801_<98>

Number: 56669_162
N=42500106250265625664064160160400401001002502506256265640664101660254150635376588441471103677759194397985994964987412468531171327928319820799551998879997199993
  ( 158 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=938555543805634759258867025023469462009038450912147151697593 (pp60)
 r2=45282462535927402072019537780515353914840639175316981835821290735171335483580567771222872954596801 (pp98)
Version: Msieve-1.39
Total time: 31.25 hours.
Scaled time: 54.35 units (timescale=1.739).
Factorization parameters were as follows:
n: 42500106250265625664064160160400401001002502506256265640664101660254150635376588441471103677759194397985994964987412468531171327928319820799551998879997199993
m: 200000000000000000000000000000000
deg: 5
c5: 425
c0: 56
skew: 0.67
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 3700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 662969 x 663217
Total sieving time: 31.25 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 31.25 hours.
 --------- CPU info (if available) ----------

(49·10¹⁵²+41)/9 = 5(4)₁₅₁9_<153> = 3 · 19 · 71 · 27067 · 54454587301_<11> · C134

C134 = P50 · P85

P50 = 71383023650434742673540327947729791872255675161503_<50>

P85 = 1278647495690664764624201577118918428375254439965018372226597323792892389586504540967_<85>

Number: 54449_152
N=91273724425455878608183269099983069058428866640355708824581369879911159793711223544499072175584234280081660305868836764124980604793401
  ( 134 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=71383023650434742673540327947729791872255675161503 (pp50)
 r2=1278647495690664764624201577118918428375254439965018372226597323792892389586504540967 (pp85)
Version: Msieve-1.39
Total time: 14.99 hours.
Scaled time: 26.07 units (timescale=1.739).
Factorization parameters were as follows:
n: 91273724425455878608183269099983069058428866640355708824581369879911159793711223544499072175584234280081660305868836764124980604793401
m: 2000000000000000000000000000000
deg: 5
c5: 1225
c0: 328
skew: 0.77
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 418620 x 418868
Total sieving time: 14.99 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 14.99 hours.
 --------- CPU info (if available) ----------

(17·10¹⁶⁸-11)/3 = 5(6)₁₆₇3_<169> = 157 · 2833506191_<10> · C158

C158 = P48 · P55 · P56

P48 = 483474821596767408759082695358090165964391803959_<48>

P55 = 1837726659308304398305992928336713542412055109386752587_<55>

P56 = 14336695821349312910842315435438406296777782235007995553_<56>

Number: 56663_168
N=12738076371128477468978940600870901594686948017709240282640546203307075948320395285636508081077478314865146941533419891948955009115764013722423058628275173949
  ( 158 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=483474821596767408759082695358090165964391803959 (pp48)
 r2=1837726659308304398305992928336713542412055109386752587 (pp55)
 r3=14336695821349312910842315435438406296777782235007995553 (pp56)
Version: Msieve-1.39
Total time: 55.51 hours.
Scaled time: 142.10 units (timescale=2.560).
Factorization parameters were as follows:
n: 12738076371128477468978940600870901594686948017709240282640546203307075948320395285636508081077478314865146941533419891948955009115764013722423058628275173949
m: 5000000000000000000000000000000000
deg: 5
c5: 136
c0: -275
skew: 1.15
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 5150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 884260 x 884508
Total sieving time: 55.51 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 55.51 hours.
 --------- CPU info (if available) ----------

Mar 31, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Mar 31, 2009

(16·10¹⁵⁷+17)/3 = 5(3)₁₅₆9_<158> = 17169989 · 6719426025889_<13> · C138

C138 = P57 · P82

P57 = 151415726802733836070298952223999025939393684802019324559_<57>

P82 = 3052991170776104521524354567572988782090802728355355198184479556190327131801237201_<82>

Number: n
N=462270877045393163584348333685350086843161288349162181866585708605048711534748880933255975279236570378999265058357048501718512986563719359
  ( 138 digits)
SNFS difficulty: 158 digits.
Divisors found:

Tue Mar 31 10:09:36 2009  prp57 factor: 151415726802733836070298952223999025939393684802019324559
Tue Mar 31 10:09:36 2009  prp82 factor: 3052991170776104521524354567572988782090802728355355198184479556190327131801237201
Tue Mar 31 10:09:36 2009  elapsed time 00:45:07 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 17.44 hours.
Scaled time: 46.39 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_3_156_9
n: 462270877045393163584348333685350086843161288349162181866585708605048711534748880933255975279236570378999265058357048501718512986563719359
skew: 0.81
deg: 5
c5: 50
c0: 17
m: 20000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2250000, 3240409)
Primes: RFBsize:315948, AFBsize:316401, largePrimes:14457525 encountered
Relations: rels:13441122, finalFF:589292
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 934151 hash collisions in 15350882 relations
Msieve: matrix is 569049 x 569297 (151.8 MB)

Total sieving time: 17.16 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000
total time: 17.44 hours.
 --------- CPU info (if available) ----------

(17·10²⁰²-11)/3 = 5(6)₂₀₁3_<203> = 25508661453125273_<17> · 1409768013786543156259_<22> · 1513242066470195178659029_<25> · 6533393411141674191648447518542097_<34> · C108

C108 = P43 · P65

P43 = 8533119906049968013405927966076339919424151_<43>

P65 = 18678297133149696415319508843765989670835661272807507536836918743_<65>

Number: n
N=159384149077995724360968874191338336220570220714108819627737775487450405265340226750529863760307117738762193
  ( 108 digits)
Divisors found:

Tue Mar 31 14:05:24 2009  prp43 factor: 8533119906049968013405927966076339919424151
Tue Mar 31 14:05:24 2009  prp65 factor: 18678297133149696415319508843765989670835661272807507536836918743
Tue Mar 31 14:05:24 2009  elapsed time 00:25:39 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 8.88 hours.
Scaled time: 23.35 units (timescale=2.629).
Factorization parameters were as follows:
name: KA_5_6_201_3
n: 159384149077995724360968874191338336220570220714108819627737775487450405265340226750529863760307117738762193
skew: 21605.08
# norm 6.21e+14
c5: 25380
c4: -660213150
c3: -24921912202565
c2: 707460791442207938
c1: 7580049824717362649974
c0: 756794256944768577900120
# alpha -5.93
Y1: 259070668967
Y0: -362737383380765073881
# Murphy_E 1.36e-09
# M 109100457503249211478622374976003187991088526352527265693883999034580980374613343265241024834765793558473934
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1250000, 2306641)
Primes: RFBsize:183072, AFBsize:183136, largePrimes:15477607 encountered
Relations: rels:13629014, finalFF:405215
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1107998 hash collisions in 14538239 relations
Msieve: matrix is 358515 x 358763 (98.6 MB)

Total sieving time: 8.41 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000
total time: 8.88 hours.
 --------- CPU info (if available) ----------

(17·10¹⁴⁰-11)/3 = 5(6)₁₃₉3_<141> = 23 · 1988582244189483800485209843958743589043_<40> · C101

C101 = P49 · P52

P49 = 3005579956989595830896695132357111722799545705839_<49>

P52 = 4122189828877880282767943433686839636744205235978853_<52>

Number: n
N=12389571128581728818477254444904148656371225081269043431614820414039285832831268485708657579962622667
  ( 101 digits)
Divisors found:
 r1=3005579956989595830896695132357111722799545705839 (pp49)
 r2=4122189828877880282767943433686839636744205235978853 (pp52)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.57 hours.
Scaled time: 8.33 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_5_6_139_3
n: 12389571128581728818477254444904148656371225081269043431614820414039285832831268485708657579962622667
skew: 4651.48
# norm 9.89e+13
c5: 69300
c4: 571486905
c3: -12839315526392
c2: -9622006559641436
c1: 57287478236820850868
c0: 2430459791125601077760
# alpha -5.44
Y1: 15320936839
Y0: -11232169038330410541
# Murphy_E 3.14e-09
# M 4060843220027718992330198455824508205853740189188640325603580098901770979732502745137967010543083242
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [900000, 1400001)
Primes: RFBsize:135072, AFBsize:135518, largePrimes:10265150 encountered
Relations: rels:8908522, finalFF:341461
Max relations in full relation-set: 48
Initial matrix: 270671 x 341461 with sparse part having weight 36163373.
Pruned matrix : 227834 x 229251 with weight 18117846.
Total sieving time: 3.78 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.40 hours.
Total square root time: 0.19 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,28,28,56,56,2.5,2.5,100000
total time: 4.57 hours.
 --------- CPU info (if available) ----------

(17·10¹⁴⁵+7)/3 = 5(6)₁₄₄9_<146> = 239 · 677 · 1049 · 292118833 · 29674305301143700049_<20> · C110

C110 = P41 · P70

P41 = 18183749665123138488743833669798206342683_<41>

P70 = 2118078478457350688003065996325803900532514144740988502378387478125357_<70>

Number: n
N=38514608823353377272641347653420217491397580608502431726839383981631414778701495850403463655142317875973712831
  ( 110 digits)
Divisors found:

Tue Mar 31 17:40:48 2009  prp41 factor: 18183749665123138488743833669798206342683
Tue Mar 31 17:40:48 2009  prp70 factor: 2118078478457350688003065996325803900532514144740988502378387478125357
Tue Mar 31 17:40:48 2009  elapsed time 00:33:50 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 13.42 hours.
Scaled time: 35.42 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_5_6_144_9
n: 38514608823353377272641347653420217491397580608502431726839383981631414778701495850403463655142317875973712831
skew: 37739.22
# norm 4.10e+15
c5: 20580
c4: -3779595533
c3: -179745057398388
c2: 4385492615468670600
c1: 77526627803213528726734
c0: -311510180055772786998885888
# alpha -6.59
Y1: 159942219547
Y0: -1133543719479839699269
# Murphy_E 9.84e-10
# M 33740392465434260340494028499491057358071137137340339477433159730462287355555309704189306725907028187501742996
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1600000, 2200141)
Primes: RFBsize:230209, AFBsize:230131, largePrimes:16112914 encountered
Relations: rels:14158601, finalFF:468589
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 786233 hash collisions in 14611703 relations
Msieve: matrix is 452695 x 452943 (125.8 MB)

Total sieving time: 12.98 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000
total time: 13.42 hours.
 --------- CPU info (if available) ----------

(17·10¹⁴⁵-11)/3 = 5(6)₁₄₄3_<146> = 352357 · 50632934702653297795467724997_<29> · C112

C112 = P39 · P73

P39 = 464627234444086771952257423350409216049_<39>

P73 = 6836077856706214117788292473821556206302849788523878355659660833037097103_<73>

Number: n
N=3176227949005868364358693738547790942522693886423918740391964916137466084652121419130404718461305044596919006047
  ( 112 digits)
Divisors found:

Tue Mar 31 20:15:07 2009  prp39 factor: 464627234444086771952257423350409216049
Tue Mar 31 20:15:07 2009  prp73 factor: 6836077856706214117788292473821556206302849788523878355659660833037097103
Tue Mar 31 20:15:07 2009  elapsed time 00:42:53 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 15.08 hours.
Scaled time: 39.96 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_6_144_3
n: 3176227949005868364358693738547790942522693886423918740391964916137466084652121419130404718461305044596919006047
skew: 54953.55
# norm 5.48e+15
c5: 11520
c4: 1446373908
c3: 134262196311763
c2: -3817045765264157060
c1: -243283989464720815205980
c0: 4747964505240438282057733040
# alpha -6.74
Y1: 316846995377
Y0: -3076739404819159933737
# Murphy_E 8.00e-10
# M 205874714480015875367168626463213627297291540683003617802622108955885926000947565141870728968097023688519563551
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1750000, 2450083)
Primes: RFBsize:250150, AFBsize:249829, largePrimes:16312727 encountered
Relations: rels:14195956, finalFF:521565
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 815780 hash collisions in 14679846 relations
Msieve: matrix is 566775 x 567023 (158.2 MB)

Total sieving time: 14.67 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,28,28,56,56,2.6,2.6,100000
total time: 15.08 hours.
 --------- CPU info (if available) ----------

(17·10¹⁴⁹-11)/3 = 5(6)₁₄₈3_<150> = 31 · 11382247123588637_<17> · C133

C133 = P40 · P93

P40 = 7590405178178339305402471611491947851643_<40>

P93 = 211579215767037376360039653308037412309227402033175342484760722035903386871514912511485607703_<93>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 1605971974953032633620272892291686979162820217563299946643348773906039149427150458389421453602769051062426587033402865804805142006029 (133 digits)
Using B1=2564000, B2=3568033570, polynomial Dickson(6), sigma=1582264560
Step 1 took 31746ms
Step 2 took 10951ms
********** Factor found in step 2: 7590405178178339305402471611491947851643
Found probable prime factor of 40 digits: 7590405178178339305402471611491947851643
Probable prime cofactor 211579215767037376360039653308037412309227402033175342484760722035903386871514912511485607703 has 93 digits

Mar 31, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Mar 31, 2009

(8·10¹⁸²+1)/9 = (8)₁₈₁9_<182> = 15236737 · C175

C175 = P52 · P124

P52 = 2110195633562623203363788636409114570248983488203027_<52>

P124 = 2764603071590345234203219159089774679474933517069560468037418091215396508782747937036376125151482683214742185677398930843011_<124>

Number: 88889_182
N=5833853330203762714345524825222676540842628502998305272899892469686186017970178843993230892473164621066104172362421750069512185508543521417275161269036073070558931934631994297
  ( 175 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=2110195633562623203363788636409114570248983488203027
 r2=2764603071590345234203219159089774679474933517069560468037418091215396508782747937036376125151482683214742185677398930843011
Version: 
Total time: 78.73 hours.
Scaled time: 187.62 units (timescale=2.383).
Factorization parameters were as follows:
n: 5833853330203762714345524825222676540842628502998305272899892469686186017970178843993230892473164621066104172362421750069512185508543521417275161269036073070558931934631994297
m: 2000000000000000000000000000000000000
deg: 5
c5: 25
c0: 1
skew: 0.53
type: snfs
lss: 1
rlim: 6600000
alim: 6600000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6600000/6600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3300000, 5400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 18294595
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1201370 x 1201618
Total sieving time: 72.82 hours.
Total relation processing time: 2.03 hours.
Matrix solve time: 3.56 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,6600000,6600000,28,28,53,53,2.5,2.5,100000
total time: 78.73 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Mar 31, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Mar 31, 2009

(17·10¹³⁸+7)/3 = 5(6)₁₃₇9_<139> = 239 · C137

C137 = P40 · P98

P40 = 2098112473379109578751455496357626967749_<40>

P98 = 11300586918872044831776718863224420912853578411193077140307922192223698599776702875788745176999879_<98>

Number: 56669_138
N=23709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902371
  ( 137 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=2098112473379109578751455496357626967749
 r2=11300586918872044831776718863224420912853578411193077140307922192223698599776702875788745176999879
Version: 
Total time: 8.22 hours.
Scaled time: 8.60 units (timescale=1.046).
Factorization parameters were as follows:
n: 23709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902371
m: 5000000000000000000000000000
deg: 5
c5: 136
c0: 175
skew: 1.05
type: snfs
lss: 1
rlim: 1540000
alim: 1540000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1540000/1540000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [770000, 1770001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 234388 x 234636
Total sieving time: 8.22 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1540000,1540000,26,26,48,48,2.3,2.3,100000
total time: 8.22 hours.
 --------- CPU info (if available) ----------

(17·10¹³⁷-11)/3 = 5(6)₁₃₆3_<138> = 89 · C136

C136 = P32 · P105

P32 = 30786338087936362186389460909151_<32>

P105 = 206813852960212896386184499990362608712079715902907975666006921434264383142752261316006717304525197630817_<105>

Number: 56663_137
N=6367041198501872659176029962546816479400749063670411985018726591760299625468164794007490636704119850187265917602996254681647940074906367
  ( 136 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=30786338087936362186389460909151
 r2=206813852960212896386184499990362608712079715902907975666006921434264383142752261316006717304525197630817
Version: 
Total time: 9.54 hours.
Scaled time: 7.45 units (timescale=0.781).
Factorization parameters were as follows:
n: 6367041198501872659176029962546816479400749063670411985018726591760299625468164794007490636704119850187265917602996254681647940074906367
m: 2000000000000000000000000000
deg: 5
c5: 425
c0: -88
skew: 0.73
type: snfs
lss: 1
rlim: 1460000
alim: 1460000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1460000/1460000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [730000, 1705001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 261625 x 261873
Total sieving time: 9.54 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1460000,1460000,26,26,48,48,2.3,2.3,75000
total time: 9.54 hours.
 --------- CPU info (if available) ----------

Mar 31, 2009

By Jo Yeong Uk / GMP-ECM / Mar 31, 2009

(17·10¹⁷⁶+7)/3 = 5(6)₁₇₅9_<177> = C177

C177 = P37 · P141

P37 = 1332900038363680881394620148129664059_<37>

P141 = 425138157668843915788962204505688086610791867911821343666941015479820678943431096734573619034309056634425509765000685116141894382558408244791_<141>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 (177 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3212400340
Step 1 took 19100ms
Step 2 took 7720ms
********** Factor found in step 2: 1332900038363680881394620148129664059
Found probable prime factor of 37 digits: 1332900038363680881394620148129664059
Probable prime cofactor 425138157668843915788962204505688086610791867911821343666941015479820678943431096734573619034309056634425509765000685116141894382558408244791 has 141 digits

Mar 30, 2009 (7th)

By Sinkiti Sibata / GGNFS

(17·10¹²⁸-11)/3 = 5(6)₁₂₇3_<129> = 29 · 17021 · 5505469367639_<13> · C111

C111 = P50 · P61

P50 = 24820327977021975378256090284946693494883960699649_<50>

P61 = 8401227213587191514482424464656102094826473116869647302619337_<61>

Number: 56663_128
N=208521214850716544221599058555411701945808374634706100934515675276173697928018386423321266670848732764836512713
  ( 111 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=24820327977021975378256090284946693494883960699649 (pp50)
 r2=8401227213587191514482424464656102094826473116869647302619337 (pp61)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 4.83 hours.
Scaled time: 2.28 units (timescale=0.473).
Factorization parameters were as follows:
name: 56663_128
n: 208521214850716544221599058555411701945808374634706100934515675276173697928018386423321266670848732764836512713
m: 50000000000000000000000000
deg: 5
c5: 136
c0: -275
skew: 1.15
type: snfs
lss: 1
rlim: 1050000
alim: 1050000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1050000/1050000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [525000, 925001)
Primes: RFBsize:82134, AFBsize:82353, largePrimes:2798952 encountered
Relations: rels:2768491, finalFF:272749
Max relations in full relation-set: 28
Initial matrix: 164554 x 272749 with sparse part having weight 20623329.
Pruned matrix : 132835 x 133721 with weight 7226487.
Total sieving time: 4.43 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1050000,1050000,26,26,47,47,2.3,2.3,50000
total time: 4.83 hours.
 --------- CPU info (if available) ----------

(17·10¹²⁹+7)/3 = 5(6)₁₂₈9_<130> = 31 · 73571 · 3748847 · 5887939 · C111

C111 = P31 · P81

P31 = 1124466814397827153397456968673_<31>

P81 = 100104050957610405407547844556194856347545057379087033154669977098606751781653141_<81>

Number: 56663_129
N=112563683288621931257893820232631592344395789058017227723897905579838046080414432892570091892364372398589051893
  ( 111 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1124466814397827153397456968673 (pp31)
 r2=100104050957610405407547844556194856347545057379087033154669977098606751781653141 (pp81)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 4.52 hours.
Scaled time: 2.14 units (timescale=0.473).
Factorization parameters were as follows:
name: 56663_129
n: 112563683288621931257893820232631592344395789058017227723897905579838046080414432892570091892364372398589051893
m: 100000000000000000000000000
deg: 5
c5: 17
c0: 70
skew: 1.33
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 890001)
Primes: RFBsize:84270, AFBsize:84768, largePrimes:2723010 encountered
Relations: rels:2604917, finalFF:205337
Max relations in full relation-set: 28
Initial matrix: 169103 x 205337 with sparse part having weight 14878093.
Pruned matrix : 154361 x 155270 with weight 8821894.
Total sieving time: 4.04 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.33 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 4.52 hours.
 --------- CPU info (if available) ----------

Mar 30, 2009 (6th)

By Wataru Sakai / Msieve / Mar 30, 2009

(14·10¹⁸⁵-11)/3 = 4(6)₁₈₄3_<186> = 5003 · C182

C182 = P51 · P53 · P79

P51 = 472028819964297438740806605192579205630100803128437_<51>

P53 = 24871243197390234627509331406490531115713301860364091_<53>

P79 = 7945299421360233896153427606410291300881548381778500398649648806810791075311763_<79>

Number: 46663_185
N=93277366913185422080085282164034912385901792257978546205609967352921580385102271970151242587780664934372709707508828036511426477446865214204810447065094276767272969551602371910187221
  ( 182 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=472028819964297438740806605192579205630100803128437
 r2=24871243197390234627509331406490531115713301860364091
 r3=7945299421360233896153427606410291300881548381778500398649648806810791075311763
Version: 
Total time: 280.59 hours.
Scaled time: 564.54 units (timescale=2.012).
Factorization parameters were as follows:
n: 93277366913185422080085282164034912385901792257978546205609967352921580385102271970151242587780664934372709707508828036511426477446865214204810447065094276767272969551602371910187221
m: 10000000000000000000000000000000000000
deg: 5
c5: 14
c0: -11
skew: 0.95
type: snfs
lss: 1
rlim: 8900000
alim: 8900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 8900000/8900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4450000, 7350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1165764 x 1166012
Total sieving time: 280.59 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,8900000,8900000,28,28,54,54,2.5,2.5,100000
total time: 280.59 hours.
 --------- CPU info (if available) ----------

Mar 30, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Mar 30, 2009

(17·10¹⁰¹-11)/3 = 5(6)₁₀₀3_<102> = 67912517003_<11> · C91

C91 = P40 · P52

P40 = 5123831568700026011372584628954576029969_<40>

P52 = 1628482120734270536821075988987892173086356834821509_<52>

Number: 56663_101
N=8344068099281822559585314721701608004037927833753428446267223188442051074345256757949803221
  ( 91 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=5123831568700026011372584628954576029969 (pp40)
 r2=1628482120734270536821075988987892173086356834821509 (pp52)
Version: Msieve-1.39
Total time: 0.27 hours.
Scaled time: 0.32 units (timescale=1.196).
Factorization parameters were as follows:
n: 8344068099281822559585314721701608004037927833753428446267223188442051074345256757949803221
m: 20000000000000000000000000
deg: 4
c4: 85
c0: -88
skew: 1.01
type: snfs
lss: 1
rlim: 370000
alim: 370000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2
Factor base limits: 370000/370000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [185000, 235001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 36875 x 37111
Total sieving time: 0.27 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103,4,0,0,0,0,0,0,0,0,370000,370000,25,25,43,43,2.2,2.2,10000
total time: 0.27 hours.
 --------- CPU info (if available) ----------

(17·10¹¹⁵+7)/3 = 5(6)₁₁₄9_<116> = 67 · 21061 · C110

C110 = P41 · P69

P41 = 95290352109099817535683452296597792913083_<41>

P69 = 421429510891924613323930011380750009408902662687024674204055392048089_<69>

Number: 56669_115
N=40158166482057213103562478193525038971138325749345480942469646922313554491442885283945402846647064756933248387
  ( 110 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=95290352109099817535683452296597792913083 (pp41)
 r2=421429510891924613323930011380750009408902662687024674204055392048089 (pp69)
Version: Msieve-1.39
Total time: 0.77 hours.
Scaled time: 0.92 units (timescale=1.198).
Factorization parameters were as follows:
n: 40158166482057213103562478193525038971138325749345480942469646922313554491442885283945402846647064756933248387
m: 100000000000000000000000
deg: 5
c5: 17
c0: 7
skew: 0.84
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [305000, 455001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 64735 x 64965
Total sieving time: 0.77 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000
total time: 0.77 hours.
 --------- CPU info (if available) ----------

(17·10¹¹⁸+7)/3 = 5(6)₁₁₇9_<119> = 101917 · 8323537 · C107

C107 = P48 · P60

P48 = 601885235402110792210900200078722304656813123651_<48>

P60 = 110983759173059900845424929359819040363022947328137613794411_<60>

Number: 56669_118
N=66799486015688331413048161090075435589653725608566758691907701831234347207760026800744726843636555435714561
  ( 107 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=601885235402110792210900200078722304656813123651 (pp48)
 r2=110983759173059900845424929359819040363022947328137613794411 (pp60)
Version: Msieve-1.39
Total time: 1.43 hours.
Scaled time: 1.71 units (timescale=1.198).
Factorization parameters were as follows:
n: 66799486015688331413048161090075435589653725608566758691907701831234347207760026800744726843636555435714561
m: 500000000000000000000000
deg: 5
c5: 136
c0: 175
skew: 1.05
type: snfs
lss: 1
rlim: 720000
alim: 720000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 720000/720000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [360000, 660001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 83421 x 83653
Total sieving time: 1.43 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,720000,720000,25,25,46,46,2.2,2.2,50000
total time: 1.43 hours.
 --------- CPU info (if available) ----------

(17·10¹²²+7)/3 = 5(6)₁₂₁9_<123> = 13725133 · C116

C116 = P47 · P69

P47 = 74312416334972309488106373427432495350587766049_<47>

P69 = 555583989609428877329491732475831696278630005512381518127600113742657_<69>

Number: 56669_122
N=41286788744900808368608644205244981354036180681576394681688451883611376783501235774303000682519190645851422107652193
  ( 116 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=74312416334972309488106373427432495350587766049 (pp47)
 r2=555583989609428877329491732475831696278630005512381518127600113742657 (pp69)
Version: Msieve-1.39
Total time: 1.80 hours.
Scaled time: 2.14 units (timescale=1.188).
Factorization parameters were as follows:
n: 41286788744900808368608644205244981354036180681576394681688451883611376783501235774303000682519190645851422107652193
m: 2000000000000000000000000
deg: 5
c5: 425
c0: 56
skew: 0.67
type: snfs
lss: 1
rlim: 820000
alim: 820000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 820000/820000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [410000, 760001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 92352 x 92600
Total sieving time: 1.80 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,46,46,2.2,2.2,50000
total time: 1.80 hours.
 --------- CPU info (if available) ----------

(17·10¹¹⁹-11)/3 = 5(6)₁₁₈3_<120> = 31 · 887 · 11731 · C112

C112 = P30 · P82

P30 = 239450380240083774854468268749_<30>

P82 = 7336548403427378900248248059735962221136819514321416423825489537237179273289440041_<82>

Number: 56663_119
N=1756739304850465415165792566407440251428414804190514777328834092497373475814356681431037481633768504216909578709
  ( 112 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=239450380240083774854468268749 (pp30)
 r2=7336548403427378900248248059735962221136819514321416423825489537237179273289440041 (pp82)
Version: Msieve-1.39
Total time: 1.34 hours.
Scaled time: 1.59 units (timescale=1.183).
Factorization parameters were as follows:
n: 1756739304850465415165792566407440251428414804190514777328834092497373475814356681431037481633768504216909578709
m: 1000000000000000000000000
deg: 5
c5: 17
c0: -110
skew: 1.45
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 565001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 84097 x 84345
Total sieving time: 1.34 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.34 hours.
 --------- CPU info (if available) ----------

(17·10¹²²-11)/3 = 5(6)₁₂₁3_<123> = 677 · C120

C120 = P39 · P82

P39 = 795291725793282443500552146174546722231_<39>

P82 = 1052476806148759029278464603331228114347816926127482451611939039647002492509057149_<82>

Number: 56663_122
N=837026095519448547513540128015755785327424913835548990645002461841457410142786804529788281634662727720334810438207779419
  ( 120 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=795291725793282443500552146174546722231 (pp39)
 r2=1052476806148759029278464603331228114347816926127482451611939039647002492509057149 (pp82)
Version: Msieve-1.39
Total time: 2.21 hours.
Scaled time: 2.65 units (timescale=1.198).
Factorization parameters were as follows:
n: 837026095519448547513540128015755785327424913835548990645002461841457410142786804529788281634662727720334810438207779419
m: 2000000000000000000000000
deg: 5
c5: 425
c0: -88
skew: 0.73
type: snfs
lss: 1
rlim: 820000
alim: 820000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 820000/820000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [410000, 860001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 110779 x 111027
Total sieving time: 2.21 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,46,46,2.2,2.2,50000
total time: 2.21 hours.
 --------- CPU info (if available) ----------

(17·10¹²⁷-11)/3 = 5(6)₁₂₆3_<128> = 3631 · C125

C125 = P37 · P88

P37 = 3958394890072113977857155948035524349_<37>

P88 = 3942596213104646669262560616780369956388402140240085425022769072444304806099790128161277_<88>

Number: 56663_127
N=15606352703571100706875975397043973193794179748462315248324612136234278894703020288258514642430918938768016157165151932433673
  ( 125 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=3958394890072113977857155948035524349 (pp37)
 r2=3942596213104646669262560616780369956388402140240085425022769072444304806099790128161277 (pp88)
Version: Msieve-1.39
Total time: 2.71 hours.
Scaled time: 3.22 units (timescale=1.186).
Factorization parameters were as follows:
n: 15606352703571100706875975397043973193794179748462315248324612136234278894703020288258514642430918938768016157165151932433673
m: 20000000000000000000000000
deg: 5
c5: 425
c0: -88
skew: 0.73
type: snfs
lss: 1
rlim: 990000
alim: 990000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 990000/990000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [495000, 995001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 154284 x 154529
Total sieving time: 2.71 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,990000,990000,26,26,47,47,2.3,2.3,50000
total time: 2.71 hours.
 --------- CPU info (if available) ----------

(17·10¹²⁵+7)/3 = 5(6)₁₂₄9_<126> = 23 · 2593 · 144228983586167_<15> · C107

C107 = P39 · P69

P39 = 589250921545742190593877958793077296379_<39>

P69 = 111800694279228050333176460851172320271408111898525575752334134383047_<69>

Number: 56669_125
N=65878662133488915633720942220528513751455616516752988633261898199458452664627642528077056373168179932086813
  ( 107 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=589250921545742190593877958793077296379 (pp39)
 r2=111800694279228050333176460851172320271408111898525575752334134383047 (pp69)
Version: Msieve-1.39
Total time: 1.49 hours.
Scaled time: 1.77 units (timescale=1.189).
Factorization parameters were as follows:
n: 65878662133488915633720942220528513751455616516752988633261898199458452664627642528077056373168179932086813
m: 10000000000000000000000000
deg: 5
c5: 17
c0: 7
skew: 0.84
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 695001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 115556 x 115804
Total sieving time: 1.49 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 1.49 hours.
 --------- CPU info (if available) ----------

(49·10¹⁶⁸+23)/9 = 5(4)₁₆₇7_<169> = 269 · 491 · 8053 · 10253 · C156

C156 = P71 · P85

P71 = 69456425612216082029462188812207301586685011392460105683467565827546433_<71>

P85 = 7187845147472167912233172898770037011894826265333750517439708363073552108865016407969_<85>

Number: 54447_168
N=499242031797528964603322450116699697726570511429147637000037655432511436237498026365668367009829901398816139852650418300760547125611219115491032386218724577
  ( 156 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=69456425612216082029462188812207301586685011392460105683467565827546433 (pp71)
 r2=7187845147472167912233172898770037011894826265333750517439708363073552108865016407969 (pp85)
Version: Msieve-1.39
Total time: 70.78 hours.
Scaled time: 181.98 units (timescale=2.571).
Factorization parameters were as follows:
n: 499242031797528964603322450116699697726570511429147637000037655432511436237498026365668367009829901398816139852650418300760547125611219115491032386218724577
m: 5000000000000000000000000000000000
deg: 5
c5: 392
c0: 575
skew: 1.08
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1006000 x 1006248
Total sieving time: 70.78 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 70.78 hours.
 --------- CPU info (if available) ----------

(17·10¹³¹-11)/3 = 5(6)₁₃₀3_<132> = 53 · 163 · 1657 · C125

C125 = P44 · P81

P44 = 57254393326442842901839185810365868132126073_<44>

P81 = 691405559039504718020667746214520013146066727040298897302914444029868559857781097_<81>

Number: 56663_131
N=39586005825336901941900830116213568736872727428531017579935614060101662917289767862771804210688924806591507744571250840242081
  ( 125 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=57254393326442842901839185810365868132126073 (pp44)
 r2=691405559039504718020667746214520013146066727040298897302914444029868559857781097 (pp81)
Version: Msieve-1.39
Total time: 2.68 hours.
Scaled time: 6.90 units (timescale=2.571).
Factorization parameters were as follows:
n: 39586005825336901941900830116213568736872727428531017579935614060101662917289767862771804210688924806591507744571250840242081
m: 100000000000000000000000000
deg: 5
c5: 170
c0: -11
skew: 0.58
type: snfs
lss: 1
rlim: 1120000
alim: 1120000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1120000/1120000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [560000, 960001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 175868 x 176116
Total sieving time: 2.68 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1120000,1120000,26,26,47,47,2.3,2.3,50000
total time: 2.68 hours.
 --------- CPU info (if available) ----------

(17·10¹⁴⁶-11)/3 = 5(6)₁₄₅3_<147> = 127 · 2678747 · C139

C139 = P38 · P101

P38 = 27811417659945137991544604657599424539_<38>

P101 = 59892042054550345949298752078376499404048130275627420744018974026631281026436704763054876687625491393_<101>

Number: 56663_146
N=1665682596086098376975829143654147064117777625860992926113503451005784075956215933906584661506748434163072836438482662037722974383897492827
  ( 139 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=27811417659945137991544604657599424539 (pp38)
 r2=59892042054550345949298752078376499404048130275627420744018974026631281026436704763054876687625491393 (pp101)
Version: Msieve-1.39
Total time: 8.27 hours.
Scaled time: 21.25 units (timescale=2.571).
Factorization parameters were as follows:
n: 1665682596086098376975829143654147064117777625860992926113503451005784075956215933906584661506748434163072836438482662037722974383897492827
m: 100000000000000000000000000000
deg: 5
c5: 170
c0: -11
skew: 0.58
type: snfs
lss: 1
rlim: 1990000
alim: 1990000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1990000/1990000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [995000, 2295001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 329154 x 329402
Total sieving time: 8.27 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1990000,1990000,26,26,49,49,2.3,2.3,100000
total time: 8.27 hours.
 --------- CPU info (if available) ----------

(17·10¹³²+7)/3 = 5(6)₁₃₁9_<133> = 43 · 2067783733_<10> · C122

C122 = P52 · P70

P52 = 9908855818710071772279685922495241980372071557069529_<52>

P70 = 6431771211676737322956945474073996162358335807731917122684415567681219_<70>

Number: 56669_132
N=63731493595434967341012437950993608144671061585793864272607916454570032027829144609646555791788131891898934762993290475851
  ( 122 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=9908855818710071772279685922495241980372071557069529 (pp52)
 r2=6431771211676737322956945474073996162358335807731917122684415567681219 (pp70)
Version: Msieve-1.39
Total time: 3.46 hours.
Scaled time: 8.90 units (timescale=2.572).
Factorization parameters were as follows:
n: 63731493595434967341012437950993608144671061585793864272607916454570032027829144609646555791788131891898934762993290475851
m: 200000000000000000000000000
deg: 5
c5: 425
c0: 56
skew: 0.67
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [600000, 1125001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 165896 x 166141
Total sieving time: 3.46 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000
total time: 3.46 hours.
 --------- CPU info (if available) ----------

(25·10¹⁸¹-61)/9 = 2(7)₁₈₀1_<182> = 3 · 7 · 23 · C179

C179 = P65 · P114

P65 = 75510615435433520332094734482048406815014663397888447357329506169_<65>

P114 = 761627047329789607062080654255561176112224466344542541980790154090969468251343258094559369704529752173237377695073_<114>

Number: 27771_181
N=57510927076144467448815274902231423970554405337014032666206579250057510927076144467448815274902231423970554405337014032666206579250057510927076144467448815274902231423970554405337
  ( 179 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=75510615435433520332094734482048406815014663397888447357329506169 (pp65)
 r2=761627047329789607062080654255561176112224466344542541980790154090969468251343258094559369704529752173237377695073 (pp114)
Version: Msieve-1.39
Total time: 164.24 hours.
Scaled time: 284.96 units (timescale=1.735).
Factorization parameters were as follows:
n: 57510927076144467448815274902231423970554405337014032666206579250057510927076144467448815274902231423970554405337014032666206579250057510927076144467448815274902231423970554405337
m: 1000000000000000000000000000000000000
deg: 5
c5: 250
c0: -61
skew: 0.75
type: snfs
lss: 1
rlim: 7700000
alim: 7700000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7700000/7700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3850000, 6650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1525062 x 1525310
Total sieving time: 164.24 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,7700000,7700000,28,28,53,53,2.5,2.5,100000
total time: 164.24 hours.
 --------- CPU info (if available) ----------

Mar 30, 2009 (4th)

By Erik Branger / GGNFS, Msieve / Mar 30, 2009

(17·10¹¹²-11)/3 = 5(6)₁₁₁3_<113> = 5827 · 252383 · C104

C104 = P44 · P60

P44 = 81164110798176097423933218771319343515292509_<44>

P60 = 474742940179331324463463707253091559418247960492922361378927_<60>

Number: 56663_112
N=38532088597367134617100718665769640550757338534360199985556223923342460549288844372419388022112993557843
  ( 104 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=81164110798176097423933218771319343515292509
 r2=474742940179331324463463707253091559418247960492922361378927
Version: 
Total time: 1.43 hours.
Scaled time: 1.51 units (timescale=1.058).
Factorization parameters were as follows:
n: 38532088597367134617100718665769640550757338534360199985556223923342460549288844372419388022112993557843
m: 20000000000000000000000
deg: 5
c5: 425
c0: -88
skew: 0.73
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [280000, 530001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 64327 x 64554
Total sieving time: 1.43 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,114,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000
total time: 1.43 hours.
 --------- CPU info (if available) ----------

(17·10¹¹⁶-11)/3 = 5(6)₁₁₅3_<117> = 61 · 83 · 2147371619171101_<16> · C98

C98 = P43 · P56

P43 = 4828924233309463931619182770068478624306471_<43>

P56 = 10793496102454005499202825484190161769189847553433786531_<56>

Number: 56663_116
N=52120974891271395662797528266595552975220418579988058726081993476367737739647564816301019335942101
  ( 98 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=4828924233309463931619182770068478624306471
 r2=10793496102454005499202825484190161769189847553433786531
Version: 
Total time: 1.35 hours.
Scaled time: 1.40 units (timescale=1.036).
Factorization parameters were as follows:
n: 52120974891271395662797528266595552975220418579988058726081993476367737739647564816301019335942101
m: 100000000000000000000000
deg: 5
c5: 170
c0: -11
skew: 0.58
type: snfs
lss: 1
rlim: 630000
alim: 630000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 630000/630000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [315000, 515001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 66128 x 66354
Total sieving time: 1.35 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,630000,630000,25,25,45,45,2.2,2.2,50000
total time: 1.35 hours.
 --------- CPU info (if available) ----------

(17·10¹²⁵-11)/3 = 5(6)₁₂₄3_<126> = C126

C126 = P59 · P67

P59 = 71785287581807633716076980461443991324728287066807910129827_<59>

P67 = 7893910935731566057306717859770778813519376767106692139028677261869_<67>

Number: 56663_125
N=566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
  ( 126 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=71785287581807633716076980461443991324728287066807910129827
 r2=7893910935731566057306717859770778813519376767106692139028677261869
Version: 
Total time: 1.96 hours.
Scaled time: 2.03 units (timescale=1.034).
Factorization parameters were as follows:
n: 566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
m: 10000000000000000000000000
deg: 5
c5: 17
c0: -11
skew: 0.92
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 695001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 118757 x 119002
Total sieving time: 1.96 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------

(17·10¹²⁴-11)/3 = 5(6)₁₂₃3_<125> = 19 · 26981 · 248309 · 310614151 · C106

C106 = P39 · P67

P39 = 804449340177554271459153452597709920213_<39>

P67 = 1781573013452190413442256085833160667959483917129251044909137802551_<67>

Number: 56663_124
N=1433185235149751598102742298752877358386848046087618306723849826450082955179103739767073691849380357863363
  ( 106 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=804449340177554271459153452597709920213
 r2=1781573013452190413442256085833160667959483917129251044909137802551
Version: 
Total time: 2.02 hours.
Scaled time: 2.14 units (timescale=1.058).
Factorization parameters were as follows:
n: 1433185235149751598102742298752877358386848046087618306723849826450082955179103739767073691849380357863363
m: 10000000000000000000000000
deg: 5
c5: 17
c0: -110
skew: 1.45
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 695001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 109917 x 110165
Total sieving time: 2.02 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 2.02 hours.
 --------- CPU info (if available) ----------

(17·10¹²⁷+7)/3 = 5(6)₁₂₆9_<128> = 227 · 6569 · C122

C122 = P44 · P79

P44 = 25921348302963192499630665485734572989144837_<44>

P79 = 1466037096889321752043564176958402615677429746334965177187281480617951278229099_<79>

Number: 56669_127
N=38001658213533105815170217251009223449526756408700233754905846420992652491153996354970359824289273987261397088491779011863
  ( 122 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=25921348302963192499630665485734572989144837
 r2=1466037096889321752043564176958402615677429746334965177187281480617951278229099
Version: 
Total time: 2.72 hours.
Scaled time: 1.08 units (timescale=0.397).
Factorization parameters were as follows:
n: 38001658213533105815170217251009223449526756408700233754905846420992652491153996354970359824289273987261397088491779011863
m: 20000000000000000000000000
deg: 5
c5: 425
c0: 56
skew: 0.67
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 139261 x 139499
Total sieving time: 2.72 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 2.72 hours.
 --------- CPU info (if available) ----------

(17·10¹⁴²+7)/3 = 5(6)₁₄₁9_<143> = 208001 · 8641465134611_<13> · 27133063997213638003_<20> · C106

C106 = P42 · P64

P42 = 227233283820335395527908096833051840478717_<42>

P64 = 5113333015204387993644768090944545112606409701910513354681529129_<64>

Number: 56669_142
N=1161919452311830061295286320108968874314420959924846927818658944252231072336726982590444060540124940047493
  ( 106 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=227233283820335395527908096833051840478717
 r2=5113333015204387993644768090944545112606409701910513354681529129
Version: 
Total time: 9.28 hours.
Scaled time: 3.70 units (timescale=0.398).
Factorization parameters were as follows:
n: 1161919452311830061295286320108968874314420959924846927818658944252231072336726982590444060540124940047493
m: 20000000000000000000000000000
deg: 5
c5: 425
c0: 56
skew: 0.67
type: snfs
lss: 1
rlim: 1770000
alim: 1770000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1770000/1770000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [885000, 1985001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 270587 x 270828
Total sieving time: 9.28 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1770000,1770000,26,26,49,49,2.3,2.3,100000
total time: 9.28 hours.
 --------- CPU info (if available) ----------

Mar 30, 2009 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Mar 30, 2009

(17·10¹³⁸-11)/3 = 5(6)₁₃₇3_<139> = 169006200297797685527_<21> · 2300927100902701975264719427_<28> · C92

C92 = P35 · P57

P35 = 31468010786775134148962698036356169_<35>

P57 = 463076646059587584495461971854363692884207025602098484963_<57>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 14572100893306753029562782655749178686780912853468794144718369748167302877578129447958786747 (92 digits)
Using B1=1734000, B2=2140281790, polynomial Dickson(6), sigma=3753322
Step 1 took 10719ms
Step 2 took 5000ms
********** Factor found in step 2: 31468010786775134148962698036356169
Found probable prime factor of 35 digits: 31468010786775134148962698036356169
Probable prime cofactor 463076646059587584495461971854363692884207025602098484963 has 57 digits

(10²⁰⁷+17)/9 = (1)₂₀₆3_<207> = 1607 · C203

C203 = P54 · P67 · P83

P54 = 115951269499650019696884731749121224100590303382217461_<54>

P67 = 8291114615663811786913421243762707131703902669337013526581555333831_<67>

P83 = 71920580989461300167938721656900149535458931816276322011236571042026371770244374549_<83>

Number: n
N=69141948420106478600566963977044873124524649104611767959621102122657816497268893037405794095277604922906727511581276360367835165594966466155016248357878725022471133236534605545184263292539583765470510959
  ( 203 digits)
SNFS difficulty: 207 digits.
Divisors found:

Mon Mar 30 09:50:31 2009  prp54 factor: 115951269499650019696884731749121224100590303382217461
Mon Mar 30 09:50:31 2009  prp67 factor: 8291114615663811786913421243762707131703902669337013526581555333831
Mon Mar 30 09:50:31 2009  prp83 factor: 71920580989461300167938721656900149535458931816276322011236571042026371770244374549
Mon Mar 30 09:50:31 2009  elapsed time 18:58:17 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20050930-k8
Total time: 107.71 hours.
Scaled time: 216.94 units (timescale=2.014).
Factorization parameters were as follows:
name: KA_1_206_3
n: 69141948420106478600566963977044873124524649104611767959621102122657816497268893037405794095277604922906727511581276360367835165594966466155016248357878725022471133236534605545184263292539583765470510959
deg: 5
c5: 100
c0: 17
m: 100000000000000000000000000000000000000000
skew: 0.70
type: snfs
rlim: 12000000
alim: 12000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [6000000, 31599990)
Primes: RFBsize:788060, AFBsize:787814, largePrimes:36906914 encountered
Relations: rels:32333155, finalFF:131025
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 7543613 hash collisions in 42811934 relations
Msieve: matrix is 3331182 x 3331430 (903.7 MB)

Total sieving time: 106.65 hours.
Total relation processing time: 1.06 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,207,5,0,0,0,0,0,0,0,0,12000000,12000000,29,29,58,58,2.5,2.5,100000
total time: 107.71 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368972k/3407296k available (2746k kernel code, 36964k reserved, 1423k data, 416k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830497)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Total of 4 processors activated (22643.71 BogoMIPS).

(49·10¹⁵⁸-13)/9 = 5(4)₁₅₇3_<159> = 3 · 29 · 922489 · 715570943 · C142

C142 = P46 · P97

P46 = 1933753263829273755790956506822876419039373431_<46>

P97 = 4902519898348793797289993772044717042707344704118234633885033167780703243173321590976815042695197_<97>

Number: n
N=9480263854419939406567288559368136851958668930098235963980024426324338005691026094222629647173171716995999099228114115163173665542864393110907
  ( 142 digits)
SNFS difficulty: 161 digits.
Divisors found:

Mon Mar 30 12:48:36 2009  prp46 factor: 1933753263829273755790956506822876419039373431
Mon Mar 30 12:48:36 2009  prp97 factor: 4902519898348793797289993772044717042707344704118234633885033167780703243173321590976815042695197
Mon Mar 30 12:48:36 2009  elapsed time 01:32:15 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 28.69 hours.
Scaled time: 76.31 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_4_157_3
n: 9480263854419939406567288559368136851958668930098235963980024426324338005691026094222629647173171716995999099228114115163173665542864393110907
skew: 1.92
deg: 5
c5: 49
c0: -1300
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2250000, 4049990)
Primes: RFBsize:315948, AFBsize:315681, largePrimes:15059121 encountered
Relations: rels:14210576, finalFF:560178
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1302492 hash collisions in 15864309 relations
Msieve: matrix is 683824 x 684072 (181.8 MB)

Total sieving time: 28.34 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000
total time: 28.69 hours.
 --------- CPU info (if available) ----------

(49·10¹⁵⁸+23)/9 = 5(4)₁₅₇7_<159> = 2039647062871998809149_<22> · C138

C138 = P40 · P42 · P56

P40 = 7561107105557510584961327966551236839939_<40>

P42 = 487659925013640987505028384915301079926139_<42>

P56 = 72392919040279406746095501779506808157490294988149843643_<56>

Number: n
N=266930712844907468956210745438042353032837564638417938008625283292057659396759594420765443389292001623725450501654132366788120505688933003
  ( 138 digits)
SNFS difficulty: 161 digits.
Divisors found:

Mon Mar 30 12:55:35 2009  prp40 factor: 7561107105557510584961327966551236839939
Mon Mar 30 12:55:35 2009  prp42 factor: 487659925013640987505028384915301079926139
Mon Mar 30 12:55:35 2009  prp56 factor: 72392919040279406746095501779506808157490294988149843643
Mon Mar 30 12:55:35 2009  elapsed time 01:38:38 (Msieve 1.39 - dependency 5)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 28.25 hours.
Scaled time: 75.15 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_4_157_7
n: 266930712844907468956210745438042353032837564638417938008625283292057659396759594420765443389292001623725450501654132366788120505688933003
skew: 2.16
deg: 5
c5: 49
c0: 2300
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2250000, 10000000
)
Primes: RFBsize:315948, AFBsize:316501, largePrimes:15420747 encountered
Relations: rels:14977241, finalFF:765435
Max relations in full relation-set: 28
Initial matrix: 632513 x 765435 with sparse part having weight 77547461.
Pruned matrix : 547396 x 550622 with weight 58136808.

Msieve: found 1271426 hash collisions in 15912073 relations
Msieve: matrix is 656971 x 657219 (174.5 MB)

Total sieving time: 27.27 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 0.56 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000
total time: 28.25 hours.
 --------- CPU info (if available) ----------

(17·10¹³⁰-11)/3 = 5(6)₁₂₉3_<131> = 821 · 957659 · 10929609074387850346393_<23> · C100

C100 = P39 · P62

P39 = 275500419214459207522978242754423626131_<39>

P62 = 23935732489875274791493269824915507905526696732420120893398499_<62>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 6594304335165789684057187749729952168894186892873528185290466032084721385086046044161848915572577369 (100 digits)
Using B1=1960000, B2=2853920170, polynomial Dickson(6), sigma=2249210397
Step 1 took 13500ms
Step 2 took 6625ms
********** Factor found in step 2: 275500419214459207522978242754423626131
Found probable prime factor of 39 digits: 275500419214459207522978242754423626131
Probable prime cofactor 23935732489875274791493269824915507905526696732420120893398499 has 62 digits

(49·10¹⁴⁸+23)/9 = 5(4)₁₄₇7_<149> = 3 · 461 · 683 · 1273580364222764178583_<22> · C122

C122 = P59 · P63

P59 = 50942162569083495932825063490147390786014622365694977329219_<59>

P63 = 888396736999855975410516186125965281921713380681765300530218399_<63>

Number: n
N=45256851002089977943223127636832110629196301893626535842317331291752486970739396762669811086799587838896573702539794100381
  ( 122 digits)
SNFS difficulty: 151 digits.
Divisors found:

Mon Mar 30 15:05:52 2009  prp59 factor: 50942162569083495932825063490147390786014622365694977329219
Mon Mar 30 15:05:52 2009  prp63 factor: 888396736999855975410516186125965281921713380681765300530218399
Mon Mar 30 15:05:52 2009  elapsed time 00:31:22 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 12.12 hours.
Scaled time: 32.24 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_4_147_7
n: 45256851002089977943223127636832110629196301893626535842317331291752486970739396762669811086799587838896573702539794100381
skew: 2.16
deg: 5
c5: 49
c0: 2300
m: 1000000000000000000000000000000
type: snfs
rlim: 2400000
alim: 2400000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [1200000, 1956533)
Primes: RFBsize:176302, AFBsize:176533, largePrimes:13701058 encountered
Relations: rels:12036131, finalFF:290665
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 887013 hash collisions in 12698429 relations
Msieve: matrix is 431379 x 431627 (115.5 MB)

Total sieving time: 11.77 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,29,29,58,58,2.4,2.4,100000
total time: 12.12 hours.
 --------- CPU info (if available) ----------

Mar 30, 2009 (2nd)

By Jo Yeong Uk / GMP-ECM / Mar 30, 2009

(16·10¹⁹⁷+17)/3 = 5(3)₁₉₆9_<198> = C198

C198 = P34 · P164

P34 = 8330730914910739494869962789866397_<34>

P164 = 64019992817046568864072386610912369178865900873939871107157058564192119869482424687933582394044661175526797445218338045141217468977459877568210571489380832289734487_<164>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 533333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339 (198 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4195428485
Step 1 took 21881ms
Step 2 took 8593ms
********** Factor found in step 2: 8330730914910739494869962789866397
Found probable prime factor of 34 digits: 8330730914910739494869962789866397
Probable prime cofactor 64019992817046568864072386610912369178865900873939871107157058564192119869482424687933582394044661175526797445218338045141217468977459877568210571489380832289734487 has 164 digits

Mar 30, 2009

By Serge Batalov / GMP-ECM 6.2.2 / Mar 30, 2009

(17·10¹⁵²+7)/3 = 5(6)₁₅₁9_<153> = 239 · 13513006159_<11> · 34315669240219_<14> · 17652303027868178773_<20> · C108

C108 = P29 · P80

P29 = 21420174711076672817390171047_<29>

P80 = 13522622829796860710833630636754411679637874455069340439451980743975628136252621_<80>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=588125940
Step 1 took 6860ms
Step 2 took 5964ms
********** Factor found in step 2: 21420174711076672817390171047
Found probable prime factor of 29 digits: 21420174711076672817390171047
Probable prime cofactor  has 80 digits

(17·10¹⁷²-11)/3 = 5(6)₁₇₁3_<173> = 4955881256811199723_<19> · 11290582017638819227_<20> · C136

C136 = P32 · C104

P32 = 11112034900286103762642201273601_<32>

C104 = [91137444731686262774627615616319827328697194596617503688409426242033418216434046022033424397591326427503_<104>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3570570968
Step 1 took 9005ms
Step 2 took 7596ms
********** Factor found in step 2: 11112034900286103762642201273601
Found probable prime factor of 32 digits: 11112034900286103762642201273601
Composite cofactor  has 104 digits

(17·10²⁰⁰+7)/3 = 5(6)₁₉₉9_<201> = 139 · 1319 · 4091 · 5953 · 4583407129440823_<16> · 1454913548016373279_<19> · C155

C155 = P32 · C124

P32 = 16235484672840827305747235427721_<32>

C124 = [1172227287557431664659229679610875208906271615395435937554333020682862854689618819963973299985339269262349249624933994874019_<124>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1267963406
Step 1 took 10029ms
Step 2 took 8524ms
********** Factor found in step 2: 16235484672840827305747235427721
Found probable prime factor of 32 digits: 16235484672840827305747235427721
Composite cofactor has 124 digits

(17·10¹⁹⁹+7)/3 = 5(6)₁₉₈9_<200> = 853 · 49108949 · 4690843055178469916009_<22> · C168

C168 = P33 · C136

P33 = 139439575860152525764642907000219_<33>

C136 = [2068145264829021522693134837565772375255413534314070907056190048608030188897413343095857160841289014207680735432647902934113992020248887_<136>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1353002088
Step 1 took 9940ms
Step 2 took 8913ms
********** Factor found in step 2: 139439575860152525764642907000219
Found probable prime factor of 33 digits: 139439575860152525764642907000219
Composite cofactor  has 136 digits

(17·10¹⁷³+7)/3 = 5(6)₁₇₂9_<174> = 239 · 3719 · C168

C168 = P28 · P140

P28 = 7509372153663948212960430553_<28>

P140 = 84898488730764227478927360584223002525621599992773503802613527890415688576632781607023486143938568208272345414025486917663448442946997504653_<140>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1914745003
Step 1 took 9889ms
Step 2 took 8913ms
********** Factor found in step 2: 7509372153663948212960430553
Found probable prime factor of 28 digits: 7509372153663948212960430553
Probable prime cofactor  has 140 digits

(17·10¹⁹⁴+7)/3 = 5(6)₁₉₃9_<195> = 239 · 2460564151_<10> · C183

C183 = P36 · C148

P36 = 159720630294001366032944725330382413_<36>

C148 = [6033010178949490073361316871767491374941752999300200709376915162995870293743735197054524436589368399019120045621934770911807822296559368927412793417_<148>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3496528567
Step 1 took 11805ms
Step 2 took 9992ms
********** Factor found in step 2: 159720630294001366032944725330382413
Found probable prime factor of 36 digits: 159720630294001366032944725330382413
Composite cofactor  has 148 digits

(17·10¹⁴⁰-11)/3 = 5(6)₁₃₉3_<141> = 23 · C140

C140 = P40 · C101

P40 = 1988582244189483800485209843958743589043_<40>

C101 = [12389571128581728818477254444904148656371225081269043431614820414039285832831268485708657579962622667_<101>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1248108625
Step 1 took 9168ms
Step 2 took 7753ms
********** Factor found in step 2: 1988582244189483800485209843958743589043
Found probable prime factor of 40 digits: 1988582244189483800485209843958743589043
Composite cofactor  has 101 digits

Mar 29, 2009 (6th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Mar 29, 2009

(49·10¹⁵⁵+23)/9 = 5(4)₁₅₄7_<156> = 17 · 106319 · 42741631 · C142

C142 = P36 · P46 · P61

P36 = 409065749093004214423575760361672489_<36>

P46 = 6534980153883198524785693798616329050629060233_<46>

P61 = 2636363466388369334313208869093679303721597028944419656356687_<61>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 7047623182591198721228603674492812887560618947204801559116644732177071109244426383906311382987479237879253592111943827457642510612559750138719 (142 digits)
Using B1=1354000, B2=1426564240, polynomial Dickson(6), sigma=3350466869
Step 1 took 18766ms
Step 2 took 6552ms
********** Factor found in step 2: 409065749093004214423575760361672489
Found probable prime factor of 36 digits: 409065749093004214423575760361672489
Composite cofactor 17228582931270708514083747678543048612110301217622656613888747449097910949597250515490753732934867455328071 has 107 digits

Number: n
N=17228582931270708514083747678543048612110301217622656613888747449097910949597250515490753732934867455328071
  ( 107 digits)
Divisors found:

Sun Mar 29 21:30:54 2009  prp46 factor: 6534980153883198524785693798616329050629060233
Sun Mar 29 21:30:54 2009  prp61 factor: 2636363466388369334313208869093679303721597028944419656356687
Sun Mar 29 21:30:54 2009  elapsed time 00:26:54 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 7.17 hours.
Scaled time: 17.91 units (timescale=2.498).
Factorization parameters were as follows:
name: KA_5_4_154_7
n: 17228582931270708514083747678543048612110301217622656613888747449097910949597250515490753732934867455328071
skew: 18099.40
# norm 8.35e+14
c5: 23100
c4: 3113741728
c3: -31044755523147
c2: -1261698035532545324
c1: 7240654224891409569948
c0: -7973236351116161462387888
# alpha -6.39
Y1: 226421965439
Y0: -236873416973092157223
# Murphy_E 1.53e-09
# M 12147195532541688516625504347878815099683545814935576793611958648061402688146723638257757268267574761915608
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2099990)
Primes: RFBsize:183072, AFBsize:183296, largePrimes:14448958 encountered
Relations: rels:12209996, finalFF:372024
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 863448 hash collisions in 13117547 relations
Msieve: matrix is 384782 x 385030 (105.4 MB)

Total sieving time: 6.79 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000
total time: 7.17 hours.
 --------- CPU info (if available) ----------

Mar 29, 2009 (5th)

By Sinkiti Sibata / Msieve / Mar 29, 2009

(13·10¹⁶⁷-31)/9 = 1(4)₁₆₆1_<168> = 3² · 11² · 17 · 173 · 1459 · 452853659 · 155695384417_<12> · C138

C138 = P67 · P71

P67 = 5417590935726697778181429215751858994416076969577660845369964579189_<67>

P71 = 80925020418520285456515411888513924913719814105591957988967280127650553_<71>

Number: 14441_167
N=438418657092873437140255716613415047002897640850210659821001335171971975493968967373742325714372536553148432048435029807813404043888141517
  ( 138 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=5417590935726697778181429215751858994416076969577660845369964579189
 r2=80925020418520285456515411888513924913719814105591957988967280127650553
Version: 
Total time: 40.05 hours.
Scaled time: 133.72 units (timescale=3.339).
Factorization parameters were as follows:
name: 14441_167
n: 438418657092873437140255716613415047002897640850210659821001335171971975493968967373742325714372536553148432048435029807813404043888141517
m: 2000000000000000000000000000000000
deg: 5
c5: 325
c0: -248
skew: 0.95
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2300000, 4400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 842418 x 842665
Total sieving time: 40.05 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000
total time: 40.05 hours.
 --------- CPU info (if available) ----------

(49·10¹⁷²-13)/9 = 5(4)₁₇₁3_<173> = C173

C173 = P50 · P123

P50 = 90457133252859086370797452249079159362984754582263_<50>

P123 = 601881161679680073414733529094278946019249854432828112732618999568591744333440032921249761043945003829360819175126160932861_<123>

Number: 54443_172
N=54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
  ( 173 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=90457133252859086370797452249079159362984754582263
 r2=601881161679680073414733529094278946019249854432828112732618999568591744333440032921249761043945003829360819175126160932861
Version: 
Total time: 134.18 hours.
Scaled time: 342.69 units (timescale=2.554).
Factorization parameters were as follows:
name: 54443_172
n: 54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
m: 20000000000000000000000000000000000
deg: 5
c5: 1225
c0: -104
skew: 0.61
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2500000, 8700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1086216 x 1086464
Total sieving time: 134.18 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 134.18 hours.
 --------- CPU info (if available) ----------

Mar 29, 2009 (4th)

By Jo Yeong Uk / GMP-ECM / Mar 29, 2009

(46·10¹⁷⁸+71)/9 = 5(1)₁₇₇9_<179> = C179

C179 = P30 · P150

P30 = 301987358663348695516213202159_<30>

P150 = 169249174327489206034164467968894139877111470560964098347821869949162177687945915103723675787020585299769888419146145185091773482803832289761745201441_<150>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 51111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119 (179 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2958435836
Step 1 took 6314ms
Step 2 took 3302ms
********** Factor found in step 2: 301987358663348695516213202159
Found probable prime factor of 30 digits: 301987358663348695516213202159
Probable prime cofactor 169249174327489206034164467968894139877111470560964098347821869949162177687945915103723675787020585299769888419146145185091773482803832289761745201441 has 150 digits

Mar 29, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Mar 29, 2009

(49·10¹⁶⁷+23)/9 = 5(4)₁₆₆7_<168> = 10559587231972013_<17> · C152

C152 = P69 · P83

P69 = 767767536287199542101945167997849215441525824338148173132657698090917_<69>

P83 = 67154772717526357740761695015258839151705607000361615191854608560565425792519343007_<83>

Number: 54447_167
N=51559254399262055672112903247669280513372718601182176087537408205257236885136324117744525371190925777657136066754141731545354083503744691559498994167419
  ( 152 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=767767536287199542101945167997849215441525824338148173132657698090917 (pp69)
 r2=67154772717526357740761695015258839151705607000361615191854608560565425792519343007 (pp83)
Version: Msieve-1.39
Total time: 76.49 hours.
Scaled time: 196.65 units (timescale=2.571).
Factorization parameters were as follows:
n: 51559254399262055672112903247669280513372718601182176087537408205257236885136324117744525371190925777657136066754141731545354083503744691559498994167419
m: 2000000000000000000000000000000000
deg: 5
c5: 1225
c0: 184
skew: 0.68
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 5750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 936316 x 936564
Total sieving time: 76.49 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000
total time: 76.49 hours.
 --------- CPU info (if available) ----------

Mar 29, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Mar 29, 2009

(49·10¹⁴⁶+23)/9 = 5(4)₁₄₅7_<147> = 367937719 · 4152854718155167_<16> · C123

C123 = P41 · P82

P41 = 42507220291575390569061312126266571436511_<41>

P82 = 8382427676288048262413847664914236679385164784376828071942780399395127187230556249_<82>

Number: 54447_146
N=356313699814174474491639870463144151088608729515701630864241104069885188680083539616515109540850294506582375609049517807239
  ( 123 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=42507220291575390569061312126266571436511
 r2=8382427676288048262413847664914236679385164784376828071942780399395127187230556249
Version: 
Total time: 18.38 hours.
Scaled time: 14.08 units (timescale=0.766).
Factorization parameters were as follows:
n: 356313699814174474491639870463144151088608729515701630864241104069885188680083539616515109540850294506582375609049517807239
m: 200000000000000000000000000000
deg: 5
c5: 245
c0: 368
skew: 1.08
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 373502 x 373745
Total sieving time: 18.38 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 18.38 hours.
 --------- CPU info (if available) ----------

Mar 29, 2009

Factorizations of 566...663 and Factorizations of 566...669 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 28, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Mar 28, 2009

(49·10¹⁵⁶+23)/9 = 5(4)₁₅₅7_<157> = 17707721075698273_<17> · 2033817327775288969990595237689_<31> · C111

C111 = P51 · P60

P51 = 454500693687026425426203190166113666052452088501549_<51>

P60 = 332616971158229236983081432079825089338499648979568233502899_<60>

Number: n
N=151174644123492849592600496381704676212629009609146369177302522320081362468179705521001158149486074548257490551
  ( 111 digits)
Divisors found:

Sat Mar 28 03:43:11 2009  prp51 factor: 454500693687026425426203190166113666052452088501549
Sat Mar 28 03:43:11 2009  prp60 factor: 332616971158229236983081432079825089338499648979568233502899
Sat Mar 28 03:43:11 2009  elapsed time 00:58:49 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 17.89 hours.
Scaled time: 32.72 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_5_4_155_7
n: 151174644123492849592600496381704676212629009609146369177302522320081362468179705521001158149486074548257490551
skew: 19769.16
# norm 3.26e+14
c5: 22800
c4: -583278862
c3: -30993018703825
c2: 215141010662061476
c1: 6053494876806255768132
c0: 15710288339883256330285332
# alpha -4.64
Y1: 611596749247
Y0: -1459855103768153476979
# Murphy_E 9.39e-10
# M 86602127258112390202379596066607795227983754583130173412703693163778176060001927693573246820648690457463833676
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1600000, 10000000
)
Primes: RFBsize:230209, AFBsize:229831, largePrimes:15089378 encountered
Relations: rels:13636040, finalFF:864157
Max relations in full relation-set: 28
Initial matrix: 460118 x 864157 with sparse part having weight 109034210.
Pruned matrix : 275917 x 278281 with weight 43207207.

Msieve: found 1625564 hash collisions in 15085140 relations
Msieve: matrix is 367792 x 368040 (99.3 MB)

Total sieving time: 17.53 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000
total time: 17.89 hours.
 --------- CPU info (if available) ----------

(49·10¹⁵⁸-31)/9 = 5(4)₁₅₇1_<159> = 23 · 2422087 · 99603367 · C143

C143 = P42 · P102

P42 = 338983214914643563511308571161310372441779_<42>

P102 = 289456816972690351532668866002715672964035429516916062876460836624896725733021164280118302721885812837_<102>

Number: n
N=98121002396362140147876046516105890668748182387245599073687682895032770426853914253252119806488821693256356417565016168442322595430837873317023
  ( 143 digits)
SNFS difficulty: 161 digits.
Divisors found:

Sat Mar 28 03:48:39 2009  prp42 factor: 338983214914643563511308571161310372441779
Sat Mar 28 03:48:39 2009  prp102 factor: 289456816972690351532668866002715672964035429516916062876460836624896725733021164280118302721885812837
Sat Mar 28 03:48:39 2009  elapsed time 01:18:48 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 30.21 hours.
Scaled time: 59.06 units (timescale=1.955).
Factorization parameters were as follows:
name: KA_5_4_157_1
n: 98121002396362140147876046516105890668748182387245599073687682895032770426853914253252119806488821693256356417565016168442322595430837873317023
skew: 2.29
deg: 5
c5: 49
c0: -3100
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 10000000
)
Primes: RFBsize:315948, AFBsize:316122, largePrimes:15660913 encountered
Relations: rels:15286806, finalFF:766542
Max relations in full relation-set: 28
Initial matrix: 632134 x 766542 with sparse part having weight 79728896.
Pruned matrix : 555964 x 559188 with weight 59562732.

Msieve: found 1378570 hash collisions in 16322804 relations
Msieve: matrix is 666431 x 666679 (176.6 MB)

Total sieving time: 29.43 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 0.30 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000
total time: 30.21 hours.
 --------- CPU info (if available) ----------

(47·10¹⁶¹-11)/9 = 5(2)₁₆₀1_<162> = 7² · 17 · 89 · 36112890957281_<14> · C144

C144 = P58 · P86

P58 = 5659520845447040182541664681416062365985670446984129683683_<58>

P86 = 34465010887937013645516458746347821551770956037600985349479839853501589174635796347271_<86>

Number: n
N=195055447558838732532493662392781748112699080604895365658760154519007772407120895016155495442547256068767076944538986843466920758834616050279093
  ( 144 digits)
SNFS difficulty: 162 digits.
Divisors found:

Sat Mar 28 04:25:58 2009  prp58 factor: 5659520845447040182541664681416062365985670446984129683683
Sat Mar 28 04:25:58 2009  prp86 factor: 34465010887937013645516458746347821551770956037600985349479839853501589174635796347271
Sat Mar 28 04:25:58 2009  elapsed time 01:22:01 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 30.24 hours.
Scaled time: 80.45 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_2_160_1
n: 195055447558838732532493662392781748112699080604895365658760154519007772407120895016155495442547256068767076944538986843466920758834616050279093
skew: 0.47
deg: 5
c5: 470
c0: -11
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 4250261)
Primes: RFBsize:315948, AFBsize:315892, largePrimes:15787994 encountered
Relations: rels:15298505, finalFF:692461
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1375752 hash collisions in 16329518 relations
Msieve: matrix is 696166 x 696414 (184.1 MB)

Total sieving time: 29.66 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000
total time: 30.24 hours.
 --------- CPU info (if available) ----------

(46·10¹⁶⁸+71)/9 = 5(1)₁₆₇9_<169> = 13 · 131 · 269 · 811 · 359987 · C155

C155 = P38 · P54 · P65

P38 = 17471464129836365814931789218571329749_<38>

P54 = 141275887934387088918433822407219888328785550169645917_<54>

P65 = 15482581541185975084705285429391126016253950713185106907656310157_<65>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 38215603508259411274979741248363330838097261366926042069863624871097160809685140681287477149915512645041996754268125206269981445882823582837890494768348781 (155 digits)
Using B1=1902000, B2=2853920170, polynomial Dickson(6), sigma=2699684377
Step 1 took 32479ms
Step 2 took 11388ms
********** Factor found in step 2: 17471464129836365814931789218571329749
Found probable prime factor of 38 digits: 17471464129836365814931789218571329749
Composite cofactor 2187315454747599957262681204066632824538375447374393308106855746227320684871358623712175018680473014032220407420678969 has 118 digits

Number: n
N=2187315454747599957262681204066632824538375447374393308106855746227320684871358623712175018680473014032220407420678969
  ( 118 digits)
Divisors found:

Sat Mar 28 05:28:03 2009  prp54 factor: 141275887934387088918433822407219888328785550169645917
Sat Mar 28 05:28:03 2009  prp65 factor: 15482581541185975084705285429391126016253950713185106907656310157
Sat Mar 28 05:28:03 2009  elapsed time 01:18:32 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 28.53 hours.
Scaled time: 75.89 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_1_167_9
n: 2187315454747599957262681204066632824538375447374393308106855746227320684871358623712175018680473014032220407420678969
skew: 43271.35
# norm 2.74e+16
c5: 56880
c4: 18038371314
c3: -333026503155184
c2: -7470405842608349126
c1: -136619444764706775747779
c0: -3058100909330477201165739940
# alpha -6.32
Y1: 864609803699
Y0: -32884378819716757892421
# Murphy_E 3.76e-10
# M 1118767806770688025859182493513034584215833027743594558217465092282461308752967594068423351362471169988009929142135920
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 4011467)
Primes: RFBsize:315948, AFBsize:315599, largePrimes:10805214 encountered
Relations: rels:9805383, finalFF:628669
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 824513 hash collisions in 10764421 relations
Msieve: matrix is 654424 x 654672 (181.7 MB)

Total sieving time: 27.92 hours.
Total relation processing time: 0.61 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,56,56,2.4,2.4,60000
total time: 28.53 hours.
 --------- CPU info (if available) ----------

(49·10¹⁶³+23)/9 = 5(4)₁₆₂7_<164> = 3 · 19³ · 697475003 · C151

C151 = P36 · P116

P36 = 281771363630732629031583706433092583_<36>

P116 = 13463129146711053496034967138964031226984131523252406266924392904522707992604894585783077441626599518226160500296939_<116>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 3793524258405435352440492779960415544269989551997559007185731146851143361170035411115019941709401493203830929177424803532593017727945863322107578503437 (151 digits)
Using B1=320000, B2=215159500, polynomial Dickson(3), sigma=1451542920
Step 1 took 4914ms
Step 2 took 2230ms
********** Factor found in step 2: 281771363630732629031583706433092583
Found probable prime factor of 36 digits: 281771363630732629031583706433092583
Probable prime cofactor 13463129146711053496034967138964031226984131523252406266924392904522707992604894585783077441626599518226160500296939 has 116 digits

(49·10¹⁶⁹+41)/9 = 5(4)₁₆₈9_<170> = 1633987 · 222842116547_<12> · 4309002319101724709_<19> · 12626797757710355343920087032327_<32> · C103

C103 = P42 · P62

P42 = 161726317463004925294893739483643455711403_<42>

P62 = 16992491013336792208581860510277455208049350422509007698567129_<62>

Number: n
N=2748132996110164316692394787675034756341704156057136951873517972369944327740468903886111422774446271987
  ( 103 digits)
Divisors found:

Sat Mar 28 06:32:51 2009  prp42 factor: 161726317463004925294893739483643455711403
Sat Mar 28 06:32:51 2009  prp62 factor: 16992491013336792208581860510277455208049350422509007698567129
Sat Mar 28 06:32:51 2009  elapsed time 00:21:51 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 5.76 hours.
Scaled time: 15.26 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_4_168_9
n: 2748132996110164316692394787675034756341704156057136951873517972369944327740468903886111422774446271987
skew: 6018.30
# norm 9.19e+13
c5: 33540
c4: 684589501
c3: 5791283135574
c2: -28206819817534566
c1: -38476561442250937966
c0: -33218737564069799087307
# alpha -5.31
Y1: 74270204899
Y0: -38255289751789543670
# Murphy_E 2.39e-09
# M 2118835397043999855895382204736405261545507460993547449580085793519358158855105205632886183942560675358
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1751117)
Primes: RFBsize:169511, AFBsize:169243, largePrimes:13837185 encountered
Relations: rels:11629589, finalFF:365377
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 666886 hash collisions in 12075964 relations
Msieve: matrix is 347056 x 347304 (95.4 MB)

Total sieving time: 5.33 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,28,28,56,56,2.6,2.6,100000
total time: 5.76 hours.
 --------- CPU info (if available) ----------

(49·10¹⁶⁴+41)/9 = 5(4)₁₆₃9_<165> = 3² · 2999 · 14383957318464271_<17> · C145

C145 = P36 · P49 · P60

P36 = 610669137960733395685042251722807251_<36>

P49 = 7186553173058630799368238546006774398260215801703_<49>

P60 = 319543210483475316340708907207542706196386873040108707971853_<60>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 1402349324633698256140012135543458744822102593646541812746298229673535472139910433762013003100546995491089384322899717818288966583222385504693409 (145 digits)
Using B1=2770000, B2=4281513610, polynomial Dickson(6), sigma=648140982
Step 1 took 38376ms
********** Factor found in step 1: 610669137960733395685042251722807251
Found probable prime factor of 36 digits: 610669137960733395685042251722807251
Composite cofactor 2296414273229361472578839807470333744690001646782988120596944464494727792347492919926882269338661235553465659 has 109 digits

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 2296414273229361472578839807470333744690001646782988120596944464494727792347492919926882269338661235553465659 (109 digits)
Using B1=3316000, B2=5707206970, polynomial Dickson(6), sigma=27217913
Step 1 took 32510ms
Step 2 took 10920ms
********** Factor found in step 2: 7186553173058630799368238546006774398260215801703
Found probable prime factor of 49 digits: 7186553173058630799368238546006774398260215801703
Probable prime cofactor 319543210483475316340708907207542706196386873040108707971853 has 60 digits

Mar 28, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Mar 28, 2009

(49·10¹⁴⁶+41)/9 = 5(4)₁₄₅9_<147> = 3² · 401 · 37781 · 246975928358611_<15> · C125

C125 = P36 · P89

P36 = 635631229052462147884290094903460557_<36>

P89 = 25435096336658932336705167917031068008789759084152689170327716094934210451817361767116803_<89>

Number: 54449_146
N=16167341545538294700472713844287897030163776178300163755670307640173965598426295954889076267540032446185900158239333122439271
  ( 125 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=635631229052462147884290094903460557 (pp36)
 r2=25435096336658932336705167917031068008789759084152689170327716094934210451817361767116803 (pp89)
Version: Msieve-1.39
Total time: 12.37 hours.
Scaled time: 31.80 units (timescale=2.571).
Factorization parameters were as follows:
n: 16167341545538294700472713844287897030163776178300163755670307640173965598426295954889076267540032446185900158239333122439271
m: 100000000000000000000000000000
deg: 5
c5: 490
c0: 41
skew: 0.61
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 360372 x 360618
Total sieving time: 12.37 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000
total time: 12.37 hours.
 --------- CPU info (if available) ----------

(14·10¹⁸⁰+1)/3 = 4(6)₁₇₉7_<181> = 23 · 19477 · C176

C176 = P82 · P94

P82 = 1172452363816037728649885943412504699468920569755011261533521576093947543910089989_<82>

P94 = 8885086784734578588942035780312830751406596097560532726566468481627824418076932918133587209093_<94>

Number: 46667_180
N=10417341003472695033086219122815241760441338092569980348430292734723155442353783317818936196018641087629928425426348282961769102613041171563933081977776835256448892152989069977
  ( 176 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=1172452363816037728649885943412504699468920569755011261533521576093947543910089989 (pp82)
 r2=8885086784734578588942035780312830751406596097560532726566468481627824418076932918133587209093 (pp94)
Version: Msieve-1.39
Total time: 102.09 hours.
Scaled time: 177.54 units (timescale=1.739).
Factorization parameters were as follows:
n: 10417341003472695033086219122815241760441338092569980348430292734723155442353783317818936196018641087629928425426348282961769102613041171563933081977776835256448892152989069977
m: 1000000000000000000000000000000000000
deg: 5
c5: 14
c0: 1
skew: 0.59
type: snfs
lss: 1
rlim: 7300000
alim: 7300000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7300000/7300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3650000, 5350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1247235 x 1247483
Total sieving time: 102.09 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7300000,7300000,28,28,53,53,2.5,2.5,100000
total time: 102.09 hours.
 --------- CPU info (if available) ----------

Mar 28, 2009

By Erik Branger / GGNFS, Msieve / Mar 28, 2009

(49·10¹⁴³+41)/9 = 5(4)₁₄₂9_<144> = 3 · 17 · 19413661 · 14241432483999782428669_<23> · C113

C113 = P50 · P63

P50 = 48208737729702173551817182097623439690535527340379_<50>

P63 = 800933607368938839181048674491588864161303805763605741405443609_<63>

Number: 54449_143
N=38611998216553428634976880852884532742105214703709972979595744163625655295796044808871492594795432863440433187811
  ( 113 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=48208737729702173551817182097623439690535527340379
 r2=800933607368938839181048674491588864161303805763605741405443609
Version: 
Total time: 16.54 hours.
Scaled time: 12.92 units (timescale=0.781).
Factorization parameters were as follows:
n: 38611998216553428634976880852884532742105214703709972979595744163625655295796044808871492594795432863440433187811
m: 50000000000000000000000000000
deg: 5
c5: 392
c0: 1025
skew: 1.21
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [950000, 2550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 321094 x 321333
Total sieving time: 16.54 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 16.54 hours.
 --------- CPU info (if available) ----------

(49·10¹⁴⁹+41)/9 = 5(4)₁₄₈9_<150> = 3 · 23 · 5059 · 7663491709_<10> · C135

C135 = P33 · P47 · P56

P33 = 131534588641078345566638760776333_<33>

P47 = 25803421214234640523206313517076073590238151873_<47>

P56 = 59964724923190813318774664569029690764738692093753141799_<56>

Number: 54449_149
N=203522818590634280245075835535627462874181435936750438917137494088318261455309665736275011729733172064884678791543045626662602717314491
  ( 135 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=131534588641078345566638760776333
 r2=25803421214234640523206313517076073590238151873
 r3=59964724923190813318774664569029690764738692093753141799
Version: 
Total time: 21.59 hours.
Scaled time: 21.70 units (timescale=1.005).
Factorization parameters were as follows:
n: 203522818590634280245075835535627462874181435936750438917137494088318261455309665736275011729733172064884678791543045626662602717314491
m: 1000000000000000000000000000000
deg: 5
c5: 49
c0: 410
skew: 1.53
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 444856 x 445104
Total sieving time: 21.59 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 21.59 hours.
 --------- CPU info (if available) ----------

Mar 27, 2009 (7th)

By Andreas Tete / Yafu v1.08 / Mar 27, 2009

(49·10¹⁵⁸+41)/9 = 5(4)₁₅₇9_<159> = 3 · 1109 · 2017 · 103231 · 1192853 · 395872333 · 3669428891409834705930932488771_<31> · C102

C102 = P51 · P52

P51 = 145182403511774248585192727630916578243588995294079_<51>

P52 = 3124137943097999819298035626042740374316930537111941_<52>

03/26/09 16:03:31 v1.08 @ LAPPIE, 
03/26/09 16:03:31 v1.08 @ LAPPIE, ****************************
03/26/09 16:03:31 v1.08 @ LAPPIE, Starting factorization of 453569855481298226564723037610642262164563210989868695838728271565250333688282786216554526112637497339
03/26/09 16:03:31 v1.08 @ LAPPIE, ****************************
03/26/09 16:03:32 v1.08 @ LAPPIE, Rho method, input has 338 bits, 1000 max iterations per poly
03/26/09 16:03:32 v1.08 @ LAPPIE, poly x^2 + 1: 0.0780 sec
03/26/09 16:03:32 v1.08 @ LAPPIE, poly x^2 + 3: 0.1360 sec
03/26/09 16:03:32 v1.08 @ LAPPIE, poly x^2 + 2: 0.1960 sec
03/26/09 16:03:32 v1.08 @ LAPPIE, Williams P+1 method, input has 338 bits, B1 = 20000, B2 = 1000000
03/26/09 16:03:32 v1.08 @ LAPPIE, base 752376243: 0.1660 sec
03/26/09 16:03:32 v1.08 @ LAPPIE, base 352856595: 0.3250 sec
03/26/09 16:03:32 v1.08 @ LAPPIE, base 2326730079: 0.4830 sec
03/26/09 16:03:32 v1.08 @ LAPPIE, Pollard P-1 method, input has 338 bits, B1 = 100000, B2 = 5000000
03/26/09 16:03:33 v1.08 @ LAPPIE, base 2045834211: 0.4800 sec
03/26/09 16:03:33 v1.08 @ LAPPIE, 25 curves using Lenstra ECM method, input has 338 bits, B1 = 2000, B2 = 200000
03/26/09 16:03:35 v1.08 @ LAPPIE, 90 curves using Lenstra ECM method, input has 338 bits, B1 = 11000, B2 = 1100000
03/26/09 16:04:12 v1.08 @ LAPPIE, 200 curves using Lenstra ECM method, input has 338 bits, B1 = 50000, B2 = 5000000
03/26/09 16:08:48 v1.08 @ LAPPIE, 400 curves using Lenstra ECM method, input has 338 bits, B1 = 250000, B2 = 25000000
03/26/09 16:51:46 v1.08 @ LAPPIE, 1000 curves using Lenstra ECM method, input has 338 bits, B1 = 1000000, B2 = 100000000
03/26/09 23:42:56 v1.08 @ LAPPIE, starting SIQS on c102: 453569855481298226564723037610642262164563210989868695838728271565250333688282786216554526112637497339
03/26/09 23:42:56 v1.08 @ LAPPIE, random seeds: 2459799540, 1414896784
03/26/09 23:42:57 v1.08 @ LAPPIE, ==== sieve params ====
03/26/09 23:42:57 v1.08 @ LAPPIE, n = 102 digits, 342 bits
03/26/09 23:42:57 v1.08 @ LAPPIE, factor base: 121000 primes (max prime = 3375233)
03/26/09 23:42:57 v1.08 @ LAPPIE, single large prime cutoff: 506284950 (150 * pmax)
03/26/09 23:42:57 v1.08 @ LAPPIE, double large prime range from 45 to 53 bits
03/26/09 23:42:57 v1.08 @ LAPPIE, double large prime cutoff: 4654907246467955
03/26/09 23:42:57 v1.08 @ LAPPIE, using 6 large prime slices of factor base
03/26/09 23:42:57 v1.08 @ LAPPIE, buckets hold 2048 elements
03/26/09 23:42:57 v1.08 @ LAPPIE, sieve interval: 40 blocks of size 32768
03/26/09 23:42:57 v1.08 @ LAPPIE, polynomial A has ~ 13 factors
03/26/09 23:42:57 v1.08 @ LAPPIE, using multiplier of 19
03/26/09 23:42:57 v1.08 @ LAPPIE, using small prime variation correction of 21 bits
03/26/09 23:42:57 v1.08 @ LAPPIE, using x128 sieve scanning
03/26/09 23:42:57 v1.08 @ LAPPIE, trial factoring cutoff at 98 bits
03/26/09 23:42:57 v1.08 @ LAPPIE, ==== sieving started ====
03/27/09 13:27:40 v1.08 @ LAPPIE, sieve time = 14761.2410, relation time = 11943.4010, poly_time = 22714.0660
03/27/09 13:27:40 v1.08 @ LAPPIE, 121065 relations found: 27879 full + 93186 from 1844469 partial, using 2695059 polys (609 A polys)
03/27/09 13:27:40 v1.08 @ LAPPIE, trial division touched 561952386 sieve locations out of 7064935464960
03/27/09 13:27:40 v1.08 @ LAPPIE, ==== post processing stage (msieve-1.38) ====
03/27/09 13:27:47 v1.08 @ LAPPIE, begin with 1872348 relations
03/27/09 13:27:48 v1.08 @ LAPPIE, reduce to 326294 relations in 15 passes
03/27/09 13:27:51 v1.08 @ LAPPIE, failed to read relation 94436
03/27/09 13:27:51 v1.08 @ LAPPIE, failed to read relation 126269
03/27/09 13:27:54 v1.08 @ LAPPIE, failed to read relation 236788
03/27/09 13:27:56 v1.08 @ LAPPIE, failed to read relation 291206
03/27/09 13:27:57 v1.08 @ LAPPIE, recovered 326290 relations
03/27/09 13:27:57 v1.08 @ LAPPIE, recovered 307271 polynomials
03/27/09 13:27:57 v1.08 @ LAPPIE, attempting to build 121061 cycles
03/27/09 13:27:57 v1.08 @ LAPPIE, found 121061 cycles in 7 passes
03/27/09 13:27:57 v1.08 @ LAPPIE, distribution of cycle lengths:
03/27/09 13:27:57 v1.08 @ LAPPIE,    length 1 : 27879
03/27/09 13:27:57 v1.08 @ LAPPIE,    length 2 : 19652
03/27/09 13:27:57 v1.08 @ LAPPIE,    length 3 : 19792
03/27/09 13:27:57 v1.08 @ LAPPIE,    length 4 : 16536
03/27/09 13:27:57 v1.08 @ LAPPIE,    length 5 : 12912
03/27/09 13:27:57 v1.08 @ LAPPIE,    length 6 : 9112
03/27/09 13:27:57 v1.08 @ LAPPIE,    length 7 : 6125
03/27/09 13:27:57 v1.08 @ LAPPIE,    length 9+: 9053
03/27/09 13:27:57 v1.08 @ LAPPIE, largest cycle: 21 relations
03/27/09 13:27:57 v1.08 @ LAPPIE, matrix is 121000 x 121061 (36.0 MB) with weight 8959249 (74.01/col)
03/27/09 13:27:57 v1.08 @ LAPPIE, sparse part has weight 8959249 (74.01/col)
03/27/09 13:27:58 v1.08 @ LAPPIE, filtering completed in 3 passes
03/27/09 13:27:58 v1.08 @ LAPPIE, matrix is 116549 x 116613 (34.9 MB) with weight 8691415 (74.53/col)
03/27/09 13:27:58 v1.08 @ LAPPIE, sparse part has weight 8691415 (74.53/col)
03/27/09 13:27:59 v1.08 @ LAPPIE, saving the first 48 matrix rows for later
03/27/09 13:27:59 v1.08 @ LAPPIE, matrix is 116501 x 116613 (24.3 MB) with weight 7166912 (61.46/col)
03/27/09 13:27:59 v1.08 @ LAPPIE, sparse part has weight 5671030 (48.63/col)
03/27/09 13:27:59 v1.08 @ LAPPIE, matrix includes 64 packed rows
03/27/09 13:27:59 v1.08 @ LAPPIE, using block size 46645 for processor cache size 3072 kB
03/27/09 13:28:00 v1.08 @ LAPPIE, commencing Lanczos iteration
03/27/09 13:28:00 v1.08 @ LAPPIE, memory use: 21.8 MB
03/27/09 13:29:28 v1.08 @ LAPPIE, lanczos halted after 1844 iterations (dim = 116501)
03/27/09 13:29:28 v1.08 @ LAPPIE, recovered 18 nontrivial dependencies
03/27/09 13:29:29 v1.08 @ LAPPIE, prp52 = 3124137943097999819298035626042740374316930537111941
03/27/09 13:29:32 v1.08 @ LAPPIE, prp51 = 145182403511774248585192727630916578243588995294079
03/27/09 13:29:32 v1.08 @ LAPPIE, Lanczos elapsed time = 107.5710 seconds.
03/27/09 13:29:32 v1.08 @ LAPPIE, Sqrt elapsed time = 4.3410 seconds.
03/27/09 13:29:32 v1.08 @ LAPPIE, SIQS elapsed time = 49596.1740 seconds.
03/27/09 13:29:32 v1.08 @ LAPPIE, 
03/27/09 13:29:32 v1.08 @ LAPPIE, 
03/27/09 13:29:32 v1.08 @ LAPPIE, Total factoring time = 77160.9650 seconds

Mar 27, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / Mar 27, 2009

(49·10¹⁴⁵+23)/9 = 5(4)₁₄₄7_<146> = 3 · 19 · 1433 · 1637 · 13441 · 19121 · 843689909 · 12546029357_<11> · C111

C111 = P41 · P70

P41 = 28099096755963360760156147612476659621363_<41>

P70 = 5326723434107357287126667494376808424483238382966320913407508042003889_<70>

Number: n
N=149676117167240055804949774649484580128526423564024288653847340628041533707950209508991314055486019230513480707
  ( 111 digits)
Divisors found:

Fri Mar 27 20:38:02 2009  prp41 factor: 28099096755963360760156147612476659621363
Fri Mar 27 20:38:02 2009  prp70 factor: 5326723434107357287126667494376808424483238382966320913407508042003889
Fri Mar 27 20:38:02 2009  elapsed time 00:28:45 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 11.59 hours.
Scaled time: 30.31 units (timescale=2.616).
Factorization parameters were as follows:
name: KA_5_4_144_7
n: 149676117167240055804949774649484580128526423564024288653847340628041533707950209508991314055486019230513480707
skew: 54054.23
# norm 5.58e+14
c5: 4080
c4: 104162355
c3: -24151431615492
c2: -413790679185675356
c1: 24983205633200245884864
c0: 600209768239263810987355997
# alpha -5.44
Y1: 213617932927
Y0: -2055408927863635415646
# Murphy_E 1.01e-09
# M 47036110769373571685223730777806106190142807887105667390924714824160485749629030815867038979515447120817685924
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2310157)
Primes: RFBsize:230209, AFBsize:230174, largePrimes:10909616 encountered
Relations: rels:9252464, finalFF:462617
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 479607 hash collisions in 9905449 relations
Msieve: matrix is 456373 x 456621 (126.1 MB)

Total sieving time: 11.29 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000
total time: 11.59 hours.
 --------- CPU info (if available) ----------

Mar 27, 2009 (5th)

By Sinkiti Sibata / Msieve, GGNFS / Mar 27, 2009

(49·10¹³⁹+23)/9 = 5(4)₁₃₈7_<140> = 3 · 17 · 2207 · 1904082082311853_<16> · 6244544042098850789167_<22> · C98

C98 = P49 · P50

P49 = 2072759047416221070534804488754052236069702934877_<49>

P50 = 19626634850383055370477280716473069938045234782973_<50>

hu Mar 26 18:13:36 2009  Msieve v. 1.39
Thu Mar 26 18:13:36 2009  random seeds: 1860eb28 af6a59ad
Thu Mar 26 18:13:36 2009  factoring 40681284956465988403080857946319072263186432526101152628954576776813427435085598802385742247449321 (98 digits)
Thu Mar 26 18:13:37 2009  searching for 15-digit factors
Thu Mar 26 18:13:39 2009  commencing quadratic sieve (98-digit input)
Thu Mar 26 18:13:39 2009  using multiplier of 1
Thu Mar 26 18:13:39 2009  using 32kb Intel Core sieve core
Thu Mar 26 18:13:39 2009  sieve interval: 36 blocks of size 32768
Thu Mar 26 18:13:39 2009  processing polynomials in batches of 6
Thu Mar 26 18:13:39 2009  using a sieve bound of 2508151 (91735 primes)
Thu Mar 26 18:13:39 2009  using large prime bound of 376222650 (28 bits)
Thu Mar 26 18:13:39 2009  using double large prime bound of 2727726703072350 (43-52 bits)
Thu Mar 26 18:13:39 2009  using trial factoring cutoff of 52 bits
Thu Mar 26 18:13:39 2009  polynomial 'A' values have 13 factors
Fri Mar 27 02:30:51 2009  92021 relations (21823 full + 70198 combined from 1396079 partial), need 91831
Fri Mar 27 02:30:53 2009  begin with 1417902 relations
Fri Mar 27 02:30:54 2009  reduce to 243523 relations in 10 passes
Fri Mar 27 02:30:54 2009  attempting to read 243523 relations
Fri Mar 27 02:30:59 2009  recovered 243523 relations
Fri Mar 27 02:30:59 2009  recovered 232972 polynomials
Fri Mar 27 02:30:59 2009  attempting to build 92021 cycles
Fri Mar 27 02:30:59 2009  found 92021 cycles in 6 passes
Fri Mar 27 02:30:59 2009  distribution of cycle lengths:
Fri Mar 27 02:30:59 2009     length 1 : 21823
Fri Mar 27 02:30:59 2009     length 2 : 15568
Fri Mar 27 02:30:59 2009     length 3 : 15478
Fri Mar 27 02:30:59 2009     length 4 : 12640
Fri Mar 27 02:30:59 2009     length 5 : 9600
Fri Mar 27 02:30:59 2009     length 6 : 6545
Fri Mar 27 02:30:59 2009     length 7 : 4289
Fri Mar 27 02:30:59 2009     length 9+: 6078
Fri Mar 27 02:30:59 2009  largest cycle: 21 relations
Fri Mar 27 02:31:00 2009  matrix is 91735 x 92021 (24.9 MB) with weight 6171846 (67.07/col)
Fri Mar 27 02:31:00 2009  sparse part has weight 6171846 (67.07/col)
Fri Mar 27 02:31:01 2009  filtering completed in 3 passes
Fri Mar 27 02:31:01 2009  matrix is 88169 x 88233 (24.0 MB) with weight 5942491 (67.35/col)
Fri Mar 27 02:31:01 2009  sparse part has weight 5942491 (67.35/col)
Fri Mar 27 02:31:01 2009  saving the first 48 matrix rows for later
Fri Mar 27 02:31:01 2009  matrix is 88121 x 88233 (15.1 MB) with weight 4742704 (53.75/col)
Fri Mar 27 02:31:01 2009  sparse part has weight 3440666 (39.00/col)
Fri Mar 27 02:31:01 2009  matrix includes 64 packed rows
Fri Mar 27 02:31:01 2009  using block size 35293 for processor cache size 1024 kB
Fri Mar 27 02:31:02 2009  commencing Lanczos iteration
Fri Mar 27 02:31:02 2009  memory use: 14.6 MB
Fri Mar 27 02:31:57 2009  lanczos halted after 1395 iterations (dim = 88118)
Fri Mar 27 02:31:57 2009  recovered 15 nontrivial dependencies
Fri Mar 27 02:31:58 2009  prp49 factor: 2072759047416221070534804488754052236069702934877
Fri Mar 27 02:31:58 2009  prp50 factor: 19626634850383055370477280716473069938045234782973
Fri Mar 27 02:31:58 2009  elapsed time 08:18:22

(49·10¹³²+23)/9 = 5(4)₁₃₁7_<133> = 16980584111_<11> · C123

C123 = P53 · P70

P53 = 65594212145907328803824064243879179779552967931235427_<53>

P70 = 4888047585303310525809787280229165861700492433207353199793648310838651_<70>

Number: 54447_132
N=320627630289675401169387043145423187759765541815903934922327033514639056249155459010608144823931872365992041959176892088977
  ( 123 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=65594212145907328803824064243879179779552967931235427 (pp53)
 r2=4888047585303310525809787280229165861700492433207353199793648310838651 (pp70)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 8.87 hours.
Scaled time: 4.20 units (timescale=0.473).
Factorization parameters were as follows:
name: 5444_132
n: 320627630289675401169387043145423187759765541815903934922327033514639056249155459010608144823931872365992041959176892088977
m: 200000000000000000000000000
deg: 5
c5: 1225
c0: 184
skew: 0.68
type: snfs
lss: 1
rlim: 1230000
alim: 1230000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1230000/1230000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [615000, 1365001)
Primes: RFBsize:95051, AFBsize:94798, largePrimes:3188611 encountered
Relations: rels:3164491, finalFF:263511
Max relations in full relation-set: 28
Initial matrix: 189914 x 263511 with sparse part having weight 23975523.
Pruned matrix : 170528 x 171541 with weight 12559364.
Total sieving time: 8.10 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1230000,1230000,26,26,47,47,2.3,2.3,75000
total time: 8.87 hours.
 --------- CPU info (if available) ----------

(49·10¹³⁶+23)/9 = 5(4)₁₃₅7_<137> = 3 · C137

C137 = P47 · P91

P47 = 11469748045393866785079980234484149679778904849_<47>

P91 = 1582262145281932184224557733322428115520702729873734992229974599729019302327043912919001701_<91>

Number: 54447_136
N=18148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149
  ( 137 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=11469748045393866785079980234484149679778904849
 r2=1582262145281932184224557733322428115520702729873734992229974599729019302327043912919001701
Version: 
Total time: 4.53 hours.
Scaled time: 15.13 units (timescale=3.339).
Factorization parameters were as follows:
name: 54447_136
n: 18148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149
m: 2000000000000000000000000000
deg: 5
c5: 245
c0: 368
skew: 1.08
type: snfs
lss: 1
rlim: 1450000
alim: 1450000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1450000/1450000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [725000, 1550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 222076 x 222324
Total sieving time: 4.53 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000
total time: 4.53 hours.
 --------- CPU info (if available) ----------

(49·10¹⁴¹+23)/9 = 5(4)₁₄₀7_<142> = 13 · 417717737 · 237649169221_<12> · 75672693320024537909317_<23> · C98

C98 = P41 · P58

P41 = 25422400608002178538937352091939883519719_<41>

P58 = 2192982932771281359086104058811103715388491439096170268589_<58>

Fri Mar 27 04:05:55 2009  Msieve v. 1.39
Fri Mar 27 04:05:55 2009  random seeds: b36ff260 c126c954
Fri Mar 27 04:05:55 2009  factoring 55750890643423023846877628970441753098432966504896865465627005857047479051479338805773750907806491 (98 digits)
Fri Mar 27 04:05:56 2009  searching for 15-digit factors
Fri Mar 27 04:05:58 2009  commencing quadratic sieve (98-digit input)
Fri Mar 27 04:05:58 2009  using multiplier of 19
Fri Mar 27 04:05:58 2009  using 32kb Intel Core sieve core
Fri Mar 27 04:05:58 2009  sieve interval: 36 blocks of size 32768
Fri Mar 27 04:05:58 2009  processing polynomials in batches of 6
Fri Mar 27 04:05:58 2009  using a sieve bound of 2508139 (91605 primes)
Fri Mar 27 04:05:58 2009  using large prime bound of 376220850 (28 bits)
Fri Mar 27 04:05:58 2009  using double large prime bound of 2727703118350350 (43-52 bits)
Fri Mar 27 04:05:58 2009  using trial factoring cutoff of 52 bits
Fri Mar 27 04:05:58 2009  polynomial 'A' values have 13 factors
Fri Mar 27 11:32:05 2009  91986 relations (22361 full + 69625 combined from 1374307 partial), need 91701
Fri Mar 27 11:32:07 2009  begin with 1396668 relations
Fri Mar 27 11:32:09 2009  reduce to 240128 relations in 13 passes
Fri Mar 27 11:32:09 2009  attempting to read 240128 relations
Fri Mar 27 11:32:13 2009  recovered 240128 relations
Fri Mar 27 11:32:13 2009  recovered 228608 polynomials
Fri Mar 27 11:32:13 2009  attempting to build 91986 cycles
Fri Mar 27 11:32:13 2009  found 91986 cycles in 6 passes
Fri Mar 27 11:32:13 2009  distribution of cycle lengths:
Fri Mar 27 11:32:13 2009     length 1 : 22361
Fri Mar 27 11:32:13 2009     length 2 : 16061
Fri Mar 27 11:32:13 2009     length 3 : 15438
Fri Mar 27 11:32:13 2009     length 4 : 12603
Fri Mar 27 11:32:13 2009     length 5 : 9395
Fri Mar 27 11:32:13 2009     length 6 : 6325
Fri Mar 27 11:32:13 2009     length 7 : 4184
Fri Mar 27 11:32:13 2009     length 9+: 5619
Fri Mar 27 11:32:13 2009  largest cycle: 21 relations
Fri Mar 27 11:32:14 2009  matrix is 91605 x 91986 (24.2 MB) with weight 5976920 (64.98/col)
Fri Mar 27 11:32:14 2009  sparse part has weight 5976920 (64.98/col)
Fri Mar 27 11:32:15 2009  filtering completed in 3 passes
Fri Mar 27 11:32:15 2009  matrix is 87537 x 87601 (23.1 MB) with weight 5707780 (65.16/col)
Fri Mar 27 11:32:15 2009  sparse part has weight 5707780 (65.16/col)
Fri Mar 27 11:32:15 2009  saving the first 48 matrix rows for later
Fri Mar 27 11:32:16 2009  matrix is 87489 x 87601 (13.3 MB) with weight 4351256 (49.67/col)
Fri Mar 27 11:32:16 2009  sparse part has weight 2973209 (33.94/col)
Fri Mar 27 11:32:16 2009  matrix includes 64 packed rows
Fri Mar 27 11:32:16 2009  using block size 35040 for processor cache size 1024 kB
Fri Mar 27 11:32:16 2009  commencing Lanczos iteration
Fri Mar 27 11:32:16 2009  memory use: 13.6 MB
Fri Mar 27 11:33:06 2009  lanczos halted after 1385 iterations (dim = 87487)
Fri Mar 27 11:33:06 2009  recovered 17 nontrivial dependencies
Fri Mar 27 11:33:07 2009  prp41 factor: 25422400608002178538937352091939883519719
Fri Mar 27 11:33:07 2009  prp58 factor: 2192982932771281359086104058811103715388491439096170268589
Fri Mar 27 11:33:07 2009  elapsed time 07:27:12

Mar 27, 2009 (4th)

By Jo Yeong Uk / GMP-ECM / Mar 27, 2009

(49·10¹⁸⁵+23)/9 = 5(4)₁₈₄7_<186> = C186

C186 = P33 · P153

P33 = 806733444214685110818405149979937_<33>

P153 = 674875261895748026104835169072656059803931384591054243173189832904384059405927583278464754459983266422994151032177491844598621496960454629394526600967231_<153>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 544444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 (186 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1723084161
Step 1 took 6221ms
Step 2 took 3400ms
********** Factor found in step 2: 806733444214685110818405149979937
Found probable prime factor of 33 digits: 806733444214685110818405149979937
Probable prime cofactor 674875261895748026104835169072656059803931384591054243173189832904384059405927583278464754459983266422994151032177491844598621496960454629394526600967231 has 153 digits

Mar 27, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Mar 27, 2009

(49·10¹³⁷+41)/9 = 5(4)₁₃₆9_<138> = 3² · 233 · 36097 · 5517307 · 160828175857_<12> · C112

C112 = P49 · P64

P49 = 2425727394160925168973174009150207745849594329787_<49>

P64 = 3341586837971065273981699845466591967077869497074885030760101097_<64>

Number: 54449_137
N=8105778732833997840998552688220217168092181072232097955983824590327356982459028278624705999411103235686078476339
  ( 112 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=2425727394160925168973174009150207745849594329787 (pp49)
 r2=3341586837971065273981699845466591967077869497074885030760101097 (pp64)
Version: Msieve-1.39
Total time: 3.99 hours.
Scaled time: 6.93 units (timescale=1.739).
Factorization parameters were as follows:
n: 8105778732833997840998552688220217168092181072232097955983824590327356982459028278624705999411103235686078476339
m: 2000000000000000000000000000
deg: 5
c5: 1225
c0: 328
skew: 0.77
type: snfs
lss: 1
rlim: 1480000
alim: 1480000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1480000/1480000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [740000, 1490001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 226080 x 226328
Total sieving time: 3.99 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1480000,1480000,26,26,48,48,2.3,2.3,75000
total time: 3.99 hours.
 --------- CPU info (if available) ----------

(49·10¹³⁸+41)/9 = 5(4)₁₃₇9_<139> = 15595643090259138670909471_<26> · C114

C114 = P47 · P68

P47 = 18533989362828478542555461551240462977930149887_<47>

P68 = 18835683030031066796183322332961649164918753989445572020809159395137_<68>

Number: 54449_138
N=349100348920204677754729896469469518001250723946393823346871892322067135526799095817938294302315163602800668899519
  ( 114 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=18533989362828478542555461551240462977930149887 (pp47)
 r2=18835683030031066796183322332961649164918753989445572020809159395137 (pp68)
Version: Msieve-1.39
Total time: 5.77 hours.
Scaled time: 10.04 units (timescale=1.739).
Factorization parameters were as follows:
n: 349100348920204677754729896469469518001250723946393823346871892322067135526799095817938294302315163602800668899519
m: 5000000000000000000000000000
deg: 5
c5: 392
c0: 1025
skew: 1.21
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1885001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 267184 x 267432
Total sieving time: 5.77 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 5.77 hours.
 --------- CPU info (if available) ----------

(49·10¹⁶⁶+41)/9 = 5(4)₁₆₅9_<167> = 2151847 · C161

C161 = P39 · P122

P39 = 403475196715413542945185597203831441517_<39>

P122 = 62708345080053725423367577282775798846310717380281419671758144564588907556000849612451063415371641841328324130172173742451_<122>

Number: 54449_166
N=25301261866872711881673950073794486524573747317743521934619164115499124447251335454818323256460354497529073602558380983612889041109541916523082005572164026738167
  ( 161 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=403475196715413542945185597203831441517 (pp39)
 r2=62708345080053725423367577282775798846310717380281419671758144564588907556000849612451063415371641841328324130172173742451 (pp122)
Version: Msieve-1.39
Total time: 51.88 hours.
Scaled time: 90.22 units (timescale=1.739).
Factorization parameters were as follows:
n: 25301261866872711881673950073794486524573747317743521934619164115499124447251335454818323256460354497529073602558380983612889041109541916523082005572164026738167
m: 1000000000000000000000000000000000
deg: 5
c5: 490
c0: 41
skew: 0.61
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 5200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 874003 x 874251
Total sieving time: 51.88 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 51.88 hours.
 --------- CPU info (if available) ----------

(8·10¹⁷⁰-53)/9 = (8)₁₆₉3_<170> = 320125693285593749063_<21> · C150

C150 = P47 · P104

P47 = 23559899128668130997812153260935382432418417441_<47>

P104 = 11785649435366880973726668861597007737603372223460325079320068596433820581085450083045755315594565351701_<104>

Number: 88883_170
N=277668711863088229130098651489614886471886915528918772949629453601534389737903588995330059164196819694470193153548947465023028184980242144797997417141
  ( 150 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=23559899128668130997812153260935382432418417441 (pp47)
 r2=11785649435366880973726668861597007737603372223460325079320068596433820581085450083045755315594565351701 (pp104)
Version: Msieve-1.39
Total time: 49.08 hours.
Scaled time: 126.18 units (timescale=2.571).
Factorization parameters were as follows:
n: 277668711863088229130098651489614886471886915528918772949629453601534389737903588995330059164196819694470193153548947465023028184980242144797997417141
m: 10000000000000000000000000000000000
deg: 5
c5: 8
c0: -53
skew: 1.46
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 4450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 866303 x 866551
Total sieving time: 49.08 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 49.08 hours.
 --------- CPU info (if available) ----------

(49·10¹⁴⁴+23)/9 = 5(4)₁₄₃7_<145> = 4463 · 5084335385724661558411_<22> · C120

C120 = P44 · P77

P44 = 18587922413311078500682008656078799844857539_<44>

P77 = 12908079806624081195761137810924158501690725662669177809379445232500203387761_<77>

Number: 54447_144
N=239934385950355890837148625513788087364983744889451972553265266567739880538425926972922707561318526301372830222221180179
  ( 120 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=18587922413311078500682008656078799844857539 (pp44)
 r2=12908079806624081195761137810924158501690725662669177809379445232500203387761 (pp77)
Version: Msieve-1.39
Total time: 9.88 hours.
Scaled time: 25.40 units (timescale=2.571).
Factorization parameters were as follows:
n: 239934385950355890837148625513788087364983744889451972553265266567739880538425926972922707561318526301372830222221180179
m: 100000000000000000000000000000
deg: 5
c5: 49
c0: 230
skew: 1.36
type: snfs
lss: 1
rlim: 1950000
alim: 1950000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1950000/1950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [975000, 2375001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 327912 x 328160
Total sieving time: 9.88 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000
total time: 9.88 hours.
 --------- CPU info (if available) ----------

Mar 27, 2009 (2nd)

By Serge Batalov / Msieve-1.40, Msieve-1.40/1.39sqrt / Mar 27, 2009

(47·10¹⁵⁷+43)/9 = 5(2)₁₅₆7_<158> = 3² · C157

C157 = P63 · P94

P63 = 863739116053015826056476279862601665119897672463708354914661277_<63>

P94 = 6717849206966234942139994623500961571684454208649571846255616026490064023572030489723138698039_<94>

SNFS difficulty: 159 digits.
Divisors found:
 r1=863739116053015826056476279862601665119897672463708354914661277 (pp63)
 r2=6717849206966234942139994623500961571684454208649571846255616026490064023572030489723138698039 (pp94)
Version: Msieve-1.40
Total time: 12.45 hours.
Scaled time: 35.34 units (timescale=2.840).
Factorization parameters were as follows:
n: 5802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135803
m: 20000000000000000000000000000000
deg: 5
c5: 1175
c0: 344
skew: 0.78
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1600000, 3100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 600280 x 600528
Total sieving time: 12.45 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,52,52,2.4,2.4,100000
total time: 12.45 hours.

(49·10¹⁵⁶-13)/9 = 5(4)₁₅₅3_<157> = 1885805722707991669898771533_<28> · C130

C130 = P55 · P76

P55 = 2210524998163295381088357432294324394655053936779965711_<55>

P76 = 1306054171647590876958690600009006792110053639951158724187114943389454925961_<76>

SNFS difficulty: 158 digits.
Divisors found:
 r1=2210524998163295381088357432294324394655053936779965711 (pp55)
 r2=1306054171647590876958690600009006792110053639951158724187114943389454925961 (pp76)
Version: Msieve-1.40
Total time: 10.84 hours.
Scaled time: 30.78 units (timescale=2.839).
Factorization parameters were as follows:
n: 2887065395382455093675160127696693984232235070487908532313326863483666488669758862609112195172261282961921826638822593725623723271
m: 20000000000000000000000000000000
deg: 5
c5: 245
c0: -208
skew: 0.97
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1600000, 2900001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 585235 x 585482
Total sieving time: 10.84 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,52,52,2.4,2.4,100000
total time: 10.84 hours.

(49·10¹⁷⁵+23)/9 = 5(4)₁₇₄7_<176> = 3 · C176

C176 = P64 · P113

P64 = 1495137986198626713891034616766476860505226920685712498786743139_<64>

P113 = 12138109201739721837657904196381001857689869557081702922551111410234045319431624045172325499708883925960213827591_<113>

SNFS difficulty: 176 digits.
Divisors found:
 r1=1495137986198626713891034616766476860505226920685712498786743139 (pp64)
 r2=12138109201739721837657904196381001857689869557081702922551111410234045319431624045172325499708883925960213827591 (pp113)
Version: Msieve-1.40/1.39
Total time: 46.80 hours.
Scaled time: 132.91 units (timescale=2.840).
Factorization parameters were as follows:
n: 18148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149
m: 100000000000000000000000000000000000
deg: 5
c5: 49
c0: 23
skew: 0.86
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved  special-q in [3100000, 3100000)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1425483 x 1425729
Total sieving time: 38.80 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 2.10 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,55,55,2.5,2.5,100000
total time: 46.80 hours.

Mar 27, 2009

By Erik Branger / GGNFS, Msieve / Mar 27, 2009

(49·10¹³⁷+23)/9 = 5(4)₁₃₆7_<138> = 367 · 41519 · C131

C131 = P48 · P84

P48 = 111686516686440099713105228891396349952349160121_<48>

P84 = 319918883357687655326884373101551813841497448613417153161897436456980513663260915959_<84>

Number: 54447_137
N=35730625704435666231824951843684608625357002729024979696071943454432663765471114826221148640883199231555287707118132018638815271039
  ( 131 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=111686516686440099713105228891396349952349160121
 r2=319918883357687655326884373101551813841497448613417153161897436456980513663260915959
Version: 
Total time: 9.81 hours.
Scaled time: 7.65 units (timescale=0.780).
Factorization parameters were as follows:
n: 35730625704435666231824951843684608625357002729024979696071943454432663765471114826221148640883199231555287707118132018638815271039
m: 2000000000000000000000000000
deg: 5
c5: 1225
c0: 184
skew: 0.68
type: snfs
lss: 1
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [750000, 1725001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 245198 x 245446
Total sieving time: 9.81 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,48,48,2.3,2.3,75000
total time: 9.81 hours.
 --------- CPU info (if available) ----------

(49·10¹⁴⁴+41)/9 = 5(4)₁₄₃9_<145> = 179 · 94593921041_<11> · C132

C132 = P65 · P67

P65 = 34618114200346796804140356391786401986013866968419090798524170021_<65>

P67 = 9288250196524313420503337155642549167984865224535302935187999437071_<67>

Number: 54449_144
N=321541706024672260551787816221255298649921458882378056825433992581094497126329589535485981556862183103890401989612491476535494248491
  ( 132 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=34618114200346796804140356391786401986013866968419090798524170021
 r2=9288250196524313420503337155642549167984865224535302935187999437071
Version: 
Total time: 13.63 hours.
Scaled time: 13.89 units (timescale=1.019).
Factorization parameters were as follows:
n: 321541706024672260551787816221255298649921458882378056825433992581094497126329589535485981556862183103890401989612491476535494248491
m: 100000000000000000000000000000
deg: 5
c5: 49
c0: 410
skew: 1.53
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 369163 x 369411
Total sieving time: 13.63 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000
total time: 13.63 hours.
 --------- CPU info (if available) ----------

Mar 26, 2009 (7th)

By Ignacio Santos / GGNFS, Msieve / Mar 26, 2009

(49·10¹¹¹+41)/9 = 5(4)₁₁₀9_<112> = 17² · 949631 · C104

C104 = P33 · P34 · P37

P33 = 971722182165766413416910057805321_<33>

P34 = 2903609920526649428880059207607911_<34>

P37 = 7031054367157515839501298639415675681_<37>

Number: 54449_111
N=19838135141191171779982639129717270529561053960298031640271697900492627494930363552518843950035039632511
  ( 104 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=971722182165766413416910057805321 (pp33)
 r2=2903609920526649428880059207607911 (pp34)
 r3=7031054367157515839501298639415675681 (pp37)
Version: Msieve-1.39
Total time: 0.94 hours.
Scaled time: 1.12 units (timescale=1.190).
Factorization parameters were as follows:
n: 19838135141191171779982639129717270529561053960298031640271697900492627494930363552518843950035039632511
m: 10000000000000000000000
deg: 5
c5: 490
c0: 41
skew: 0.61
type: snfs
lss: 1
rlim: 530000
alim: 530000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 530000/530000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [265000, 465001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 58703 x 58941
Total sieving time: 0.94 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000
total time: 0.94 hours.
 --------- CPU info (if available) ----------

(49·10¹¹⁵+41)/9 = 5(4)₁₁₄9_<116> = 4794897909653311_<16> · C101

C101 = P32 · P35 · P35

P32 = 10186924979578406583472433052629_<32>

P35 = 16338425213924652585496712373192443_<35>

P35 = 68221443328719721898218651146386297_<35>

Number: 54449_115
N=11354661865653982362261839676089086822686511351795352067983241640600745659167261885722919030896288159
  ( 101 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=10186924979578406583472433052629 (pp32)
 r2=16338425213924652585496712373192443 (pp35)
 r3=68221443328719721898218651146386297 (pp35)
Version: Msieve-1.39
Total time: 1.04 hours.
Scaled time: 1.24 units (timescale=1.193).
Factorization parameters were as follows:
n: 11354661865653982362261839676089086822686511351795352067983241640600745659167261885722919030896288159
m: 100000000000000000000000
deg: 5
c5: 49
c0: 41
skew: 0.96
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 510001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 64279 x 64517
Total sieving time: 1.04 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 1.04 hours.
 --------- CPU info (if available) ----------

(49·10¹¹⁸+23)/9 = 5(4)₁₁₇7_<119> = 3 · 163 · 1593269 · C110

C110 = P47 · P64

P47 = 15910289293665460540700312777954637144135377863_<47>

P64 = 4392153693257523977981110166469894720194709254490343305931044509_<64>

Number: 54447_118
N=69880435881968395010117652457418567106228712803245272656360783554090757226655078402541147914901942326986304267
  ( 110 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=15910289293665460540700312777954637144135377863 (pp47)
 r2=4392153693257523977981110166469894720194709254490343305931044509 (pp64)
Version: Msieve-1.39
Total time: 1.50 hours.
Scaled time: 1.78 units (timescale=1.190).
Factorization parameters were as follows:
n: 69880435881968395010117652457418567106228712803245272656360783554090757226655078402541147914901942326986304267
m: 500000000000000000000000
deg: 5
c5: 392
c0: 575
skew: 1.08
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 665001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 80344 x 80581
Total sieving time: 1.50 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.50 hours.
 --------- CPU info (if available) ----------

(49·10¹²²+41)/9 = 5(4)₁₂₁9_<123> = 3 · 61 · 16421 · 269527 · C111

C111 = P39 · P73

P39 = 194427825632112280839477791635994595997_<39>

P73 = 3457340734650925945845897206191168163665361420064678013468291084068546497_<73>

Number: 54449_122
N=672203241507509203306318147571058464803415911356671337559948980034010718106973978089196178664520519414524572509
  ( 111 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=194427825632112280839477791635994595997 (pp39)
 r2=3457340734650925945845897206191168163665361420064678013468291084068546497 (pp73)
Version: Msieve-1.39
Total time: 1.69 hours.
Scaled time: 2.02 units (timescale=1.194).
Factorization parameters were as follows:
n: 672203241507509203306318147571058464803415911356671337559948980034010718106973978089196178664520519414524572509
m: 2000000000000000000000000
deg: 5
c5: 1225
c0: 328
skew: 0.77
type: snfs
lss: 1
rlim: 830000
alim: 830000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 830000/830000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [415000, 765001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 92849 x 93096
Total sieving time: 1.69 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,830000,830000,25,25,46,46,2.2,2.2,50000
total time: 1.69 hours.
 --------- CPU info (if available) ----------

(16·10¹⁷⁰+17)/3 = 5(3)₁₆₉9_<171> = 7⁴ · 11² · 3277640053_<10> · C156

C156 = P36 · P121

P36 = 132352806904194982440252584077327919_<36>

P121 = 4231816069054994431419448863751815900867250965737302061112758210469770212260400845121738062490712318340173811038583094537_<121>

Number: 53339_170
N=560092735041705137562298026759894588633998295834374639822117020159143485878569329742355372234945155356505826309236855960429115016162119308543393017126478503
  ( 156 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=132352806904194982440252584077327919 (pp36)
 r2=4231816069054994431419448863751815900867250965737302061112758210469770212260400845121738062490712318340173811038583094537 (pp121)
Version: Msieve-1.39
Total time: 36.83 hours.
Scaled time: 64.05 units (timescale=1.739).
Factorization parameters were as follows:
n: 560092735041705137562298026759894588633998295834374639822117020159143485878569329742355372234945155356505826309236855960429115016162119308543393017126478503
m: 10000000000000000000000000000000000
deg: 5
c5: 16
c0: 17
skew: 1.01
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 4400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 812802 x 813050
Total sieving time: 36.83 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 36.83 hours.
 --------- CPU info (if available) ----------

(49·10¹²⁹+41)/9 = 5(4)₁₂₈9_<130> = 103 · C128

C128 = P34 · P38 · P57

P34 = 1933030102714732371359649944976571_<34>

P38 = 67460989330069140041565000686446989847_<38>

P57 = 405345188912107832212622449426391920980159997852887421459_<57>

Number: 54449_129
N=52858683926645091693635382955771305285868392664509169363538295577130528586839266450916936353829557713052858683926645091693635383
  ( 128 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1933030102714732371359649944976571 (pp34)
 r2=67460989330069140041565000686446989847 (pp38)
 r3=405345188912107832212622449426391920980159997852887421459 (pp57)
Version: Msieve-1.39
Total time: 2.74 hours.
Scaled time: 4.75 units (timescale=1.735).
Factorization parameters were as follows:
n: 52858683926645091693635382955771305285868392664509169363538295577130528586839266450916936353829557713052858683926645091693635383
m: 100000000000000000000000000
deg: 5
c5: 49
c0: 410
skew: 1.53
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 168168 x 168416
Total sieving time: 2.74 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.74 hours.
 --------- CPU info (if available) ----------

(49·10¹²⁴+41)/9 = 5(4)₁₂₃9_<125> = 116538371 · 204661783981_<12> · C106

C106 = P41 · P65

P41 = 37428052363683529029244596049442228725609_<41>

P65 = 60988877974397866287182423059627153170887298299087679623642765311_<65>

Number: 54449_124
N=2282694918428068381348693425024345271947221342778726134596358771658935004775994118288821273088756202549399
  ( 106 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=37428052363683529029244596049442228725609 (pp41)
 r2=60988877974397866287182423059627153170887298299087679623642765311 (pp65)
Version: Msieve-1.39
Total time: 1.93 hours.
Scaled time: 3.35 units (timescale=1.739).
Factorization parameters were as follows:
n: 2282694918428068381348693425024345271947221342778726134596358771658935004775994118288821273088756202549399
m: 10000000000000000000000000
deg: 5
c5: 49
c0: 410
skew: 1.53
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 130255 x 130496
Total sieving time: 1.93 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 1.93 hours.
 --------- CPU info (if available) ----------

(49·10¹³¹+41)/9 = 5(4)₁₃₀9_<132> = 3 · 127 · 151 · C127

C127 = P48 · P80

P48 = 495966937574525418753568714951542682334528456989_<48>

P80 = 19080902894169119340618115193581337119237563669324766720592482700362221956219311_<80>

Number: 54449_131
N=9463496974577957004822520805208399722661598867470484511731839259606897923631510741069066145981200473561113911533685220914714579
  ( 127 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=495966937574525418753568714951542682334528456989 (pp48)
 r2=19080902894169119340618115193581337119237563669324766720592482700362221956219311 (pp80)
Version: Msieve-1.39
Total time: 2.75 hours.
Scaled time: 4.78 units (timescale=1.735).
Factorization parameters were as follows:
n: 9463496974577957004822520805208399722661598867470484511731839259606897923631510741069066145981200473561113911533685220914714579
m: 100000000000000000000000000
deg: 5
c5: 490
c0: 41
skew: 0.61
type: snfs
lss: 1
rlim: 1140000
alim: 1140000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1140000/1140000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [570000, 1120001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 191855 x 192103
Total sieving time: 2.75 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1140000,1140000,26,26,47,47,2.3,2.3,50000
total time: 2.75 hours.
 --------- CPU info (if available) ----------

(35·10¹⁶⁹-71)/9 = 3(8)₁₆₈1_<170> = 8143481792871063619_<19> · C151

C151 = P75 · P77

P75 = 118340978066617131616605003668155243043376160853287972504030188576447929869_<75>

P77 = 40353411013219617905735168316884121943560908269453282029870176563425168687271_<77>

Number: 38881_169
N=4775462127628609004397620791239844944136870989009288523975169563758497738965996401945642214198142722452627484918282805662237004596874406817488200997499
  ( 151 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=118340978066617131616605003668155243043376160853287972504030188576447929869 (pp75)
 r2=40353411013219617905735168316884121943560908269453282029870176563425168687271 (pp77)
Version: Msieve-1.39
Total time: 48.10 hours.
Scaled time: 123.68 units (timescale=2.571).
Factorization parameters were as follows:
n: 4775462127628609004397620791239844944136870989009288523975169563758497738965996401945642214198142722452627484918282805662237004596874406817488200997499
m: 5000000000000000000000000000000000
deg: 5
c5: 112
c0: -71
skew: 0.91
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 4750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 929709 x 929957
Total sieving time: 48.10 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 48.10 hours.
 --------- CPU info (if available) ----------

(49·10¹³⁰+41)/9 = 5(4)₁₂₉9_<131> = 980924498657_<12> · C119

C119 = P26 · P93

P26 = 91157362108708740542600653_<26>

P93 = 608872332910711521932266724140424623918336615769247686425689983577184398681484932263575936069_<93>

Number: 54449_130
N=55503195729115988344309084736747369696542559541433720850677021062175206889975474460757689960075441138258614086125653057
  ( 119 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=91157362108708740542600653 (pp26)
 r2=608872332910711521932266724140424623918336615769247686425689983577184398681484932263575936069 (pp93)
Version: Msieve-1.39
Total time: 2.09 hours.
Scaled time: 3.63 units (timescale=1.735).
Factorization parameters were as follows:
n: 55503195729115988344309084736747369696542559541433720850677021062175206889975474460757689960075441138258614086125653057
m: 100000000000000000000000000
deg: 5
c5: 49
c0: 41
skew: 0.96
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 164089 x 164337
Total sieving time: 2.09 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.09 hours.
 --------- CPU info (if available) ----------

(49·10¹⁶²+41)/9 = 5(4)₁₆₁9_<163> = 1062458317_<10> · C154

C154 = P71 · P84

P71 = 34363196394391077614856507380930780469359185367467522330450410543511411_<71>

P84 = 149124196210808318999806998432402432647174526275866338390959675701508450716087029127_<84>

Number: 54449_162
N=5124384041547716026250886268364017564036297571233982296968027259034995576625943476373054214083058888082895438847079442124075766865538541823513669613868197
  ( 154 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=34363196394391077614856507380930780469359185367467522330450410543511411 (pp71)
 r2=149124196210808318999806998432402432647174526275866338390959675701508450716087029127 (pp84)
Version: Msieve-1.39
Total time: 40.66 hours.
Scaled time: 104.54 units (timescale=2.571).
Factorization parameters were as follows:
n: 5124384041547716026250886268364017564036297571233982296968027259034995576625943476373054214083058888082895438847079442124075766865538541823513669613868197
m: 200000000000000000000000000000000
deg: 5
c5: 1225
c0: 328
skew: 0.77
type: snfs
lss: 1
rlim: 3900000
alim: 3900000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3900000/3900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1950000, 3850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 679933 x 680181
Total sieving time: 40.66 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3900000,3900000,27,27,51,51,2.4,2.4,100000
total time: 40.66 hours.
 --------- CPU info (if available) ----------

Mar 26, 2009 (6th)

By Andreas Tete / Msieve v1.40beta2, GGNFS / Mar 26, 2009

(25·10¹⁹⁰-7)/9 = 2(7)₁₉₀_<191> = 3³ · 2797 · 32987 · 126410761 · 1898586340075031513_<19> · 41055377346413536886441_<23> · C133

C133 = P45 · P88

P45 = 795128268408707329677455854041947365447846189_<45>

P88 = 1423235633423252778206479630683161968045089225219334698844656222491689510969378337996137_<88>

Wed Mar 25 16:28:21 2009  
Wed Mar 25 16:28:21 2009  
Wed Mar 25 16:28:21 2009  Msieve v. 1.40
Wed Mar 25 16:28:21 2009  random seeds: 205c5d10 e64a3f8d
Wed Mar 25 16:28:21 2009  factoring 1131654884741400727699726376138663572315929999578565409629799410879508529632871965546762957227601037045689888661925111699728852171893 (133 digits)
Wed Mar 25 16:28:22 2009  searching for 15-digit factors
Wed Mar 25 16:28:24 2009  commencing number field sieve (133-digit input)
Wed Mar 25 16:28:24 2009  R0: -28472200377097373513764874
Wed Mar 25 16:28:24 2009  R1:  468852546756907
Wed Mar 25 16:28:24 2009  A0:  3540594829011056504452269227293095
Wed Mar 25 16:28:24 2009  A1:  37878618697434955116910807726
Wed Mar 25 16:28:24 2009  A2:  37056681488483502513677
Wed Mar 25 16:28:24 2009  A3: -141162992671673610
Wed Mar 25 16:28:24 2009  A4: -24837161256
Wed Mar 25 16:28:24 2009  A5:  60480
Wed Mar 25 16:28:24 2009  skew 821183.19, size 9.199391e-013, alpha -7.661392, combined = 5.642171e-011
Wed Mar 25 16:28:24 2009  
Wed Mar 25 16:28:24 2009  commencing relation filtering
Wed Mar 25 16:28:24 2009  commencing duplicate removal, pass 1
Wed Mar 25 16:28:59 2009  error -15 reading relation 3007155
Wed Mar 25 16:28:59 2009  error -15 reading relation 3007384
Wed Mar 25 16:29:22 2009  error -15 reading relation 5139341
Wed Mar 25 16:31:29 2009  found 3944235 hash collisions in 16830320 relations
Wed Mar 25 16:32:12 2009  added 106165 free relations
Wed Mar 25 16:32:12 2009  commencing duplicate removal, pass 2
Wed Mar 25 16:33:20 2009  found 4190313 duplicates and 12746171 unique relations
Wed Mar 25 16:33:20 2009  memory use: 106.6 MB
Wed Mar 25 16:33:20 2009  reading rational ideals above 12255232
Wed Mar 25 16:33:20 2009  reading algebraic ideals above 12255232
Wed Mar 25 16:33:20 2009  commencing singleton removal, pass 1
Wed Mar 25 16:35:52 2009  relations with 0 large ideals: 482609
Wed Mar 25 16:35:52 2009  relations with 1 large ideals: 3067106
Wed Mar 25 16:35:52 2009  relations with 2 large ideals: 5577151
Wed Mar 25 16:35:52 2009  relations with 3 large ideals: 2996424
Wed Mar 25 16:35:52 2009  relations with 4 large ideals: 502027
Wed Mar 25 16:35:52 2009  relations with 5 large ideals: 21449
Wed Mar 25 16:35:52 2009  relations with 6 large ideals: 99405
Wed Mar 25 16:35:52 2009  relations with 7+ large ideals: 0
Wed Mar 25 16:35:52 2009  12746171 relations and about 11981739 large ideals
Wed Mar 25 16:35:52 2009  commencing singleton removal, pass 2
Wed Mar 25 16:38:27 2009  found 5973933 singletons
Wed Mar 25 16:38:27 2009  current dataset: 6772238 relations and about 4800496 large ideals
Wed Mar 25 16:38:27 2009  commencing singleton removal, pass 3
Wed Mar 25 16:40:07 2009  found 1081690 singletons
Wed Mar 25 16:40:07 2009  current dataset: 5690548 relations and about 3657854 large ideals
Wed Mar 25 16:40:07 2009  commencing singleton removal, pass 4
Wed Mar 25 16:41:38 2009  found 253805 singletons
Wed Mar 25 16:41:38 2009  current dataset: 5436743 relations and about 3399748 large ideals
Wed Mar 25 16:41:38 2009  commencing singleton removal, final pass
Wed Mar 25 16:43:11 2009  memory use: 77.7 MB
Wed Mar 25 16:43:11 2009  commencing in-memory singleton removal
Wed Mar 25 16:43:11 2009  begin with 5436743 relations and 3712401 unique ideals
Wed Mar 25 16:43:16 2009  reduce to 4643827 relations and 2899656 ideals in 13 passes
Wed Mar 25 16:43:16 2009  max relations containing the same ideal: 24
Wed Mar 25 16:43:18 2009  reading rational ideals above 720000
Wed Mar 25 16:43:18 2009  reading algebraic ideals above 720000
Wed Mar 25 16:43:18 2009  commencing singleton removal, final pass
Wed Mar 25 16:44:51 2009  keeping 4349772 ideals with weight <= 20, new excess is 364446
Wed Mar 25 16:44:58 2009  memory use: 130.1 MB
Wed Mar 25 16:44:58 2009  commencing in-memory singleton removal
Wed Mar 25 16:44:59 2009  begin with 4680910 relations and 4349772 unique ideals
Wed Mar 25 16:45:07 2009  reduce to 4548935 relations and 4035647 ideals in 12 passes
Wed Mar 25 16:45:07 2009  max relations containing the same ideal: 20
Wed Mar 25 16:45:10 2009  removing 383563 relations and 338298 ideals in 45265 cliques
Wed Mar 25 16:45:10 2009  commencing in-memory singleton removal
Wed Mar 25 16:45:11 2009  begin with 4165372 relations and 4035647 unique ideals
Wed Mar 25 16:45:15 2009  reduce to 4146785 relations and 3678522 ideals in 8 passes
Wed Mar 25 16:45:15 2009  max relations containing the same ideal: 20
Wed Mar 25 16:45:18 2009  removing 284996 relations and 239731 ideals in 45265 cliques
Wed Mar 25 16:45:19 2009  commencing in-memory singleton removal
Wed Mar 25 16:45:19 2009  begin with 3861789 relations and 3678522 unique ideals
Wed Mar 25 16:45:23 2009  reduce to 3849829 relations and 3426710 ideals in 7 passes
Wed Mar 25 16:45:23 2009  max relations containing the same ideal: 20
Wed Mar 25 16:45:26 2009  relations with 0 large ideals: 9503
Wed Mar 25 16:45:26 2009  relations with 1 large ideals: 90848
Wed Mar 25 16:45:26 2009  relations with 2 large ideals: 396535
Wed Mar 25 16:45:26 2009  relations with 3 large ideals: 914667
Wed Mar 25 16:45:26 2009  relations with 4 large ideals: 1186000
Wed Mar 25 16:45:26 2009  relations with 5 large ideals: 853357
Wed Mar 25 16:45:26 2009  relations with 6 large ideals: 327220
Wed Mar 25 16:45:26 2009  relations with 7+ large ideals: 71699
Wed Mar 25 16:45:26 2009  commencing 2-way merge
Wed Mar 25 16:45:30 2009  reduce to 2378718 relation sets and 1955599 unique ideals
Wed Mar 25 16:45:30 2009  commencing full merge
Wed Mar 25 16:46:08 2009  memory use: 176.4 MB
Wed Mar 25 16:46:09 2009  found 1217257 cycles, need 1159799
Wed Mar 25 16:46:09 2009  weight of 1159799 cycles is about 81408641 (70.19/cycle)
Wed Mar 25 16:46:09 2009  distribution of cycle lengths:
Wed Mar 25 16:46:09 2009  1 relations: 114539
Wed Mar 25 16:46:09 2009  2 relations: 137131
Wed Mar 25 16:46:09 2009  3 relations: 143480
Wed Mar 25 16:46:09 2009  4 relations: 133059
Wed Mar 25 16:46:09 2009  5 relations: 119083
Wed Mar 25 16:46:09 2009  6 relations: 102704
Wed Mar 25 16:46:09 2009  7 relations: 86519
Wed Mar 25 16:46:09 2009  8 relations: 73187
Wed Mar 25 16:46:09 2009  9 relations: 61798
Wed Mar 25 16:46:09 2009  10+ relations: 188299
Wed Mar 25 16:46:09 2009  heaviest cycle: 17 relations
Wed Mar 25 16:46:09 2009  commencing cycle optimization
Wed Mar 25 16:46:12 2009  start with 6536252 relations
Wed Mar 25 16:46:29 2009  pruned 174023 relations
Wed Mar 25 16:46:29 2009  memory use: 172.4 MB
Wed Mar 25 16:46:29 2009  distribution of cycle lengths:
Wed Mar 25 16:46:29 2009  1 relations: 114539
Wed Mar 25 16:46:29 2009  2 relations: 140634
Wed Mar 25 16:46:29 2009  3 relations: 149409
Wed Mar 25 16:46:29 2009  4 relations: 137047
Wed Mar 25 16:46:29 2009  5 relations: 122430
Wed Mar 25 16:46:29 2009  6 relations: 103915
Wed Mar 25 16:46:29 2009  7 relations: 87256
Wed Mar 25 16:46:29 2009  8 relations: 73271
Wed Mar 25 16:46:29 2009  9 relations: 60820
Wed Mar 25 16:46:29 2009  10+ relations: 170478
Wed Mar 25 16:46:29 2009  heaviest cycle: 17 relations
Wed Mar 25 16:46:31 2009  RelProcTime: 935
Wed Mar 25 16:46:31 2009  
Wed Mar 25 16:46:31 2009  commencing linear algebra
Wed Mar 25 16:46:31 2009  read 1159799 cycles
Wed Mar 25 16:46:34 2009  cycles contain 3561496 unique relations
Wed Mar 25 16:47:39 2009  read 3561496 relations
Wed Mar 25 16:47:45 2009  using 20 quadratic characters above 268431422
Wed Mar 25 16:48:08 2009  building initial matrix
Wed Mar 25 16:49:06 2009  memory use: 417.3 MB
Wed Mar 25 16:49:11 2009  read 1159799 cycles
Wed Mar 25 16:49:13 2009  matrix is 1159583 x 1159799 (333.0 MB) with weight 110624004 (95.38/col)
Wed Mar 25 16:49:13 2009  sparse part has weight 78015465 (67.27/col)
Wed Mar 25 16:49:32 2009  filtering completed in 2 passes
Wed Mar 25 16:49:33 2009  matrix is 1155802 x 1156002 (332.5 MB) with weight 110419103 (95.52/col)
Wed Mar 25 16:49:33 2009  sparse part has weight 77923718 (67.41/col)
Wed Mar 25 16:49:37 2009  read 1156002 cycles
Wed Mar 25 16:49:38 2009  matrix is 1155802 x 1156002 (332.5 MB) with weight 110419103 (95.52/col)
Wed Mar 25 16:49:38 2009  sparse part has weight 77923718 (67.41/col)
Wed Mar 25 16:49:38 2009  saving the first 48 matrix rows for later
Wed Mar 25 16:49:39 2009  matrix is 1155754 x 1156002 (318.0 MB) with weight 87730479 (75.89/col)
Wed Mar 25 16:49:39 2009  sparse part has weight 76424675 (66.11/col)
Wed Mar 25 16:49:39 2009  matrix includes 64 packed rows
Wed Mar 25 16:49:39 2009  using block size 65536 for processor cache size 3072 kB
Wed Mar 25 16:49:49 2009  commencing Lanczos iteration
Wed Mar 25 16:49:49 2009  memory use: 315.4 MB
Wed Mar 25 20:18:27 2009  lanczos halted after 18278 iterations (dim = 1155754)
Wed Mar 25 20:18:30 2009  recovered 29 nontrivial dependencies
Wed Mar 25 20:18:30 2009  BLanczosTime: 12586
Wed Mar 25 20:18:30 2009  
Wed Mar 25 20:18:30 2009  commencing square root phase
Wed Mar 25 20:18:30 2009  reading relations for dependency 1
Wed Mar 25 20:18:31 2009  read 578022 cycles
Wed Mar 25 20:18:33 2009  cycles contain 2175074 unique relations
Wed Mar 25 20:19:35 2009  read 2175074 relations
Wed Mar 25 20:19:49 2009  multiplying 1779100 relations
Wed Mar 25 20:26:58 2009  multiply complete, coefficients have about 84.98 million bits
Wed Mar 25 20:27:01 2009  initial square root is modulo 1258819
Wed Mar 25 20:35:30 2009  sqrtTime: 1020
Wed Mar 25 20:35:30 2009  prp45 factor: 795128268408707329677455854041947365447846189
Wed Mar 25 20:35:30 2009  prp88 factor: 1423235633423252778206479630683161968045089225219334698844656222491689510969378337996137
Wed Mar 25 20:35:30 2009  elapsed time 04:07:09

Msieve v1.40beta2 Polynomial Search take elapsed time 23:28:43 GGNFS for Sieving need 206.94 hours Final Factorization with Msieve v1.40 need 04:07:09 Total time ~ 234 hours

Mar 26, 2009 (5th)

By Sinkiti Sibata / GGNFS / Mar 26, 2009

(49·10¹³¹+23)/9 = 5(4)₁₃₀7_<132> = 1663 · 23449818043019_<14> · C116

C116 = P40 · P77

P40 = 1155209557118607634866301603249630313369_<40>

P77 = 12085401163911818634847149173022128361640247401446141329665954189440760421179_<77>

Number: 54447_131
N=13961170926163277240688149356007896284655518876882225973901486035584422030375138157157355587292818264737566194442051
  ( 116 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=1155209557118607634866301603249630313369 (pp40)
 r2=12085401163911818634847149173022128361640247401446141329665954189440760421179 (pp77)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 3.30 hours.
Scaled time: 11.02 units (timescale=3.339).
Factorization parameters were as follows:
name: 54447_131
n: 13961170926163277240688149356007896284655518876882225973901486035584422030375138157157355587292818264737566194442051
m: 200000000000000000000000000
deg: 5
c5: 245
c0: 368
skew: 1.08
type: snfs
lss: 1
rlim: 1190000
alim: 1190000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1190000/1190000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [595000, 1195001)
Primes: RFBsize:92225, AFBsize:92072, largePrimes:3029635 encountered
Relations: rels:2969240, finalFF:249592
Max relations in full relation-set: 28
Initial matrix: 184363 x 249592 with sparse part having weight 20809548.
Pruned matrix : 166372 x 167357 with weight 10744253.
Total sieving time: 3.15 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1190000,1190000,26,26,47,47,2.3,2.3,75000
total time: 3.30 hours.
 --------- CPU info (if available) ----------

Mar 26, 2009 (4th)

By Erik Branger / GGNFS, Msieve / Mar 26, 2009

(47·10¹⁵⁵+7)/9 = 5(2)₁₅₄3_<156> = 13 · 19 · 48779 · 1340071 · 49118467 · C135

C135 = P37 · P37 · P63

P37 = 1057730668417200572838874936212859657_<37>

P37 = 5105488992144329951453710753573117397_<37>

P63 = 121938387829153761107662905698626411651559749568993099534450107_<63>

Number: 52223_155
N=658495618645305733221984821404460863586812480725034488110267055018883740631864279001729002904992935850854797600803454626685203897402703
  ( 135 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=1057730668417200572838874936212859657
 r2=5105488992144329951453710753573117397
 r3=121938387829153761107662905698626411651559749568993099534450107
Version: 
Total time: 25.04 hours.
Scaled time: 25.71 units (timescale=1.027).
Factorization parameters were as follows:
n: 658495618645305733221984821404460863586812480725034488110267055018883740631864279001729002904992935850854797600803454626685203897402703
m: 10000000000000000000000000000000
deg: 5
c5: 47
c0: 7
skew: 0.68
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1450000, 2350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 521816 x 522064
Total sieving time: 25.04 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000
total time: 25.04 hours.
 --------- CPU info (if available) ----------

(49·10¹²⁶+41)/9 = 5(4)₁₂₅9_<127> = C127

C127 = P50 · P77

P50 = 89509726479899433582217775103987526302712114761893_<50>

P77 = 60825171280878227682314694429796797662398614282260359785768606811199736018893_<77>

Number: 54449_126
N=5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
  ( 127 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=89509726479899433582217775103987526302712114761893
 r2=60825171280878227682314694429796797662398614282260359785768606811199736018893
Version: 
Total time: 3.13 hours.
Scaled time: 2.97 units (timescale=0.948).
Factorization parameters were as follows:
n: 5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
m: 10000000000000000000000000
deg: 5
c5: 490
c0: 41
skew: 0.61
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [500000, 900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 149326 x 149573
Total sieving time: 3.13 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,46,46,2.3,2.3,50000
total time: 3.13 hours.
 --------- CPU info (if available) ----------

(49·10¹⁰⁷+23)/9 = 5(4)₁₀₆7_<108> = 17 · 412784461 · C98

C98 = P47 · P52

P47 = 63256444323242069473713196879638132828513180833_<47>

P52 = 1226525361201857409856065873971323956702057027360907_<52>

Number: 54447_107
N=77585633221909661959427244730918590129384517933033400072176771385787737729509559518669570045895531
  ( 98 digits)
SNFS difficulty: 109 digits.
Divisors found:
 r1=63256444323242069473713196879638132828513180833
 r2=1226525361201857409856065873971323956702057027360907
Version: 
Total time: 1.22 hours.
Scaled time: 0.96 units (timescale=0.787).
Factorization parameters were as follows:
n: 77585633221909661959427244730918590129384517933033400072176771385787737729509559518669570045895531
m: 2000000000000000000000
deg: 5
c5: 1225
c0: 184
skew: 0.68
type: snfs
lss: 1
rlim: 470000
alim: 470000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 470000/470000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [235000, 385001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 50478 x 50708
Total sieving time: 1.22 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,109,5,0,0,0,0,0,0,0,0,470000,470000,25,25,44,44,2.2,2.2,50000
total time: 1.22 hours.
 --------- CPU info (if available) ----------

(49·10¹⁴²+23)/9 = 5(4)₁₄₁7_<143> = 3³ · 59 · 347 · 883 · 2606809451_<10> · 10974894967_<11> · C115

C115 = P48 · P67

P48 = 422487548822494189048430737716463004689438550629_<48>

P67 = 9228349684211586458646457759478541784731866561768689933021851095303_<67>

Number: 54447_142
N=3898862837759391465874496029507318729058503037759396950405744980149335186198631726209810851867165775544356469595587
  ( 115 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=422487548822494189048430737716463004689438550629
 r2=9228349684211586458646457759478541784731866561768689933021851095303
Version: 
Total time: 10.83 hours.
Scaled time: 10.74 units (timescale=0.992).
Factorization parameters were as follows:
n: 3898862837759391465874496029507318729058503037759396950405744980149335186198631726209810851867165775544356469595587
m: 20000000000000000000000000000
deg: 5
c5: 1225
c0: 184
skew: 0.68
type: snfs
lss: 1
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [900000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 298355 x 298603
Total sieving time: 10.83 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,49,49,2.3,2.3,100000
total time: 10.83 hours.
 --------- CPU info (if available) ----------

(49·10¹³⁶+41)/9 = 5(4)₁₃₅9_<137> = 9257 · C133

C133 = P47 · P86

P47 = 71304781245914521607230391735935498351049913551_<47>

P86 = 82483039249126102767427949027373155037745463880624218563063734706630914560237529727607_<86>

Number: 54449_136
N=5881435070157118336874197304142210699410656200112827529917299821156362152365177103213184016900123630165760445548713886188229928102457
  ( 133 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=71304781245914521607230391735935498351049913551
 r2=82483039249126102767427949027373155037745463880624218563063734706630914560237529727607
Version: 
Total time: 8.16 hours.
Scaled time: 6.41 units (timescale=0.786).
Factorization parameters were as follows:
n: 5881435070157118336874197304142210699410656200112827529917299821156362152365177103213184016900123630165760445548713886188229928102457
m: 1000000000000000000000000000
deg: 5
c5: 490
c0: 41
skew: 0.61
type: snfs
lss: 1
rlim: 1380000
alim: 1380000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1380000/1380000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [690000, 1515001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 242546 x 242794
Total sieving time: 8.16 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1380000,1380000,26,26,48,48,2.3,2.3,75000
total time: 8.16 hours.
 --------- CPU info (if available) ----------

Mar 26, 2009 (3rd)

By Robert Backstrom / Msieve, GGNFS, GMP-ECM / Mar 26, 2009

(49·10¹⁵⁴+41)/9 = 5(4)₁₅₃9_<155> = 111227 · 30989490023981_<14> · 19438696293455187099283_<23> · 4709579273971574805918139_<25> · C90

C90 = P35 · P55

P35 = 85398388677124700509979518851635059_<35>

P55 = 2020365738813114803260409765581225522390963662391877669_<55>

Thu Mar 26 03:57:27 2009  
Thu Mar 26 03:57:27 2009  
Thu Mar 26 03:57:27 2009  Msieve v. 1.39
Thu Mar 26 03:57:27 2009  random seeds: 3388a570 6268f5cc
Thu Mar 26 03:57:27 2009  factoring 172535978633108583271830002807599001693998076198225974666984044214182960439546361759597471 (90 digits)
Thu Mar 26 03:57:28 2009  searching for 15-digit factors
Thu Mar 26 03:57:29 2009  commencing quadratic sieve (90-digit input)
Thu Mar 26 03:57:29 2009  using multiplier of 21
Thu Mar 26 03:57:29 2009  using 64kb Opteron sieve core
Thu Mar 26 03:57:29 2009  sieve interval: 18 blocks of size 65536
Thu Mar 26 03:57:29 2009  processing polynomials in batches of 6
Thu Mar 26 03:57:29 2009  using a sieve bound of 1573577 (59667 primes)
Thu Mar 26 03:57:29 2009  using large prime bound of 125886160 (26 bits)
Thu Mar 26 03:57:29 2009  using double large prime bound of 380154676666640 (42-49 bits)
Thu Mar 26 03:57:29 2009  using trial factoring cutoff of 49 bits
Thu Mar 26 03:57:29 2009  polynomial 'A' values have 12 factors
Thu Mar 26 04:57:17 2009  60155 relations (15845 full + 44310 combined from 635792 partial), need 59763
Thu Mar 26 04:57:18 2009  begin with 651637 relations
Thu Mar 26 04:57:19 2009  reduce to 146951 relations in 10 passes
Thu Mar 26 04:57:19 2009  attempting to read 146951 relations
Thu Mar 26 04:57:20 2009  recovered 146951 relations
Thu Mar 26 04:57:20 2009  recovered 127740 polynomials
Thu Mar 26 04:57:20 2009  attempting to build 60155 cycles
Thu Mar 26 04:57:20 2009  found 60155 cycles in 5 passes
Thu Mar 26 04:57:21 2009  distribution of cycle lengths:
Thu Mar 26 04:57:21 2009     length 1 : 15845
Thu Mar 26 04:57:21 2009     length 2 : 11577
Thu Mar 26 04:57:21 2009     length 3 : 10639
Thu Mar 26 04:57:21 2009     length 4 : 8071
Thu Mar 26 04:57:21 2009     length 5 : 5683
Thu Mar 26 04:57:21 2009     length 6 : 3657
Thu Mar 26 04:57:21 2009     length 7 : 2161
Thu Mar 26 04:57:21 2009     length 9+: 2522
Thu Mar 26 04:57:21 2009  largest cycle: 18 relations
Thu Mar 26 04:57:21 2009  matrix is 59667 x 60155 (15.0 MB) with weight 3692255 (61.38/col)
Thu Mar 26 04:57:21 2009  sparse part has weight 3692255 (61.38/col)
Thu Mar 26 04:57:22 2009  filtering completed in 3 passes
Thu Mar 26 04:57:22 2009  matrix is 55810 x 55874 (13.9 MB) with weight 3430899 (61.40/col)
Thu Mar 26 04:57:22 2009  sparse part has weight 3430899 (61.40/col)
Thu Mar 26 04:57:22 2009  saving the first 48 matrix rows for later
Thu Mar 26 04:57:22 2009  matrix is 55762 x 55874 (8.9 MB) with weight 2702698 (48.37/col)
Thu Mar 26 04:57:22 2009  sparse part has weight 1988182 (35.58/col)
Thu Mar 26 04:57:22 2009  matrix includes 64 packed rows
Thu Mar 26 04:57:22 2009  using block size 22349 for processor cache size 1024 kB
Thu Mar 26 04:57:22 2009  commencing Lanczos iteration
Thu Mar 26 04:57:22 2009  memory use: 8.5 MB
Thu Mar 26 04:57:40 2009  lanczos halted after 883 iterations (dim = 55760)
Thu Mar 26 04:57:40 2009  recovered 18 nontrivial dependencies
Thu Mar 26 04:57:40 2009  prp35 factor: 85398388677124700509979518851635059
Thu Mar 26 04:57:40 2009  prp55 factor: 2020365738813114803260409765581225522390963662391877669
Thu Mar 26 04:57:40 2009  elapsed time 01:00:13

(49·10¹¹⁷+41)/9 = 5(4)₁₁₆9_<118> = 59 · 71 · 863 · 2411 · 3142187 · 11039507 · C95

C95 = P42 · P53

P42 = 336604968389700345229006632632467724043359_<42>

P53 = 53497436933044664478816389244926048170274046484553327_<53>

Thu Mar 26 12:17:04 2009  
Thu Mar 26 12:17:04 2009  
Thu Mar 26 12:17:04 2009  Msieve v. 1.39
Thu Mar 26 12:17:04 2009  random seeds: 51e810a4 dba85ca5
Thu Mar 26 12:17:04 2009  factoring 18007503067777487071137242913972238984183195788228068696022682661075151599635220265841495705393 (95 digits)
Thu Mar 26 12:17:04 2009  searching for 15-digit factors
Thu Mar 26 12:17:05 2009  commencing quadratic sieve (95-digit input)
Thu Mar 26 12:17:05 2009  using multiplier of 17
Thu Mar 26 12:17:05 2009  using 64kb Opteron sieve core
Thu Mar 26 12:17:05 2009  sieve interval: 18 blocks of size 65536
Thu Mar 26 12:17:05 2009  processing polynomials in batches of 6
Thu Mar 26 12:17:05 2009  using a sieve bound of 2117273 (78824 primes)
Thu Mar 26 12:17:05 2009  using large prime bound of 309121858 (28 bits)
Thu Mar 26 12:17:05 2009  using double large prime bound of 1915285337885478 (43-51 bits)
Thu Mar 26 12:17:05 2009  using trial factoring cutoff of 51 bits
Thu Mar 26 12:17:05 2009  polynomial 'A' values have 12 factors
Thu Mar 26 14:53:41 2009  78965 relations (19422 full + 59543 combined from 1158503 partial), need 78920
Thu Mar 26 14:53:43 2009  begin with 1177925 relations
Thu Mar 26 14:53:44 2009  reduce to 204547 relations in 11 passes
Thu Mar 26 14:53:44 2009  attempting to read 204547 relations
Thu Mar 26 14:53:47 2009  recovered 204547 relations
Thu Mar 26 14:53:47 2009  recovered 189076 polynomials
Thu Mar 26 14:53:47 2009  attempting to build 78965 cycles
Thu Mar 26 14:53:47 2009  found 78965 cycles in 5 passes
Thu Mar 26 14:53:48 2009  distribution of cycle lengths:
Thu Mar 26 14:53:48 2009     length 1 : 19422
Thu Mar 26 14:53:48 2009     length 2 : 13884
Thu Mar 26 14:53:48 2009     length 3 : 13302
Thu Mar 26 14:53:48 2009     length 4 : 10834
Thu Mar 26 14:53:48 2009     length 5 : 8180
Thu Mar 26 14:53:48 2009     length 6 : 5355
Thu Mar 26 14:53:48 2009     length 7 : 3494
Thu Mar 26 14:53:48 2009     length 9+: 4494
Thu Mar 26 14:53:48 2009  largest cycle: 20 relations
Thu Mar 26 14:53:48 2009  matrix is 78824 x 78965 (21.3 MB) with weight 5257190 (66.58/col)
Thu Mar 26 14:53:48 2009  sparse part has weight 5257190 (66.58/col)
Thu Mar 26 14:53:49 2009  filtering completed in 4 passes
Thu Mar 26 14:53:49 2009  matrix is 75072 x 75136 (20.4 MB) with weight 5039369 (67.07/col)
Thu Mar 26 14:53:49 2009  sparse part has weight 5039369 (67.07/col)
Thu Mar 26 14:53:49 2009  saving the first 48 matrix rows for later
Thu Mar 26 14:53:49 2009  matrix is 75024 x 75136 (13.8 MB) with weight 4076805 (54.26/col)
Thu Mar 26 14:53:49 2009  sparse part has weight 3163131 (42.10/col)
Thu Mar 26 14:53:49 2009  matrix includes 64 packed rows
Thu Mar 26 14:53:49 2009  using block size 30054 for processor cache size 1024 kB
Thu Mar 26 14:53:50 2009  commencing Lanczos iteration
Thu Mar 26 14:53:50 2009  memory use: 12.7 MB
Thu Mar 26 14:54:31 2009  lanczos halted after 1188 iterations (dim = 75022)
Thu Mar 26 14:54:32 2009  recovered 16 nontrivial dependencies
Thu Mar 26 14:54:33 2009  prp42 factor: 336604968389700345229006632632467724043359
Thu Mar 26 14:54:33 2009  prp53 factor: 53497436933044664478816389244926048170274046484553327
Thu Mar 26 14:54:33 2009  elapsed time 02:37:29

(49·10¹⁶⁶-13)/9 = 5(4)₁₆₅3_<167> = 3392460707_<10> · C158

C158 = P39 · P119

P39 = 228606663332069098898658208677726772027_<39>

P119 = 70202060540836190435027353842202723932903383646206976045490228370900250805488572773763887061548507188806030834957521387_<119>

Number: n
N=16048658819276471709608645570215131881391734700037144584809613962743075168193670826338164701532811134323462171331921176012737955182584357769083055276325841449
  ( 158 digits)
SNFS difficulty: 167 digits.
Divisors found:

Thu Mar 26 15:24:14 2009  prp39 factor: 228606663332069098898658208677726772027
Thu Mar 26 15:24:14 2009  prp119 factor: 70202060540836190435027353842202723932903383646206976045490228370900250805488572773763887061548507188806030834957521387
Thu Mar 26 15:24:14 2009  elapsed time 01:17:51 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 46.22 hours.
Scaled time: 122.94 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_4_165_3
n: 16048658819276471709608645570215131881391734700037144584809613962743075168193670826338164701532811134323462171331921176012737955182584357769083055276325841449
skew: 0.48
deg: 5
c5: 490
c0: -13
m: 1000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 5400709)
Primes: RFBsize:348513, AFBsize:347801, largePrimes:16583950 encountered
Relations: rels:15857481, finalFF:721908
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1654776 hash collisions in 17166877 relations
Msieve: matrix is 879243 x 879491 (235.5 MB)

Total sieving time: 45.64 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 46.22 hours.
 --------- CPU info (if available) ----------

(49·10¹⁷⁷+41)/9 = 5(4)₁₇₆9_<178> = 131 · 191 · 449 · 331391 · 472840087 · 726941215300706671579_<21> · 2433838839766455950342062363_<28> · C109

C109 = P35 · P74

P35 = 83034203406922062183051715629104539_<35>

P74 = 21052294409786281603774327103314927783566223455754104095544829887091074031_<74>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 1748060496204602348217928342045955454659092137537713587969915638714670667753586844090191544518365344287126709 (109 digits)
Using B1=720000, B2=696728352, polynomial Dickson(3), sigma=2714175444
Step 1 took 7176ms
Step 2 took 2964ms
********** Factor found in step 2: 83034203406922062183051715629104539
Found probable prime factor of 35 digits: 83034203406922062183051715629104539
Probable prime cofactor 21052294409786281603774327103314927783566223455754104095544829887091074031 has 74 digits

(49·10¹³³+41)/9 = 5(4)₁₃₂9_<134> = 1847 · 17191 · 15928399 · 2569725611564596134156953_<25> · C95

C95 = P38 · P58

P38 = 31123736301946053601072239401392732729_<38>

P58 = 1345968600983785417249315598989980743105211831323133158399_<58>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 41891571807718584945127829778318507717751879939979549720467854224774931298243603645127428540871 (95 digits)
Using B1=1538000, B2=2140123450, polynomial Dickson(6), sigma=100538867
Step 1 took 9438ms
Step 2 took 5125ms
********** Factor found in step 2: 31123736301946053601072239401392732729
Found probable prime factor of 38 digits: 31123736301946053601072239401392732729
Probable prime cofactor 1345968600983785417249315598989980743105211831323133158399 has 58 digits

Mar 26, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.40 / Mar 26, 2009

(49·10¹⁷⁹+23)/9 = 5(4)₁₇₈7_<180> = 31 · 263 · C176

C176 = P32 · C145

P32 = 49019269914862359235884231368959_<32>

C145 = [1362289124694138590647084383486475677068698804342845520947990557153490588446492978754390220171132857402672722825249805305208753255232760139820361_<145>]

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=2685186263
Step 1 took 7737ms
Step 2 took 5812ms
********** Factor found in step 2: 49019269914862359235884231368959
Found probable prime factor of 32 digits: 49019269914862359235884231368959
Composite cofactor has 145 digits

(49·10¹⁸⁰+23)/9 = 5(4)₁₇₉7_<181> = 14699 · 1856297 · 10162351 · 176396963 · 395885210069_<12> · 93495456952771_<14> · C130

C130 = P32 · P99

P32 = 19570989095089334341692051382711_<32>

P99 = 153659870377095098863641301496034790203531138412155043393272991554591626364446428220183087152397057_<99>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=148828922
Step 1 took 7357ms
Step 2 took 7044ms
********** Factor found in step 2: 19570989095089334341692051382711
Found probable prime factor of 32 digits: 19570989095089334341692051382711
Probable prime cofactor has 99 digits

(49·10¹⁶⁹+23)/9 = 5(4)₁₆₈7_<170> = 3³ · 7757 · C165

C165 = P33 · P133

P33 = 124536554543997314979024046350781_<33>

P133 = 2087368708499167158827513265956753940583325925005520026107942223059166689438339761676704306516497762484131504693365842596878578550933_<133>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=934136197
Step 1 took 9996ms
Step 2 took 8941ms
********** Factor found in step 2: 124536554543997314979024046350781
Found probable prime factor of 33 digits: 124536554543997314979024046350781
Probable prime cofactor has 133 digits

(49·10¹⁸¹+23)/9 = 5(4)₁₈₀7_<182> = 3 · 19 · 25343 · 4898143973671943075533_<22> · C154

C154 = P30 · C125

P30 = 165703440094533134905772423687_<30>

C125 = [46436301276070201899460398906248605364338025400814138874003744066901307471773211792610214257185020149990475282233636591208907_<125>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=946105213
Step 1 took 9201ms
Step 2 took 7804ms
********** Factor found in step 2: 165703440094533134905772423687
Found probable prime factor of 30 digits: 165703440094533134905772423687
Composite cofactor has 125 digits

(49·10¹⁹⁰+23)/9 = 5(4)₁₈₉7_<191> = 3 · 64109 · 4225530117516618479761_<22> · C164

C164 = P39 · P126

P39 = 220761939500028598302869393980575061631_<39>

P126 = 303464512073770648945878490978300439558503103582063123665138950766375927106303506145444934484669950085539836507940085379564071_<126>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2573314229
Step 1 took 9876ms
Step 2 took 8681ms
********** Factor found in step 2: 220761939500028598302869393980575061631
Found probable prime factor of 39 digits: 220761939500028598302869393980575061631
Probable prime cofactor has 126 digits

(49·10¹²⁵+41)/9 = 5(4)₁₂₄9_<126> = 3 · 661439 · 3876997 · 4170227 · C107

C107 = P32 · P75

P32 = 74576531666662530089711767310951_<32>

P75 = 227554367291850453101197310205051455465156475107583107302535931180466407613_<75>

SNFS difficulty: 126 digits.
Divisors found:
 r1=74576531666662530089711767310951 (pp32)
 r2=227554367291850453101197310205051455465156475107583107302535931180466407613 (pp75)
Version: Msieve-1.39
Total time: 1.26 hours.
Scaled time: 3.56 units (timescale=2.838).
Factorization parameters were as follows:
n: 16970215478228041594814063236791347986814014122707645679199223191602665685124329148314728537601692084669963
m: 10000000000000000000000000
deg: 5
c5: 49
c0: 41
skew: 0.96
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved  special-q in [450000, 450000)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 112947 x 113192
Total sieving time: 1.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 1.26 hours.

(49·10¹²¹+23)/9 = 5(4)₁₂₀7_<122> = 3 · 15083 · 52627 · 1866461 · 2198407 · C100

C100 = P37 · P63

P37 = 7124603840479919365732898437556681717_<37>

P63 = 782074692248656594203654067738974568526834648445247639018273171_<63>

SNFS difficulty: 123 digits.
Divisors found:
 r1=7124603840479919365732898437556681717 (pp37)
 r2=782074692248656594203654067738974568526834648445247639018273171 (pp63)
Version: Msieve-1.39
Total time: 1.06 hours.
Scaled time: 3.02 units (timescale=2.840).
Factorization parameters were as follows:
n: 5571972355936929796164402527839661785202415009775857808001397525490794471008880872643822230207314607
m: 2000000000000000000000000
deg: 5
c5: 245
c0: 368
skew: 1.08
type: snfs
lss: 1
rlim: 810000
alim: 810000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 810000/810000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [405000, 905001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 90728 x 90976
Total sieving time: 1.06 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,810000,810000,25,25,46,46,2.2,2.2,50000
total time: 1.06 hours.

(49·10¹²⁸+23)/9 = 5(4)₁₂₇7_<129> = 5791 · 16451 · C121

C121 = P38 · P84

P38 = 13430260892711496624143275808375396407_<38>

P84 = 425523210547380281621608549880770539602816541215414945259160078414911239467806700781_<84>

SNFS difficulty: 131 digits.
Divisors found:
 r1=13430260892711496624143275808375396407 (pp38)
 r2=425523210547380281621608549880770539602816541215414945259160078414911239467806700781 (pp84)
Version: Msieve-1.40
Total time: 1.50 hours.
Scaled time: 4.25 units (timescale=2.840).
Factorization parameters were as follows:
n: 5714887733555521637113705093988157486010342624209431442742454074191225384933231957756240325300087092906343233691711493867
m: 50000000000000000000000000
deg: 5
c5: 392
c0: 575
skew: 1.08
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 1135001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 134952 x 135200
Total sieving time: 1.50 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 1.50 hours.

Mar 26, 2009

By 10metreh / GMP-ECM 6.2.1 / Mar 26, 2009

(49·10¹³⁵+23)/9 = 5(4)₁₃₄7_<136> = 13 · 15551 · C131

C131 = P34 · P98

P34 = 1005344693062810933520912027258803_<34>

P98 = 26787791325737202548916567410163297961651803940100230936923958001195768311232370875084900124086023_<98>

Factored with Markus Tervooren's wonderful database workers in just a few minutes!

26930963848203897075352287235767397814854570047162163424783192000734280973493885846789197056060923336339708277204258170112456010469 = 1005344693062810933520912027258803 * 26787791325737202548916567410163297961651803940100230936923958001195768311232370875084900124086023

Mar 25, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Mar 25, 2009

(49·10¹⁵⁹-13)/9 = 5(4)₁₅₈3_<160> = 2428024769_<10> · C151

C151 = P63 · P88

P63 = 601351575708202483414719598577935244714095030835679564985254607_<63>

P88 = 3728825024421394506143678851589601389969611659833649468122314998192459819730376930996021_<88>

Number: n
N=2242334803975982192480032498566510482103094412231856620093830865052614479504284020936379683383882499612360603741618767829153247177786284125194788918747
  ( 151 digits)
SNFS difficulty: 161 digits.
Divisors found:

Wed Mar 25 17:13:26 2009  prp63 factor: 601351575708202483414719598577935244714095030835679564985254607
Wed Mar 25 17:13:26 2009  prp88 factor: 3728825024421394506143678851589601389969611659833649468122314998192459819730376930996021
Wed Mar 25 17:13:26 2009  elapsed time 00:56:02 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 25.50 hours.
Scaled time: 67.54 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_4_158_3
n: 2242334803975982192480032498566510482103094412231856620093830865052614479504284020936379683383882499612360603741618767829153247177786284125194788918747
skew: 1.22
deg: 5
c5: 49
c0: -130
m: 100000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 3700049)
Primes: RFBsize:283146, AFBsize:283762, largePrimes:14472488 encountered
Relations: rels:13551879, finalFF:611318
Max relations in full relation-set: 28
Initial matrix:
Pruned matrix :

Msieve: found 1159398 hash collisions in 14440877 relations
Msieve: matrix is 697476 x 697724 (187.1 MB)

Total sieving time: 25.15 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.4,2.4,100000
total time: 25.50 hours.
 --------- CPU info (if available) ----------

(49·10¹⁶⁵-13)/9 = 5(4)₁₆₄3_<166> = 21685402247_<11> · C156

C156 = P77 · P80

P77 = 14324711689563372779335680404766103636224125956636359995327793344470127538869_<77>

P80 = 17526701832941984245416388922140767102049667569465043187924398853225270451740601_<80>

Number: n
N=251064950625835833703382280840771182234664703586415536986577735970020000544583139843679582377840521338633043270402953869839020673640559582673460585332920269
  ( 156 digits)
SNFS difficulty: 166 digits.
Divisors found:

Wed Mar 25 22:46:33 2009  prp77 factor: 14324711689563372779335680404766103636224125956636359995327793344470127538869
Wed Mar 25 22:46:33 2009  prp80 factor: 17526701832941984245416388922140767102049667569465043187924398853225270451740601
Wed Mar 25 22:46:33 2009  elapsed time 01:28:09 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 30.41 hours.
Scaled time: 80.57 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_4_164_3
n: 251064950625835833703382280840771182234664703586415536986577735970020000544583139843679582377840521338633043270402953869839020673640559582673460585332920269
skew: 0.77
deg: 5
c5: 49
c0: -13
m: 1000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 4400587)
Primes: RFBsize:348513, AFBsize:348526, largePrimes:15470826 encountered
Relations: rels:14467287, finalFF:713923
Max relations in full relation-set: 28
Initial matrix:
Pruned matrix :

Msieve: found 1171408 hash collisions in 15321624 relations
Msieve: matrix is 838936 x 839183 (226.7 MB)

Total sieving time: 30.00 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000
total time: 30.41 hours.
 --------- CPU info (if available) ----------

Mar 25, 2009 (3rd)

By Erik Branger / GGNFS, Msieve / Mar 25, 2009

(47·10¹⁵⁴+43)/9 = 5(2)₁₅₃7_<155> = 3 · 7 · 217015951 · 23192531703414525073_<20> · C126

C126 = P49 · P78

P49 = 1465580419519146912565525021259863883123452963969_<49>

P78 = 337121603846980406888182918563839484405915367888409034254610751275644373799801_<78>

Number: 52227_154
N=494078821595025196408271508880661445720441071385869313691441666275744356652202763243018257244781008472892898153247400472370169
  ( 126 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=1465580419519146912565525021259863883123452963969
 r2=337121603846980406888182918563839484405915367888409034254610751275644373799801
Version: 
Total time: 34.14 hours.
Scaled time: 33.66 units (timescale=0.986).
Factorization parameters were as follows:
n: 494078821595025196408271508880661445720441071385869313691441666275744356652202763243018257244781008472892898153247400472370169
m: 10000000000000000000000000000000
deg: 5
c5: 47
c0: 430
skew: 1.56
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1450000, 2750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 556521 x 556769
Total sieving time: 34.14 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000
total time: 34.14 hours.
 --------- CPU info (if available) ----------

Mar 25, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Mar 25, 2009

(47·10¹⁶⁸-11)/9 = 5(2)₁₆₇1_<169> = 42953 · 632473 · C159

C159 = P77 · P82

P77 = 93041312338394025755066831403637404825315085178858933751516025618646156596093_<77>

P82 = 2066065228441269232877887311452109654918977329340570718751096746897800608390142513_<82>

Number: 52221_168
N=192229420230899534496995068580248964574999947142737668924522307723339501553382715800958683080724049548225892858355344941318481757986963936844497016735249001709
  ( 159 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=93041312338394025755066831403637404825315085178858933751516025618646156596093 (pp77)
 r2=2066065228441269232877887311452109654918977329340570718751096746897800608390142513 (pp82)
Version: Msieve-1.39
Total time: 57.84 hours.
Scaled time: 148.72 units (timescale=2.571).
Factorization parameters were as follows:
n: 192229420230899534496995068580248964574999947142737668924522307723339501553382715800958683080724049548225892858355344941318481757986963936844497016735249001709
m: 5000000000000000000000000000000000
deg: 5
c5: 376
c0: -275
skew: 0.94
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 913109 x 913357
Total sieving time: 57.84 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 57.84 hours.
 --------- CPU info (if available) ----------

(4·10²⁴¹-1)/3 = 1(3)₂₄₁_<242> = 13 · 3784757 · 4646801 · 183261467 · 52651626410827_<14> · 3917565792818569_<16> · 9984057494986111353041_<22> · 423978422171785937525330791300274672892443_<42> · C126

C126 = P44 · P82

P44 = 56919955399919399921032613355018851582842693_<44>

P82 = 6403076371209830662961764899764369901555755044549161602051092579478800140181888067_<82>

Number: 13333_241
N=364462821471541316916182370125769150792316542042148094133332048440810743632250528660469332549245321864282313669340167794844431
  ( 126 digits)
Divisors found:
 r1=56919955399919399921032613355018851582842693 (pp44)
 r2=6403076371209830662961764899764369901555755044549161602051092579478800140181888067 (pp82)
Version: Msieve-1.39
Total time: 90.96 hours.
Scaled time: 158.17 units (timescale=1.739).
Factorization parameters were as follows:
name: 13333_241
n: 364462821471541316916182370125769150792316542042148094133332048440810743632250528660469332549245321864282313669340167794844431
skew: 104881.74
# norm 1.56e+017
c5: 68280
c4: 20246049836
c3: 1031581154766598
c2: -149265930358695771868
c1: 3984915003571139614187031
c0: -123380521066506364881614258895
# alpha -5.78
Y1: 13341754081406329
Y0: -1397095912174927126195306
# Murphy_E 1.34e-010
# M 234978542453448223942047299040150843515415198217211451624943835103861081502650739162475339104672263335331634329759394120672071
type: gnfs
rlim: 8000000
alim: 8000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [4000000, 8200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1001662 x 1001910
Total sieving time: 90.96 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,125,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,27,27,51,51,2.5,2.5,100000
total time: 90.96 hours.
 --------- CPU info (if available) ----------

Mar 25, 2009

Factorizations of 544...447 and Factorizations of 544...449 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 24, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Mar 24, 2009

(47·10¹⁷⁰+43)/9 = 5(2)₁₆₉7_<171> = 397² · 12821581 · 709741139417_<12> · 2301500138073341378612732863_<28> · C120

C120 = P51 · P69

P51 = 480083270638162015012277626457696051905424961830297_<51>

P69 = 329537769239250933349558669210841259940463368184107656991978047362249_<69>

Number: n
N=158205570055183487273379513322996014641789534534660875883619430317468638627535936866361100062189469901987850488022257953
  ( 120 digits)
Divisors found:
 r1=480083270638162015012277626457696051905424961830297 (pp51)
 r2=329537769239250933349558669210841259940463368184107656991978047362249 (pp69)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 39.86 hours.
Scaled time: 106.47 units (timescale=2.671).
Factorization parameters were as follows:
name: KA_5_2_169_7
n: 158205570055183487273379513322996014641789534534660875883619430317468638627535936866361100062189469901987850488022257953
skew: 55677.21
# norm 2.84e+16
c5: 59400
c4: -15665912550
c3: -807592077619909
c2: 33222887004005503474
c1: 931840140544419999583792
c0: -24071922341916760519440992512
# alpha -6.24
Y1: 242445705203
Y0: -76751546911839328392471
# Murphy_E 3.27e-10
# M 1685311989380475577265181398064331751532813417905642689191093594604343860789446220243040490401329161826299123753053845
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4230001)
Primes: RFBsize:315948, AFBsize:315721, largePrimes:7686811 encountered
Relations: rels:7783655, finalFF:763522
Max relations in full relation-set: 28
Initial matrix: 631751 x 763522 with sparse part having weight 65387348.
Pruned matrix : 522836 x 526058 with weight 41896142.
Polynomial selection time: 5.21 hours.
Total sieving time: 32.60 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 1.50 hours.
Total square root time: 0.27 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 39.86 hours.
 --------- CPU info (if available) ----------

(47·10²⁰⁴+7)/9 = 5(2)₂₀₃3_<205> = 3² · C204

C204 = P56 · P149

P56 = 32435427185289642780743836726941466290571494203044552823_<56>

P149 = 17889294636557302013414769601901685301211205126351365730228586586267267345613074310366048610450327741439568237044298792141368152216691075010970173089_<149>

Number: n
N=580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247
  ( 204 digits)
SNFS difficulty: 206 digits.
Divisors found:

Tue Mar 24 14:41:42 2009  prp56 factor: 32435427185289642780743836726941466290571494203044552823
Tue Mar 24 14:41:42 2009  prp149 factor: 17889294636557302013414769601901685301211205126351365730228586586267267345613074310366048610450327741439568237044298792141368152216691075010970173089
Tue Mar 24 14:41:42 2009  elapsed time 25:05:37 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 157.28 hours.
Scaled time: 317.07 units (timescale=2.016).
Factorization parameters were as follows:
name: KA_5_2_203_3
n: 580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247
deg: 5
c5: 47
c0: 70
m: 100000000000000000000000000000000000000000
skew: 1.08
type: snfs
rlim: 12000000
alim: 12000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [6000000, 9099990)
Primes: RFBsize:788060, AFBsize:788074, largePrimes:37054617 encountered
Relations: rels:31751478, finalFF:79075
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 9063074 hash collisions in 46888137 relations
Msieve: matrix is 3779800 x 3780048 (1027.0 MB)

Total sieving time: 156.12 hours.
Total relation processing time: 1.15 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,12000000,12000000,29,29,58,58,2.5,2.5,100000
total time: 157.28 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368976k/3407296k available (2745k kernel code, 36940k reserved, 1424k data, 412k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830498)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454)
Total of 4 processors activated (22643.71 BogoMIPS).

(47·10¹⁶²+7)/9 = 5(2)₁₆₁3_<163> = 3 · 83 · 28447 · 59910937 · C149

C149 = P33 · P37 · P79

P33 = 677169855882163806082378185483179_<33>

P37 = 5496731340466694320360386942697835693_<37>

P79 = 3306064243695495188858715370392906167979916663834620388391227511084523258179119_<79>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 12305900993670026619980338207680961830364582789630242898677969682151698305106408426947801975811893341357262263082403247088756161137232942831386070593 (149 digits)
Using B1=1448000, B2=2140044280, polynomial Dickson(6), sigma=344506990
Step 1 took 22198ms
Step 2 took 8736ms
********** Factor found in step 2: 677169855882163806082378185483179
Found probable prime factor of 33 digits: 677169855882163806082378185483179
Composite cofactor 18172546941917347226698165407954137115963849562056879758917105037777316590135405923860492225765462654110141425494467 has 116 digits

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM]
Input number is 18172546941917347226698165407954137115963849562056879758917105037777316590135405923860492225765462654110141425494467 (116 digits)
Using B1=3640000, B2=8561127130, polynomial Dickson(6), sigma=2816991832
Step 1 took 36332ms
Step 2 took 14227ms
********** Factor found in step 2: 5496731340466694320360386942697835693
Found probable prime factor of 37 digits: 5496731340466694320360386942697835693
Probable prime cofactor 3306064243695495188858715370392906167979916663834620388391227511084523258179119 has 79 digits

Mar 24, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Mar 24, 2009

(49·10¹⁹⁹-13)/9 = 5(4)₁₉₈3_<200> = 1913 · 4583 · 5882926056937_<13> · 1218401765880031784578024309927_<31> · 4907818000181670992135063669683_<31> · C120

C120 = P54 · P66

P54 = 382862862267837988347685597468140406206315789449064437_<54>

P66 = 461076664664287937538598147921472880754573683407889104041697315173_<66>

Number: 54443_199
N=176529131558277395295848214656542631892093690847442977004772986008117440783537228870033700974644012582018395859574802601
  ( 120 digits)
Divisors found:
 r1=382862862267837988347685597468140406206315789449064437 (pp54)
 r2=461076664664287937538598147921472880754573683407889104041697315173 (pp66)
Version: Msieve-1.39
Total time: 34.80 hours.
Scaled time: 60.38 units (timescale=1.735).
Factorization parameters were as follows:
name: 54443_199
n: 176529131558277395295848214656542631892093690847442977004772986008117440783537228870033700974644012582018395859574802601
skew: 59649.00
# norm 2.13e+016
c5: 49140
c4: -7417611066
c3: -888921018349013
c2: 25278019887156247159
c1: 886039038126969350535769
c0: -11713735379912792142821591589
# alpha -5.96
Y1: 3967998397231
Y0: -81484852731824154537860
# Murphy_E 3.16e-010
# M 128248013014603672007157954630463537972435946001750055529136290548333258835222509238735059376381621761948624658563372549
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4170001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 637939 x 638187
Total sieving time: 34.80 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 34.80 hours.
 --------- CPU info (if available) ----------

(49·10¹⁵⁷-13)/9 = 5(4)₁₅₆3_<158> = 47 · 53² · 3067 · C150

C150 = P46 · P104

P46 = 3500992370764356766315734545757211678902724333_<46>

P104 = 38405996066735363768333922495487422849558454494069750646053519783449675603954475673158889673318407032931_<104>

Number: 54443_157
N=134459099221246402322816172819154065510441731566376235533720791826155841719807351755353346138400212316515559376872179170380656802454630653643146010023
  ( 150 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=3500992370764356766315734545757211678902724333 (pp46)
 r2=38405996066735363768333922495487422849558454494069750646053519783449675603954475673158889673318407032931 (pp104)
Version: Msieve-1.39
Total time: 27.90 hours.
Scaled time: 71.73 units (timescale=2.571).
Factorization parameters were as follows:
n: 134459099221246402322816172819154065510441731566376235533720791826155841719807351755353346138400212316515559376872179170380656802454630653643146010023
m: 20000000000000000000000000000000
deg: 5
c5: 1225
c0: -104
skew: 0.61
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1600000, 3100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 570062 x 570310
Total sieving time: 27.90 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000
total time: 27.90 hours.
 --------- CPU info (if available) ----------

(16·10¹⁶⁹+17)/3 = 5(3)₁₆₈9_<170> = 25717 · 4507879 · C159

C159 = P36 · P124

P36 = 117980842480867583939408945317682323_<36>

P124 = 3899372097972789414698208696244062153377248699113952186123882034637330975141875979630721018894931532069809165030022672431651_<124>

Number: 53339_169
N=460051205265217827867701313446325309642435347740758774579621175352669685683423258785786058802508686637912682582855982468213333463621214818058817838949948405273
  ( 159 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=117980842480867583939408945317682323 (pp36)
 r2=3899372097972789414698208696244062153377248699113952186123882034637330975141875979630721018894931532069809165030022672431651 (pp124)
Version: Msieve-1.39
Total time: 42.98 hours.
Scaled time: 110.50 units (timescale=2.571).
Factorization parameters were as follows:
n: 460051205265217827867701313446325309642435347740758774579621175352669685683423258785786058802508686637912682582855982468213333463621214818058817838949948405273
m: 10000000000000000000000000000000000
deg: 5
c5: 8
c0: 85
skew: 1.60
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 4450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 819069 x 819316
Total sieving time: 42.98 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 42.98 hours.
 --------- CPU info (if available) ----------

Mar 24, 2009 (3rd)

By Erik Branger / GGNFS, Msieve / Mar 24, 2009

(16·10¹⁵³+17)/3 = 5(3)₁₅₂9_<154> = 181 · 35354371022851_<14> · 7978261056929857142957_<22> · C117

C117 = P48 · P69

P48 = 264723415122518858514699565296543054555719138609_<48>

P69 = 394617588357467205736723452214598506058331081720963009624925936387913_<69>

Number: 53339_153
N=104464515657401055928513502186110775732201553600729263450936442463049596896934901716742173064842467251215741239233017
  ( 117 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=264723415122518858514699565296543054555719138609
 r2=394617588357467205736723452214598506058331081720963009624925936387913
Version: 
Total time: 26.42 hours.
Scaled time: 20.69 units (timescale=0.783).
Factorization parameters were as follows:
n: 104464515657401055928513502186110775732201553600729263450936442463049596896934901716742173064842467251215741239233017
m: 4000000000000000000000000000000
deg: 5
c5: 125
c0: 136
skew: 1.02
type: snfs
lss: 1
rlim: 2700000
alim: 2700000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2700000/2700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1350000, 2050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 387890 x 388138
Total sieving time: 26.42 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,50,50,2.4,2.4,100000
total time: 26.42 hours.
 --------- CPU info (if available) ----------

Mar 24, 2009 (2nd)

By Max Dettweiler / GGNFS, msieve v1.40beta2 / Mar 24, 2009

(49·10¹²⁹-13)/9 = 5(4)₁₂₈3_<130> = C130

C130 = P44 · P87

P44 = 20839062423751865311924060808738807499975091_<44>

P87 = 261261487380497348335111454787673218382349317230937862709249245977725305196403288090873_<87>

Number: 54443_129
N=5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
  ( 130 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=20839062423751865311924060808738807499975091 (pp44)
 r2=261261487380497348335111454787673218382349317230937862709249245977725305196403288090873 (pp87)
Version: Msieve-1.39
Total time: 3.19 hours.
Scaled time: 5.21 units (timescale=1.633).
Factorization parameters were as follows:
n: 5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
m: 100000000000000000000000000
deg: 5
c5: 49
c0: -130
skew: 1.22
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3

Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 157349 x 157597
Total sieving time: 3.19 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 3.19 hours.
 --------- CPU info (if available) ----------
[    0.371579] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456481] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.12 BogoMIPS (lpj=8800256)
[    0.004000] Calibrating delay using timer specific routine.. 4400.40 BogoMIPS (lpj=8800811)
[    0.460049] Total of 2 processors activated (8800.53 BogoMIPS).

Mar 24, 2009

GMP-ECM 6.2.2 has been released

Mar 23, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Mar 23, 2009

(49·10¹³⁶-13)/9 = 5(4)₁₃₅3_<137> = 79 · 139 · 26881 · 84933809214398144209871_<23> · C106

C106 = P33 · P74

P33 = 125847487970644875553830835870751_<33>

P74 = 17256038650001398282032180042544723209657376815989641751284647004305394703_<74>

Number: n
N=2171629116427034008262569406122406716652087870362523529087901011585934547193430581966660132012993748031953
  ( 106 digits)
SNFS difficulty: 137 digits.
Divisors found:

Mon Mar 23 03:16:52 2009  prp33 factor: 125847487970644875553830835870751
Mon Mar 23 03:16:52 2009  prp74 factor: 17256038650001398282032180042544723209657376815989641751284647004305394703
Mon Mar 23 03:16:52 2009  elapsed time 00:11:15 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 3.90 hours.
Scaled time: 10.37 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_4_135_3
n: 2171629116427034008262569406122406716652087870362523529087901011585934547193430581966660132012993748031953
skew: 0.48
deg: 5
c5: 490
c0: -13
m: 1000000000000000000000000000
type: snfs
rlim: 900000
alim: 900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 1353901)
Primes: RFBsize:71274, AFBsize:71505, largePrimes:6541331 encountered
Relations: rels:6007484, finalFF:107350
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 727967 hash collisions in 6710840 relations
Msieve: matrix is 176657 x 176893 (45.9 MB)

Total sieving time: 3.80 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,900000,900000,28,28,56,56,2.4,2.4,75000
total time: 3.90 hours.
 --------- CPU info (if available) ----------

(49·10¹⁴⁶-13)/9 = 5(4)₁₄₅3_<147> = 3 · 23 · C145

C145 = P65 · P81

P65 = 73830498158509907022394810208166019095040149681165283254334567363_<65>

P81 = 106873167480281185337382613792493068629199332855411315792688634423552805727583669_<81>

Number: n
N=7890499194847020933977455716586151368760064412238325281803542673107890499194847020933977455716586151368760064412238325281803542673107890499194847
  ( 145 digits)
SNFS difficulty: 147 digits.
Divisors found:

Mon Mar 23 13:37:42 2009  prp65 factor: 73830498158509907022394810208166019095040149681165283254334567363
Mon Mar 23 13:37:42 2009  prp81 factor: 106873167480281185337382613792493068629199332855411315792688634423552805727583669
Mon Mar 23 13:37:42 2009  elapsed time 00:16:47 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 9.42 hours.
Scaled time: 25.05 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_4_145_3
n: 7890499194847020933977455716586151368760064412238325281803542673107890499194847020933977455716586151368760064412238325281803542673107890499194847
skew: 0.48
deg: 5
c5: 490
c0: -13
m: 100000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2849741)
Primes: RFBsize:114155, AFBsize:114387, largePrimes:9440774 encountered
Relations: rels:8881276, finalFF:237685
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1299095 hash collisions in 10127488 relations
Msieve: matrix is 296878 x 297126 (77.5 MB)

Total sieving time: 9.21 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,56,56,2.4,2.4,100000
total time: 9.42 hours.
 --------- CPU info (if available) ----------

(47·10¹⁶⁰-11)/9 = 5(2)₁₅₉1_<161> = 3² · 13² · 929 · 615289 · 1614723877096292986341793487631067_<34> · C116

C116 = P55 · P62

P55 = 3417337460494739626420771102558070436997856679143288723_<55>

P62 = 10885418609842797831468671827111280439846804963174619275986981_<62>

Number: n
N=37199148788582365677151994359438136376925389872701302600149177581980521614758458078941790703622822529963458072115263
  ( 116 digits)
Divisors found:

Mon Mar 23 18:21:00 2009  prp55 factor: 3417337460494739626420771102558070436997856679143288723
Mon Mar 23 18:21:00 2009  prp62 factor: 10885418609842797831468671827111280439846804963174619275986981
Mon Mar 23 18:21:00 2009  elapsed time 00:43:35 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 21.22 hours.
Scaled time: 56.01 units (timescale=2.639).
Factorization parameters were as follows:
name: KA_5_2_159_1
n: 37199148788582365677151994359438136376925389872701302600149177581980521614758458078941790703622822529963458072115263
skew: 71051.95
# norm 1.50e+16
c5: 31020
c4: -4568203496
c3: -650994879945791
c2: 21226493527766243622
c1: 1134333360693395111011895
c0: -8668750557182613034144373155
# alpha -6.50
Y1: 646741172849
Y0: -16435341978766525421481
# Murphy_E 4.84e-10
# M 28697786502530949098227155344670279630021951848559771566053143617605185826843583689525558783262810034586906964477928
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 3510491)
Primes: RFBsize:315948, AFBsize:315927, largePrimes:7299564 encountered
Relations: rels:7154500, finalFF:669197
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 567717 hash collisions in 7651579 relations
Msieve: matrix is 560477 x 560725 (154.2 MB)

Total sieving time: 20.95 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 21.22 hours.
 --------- CPU info (if available) ----------

(46·10¹⁷⁴+53)/9 = 5(1)₁₇₃7_<175> = 11 · 110557 · 77883837686821_<14> · 111420482169715189_<18> · 2910487467143313244591_<22> · C117

C117 = P42 · P75

P42 = 536853205010070477751570463792644371118157_<42>

P75 = 309957915371554430586833991064591498214078894243423889658794630549706504457_<75>

Number: n
N=166401900285459186183164258465440493370443079394472429719834326550583531484317913711130389138522747212789132994125749
  ( 117 digits)
Divisors found:

Mon Mar 23 20:10:51 2009  prp42 factor: 536853205010070477751570463792644371118157
Mon Mar 23 20:10:51 2009  prp75 factor: 309957915371554430586833991064591498214078894243423889658794630549706504457
Mon Mar 23 20:10:51 2009  elapsed time 00:34:07 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 22.73 hours.
Scaled time: 60.50 units (timescale=2.662).
Factorization parameters were as follows:
name: KA_5_1_173_7
n: 166401900285459186183164258465440493370443079394472429719834326550583531484317913711130389138522747212789132994125749
skew: 40828.59
# norm 4.82e+15
c5: 68640
c4: 381354376
c3: -346318543916472
c2: -1356621578298215941
c1: 235682672015256546584246
c0: 1514919480965173090953299231
# alpha -5.53
Y1: 1090532184019
Y0: -18919783983081763516780
# Murphy_E 4.53e-10
# M 111681274936674277178175601615880864336178708841231058862797851527797567703832190659576344088915678181723073994938108
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 3630281)
Primes: RFBsize:315948, AFBsize:316486, largePrimes:7414964 encountered
Relations: rels:7356594, finalFF:692768
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 607005 hash collisions in 7889899 relations
Msieve: matrix is 528742 x 528990 (145.4 MB)

Total sieving time: 22.42 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 22.73 hours.
 --------- CPU info (if available) ----------

(49·10²⁰⁵-31)/9 = 5(4)₂₀₄1_<206> = 3 · 47 · C204

C204 = P38 · P166

P38 = 63857407154518619099432007817527624871_<38>

P166 = 6046766207221483202200867690264664743792040332470375333789197689476780699012131797397027054060393163481932245065472333058710972868763794831723965812621141889670190331_<166>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 386130811662726556343577620173364854215918045705279747832939322301024428684003152088258471237194641449960598896769109535066981875492513790386130811662726556343577620173364854215918045705279747832939322301 (204 digits)
Using B1=2254000, B2=3567637720, polynomial Dickson(6), sigma=1092356064
Step 1 took 44047ms
Step 2 took 17234ms
********** Factor found in step 2: 63857407154518619099432007817527624871
Found probable prime factor of 38 digits: 63857407154518619099432007817527624871
Probable prime cofactor 6046766207221483202200867690264664743792040332470375333789197689476780699012131797397027054060393163481932245065472333058710972868763794831723965812621141889670190331 has 166 digits

Mar 23, 2009 (4th)

By Erik Branger / GGNFS, Msieve / Mar 23, 2009

(16·10¹⁵⁵+17)/3 = 5(3)₁₅₄9_<156> = 269 · 857 · 5345787068339760725287117_<25> · C126

C126 = P36 · P40 · P52

P36 = 133580396914047305026081348186586773_<36>

P40 = 1641967491171100517839361762257277209237_<40>

P52 = 1973089047991938179155944152604719461286180910126899_<52>

Number: 53339_155
N=432766833624903841995769451831156239493595362335642487063658241830861851563850104811991408368391566906660453126060429189684699
  ( 126 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=133580396914047305026081348186586773
 r2=1641967491171100517839361762257277209237
 r3=1973089047991938179155944152604719461286180910126899
Version: 
Total time: 19.87 hours.
Scaled time: 20.08 units (timescale=1.011).
Factorization parameters were as follows:
n: 432766833624903841995769451831156239493595362335642487063658241830861851563850104811991408368391566906660453126060429189684699
m: 10000000000000000000000000000000
deg: 5
c5: 16
c0: 17
skew: 1.01
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 401024 x 401272
Total sieving time: 19.87 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 19.87 hours.
 --------- CPU info (if available) ----------

Mar 23, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Mar 23, 2009

(49·10¹⁴⁰-13)/9 = 5(4)₁₃₉3_<141> = 3 · 10501 · 22541 · 689699 · C127

C127 = P33 · P41 · P54

P33 = 207071850488006696795938318543661_<33>

P41 = 22474022215667142175693151054126926046513_<41>

P54 = 238872971288671773181147192316633901673882791915267263_<54>

Number: 54443_140
N=1111652072716786806280199894478985340144711508394996871064426887611081159266241363692668499358204687809656342000550329708807459
  ( 127 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=207071850488006696795938318543661 (pp33)
 r2=22474022215667142175693151054126926046513 (pp41)
 r3=238872971288671773181147192316633901673882791915267263 (pp54)
Version: Msieve-1.39
Total time: 4.00 hours.
Scaled time: 6.94 units (timescale=1.735).
Factorization parameters were as follows:
n: 1111652072716786806280199894478985340144711508394996871064426887611081159266241363692668499358204687809656342000550329708807459
m: 10000000000000000000000000000
deg: 5
c5: 49
c0: -13
skew: 0.77
type: snfs
lss: 1
rlim: 1610000
alim: 1610000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1610000/1610000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [805000, 1505001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 220560 x 220808
Total sieving time: 4.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000
total time: 4.00 hours.
 --------- CPU info (if available) ----------

(49·10¹⁴⁵-13)/9 = 5(4)₁₄₄3_<146> = 1687354103_<10> · 3505546146359_<13> · C124

C124 = P40 · P85

P40 = 7140402236701543140617963582986208678971_<40>

P85 = 1289047654260669015173951513328700605459640910666217630944435952587966282067732957329_<85>

Number: 54443_145
N=9204318753697758502580249941200569767639330400560493094684823652953383377250635701260550464876367513699991278670232202628459
  ( 124 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=7140402236701543140617963582986208678971 (pp40)
 r2=1289047654260669015173951513328700605459640910666217630944435952587966282067732957329 (pp85)
Version: Msieve-1.39
Total time: 5.93 hours.
Scaled time: 10.31 units (timescale=1.739).
Factorization parameters were as follows:
n: 9204318753697758502580249941200569767639330400560493094684823652953383377250635701260550464876367513699991278670232202628459
m: 100000000000000000000000000000
deg: 5
c5: 49
c0: -13
skew: 0.77
type: snfs
lss: 1
rlim: 1950000
alim: 1950000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1950000/1950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [975000, 1975001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 285559 x 285807
Total sieving time: 5.93 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000
total time: 5.93 hours.
 --------- CPU info (if available) ----------

(49·10¹⁴⁴-31)/9 = 5(4)₁₄₃1_<145> = 173 · 2999 · 16657 · 951427 · 2585941 · C123

C123 = P55 · P68

P55 = 3257882588377989083926255526466788253796211702624682169_<55>

P68 = 78596770878296901617141918915241683753362330196819502016865089290893_<68>

Number: 54441_144
N=256059051347137664296684943791344848347371374573110192549585933050014669914539392291032586449386941150008047188499711186917
  ( 123 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=3257882588377989083926255526466788253796211702624682169 (pp55)
 r2=78596770878296901617141918915241683753362330196819502016865089290893 (pp68)
Version: Msieve-1.39
Total time: 9.85 hours.
Scaled time: 25.32 units (timescale=2.571).
Factorization parameters were as follows:
n: 256059051347137664296684943791344848347371374573110192549585933050014669914539392291032586449386941150008047188499711186917
m: 100000000000000000000000000000
deg: 5
c5: 49
c0: -310
skew: 1.45
type: snfs
lss: 1
rlim: 1950000
alim: 1950000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1950000/1950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [975000, 2575001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 330263 x 330511
Total sieving time: 9.85 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000
total time: 9.85 hours.
 --------- CPU info (if available) ----------

(49·10¹⁵²-13)/9 = 5(4)₁₅₁3_<153> = 3² · 491 · 632557 · 1592703598113809_<16> · C129

C129 = P55 · P74

P55 = 2146907550860162740600213632708655391877338081071796699_<55>

P74 = 56961523739466424569149913442650025242540002908402280547451425617956522631_<74>

Number: 54443_152
N=122291125424760880247517015235560595578717771861593788079807861507241681725560766919603504057041448257822793649727924561424595069
  ( 129 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=2146907550860162740600213632708655391877338081071796699 (pp55)
 r2=56961523739466424569149913442650025242540002908402280547451425617956522631 (pp74)
Version: Msieve-1.39
Total time: 16.42 hours.
Scaled time: 28.56 units (timescale=1.739).
Factorization parameters were as follows:
n: 122291125424760880247517015235560595578717771861593788079807861507241681725560766919603504057041448257822793649727924561424595069
m: 2000000000000000000000000000000
deg: 5
c5: 1225
c0: -104
skew: 0.61
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 534392 x 534640
Total sieving time: 16.42 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 16.42 hours.
 --------- CPU info (if available) ----------

(49·10¹⁶¹-13)/9 = 5(4)₁₆₀3_<162> = 3² · C161

C161 = P41 · P120

P41 = 89340062336934973963648121180445133883587_<41>

P120 = 677118703279485685836228095722187177748680567602212027120674408179765141637070828398608720395665830122030286741076835521_<120>

Number: 54443_161
N=60493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827
  ( 161 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=89340062336934973963648121180445133883587 (pp41)
 r2=677118703279485685836228095722187177748680567602212027120674408179765141637070828398608720395665830122030286741076835521 (pp120)
Version: Msieve-1.39
Total time: 36.44 hours.
Scaled time: 93.68 units (timescale=2.571).
Factorization parameters were as follows:
n: 60493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827
m: 200000000000000000000000000000000
deg: 5
c5: 245
c0: -208
skew: 0.97
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 3800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 705300 x 705548
Total sieving time: 36.44 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 36.44 hours.
 --------- CPU info (if available) ----------

Mar 23, 2009 (2nd)

By Sinkiti Sibata / Msieve, GGNFS / Mar 23, 2009

(49·10¹²³-13)/9 = 5(4)₁₂₂3_<124> = 79 · 7854023 · 96574919997336701_<17> · C98

C98 = P39 · P60

P39 = 155032799336605825909522832709907573331_<39>

P60 = 586065780886139499566709891878394247094033801102050578861509_<60>

Sun Mar 22 22:14:39 2009  Msieve v. 1.39
Sun Mar 22 22:14:39 2009  random seeds: 13f8fae4 833acdc7
Sun Mar 22 22:14:39 2009  Msieve v. 1.39
Sun Mar 22 22:14:39 2009  factoring 90859418606172063134774748261539956958066980337601966602849256308594895491730641401085698910816479 (98 digits)
Sun Mar 22 22:14:40 2009  searching for 15-digit factors
Sun Mar 22 22:14:41 2009  commencing quadratic sieve (98-digit input)
Sun Mar 22 22:14:42 2009  using multiplier of 1
Sun Mar 22 22:14:42 2009  using 32kb Intel Core sieve core
Sun Mar 22 22:14:42 2009  sieve interval: 36 blocks of size 32768
Sun Mar 22 22:14:42 2009  processing polynomials in batches of 6
Sun Mar 22 22:14:42 2009  using a sieve bound of 2540407 (92941 primes)
Sun Mar 22 22:14:42 2009  using large prime bound of 381061050 (28 bits)
Sun Mar 22 22:14:42 2009  using double large prime bound of 2791194835856850 (43-52 bits)
Sun Mar 22 22:14:42 2009  using trial factoring cutoff of 52 bits
Sun Mar 22 22:14:42 2009  polynomial 'A' values have 13 factors
Mon Mar 23 05:36:50 2009  93057 relations (22480 full + 70577 combined from 1401100 partial), need 93037
Mon Mar 23 05:36:52 2009  begin with 1423580 relations
Mon Mar 23 05:36:53 2009  reduce to 244565 relations in 11 passes
Mon Mar 23 05:36:53 2009  attempting to read 244565 relations
Mon Mar 23 05:36:57 2009  recovered 244565 relations
Mon Mar 23 05:36:57 2009  recovered 232392 polynomials
Mon Mar 23 05:36:57 2009  attempting to build 93057 cycles
Mon Mar 23 05:36:58 2009  found 93057 cycles in 5 passes
Mon Mar 23 05:36:58 2009  distribution of cycle lengths:
Mon Mar 23 05:36:58 2009     length 1 : 22480
Mon Mar 23 05:36:58 2009     length 2 : 16000
Mon Mar 23 05:36:58 2009     length 3 : 15708
Mon Mar 23 05:36:58 2009     length 4 : 12614
Mon Mar 23 05:36:58 2009     length 5 : 9517
Mon Mar 23 05:36:58 2009     length 6 : 6655
Mon Mar 23 05:36:58 2009     length 7 : 4213
Mon Mar 23 05:36:58 2009     length 9+: 5870
Mon Mar 23 05:36:58 2009  largest cycle: 22 relations
Mon Mar 23 05:36:58 2009  matrix is 92941 x 93057 (25.3 MB) with weight 6271809 (67.40/col)
Mon Mar 23 05:36:58 2009  sparse part has weight 6271809 (67.40/col)
Mon Mar 23 05:37:00 2009  filtering completed in 3 passes
Mon Mar 23 05:37:00 2009  matrix is 88962 x 89026 (24.4 MB) with weight 6046007 (67.91/col)
Mon Mar 23 05:37:00 2009  sparse part has weight 6046007 (67.91/col)
Mon Mar 23 05:37:00 2009  saving the first 48 matrix rows for later
Mon Mar 23 05:37:00 2009  matrix is 88914 x 89026 (15.1 MB) with weight 4767098 (53.55/col)
Mon Mar 23 05:37:00 2009  sparse part has weight 3421741 (38.44/col)
Mon Mar 23 05:37:00 2009  matrix includes 64 packed rows
Mon Mar 23 05:37:00 2009  using block size 35610 for processor cache size 1024 kB
Mon Mar 23 05:37:01 2009  commencing Lanczos iteration
Mon Mar 23 05:37:01 2009  memory use: 14.6 MB
Mon Mar 23 05:37:56 2009  lanczos halted after 1407 iterations (dim = 88908)
Mon Mar 23 05:37:56 2009  recovered 14 nontrivial dependencies
Mon Mar 23 05:37:57 2009  prp39 factor: 155032799336605825909522832709907573331
Mon Mar 23 05:37:57 2009  prp60 factor: 586065780886139499566709891878394247094033801102050578861509
Mon Mar 23 05:37:57 2009  elapsed time 07:23:18

(49·10¹²⁷-13)/9 = 5(4)₁₂₆3_<128> = C128

C128 = P31 · P42 · P55

P31 = 6388426039807794712107618364273_<31>

P42 = 952116963596930070553655728861886818163819_<42>

P55 = 8950955467063706290214969828203183230927212987298134689_<55>

Number: 54443_127
N=54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
  ( 128 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=6388426039807794712107618364273 (pp31)
 r2=952116963596930070553655728861886818163819 (pp42)
 r3=8950955467063706290214969828203183230927212987298134689 (pp55)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 5.21 hours.
Scaled time: 2.47 units (timescale=0.473).
Factorization parameters were as follows:
name: 54443_127
n: 54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
m: 20000000000000000000000000
deg: 5
c5: 1225
c0: -104
skew: 0.61
type: snfs
lss: 1
rlim: 1010000
alim: 1010000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1010000/1010000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [505000, 955001)
Primes: RFBsize:79251, AFBsize:79761, largePrimes:2639543 encountered
Relations: rels:2518399, finalFF:189964
Max relations in full relation-set: 28
Initial matrix: 159077 x 189964 with sparse part having weight 14598093.
Pruned matrix : 149777 x 150636 with weight 9259399.
Total sieving time: 4.74 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1010000,1010000,26,26,47,47,2.3,2.3,50000
total time: 5.21 hours.
 --------- CPU info (if available) ----------

(49·10¹⁴⁸-13)/9 = 5(4)₁₄₇3_<149> = C149

C149 = P43 · P107

P43 = 2400513117999809722405970619454289674628549_<43>

P107 = 22680336148218774284672959283888357977629962447175151940084971677874951003250148874102472003345354598125407_<107>

Number: 54443_148
N=54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
  ( 149 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=2400513117999809722405970619454289674628549 (pp43)
 r2=22680336148218774284672959283888357977629962447175151940084971677874951003250148874102472003345354598125407 (pp107)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 24.37 hours.
Scaled time: 62.76 units (timescale=2.575).
Factorization parameters were as follows:
name: 54443_148
n: 54444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
m: 500000000000000000000000000000
deg: 5
c5: 392
c0: -325
skew: 0.96
type: snfs
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 2050001)
Primes: RFBsize:169511, AFBsize:169201, largePrimes:6871087 encountered
Relations: rels:6772219, finalFF:417043
Max relations in full relation-set: 28
Initial matrix: 338777 x 417043 with sparse part having weight 43198668.
Pruned matrix : 312178 x 313935 with weight 29224094.
Total sieving time: 23.29 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.86 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 24.37 hours.
 --------- CPU info (if available) ----------

Mar 23, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Mar 23, 2009

4·10¹⁸⁹+1 = 4(0)₁₈₈1_<190> = 53 · 18077 · 2643247 · 96964568413_<11> · 3643105412001703_<16> · C151

C151 = P65 · P87

P65 = 13506270059310058545933600271041349759458769588496747569910410889_<65>

P87 = 331054716915185039351115638053193982176316954185352183355312068630530447500029226468933_<87>

Number: 40001_189
N=4471314411064930883583891865633043659313970480829502358467553263209442083755243393829592046821388226901398045864511661002729970137066357369440623411437
  ( 151 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=13506270059310058545933600271041349759458769588496747569910410889
 r2=331054716915185039351115638053193982176316954185352183355312068630530447500029226468933
Version: 
Total time: 141.02 hours.
Scaled time: 336.91 units (timescale=2.389).
Factorization parameters were as follows:
n: 4471314411064930883583891865633043659313970480829502358467553263209442083755243393829592046821388226901398045864511661002729970137066357369440623411437
m: 100000000000000000000000000000000000000
deg: 5
c5: 2
c0: 5
skew: 1.20
type: snfs
lss: 1
rlim: 10000000
alim: 10000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5000000, 8500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 20345343
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1869145 x 1869393
Total sieving time: 127.54 hours.
Total relation processing time: 3.81 hours.
Matrix solve time: 9.25 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,54,54,2.5,2.5,100000
total time: 141.02 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Mar 22, 2009 (7th)

By Ignacio Santos / GGNFS, Msieve / Mar 22, 2009

(47·10¹⁵⁶+43)/9 = 5(2)₁₅₅7_<157> = 337 · 9491 · 51820057 · C143

C143 = P66 · P78

P66 = 113581577204809565513012062452451703276361480125789394032540587489_<66>

P78 = 277400789537348018726881092733478275821865326592097829516429044974540705826297_<78>

Number: 52227_156
N=31507619193511423542935436939709466487629251657249002190486601003992558407642434351504182852325940175227371864963648554636926509550429565398233
  ( 143 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=113581577204809565513012062452451703276361480125789394032540587489 (pp66)
 r2=277400789537348018726881092733478275821865326592097829516429044974540705826297 (pp78)
Version: Msieve-1.39
Total time: 22.76 hours.
Scaled time: 58.51 units (timescale=2.571).
Factorization parameters were as follows:
n: 31507619193511423542935436939709466487629251657249002190486601003992558407642434351504182852325940175227371864963648554636926509550429565398233
m: 10000000000000000000000000000000
deg: 5
c5: 470
c0: 43
skew: 0.62
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 546997 x 547245
Total sieving time: 22.76 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 22.76 hours.
 --------- CPU info (if available) ----------

(11·10¹⁸⁰-17)/3 = 3(6)₁₇₉1_<181> = 29 · 160907 · C174

C174 = P60 · P115

P60 = 176325185615773625215171251016539484947995017242946993964977_<60>

P115 = 4456399789592708971102926999895272616391578598936752012977840464910707166020866224669377586464398546940798085854731_<115>

Number: 36661_180
N=785775520078028937826512051760605058579922192508001873574576418776634664887099416104497857654478645443012737635482879415817332622135053524528232878719334485280245767723756187
  ( 174 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=176325185615773625215171251016539484947995017242946993964977 (pp60)
 r2=4456399789592708971102926999895272616391578598936752012977840464910707166020866224669377586464398546940798085854731 (pp115)
Version: Msieve-1.39
Total time: 125.86 hours.
Scaled time: 218.88 units (timescale=1.739).
Factorization parameters were as follows:
n: 785775520078028937826512051760605058579922192508001873574576418776634664887099416104497857654478645443012737635482879415817332622135053524528232878719334485280245767723756187
m: 1000000000000000000000000000000000000
deg: 5
c5: 11
c0: -17
skew: 1.09
type: snfs
lss: 1
rlim: 7300000
alim: 7300000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7300000/7300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3650000, 5750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1437252 x 1437500
Total sieving time: 125.86 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7300000,7300000,28,28,53,53,2.5,2.5,100000
total time: 125.86 hours.
 --------- CPU info (if available) ----------

(11·10¹⁶⁷+1)/3 = 3(6)₁₆₆7_<168> = 7 · 36549260837_<11> · C157

C157 = P39 · P43 · P75

P39 = 759382237599703068226186568773861458713_<39>

P43 = 2871319944773339904197170463553741091654931_<43>

P75 = 657283560153017018445541294295980692946948772344737839113428718868371336571_<75>

Number: 36667_167
N=1433160375378246967538829528995992399920964573485346432325743080005051346816679054388297120909596040511367262821916323312932145259760301536419849988687539513
  ( 157 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=759382237599703068226186568773861458713 (pp39)
 r2=2871319944773339904197170463553741091654931 (pp43)
 r3=657283560153017018445541294295980692946948772344737839113428718868371336571 (pp75)
Version: Msieve-1.39
Total time: 48.74 hours.
Scaled time: 84.76 units (timescale=1.739).
Factorization parameters were as follows:
n: 1433160375378246967538829528995992399920964573485346432325743080005051346816679054388297120909596040511367262821916323312932145259760301536419849988687539513
m: 5000000000000000000000000000000000
deg: 5
c5: 44
c0: 125
skew: 1.23
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2400000, 5100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 953625 x 953873
Total sieving time: 48.74 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,52,52,2.4,2.4,100000
total time: 48.74 hours.
 --------- CPU info (if available) ----------

(49·10¹³⁴-13)/9 = 5(4)₁₃₃3_<135> = 3² · 419 · 7625281 · 10726355401104146640073_<23> · C103

C103 = P40 · P63

P40 = 3053575784592854265729449920832931528209_<40>

P63 = 578069825269579937655670787941745063303826005806320438808706249_<63>

Number: 54443_134
N=1765180020247011731278134277411512103003119124883459439773398747293564455928072644004637247393738078041
  ( 103 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=3053575784592854265729449920832931528209 (pp40)
 r2=578069825269579937655670787941745063303826005806320438808706249 (pp63)
Version: Msieve-1.39
Total time: 3.55 hours.
Scaled time: 6.18 units (timescale=1.739).
Factorization parameters were as follows:
n: 1765180020247011731278134277411512103003119124883459439773398747293564455928072644004637247393738078041
m: 1000000000000000000000000000
deg: 5
c5: 49
c0: -130
skew: 1.22
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1340001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 188447 x 188695
Total sieving time: 3.55 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 3.55 hours.
 --------- CPU info (if available) ----------

(16·10¹⁶⁸+17)/3 = 5(3)₁₆₇9_<169> = 11 · 227 · 5715255044861_<13> · C153

C153 = P57 · P97

P57 = 237162299947870602923360845817776486574128966845412187779_<57>

P97 = 1575792091453108964971588622205552962509706167218824000441526861593990073743591728636132377122173_<97>

Number: 53339_168
N=373718476648684572637694595120833703274454218519866059110650467541553477345097898834202957714009891476604066068299185279577128527994396935030163900523767
  ( 153 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=237162299947870602923360845817776486574128966845412187779 (pp57)
 r2=1575792091453108964971588622205552962509706167218824000441526861593990073743591728636132377122173 (pp97)
Version: Msieve-1.39
Total time: 42.58 hours.
Scaled time: 109.01 units (timescale=2.560).
Factorization parameters were as follows:
n: 373718476648684572637694595120833703274454218519866059110650467541553477345097898834202957714009891476604066068299185279577128527994396935030163900523767
m: 4000000000000000000000000000000000
deg: 5
c5: 125
c0: 136
skew: 1.02
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2400000, 4300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 836237 x 836485
Total sieving time: 42.58 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,52,52,2.4,2.4,100000
total time: 42.58 hours.
 --------- CPU info (if available) ----------

Mar 22, 2009 (6th)

By Sinkiti Sibata / GGNFS, Msieve / Mar 22, 2009

(49·10¹⁴²-31)/9 = 5(4)₁₄₁1_<143> = 3 · 151 · 2023864397_<10> · 93445315257300767_<17> · C114

C114 = P43 · P72

P43 = 1716464456102413811533728553420001764417351_<43>

P72 = 370238527354276951849469480548758543807489129866387577784804649042444353_<72>

Number: 54441_142
N=635501272483317646192623949232245073819008743834263346476971567061448712480937188483427830079004753214351885168903
  ( 114 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=1716464456102413811533728553420001764417351 (pp43)
 r2=370238527354276951849469480548758543807489129866387577784804649042444353 (pp72)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 17.43 hours.
Scaled time: 8.25 units (timescale=0.473).
Factorization parameters were as follows:
name: 54441_142
n: 635501272483317646192623949232245073819008743834263346476971567061448712480937188483427830079004753214351885168903
m: 20000000000000000000000000000
deg: 5
c5: 1225
c0: -248
skew: 0.73
type: snfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 2300001)
Primes: RFBsize:135072, AFBsize:135069, largePrimes:3971918 encountered
Relations: rels:4090853, finalFF:368042
Max relations in full relation-set: 28
Initial matrix: 270206 x 368042 with sparse part having weight 36737791.
Pruned matrix : 237779 x 239194 with weight 21727203.
Total sieving time: 15.54 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 1.60 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,49,49,2.3,2.3,100000
total time: 17.43 hours.
 --------- CPU info (if available) ----------

(49·10¹⁵¹-31)/9 = 5(4)₁₅₀1_<152> = 3 · 59 · 911 · 3407 · 339851027 · C135

C135 = P42 · P94

P42 = 286120041668600745533526907489500541024577_<42>

P94 = 1019184775083452183488830452860126346217069699358811608060108774820628340331919578837659937651_<94>

Number: 54441_151
N=291609190314880817618579760477553066552329881899773875289977893723653566933468795197023008294377682242284847777615153600283937478648627
  ( 135 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=286120041668600745533526907489500541024577 (pp42)
 r2=1019184775083452183488830452860126346217069699358811608060108774820628340331919578837659937651 (pp94)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 33.36 hours.
Scaled time: 85.21 units (timescale=2.554).
Factorization parameters were as follows:
name: 54441_151
n: 291609190314880817618579760477553066552329881899773875289977893723653566933468795197023008294377682242284847777615153600283937478648627
m: 1000000000000000000000000000000
deg: 5
c5: 490
c0: -31
skew: 0.58
type: snfs
lss: 1
rlim: 2500000
alim: 2500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1250000, 2150001)
Primes: RFBsize:183072, AFBsize:183427, largePrimes:8957809 encountered
Relations: rels:10343365, finalFF:1581511
Max relations in full relation-set: 28
Initial matrix: 366565 x 1581511 with sparse part having weight 194579687.
Pruned matrix : 248031 x 249927 with weight 42723486.
Total sieving time: 32.29 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.81 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000
total time: 33.36 hours.
 --------- CPU info (if available) ----------

(16·10¹²⁹+17)/3 = 5(3)₁₂₈9_<130> = 19 · 47 · 485858449 · C119

C119 = P39 · P80

P39 = 623219998062802938785799973843610813257_<39>

P80 = 19724051551602642903450015600131998699589330106576447898110400616964952612756111_<80>

Number: 53339_129
N=12292423369780424409286096691655132415558349762911633736102345174234635424394221190217084491352027704098652792906563527
  ( 119 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=623219998062802938785799973843610813257 (pp39)
 r2=19724051551602642903450015600131998699589330106576447898110400616964952612756111 (pp80)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.40 hours.
Scaled time: 1.61 units (timescale=0.473).
Factorization parameters were as follows:
name: 53339_129
n: 12292423369780424409286096691655132415558349762911633736102345174234635424394221190217084491352027704098652792906563527
m: 100000000000000000000000000
deg: 5
c5: 8
c0: 85
skew: 1.60
type: snfs
lss: 1
rlim: 1060000
alim: 1060000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1060000/1060000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [530000, 780001)
Primes: RFBsize:82832, AFBsize:82838, largePrimes:2518222 encountered
Relations: rels:2385744, finalFF:190256
Max relations in full relation-set: 28
Initial matrix: 165735 x 190256 with sparse part having weight 11939402.
Pruned matrix : 153355 x 154247 with weight 7704026.
Total sieving time: 2.98 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1060000,1060000,26,26,47,47,2.3,2.3,50000
total time: 3.40 hours.
 --------- CPU info (if available) ----------

(49·10¹⁵⁹-31)/9 = 5(4)₁₅₈1_<160> = 19 · 47 · 292246842172269949747673873_<27> · 3567663311467094797752460691_<28> · C103

C103 = P31 · P36 · P37

P31 = 1286968891444224528016148245727_<31>

P36 = 827600391338879236747200546595124171_<36>

P37 = 5490092802033096484410654870220759027_<37>

Sat Mar 21 15:17:17 2009  Msieve v. 1.39
Sat Mar 21 15:17:17 2009  random seeds: 58f44c04 9e64a594
Sat Mar 21 15:17:17 2009  factoring 5847475653589482742496899192309564306665185208063887360339104592368359867530932457634445089863133120559 (103 digits)
Sat Mar 21 15:17:18 2009  searching for 15-digit factors
Sat Mar 21 15:17:19 2009  commencing quadratic sieve (103-digit input)
Sat Mar 21 15:17:20 2009  using multiplier of 1
Sat Mar 21 15:17:20 2009  using 32kb Intel Core sieve core
Sat Mar 21 15:17:20 2009  sieve interval: 36 blocks of size 32768
Sat Mar 21 15:17:20 2009  processing polynomials in batches of 6
Sat Mar 21 15:17:20 2009  using a sieve bound of 3499337 (124945 primes)
Sat Mar 21 15:17:20 2009  using large prime bound of 524900550 (28 bits)
Sat Mar 21 15:17:20 2009  using double large prime bound of 4967508683642700 (44-53 bits)
Sat Mar 21 15:17:20 2009  using trial factoring cutoff of 53 bits
Sat Mar 21 15:17:20 2009  polynomial 'A' values have 13 factors
Sun Mar 22 13:17:00 2009  125221 relations (29552 full + 95669 combined from 1877452 partial), need 125041
Sun Mar 22 13:17:02 2009  begin with 1907004 relations
Sun Mar 22 13:17:05 2009  reduce to 331621 relations in 12 passes
Sun Mar 22 13:17:05 2009  attempting to read 331621 relations
Sun Mar 22 13:17:11 2009  recovered 331621 relations
Sun Mar 22 13:17:11 2009  recovered 323390 polynomials
Sun Mar 22 13:17:12 2009  attempting to build 125221 cycles
Sun Mar 22 13:17:12 2009  found 125221 cycles in 7 passes
Sun Mar 22 13:17:12 2009  distribution of cycle lengths:
Sun Mar 22 13:17:12 2009     length 1 : 29552
Sun Mar 22 13:17:12 2009     length 2 : 21309
Sun Mar 22 13:17:12 2009     length 3 : 20439
Sun Mar 22 13:17:12 2009     length 4 : 17242
Sun Mar 22 13:17:12 2009     length 5 : 13129
Sun Mar 22 13:17:12 2009     length 6 : 9202
Sun Mar 22 13:17:12 2009     length 7 : 6019
Sun Mar 22 13:17:12 2009     length 9+: 8329
Sun Mar 22 13:17:12 2009  largest cycle: 24 relations
Sun Mar 22 13:17:12 2009  matrix is 124945 x 125221 (37.4 MB) with weight 9296264 (74.24/col)
Sun Mar 22 13:17:12 2009  sparse part has weight 9296264 (74.24/col)
Sun Mar 22 13:17:15 2009  filtering completed in 3 passes
Sun Mar 22 13:17:15 2009  matrix is 120045 x 120109 (36.0 MB) with weight 8961886 (74.61/col)
Sun Mar 22 13:17:15 2009  sparse part has weight 8961886 (74.61/col)
Sun Mar 22 13:17:15 2009  saving the first 48 matrix rows for later
Sun Mar 22 13:17:15 2009  matrix is 119997 x 120109 (26.3 MB) with weight 7548817 (62.85/col)
Sun Mar 22 13:17:15 2009  sparse part has weight 6175038 (51.41/col)
Sun Mar 22 13:17:15 2009  matrix includes 64 packed rows
Sun Mar 22 13:17:15 2009  using block size 43690 for processor cache size 1024 kB
Sun Mar 22 13:17:17 2009  commencing Lanczos iteration
Sun Mar 22 13:17:17 2009  memory use: 23.0 MB
Sun Mar 22 13:19:16 2009  lanczos halted after 1899 iterations (dim = 119995)
Sun Mar 22 13:19:16 2009  recovered 17 nontrivial dependencies
Sun Mar 22 13:19:18 2009  prp31 factor: 1286968891444224528016148245727
Sun Mar 22 13:19:18 2009  prp36 factor: 827600391338879236747200546595124171
Sun Mar 22 13:19:18 2009  prp37 factor: 5490092802033096484410654870220759027
Sun Mar 22 13:19:18 2009  elapsed time 22:02:01

(49·10¹³⁹-13)/9 = 5(4)₁₃₈3_<140> = 43² · 5879 · 6361 · 259993 · 2700760419073_<13> · 10123937678771113627_<20> · C93

C93 = P46 · P47

P46 = 1205299344754500667641838377887933065643674837_<46>

P47 = 91895808846580213792838373174075953576019739123_<47>

Sun Mar 22 13:51:54 2009  Msieve v. 1.39
Sun Mar 22 13:51:54 2009  random seeds: 1c254e34 3755ed4b
Sun Mar 22 13:51:54 2009  factoring 110761958188467977456119371945228710724443759220876141066030782141391152874649874683779547951 (93 digits)
Sun Mar 22 13:51:55 2009  searching for 15-digit factors
Sun Mar 22 13:51:57 2009  commencing quadratic sieve (93-digit input)
Sun Mar 22 13:51:57 2009  using multiplier of 1
Sun Mar 22 13:51:57 2009  using 32kb Intel Core sieve core
Sun Mar 22 13:51:57 2009  sieve interval: 36 blocks of size 32768
Sun Mar 22 13:51:57 2009  processing polynomials in batches of 6
Sun Mar 22 13:51:57 2009  using a sieve bound of 1854599 (69412 primes)
Sun Mar 22 13:51:57 2009  using large prime bound of 209569687 (27 bits)
Sun Mar 22 13:51:57 2009  using double large prime bound of 951461467997464 (42-50 bits)
Sun Mar 22 13:51:57 2009  using trial factoring cutoff of 50 bits
Sun Mar 22 13:51:57 2009  polynomial 'A' values have 12 factors
Sun Mar 22 16:03:41 2009  69822 relations (17555 full + 52267 combined from 897392 partial), need 69508
Sun Mar 22 16:03:42 2009  begin with 914947 relations
Sun Mar 22 16:03:43 2009  reduce to 177819 relations in 9 passes
Sun Mar 22 16:03:43 2009  attempting to read 177819 relations
Sun Mar 22 16:03:45 2009  recovered 177819 relations
Sun Mar 22 16:03:45 2009  recovered 158523 polynomials
Sun Mar 22 16:03:46 2009  attempting to build 69822 cycles
Sun Mar 22 16:03:46 2009  found 69822 cycles in 6 passes
Sun Mar 22 16:03:46 2009  distribution of cycle lengths:
Sun Mar 22 16:03:46 2009     length 1 : 17555
Sun Mar 22 16:03:46 2009     length 2 : 12647
Sun Mar 22 16:03:46 2009     length 3 : 12035
Sun Mar 22 16:03:46 2009     length 4 : 9404
Sun Mar 22 16:03:46 2009     length 5 : 7018
Sun Mar 22 16:03:46 2009     length 6 : 4605
Sun Mar 22 16:03:46 2009     length 7 : 2822
Sun Mar 22 16:03:46 2009     length 9+: 3736
Sun Mar 22 16:03:46 2009  largest cycle: 21 relations
Sun Mar 22 16:03:46 2009  matrix is 69412 x 69822 (17.5 MB) with weight 4299783 (61.58/col)
Sun Mar 22 16:03:46 2009  sparse part has weight 4299783 (61.58/col)
Sun Mar 22 16:03:47 2009  filtering completed in 3 passes
Sun Mar 22 16:03:47 2009  matrix is 65537 x 65601 (16.5 MB) with weight 4051076 (61.75/col)
Sun Mar 22 16:03:47 2009  sparse part has weight 4051076 (61.75/col)
Sun Mar 22 16:03:47 2009  saving the first 48 matrix rows for later
Sun Mar 22 16:03:47 2009  matrix is 65489 x 65601 (9.7 MB) with weight 3112910 (47.45/col)
Sun Mar 22 16:03:47 2009  sparse part has weight 2157274 (32.88/col)
Sun Mar 22 16:03:47 2009  matrix includes 64 packed rows
Sun Mar 22 16:03:47 2009  using block size 26240 for processor cache size 1024 kB
Sun Mar 22 16:03:48 2009  commencing Lanczos iteration
Sun Mar 22 16:03:48 2009  memory use: 9.8 MB
Sun Mar 22 16:04:14 2009  lanczos halted after 1037 iterations (dim = 65489)
Sun Mar 22 16:04:14 2009  recovered 18 nontrivial dependencies
Sun Mar 22 16:04:14 2009  prp46 factor: 1205299344754500667641838377887933065643674837
Sun Mar 22 16:04:14 2009  prp47 factor: 91895808846580213792838373174075953576019739123
Sun Mar 22 16:04:14 2009  elapsed time 02:12:20

(49·10¹¹³-13)/9 = 5(4)₁₁₂3_<114> = 3 · C114

C114 = P47 · P67

P47 = 49270994758445485506745344522078417472249246961_<47>

P67 = 3683333011058680643342779360261730707241153817449805238013851687321_<67>

Number: 54443_113
N=181481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481
  ( 114 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=49270994758445485506745344522078417472249246961 (pp47)
 r2=3683333011058680643342779360261730707241153817449805238013851687321 (pp67)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.44 hours.
Scaled time: 1.15 units (timescale=0.473).
Factorization parameters were as follows:
name: 54443_113
n: 181481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481
m: 50000000000000000000000
deg: 5
c5: 392
c0: -325
skew: 0.96
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [300000, 550001)
Primes: RFBsize:49098, AFBsize:49136, largePrimes:1303299 encountered
Relations: rels:1299767, finalFF:165600
Max relations in full relation-set: 28
Initial matrix: 98299 x 165600 with sparse part having weight 8125362.
Pruned matrix : 77886 x 78441 with weight 2834014.
Total sieving time: 2.32 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000
total time: 2.44 hours.
 --------- CPU info (if available) ----------

(49·10¹⁴¹-13)/9 = 5(4)₁₄₀3_<142> = C142

C142 = P53 · P90

P53 = 29895894509244796665860680741717481942098627486442047_<53>

P90 = 182113448479049276921181897697664273046509544887453509951853505999576736492064061755845669_<90>

Number: 54443_141
N=5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
  ( 142 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=29895894509244796665860680741717481942098627486442047 (pp53)
 r2=182113448479049276921181897697664273046509544887453509951853505999576736492064061755845669 (pp90)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 14.53 hours.
Scaled time: 37.10 units (timescale=2.554).
Factorization parameters were as follows:
name: 54443_141
n: 5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443
m: 20000000000000000000000000000
deg: 5
c5: 245
c0: -208
skew: 0.97
type: snfs
lss: 1
rlim: 1750000
alim: 1750000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1750000/1750000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [875000, 2175001)
Primes: RFBsize:131608, AFBsize:131782, largePrimes:4300365 encountered
Relations: rels:4799866, finalFF:622644
Max relations in full relation-set: 28
Initial matrix: 263456 x 622644 with sparse part having weight 71808746.
Pruned matrix : 194268 x 195649 with weight 27959680.
Total sieving time: 14.09 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1750000,1750000,26,26,48,48,2.3,2.3,100000
total time: 14.53 hours.
 --------- CPU info (if available) ----------

(49·10¹²⁰-13)/9 = 5(4)₁₁₉3_<121> = 433 · 24517 · 1153799 · 1500979523_<10> · C99

C99 = P28 · P71

P28 = 9666149732721867133816317637_<28>

P71 = 30636553223357949753688263264707804811627036708515492327059389308255287_<71>

Number: 54443_120
N=296137510751480703017039742522270090064956369608944183048399620173500991977630933097560191476596819
  ( 99 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=9666149732721867133816317637 (pp28)
 r2=30636553223357949753688263264707804811627036708515492327059389308255287 (pp71)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.32 hours.
Scaled time: 1.03 units (timescale=0.446).
Factorization parameters were as follows:
name: 54443_120
n: 296137510751480703017039742522270090064956369608944183048399620173500991977630933097560191476596819
m: 1000000000000000000000000
deg: 5
c5: 49
c0: -13
skew: 0.77
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 575001)
Primes: RFBsize:60238, AFBsize:59821, largePrimes:1299470 encountered
Relations: rels:1274107, finalFF:150534
Max relations in full relation-set: 28
Initial matrix: 120123 x 150534 with sparse part having weight 6474460.
Pruned matrix : 102811 x 103475 with weight 3409529.
Total sieving time: 2.15 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 2.32 hours.
 --------- CPU info (if available) ----------

(49·10¹¹²-13)/9 = 5(4)₁₁₁3_<113> = 33751 · 713542013531_<12> · C97

C97 = P34 · P63

P34 = 3237808002986528818226382726266713_<34>

P63 = 698226429531598067180105615871883648384973706998991877568268031_<63>

Sun Mar 22 16:28:56 2009  Msieve v. 1.39
Sun Mar 22 16:28:56 2009  random seeds: d3015b48 7ed2183f
Sun Mar 22 16:28:56 2009  factoring 2260723121434117828143713675810233409179298217736488423452589864962066789740202246598297977352103 (97 digits)
Sun Mar 22 16:28:57 2009  searching for 15-digit factors
Sun Mar 22 16:28:58 2009  commencing quadratic sieve (97-digit input)
Sun Mar 22 16:28:59 2009  using multiplier of 7
Sun Mar 22 16:28:59 2009  using 32kb Intel Core sieve core
Sun Mar 22 16:28:59 2009  sieve interval: 36 blocks of size 32768
Sun Mar 22 16:28:59 2009  processing polynomials in batches of 6
Sun Mar 22 16:28:59 2009  using a sieve bound of 2363903 (87059 primes)
Sun Mar 22 16:28:59 2009  using large prime bound of 354585450 (28 bits)
Sun Mar 22 16:28:59 2009  using double large prime bound of 2451870804143850 (43-52 bits)
Sun Mar 22 16:28:59 2009  using trial factoring cutoff of 52 bits
Sun Mar 22 16:28:59 2009  polynomial 'A' values have 13 factors
Sun Mar 22 22:04:35 2009  87192 relations (21295 full + 65897 combined from 1307645 partial), need 87155
Sun Mar 22 22:04:37 2009  begin with 1328940 relations
Sun Mar 22 22:04:38 2009  reduce to 227421 relations in 10 passes
Sun Mar 22 22:04:38 2009  attempting to read 227421 relations
Sun Mar 22 22:04:42 2009  recovered 227421 relations
Sun Mar 22 22:04:42 2009  recovered 213881 polynomials
Sun Mar 22 22:04:42 2009  attempting to build 87192 cycles
Sun Mar 22 22:04:43 2009  found 87192 cycles in 5 passes
Sun Mar 22 22:04:43 2009  distribution of cycle lengths:
Sun Mar 22 22:04:43 2009     length 1 : 21295
Sun Mar 22 22:04:43 2009     length 2 : 15274
Sun Mar 22 22:04:43 2009     length 3 : 14822
Sun Mar 22 22:04:43 2009     length 4 : 11786
Sun Mar 22 22:04:43 2009     length 5 : 8794
Sun Mar 22 22:04:43 2009     length 6 : 5923
Sun Mar 22 22:04:43 2009     length 7 : 3909
Sun Mar 22 22:04:43 2009     length 9+: 5389
Sun Mar 22 22:04:43 2009  largest cycle: 20 relations
Sun Mar 22 22:04:43 2009  matrix is 87059 x 87192 (23.4 MB) with weight 5778193 (66.27/col)
Sun Mar 22 22:04:43 2009  sparse part has weight 5778193 (66.27/col)
Sun Mar 22 22:04:45 2009  filtering completed in 3 passes
Sun Mar 22 22:04:45 2009  matrix is 83157 x 83220 (22.4 MB) with weight 5551015 (66.70/col)
Sun Mar 22 22:04:45 2009  sparse part has weight 5551015 (66.70/col)
Sun Mar 22 22:04:45 2009  saving the first 48 matrix rows for later
Sun Mar 22 22:04:45 2009  matrix is 83109 x 83220 (14.0 MB) with weight 4373772 (52.56/col)
Sun Mar 22 22:04:45 2009  sparse part has weight 3161875 (37.99/col)
Sun Mar 22 22:04:45 2009  matrix includes 64 packed rows
Sun Mar 22 22:04:45 2009  using block size 33288 for processor cache size 1024 kB
Sun Mar 22 22:04:46 2009  commencing Lanczos iteration
Sun Mar 22 22:04:46 2009  memory use: 13.5 MB
Sun Mar 22 22:05:32 2009  lanczos halted after 1315 iterations (dim = 83108)
Sun Mar 22 22:05:32 2009  recovered 17 nontrivial dependencies
Sun Mar 22 22:05:33 2009  prp34 factor: 3237808002986528818226382726266713
Sun Mar 22 22:05:33 2009  prp63 factor: 698226429531598067180105615871883648384973706998991877568268031
Sun Mar 22 22:05:33 2009  elapsed time 05:36:37

Mar 22, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Mar 22, 2009

(47·10¹⁵⁴+61)/9 = 5(2)₁₅₃9_<155> = 223 · 2041669007527_<13> · C141

C141 = P67 · P74

P67 = 6287405169625602502477237795484824113448923850663462083007464764063_<67>

P74 = 18242892600702144900224066166443686086519340119714997012668019979791537123_<74>

Number: n
N=114700457246579318138478529527468263717968577260197719911362953388175243029481033280139922014098783960013610492455511266691921061547300810749
  ( 141 digits)
SNFS difficulty: 156 digits.
Divisors found:

Sun Mar 22 13:39:49 2009  prp67 factor: 6287405169625602502477237795484824113448923850663462083007464764063
Sun Mar 22 13:39:49 2009  prp74 factor: 18242892600702144900224066166443686086519340119714997012668019979791537123
Sun Mar 22 13:39:49 2009  elapsed time 01:25:39 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.36 hours.
Scaled time: 44.42 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_5_2_153_9
n: 114700457246579318138478529527468263717968577260197719911362953388175243029481033280139922014098783960013610492455511266691921061547300810749
deg: 5
c5: 47
c0: 610
m: 10000000000000000000000000000000
skew: 1.67
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [1500000, 10000000
)
Primes: RFBsize:216816, AFBsize:217102, largePrimes:24249774 encountered
Relations: rels:22372236, finalFF:558517
Max relations in full relation-set: 28
Initial matrix: 433983 x 558517 with sparse part having weight 89057458.
Pruned matrix : 399040 x 401273 with weight 56926209.

Msieve: found 2110438 hash collisions in 23723689 relations
Msieve: matrix is 535966 x 536214 (141.4 MB)

Total sieving time: 23.82 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,29,29,58,58,2.5,2.5,100000
total time: 24.36 hours.
 --------- CPU info (if available) ----------

(47·10¹²²+43)/9 = 5(2)₁₂₁7_<123> = 31 · C122

C122 = P58 · P64

P58 = 3553753901649698354047921541097460083255890435040418905481_<58>

P64 = 4740305210324396166746716284276132282091713424142937278623424357_<64>

Number: n
N=16845878136200716845878136200716845878136200716845878136200716845878136200716845878136200716845878136200716845878136200717
  ( 122 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=3553753901649698354047921541097460083255890435040418905481 (pp58)
 r2=4740305210324396166746716284276132282091713424142937278623424357 (pp64)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 1.59 hours.
Scaled time: 4.23 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_2_121_7
n: 16845878136200716845878136200716845878136200716845878136200716845878136200716845878136200716845878136200716845878136200717
skew: 0.39
deg: 5
c5: 4700
c0: 43
m: 1000000000000000000000000
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [300000, 660001)
Primes: RFBsize:49098, AFBsize:49206, largePrimes:4778585 encountered
Relations: rels:4334253, finalFF:160209
Max relations in full relation-set: 28
Initial matrix: 98371 x 160209 with sparse part having weight 17227502.
Pruned matrix : 87616 x 88171 with weight 7733167.
Total sieving time: 1.48 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,600000,600000,28,28,56,56,2.4,2.4,50000
total time: 1.59 hours.
 --------- CPU info (if available) ----------

(49·10¹¹⁷-13)/9 = 5(4)₁₁₆3_<118> = 223 · 185904631079077_<15> · C102

C102 = P47 · P55

P47 = 39440726016344745653943373742754827920013325257_<47>

P55 = 3329765108465687231084607438784113510264349945122473369_<55>

Number: n
N=131328353341779614268153512653441448934258520553999210062837824880361345306679232117334355334117580833
  ( 102 digits)
SNFS difficulty: 121 digits.
Divisors found:

Sun Mar 22 20:10:43 2009  prp47 factor: 39440726016344745653943373742754827920013325257
Sun Mar 22 20:10:43 2009  prp55 factor: 3329765108465687231084607438784113510264349945122473369
Sun Mar 22 20:10:43 2009  elapsed time 00:04:08 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 1.08 hours.
Scaled time: 2.88 units (timescale=2.660).
Factorization parameters were as follows:
name: KA_5_4_116_3
n: 131328353341779614268153512653441448934258520553999210062837824880361345306679232117334355334117580833
skew: 3.05
deg: 5
c5: 49
c0: -13000
m: 1000000000000000000000000
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 540613)
Primes: RFBsize:49098, AFBsize:49661, largePrimes:3831306 encountered
Relations: rels:3248478, finalFF:82968
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 187218 hash collisions in 3421566 relations
Msieve: matrix is 111486 x 111726 (29.9 MB)

Total sieving time: 1.04 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,28,28,56,56,2.4,2.4,50000
total time: 1.08 hours.
 --------- CPU info (if available) ----------

(49·10¹³⁰-13)/9 = 5(4)₁₂₉3_<131> = 29 · 8837 · C126

C126 = P38 · P89

P38 = 15365173779343757359334278547951668963_<38>

P89 = 13826531303417091869063585125914867774939884422495793079249247555637563832749104437904857_<89>

Number: n
N=212447056242539964976585299444125773860080634496979566495278255783654323492698975094701527060768962959205395981802392153853291
  ( 126 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=15365173779343757359334278547951668963 (pp38)
 r2=13826531303417091869063585125914867774939884422495793079249247555637563832749104437904857 (pp89)
Version: GGNFS-0.77.1-20060513-pentium-m
Total time: 1.87 hours.
Scaled time: 4.96 units (timescale=2.649).
Factorization parameters were as follows:
name: KA_5_4_129_3
n: 212447056242539964976585299444125773860080634496979566495278255783654323492698975094701527060768962959205395981802392153853291
skew: 0.77
deg: 5
c5: 49
c0: -13
m: 100000000000000000000000000
type: snfs
rlim: 850000
alim: 850000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 850000/850000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [425000, 785001)
Primes: RFBsize:67617, AFBsize:67170, largePrimes:5700028 encountered
Relations: rels:5209170, finalFF:264753
Max relations in full relation-set: 28
Initial matrix: 134851 x 264753 with sparse part having weight 26750384.
Pruned matrix : 109263 x 110001 with weight 8945134.
Total sieving time: 1.74 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.03 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,850000,850000,28,28,56,56,2.4,2.4,50000
total time: 1.87 hours.
 --------- CPU info (if available) ----------

Mar 22, 2009 (4th)

By Erik Branger / GMP-ECM, GGNFS, Msieve / Mar 22, 2009

(10²⁰⁴+17)/9 = (1)₂₀₃3_<204> = 23 · 773909 · 1540195883333_<13> · 1282146599377795849_<19> · 21676096960363463710282387103_<29> · C138

C138 = P37 · P101

P37 = 3563655936076273099916412456811109387_<37>

P101 = 40921284929194423257867202290995071601945357815830179626243613336714911803694463810877773792377543507_<101>

GMP-ECM 6.2 [powered by GMP 4.2.2] [ECM]
Input number is 145829379949792239395107343637243079763628528658681310890575160988171862082801967137706829973725352350567726447106111950156737778528600209 (138 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=560508884
Step 1 took 46594ms
********** Factor found in step 1: 3563655936076273099916412456811109387
Found probable prime factor of 37 digits: 3563655936076273099916412456811109387
Probable prime cofactor 40921284929194423257867202290995071601945357815830179626243613336714911803694463810877773792377543507 has 101 digits

(49·10¹⁰²-13)/9 = 5(4)₁₀₁3_<103> = 23 · 29 · C100

C100 = P36 · P64

P36 = 856284975732961798770754067476869163_<36>

P64 = 9532557040362265696725320268206781344444145146303960880095399683_<64>

Number: 54443_102
N=8162585373979676828252540396468432450441445943694819257038147592870231550891221056138597367982675329
  ( 100 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=856284975732961798770754067476869163
 r2=9532557040362265696725320268206781344444145146303960880095399683
Version: 
Total time: 0.67 hours.
Scaled time: 0.52 units (timescale=0.774).
Factorization parameters were as follows:
n: 8162585373979676828252540396468432450441445943694819257038147592870231550891221056138597367982675329
m: 50000000000000000000000000
deg: 4
c4: 196
c0: -325
skew: 1.13
type: snfs
lss: 1
rlim: 390000
alim: 390000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 390000/390000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [195000, 255001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 33044 x 33269
Total sieving time: 0.67 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105,4,0,0,0,0,0,0,0,0,390000,390000,25,25,44,44,2.2,2.2,20000
total time: 0.67 hours.
 --------- CPU info (if available) ----------

(49·10¹²⁶-13)/9 = 5(4)₁₂₅3_<127> = 1935510386548969_<16> · C112

C112 = P33 · P34 · P46

P33 = 886472740761278554450087477716581_<33>

P34 = 1905222917172293197745705906814437_<34>

P46 = 1665508609598934955964817532355973948697940251_<46>

Number: 54443_126
N=2812924426694466797269053611378786655841506454604882955955606250617376556226484570126893360140540172447027234147
  ( 112 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=886472740761278554450087477716581
 r2=1905222917172293197745705906814437
 r3=1665508609598934955964817532355973948697940251
Version: 
Total time: 3.21 hours.
Scaled time: 3.00 units (timescale=0.934).
Factorization parameters were as follows:
n: 2812924426694466797269053611378786655841506454604882955955606250617376556226484570126893360140540172447027234147
m: 20000000000000000000000000
deg: 5
c5: 245
c0: -208
skew: 0.97
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 137383 x 137631
Total sieving time: 3.21 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 3.21 hours.
 --------- CPU info (if available) ----------

Mar 22, 2009 (3rd)

By Max Dettweiler / GGNFS, msieve v1.40beta2 / Mar 22, 2009

(49·10¹²⁹-31)/9 = 5(4)₁₂₈1_<130> = 17 · 1051 · 1223 · 188833 · C118

C118 = P34 · P84

P34 = 7162696482730668159103867263627691_<34>

P84 = 184213322171955253139200172783060241904468670066761404841591156427180089235354386967_<84>

Number: 54441_129
N=1319464114793195299715358693826383356772564901259144652368208640721475989621654185864368906977656604154533991830703197
  ( 118 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=7162696482730668159103867263627691 (pp34)
 r2=184213322171955253139200172783060241904468670066761404841591156427180089235354386967 (pp84)
Version: Msieve-1.40
Total time: 3.93 hours.
Scaled time: 6.40 units (timescale=1.631).
Factorization parameters were as follows:
n: 1319464114793195299715358693826383356772564901259144652368208640721475989621654185864368906977656604154533991830703197
m: 100000000000000000000000000
deg: 5
c5: 49
c0: -310
skew: 1.45
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 167913 x 168161
Total sieving time: 3.93 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 3.93 hours.
 --------- CPU info (if available) ----------
[    0.371529] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.10 BogoMIPS (lpj=8800216)
[    0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800821)
[    0.460049] Total of 2 processors activated (8800.51 BogoMIPS).

Mar 22, 2009 (2nd)

By Serge Batalov / Msieve-1.40b2 / Mar 22, 2009

(47·10¹⁵⁸+7)/9 = 5(2)₁₅₇3_<159> = 103 · C157

C157 = P56 · P101

P56 = 71303755236789181010241436764968018401427992819337740943_<56>

P101 = 71105913643882583795061215112708628113247174708582329597976670564566008135825025418369512291553408087_<101>

SNFS difficulty: 161 digits.
Divisors found:
 r1=71303755236789181010241436764968018401427992819337740943 (pp56)
 r2=71105913643882583795061215112708628113247174708582329597976670564566008135825025418369512291553408087 (pp101)
Version: Msieve-1.40b2
Total time: 9.38 hours.
Scaled time: 26.62 units (timescale=2.840).
Factorization parameters were as follows:
n: 5070118662351672060409924487594390507011866235167206040992448759439050701186623516720604099244875943905070118662351672060409924487594390507011866235167206041
m: 50000000000000000000000000000000
deg: 5
c5: 376
c0: 175
skew: 0.86
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 655490 x 655738
Total sieving time: 9.38 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.55 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 9.38 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU1: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU2: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU3: AMD Phenom(tm) II X4 940 Processor stepping 02
Memory: 8173900k/9175040k available (2699k kernel code, 213168k reserved, 3164k data, 788k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 6012.77 BogoMIPS (lpj=12025552)
Calibrating delay using timer specific routine.. 6012.90 BogoMIPS (lpj=12025812)
Calibrating delay using timer specific routine.. 6012.85 BogoMIPS (lpj=12025719)
Calibrating delay using timer specific routine.. 6012.90 BogoMIPS (lpj=12025802)
Total of 4 processors activated (24051.44 BogoMIPS).

Mar 22, 2009

Factorizations of 544...443 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 21, 2009 (5th)

By Sinkiti Sibata / GGNFS, Msieve / Mar 21, 2009

(16·10¹⁴⁶+17)/3 = 5(3)₁₄₅9_<147> = 7 · 11 · 114391987 · 10724771108770309319_<20> · C118

C118 = P41 · P77

P41 = 86647924148580878037180406898757962104657_<41>

P77 = 65157768781765977762053170572689023638293806097473705832942639134885363376267_<77>

Number: 53339_146
N=5645785407093229523450444930076978097985520970778427251742486562229340790332525704995666239342427900024865562723975419
  ( 118 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=86647924148580878037180406898757962104657 (pp41)
 r2=65157768781765977762053170572689023638293806097473705832942639134885363376267 (pp77)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 13.73 hours.
Scaled time: 6.48 units (timescale=0.472).
Factorization parameters were as follows:
name: 53339_146
n: 5645785407093229523450444930076978097985520970778427251742486562229340790332525704995666239342427900024865562723975419
m: 200000000000000000000000000000
deg: 5
c5: 5
c0: 17
skew: 1.28
type: snfs
rlim: 1990000
alim: 1990000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1990000/1990000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [995000, 1995001)
Primes: RFBsize:148219, AFBsize:148151, largePrimes:3891517 encountered
Relations: rels:3932779, finalFF:384477
Max relations in full relation-set: 28
Initial matrix: 296435 x 384477 with sparse part having weight 29846694.
Pruned matrix : 262135 x 263681 with weight 17013240.
Total sieving time: 11.83 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.65 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1990000,1990000,26,26,49,49,2.3,2.3,100000
total time: 13.73 hours.
 --------- CPU info (if available) ----------

(16·10¹⁴⁸+17)/3 = 5(3)₁₄₇9_<149> = 11³ · 13 · 53 · 8387 · C139

C139 = P52 · P88

P52 = 1970805129651612702855917094141798731030723421241267_<52>

P88 = 3518447892045144824283402589333190568229454329679224368597593827794731475863057750227249_<88>

Number: 53339_148
N=6934175154054475060038774393210973357889745590439477645571012428168544246773102249928479498122105298705396229221788410415615970922906684483
  ( 139 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1970805129651612702855917094141798731030723421241267 (pp52)
 r2=3518447892045144824283402589333190568229454329679224368597593827794731475863057750227249 (pp88)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 23.56 hours.
Scaled time: 60.66 units (timescale=2.575).
Factorization parameters were as follows:
name: 53339_148
n: 6934175154054475060038774393210973357889745590439477645571012428168544246773102249928479498122105298705396229221788410415615970922906684483
m: 400000000000000000000000000000
deg: 5
c5: 125
c0: 136
skew: 1.02
type: snfs
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [1100000, 1600001)
Primes: RFBsize:162662, AFBsize:161875, largePrimes:8008307 encountered
Relations: rels:9347537, finalFF:1756819
Max relations in full relation-set: 28
Initial matrix: 324603 x 1756819 with sparse part having weight 181642673.
Pruned matrix : 188940 x 190627 with weight 44204690.
Total sieving time: 22.89 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.46 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,49,49,2.4,2.4,100000
total time: 23.56 hours.
 --------- CPU info (if available) ----------

(49·10¹⁴⁶-31)/9 = 5(4)₁₄₅1_<147> = 643 · C144

C144 = P37 · P108

P37 = 3042106189827290624120844036782865833_<37>

P108 = 278335260575092870871504582135628218174720978379908946178727055375423453765822803874949132681646831312143739_<108>

Number: 54441_146
N=846725419042681873163988249524796958700535683428373941593226196647658545014688094003801624330395714532573008467254190426818731639882495247969587
  ( 144 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=3042106189827290624120844036782865833 (pp37)
 r2=278335260575092870871504582135628218174720978379908946178727055375423453765822803874949132681646831312143739 (pp108)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 17.67 hours.
Scaled time: 45.31 units (timescale=2.564).
Factorization parameters were as follows:
name:54441_146
n: 846725419042681873163988249524796958700535683428373941593226196647658545014688094003801624330395714532573008467254190426818731639882495247969587
m: 100000000000000000000000000000
deg: 5
c5: 490
c0: -31
skew: 0.58
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1000000, 2700001)
Primes: RFBsize:148933, AFBsize:149076, largePrimes:4248112 encountered
Relations: rels:4418526, finalFF:360963
Max relations in full relation-set: 28
Initial matrix: 298075 x 360963 with sparse part having weight 39507402.
Pruned matrix : 276783 x 278337 with weight 28392277.
Total sieving time: 16.91 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.59 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000
total time: 17.67 hours.
 --------- CPU info (if available) ----------

(16·10¹⁵⁹+17)/3 = 5(3)₁₅₈9_<160> = 4201 · 11369 · 20060626646968543458887062589_<29> · 181460042160288350794014941791_<30> · C95

C95 = P29 · P67

P29 = 16433336450614236706160575327_<29>

P67 = 1866691415650896562187704322494751573492502375255655246746456677447_<67>

Sat Mar 21 07:47:23 2009  Msieve v. 1.39
Sat Mar 21 07:47:23 2009  random seeds: 2dc22e14 ac7a317a
Sat Mar 21 07:47:23 2009  factoring 30675968082864569337146521319456691256436797450754597199363823113423792359722327736654385550169 (95 digits)
SSSat Mar 21 07:47:24 2009  searching for 15-digit factors
Sat Mar 21 07:47:26 2009  commencing quadratic sieve (95-digit input)
Sat Mar 21 07:47:26 2009  using multiplier of 5
Sat Mar 21 07:47:26 2009  using 32kb Intel Core sieve core
Sat Mar 21 07:47:26 2009  sieve interval: 36 blocks of size 32768
Sat Mar 21 07:47:26 2009  processing polynomials in batches of 6
SSat Mar 21 07:47:26 2009  using a sieve bound of 2120351 (78824 primes)
Sat Mar 21 07:47:26 2009  using large prime bound of 309571246 (28 bits)
Sat Mar 21 07:47:26 2009  using double large prime bound of 1920299848206370 (43-51 bits)
Sat Mar 21 07:47:26 2009  using trial factoring cutoff of 51 bits
Sat Mar 21 07:47:26 2009  polynomial 'A' values have 12 factors
Sat Mar 21 11:37:13 2009  79215 relations (19218 full + 59997 combined from 1172811 partial), need 78920
Sat Mar 21 11:37:14 2009  begin with 1192029 relations
Sat Mar 21 11:37:16 2009  reduce to 207251 relations in 11 passes
Sat Mar 21 11:37:16 2009  attempting to read 207251 relations
Sat Mar 21 11:37:19 2009  recovered 207251 relations
Sat Mar 21 11:37:19 2009  recovered 191354 polynomials
Sat Mar 21 11:37:19 2009  attempting to build 79215 cycles
Sat Mar 21 11:37:19 2009  found 79215 cycles in 5 passes
Sat Mar 21 11:37:19 2009  distribution of cycle lengths:
Sat Mar 21 11:37:19 2009     length 1 : 19218
Sat Mar 21 11:37:19 2009     length 2 : 13842
Sat Mar 21 11:37:19 2009     length 3 : 13308
Sat Mar 21 11:37:19 2009     length 4 : 10659
Sat Mar 21 11:37:19 2009     length 5 : 8146
Sat Mar 21 11:37:19 2009     length 6 : 5481
Sat Mar 21 11:37:19 2009     length 7 : 3649
Sat Mar 21 11:37:19 2009     length 9+: 4912
Sat Mar 21 11:37:19 2009  largest cycle: 20 relations
Sat Mar 21 11:37:19 2009  matrix is 78824 x 79215 (21.5 MB) with weight 5319220 (67.15/col)
Sat Mar 21 11:37:19 2009  sparse part has weight 5319220 (67.15/col)
Sat Mar 21 11:37:21 2009  filtering completed in 3 passes
Sat Mar 21 11:37:21 2009  matrix is 75158 x 75222 (20.5 MB) with weight 5063299 (67.31/col)
Sat Mar 21 11:37:21 2009  sparse part has weight 5063299 (67.31/col)
Sat Mar 21 11:37:21 2009  saving the first 48 matrix rows for later
Sat Mar 21 11:37:21 2009  matrix is 75110 x 75222 (13.9 MB) with weight 4111085 (54.65/col)
Sat Mar 21 11:37:21 2009  sparse part has weight 3194501 (42.47/col)
Sat Mar 21 11:37:21 2009  matrix includes 64 packed rows
Sat Mar 21 11:37:21 2009  using block size 30088 for processor cache size 1024 kB
Sat Mar 21 11:37:22 2009  commencing Lanczos iteration
Sat Mar 21 11:37:22 2009  memory use: 12.8 MB
Sat Mar 21 11:38:01 2009  lanczos halted after 1189 iterations (dim = 75109)
Sat Mar 21 11:38:01 2009  recovered 17 nontrivial dependencies
Sat Mar 21 11:38:04 2009  prp29 factor: 16433336450614236706160575327
Sat Mar 21 11:38:04 2009  prp67 factor: 1866691415650896562187704322494751573492502375255655246746456677447
Sat Mar 21 11:38:04 2009  elapsed time 03:50:41

(49·10¹⁴⁸-31)/9 = 5(4)₁₄₇1_<149> = 3² · 1522307981_<10> · 32325361034799231983_<20> · C120

C120 = P47 · P73

P47 = 41174538329149687535593202758980475987623219157_<47>

P73 = 2985632945849170426739484835964697951250750532381210173726652975197022159_<73>

Number: 54441_148
N=122932058165638761226488241379896999017363022195995159595839729811725901694163162728063867754278449558440225991842299963
  ( 120 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=41174538329149687535593202758980475987623219157 (pp47)
 r2=2985632945849170426739484835964697951250750532381210173726652975197022159 (pp73)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 24.50 hours.
Scaled time: 63.09 units (timescale=2.575).
Factorization parameters were as follows:
name: 54441_148
n: 122932058165638761226488241379896999017363022195995159595839729811725901694163162728063867754278449558440225991842299963
m: 500000000000000000000000000000
deg: 5
c5: 392
c0: -775
skew: 1.15
type: snfs
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 2050001)
Primes: RFBsize:169511, AFBsize:169652, largePrimes:7433177 encountered
Relations: rels:7869366, finalFF:804921
Max relations in full relation-set: 28
Initial matrix: 339228 x 804921 with sparse part having weight 96545322.
Pruned matrix : 240416 x 242176 with weight 52494306.
Total sieving time: 23.51 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.76 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 24.50 hours.
 --------- CPU info (if available) ----------

Mar 21, 2009 (4th)

By Max Dettweiler / GGNFS, msieve v1.40beta2, Yafu v1.07 / Mar 21, 2009

(49·10¹⁰²-31)/9 = 5(4)₁₀₁1_<103> = 383 · 1877279 · C94

C94 = P39 · P56

P39 = 473755973482677914291347623099642100603_<39>

P56 = 15983477561793208607093630496325319497714439131327943771_<56>

Number: 54441_102
N=7572267971925880781094517844222788058246527492006759130638750213193534517648005235215109193913
  ( 94 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=473755973482677914291347623099642100603 (pp39)
 r2=15983477561793208607093630496325319497714439131327943771 (pp56)
Version: GGNFS-0.77.1-20060722-prescott
Total time: 0.66 hours.
Scaled time: 1.07 units (timescale=1.608).
Factorization parameters were as follows:
n: 7572267971925880781094517844222788058246527492006759130638750213193534517648005235215109193913
m: 50000000000000000000000000
deg: 4
c4: 196
c0: -775
skew: 1.41
type: snfs
lss: 1
rlim: 390000
alim: 390000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2

Factor base limits: 390000/390000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [195000, 275001)
Primes: RFBsize:33067, AFBsize:33072, largePrimes:1135645 encountered
Relations: rels:1107071, finalFF:140559
Max relations in full relation-set: 32
Initial matrix: 66207 x 140559 with sparse part having weight 5846477.
Pruned matrix : 43382 x 43777 with weight 1352172.
Total sieving time: 0.63 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,105,4,0,0,0,0,0,0,0,0,390000,390000,25,25,44,44,2.2,2.2,20000
total time: 0.66 hours.
 --------- CPU info (if available) ----------
[    0.371529] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.10 BogoMIPS (lpj=8800216)
[    0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800821)
[    0.460049] Total of 2 processors activated (8800.51 BogoMIPS).

(49·10¹²¹-31)/9 = 5(4)₁₂₀1_<122> = 3² · 131 · 1275455269903484432893507007_<28> · C92

C92 = P41 · P51

P41 = 36277844381237430670455147233624365514761_<41>

P51 = 998005786686987798358882485633772896334040422474877_<51>

Number: 54441_121
N=36205498621004982089560554169086346790384341114722758168707702248023354316750849491695159397
  ( 92 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=36277844381237430670455147233624365514761 (pp41)
 r2=998005786686987798358882485633772896334040422474877 (pp51)
Version: GGNFS-0.77.1-20060722-prescott
Total time: 2.30 hours.
Scaled time: 3.65 units (timescale=1.587).
Factorization parameters were as follows:
n: 36205498621004982089560554169086346790384341114722758168707702248023354316750849491695159397
m: 1000000000000000000000000
deg: 5
c5: 490
c0: -31
skew: 0.58
type: snfs
lss: 1
rlim: 780000
alim: 780000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2

Factor base limits: 780000/780000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [390000, 690001)
Primes: RFBsize:62468, AFBsize:62381, largePrimes:1358161 encountered
Relations: rels:1333530, finalFF:152464
Max relations in full relation-set: 32
Initial matrix: 124915 x 152464 with sparse part having weight 7336245.
Pruned matrix : 112805 x 113493 with weight 4186936.
Total sieving time: 2.17 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,780000,780000,25,25,46,46,2.2,2.2,50000
total time: 2.30 hours.
 --------- CPU info (if available) ----------
[    0.371529] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.10 BogoMIPS (lpj=8800216)
[    0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800821)
[    0.460049] Total of 2 processors activated (8800.51 BogoMIPS).

(49·10¹²⁸-31)/9 = 5(4)₁₂₇1_<129> = 157 · 653 · 1801003 · C118

C118 = P36 · P40 · P43

P36 = 334785113105198068383674639652573199_<36>

P40 = 2656934680962281058637638782134286920741_<40>

P43 = 3314967576878842350279855338342491270012073_<43>

Number: 54441_128
N=2948670878569275337440589887212647142554801661452814756709502398448268894092307014198822999294104956368884068184401507
  ( 118 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=334785113105198068383674639652573199 (pp36)
 r2=2656934680962281058637638782134286920741 (pp40)
 r3=3314967576878842350279855338342491270012073 (pp43)
Version: Msieve-1.40
Total time: 4.04 hours.
Scaled time: 6.58 units (timescale=1.630).
Factorization parameters were as follows:
n: 2948670878569275337440589887212647142554801661452814756709502398448268894092307014198822999294104956368884068184401507
m: 50000000000000000000000000
deg: 5
c5: 392
c0: -775
skew: 1.15
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 1035001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 159940 x 160188
Total sieving time: 4.04 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 4.04 hours.
 --------- CPU info (if available) ----------
[    0.371529] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.10 BogoMIPS (lpj=8800216)
[    0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800821)
[    0.460049] Total of 2 processors activated (8800.51 BogoMIPS).

(49·10¹⁴⁵-31)/9 = 5(4)₁₄₄1_<146> = 3 · 17 · 182773 · 1476511 · 1360874413_<10> · 49121077427_<11> · 215691204456149170031_<21> · C93

C93 = P39 · P54

P39 = 434960582530030125624174611913048830633_<39>

P54 = 630763272083566084158310359068270763055519969092874889_<54>

03/21/09 00:53:21 v1.07 @ Core2Duo, starting SIQS on c93: 274357160264015792942527616510918476292414957531453870300145327758573457549272898173619674737
03/21/09 00:53:21 v1.07 @ Core2Duo, random seeds: 1948697553, 1062661827
03/21/09 00:53:21 v1.07 @ Core2Duo, ==== sieve params ====
03/21/09 00:53:21 v1.07 @ Core2Duo, n = 93 digits, 314 bits
03/21/09 00:53:21 v1.07 @ Core2Duo, factor base: 76080 primes (max prime = 2050033)
03/21/09 00:53:21 v1.07 @ Core2Duo, single large prime cutoff: 246003960 (120 * pmax)
03/21/09 00:53:21 v1.07 @ Core2Duo, double large prime range from 43 to 51 bits
03/21/09 00:53:21 v1.07 @ Core2Duo, double large prime cutoff: 1269684379467337
03/21/09 00:53:21 v1.07 @ Core2Duo, using 5 large prime slices of factor base
03/21/09 00:53:21 v1.07 @ Core2Duo, buckets hold 2048 elements
03/21/09 00:53:21 v1.07 @ Core2Duo, sieve interval: 22 blocks of size 32768
03/21/09 00:53:21 v1.07 @ Core2Duo, polynomial A has ~ 12 factors
03/21/09 00:53:21 v1.07 @ Core2Duo, using multiplier of 73
03/21/09 00:53:21 v1.07 @ Core2Duo, using small prime variation correction of 23 bits
03/21/09 00:53:21 v1.07 @ Core2Duo, using x128 sieve scanning
03/21/09 00:53:21 v1.07 @ Core2Duo, trial factoring cutoff at 98 bits
03/21/09 00:53:21 v1.07 @ Core2Duo, ==== sieving started ====
03/21/09 02:55:00 v1.07 @ Core2Duo, sieve time = 2128.9600, relation time = 1238.0100, poly_time = 2958.2200
03/21/09 02:55:00 v1.07 @ Core2Duo, 76157 relations found: 20962 full + 55195 from 959290 partial, using 664939 polys (324 A polys)
03/21/09 02:55:00 v1.07 @ Core2Duo, trial division touched 46556240 sieve locations out of 958703730688
03/21/09 02:55:00 v1.07 @ Core2Duo, ==== post processing stage (msieve-1.38) ====
03/21/09 02:55:01 v1.07 @ Core2Duo, begin with 980252 relations
03/21/09 02:55:02 v1.07 @ Core2Duo, reduce to 183836 relations in 9 passes
03/21/09 02:55:02 v1.07 @ Core2Duo, failed to read relation 27535
03/21/09 02:55:06 v1.07 @ Core2Duo, recovered 183835 relations
03/21/09 02:55:06 v1.07 @ Core2Duo, recovered 160637 polynomials
03/21/09 02:55:06 v1.07 @ Core2Duo, attempting to build 76156 cycles
03/21/09 02:55:06 v1.07 @ Core2Duo, found 76156 cycles in 6 passes
03/21/09 02:55:06 v1.07 @ Core2Duo, distribution of cycle lengths:
03/21/09 02:55:06 v1.07 @ Core2Duo,    length 1 : 20962
03/21/09 02:55:06 v1.07 @ Core2Duo,    length 2 : 15209
03/21/09 02:55:06 v1.07 @ Core2Duo,    length 3 : 13707
03/21/09 02:55:06 v1.07 @ Core2Duo,    length 4 : 10124
03/21/09 02:55:06 v1.07 @ Core2Duo,    length 5 : 6651
03/21/09 02:55:06 v1.07 @ Core2Duo,    length 6 : 4256
03/21/09 02:55:06 v1.07 @ Core2Duo,    length 7 : 2395
03/21/09 02:55:06 v1.07 @ Core2Duo,    length 9+: 2852
03/21/09 02:55:06 v1.07 @ Core2Duo, largest cycle: 21 relations
03/21/09 02:55:06 v1.07 @ Core2Duo, matrix is 76080 x 76156 (18.8 MB) with weight 4623885 (60.72/col)
03/21/09 02:55:06 v1.07 @ Core2Duo, sparse part has weight 4623885 (60.72/col)
03/21/09 02:55:07 v1.07 @ Core2Duo, filtering completed in 3 passes
03/21/09 02:55:07 v1.07 @ Core2Duo, matrix is 71114 x 71178 (17.8 MB) with weight 4370124 (61.40/col)
03/21/09 02:55:07 v1.07 @ Core2Duo, sparse part has weight 4370124 (61.40/col)
03/21/09 02:55:07 v1.07 @ Core2Duo, saving the first 48 matrix rows for later
03/21/09 02:55:07 v1.07 @ Core2Duo, matrix is 71066 x 71178 (11.9 MB) with weight 3488332 (49.01/col)
03/21/09 02:55:07 v1.07 @ Core2Duo, sparse part has weight 2684687 (37.72/col)
03/21/09 02:55:07 v1.07 @ Core2Duo, matrix includes 64 packed rows
03/21/09 02:55:07 v1.07 @ Core2Duo, using block size 28471 for processor cache size 2048 kB
03/21/09 02:55:08 v1.07 @ Core2Duo, commencing Lanczos iteration
03/21/09 02:55:08 v1.07 @ Core2Duo, memory use: 11.2 MB
03/21/09 02:55:37 v1.07 @ Core2Duo, lanczos halted after 1125 iterations (dim = 71065)
03/21/09 02:55:37 v1.07 @ Core2Duo, recovered 17 nontrivial dependencies
03/21/09 02:55:38 v1.07 @ Core2Duo, prp54 = 630763272083566084158310359068270763055519969092874889
03/21/09 02:55:40 v1.07 @ Core2Duo, prp39 = 434960582530030125624174611913048830633
03/21/09 02:55:40 v1.07 @ Core2Duo, Lanczos elapsed time = 34.4500 seconds.
03/21/09 02:55:40 v1.07 @ Core2Duo, Sqrt elapsed time = 2.8200 seconds.
03/21/09 02:55:40 v1.07 @ Core2Duo, SIQS elapsed time = 2099.7127 seconds.
03/21/09 02:55:40 v1.07 @ Core2Duo, 
03/21/09 02:55:40 v1.07 @ Core2Duo, 
03/21/09 02:55:40 v1.07 @ Core2Duo, Total factoring time = 2106.7827 seconds

Mar 21, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.2 / Mar 21, 2009

(49·10¹³⁶-31)/9 = 5(4)₁₃₅1_<137> = 3 · 23 · 665857 · 13972061 · 39460147 · 11671026512077_<14> · C102

C102 = P29 · P31 · P43

P29 = 18667939549767870850524668531_<29>

P31 = 3022782052436438642593509297659_<31>

P43 = 3263563458913913551196308954723352628160607_<43>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1100200419
Step 1 took 5688ms
Step 2 took 6513ms
********** Factor found in step 2: 18667939549767870850524668531
Found probable prime factor of 29 digits: 18667939549767870850524668531
Composite cofactor has 73 digits

54441_136

Fri Mar 20 17:56:23 2009  Msieve v. 1.40
Fri Mar 20 17:56:23 2009  random seeds: 2779744d bad5cbc1
Fri Mar 20 17:56:23 2009  factoring 9865041050592362501661952318539719039996375986698139725961087645621119013 (73 digits)
Fri Mar 20 17:56:23 2009  searching for 15-digit factors
Fri Mar 20 17:56:23 2009  commencing quadratic sieve (73-digit input)
Fri Mar 20 17:56:23 2009  using multiplier of 13
Fri Mar 20 17:56:23 2009  using 64kb Opteron sieve core
Fri Mar 20 17:56:23 2009  sieve interval: 6 blocks of size 65536
Fri Mar 20 17:56:23 2009  processing polynomials in batches of 17
Fri Mar 20 17:56:23 2009  using a sieve bound of 497561 (20551 primes)
Fri Mar 20 17:56:23 2009  using large prime bound of 49756100 (25 bits)
Fri Mar 20 17:56:23 2009  using trial factoring cutoff of 26 bits
Fri Mar 20 17:56:23 2009  polynomial 'A' values have 9 factors
Fri Mar 20 17:57:54 2009  20938 relations (10558 full + 10380 combined from 114926 partial), need 20647
Fri Mar 20 17:57:54 2009  begin with 125484 relations
Fri Mar 20 17:57:54 2009  reduce to 30024 relations in 2 passes
Fri Mar 20 17:57:54 2009  attempting to read 30024 relations
Fri Mar 20 17:57:55 2009  recovered 30024 relations
Fri Mar 20 17:57:55 2009  recovered 23652 polynomials
Fri Mar 20 17:57:55 2009  attempting to build 20938 cycles
Fri Mar 20 17:57:55 2009  found 20938 cycles in 1 passes
Fri Mar 20 17:57:55 2009  distribution of cycle lengths:
Fri Mar 20 17:57:55 2009     length 1 : 10558
Fri Mar 20 17:57:55 2009     length 2 : 10380
Fri Mar 20 17:57:55 2009  largest cycle: 2 relations
Fri Mar 20 17:57:55 2009  matrix is 20551 x 20938 (2.9 MB) with weight 602761 (28.79/col)
Fri Mar 20 17:57:55 2009  sparse part has weight 602761 (28.79/col)
Fri Mar 20 17:57:55 2009  filtering completed in 3 passes
Fri Mar 20 17:57:55 2009  matrix is 15156 x 15220 (2.3 MB) with weight 484811 (31.85/col)
Fri Mar 20 17:57:55 2009  sparse part has weight 484811 (31.85/col)
Fri Mar 20 17:57:55 2009  saving the first 48 matrix rows for later
Fri Mar 20 17:57:55 2009  matrix is 15108 x 15220 (1.7 MB) with weight 379916 (24.96/col)
Fri Mar 20 17:57:55 2009  sparse part has weight 304295 (19.99/col)
Fri Mar 20 17:57:55 2009  matrix includes 64 packed rows
Fri Mar 20 17:57:55 2009  commencing Lanczos iteration
Fri Mar 20 17:57:55 2009  memory use: 2.3 MB
Fri Mar 20 17:57:57 2009  lanczos halted after 240 iterations (dim = 15106)
Fri Mar 20 17:57:57 2009  recovered 16 nontrivial dependencies
Fri Mar 20 17:57:57 2009  prp31 factor: 3022782052436438642593509297659
Fri Mar 20 17:57:57 2009  prp43 factor: 3263563458913913551196308954723352628160607
Fri Mar 20 17:57:57 2009  elapsed time 00:01:34

(49·10²⁰¹-31)/9 = 5(4)₂₀₀1_<202> = 1319 · 178067 · 5439093729791_<13> · C181

C181 = P33 · C149

P33 = 424468423345885433156577302198219_<33>

C149 = [10040455184883628723379516918972718663570880925820870748754105264964125669194550840151796264594212956524156346638928243460828919631807445780254353073_<149>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1761079087
Step 1 took 11284ms
Step 2 took 10537ms
********** Factor found in step 2: 424468423345885433156577302198219
Found probable prime factor of 33 digits: 424468423345885433156577302198219
Composite cofactor has 149 digits

(49·10²⁰³-31)/9 = 5(4)₂₀₂1_<204> = 787 · 7433 · C197

C197 = P30 · P168

P30 = 250258947013949118526184405219_<30>

P168 = 371899070167657494778515770799102838016236456489920897993331203914363646004089375009102210345490410627952983442877093935149349822956554542662818169335938886868137369209_<168>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1435368007
Step 1 took 13265ms
Step 2 took 12292ms
********** Factor found in step 2: 250258947013949118526184405219
Found probable prime factor of 30 digits: 250258947013949118526184405219
Probable prime cofactor  has 168 digits

(49·10¹⁵²-31)/9 = 5(4)₁₅₁1_<153> = 139066913 · 143811039393017_<15> · C131

C131 = P30 · P101

P30 = 812352607758978810286632150707_<30>

P101 = 33511429361318384365714365555561437168521607903032200299203243906271811241705138132135209592480782203_<101>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1803878505
Step 1 took 6969ms
Step 2 took 7556ms
********** Factor found in step 2: 812352607758978810286632150707
Found probable prime factor of 30 digits: 812352607758978810286632150707
Probable prime cofactor  has 101 digits

(49·10¹⁹⁰-31)/9 = 5(4)₁₈₉1_<191> = 3 · 63389 · 8043221326363661_<16> · C170

C170 = P32 · C139

P32 = 10488120350258049738490426522001_<32>

C139 = [3393835074574017376539546445699521745886417441021383295473943155188861165490674176590119566336901074380489532848268861497947052610509364443_<139>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=135339706
Step 1 took 9849ms
Step 2 took 9693ms
********** Factor found in step 2: 10488120350258049738490426522001
Found probable prime factor of 32 digits: 10488120350258049738490426522001
Composite cofactor  has 139 digits

(49·10¹⁸⁶-31)/9 = 5(4)₁₈₅1_<187> = 4861 · C184

C184 = P31 · C153

P31 = 1241191640392313005099385818109_<31>

C153 = [902379265325329705591066395933044306860508809089952038926144254478684282445955327984884168429055650670735545558654745328579151448711225262133357429176209_<153>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1750105925
Step 1 took 11496ms
Step 2 took 10725ms
********** Factor found in step 2: 1241191640392313005099385818109
Found probable prime factor of 31 digits: 1241191640392313005099385818109
Composite cofactor  has 153 digits

(49·10¹⁶⁹-31)/9 = 5(4)₁₆₈1_<170> = 3 · 1087 · 675074612021_<12> · 2254401221812081_<16> · 910389927427035326570473463_<27> · C113

C113 = P35 · P78

P35 = 29391527720593538801969447888738177_<35>

P78 = 409987089110436215559923537098846799981853399910166677561191189758960834735231_<78>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3128579257
Step 1 took 5816ms
Step 2 took 6796ms
********** Factor found in step 2: 29391527720593538801969447888738177
Found probable prime factor of 35 digits: 29391527720593538801969447888738177
Probable prime cofactor  has 78 digits

(49·10¹⁶⁵-31)/9 = 5(4)₁₆₄1_<166> = 2657 · 3415503671_<10> · 97183337723738729_<17> · 17795071470385183553_<20> · C117

C117 = P31 · P86

P31 = 3634817774191577551868236530631_<31>

P86 = 95440579885143177494526759532437749091043702738081194606442117590125371568906001930449_<86>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1236416677
Step 1 took 7152ms
Step 2 took 4841ms
********** Factor found in step 2: 3634817774191577551868236530631
Found probable prime factor of 31 digits: 3634817774191577551868236530631
Probable prime cofactor 95440579885143177494526759532437749091043702738081194606442117590125371568906001930449 has 86 digits

Mar 21, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Mar 21, 2009

(49·10¹²⁷-31)/9 = 5(4)₁₂₆1_<128> = 3 · C128

C128 = P42 · P86

P42 = 212686756056207820346328747855854527191863_<42>

P86 = 85328059370805598805282609306653258989436996598344573461264897015482912785725445799269_<86>

Number: 54441_127
N=18148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147
  ( 128 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=212686756056207820346328747855854527191863
 r2=85328059370805598805282609306653258989436996598344573461264897015482912785725445799269
Version: 
Total time: 3.09 hours.
Scaled time: 3.10 units (timescale=1.003).
Factorization parameters were as follows:
n: 18148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147
m: 20000000000000000000000000
deg: 5
c5: 1225
c0: -248
skew: 0.73
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 135042 x 135285
Total sieving time: 3.09 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 3.09 hours.
 --------- CPU info (if available) ----------

(49·10¹²⁰-31)/9 = 5(4)₁₁₉1_<121> = 257 · 35597 · C114

C114 = P54 · P61

P54 = 536245068924591737124655246514569309654380430554957439_<54>

P61 = 1109797486936534216431504198518455998801702013987553663743811_<61>

Number: 54441_120
N=595123429874620488877865745522476530609183767447333792987237966698374600102864048509798178949024411125062504660029
  ( 114 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=536245068924591737124655246514569309654380430554957439
 r2=1109797486936534216431504198518455998801702013987553663743811
Version: 
Total time: 2.27 hours.
Scaled time: 1.79 units (timescale=0.789).
Factorization parameters were as follows:
n: 595123429874620488877865745522476530609183767447333792987237966698374600102864048509798178949024411125062504660029
m: 1000000000000000000000000
deg: 5
c5: 49
c0: -31
skew: 0.91
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 625001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 80161 x 80380
Total sieving time: 2.27 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 2.27 hours.
 --------- CPU info (if available) ----------

Mar 21, 2009

By Ignacio Santos / GGNFS, Msieve / Mar 21, 2009

(47·10¹⁶²+61)/9 = 5(2)₁₆₁9_<163> = 3 · 329083 · C157

C157 = P42 · P115

P42 = 971829109621331280713052310611805906814693_<42>

P115 = 5443005115212690963075124445015554464452373759718062686515066448009637291266093021375952448364071566322188969133697_<115>

Number: 52229_162
N=5289670814781501143300446211869773706757081771895663831740748506427681590178589415863902847429799596882065438630195849499186347337117811435840626044921010021
  ( 157 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=971829109621331280713052310611805906814693 (pp42)
 r2=5443005115212690963075124445015554464452373759718062686515066448009637291266093021375952448364071566322188969133697 (pp115)
Version: Msieve-1.39
Total time: 53.98 hours.
Scaled time: 138.18 units (timescale=2.560).
Factorization parameters were as follows:
n: 5289670814781501143300446211869773706757081771895663831740748506427681590178589415863902847429799596882065438630195849499186347337117811435840626044921010021
m: 200000000000000000000000000000000
deg: 5
c5: 1175
c0: 488
skew: 0.84
type: snfs
lss: 1
rlim: 3900000
alim: 3900000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3900000/3900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1950000, 4850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 809812 x 810060
Total sieving time: 53.98 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3900000,3900000,27,27,51,51,2.4,2.4,100000
total time: 53.98 hours.
 --------- CPU info (if available) ----------

(49·10¹¹⁴-31)/9 = 5(4)₁₁₃1_<115> = 23 · 43 · 109 · 4813 · C107

C107 = P53 · P54

P53 = 22217334636516340591183544712573576415815305878084841_<53>

P54 = 472305456504688210183240694188825900424928109872524477_<54>

Number: 54441_114
N=10493368377817271347115806055703917115117200333973420452515559643189386533008085084441860317566670655153157
  ( 107 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=22217334636516340591183544712573576415815305878084841 (pp53)
 r2=472305456504688210183240694188825900424928109872524477 (pp54)
Version: Msieve-1.39
Total time: 0.96 hours.
Scaled time: 2.48 units (timescale=2.571).
Factorization parameters were as follows:
n: 10493368377817271347115806055703917115117200333973420452515559643189386533008085084441860317566670655153157
m: 100000000000000000000000
deg: 5
c5: 49
c0: -310
skew: 1.45
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 510001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 75195 x 75435
Total sieving time: 0.96 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 0.96 hours.
 --------- CPU info (if available) ----------

(49·10¹¹⁷-31)/9 = 5(4)₁₁₆1_<118> = C118

C118 = P39 · P80

P39 = 154246452441159111248982572678667916573_<39>

P80 = 35297048057045941607042149181609332851433750679475844777668550528971140848239917_<80>

Number: 54441_117
N=5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
  ( 118 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=154246452441159111248982572678667916573 (pp39)
 r2=35297048057045941607042149181609332851433750679475844777668550528971140848239917 (pp80)
Version: Msieve-1.39
Total time: 1.25 hours.
Scaled time: 3.21 units (timescale=2.571).
Factorization parameters were as follows:
n: 5444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
m: 200000000000000000000000
deg: 5
c5: 1225
c0: -248
skew: 0.73
type: snfs
lss: 1
rlim: 690000
alim: 690000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 690000/690000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [345000, 595001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 74942 x 75178
Total sieving time: 1.25 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,690000,690000,25,25,45,45,2.2,2.2,50000
total time: 1.25 hours.
 --------- CPU info (if available) ----------

(49·10¹²⁵-31)/9 = 5(4)₁₂₄1_<126> = 4804924649857833704429_<22> · C105

C105 = P40 · P66

P40 = 1025115644707967819539554614441428582207_<40>

P66 = 110533552316652305766096265640112667609906689555884231601589422947_<66>

Number: 54441_125
N=113309673744946918369078305215256276714041773591243698665463621421495132893957196327768571317221481704029
  ( 105 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=1025115644707967819539554614441428582207 (pp40)
 r2=110533552316652305766096265640112667609906689555884231601589422947 (pp66)
Version: Msieve-1.39
Total time: 1.87 hours.
Scaled time: 4.82 units (timescale=2.571).
Factorization parameters were as follows:
n: 113309673744946918369078305215256276714041773591243698665463621421495132893957196327768571317221481704029
m: 10000000000000000000000000
deg: 5
c5: 49
c0: -31
skew: 0.91
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 112522 x 112770
Total sieving time: 1.87 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 1.87 hours.
 --------- CPU info (if available) ----------

(49·10¹³⁰-31)/9 = 5(4)₁₂₉1_<131> = 3³ · C130

C130 = P43 · P87

P43 = 3485194438046429071043711780795569694241101_<43>

P87 = 578579170027623963886718225384340201589963557785325638183886905382835163611758103197383_<87>

Number: 54441_130
N=2016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683
  ( 130 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=3485194438046429071043711780795569694241101 (pp43)
 r2=578579170027623963886718225384340201589963557785325638183886905382835163611758103197383 (pp87)
Version: Msieve-1.39
Total time: 2.36 hours.
Scaled time: 6.06 units (timescale=2.571).
Factorization parameters were as follows:
n: 2016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683
m: 100000000000000000000000000
deg: 5
c5: 49
c0: -31
skew: 0.91
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 146156 x 146404
Total sieving time: 2.36 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.36 hours.
 --------- CPU info (if available) ----------

(49·10¹²⁴-31)/9 = 5(4)₁₂₃1_<125> = 3 · 149 · C123

C123 = P46 · P77

P46 = 3678469373978815613162658522544463360181425083_<46>

P77 = 33111503622293235320810964516155255520009807603765550297505951353818595518341_<77>

Number: 54441_124
N=121799652000994282873477504349987571464081531195625155356698980860054685558041262739249316430524484215759383544618443947303
  ( 123 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=3678469373978815613162658522544463360181425083 (pp46)
 r2=33111503622293235320810964516155255520009807603765550297505951353818595518341 (pp77)
Version: Msieve-1.39
Total time: 1.91 hours.
Scaled time: 4.88 units (timescale=2.560).
Factorization parameters were as follows:
n: 121799652000994282873477504349987571464081531195625155356698980860054685558041262739249316430524484215759383544618443947303
m: 10000000000000000000000000
deg: 5
c5: 49
c0: -310
skew: 1.45
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 135026 x 135274
Total sieving time: 1.91 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 1.91 hours.
 --------- CPU info (if available) ----------

(49·10¹³²-31)/9 = 5(4)₁₃₁1_<133> = 937 · 4933 · 135039659411715644318569_<24> · C103

C103 = P48 · P55

P48 = 917343383904947349456475388877809429569624434029_<48>

P55 = 9508447156545723192298461689453019352567992309220057321_<55>

Number: 54441_132
N=8722511090267028359167642705465348623623120554971794762786759770704907991910292127174579618889562976309
  ( 103 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=917343383904947349456475388877809429569624434029 (pp48)
 r2=9508447156545723192298461689453019352567992309220057321 (pp55)
Version: Msieve-1.39
Total time: 3.04 hours.
Scaled time: 7.78 units (timescale=2.560).
Factorization parameters were as follows:
n: 8722511090267028359167642705465348623623120554971794762786759770704907991910292127174579618889562976309
m: 200000000000000000000000000
deg: 5
c5: 1225
c0: -248
skew: 0.73
type: snfs
lss: 1
rlim: 1230000
alim: 1230000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1230000/1230000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [615000, 1140001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 190721 x 190969
Total sieving time: 3.04 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1230000,1230000,26,26,47,47,2.3,2.3,75000
total time: 3.04 hours.
 --------- CPU info (if available) ----------

(49·10¹³⁹-31)/9 = 5(4)₁₃₈1_<140> = 3² · 29 · 141301 · 452326029838012123503316567_<27> · C106

C106 = P45 · P61

P45 = 750377221650197702999288202630635030091562231_<45>

P61 = 4349472657235673314417701685009106480893148418132764187177953_<61>

Number: 54441_139
N=3263745208180007214729459399101391881242230962552165253868053894917788151729797936352756748668504970693143
  ( 106 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=750377221650197702999288202630635030091562231 (pp45)
 r2=4349472657235673314417701685009106480893148418132764187177953 (pp61)
Version: Msieve-1.39
Total time: 6.53 hours.
Scaled time: 16.72 units (timescale=2.560).
Factorization parameters were as follows:
n: 3263745208180007214729459399101391881242230962552165253868053894917788151729797936352756748668504970693143
m: 10000000000000000000000000000
deg: 5
c5: 49
c0: -310
skew: 1.45
type: snfs
lss: 1
rlim: 1610000
alim: 1610000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1610000/1610000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [805000, 1905001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 254680 x 254928
Total sieving time: 6.53 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000
total time: 6.53 hours.
 --------- CPU info (if available) ----------

(49·10¹⁵⁷-31)/9 = 5(4)₁₅₆1_<158> = 3³ · 6122309 · C150

C150 = P31 · P120

P31 = 1923220060004563723065726411371_<31>

P120 = 171255915216534977122827386763108934627093798220839334994149913976056197515328298881509804914207268712955084143436490397_<120>

Number: 54441_157
N=329362811538880876264678501528828568657641134853390701452092814222508899613385664136922998389952914608381833065998613488766123807721493968445713104287
  ( 150 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=1923220060004563723065726411371 (pp31)
 r2=171255915216534977122827386763108934627093798220839334994149913976056197515328298881509804914207268712955084143436490397 (pp120)
Version: Msieve-1.39
Total time: 24.52 hours.
Scaled time: 62.77 units (timescale=2.560).
Factorization parameters were as follows:
n: 329362811538880876264678501528828568657641134853390701452092814222508899613385664136922998389952914608381833065998613488766123807721493968445713104287
m: 20000000000000000000000000000000
deg: 5
c5: 1225
c0: -248
skew: 0.73
type: snfs
lss: 1
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1600000, 2900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 608559 x 608807
Total sieving time: 24.52 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000
total time: 24.52 hours.
 --------- CPU info (if available) ----------

(47·10¹⁷⁴+43)/9 = 5(2)₁₇₃7_<175> = 23² · C172

C172 = P47 · P126

P47 = 20155372881344237249701760518000538181423547561_<47>

P126 = 489788788056215750930608840816878998358650966697873970244482403849329672929816622034720262339309577873049188174812546664400683_<126>

Number: 52227_174
N=9871875656374711195127074144087376601554295316110060911573198907792480571308548624238605335013652593992858643142197017433312329342575089266960722537282083595883217811384163
  ( 172 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=20155372881344237249701760518000538181423547561 (pp47)
 r2=489788788056215750930608840816878998358650966697873970244482403849329672929816622034720262339309577873049188174812546664400683 (pp126)
Version: Msieve-1.39
Total time: 101.80 hours.
Scaled time: 177.03 units (timescale=1.739).
Factorization parameters were as follows:
n: 9871875656374711195127074144087376601554295316110060911573198907792480571308548624238605335013652593992858643142197017433312329342575089266960722537282083595883217811384163
m: 100000000000000000000000000000000000
deg: 5
c5: 47
c0: 430
skew: 1.56
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3100000, 8400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1363720 x 1363968
Total sieving time: 101.80 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,53,53,2.5,2.5,100000
total time: 101.80 hours.
 --------- CPU info (if available) ----------

Mar 20, 2009 (8th)

By Wataru Sakai / GMP-ECM / Mar 20, 2009

(23·10¹⁹¹-41)/9 = 2(5)₁₉₀1_<192> = 536749 · 1049437 · 2222514223_<10> · 164646728337905536231_<21> · 640556862356338194459757_<24> · C127

C127 = P44 · P84

P44 = 18183469352047122005819738271467857341848407_<44>

P84 = 106445086486657196807532944997246788012201790725070046199662462071658155594075770621_<84>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3307947160
Step 1 took 151244ms
Step 2 took 48221ms
********** Factor found in step 2: 18183469352047122005819738271467857341848407
Found probable prime factor of 44 digits: 18183469352047122005819738271467857341848407
Probable prime cofactor 106445086486657196807532944997246788012201790725070046199662462071658155594075770621 has 84 digits

Mar 20, 2009 (7th)

By Erik Branger / GGNFS, Msieve / Mar 20, 2009

(47·10¹⁵²+61)/9 = 5(2)₁₅₁9_<153> = 67 · 5963899 · 50127534151990733094529_<23> · C122

C122 = P58 · P65

P58 = 1142881122706237152034929100702236331731481069594600653461_<58>

P65 = 22812499110881731749464498894319372578237508831024251483110858577_<65>

Number: 52229_152
N=26071974595579550393999475913790933972486860700120637626726518445387274546574219539309075431750905426207893727988956584997
  ( 122 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=1142881122706237152034929100702236331731481069594600653461
 r2=22812499110881731749464498894319372578237508831024251483110858577
Version: 
Total time: 35.93 hours.
Scaled time: 36.25 units (timescale=1.009).
Factorization parameters were as follows:
n: 26071974595579550393999475913790933972486860700120637626726518445387274546574219539309075431750905426207893727988956584997
m: 2000000000000000000000000000000
deg: 5
c5: 1175
c0: 488
skew: 0.84
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 508553 x 508801
Total sieving time: 35.93 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 35.93 hours.
 --------- CPU info (if available) ----------

(16·10¹⁴⁷+17)/3 = 5(3)₁₄₆9_<148> = 19² · 844735909 · C137

C137 = P31 · P49 · P58

P31 = 1027482580059048117497952822277_<31>

P49 = 9409699702063826388217071571541161674436721450537_<49>

P58 = 1808924074299550618481698414759567874414711834398853215939_<58>

Number: 53339_147
N=17489225199528876930103479638040835832191914225321633209217253619853852876614293076683294006157083460741282726660636470553825466010806311
  ( 137 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=1027482580059048117497952822277
 r2=9409699702063826388217071571541161674436721450537
 r3=1808924074299550618481698414759567874414711834398853215939
Version: 
Total time: 9.11 hours.
Scaled time: 9.07 units (timescale=0.995).
Factorization parameters were as follows:
n: 17489225199528876930103479638040835832191914225321633209217253619853852876614293076683294006157083460741282726660636470553825466010806311
m: 200000000000000000000000000000
deg: 5
c5: 50
c0: 17
skew: 0.81
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1050000, 2150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 299724 x 299972
Total sieving time: 9.11 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000
total time: 9.11 hours.
 --------- CPU info (if available) ----------

(16·10¹⁴¹+17)/3 = 5(3)₁₄₀9_<142> = 627491 · C136

C136 = P53 · P83

P53 = 98531454093262507723164589411652625162805522024873067_<53>

P83 = 86261366709419004879256051310572074798571199905749754449998290361726951365465220987_<83>

Number: 53339_141
N=8499457893951201424934115920918918890204534142056751942790148915814463208768465736294756950033280689816002673079507647652848141779457129
  ( 136 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=98531454093262507723164589411652625162805522024873067
 r2=86261366709419004879256051310572074798571199905749754449998290361726951365465220987
Version: 
Total time: 7.22 hours.
Scaled time: 5.69 units (timescale=0.789).
Factorization parameters were as follows:
n: 8499457893951201424934115920918918890204534142056751942790148915814463208768465736294756950033280689816002673079507647652848141779457129
m: 20000000000000000000000000000
deg: 5
c5: 5
c0: 17
skew: 1.28
type: snfs
lss: 1
rlim: 1700000
alim: 1700000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1700000/1700000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [850000, 1450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 218106 x 218354
Total sieving time: 7.22 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1700000,1700000,26,26,48,48,2.3,2.3,100000
total time: 7.22 hours.
 --------- CPU info (if available) ----------

Mar 20, 2009 (6th)

By Robert Backstrom / Msieve / Mar 20, 2009

(16·10¹²⁶+17)/3 = 5(3)₁₂₅9_<127> = 11² · 937 · 1537258295437_<13> · 9025370693297974973_<19> · C91

C91 = P41 · P50

P41 = 77645603363146301434635923149259748641629_<41>

P50 = 43666160215801579806770536601220923608024965501583_<50>

Fri Mar 20 03:19:19 2009  
Fri Mar 20 03:19:19 2009  
Fri Mar 20 03:19:19 2009  Msieve v. 1.39
Fri Mar 20 03:19:19 2009  random seeds: 01ab27d4 f393454b
Fri Mar 20 03:19:19 2009  factoring 3390485356507728372669909109598783194410042535424399523149281361272522288277422770899198707 (91 digits)
Fri Mar 20 03:19:20 2009  searching for 15-digit factors
Fri Mar 20 03:19:22 2009  commencing quadratic sieve (91-digit input)
Fri Mar 20 03:19:22 2009  using multiplier of 43
Fri Mar 20 03:19:22 2009  using 64kb Opteron sieve core
Fri Mar 20 03:19:22 2009  sieve interval: 18 blocks of size 65536
Fri Mar 20 03:19:22 2009  processing polynomials in batches of 6
Fri Mar 20 03:19:22 2009  using a sieve bound of 1683637 (63529 primes)
Fri Mar 20 03:19:22 2009  using large prime bound of 154894604 (27 bits)
Fri Mar 20 03:19:22 2009  using double large prime bound of 552160384714396 (42-49 bits)
Fri Mar 20 03:19:22 2009  using trial factoring cutoff of 49 bits
Fri Mar 20 03:19:22 2009  polynomial 'A' values have 12 factors
Fri Mar 20 04:18:10 2009  64199 relations (17518 full + 46681 combined from 716708 partial), need 63625
Fri Mar 20 04:18:11 2009  begin with 734226 relations
Fri Mar 20 04:18:11 2009  reduce to 155637 relations in 9 passes
Fri Mar 20 04:18:11 2009  attempting to read 155637 relations
Fri Mar 20 04:18:12 2009  recovered 155637 relations
Fri Mar 20 04:18:12 2009  recovered 132969 polynomials
Fri Mar 20 04:18:13 2009  attempting to build 64199 cycles
Fri Mar 20 04:18:13 2009  found 64199 cycles in 6 passes
Fri Mar 20 04:18:13 2009  distribution of cycle lengths:
Fri Mar 20 04:18:13 2009     length 1 : 17518
Fri Mar 20 04:18:13 2009     length 2 : 12567
Fri Mar 20 04:18:13 2009     length 3 : 11363
Fri Mar 20 04:18:13 2009     length 4 : 8435
Fri Mar 20 04:18:13 2009     length 5 : 5794
Fri Mar 20 04:18:13 2009     length 6 : 3759
Fri Mar 20 04:18:13 2009     length 7 : 2181
Fri Mar 20 04:18:13 2009     length 9+: 2582
Fri Mar 20 04:18:13 2009  largest cycle: 18 relations
Fri Mar 20 04:18:13 2009  matrix is 63529 x 64199 (15.4 MB) with weight 3775271 (58.81/col)
Fri Mar 20 04:18:13 2009  sparse part has weight 3775271 (58.81/col)
Fri Mar 20 04:18:14 2009  filtering completed in 3 passes
Fri Mar 20 04:18:14 2009  matrix is 58990 x 59053 (14.2 MB) with weight 3474411 (58.84/col)
Fri Mar 20 04:18:14 2009  sparse part has weight 3474411 (58.84/col)
Fri Mar 20 04:18:14 2009  saving the first 48 matrix rows for later
Fri Mar 20 04:18:14 2009  matrix is 58942 x 59053 (8.3 MB) with weight 2643233 (44.76/col)
Fri Mar 20 04:18:14 2009  sparse part has weight 1831762 (31.02/col)
Fri Mar 20 04:18:14 2009  matrix includes 64 packed rows
Fri Mar 20 04:18:14 2009  using block size 23621 for processor cache size 1024 kB
Fri Mar 20 04:18:15 2009  commencing Lanczos iteration
Fri Mar 20 04:18:15 2009  memory use: 8.5 MB
Fri Mar 20 04:18:33 2009  lanczos halted after 934 iterations (dim = 58938)
Fri Mar 20 04:18:33 2009  recovered 16 nontrivial dependencies
Fri Mar 20 04:18:34 2009  prp41 factor: 77645603363146301434635923149259748641629
Fri Mar 20 04:18:34 2009  prp50 factor: 43666160215801579806770536601220923608024965501583
Fri Mar 20 04:18:34 2009  elapsed time 00:59:15

(16·10¹³⁷+17)/3 = 5(3)₁₃₆9_<138> = 2087 · 7759 · 28201 · 792993427 · 20925773837827387826419_<23> · C95

C95 = P34 · P61

P34 = 7354562144409310904345832577230403_<34>

P61 = 9569694675376026666594225015995206118078921791743315366068497_<61>

Fri Mar 20 04:35:22 2009  
Fri Mar 20 04:35:22 2009  
Fri Mar 20 04:35:22 2009  Msieve v. 1.39
Fri Mar 20 04:35:22 2009  random seeds: bb7c5658 294ba63c
Fri Mar 20 04:35:22 2009  factoring 70380914193075875069160056899381282352396507812412050756086369583463941326145489766315048914291 (95 digits)
Fri Mar 20 04:35:22 2009  searching for 15-digit factors
Fri Mar 20 04:35:23 2009  commencing quadratic sieve (95-digit input)
Fri Mar 20 04:35:23 2009  using multiplier of 1
Fri Mar 20 04:35:23 2009  using 64kb Opteron sieve core
Fri Mar 20 04:35:23 2009  sieve interval: 18 blocks of size 65536
Fri Mar 20 04:35:23 2009  processing polynomials in batches of 6
Fri Mar 20 04:35:23 2009  using a sieve bound of 2196599 (80820 primes)
Fri Mar 20 04:35:23 2009  using large prime bound of 329489850 (28 bits)
Fri Mar 20 04:35:23 2009  using double large prime bound of 2148402323041500 (43-51 bits)
Fri Mar 20 04:35:23 2009  using trial factoring cutoff of 51 bits
Fri Mar 20 04:35:23 2009  polynomial 'A' values have 12 factors
Fri Mar 20 07:49:29 2009  81047 relations (19018 full + 62029 combined from 1236147 partial), need 80916
Fri Mar 20 07:49:31 2009  begin with 1255165 relations
Fri Mar 20 07:49:32 2009  reduce to 215317 relations in 11 passes
Fri Mar 20 07:49:32 2009  attempting to read 215317 relations
Fri Mar 20 07:49:35 2009  recovered 215317 relations
Fri Mar 20 07:49:35 2009  recovered 201777 polynomials
Fri Mar 20 07:49:35 2009  attempting to build 81047 cycles
Fri Mar 20 07:49:35 2009  found 81047 cycles in 7 passes
Fri Mar 20 07:49:36 2009  distribution of cycle lengths:
Fri Mar 20 07:49:36 2009     length 1 : 19018
Fri Mar 20 07:49:36 2009     length 2 : 13676
Fri Mar 20 07:49:36 2009     length 3 : 13585
Fri Mar 20 07:49:36 2009     length 4 : 11033
Fri Mar 20 07:49:36 2009     length 5 : 8460
Fri Mar 20 07:49:36 2009     length 6 : 5900
Fri Mar 20 07:49:36 2009     length 7 : 3881
Fri Mar 20 07:49:36 2009     length 9+: 5494
Fri Mar 20 07:49:36 2009  largest cycle: 23 relations
Fri Mar 20 07:49:36 2009  matrix is 80820 x 81047 (22.0 MB) with weight 5430538 (67.00/col)
Fri Mar 20 07:49:36 2009  sparse part has weight 5430538 (67.00/col)
Fri Mar 20 07:49:38 2009  filtering completed in 3 passes
Fri Mar 20 07:49:38 2009  matrix is 77513 x 77577 (21.1 MB) with weight 5218749 (67.27/col)
Fri Mar 20 07:49:38 2009  sparse part has weight 5218749 (67.27/col)
Fri Mar 20 07:49:38 2009  saving the first 48 matrix rows for later
Fri Mar 20 07:49:38 2009  matrix is 77465 x 77577 (13.7 MB) with weight 4138441 (53.35/col)
Fri Mar 20 07:49:38 2009  sparse part has weight 3127760 (40.32/col)
Fri Mar 20 07:49:38 2009  matrix includes 64 packed rows
Fri Mar 20 07:49:38 2009  using block size 31030 for processor cache size 1024 kB
Fri Mar 20 07:49:38 2009  commencing Lanczos iteration
Fri Mar 20 07:49:38 2009  memory use: 13.0 MB
Fri Mar 20 07:50:22 2009  lanczos halted after 1226 iterations (dim = 77462)
Fri Mar 20 07:50:22 2009  recovered 15 nontrivial dependencies
Fri Mar 20 07:50:23 2009  prp34 factor: 7354562144409310904345832577230403
Fri Mar 20 07:50:23 2009  prp61 factor: 9569694675376026666594225015995206118078921791743315366068497
Fri Mar 20 07:50:23 2009  elapsed time 03:15:01

Mar 20, 2009 (5th)

By Sinkiti Sibata / GGNFS, Msieve / Mar 20, 2009

(47·10¹⁵⁵+61)/9 = 5(2)₁₅₄9_<156> = 43 · 35909329 · 58770731 · 20170670960464360204959468810331_<32> · C108

C108 = P40 · P69

P40 = 1362060369851719248423367258847794687379_<40>

P69 = 209460342073774190375828058205240979575586001449705679614534145203053_<69>

Number: 52227_155
N=285297630994272504091552978449388295403830314074853375107757128116579477814437793906499110695817310611368087
  ( 108 digits)
Divisors found:
 r1=1362060369851719248423367258847794687379 (pp40)
 r2=209460342073774190375828058205240979575586001449705679614534145203053 (pp69)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 20.73 hours.
Scaled time: 9.78 units (timescale=0.472).
Factorization parameters were as follows:
name: 52227_155
n: 285297630994272504091552978449388295403830314074853375107757128116579477814437793906499110695817310611368087
skew: 12217.28
# norm 5.15e+14
c5: 24480
c4: 2762001072
c3: -4673288308058
c2: -155456926716493285
c1: 560007686009585776790
c0: -3036206145102312397412120
# alpha -6.01
Y1: 239892078833
Y0: -410479642376546949693
# Murphy_E 1.42e-09
# M 253874833941645235923460218686059303773393118734419260658942706884390200216848854565959869477840516971217388
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2450001)
Primes: RFBsize:183072, AFBsize:182725, largePrimes:4485821 encountered
Relations: rels:4584016, finalFF:461794
Max relations in full relation-set: 28
Initial matrix: 365882 x 461794 with sparse part having weight 37155706.
Pruned matrix : 295333 x 297226 with weight 21432233.
Total sieving time: 17.67 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 2.50 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 20.73 hours.
 --------- CPU info (if available) ----------

(16·10¹¹⁹+17)/3 = 5(3)₁₁₈9_<120> = 31 · 7079 · 7507 · 32909 · C106

C106 = P37 · P70

P37 = 4977605857740139864313943677940325771_<37>

P70 = 1976348440568735697281734967191062750712135499265960643476367149133007_<70>

Number: 53339_119
N=9837483574710529484514161171773761501488325082032517410013632145633355081949361660424442639434305788823397
  ( 106 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=4977605857740139864313943677940325771 (pp37)
 r2=1976348440568735697281734967191062750712135499265960643476367149133007 (pp70)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.22 hours.
Scaled time: 1.05 units (timescale=0.471).
Factorization parameters were as follows:
name: 53339_119
n: 9837483574710529484514161171773761501488325082032517410013632145633355081949361660424442639434305788823397
m: 1000000000000000000000000
deg: 5
c5: 8
c0: 85
skew: 1.60
type: snfs
lss: 1
rlim: 720000
alim: 720000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 720000/720000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [360000, 560001)
Primes: RFBsize:58029, AFBsize:58122, largePrimes:1442756 encountered
Relations: rels:1515012, finalFF:240263
Max relations in full relation-set: 28
Initial matrix: 116216 x 240263 with sparse part having weight 10375872.
Pruned matrix : 73227 x 73872 with weight 2689877.
Total sieving time: 2.11 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,720000,720000,25,25,46,46,2.2,2.2,50000
total time: 2.22 hours.
 --------- CPU info (if available) ----------

(16·10¹³⁴+17)/3 = 5(3)₁₃₃9_<135> = 7 · 11 · 31 · 4163857 · 129955037024232517_<18> · C108

C108 = P34 · P37 · P38

P34 = 7099268159581713691554413997525083_<34>

P37 = 4760738577651298269591554866833674069_<37>

P38 = 12217137744962110664685060042692824819_<38>

Number: 53339_134
N=412911886952778951482599343105106825878811600735884610546214381342461568817914643805148222356406506358511413
  ( 108 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=7099268159581713691554413997525083
 r2=4760738577651298269591554866833674069
 r3=12217137744962110664685060042692824819
Version: 
Total time: 2.82 hours.
Scaled time: 7.21 units (timescale=2.554).
Factorization parameters were as follows:
name: 53339_134
n: 412911886952778951482599343105106825878811600735884610546214381342461568817914643805148222356406506358511413
m: 1000000000000000000000000000
deg: 5
c5: 8
c0: 85
skew: 1.60
type: snfs
lss: 1
rlim: 1290000
alim: 1290000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1290000/1290000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [645000, 1020001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 153532 x 153780
Total sieving time: 2.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,47,47,2.3,2.3,75000
total time: 2.82 hours.
 --------- CPU info (if available) ----------

(16·10¹³⁵+17)/3 = 5(3)₁₃₄9_<136> = 53 · 109 · 39983 · C128

C128 = P42 · P87

P42 = 133371437502545860492092625754017350087647_<42>

P87 = 173124348209509979320647923853723089400683536821989636733066792235614750308712167807707_<87>

Number: 53339_135
N=23089843187393647550915965204085430843911558956321943721240490915291817671174492422795930841723074756716789564305237088292095429
  ( 128 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=133371437502545860492092625754017350087647
 r2=173124348209509979320647923853723089400683536821989636733066792235614750308712167807707
Version: 
Total time: 2.81 hours.
Scaled time: 7.21 units (timescale=2.564).
Factorization parameters were as follows:
name: 53339_135
n: 23089843187393647550915965204085430843911558956321943721240490915291817671174492422795930841723074756716789564305237088292095429
m: 1000000000000000000000000000
deg: 5
c5: 16
c0: 17
skew: 1.01
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1025001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 165863 x 166111
Total sieving time: 2.81 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 2.81 hours.
 --------- CPU info (if available) ----------

(16·10¹³⁰+17)/3 = 5(3)₁₂₉9_<131> = 11 · 13 · 499 · 32102129 · C119

C119 = P42 · P77

P42 = 275816506470850227753681936494105767780247_<42>

P77 = 84412751354152141283549803205638828396580374356093958903094653958614394263729_<77>

Number: 53339_130
N=23282430180094775401664521018455232150876520275482514920064567080964332978328610680296163882721213301511223106234761063
  ( 119 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=275816506470850227753681936494105767780247 (pp42)
 r2=84412751354152141283549803205638828396580374356093958903094653958614394263729 (pp77)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.44 hours.
Scaled time: 1.62 units (timescale=0.471).
Factorization parameters were as follows:
name: 53339_130
n: 23282430180094775401664521018455232150876520275482514920064567080964332978328610680296163882721213301511223106234761063
m: 100000000000000000000000000
deg: 5
c5: 16
c0: 17
skew: 1.01
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 790001)
Primes: RFBsize:84270, AFBsize:83658, largePrimes:2549375 encountered
Relations: rels:2425796, finalFF:198554
Max relations in full relation-set: 28
Initial matrix: 167992 x 198554 with sparse part having weight 12368837.
Pruned matrix : 152731 x 153634 with weight 7390128.
Total sieving time: 3.02 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 3.44 hours.
 --------- CPU info (if available) ----------

(16·10¹³¹+17)/3 = 5(3)₁₃₀9_<132> = 61 · 113 · 1171 · 1184923 · 754627619 · 7329756391_<10> · C101

C101 = P46 · P55

P46 = 1715422178096007542208514188552440247371207737_<46>

P55 = 5876925256617012992829424695030398752503942555565595747_<55>

Number: 53339_131
N=10081407924213394489644691046726487228205642771742243655608201909603448312917038974804331061300694539
  ( 101 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=1715422178096007542208514188552440247371207737 (pp46)
 r2=5876925256617012992829424695030398752503942555565595747 (pp55)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.88 hours.
Scaled time: 1.83 units (timescale=0.471).
Factorization parameters were as follows:
name: 53339_131
n: 10081407924213394489644691046726487228205642771742243655608201909603448312917038974804331061300694539
m: 200000000000000000000000000
deg: 5
c5: 5
c0: 17
skew: 1.28
type: snfs
rlim: 1120000
alim: 1120000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1120000/1120000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [560000, 860001)
Primes: RFBsize:87166, AFBsize:87008, largePrimes:2732090 encountered
Relations: rels:2654691, finalFF:241993
Max relations in full relation-set: 28
Initial matrix: 174239 x 241993 with sparse part having weight 16453366.
Pruned matrix : 145300 x 146235 with weight 7280426.
Total sieving time: 3.47 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1120000,1120000,26,26,47,47,2.3,2.3,50000
total time: 3.88 hours.
 --------- CPU info (if available) ----------

(16·10¹³⁸+17)/3 = 5(3)₁₃₇9_<139> = 11 · 9187 · 15215909 · C127

C127 = P39 · P88

P39 = 454899394030094871696840828218919010961_<39>

P88 = 7624635131405306021976110358540209676561181550632754418412763175674346292489709058390223_<88>

Number: 53339_138
N=3468441900976846493796351077859498146675611652658964776630576869620175883842676469694774931859655655146040671758074217952234303
  ( 127 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=454899394030094871696840828218919010961
 r2=7624635131405306021976110358540209676561181550632754418412763175674346292489709058390223
Version: 
Total time: 4.22 hours.
Scaled time: 10.83 units (timescale=2.564).
Factorization parameters were as follows:
name: 53339_138
n: 3468441900976846493796351077859498146675611652658964776630576869620175883842676469694774931859655655146040671758074217952234303
m: 4000000000000000000000000000
deg: 5
c5: 125
c0: 136
skew: 1.02
type: snfs
rlim: 1510000
alim: 1510000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1510000/1510000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [755000, 1355001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 207358 x 207606
Total sieving time: 4.22 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1510000,1510000,26,26,48,48,2.3,2.3,75000
total time: 4.22 hours.
 --------- CPU info (if available) ----------

(16·10¹²⁷+17)/3 = 5(3)₁₂₆9_<128> = 5246909 · 4320900800743087688077_<22> · C100

C100 = P31 · P69

P31 = 9558968044013240910768539170267_<31>

P69 = 246099023374013580364688187219244824856754420286164173821931207411369_<69>

Fri Mar 20 02:52:59 2009  Msieve v. 1.39
Fri Mar 20 02:52:59 2009  random seeds: 487af480 a062588b
Fri Mar 20 02:52:59 2009  factoring 2352452700095063449936800197036820541946192934736737492782356811379725987285009842257277012202565523 (100 digits)
Fri Mar 20 02:53:00 2009  searching for 15-digit factors
Fri Mar 20 02:53:02 2009  commencing quadratic sieve (100-digit input)
Fri Mar 20 02:53:02 2009  using multiplier of 7
Fri Mar 20 02:53:02 2009  using 32kb Intel Core sieve core
Fri Mar 20 02:53:02 2009  sieve interval: 36 blocks of size 32768
Fri Mar 20 02:53:02 2009  processing polynomials in batches of 6
Fri Mar 20 02:53:02 2009  using a sieve bound of 2712223 (98824 primes)
Fri Mar 20 02:53:02 2009  using large prime bound of 406833450 (28 bits)
Fri Mar 20 02:53:02 2009  using double large prime bound of 3140146831659150 (43-52 bits)
Fri Mar 20 02:53:02 2009  using trial factoring cutoff of 52 bits
Fri Mar 20 02:53:02 2009  polynomial 'A' values have 13 factors
Fri Mar 20 15:36:05 2009  99080 relations (22548 full + 76532 combined from 1498989 partial), need 98920
Fri Mar 20 15:36:07 2009  begin with 1521537 relations
Fri Mar 20 15:36:08 2009  reduce to 264208 relations in 11 passes
Fri Mar 20 15:36:08 2009  attempting to read 264208 relations
Fri Mar 20 15:36:13 2009  recovered 264208 relations
Fri Mar 20 15:36:13 2009  recovered 256016 polynomials
Fri Mar 20 15:36:14 2009  attempting to build 99080 cycles
Fri Mar 20 15:36:14 2009  found 99080 cycles in 6 passes
Fri Mar 20 15:36:14 2009  distribution of cycle lengths:
Fri Mar 20 15:36:14 2009     length 1 : 22548
Fri Mar 20 15:36:14 2009     length 2 : 16737
Fri Mar 20 15:36:14 2009     length 3 : 16641
Fri Mar 20 15:36:14 2009     length 4 : 13788
Fri Mar 20 15:36:14 2009     length 5 : 10419
Fri Mar 20 15:36:14 2009     length 6 : 7348
Fri Mar 20 15:36:14 2009     length 7 : 4725
Fri Mar 20 15:36:14 2009     length 9+: 6874
Fri Mar 20 15:36:14 2009  largest cycle: 21 relations
Fri Mar 20 15:36:14 2009  matrix is 98824 x 99080 (26.9 MB) with weight 6658301 (67.20/col)
Fri Mar 20 15:36:14 2009  sparse part has weight 6658301 (67.20/col)
Fri Mar 20 15:36:16 2009  filtering completed in 3 passes
Fri Mar 20 15:36:16 2009  matrix is 95296 x 95360 (26.0 MB) with weight 6432846 (67.46/col)
Fri Mar 20 15:36:16 2009  sparse part has weight 6432846 (67.46/col)
Fri Mar 20 15:36:16 2009  saving the first 48 matrix rows for later
Fri Mar 20 15:36:16 2009  matrix is 95248 x 95360 (15.2 MB) with weight 4959974 (52.01/col)
Fri Mar 20 15:36:16 2009  sparse part has weight 3417728 (35.84/col)
Fri Mar 20 15:36:16 2009  matrix includes 64 packed rows
Fri Mar 20 15:36:16 2009  using block size 38144 for processor cache size 1024 kB
Fri Mar 20 15:36:17 2009  commencing Lanczos iteration
Fri Mar 20 15:36:17 2009  memory use: 15.4 MB
Fri Mar 20 15:37:20 2009  lanczos halted after 1508 iterations (dim = 95246)
Fri Mar 20 15:37:20 2009  recovered 17 nontrivial dependencies
Fri Mar 20 15:37:21 2009  prp31 factor: 9558968044013240910768539170267
Fri Mar 20 15:37:21 2009  prp69 factor: 246099023374013580364688187219244824856754420286164173821931207411369
Fri Mar 20 15:37:21 2009  elapsed time 12:44:22

(16·10¹⁴⁵+17)/3 = 5(3)₁₄₄9_<146> = 29 · 751 · 750670353889_<12> · C130

C130 = P37 · P94

P37 = 1017920604757100124175506379483305391_<37>

P94 = 3204775581603897617400152633317975172533435467301482055633599256186949556972877362944784052759_<94>

Number: 53339_145
N=3262207098137026742245065842599988326637156703447034000654332100641563831391951069640537622805004889844622538445754817690253123769
  ( 130 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1017920604757100124175506379483305391 (pp37)
 r2=3204775581603897617400152633317975172533435467301482055633599256186949556972877362944784052759 (pp94)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 17.11 hours.
Scaled time: 44.07 units (timescale=2.575).
Factorization parameters were as follows:
name: 53339_145
n: 3262207098137026742245065842599988326637156703447034000654332100641563831391951069640537622805004889844622538445754817690253123769
m: 100000000000000000000000000000
deg: 5
c5: 16
c0: 17
skew: 1.01
type: snfs
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [955000, 2255001)
Primes: RFBsize:142718, AFBsize:142015, largePrimes:4682805 encountered
Relations: rels:5729679, finalFF:1220613
Max relations in full relation-set: 28
Initial matrix: 284797 x 1220613 with sparse part having weight 121044188.
Pruned matrix : 178108 x 179595 with weight 38970759.
Total sieving time: 16.63 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.33 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 17.11 hours.
 --------- CPU info (if available) ----------

Mar 20, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.39 / Mar 20, 2009

(16·10¹³⁶+17)/3 = 5(3)₁₃₅9_<137> = 11 · 13 · 347897551 · 2941447767611012578678018619_<28> · C99

C99 = P30 · P69

P30 = 771382818250946354031587328347_<30>

P69 = 472476504763422496979618639544003838355917850725179339642495333077011_<69>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1151270288
Step 1 took 5788ms
Step 2 took 6180ms
********** Factor found in step 2: 771382818250946354031587328347
Found probable prime factor of 30 digits: 771382818250946354031587328347
Probable prime cofactor has 69 digits

(16·10¹⁵⁹+17)/3 = 5(3)₁₅₈9_<160> = 4201 · 11369 · 20060626646968543458887062589_<29> · C124

C124 = P30 · C95

P30 = 181460042160288350794014941791_<30>

C95 = [30675968082864569337146521319456691256436797450754597199363823113423792359722327736654385550169_<95>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1862731850
Step 1 took 6880ms
Step 2 took 7373ms
********** Factor found in step 2: 181460042160288350794014941791
Found probable prime factor of 30 digits: 181460042160288350794014941791
Composite cofactor has 95 digits

(10²¹¹+53)/9 = (1)₂₁₀7_<211> = 7 · 181 · C207

C207 = P60 · P148

P60 = 775679158324538211798792416886447302960143319020119609397291_<60>

P148 = 1130573373691367761073599909764570902857706940533980710309137548448013445674329861601139507177146771800294938047935087576614132552921906658313292861_<148>

SNFS difficulty: 211 digits.
Divisors found:
 r1=775679158324538211798792416886447302960143319020119609397291 (pp60)
 r2=1130573373691367761073599909764570902857706940533980710309137548448013445674329861601139507177146771800294938047935087576614132552921906658313292861 (pp148)
Version: Msieve-1.39
Total time: 700 hours.
Factorization parameters were as follows:
n: 876962202929053757783039550995352100324476015083749890379724633868280277120056125580987459440498114531263702534420766464965359992984302376567569937735683592037183197404191879330000876962202929053757783039551
m: 100000000000000000000000000000000000
c6: 10
c0: 53
skew: 1.32
type: snfs
lss: 0
rlim: 24000000
alim: 24000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
rlambda: 2.6
alambda: 2.6
Factor base limits: 24000000/24000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 57/57
Sieved  special-q in [12000000, 12000000)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3105940 x 3106188
Total sieving time: 638.24 hours.
Total relation processing time: 13.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.70 hours.
Prototype def-par.txt line would be:
snfs,211,6,0,0,0,0,0,0,0,0,24000000,24000000,29,29,57,57,2.6,2.6,100000
total time: 700 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU1: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU2: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU3: AMD Phenom(tm) II X4 940 Processor stepping 02
Memory: 3529040k/4980736k available (2699k kernel code, 139436k reserved, 3164k data, 788k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 6012.71 BogoMIPS (lpj=12025428)
Calibrating delay using timer specific routine.. 6012.89 BogoMIPS (lpj=12025792)
Calibrating delay using timer specific routine.. 6012.90 BogoMIPS (lpj=12025816)
Calibrating delay using timer specific routine.. 6012.92 BogoMIPS (lpj=12025858)
Total of 4 processors activated (24051.44 BogoMIPS).

(16·10¹⁷⁸+17)/3 = 5(3)₁₇₇9_<179> = 11 · 13² · 347 · 32983 · 12815736715308752903_<20> · C150

C150 = P31 · P119

P31 = 8027904486080268433980556857271_<31>

P119 = 24364299818203828966518485563165406695156284904992604114161373746380016498564692263558254965206297584342752781795141517_<119>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1159831445
Step 1 took 8153ms
Step 2 took 8392ms
********** Factor found in step 2: 8027904486080268433980556857271
Found probable prime factor of 31 digits: 8027904486080268433980556857271
Probable prime cofactor  has 119 digits

(16·10¹⁹⁸+17)/3 = 5(3)₁₉₇9_<199> = 11 · 785468738335223_<15> · C183

C183 = P29 · C155

P29 = 10809721554503831623054520711_<29>

C155 = [57103487227479446124405422629494541923845415148310131046666472629860297816874516504637895482742596878953891789085625659624914076124765874321722241320269233_<155>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2135270727
Step 1 took 11285ms
Step 2 took 10733ms
********** Factor found in step 2: 10809721554503831623054520711
Found probable prime factor of 29 digits: 10809721554503831623054520711
Composite cofactor  has 155 digits

(16·10²⁰¹+17)/3 = 5(3)₂₀₀9_<202> = 19 · 29 · 313 · 1901 · 94360271 · C186

C186 = P31 · C155

P31 = 2501174201872189797561830194829_<31>

C155 = [68926710845622768023245400986497791282629481535689213308309687739001187639469203420891227576987844761091134389590016352081985710450401698271387066361347267_<155>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1396396328
Step 1 took 11309ms
Step 2 took 10765ms
********** Factor found in step 2: 2501174201872189797561830194829
Found probable prime factor of 31 digits: 2501174201872189797561830194829
Composite cofactor has 155 digits

(16·10¹⁷⁹+17)/3 = 5(3)₁₇₈9_<180> = 31 · C179

C179 = P28 · C151

P28 = 4352766929105745465096103339_<28>

C151 = [3952497653901114378182237986523852819615423623387147757833038683132838563176883622310981910798946192505014288043510847790520570489159500579928667953871_<151>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1608146848
Step 1 took 11397ms
Step 2 took 10308ms
********** Factor found in step 2: 4352766929105745465096103339
Found probable prime factor of 28 digits: 4352766929105745465096103339
Composite cofactor has 151 digits

(10²¹⁴+17)/9 = (1)₂₁₃3_<214> = 3⁴ · 7 · C211

C211 = P31 · C180

P31 = 2400620043423893687330474477519_<31>

C180 = [816302269336336417450842188577028118534151673845025146540677993240102379833555401451594875762033128334475072601234838476484961787092961779341206131926579524992582962870838310352081_<180>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4255587043
Step 1 took 13105ms
Step 2 took 11832ms
********** Factor found in step 2: 2400620043423893687330474477519
Found probable prime factor of 31 digits: 2400620043423893687330474477519
Composite cofactor has 180 digits

Mar 20, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Mar 20, 2009

(16·10¹⁰²+17)/3 = 5(3)₁₀₁9_<103> = 11 · C102

C102 = P37 · P66

P37 = 2216835011184651104357370439054681171_<37>

P66 = 218712029719066643999777936156525071087223952004261785269174040619_<66>

Number: 53339_102
N=484848484848484848484848484848484848484848484848484848484848484848484848484848484848484848484848484849
  ( 102 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=2216835011184651104357370439054681171 (pp37)
 r2=218712029719066643999777936156525071087223952004261785269174040619 (pp66)
Version: Msieve-1.39
Total time: 0.22 hours.
Scaled time: 0.26 units (timescale=1.161).
Factorization parameters were as follows:
n: 484848484848484848484848484848484848484848484848484848484848484848484848484848484848484848484848484849
m: 40000000000000000000000000
deg: 4
c4: 25
c0: 68
skew: 1.28
type: snfs
lss: 1
rlim: 380000
alim: 380000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2
Factor base limits: 380000/380000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [190000, 230001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 37393 x 37641
Total sieving time: 0.22 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103,4,0,0,0,0,0,0,0,0,380000,380000,25,25,43,43,2.2,2.2,10000
total time: 0.22 hours.
 --------- CPU info (if available) ----------

(16·10¹¹⁰+17)/3 = 5(3)₁₀₉9_<111> = 7 · 11 · C109

C109 = P51 · P59

P51 = 135086690288448751461631065121489142470928690167339_<51>

P59 = 51273792492932242100515971807088862039055864903322893309013_<59>

Number: 53339_110
N=6926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926407
  ( 109 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=135086690288448751461631065121489142470928690167339 (pp51)
 r2=51273792492932242100515971807088862039055864903322893309013 (pp59)
Version: Msieve-1.39
Total time: 0.60 hours.
Scaled time: 0.69 units (timescale=1.141).
Factorization parameters were as follows:
n: 6926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926406926407
m: 10000000000000000000000
deg: 5
c5: 16
c0: 17
skew: 1.01
type: snfs
lss: 1
rlim: 500000
alim: 500000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [250000, 350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 41203 x 41434
Total sieving time: 0.60 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000
total time: 0.60 hours.
 --------- CPU info (if available) ----------

(16·10¹¹²+17)/3 = 5(3)₁₁₁9_<113> = 11 · 13 · 991 · 5851 · C104

C104 = P44 · P61

P44 = 10052627114734674217024858005477241449308291_<44>

P61 = 6398517534744581605598630845005091076336770653616769994460283_<61>

Number: 53339_112
N=64321910863878643972984750803785593219329524248465718103326515801739318258957238451545530070232222106353
  ( 104 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=10052627114734674217024858005477241449308291 (pp44)
 r2=6398517534744581605598630845005091076336770653616769994460283 (pp61)
Version: Msieve-1.39
Total time: 0.55 hours.
Scaled time: 0.64 units (timescale=1.153).
Factorization parameters were as follows:
n: 64321910863878643972984750803785593219329524248465718103326515801739318258957238451545530070232222106353
m: 20000000000000000000000
deg: 5
c5: 50
c0: 17
skew: 0.81
type: snfs
lss: 1
rlim: 540000
alim: 540000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 540000/540000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [270000, 370001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 53786 x 54015
Total sieving time: 0.55 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,540000,540000,25,25,45,45,2.2,2.2,50000
total time: 0.55 hours.
 --------- CPU info (if available) ----------

(16·10¹¹⁸+17)/3 = 5(3)₁₁₇9_<119> = 11 · 13 · 283 · 364415983 · C106

C106 = P40 · P67

P40 = 2517482123877466831458022023288845848163_<40>

P67 = 1436522534239865706135598288861372125341339035520699265067882825739_<67>

Number: 53339_118
N=3616419800496018185554643018778838665393873550895999781300841991930045462239647250842316622568282582267457
  ( 106 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=2517482123877466831458022023288845848163 (pp40)
 r2=1436522534239865706135598288861372125341339035520699265067882825739 (pp67)
Version: Msieve-1.39
Total time: 0.85 hours.
Scaled time: 1.01 units (timescale=1.188).
Factorization parameters were as follows:
n: 3616419800496018185554643018778838665393873550895999781300841991930045462239647250842316622568282582267457
m: 400000000000000000000000
deg: 5
c5: 125
c0: 136
skew: 1.02
type: snfs
lss: 1
rlim: 700000
alim: 700000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [350000, 500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 68036 x 68272
Total sieving time: 0.85 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.2,2.2,50000
total time: 0.85 hours.
 --------- CPU info (if available) ----------

(47·10¹⁷⁴+7)/9 = 5(2)₁₇₃3_<175> = 3 · C175

C175 = P75 · P100

P75 = 620557364544933209347505543283287271715542928474811138177123479741287954493_<75>

P100 = 2805124618925858366785530971753399005552313623794237404028517151752362815052615083829211038292546537_<100>

Number: 52223_174
N=1740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741
  ( 175 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=620557364544933209347505543283287271715542928474811138177123479741287954493 (pp75)
 r2=2805124618925858366785530971753399005552313623794237404028517151752362815052615083829211038292546537 (pp100)
Version: Msieve-1.39
Total time: 102.99 hours.
Scaled time: 179.10 units (timescale=1.739).
Factorization parameters were as follows:
n: 1740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741
m: 100000000000000000000000000000000000
deg: 5
c5: 47
c0: 70
skew: 1.08
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3100000, 8500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1410995 x 1411243
Total sieving time: 102.99 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,53,53,2.5,2.5,100000
total time: 102.99 hours.
 --------- CPU info (if available) ----------

(16·10¹²⁴+17)/3 = 5(3)₁₂₃9_<125> = 11 · 13 · C123

C123 = P37 · P86

P37 = 4344103805341820701058553135691460443_<37>

P86 = 85854387849055129411080779368254210843202081626934091049880827926685804285234450918511_<86>

Number: 53339_124
N=372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960373
  ( 123 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=4344103805341820701058553135691460443
 r2=85854387849055129411080779368254210843202081626934091049880827926685804285234450918511
Version: 
Total time: 2.03 hours.
Scaled time: 5.16 units (timescale=2.544).
Factorization parameters were as follows:
n: 372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960373
m: 10000000000000000000000000
deg: 5
c5: 8
c0: 85
skew: 1.60
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 640001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 95005 x 95253
Total sieving time: 2.03 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 2.03 hours.
 --------- CPU info (if available) ----------

(47·10¹⁶⁵+61)/9 = 5(2)₁₆₄9_<166> = 3² · 7 · 5591 · 57457 · C156

C156 = P77 · P79

P77 = 72533535683897919367050843049102695262622230330026538812469651505101456980937_<77>

P79 = 3557488562285399128352167251090547646264542317070408776923597887660186679045557_<79>

Number: 52229_165
N=258037223577586703584366939521687141457565042608347763233440879201328184257788165302728714631007910945833069136088685122225466935446774836043071413903546909
  ( 156 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=72533535683897919367050843049102695262622230330026538812469651505101456980937 (pp77)
 r2=3557488562285399128352167251090547646264542317070408776923597887660186679045557 (pp79)
Version: Msieve-1.39
Total time: 43.32 hours.
Scaled time: 110.89 units (timescale=2.560).
Factorization parameters were as follows:
n: 258037223577586703584366939521687141457565042608347763233440879201328184257788165302728714631007910945833069136088685122225466935446774836043071413903546909
m: 1000000000000000000000000000000000
deg: 5
c5: 47
c0: 61
skew: 1.05
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 743624 x 743872
Total sieving time: 43.32 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 43.32 hours.
 --------- CPU info (if available) ----------

(16·10¹⁶⁶+17)/3 = 5(3)₁₆₅9_<167> = 11 · 13 · C165

C165 = P32 · P134

P32 = 18446113805573149007822003131717_<32>

P134 = 20218913148399309160757726082320481802184037361213630414348530230821676575403409534317023506556541934147864836343737525024390817510769_<134>

Number: 53339_166
N=372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960373
  ( 165 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=18446113805573149007822003131717 (pp32)
 r2=20218913148399309160757726082320481802184037361213630414348530230821676575403409534317023506556541934147864836343737525024390817510769 (pp134)
Version: Msieve-1.39
Total time: 26.55 hours.
Scaled time: 46.17 units (timescale=1.739).
Factorization parameters were as follows:
n: 372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960372960373
m: 2000000000000000000000000000000000
deg: 5
c5: 5
c0: 17
skew: 1.28
type: snfs
lss: 1
rlim: 4300000
alim: 4300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4300000/4300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2150000, 3550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 705711 x 705959
Total sieving time: 26.55 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,4300000,4300000,27,27,51,51,2.4,2.4,100000
total time: 26.55 hours.
 --------- CPU info (if available) ----------

Mar 20, 2009 (2nd)

By Tyler Cadigan / GGNFS, msieve / Mar 20, 2009

(10¹⁸⁵+53)/9 = (1)₁₈₄7_<185> = 8527 · 29587001068429855351442206649_<29> · C152

C152 = P67 · P85

P67 = 5477538869759508716233535573334454107332303923923355918060914957961_<67>

P85 = 8040347369121449262829305304011094341740754632560203590976683381742939344017026888739_<85>

Number: 11117_185
N=44041315240731342627152033825315210424898830618066156602341326236451254516042808567074969782491829929498528258973637320140692358628653317197742809301179
  ( 152 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=5477538869759508716233535573334454107332303923923355918060914957961 (pp67)
 r2=8040347369121449262829305304011094341740754632560203590976683381742939344017026888739 (pp85)
Version: Msieve-1.39
Total time: 250.09 hours.
Scaled time: 641.24 units (timescale=2.564).
Factorization parameters were as follows:
n: 44041315240731342627152033825315210424898830618066156602341326236451254516042808567074969782491829929498528258973637320140692358628653317197742809301179
m: 10000000000000000000000000000000000000
deg: 5
c5: 1
c0: 53
skew: 2.21
type: snfs
lss: 1
rlim: 8500000
alim: 8500000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4250000, 8250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1207241 x 1207489
Total sieving time: 250.09 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,8500000,8500000,28,28,54,54,2.5,2.5,100000
total time: 250.09 hours.
 --------- CPU info (if available) ----------

Mar 20, 2009

Factorizations of 544...441 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 19, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Mar 19, 2009

(47·10¹⁵⁵+43)/9 = 5(2)₁₅₄7_<156> = 53 · 1123 · 6854419180999669_<16> · 9562893297694897418761_<22> · C114

C114 = P43 · P71

P43 = 1397470491947633752572738006663140974036393_<43>

P71 = 95784912349718487411932418288029995627417379622853984198602872452343209_<71>

Number: n
N=133856588582522074245145041981306385740123220548779419003259092949533192359296116928474190874485652535703692405137
  ( 114 digits)
Divisors found:

Thu Mar 19 20:53:29 2009  prp43 factor: 1397470491947633752572738006663140974036393
Thu Mar 19 20:53:29 2009  prp71 factor: 95784912349718487411932418288029995627417379622853984198602872452343209
Thu Mar 19 20:53:29 2009  elapsed time 01:42:06 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.11 hours.
Scaled time: 34.84 units (timescale=1.823).
Factorization parameters were as follows:
n: 133856588582522074245145041981306385740123220548779419003259092949533192359296116928474190874485652535703692405137
skew: 80691.62
Y0: -8289403519030582587562
Y1:  509751010163
c0: -2041210546406800131753532935
c1:  1083180025265749843277181
c2:  3650027098564077305
c3: -235277594845393
c4: -353315578
c5:  3420
type: gnfs
name: KA_5_2_154_7
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1750000, 2602283)
Primes: RFBsize:250150, AFBsize:248462, largePrimes:16642854 encountered
Relations: rels:14546049, finalFF:509469
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 905433 hash collisions in 15107156 relations
Msieve: matrix is 598018 x 598266 (167.6 MB)

Total sieving time: 18.64 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,28,28,56,56,2.6,2.6,100000
total time: 19.11 hours.
 --------- CPU info (if available) ----------

Mar 19, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Mar 19, 2009

(47·10¹⁴⁸+43)/9 = 5(2)₁₄₇7_<149> = 3³ · 7 · 29 · 67 · 1223 · 21705793 · 2017078085045614618421_<22> · C112

C112 = P55 · P57

P55 = 3980941556193166603838231490318104342696694098555483207_<55>

P57 = 667129456521162682500034200289208198670786991776880206997_<57>

Number: 52227_148
N=2655803376825658847637458230916276479422795676367628311147056956567958355588426064464073349447932249543517399379
  ( 112 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=3980941556193166603838231490318104342696694098555483207 (pp55)
 r2=667129456521162682500034200289208198670786991776880206997 (pp57)
Version: Msieve-1.39
Total time: 17.37 hours.
Scaled time: 44.66 units (timescale=2.571).
Factorization parameters were as follows:
n: 2655803376825658847637458230916276479422795676367628311147056956567958355588426064464073349447932249543517399379
m: 500000000000000000000000000000
deg: 5
c5: 376
c0: 1075
skew: 1.23
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 2150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 431941 x 432189
Total sieving time: 17.37 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 17.37 hours.
 --------- CPU info (if available) ----------

Mar 19, 2009 (2nd)

By Erik Branger / GGNFS, Msieve, GMP-ECM / Mar 19, 2009

(47·10¹⁵³+43)/9 = 5(2)₁₅₂7_<154> = 2002540933830131711_<19> · C136

C136 = P36 · P101

P36 = 257352985880137140848352215811551723_<36>

P101 = 10133156143982625350749263738927449627185877360057069960197245768769800614330181000523922313277930759_<101>

Number: 52227_153
N=2607797990043585498486776563577293170179160358822379016514029370980619932719161276506780892488605173914090155178598786073131670341147757
  ( 136 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=257352985880137140848352215811551723
 r2=10133156143982625350749263738927449627185877360057069960197245768769800614330181000523922313277930759
Version: 
Total time: 37.46 hours.
Scaled time: 36.11 units (timescale=0.964).
Factorization parameters were as follows:
n: 2607797990043585498486776563577293170179160358822379016514029370980619932719161276506780892488605173914090155178598786073131670341147757
m: 5000000000000000000000000000000
deg: 5
c5: 376
c0: 1075
skew: 1.23
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 570944 x 571192
Total sieving time: 37.46 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 37.46 hours.
 --------- CPU info (if available) ----------

(10²²⁵-7)/3 = (3)₂₂₄1_<225> = 137737 · 134156123 · 67743226688030353193_<20> · 199494502930691408785361_<24> · 122625043098363429270779593379_<30> · C140

C140 = P42 · P98

P42 = 860214666824601272460880156994772578011619_<42>

P98 = 12654203042712555984328454204858279619330389192948935697292522058994841156413713475656590209377697_<98>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 10885331054317837011064517548146007631894457980921054037615043412068918053334979676466099035906851721409340820885267078426597342035625461443 (140 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1082531224
Step 1 took 42901ms
Step 2 took 15132ms
********** Factor found in step 2: 860214666824601272460880156994772578011619
Found probable prime factor of 42 digits: 860214666824601272460880156994772578011619
Probable prime cofactor 12654203042712555984328454204858279619330389192948935697292522058994841156413713475656590209377697 has 98 digits

(47·10¹⁵²+43)/9 = 5(2)₁₅₁7_<153> = 23 · 31 · 5977957 · C144

C144 = P42 · P103

P42 = 102954757437537587020286226041931725738471_<42>

P103 = 1190053845694343160057405598164702056965447494076340682927117292004770107354365772690735150938069056457_<103>

Number: 52227_152
N=122521705021069884387637246526784156891699758592426768050055408604573625933007212113030244983476855679600447806602593063561942636751192515857247
  ( 144 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=102954757437537587020286226041931725738471
 r2=1190053845694343160057405598164702056965447494076340682927117292004770107354365772690735150938069056457
Version: 
Total time: 33.77 hours.
Scaled time: 26.44 units (timescale=0.783).
Factorization parameters were as follows:
n: 122521705021069884387637246526784156891699758592426768050055408604573625933007212113030244983476855679600447806602593063561942636751192515857247
m: 2000000000000000000000000000000
deg: 5
c5: 1175
c0: 344
skew: 0.78
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 499587 x 499835
Total sieving time: 33.77 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 33.77 hours.
 --------- CPU info (if available) ----------

Mar 19, 2009

Factorizations of 533...339 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 18, 2009 (4th)

By Sinkiti Sibata / GGNFS / Mar 18, 2009

(47·10¹⁴³+43)/9 = 5(2)₁₄₂7_<144> = 1256797 · C138

C138 = P37 · P101

P37 = 4843817090846848103800130938749666541_<37>

P101 = 85783246430773379911102166695200551942332371371885262915582905035373010589522772606960016182845664651_<101>

Number: 52227_143
N=415518355169706979108179142870505119141931610452779742649148766445354518050426777134431592550127206081986368699338256076536005593761142191
  ( 138 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=4843817090846848103800130938749666541 (pp37)
 r2=85783246430773379911102166695200551942332371371885262915582905035373010589522772606960016182845664651 (pp101)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 30.82 hours.
Scaled time: 14.52 units (timescale=0.471).
Factorization parameters were as follows:
name: 52227_143
n: 415518355169706979108179142870505119141931610452779742649148766445354518050426777134431592550127206081986368699338256076536005593761142191
m: 50000000000000000000000000000
deg: 5
c5: 376
c0: 1075
skew: 1.23
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [950000, 3450001)
Primes: RFBsize:142029, AFBsize:141497, largePrimes:4391493 encountered
Relations: rels:4701517, finalFF:334993
Max relations in full relation-set: 28
Initial matrix: 283593 x 334993 with sparse part having weight 40541816.
Pruned matrix : 267398 x 268879 with weight 31033526.
Total sieving time: 27.63 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 2.77 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 30.82 hours.
 --------- CPU info (if available) ----------

Mar 18, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Mar 18, 2009

(46·10¹⁶⁷+71)/9 = 5(1)₁₆₆9_<168> = 3² · 7 · 19 · 1117 · 4679 · 27883 · C154

C154 = P54 · P101

P54 = 107947980468983175179209407936978627331988033676681083_<54>

P101 = 27143192890863234580560273644490456064319074781755462331364854263414746355660087083256912160513206201_<101>

Number: 51119_167
N=2930052856048747415696412580021740877656459525605510537337184012695666922105062747081510430361540113889889941395993487864740777776024112205338840894995683
  ( 154 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=107947980468983175179209407936978627331988033676681083 (pp54)
 r2=27143192890863234580560273644490456064319074781755462331364854263414746355660087083256912160513206201 (pp101)
Version: Msieve-1.39
Total time: 62.79 hours.
Scaled time: 161.43 units (timescale=2.571).
Factorization parameters were as follows:
n: 2930052856048747415696412580021740877656459525605510537337184012695666922105062747081510430361540113889889941395993487864740777776024112205338840894995683
m: 2000000000000000000000000000000000
deg: 5
c5: 575
c0: 284
skew: 0.87
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2300000, 5500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 916037 x 916285
Total sieving time: 62.79 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000
total time: 62.79 hours.
 --------- CPU info (if available) ----------

(47·10¹⁶¹+61)/9 = 5(2)₁₆₀9_<162> = 140853961 · C154

C154 = P63 · P92

P63 = 219943733041963750242646478617524491832623759499803899627166611_<63>

P92 = 16856782845527874382183048874522274027542137890355911903085056358760184087391042615656550399_<92>

Number: 52229_161
N=3707543746123136872396667795676844488755429619918336710617759781865291116820081632082907645190199672284844174330477097638895807993800204328099954691527789
  ( 154 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=219943733041963750242646478617524491832623759499803899627166611 (pp63)
 r2=16856782845527874382183048874522274027542137890355911903085056358760184087391042615656550399 (pp92)
Version: Msieve-1.39
Total time: 36.14 hours.
Scaled time: 92.92 units (timescale=2.571).
Factorization parameters were as follows:
n: 3707543746123136872396667795676844488755429619918336710617759781865291116820081632082907645190199672284844174330477097638895807993800204328099954691527789
m: 100000000000000000000000000000000
deg: 5
c5: 470
c0: 61
skew: 0.66
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1800000, 3700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 669486 x 669734
Total sieving time: 36.14 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000
total time: 36.14 hours.
 --------- CPU info (if available) ----------

(47·10¹⁴⁹+61)/9 = 5(2)₁₄₈9_<150> = 4076210434301839_<16> · 211174768175632908845141_<24> · C111

C111 = P54 · P58

P54 = 219213132009021623869566675173488915702299783936522029_<54>

P58 = 2767516118398801454302828847039547607150038471761799341899_<58>

Number: 52229_149
N=606675876199651581317035127957145483690901889131660586888217858313407073692363357548983792092630032283116193071
  ( 111 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=219213132009021623869566675173488915702299783936522029 (pp54)
 r2=2767516118398801454302828847039547607150038471761799341899 (pp58)
Version: Msieve-1.39
Total time: 16.20 hours.
Scaled time: 41.65 units (timescale=2.571).
Factorization parameters were as follows:
n: 606675876199651581317035127957145483690901889131660586888217858313407073692363357548983792092630032283116193071
m: 1000000000000000000000000000000
deg: 5
c5: 47
c0: 610
skew: 1.67
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 436101 x 436349
Total sieving time: 16.20 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 16.20 hours.
 --------- CPU info (if available) ----------

Mar 18, 2009 (2nd)

By Max Dettweiler / GGNFS, msieve v1.40beta2 / Mar 18, 2009

(47·10¹⁵¹+61)/9 = 5(2)₁₅₀9_<152> = 73 · 691 · 5003 · 84389 · 6105956179_<10> · C129

C129 = P47 · P83

P47 = 13551298952508005615508715858630155784976003377_<47>

P83 = 29634901503428958238102266429923613340973044009914909611452496602972186130738987123_<83>

Number: 52229_151
N=401591409701094762557236606442942058249930610119999828677048360538804414672459347923455562310561948894319531364533784369607514371
  ( 129 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=13551298952508005615508715858630155784976003377 (pp47)
 r2=29634901503428958238102266429923613340973044009914909611452496602972186130738987123 (pp83)
Version: Msieve-1.40
Total time: 21.55 hours.
Scaled time: 35.41 units (timescale=1.643).
Factorization parameters were as follows:
n: 401591409701094762557236606442942058249930610119999828677048360538804414672459347923455562310561948894319531364533784369607514371
m: 1000000000000000000000000000000
deg: 5
c5: 470
c0: 61
skew: 0.66
type: snfs
lss: 1
rlim: 2500000
alim: 2500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4

Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1250000, 2150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 433946 x 434194
Total sieving time: 21.55 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000
total time: 21.55 hours.
 --------- CPU info (if available) ----------
[    0.366872] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456430] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.13 BogoMIPS (lpj=8800268)
[    0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800821)
[    0.460050] Total of 2 processors activated (8800.54 BogoMIPS).

Mar 18, 2009

By Robert Backstrom / GGNFS, Msieve / Mar 18, 2009

(47·10¹⁴⁷+43)/9 = 5(2)₁₄₆7_<148> = 419 · 1230122762141569_<16> · 384189113824853757332970331_<27> · C104

C104 = P48 · P57

P48 = 185767993337027714455265134749591365614059015697_<48>

P57 = 141963574575550541691236928123164412858691879492806034451_<57>

Number: n
N=26372288375851510075141295091256465723888801319948296741264515789328641332678379950721528722522931777347
  ( 104 digits)
Divisors found:

Wed Mar 18 02:57:01 2009  prp48 factor: 185767993337027714455265134749591365614059015697
Wed Mar 18 02:57:01 2009  prp57 factor: 141963574575550541691236928123164412858691879492806034451
Wed Mar 18 02:57:01 2009  elapsed time 00:31:08 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.77 hours.
Scaled time: 12.35 units (timescale=1.823).
Factorization parameters were as follows:
n: 26372288375851510075141295091256465723888801319948296741264515789328641332678379950721528722522931777347
skew: 29710.99
Y0: -144401432342722261807
Y1:  36431541157
c0: -15122488454704756317858600
c1: -13242623711720306931140
c2: -210177813641840938
c3:  18447924067323
c4:  157240256
c5:  420
type: gnfs
name: KA_5_2_146_7
rlim: 2300000
alim: 2300000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1150000, 10000000
)
Primes: RFBsize:169511, AFBsize:169780, largePrimes:14660589 encountered
Relations: rels:12861753, finalFF:536940
Max relations in full relation-set: 28
Initial matrix: 339372 x 536940 with sparse part having weight 62352556.
Pruned matrix : 237664 x 239424 with weight 22900522.

Msieve: found 823997 hash collisions in 13420417 relations
Msieve: matrix is 276291 x 276539 (76.0 MB)

Total sieving time: 6.44 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,28,28,56,56,2.6,2.6,100000
total time: 6.77 hours.
 --------- CPU info (if available) ----------

Mar 17, 2009 (10th)

By Luigi Morelli / GGNFS 0.77.1 Msieve 1.39 / Mar 17, 2009

(4·10¹⁷⁴+41)/9 = (4)₁₇₃9_<174> = 401 · 1531 · 2333 · 11103172231868232665208082632227_<32> · C134

C134 = P41 · P93

P41 = 38399983418304274738274024976546740584967_<41>

P93 = 727788294601551888099993904173706931765025315072705833126180244134209183779214775385936665507_<93>

Tue Mar 17 12:36:41 2009  Msieve v. 1.39
Tue Mar 17 12:36:41 2009  random seeds: 9f714800 598b1444
Tue Mar 17 12:36:41 2009  factoring 27947058444735539012965143631675640717984624676970856746909322865014587987121750699821648616857592608427104241739512228516510591633269 (134 digits)
Tue Mar 17 12:36:43 2009  searching for 15-digit factors
Tue Mar 17 12:36:44 2009  commencing number field sieve (134-digit input)
Tue Mar 17 12:36:44 2009  R0: -100000000000000000000000000000000000
Tue Mar 17 12:36:44 2009  R1:  1
Tue Mar 17 12:36:44 2009  A0:  205
Tue Mar 17 12:36:44 2009  A1:  0
Tue Mar 17 12:36:44 2009  A2:  0
Tue Mar 17 12:36:44 2009  A3:  0
Tue Mar 17 12:36:44 2009  A4:  0
Tue Mar 17 12:36:44 2009  A5:  2
Tue Mar 17 12:36:44 2009  skew 1.00, size 4.781583e-12, alpha 0.465368, combined = 4.094518e-12
Tue Mar 17 12:36:44 2009  
Tue Mar 17 12:36:44 2009  commencing relation filtering
Tue Mar 17 12:36:44 2009  commencing duplicate removal, pass 1
Tue Mar 17 12:39:42 2009  found 2143411 hash collisions in 17416460 relations
Tue Mar 17 12:40:21 2009  added 671889 free relations
Tue Mar 17 12:40:21 2009  commencing duplicate removal, pass 2
Tue Mar 17 12:41:43 2009  found 1937728 duplicates and 16150621 unique relations
Tue Mar 17 12:41:43 2009  memory use: 94.6 MB
Tue Mar 17 12:41:43 2009  reading rational ideals above 7012352
Tue Mar 17 12:41:43 2009  reading algebraic ideals above 7012352
Tue Mar 17 12:41:43 2009  commencing singleton removal, pass 1
Tue Mar 17 12:44:56 2009  relations with 0 large ideals: 244208
Tue Mar 17 12:44:56 2009  relations with 1 large ideals: 1795043
Tue Mar 17 12:44:56 2009  relations with 2 large ideals: 5122439
Tue Mar 17 12:44:56 2009  relations with 3 large ideals: 5971131
Tue Mar 17 12:44:56 2009  relations with 4 large ideals: 2369746
Tue Mar 17 12:44:56 2009  relations with 5 large ideals: 119
Tue Mar 17 12:44:56 2009  relations with 6 large ideals: 647935
Tue Mar 17 12:44:56 2009  relations with 7+ large ideals: 0
Tue Mar 17 12:44:56 2009  16150621 relations and about 15885771 large ideals
Tue Mar 17 12:44:56 2009  commencing singleton removal, pass 2
Tue Mar 17 12:48:09 2009  found 6116062 singletons
Tue Mar 17 12:48:09 2009  current dataset: 10034559 relations and about 7925909 large ideals
Tue Mar 17 12:48:09 2009  commencing singleton removal, pass 3
Tue Mar 17 12:50:11 2009  found 1790905 singletons
Tue Mar 17 12:50:11 2009  current dataset: 8243654 relations and about 6034970 large ideals
Tue Mar 17 12:50:11 2009  commencing singleton removal, pass 4
Tue Mar 17 12:52:06 2009  found 425142 singletons
Tue Mar 17 12:52:06 2009  current dataset: 7818512 relations and about 5601775 large ideals
Tue Mar 17 12:52:07 2009  commencing singleton removal, final pass
Tue Mar 17 12:54:13 2009  memory use: 130.9 MB
Tue Mar 17 12:54:13 2009  commencing in-memory singleton removal
Tue Mar 17 12:54:14 2009  begin with 7818512 relations and 6159339 unique ideals
Tue Mar 17 12:54:28 2009  reduce to 6545569 relations and 4850622 ideals in 15 passes
Tue Mar 17 12:54:28 2009  max relations containing the same ideal: 23
Tue Mar 17 12:54:30 2009  reading rational ideals above 720000
Tue Mar 17 12:54:30 2009  reading algebraic ideals above 720000
Tue Mar 17 12:54:30 2009  commencing singleton removal, final pass
Tue Mar 17 12:56:38 2009  keeping 5403754 ideals with weight <= 20, new excess is 646417
Tue Mar 17 12:56:44 2009  memory use: 180.2 MB
Tue Mar 17 12:56:44 2009  commencing in-memory singleton removal
Tue Mar 17 12:56:45 2009  begin with 6587026 relations and 5403754 unique ideals
Tue Mar 17 12:56:55 2009  reduce to 6544199 relations and 5158066 ideals in 9 passes
Tue Mar 17 12:56:55 2009  max relations containing the same ideal: 20
Tue Mar 17 12:57:01 2009  removing 1565742 relations and 1247597 ideals in 318145 cliques
Tue Mar 17 12:57:03 2009  commencing in-memory singleton removal
Tue Mar 17 12:57:03 2009  begin with 4978457 relations and 5158066 unique ideals
Tue Mar 17 12:57:12 2009  reduce to 4751966 relations and 3671154 ideals in 10 passes
Tue Mar 17 12:57:12 2009  max relations containing the same ideal: 20
Tue Mar 17 12:57:16 2009  removing 1201681 relations and 883536 ideals in 318145 cliques
Tue Mar 17 12:57:17 2009  commencing in-memory singleton removal
Tue Mar 17 12:57:18 2009  begin with 3550285 relations and 3671154 unique ideals
Tue Mar 17 12:57:22 2009  reduce to 3350302 relations and 2574646 ideals in 9 passes
Tue Mar 17 12:57:22 2009  max relations containing the same ideal: 19
Tue Mar 17 12:57:26 2009  removing 166581 relations and 140769 ideals in 25812 cliques
Tue Mar 17 12:57:26 2009  commencing in-memory singleton removal
Tue Mar 17 12:57:26 2009  begin with 3183721 relations and 2574646 unique ideals
Tue Mar 17 12:57:30 2009  reduce to 3178656 relations and 2428761 ideals in 7 passes
Tue Mar 17 12:57:30 2009  max relations containing the same ideal: 19
Tue Mar 17 12:57:31 2009  relations with 0 large ideals: 94799
Tue Mar 17 12:57:31 2009  relations with 1 large ideals: 482369
Tue Mar 17 12:57:31 2009  relations with 2 large ideals: 1004006
Tue Mar 17 12:57:31 2009  relations with 3 large ideals: 988933
Tue Mar 17 12:57:31 2009  relations with 4 large ideals: 473837
Tue Mar 17 12:57:31 2009  relations with 5 large ideals: 110708
Tue Mar 17 12:57:31 2009  relations with 6 large ideals: 23262
Tue Mar 17 12:57:31 2009  relations with 7+ large ideals: 742
Tue Mar 17 12:57:31 2009  commencing 2-way merge
Tue Mar 17 12:57:34 2009  reduce to 2015714 relation sets and 1265819 unique ideals
Tue Mar 17 12:57:34 2009  commencing full merge
Tue Mar 17 12:58:00 2009  memory use: 112.3 MB
Tue Mar 17 12:58:00 2009  found 985977 cycles, need 886019
Tue Mar 17 12:58:01 2009  weight of 886019 cycles is about 62112073 (70.10/cycle)
Tue Mar 17 12:58:01 2009  distribution of cycle lengths:
Tue Mar 17 12:58:01 2009  1 relations: 119487
Tue Mar 17 12:58:01 2009  2 relations: 88429
Tue Mar 17 12:58:01 2009  3 relations: 87433
Tue Mar 17 12:58:01 2009  4 relations: 84047
Tue Mar 17 12:58:01 2009  5 relations: 80706
Tue Mar 17 12:58:01 2009  6 relations: 74925
Tue Mar 17 12:58:01 2009  7 relations: 68225
Tue Mar 17 12:58:01 2009  8 relations: 61469
Tue Mar 17 12:58:01 2009  9 relations: 53842
Tue Mar 17 12:58:01 2009  10+ relations: 167456
Tue Mar 17 12:58:01 2009  heaviest cycle: 17 relations
Tue Mar 17 12:58:01 2009  commencing cycle optimization
Tue Mar 17 12:58:03 2009  start with 5154831 relations
Tue Mar 17 12:58:17 2009  pruned 188003 relations
Tue Mar 17 12:58:17 2009  memory use: 165.8 MB
Tue Mar 17 12:58:17 2009  distribution of cycle lengths:
Tue Mar 17 12:58:17 2009  1 relations: 119487
Tue Mar 17 12:58:17 2009  2 relations: 91154
Tue Mar 17 12:58:17 2009  3 relations: 91767
Tue Mar 17 12:58:17 2009  4 relations: 87747
Tue Mar 17 12:58:17 2009  5 relations: 84891
Tue Mar 17 12:58:17 2009  6 relations: 78509
Tue Mar 17 12:58:17 2009  7 relations: 71066
Tue Mar 17 12:58:17 2009  8 relations: 62784
Tue Mar 17 12:58:17 2009  9 relations: 54055
Tue Mar 17 12:58:17 2009  10+ relations: 144559
Tue Mar 17 12:58:17 2009  heaviest cycle: 16 relations
Tue Mar 17 12:58:18 2009  
Tue Mar 17 12:58:18 2009  commencing linear algebra
Tue Mar 17 12:58:20 2009  read 886019 cycles
Tue Mar 17 12:58:24 2009  cycles contain 2746427 unique relations
Tue Mar 17 13:00:07 2009  read 2746427 relations
Tue Mar 17 13:00:21 2009  using 20 quadratic characters above 268435130
Tue Mar 17 13:00:44 2009  building initial matrix
Tue Mar 17 13:01:30 2009  memory use: 345.1 MB
Tue Mar 17 13:01:34 2009  read 886019 cycles
Tue Mar 17 13:01:35 2009  matrix is 885691 x 886019 (261.2 MB) with weight 78785843 (88.92/col)
Tue Mar 17 13:01:35 2009  sparse part has weight 58716555 (66.27/col)
Tue Mar 17 13:02:07 2009  filtering completed in 3 passes
Tue Mar 17 13:02:07 2009  matrix is 882183 x 882383 (260.5 MB) with weight 78558142 (89.03/col)
Tue Mar 17 13:02:07 2009  sparse part has weight 58574600 (66.38/col)
Tue Mar 17 13:02:17 2009  read 882383 cycles
Tue Mar 17 13:02:18 2009  matrix is 882183 x 882383 (260.5 MB) with weight 78558142 (89.03/col)
Tue Mar 17 13:02:18 2009  sparse part has weight 58574600 (66.38/col)
Tue Mar 17 13:02:18 2009  saving the first 48 matrix rows for later
Tue Mar 17 13:02:18 2009  matrix is 882135 x 882383 (248.1 MB) with weight 62087525 (70.36/col)
Tue Mar 17 13:02:18 2009  sparse part has weight 56205277 (63.70/col)
Tue Mar 17 13:02:18 2009  matrix includes 64 packed rows
Tue Mar 17 13:02:18 2009  using block size 65536 for processor cache size 2048 kB
Tue Mar 17 13:02:28 2009  commencing Lanczos iteration (2 threads)
Tue Mar 17 13:02:28 2009  memory use: 242.6 MB
Tue Mar 17 15:14:35 2009  lanczos halted after 13949 iterations (dim = 882135)
Tue Mar 17 15:14:38 2009  recovered 38 nontrivial dependencies
Tue Mar 17 15:14:38 2009  
Tue Mar 17 15:14:38 2009  commencing square root phase
Tue Mar 17 15:14:38 2009  reading relations for dependency 1
Tue Mar 17 15:14:38 2009  read 441047 cycles
Tue Mar 17 15:14:40 2009  cycles contain 1685937 unique relations
Tue Mar 17 15:16:01 2009  read 1685937 relations
Tue Mar 17 15:16:14 2009  multiplying 1370800 relations
Tue Mar 17 15:18:54 2009  multiply complete, coefficients have about 32.47 million bits
Tue Mar 17 15:18:55 2009  initial square root is modulo 2113031471
Tue Mar 17 15:23:50 2009  reading relations for dependency 2
Tue Mar 17 15:23:52 2009  read 441001 cycles
Tue Mar 17 15:23:54 2009  cycles contain 1685340 unique relations
Tue Mar 17 15:25:24 2009  read 1685340 relations
Tue Mar 17 15:25:37 2009  multiplying 1371486 relations
Tue Mar 17 15:28:15 2009  multiply complete, coefficients have about 32.49 million bits
Tue Mar 17 15:28:16 2009  initial square root is modulo 2141250271
Tue Mar 17 15:33:06 2009  reading relations for dependency 3
Tue Mar 17 15:33:09 2009  read 441310 cycles
Tue Mar 17 15:33:11 2009  cycles contain 1685743 unique relations
Tue Mar 17 15:34:57 2009  read 1685743 relations
Tue Mar 17 15:35:10 2009  multiplying 1370442 relations
Tue Mar 17 15:37:50 2009  multiply complete, coefficients have about 32.46 million bits
Tue Mar 17 15:37:50 2009  initial square root is modulo 2103565001
Tue Mar 17 15:42:49 2009  prp41 factor: 38399983418304274738274024976546740584967
Tue Mar 17 15:42:49 2009  prp93 factor: 727788294601551888099993904173706931765025315072705833126180244134209183779214775385936665507
Tue Mar 17 15:42:49 2009  elapsed time 03:06:08

Mar 17, 2009 (9th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Mar 17, 2009

(47·10¹²⁹+43)/9 = 5(2)₁₂₈7_<130> = 53 · 1709 · 39563 · 664394297591_<12> · C109

C109 = P50 · P60

P50 = 11392640902908865486786962808915005513936037420777_<50>

P60 = 192529771430516722768552082971149709013406250854830961537511_<60>

Number: n
N=2193422549026999531240180405969308634774081473846196681195301222164747803070319802746246945986037686776266047
  ( 109 digits)
Divisors found:

Tue Mar 17 07:53:13 2009  prp50 factor: 11392640902908865486786962808915005513936037420777
Tue Mar 17 07:53:13 2009  prp60 factor: 192529771430516722768552082971149709013406250854830961537511
Tue Mar 17 07:53:13 2009  elapsed time 01:04:28 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.69 hours.
Scaled time: 19.17 units (timescale=1.793).
Factorization parameters were as follows:
n: 2193422549026999531240180405969308634774081473846196681195301222164747803070319802746246945986037686776266047
skew: 35509.20
Y0: -789741278560127834899
Y1:  216704254129
c0: -302573579818317197066484660
c1:  16492546007944770846450
c2:  278514279697725838
c3: -23720825775976
c4: -6014549
c5:  7140
type: gnfs
name: KA_5_2_128_7
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1600000, 10000000
)
Primes: RFBsize:230209, AFBsize:231161, largePrimes:15904187 encountered
Relations: rels:13829817, finalFF:539057
Max relations in full relation-set: 28
Initial matrix: 461452 x 539057 with sparse part having weight 57962085.
Pruned matrix : 401595 x 403966 with weight 35176102.

Msieve: found 968534 hash collisions in 14496195 relations
Msieve: matrix is 437224 x 437472 (120.1 MB)

Total sieving time: 10.26 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000
total time: 10.69 hours.
 --------- CPU info (if available) ----------

(47·10¹⁷⁷-11)/9 = 5(2)₁₇₆1_<178> = 17 · 491 · 476994724582963119809_<21> · 29336523767341974250914648586797711269_<38> · C116

C116 = P33 · P83

P33 = 614088122589594009791062335998749_<33>

P83 = 72806811291749103675145316370430609189394369231815902251648901884514781346021057767_<83>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 44709798057885060980656834282070292023087303425981948741349201177796626681785466973031767603121232173890091368733483 (116 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=3266589655
Step 1 took 33988ms
Step 2 took 15123ms
********** Factor found in step 2: 614088122589594009791062335998749
Found probable prime factor of 33 digits: 614088122589594009791062335998749
Probable prime cofactor 72806811291749103675145316370430609189394369231815902251648901884514781346021057767 has 83 digits

Mar 17, 2009 (8th)

By Sinkiti Sibata / GGNFS, Msieve / Mar 17, 2009

(47·10¹³³+43)/9 = 5(2)₁₃₂7_<134> = 3 · 188443 · 2797019 · C122

C122 = P42 · P81

P42 = 237701512526503316094085015925914398939871_<42>

P81 = 138939816988084835328310231759557123542468331563336367798939674241466623501737287_<81>

Number: 52227_133
N=33026204648223325723542311678054028103025705149354813007075200971205810804912651075595987113664903079159513943959551669977
  ( 122 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=237701512526503316094085015925914398939871 (pp42)
 r2=138939816988084835328310231759557123542468331563336367798939674241466623501737287 (pp81)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 12.01 hours.
Scaled time: 5.67 units (timescale=0.472).
Factorization parameters were as follows:
name: 52227_133
n: 33026204648223325723542311678054028103025705149354813007075200971205810804912651075595987113664903079159513943959551669977
m: 500000000000000000000000000
deg: 5
c5: 376
c0: 1075
skew: 1.23
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1700001)
Primes: RFBsize:100021, AFBsize:99643, largePrimes:3416033 encountered
Relations: rels:3427270, finalFF:250618
Max relations in full relation-set: 28
Initial matrix: 199731 x 250618 with sparse part having weight 26073288.
Pruned matrix : 186068 x 187130 with weight 17115454.
Total sieving time: 10.98 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.78 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 12.01 hours.
 --------- CPU info (if available) ----------

(47·10¹⁵⁹+43)/9 = 5(2)₁₅₈7_<160> = C160

C160 = P45 · P116

P45 = 447820738433104994589571533297604237016615893_<45>

P116 = 11661412199208171450910796477053685957193762778984934328207442349695941331544774427207372189329106930197283990416839_<116>

Number: 52227_159
N=5222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
  ( 160 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=447820738433104994589571533297604237016615893
 r2=11661412199208171450910796477053685957193762778984934328207442349695941331544774427207372189329106930197283990416839
Version: 
Total time: 41.14 hours.
Scaled time: 105.07 units (timescale=2.554).
Factorization parameters were as follows:
name: 52227_159
n: 5222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
m: 100000000000000000000000000000000
deg: 5
c5: 47
c0: 430
skew: 1.56
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 712197 x 712445
Total sieving time: 41.14 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 41.14 hours.
 --------- CPU info (if available) ----------

(47·10¹⁴⁶+61)/9 = 5(2)₁₄₅9_<147> = 118268440765127268526454053_<27> · C121

C121 = P50 · P72

P50 = 12822898127825871123041260367860744391887985989183_<50>

P72 = 344350156992285033341866116549986062298882723986694029020884286713875471_<72>

Number: 52229_146
N=4415566983412916558364200333566126155840383990444855088058423457637337768106379951019223089264831632838735255607415030193
  ( 121 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=12822898127825871123041260367860744391887985989183 (pp50)
 r2=344350156992285033341866116549986062298882723986694029020884286713875471 (pp72)
Version: GGNFS-0.77.1-20060513-nocona
Total time: 23.49 hours.
Scaled time: 60.22 units (timescale=2.564).
Factorization parameters were as follows:
name: 52229_146
n: 4415566983412916558364200333566126155840383990444855088058423457637337768106379951019223089264831632838735255607415030193
m: 100000000000000000000000000000
deg: 5
c5: 470
c0: 61
skew: 0.66
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 3100001)
Primes: RFBsize:148933, AFBsize:149036, largePrimes:4703269 encountered
Relations: rels:5381201, finalFF:641992
Max relations in full relation-set: 28
Initial matrix: 298036 x 641992 with sparse part having weight 79596977.
Pruned matrix : 227418 x 228972 with weight 37582236.
Total sieving time: 22.80 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.51 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000
total time: 23.49 hours.
 --------- CPU info (if available) ----------

Mar 17, 2009 (7th)

By Serge Batalov / GMP-ECM 6.2.2 / Mar 17, 2009

(47·10¹⁵⁵+61)/9 = 5(2)₁₅₄9_<156> = 43 · 35909329 · 58770731 · C139

C139 = P32 · C108

P32 = 20170670960464360204959468810331_<32>

C108 = [285297630994272504091552978449388295403830314074853375107757128116579477814437793906499110695817310611368087_<108>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=958636256
Step 1 took 7668ms
Step 2 took 7649ms
********** Factor found in step 2: 20170670960464360204959468810331
Found probable prime factor of 32 digits: 20170670960464360204959468810331
Composite cofactor has 108 digits

(47·10¹⁸⁸+61)/9 = 5(2)₁₈₇9_<189> = 967 · 550690601939_<12> · 605847532138397_<15> · 109183642953133633_<18> · C143

C143 = P35 · P108

P35 = 34461699539841418825579125628841351_<35>

P108 = 430193252317702480711040497680446163331824874304874768856386928623928612241031321894543131893971208149393683_<108>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2141233825
Step 1 took 7765ms
Step 2 took 7620ms
********** Factor found in step 2: 34461699539841418825579125628841351
Found probable prime factor of 35 digits: 34461699539841418825579125628841351
Probable prime cofactor has 108 digits

(47·10¹⁷⁹+61)/9 = 5(2)₁₇₈9_<180> = 109 · 668111 · C172

C172 = P29 · P144

P29 = 46086527706787783863770048419_<29>

P144 = 155598798818920185760682857386549258894779410779794936254768626444142587537228894385588949913316988978207015735754666249496968259470947413724909_<144>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1444878925
Step 1 took 9129ms
Step 2 took 8957ms
********** Factor found in step 2: 46086527706787783863770048419
Found probable prime factor of 29 digits: 46086527706787783863770048419
Probable prime cofactor has 144 digits

(47·10¹⁹⁰+61)/9 = 5(2)₁₈₉9_<191> = 701 · 12441484225824125533_<20> · C169

C169 = P35 · C134

P35 = 93603981074749332057833540879042243_<35>

C134 = [63969184928555725419888542337471071127268261667483265316817211212893362944495734135745868593470357733678892956596854054764423090641391_<134>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2046487259
Step 1 took 8953ms
Step 2 took 8917ms
********** Factor found in step 2: 93603981074749332057833540879042243
Found probable prime factor of 35 digits: 93603981074749332057833540879042243
Composite cofactor has 134 digits

(47·10¹⁸³+61)/9 = 5(2)₁₈₂9_<184> = 3⁴ · 7² · 73 · 13159 · C175

C175 = P35 · C140

P35 = 23580467869898578816558113541392511_<35>

C140 = [58086617139822417192309155633607444600006416172320696813705786684420593367822572818386028872976485426874441318380077890295282806517242070133_<140>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2046773793
Step 1 took 11001ms
********** Factor found in step 1: 23580467869898578816558113541392511
Found probable prime factor of 35 digits: 23580467869898578816558113541392511
Composite cofactor has 140 digits

Mar 17, 2009 (6th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Mar 17, 2009

4·10¹⁸⁷+1 = 4(0)₁₈₆1_<188> = 173 · 466357 · C180

C180 = P53 · P128

P53 = 17220341786228465534537012038573242088381604649445961_<53>

P128 = 28790792619619581217940562985478392520067468106423516010341011616813295711690892727971687568687842629056533596007927442531799081_<128>

Number: 40001_187
N=495787289206273181696708298379812999198150822484464226412371251322868941071850721025313895017611665954240989880969032617734204740641212360557191040761759321523027317842451218961841
  ( 180 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=17220341786228465534537012038573242088381604649445961
 r2=28790792619619581217940562985478392520067468106423516010341011616813295711690892727971687568687842629056533596007927442531799081
Version: 
Total time: 123.18 hours.
Scaled time: 294.16 units (timescale=2.388).
Factorization parameters were as follows:
n: 495787289206273181696708298379812999198150822484464226412371251322868941071850721025313895017611665954240989880969032617734204740641212360557191040761759321523027317842451218961841
m: 20000000000000000000000000000000000000
deg: 5
c5: 25
c0: 2
skew: 0.60
type: snfs
lss: 1
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 7600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 20253983
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1689001 x 1689249
Total sieving time: 112.04 hours.
Total relation processing time: 3.38 hours.
Matrix solve time: 7.54 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000
total time: 123.18 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Mar 17, 2009 (5th)

By Max Dettweiler / YAFU v1.07, GMP-ECM / Mar 17, 2009

(47·10¹³⁷+61)/9 = 5(2)₁₃₆9_<138> = 739 · 877 · 295289375079011_<15> · 6661471907757357183761_<22> · C96

C96 = P40 · P57

P40 = 1229958574412209062018051100217580143117_<40>

P57 = 333044917807515859998647944588270739048031866360687340149_<57>

03/16/09 14:26:52 v1.07 @ Core2Duo, starting SIQS on c96: 409631452321763546825635704242285696253772845989896048275809030748571767303698583312109480104433
03/16/09 14:26:52 v1.07 @ Core2Duo, random seeds: 3914057527, 3818987683
03/16/09 14:26:54 v1.07 @ Core2Duo, ==== sieve params ====
03/16/09 14:26:54 v1.07 @ Core2Duo, n = 96 digits, 318 bits
03/16/09 14:26:54 v1.07 @ Core2Duo, factor base: 88192 primes (max prime = 2397251)
03/16/09 14:26:54 v1.07 @ Core2Duo, single large prime cutoff: 311642630 (130 * pmax)
03/16/09 14:26:54 v1.07 @ Core2Duo, double large prime range from 44 to 51 bits
03/16/09 14:26:54 v1.07 @ Core2Duo, double large prime cutoff: 1943490174637453
03/16/09 14:26:54 v1.07 @ Core2Duo, using 6 large prime slices of factor base
03/16/09 14:26:54 v1.07 @ Core2Duo, buckets hold 2048 elements
03/16/09 14:26:54 v1.07 @ Core2Duo, sieve interval: 26 blocks of size 32768
03/16/09 14:26:54 v1.07 @ Core2Duo, polynomial A has ~ 12 factors
03/16/09 14:26:54 v1.07 @ Core2Duo, using multiplier of 1
03/16/09 14:26:54 v1.07 @ Core2Duo, using small prime variation correction of 17 bits
03/16/09 14:26:54 v1.07 @ Core2Duo, using x128 sieve scanning
03/16/09 14:26:54 v1.07 @ Core2Duo, trial factoring cutoff at 100 bits
03/16/09 14:26:54 v1.07 @ Core2Duo, ==== sieving started ====
03/16/09 17:11:19 v1.07 @ Core2Duo, sieve time = 3229.1400, relation time = 1905.8000, poly_time = 4442.4100
03/16/09 17:11:19 v1.07 @ Core2Duo, 88271 relations found: 21574 full + 66697 from 1222577 partial, using 835916 polys (394 A polys)
03/16/09 17:11:19 v1.07 @ Core2Duo, trial division touched 69874537 sieve locations out of 1424347365376
03/16/09 17:11:19 v1.07 @ Core2Duo, ==== post processing stage (msieve-1.38) ====
03/16/09 17:11:20 v1.07 @ Core2Duo, begin with 1244251 relations
03/16/09 17:11:21 v1.07 @ Core2Duo, reduce to 229300 relations in 12 passes
03/16/09 17:11:26 v1.07 @ Core2Duo, failed to read relation 207209
03/16/09 17:11:26 v1.07 @ Core2Duo, recovered 229299 relations
03/16/09 17:11:26 v1.07 @ Core2Duo, recovered 208310 polynomials
03/16/09 17:11:26 v1.07 @ Core2Duo, attempting to build 88257 cycles
03/16/09 17:11:26 v1.07 @ Core2Duo, found 88257 cycles in 5 passes
03/16/09 17:11:26 v1.07 @ Core2Duo, distribution of cycle lengths:
03/16/09 17:11:26 v1.07 @ Core2Duo,    length 1 : 21574
03/16/09 17:11:26 v1.07 @ Core2Duo,    length 2 : 15434
03/16/09 17:11:26 v1.07 @ Core2Duo,    length 3 : 14923
03/16/09 17:11:26 v1.07 @ Core2Duo,    length 4 : 11922
03/16/09 17:11:26 v1.07 @ Core2Duo,    length 5 : 8967
03/16/09 17:11:26 v1.07 @ Core2Duo,    length 6 : 6126
03/16/09 17:11:26 v1.07 @ Core2Duo,    length 7 : 3975
03/16/09 17:11:26 v1.07 @ Core2Duo,    length 9+: 5336
03/16/09 17:11:26 v1.07 @ Core2Duo, largest cycle: 18 relations
03/16/09 17:11:27 v1.07 @ Core2Duo, matrix is 88192 x 88257 (23.5 MB) with weight 5796900 (65.68/col)
03/16/09 17:11:27 v1.07 @ Core2Duo, sparse part has weight 5796900 (65.68/col)
03/16/09 17:11:27 v1.07 @ Core2Duo, filtering completed in 3 passes
03/16/09 17:11:27 v1.07 @ Core2Duo, matrix is 84165 x 84229 (22.6 MB) with weight 5587386 (66.34/col)
03/16/09 17:11:27 v1.07 @ Core2Duo, sparse part has weight 5587386 (66.34/col)
03/16/09 17:11:28 v1.07 @ Core2Duo, saving the first 48 matrix rows for later
03/16/09 17:11:28 v1.07 @ Core2Duo, matrix is 84117 x 84229 (15.3 MB) with weight 4514775 (53.60/col)
03/16/09 17:11:28 v1.07 @ Core2Duo, sparse part has weight 3511399 (41.69/col)
03/16/09 17:11:28 v1.07 @ Core2Duo, matrix includes 64 packed rows
03/16/09 17:11:28 v1.07 @ Core2Duo, using block size 33691 for processor cache size 2048 kB
03/16/09 17:11:29 v1.07 @ Core2Duo, commencing Lanczos iteration
03/16/09 17:11:29 v1.07 @ Core2Duo, memory use: 14.3 MB
03/16/09 17:12:10 v1.07 @ Core2Duo, lanczos halted after 1331 iterations (dim = 84113)
03/16/09 17:12:10 v1.07 @ Core2Duo, recovered 14 nontrivial dependencies
03/16/09 17:12:14 v1.07 @ Core2Duo, prp40 = 1229958574412209062018051100217580143117
03/16/09 17:12:21 v1.07 @ Core2Duo, prp57 = 333044917807515859998647944588270739048031866360687340149
03/16/09 17:12:21 v1.07 @ Core2Duo, Lanczos elapsed time = 51.2800 seconds.
03/16/09 17:12:21 v1.07 @ Core2Duo, Sqrt elapsed time = 10.8300 seconds.
03/16/09 17:12:21 v1.07 @ Core2Duo, SIQS elapsed time = 1096.3454 seconds.

(67·10¹⁹¹+23)/9 = 7(4)₁₉₀7_<192> = 3² · 11² · 9956010343_<10> · 561750256945597_<15> · C165

C165 = P34 · P131

P34 = 8742382186818513270120447634366543_<34>

P131 = 13981250154135229763977812263070237818367049830931795609270922886301496724935321192761453876499684380506757087169425148648104581491_<131>

p34=8742382186818513270120447634366543
p131=13981250154135229763977812263070237818367049830931795609270922886301496724935321192761453876499684380506757087169425148648104581491

B1=1000000
B2=900000000
Method=ECM

Found by the ECM "workers" at http://factorization.ath.cx/

Mar 17, 2009 (4th)

By Erik Branger / GMP-ECM, GGNFS, Msieve / Mar 17, 2009

3·10¹⁹⁷-7 = 2(9)₁₉₆3_<198> = 67 · 25681669240470105277_<20> · 21451079937695822139779_<23> · 1876671100474280819361703093_<28> · C127

C127 = P41 · P87

P41 = 18169475745070368235047593594222882815709_<41>

P87 = 238365545013807894815720084404080433701714960158653579266908647472548106703098919265349_<87>

GMP-ECM 6.2 [powered by GMP 4.2.2] [ECM]
Input number is 4330976988588861597642516703502643572946498675819236690760299247042532595697073682060977818571773462597312462576121850836567441 (127 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3289226908
Step 1 took 46469ms
Step 2 took 20219ms
********** Factor found in step 2: 18169475745070368235047593594222882815709
Found probable prime factor of 41 digits: 18169475745070368235047593594222882815709
Probable prime cofactor 238365545013807894815720084404080433701714960158653579266908647472548106703098919265349 has 87 digits

(47·10¹⁴⁴+61)/9 = 5(2)₁₄₃9_<145> = 3 · 29 · C143

C143 = P29 · P34 · P81

P29 = 35665836196780192728533512673_<29>

P34 = 1976709432008267264427519070426499_<34>

P81 = 851414124657241695767207870881297397947237108071634876732657125843696881206420721_<81>

Number: 52229_144
N=60025542784163473818646232439335887611749680715197956577266922094508301404853128991060025542784163473818646232439335887611749680715197956577267
  ( 143 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=35665836196780192728533512673
 r2=1976709432008267264427519070426499
 r3=851414124657241695767207870881297397947237108071634876732657125843696881206420721
Version: 
Total time: 12.31 hours.
Scaled time: 12.75 units (timescale=1.036).
Factorization parameters were as follows:
n: 60025542784163473818646232439335887611749680715197956577266922094508301404853128991060025542784163473818646232439335887611749680715197956577267
m: 100000000000000000000000000000
deg: 5
c5: 47
c0: 610
skew: 1.67
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 364332 x 364580
Total sieving time: 12.31 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000
total time: 12.31 hours.
 --------- CPU info (if available) ----------

(47·10¹⁴³+61)/9 = 5(2)₁₄₂9_<144> = 73 · 4041006941_<10> · 22110538207_<11> · 132175148290802436241_<21> · C102

C102 = P39 · P63

P39 = 843533943620266080062357916034467423067_<39>

P63 = 718110386575849847385899895133421039103985314002695286774474957_<63>

Number: 52229_143
N=605750486343000404874843255841407322336179563269398224619563116036694385526322917940252330159715633119
  ( 102 digits)
Divisors found:
 r1=843533943620266080062357916034467423067
 r2=718110386575849847385899895133421039103985314002695286774474957
Version: 
Total time: 9.17 hours.
Scaled time: 7.24 units (timescale=0.789).
Factorization parameters were as follows:
name: 52229_143
n: 605750486343000404874843255841407322336179563269398224619563116036694385526322917940252330159715633119
skew: 2028.19
# norm 3.98e+013
c5: 484680
c4: -957011292
c3: -7259569440258
c2: 12296856586459339
c1: 22812751531700371574
c0: -73288405825787053568
# alpha -5.27
Y1: 25932542933
Y0: -16571735877576221307
# Murphy_E 2.82e-009
# M 383023636319566478011625387693809335917375317312372669279878183539994291798391880866888635246176265339
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 232156 x 232404
Polynomial selection time: 0.62 hours.
Total sieving time: 8.55 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 9.17 hours.
 --------- CPU info (if available) ----------

(47·10²⁰⁰+43)/9 = 5(2)₁₉₉7_<201> = 113 · 853 · 24859327 · 4022503938417172421_<19> · 81661159834850505446996196467_<29> · C141

C141 = P35 · P107

P35 = 14203539304945934778007887162430733_<35>

P107 = 46712155440985981607753930130389120385682882442511927976679692258734669248416395002564591942933159986827539_<107>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 663477935824788494666093050738147217914783193816803634989617103134072298117191799321453512055544348268243496237828509997594797466760504356087 (141 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1727023116
Step 1 took 93569ms
Step 2 took 17098ms
********** Factor found in step 2: 14203539304945934778007887162430733
Found probable prime factor of 35 digits: 14203539304945934778007887162430733
Probable prime cofactor 46712155440985981607753930130389120385682882442511927976679692258734669248416395002564591942933159986827539 has 107 digits

Mar 17, 2009 (3rd)

By Markus Tervooren / Msieve / Mar 17, 2009

(47·10¹²⁵+61)/9 = 5(2)₁₂₄9_<126> = 17 · 41668745081_<11> · 71510375148277575668027_<23> · C92

C92 = P38 · P54

P38 = 36119310367160443267030313272188255347_<38>

P54 = 285422036073732811972082844292589214988221463070831533_<54>

Msieve v. 1.40
Mon Mar 16 18:48:35 2009
random seeds: 09b0ea96 fc39a54b
factoring 10309247106574019575801427213546091197756556283296533777875259460763507614969253051823456951 (92 digits)
searching for 15-digit factors
commencing quadratic sieve (92-digit input)
using multiplier of 11
using 32kb Intel Core sieve core
sieve interval: 36 blocks of size 32768
processing polynomials in batches of 6
using a sieve bound of 1748333 (65882 primes)
using large prime bound of 176581633 (27 bits)
using double large prime bound of 699039714332622 (42-50 bits)
using trial factoring cutoff of 50 bits
polynomial 'A' values have 12 factors

sieving in progress (press Ctrl-C to pause)
66430 relations (16969 full + 49461 combined from 801476 partial), need 65978
66430 relations (16969 full + 49461 combined from 801476 partial), need 65978
sieving complete, commencing postprocessing
begin with 818445 relations
reduce to 166376 relations in 11 passes
attempting to read 166376 relations
recovered 166376 relations
recovered 147930 polynomials
attempting to build 66430 cycles
found 66430 cycles in 5 passes
distribution of cycle lengths:
   length 1 : 16969
   length 2 : 12288
   length 3 : 11501
   length 4 : 9184
   length 5 : 6476
   length 6 : 4214
   length 7 : 2619
   length 9+: 3179
largest cycle: 19 relations
matrix is 65882 x 66430 (17.4 MB) with weight 4026396 (60.61/col)
sparse part has weight 4026396 (60.61/col)
filtering completed in 3 passes
matrix is 62105 x 62169 (16.3 MB) with weight 3763927 (60.54/col)
sparse part has weight 3763927 (60.54/col)
saving the first 48 matrix rows for later
matrix is 62057 x 62169 (10.1 MB) with weight 2907251 (46.76/col)
sparse part has weight 2023206 (32.54/col)
matrix includes 64 packed rows
using block size 24867 for processor cache size 4096 kB
commencing Lanczos iteration
memory use: 9.2 MB
linear algebra completed 56196 of 62169 dimensions (90.4%, ETA 0h 0m)
lanczos halted after 983 iterations (dim = 62057)
recovered 18 nontrivial dependencies
prp38 factor: 36119310367160443267030313272188255347
prp54 factor: 285422036073732811972082844292589214988221463070831533
elapsed time 01:26:49

Mar 17, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Mar 17, 2009

(47·10¹⁷²-11)/9 = 5(2)₁₇₁1_<173> = 3 · 13 · C172

C172 = P38 · P40 · P94

P38 = 57326470280112762825482407875021619271_<38>

P40 = 2765222216575167074537458175588223153487_<40>

P94 = 8447058499970139658223220341483759714366251045724118947254686381744093301848283714760444491507_<94>

Number: 52221_172
N=1339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339
  ( 172 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=57326470280112762825482407875021619271 (pp38)
 r2=2765222216575167074537458175588223153487 (pp40)
 r3=8447058499970139658223220341483759714366251045724118947254686381744093301848283714760444491507 (pp94)
Version: Msieve-1.39
Total time: 76.71 hours.
Scaled time: 133.09 units (timescale=1.735).
Factorization parameters were as follows:
n: 1339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339031339
m: 20000000000000000000000000000000000
deg: 5
c5: 1175
c0: -88
skew: 0.60
type: snfs
lss: 1
rlim: 5700000
alim: 5700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5700000/5700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2850000, 6950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1063299 x 1063547
Total sieving time: 76.71 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,5700000,5700000,27,27,52,52,2.4,2.4,100000
total time: 76.71 hours.
 --------- CPU info (if available) ----------

(47·10¹²⁴+61)/9 = 5(2)₁₂₃9_<125> = 5474531 · 10669691 · 130625682749_<12> · C100

C100 = P40 · P61

P40 = 4060994832987603706866691724669597451559_<40>

P61 = 1685371232188603324955176401904084463066907092390985334424239_<61>

Number: 52229_124
N=6844283865583869028296936434404561653472298359609743449444989938676734020553820586253449788957938601
  ( 100 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=4060994832987603706866691724669597451559 (pp40)
 r2=1685371232188603324955176401904084463066907092390985334424239 (pp61)
Version: Msieve-1.39
Total time: 1.72 hours.
Scaled time: 2.98 units (timescale=1.739).
Factorization parameters were as follows:
n: 6844283865583869028296936434404561653472298359609743449444989938676734020553820586253449788957938601
m: 10000000000000000000000000
deg: 5
c5: 47
c0: 610
skew: 1.67
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 144287 x 144535
Total sieving time: 1.72 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 1.72 hours.
 --------- CPU info (if available) ----------

(47·10¹²⁰+61)/9 = 5(2)₁₁₉9_<121> = 3² · 953 · 541999 · 556403 · 246792659 · C97

C97 = P46 · P51

P46 = 9009871097094871337526875860959775050975172901_<46>

P51 = 907990229708034753497605253062135272842718763548199_<51>

Number: 52229_120
N=8180874927090955321763329739007171305207975714973516401847502742135482630269011446011380272155299
  ( 97 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=9009871097094871337526875860959775050975172901 (pp46)
 r2=907990229708034753497605253062135272842718763548199 (pp51)
Version: Msieve-1.39
Total time: 1.40 hours.
Scaled time: 1.69 units (timescale=1.205).
Factorization parameters were as follows:
n: 8180874927090955321763329739007171305207975714973516401847502742135482630269011446011380272155299
m: 1000000000000000000000000
deg: 5
c5: 47
c0: 61
skew: 1.05
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 675001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 84053 x 84301
Total sieving time: 1.40 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 1.40 hours.
 --------- CPU info (if available) ----------

(47·10¹²⁶+61)/9 = 5(2)₁₂₅9_<127> = 3 · 31 · 83 · 241 · 128629 · 897861760885987_<15> · C101

C101 = P41 · P61

P41 = 23894510075301486165654975089685133299839_<41>

P61 = 1017257184052053219025068016261178571707894387955363477622483_<61>

Number: 52229_126
N=24306862033504603934335500192850107717193325380275387792278851810924822007257197746988141412086680237
  ( 101 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=23894510075301486165654975089685133299839 (pp41)
 r2=1017257184052053219025068016261178571707894387955363477622483 (pp61)
Version: Msieve-1.39
Total time: 1.75 hours.
Scaled time: 3.04 units (timescale=1.739).
Factorization parameters were as follows:
n: 24306862033504603934335500192850107717193325380275387792278851810924822007257197746988141412086680237
m: 10000000000000000000000000
deg: 5
c5: 470
c0: 61
skew: 0.66
type: snfs
lss: 1
rlim: 940000
alim: 940000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 940000/940000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [470000, 820001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 139863 x 140111
Total sieving time: 1.75 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,940000,940000,26,26,46,46,2.3,2.3,50000
total time: 1.75 hours.
 --------- CPU info (if available) ----------

(47·10¹¹⁹+61)/9 = 5(2)₁₁₈9_<120> = 67 · 73 · 84499 · 51527471 · 13944102105239_<14> · C91

C91 = P39 · P52

P39 = 449984349489798173821454543304923876501_<39>

P52 = 3908222901972372478578448309529138923621476871226249_<52>

Number: 52229_119
N=1758639140205169286031893103550385204774521808095693803127341596688532507052227630505474749
  ( 91 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=449984349489798173821454543304923876501 (pp39)
 r2=3908222901972372478578448309529138923621476871226249 (pp52)
Version: Msieve-1.39
Total time: 1.57 hours.
Scaled time: 1.89 units (timescale=1.203).
Factorization parameters were as follows:
n: 1758639140205169286031893103550385204774521808095693803127341596688532507052227630505474749
m: 1000000000000000000000000
deg: 5
c5: 47
c0: 610
skew: 1.67
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 725001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 89511 x 89759
Total sieving time: 1.57 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 1.57 hours.
 --------- CPU info (if available) ----------

(47·10¹¹⁸+61)/9 = 5(2)₁₁₇9_<119> = C119

C119 = P29 · P41 · P51

P29 = 18545033725620385839073282769_<29>

P41 = 18245443874384613460664481658963115751599_<41>

P51 = 154338149112696928687790210316254402187911944002059_<51>

Number: 52229_118
N=52222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
  ( 119 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=18545033725620385839073282769 (pp29)
 r2=18245443874384613460664481658963115751599 (pp41)
 r3=154338149112696928687790210316254402187911944002059 (pp51)
Version: Msieve-1.39
Total time: 1.87 hours.
Scaled time: 3.26 units (timescale=1.739).
Factorization parameters were as follows:
n: 52222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
m: 500000000000000000000000
deg: 5
c5: 376
c0: 1525
skew: 1.32
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 815001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 96047 x 96284
Total sieving time: 1.87 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.87 hours.
 --------- CPU info (if available) ----------

(47·10¹⁵¹+7)/9 = 5(2)₁₅₀3_<152> = 54377 · C147

C147 = P67 · P81

P67 = 1396878228389702772023212273444635430643248153499312015251540972847_<67>

P81 = 687514015860989579211268857010371322143295142608516624964678470259632117016644217_<81>

Number: 52223_151
N=960373360468989135520941247627162627990183758247461651474377443077444916457734377075274881332589554815863733236887327771341232915060084635456575799
  ( 147 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=1396878228389702772023212273444635430643248153499312015251540972847 (pp67)
 r2=687514015860989579211268857010371322143295142608516624964678470259632117016644217 (pp81)
Version: Msieve-1.39
Total time: 18.35 hours.
Scaled time: 47.19 units (timescale=2.571).
Factorization parameters were as follows:
n: 960373360468989135520941247627162627990183758247461651474377443077444916457734377075274881332589554815863733236887327771341232915060084635456575799
m: 2000000000000000000000000000000
deg: 5
c5: 235
c0: 112
skew: 0.86
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 436659 x 436907
Total sieving time: 18.35 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 18.35 hours.
 --------- CPU info (if available) ----------

(47·10¹⁴¹+61)/9 = 5(2)₁₄₀9_<142> = 3 · 7² · 17 · 19 · 31 · C136

C136 = P33 · P49 · P55

P33 = 237889815236994003472994542573001_<33>

P49 = 2770758482137124969166412549823186766443947403693_<49>

P55 = 5382688866148215158381784090133347240153974065965281623_<55>

Number: 52229_141
N=3547919828184056116315607548433446194927697545722684470883241053448355384409942056430193280858844197931955275979473094651933589885680739
  ( 136 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=237889815236994003472994542573001 (pp33)
 r2=2770758482137124969166412549823186766443947403693 (pp49)
 r3=5382688866148215158381784090133347240153974065965281623 (pp55)
Version: Msieve-1.39
Total time: 5.65 hours.
Scaled time: 6.78 units (timescale=1.200).
Factorization parameters were as follows:
n: 3547919828184056116315607548433446194927697545722684470883241053448355384409942056430193280858844197931955275979473094651933589885680739
m: 10000000000000000000000000000
deg: 5
c5: 470
c0: 61
skew: 0.66
type: snfs
lss: 1
rlim: 1670000
alim: 1670000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1670000/1670000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [835000, 1835001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 274463 x 274711
Total sieving time: 5.65 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1670000,1670000,26,26,48,48,2.3,2.3,100000
total time: 5.65 hours.
 --------- CPU info (if available) ----------

(47·10¹⁴²+61)/9 = 5(2)₁₄₁9_<143> = 1487 · 4300297 · C133

C133 = P37 · P97

P37 = 4565845753121195746924551387258397021_<37>

P97 = 1788647224960539742443560414147995611121695950816486297797249923096857197776551827973807510280991_<97>

Number: 52229_142
N=8166687335918092412037262866937791195485907167805717719906495118566264796547401483301565255820867166648568323166129315468551947327811
  ( 133 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=4565845753121195746924551387258397021 (pp37)
 r2=1788647224960539742443560414147995611121695950816486297797249923096857197776551827973807510280991 (pp97)
Version: Msieve-1.39
Total time: 10.51 hours.
Scaled time: 27.01 units (timescale=2.571).
Factorization parameters were as follows:
n: 8166687335918092412037262866937791195485907167805717719906495118566264796547401483301565255820867166648568323166129315468551947327811
m: 20000000000000000000000000000
deg: 5
c5: 1175
c0: 488
skew: 0.84
type: snfs
lss: 1
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [900000, 2700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 344241 x 344489
Total sieving time: 10.51 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,49,49,2.3,2.3,100000
total time: 10.51 hours.
 --------- CPU info (if available) ----------

Mar 17, 2009

Factorizations of 522...229 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 16, 2009 (7th)

By matsui / GGNFS / Mar 16, 2009

6·10¹⁹²-1 = 5(9)₁₉₂_<193> = 23 · 267413 · C186

C186 = P84 · P103

P84 = 890232504322972376418629865797962384943059627593763817566906419095999519232749088479_<84>

P103 = 1095815529709465005938774668510968742822557932763346596236533113736034194519679191569679150889348208619_<103>

N=975530603289261570483955854638786218809238079707028649220168965152258377734879722767209619902385156066198856385473763998660921658551606950915689930199159450314519195922152007503781400501
  ( 186 digits)
SNFS difficulty: 193 digits.
Divisors found:
 r1=890232504322972376418629865797962384943059627593763817566906419095999519232749088479 (pp84)
 r2=1095815529709465005938774668510968742822557932763346596236533113736034194519679191569679150889348208619 (pp103)
Version: GGNFS-0.77.1-20060722-nocona

Mar 16, 2009 (6th)

By Robert Backstrom / GMP-ECM, Msieve, GGNFS / Mar 16, 2009

(47·10¹⁵⁰+7)/9 = 5(2)₁₄₉3_<151> = 3² · 12227 · 612162408550839449_<18> · C128

C128 = P38 · P43 · P48

P38 = 12981001349455405687802789400335433709_<38>

P43 = 8235387083643003571164062884161771612247309_<43>

P48 = 725160363174653876136764441831634563361439526269_<48>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 77522232259394358631908094737783731115797641883602078896925959594795952897334482639214941425170554281822871672429199668480018789 (128 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=652276842
Step 1 took 38621ms
Step 2 took 16218ms
********** Factor found in step 2: 12981001349455405687802789400335433709
Found probable prime factor of 38 digits: 12981001349455405687802789400335433709
Composite cofactor 5971976288458414107720523065381110836076091172026394562990564642925121822831406723430060121 has 91 digits

Mon Mar 16 04:27:42 2009  
Mon Mar 16 04:27:42 2009  
Mon Mar 16 04:27:42 2009  Msieve v. 1.39
Mon Mar 16 04:27:42 2009  random seeds: 548c4a60 89bde685
Mon Mar 16 04:27:42 2009  factoring 5971976288458414107720523065381110836076091172026394562990564642925121822831406723430060121 (91 digits)
Mon Mar 16 04:27:43 2009  searching for 15-digit factors
Mon Mar 16 04:27:44 2009  commencing quadratic sieve (91-digit input)
Mon Mar 16 04:27:44 2009  using multiplier of 1
Mon Mar 16 04:27:44 2009  using 32kb Intel Core sieve core
Mon Mar 16 04:27:44 2009  sieve interval: 36 blocks of size 32768
Mon Mar 16 04:27:44 2009  processing polynomials in batches of 6
Mon Mar 16 04:27:44 2009  using a sieve bound of 1716163 (64706 primes)
Mon Mar 16 04:27:44 2009  using large prime bound of 164751648 (27 bits)
Mon Mar 16 04:27:44 2009  using double large prime bound of 617011891179744 (42-50 bits)
Mon Mar 16 04:27:44 2009  using trial factoring cutoff of 50 bits
Mon Mar 16 04:27:44 2009  polynomial 'A' values have 12 factors
Mon Mar 16 05:26:25 2009  65029 relations (16951 full + 48078 combined from 761306 partial), need 64802
Mon Mar 16 05:26:26 2009  begin with 778257 relations
Mon Mar 16 05:26:26 2009  reduce to 161404 relations in 9 passes
Mon Mar 16 05:26:26 2009  attempting to read 161404 relations
Mon Mar 16 05:26:28 2009  recovered 161404 relations
Mon Mar 16 05:26:28 2009  recovered 139326 polynomials
Mon Mar 16 05:26:28 2009  attempting to build 65029 cycles
Mon Mar 16 05:26:28 2009  found 65029 cycles in 6 passes
Mon Mar 16 05:26:28 2009  distribution of cycle lengths:
Mon Mar 16 05:26:28 2009     length 1 : 16951
Mon Mar 16 05:26:28 2009     length 2 : 12287
Mon Mar 16 05:26:28 2009     length 3 : 11392
Mon Mar 16 05:26:28 2009     length 4 : 8627
Mon Mar 16 05:26:28 2009     length 5 : 6184
Mon Mar 16 05:26:28 2009     length 6 : 4044
Mon Mar 16 05:26:28 2009     length 7 : 2499
Mon Mar 16 05:26:28 2009     length 9+: 3045
Mon Mar 16 05:26:28 2009  largest cycle: 21 relations
Mon Mar 16 05:26:28 2009  matrix is 64706 x 65029 (15.9 MB) with weight 3898076 (59.94/col)
Mon Mar 16 05:26:28 2009  sparse part has weight 3898076 (59.94/col)
Mon Mar 16 05:26:28 2009  filtering completed in 3 passes
Mon Mar 16 05:26:28 2009  matrix is 60820 x 60884 (14.9 MB) with weight 3665169 (60.20/col)
Mon Mar 16 05:26:28 2009  sparse part has weight 3665169 (60.20/col)
Mon Mar 16 05:26:28 2009  saving the first 48 matrix rows for later
Mon Mar 16 05:26:28 2009  matrix is 60772 x 60884 (9.3 MB) with weight 2866426 (47.08/col)
Mon Mar 16 05:26:28 2009  sparse part has weight 2067717 (33.96/col)
Mon Mar 16 05:26:28 2009  matrix includes 64 packed rows
Mon Mar 16 05:26:28 2009  using block size 24353 for processor cache size 6144 kB
Mon Mar 16 05:26:29 2009  commencing Lanczos iteration
Mon Mar 16 05:26:29 2009  memory use: 9.2 MB
Mon Mar 16 05:26:41 2009  lanczos halted after 962 iterations (dim = 60769)
Mon Mar 16 05:26:42 2009  recovered 15 nontrivial dependencies
Mon Mar 16 05:26:42 2009  prp43 factor: 8235387083643003571164062884161771612247309
Mon Mar 16 05:26:42 2009  prp48 factor: 725160363174653876136764441831634563361439526269
Mon Mar 16 05:26:42 2009  elapsed time 00:59:00

(46·10¹⁶⁵+53)/9 = 5(1)₁₆₄7_<166> = 7 · 4253 · 4844406113_<10> · 4523158715685319_<16> · 10446812610506949093142876229_<29> · C108

C108 = P52 · P56

P52 = 9805395862581591558891811743241601906381832514763117_<52>

P56 = 76487522248477928542358689183140209557258551332628166337_<56>

Number: n
N=749990434194342913627839994778316141735461561144432665049318858824500331417760967267346175218968089628592429
  ( 108 digits)
Divisors found:
 r1=9805395862581591558891811743241601906381832514763117 (pp52)
 r2=76487522248477928542358689183140209557258551332628166337 (pp56)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 13.07 hours.
Scaled time: 23.90 units (timescale=1.829).
Factorization parameters were as follows:
n: 749990434194342913627839994778316141735461561144432665049318858824500331417760967267346175218968089628592429
skew: 60805.78
Y0: -788541049841131603807
Y1:  173557720067
c0: -882568465664650229685322800
c1:  66651423558043426366728
c2:  163379316995626583
c3: -27437337795142
c4: -23583382
c5:  2460
type: gnfs
name: KA_5_1_164_7
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1250000, 2450001)
Primes: RFBsize:183072, AFBsize:183340, largePrimes:15881747 encountered
Relations: rels:14006430, finalFF:471490
Max relations in full relation-set: 48
Initial matrix: 366494 x 471490 with sparse part having weight 64122111.
Pruned matrix : 317653 x 319549 with weight 36740128.
Total sieving time: 10.80 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 1.22 hours.
Total square root time: 0.58 hours, sqrts: 3.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000
total time: 13.07 hours.
 --------- CPU info (if available) ----------

(41·10²⁰³-23)/9 = 4(5)₂₀₂3_<204> = 3³ · 7 · C202

C202 = P86 · P117

P86 = 15094125456308490465551318878115996120339025537086545292989082174692040718527594086663_<86>

P117 = 159687744862615450159285579376615435998685210599348040474599213834374916299730103004717447075079045798991536586802979_<117>

Number: n
N=2410346854791299235743680188124632569077013521457965902410346854791299235743680188124632569077013521457965902410346854791299235743680188124632569077013521457965902410346854791299235743680188124632569077
  ( 202 digits)
SNFS difficulty: 204 digits.
Divisors found:

Mon Mar 16 16:21:54 2009  prp86 factor: 15094125456308490465551318878115996120339025537086545292989082174692040718527594086663
Mon Mar 16 16:21:54 2009  prp117 factor: 159687744862615450159285579376615435998685210599348040474599213834374916299730103004717447075079045798991536586802979
Mon Mar 16 16:21:54 2009  elapsed time 21:39:56 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 125.18 hours.
Scaled time: 252.35 units (timescale=2.016).
Factorization parameters were as follows:
name: KA_4_5_202_3
n: 2410346854791299235743680188124632569077013521457965902410346854791299235743680188124632569077013521457965902410346854791299235743680188124632569077013521457965902410346854791299235743680188124632569077
deg: 5
c5: 41000
c0: -23
m: 10000000000000000000000000000000000000000
skew: 0.22
type: snfs
rlim: 12000000
alim: 12000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [6000000, 36099990)
Primes: RFBsize:788060, AFBsize:789435, largePrimes:34237679 encountered
Relations: rels:27085591, finalFF:93251
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 8491922 hash collisions in 45468912 relations
Msieve: matrix is 3545224 x 3545472 (963.9 MB)

Total sieving time: 124.26 hours.
Total relation processing time: 0.92 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,204,5,0,0,0,0,0,0,0,0,12000000,12000000,29,29,58,58,2.5,2.5,100000
total time: 125.18 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368976k/3407296k available (2745k kernel code, 36940k reserved, 1424k data, 412k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830498)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454)
Total of 4 processors activated (22643.71 BogoMIPS).

(46·10¹⁷⁰+53)/9 = 5(1)₁₆₉7_<171> = 11 · 19387 · 1665479 · 1794248597877849317_<19> · 5408617979271676407647398602101_<31> · C111

C111 = P55 · P56

P55 = 9374595531922456602937532247107542324675101892801624967_<55>

P56 = 15817993895177507742759884041742063160131832583292046701_<56>

Number: n
N=148287294893707759450826773884287490623864556110591552787817847024979548974477424569602377450628469980051583867
  ( 111 digits)
Divisors found:

Mon Mar 16 20:53:16 2009  prp55 factor: 9374595531922456602937532247107542324675101892801624967
Mon Mar 16 20:53:16 2009  prp56 factor: 15817993895177507742759884041742063160131832583292046701
Mon Mar 16 20:53:16 2009  elapsed time 01:30:27 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 20.68 hours.
Scaled time: 27.03 units (timescale=1.307).
Factorization parameters were as follows:
n: 148287294893707759450826773884287490623864556110591552787817847024979548974477424569602377450628469980051583867
skew: 63714.37
Y0: -2083158238752119845248
Y1:  469520352907
c0: -2678946942485839684630308575
c1:  101572738408480540974053
c2:  414611238680719735
c3: -50779098672521
c4:  32437288
c5:  3780
type: gnfs
name: KA_5_1_169_7
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1600000, 10000000
)
Primes: RFBsize:230209, AFBsize:230792, largePrimes:16366686 encountered
Relations: rels:14572121, finalFF:522575
Max relations in full relation-set: 28
Initial matrix: 461084 x 522575 with sparse part having weight 45745102.
Pruned matrix : 412416 x 414785 with weight 31728828.

Msieve: found 814083 hash collisions in 15032833 relations
Msieve: matrix is 427960 x 428207 (118.9 MB)

Total sieving time: 20.02 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 0.05 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000
total time: 20.68 hours.
 --------- CPU info (if available) ----------

Mar 16, 2009 (5th)

By Max Dettweiler / GMP-ECM / Mar 16, 2009

(67·10¹⁷⁷+23)/9 = 7(4)₁₇₆7_<178> = 11 · 3313 · 43467157849_<11> · C163

C163 = P32 · P132

P32 = 10508727647188092857659286600551_<32>

P132 = 447205144929609509317687519376751730320168590535112616587559943697202952809222522383487947174800411997675493575507903924616064217571_<132>

p32 = 10508727647188092857659286600551
p132 = 447205144929609509317687519376751730320168590535112616587559943697202952809222522383487947174800411997675493575507903924616064217571

B1=600000
B2=600000000
Application: GMP-ECM

Note: This result was found by the ECM "workers" at http://factorization.ath.cx/. They don't report tons of information to the user when a factor is found, so I don't know the sigma of the factor-finding curve, the exact GMP-ECM version used, or what hardware/OS the factor was found on.

(67·10¹⁷⁸+23)/9 = 7(4)₁₇₇7_<179> = 20795833 · 235531171 · C164

C164 = P33 · C131

P33 = 198704163317525547507605592238973_<33>

C131 = [76489287256485156251050899344113604927615140216976893295676856936461741706567528717104729246446033285942552667734816863911083369473_<131>]

p33 = 198704163317525547507605592238973
c131 = 76489287256485156251050899344113604927615140216976893295676856936461741706567528717104729246446033285942552667734816863911083369473

B1=600000
B2=600000000
Method=ECM
Found with: GMP-ECM (version unknown)

Found by the ECM "workers" at http://factorization.ath.cx/

Mar 16, 2009 (4th)

By Sinkiti Sibata / Msieve, GGNFS / Mar 16, 2009

(47·10¹¹⁹+7)/9 = 5(2)₁₁₈3_<120> = 13 · 19 · 2893741 · 143729909341_<12> · C100

C100 = P50 · P51

P50 = 39630807092145422370870826294127675253372111261851_<50>

P51 = 128268102157416318560550976482838943377755476654339_<51>

Sun Mar 15 20:54:05 2009  Msieve v. 1.39
Sun Mar 15 20:54:05 2009  random seeds: 4ac18da0 1b5e6302
Sun Mar 15 20:54:05 2009  factoring 5083368412676168189528847700401902044764602883805115375607617419999378580510744455954739057044321489 (100 digits)
Sun Mar 15 20:54:06 2009  searching for 15-digit factors
Sun Mar 15 20:54:07 2009  commencing quadratic sieve (100-digit input)
Sun Mar 15 20:54:08 2009  using multiplier of 1
Sun Mar 15 20:54:08 2009  using 32kb Intel Core sieve core
Sun Mar 15 20:54:08 2009  sieve interval: 36 blocks of size 32768
Sun Mar 15 20:54:08 2009  processing polynomials in batches of 6
Sun Mar 15 20:54:08 2009  using a sieve bound of 2751557 (99748 primes)
Sun Mar 15 20:54:08 2009  using large prime bound of 412733550 (28 bits)
Sun Mar 15 20:54:08 2009  using double large prime bound of 3222593841584400 (43-52 bits)
Sun Mar 15 20:54:08 2009  using trial factoring cutoff of 52 bits
Sun Mar 15 20:54:08 2009  polynomial 'A' values have 13 factors
Mon Mar 16 04:22:33 2009  100300 relations (24922 full + 75378 combined from 1480412 partial), need 99844
Mon Mar 16 04:22:34 2009  begin with 1505334 relations
Mon Mar 16 04:22:36 2009  reduce to 258872 relations in 11 passes
Mon Mar 16 04:22:36 2009  attempting to read 258872 relations
Mon Mar 16 04:22:40 2009  recovered 258872 relations
Mon Mar 16 04:22:40 2009  recovered 245085 polynomials
Mon Mar 16 04:22:41 2009  attempting to build 100300 cycles
Mon Mar 16 04:22:41 2009  found 100300 cycles in 7 passes
Mon Mar 16 04:22:41 2009  distribution of cycle lengths:
Mon Mar 16 04:22:41 2009     length 1 : 24922
Mon Mar 16 04:22:41 2009     length 2 : 17935
Mon Mar 16 04:22:41 2009     length 3 : 16953
Mon Mar 16 04:22:41 2009     length 4 : 13617
Mon Mar 16 04:22:41 2009     length 5 : 10084
Mon Mar 16 04:22:41 2009     length 6 : 6762
Mon Mar 16 04:22:41 2009     length 7 : 4343
Mon Mar 16 04:22:41 2009     length 9+: 5684
Mon Mar 16 04:22:41 2009  largest cycle: 21 relations
Mon Mar 16 04:22:41 2009  matrix is 99748 x 100300 (26.1 MB) with weight 6448649 (64.29/col)
Mon Mar 16 04:22:41 2009  sparse part has weight 6448649 (64.29/col)
Mon Mar 16 04:22:43 2009  filtering completed in 3 passes
Mon Mar 16 04:22:43 2009  matrix is 94724 x 94788 (24.7 MB) with weight 6106123 (64.42/col)
Mon Mar 16 04:22:43 2009  sparse part has weight 6106123 (64.42/col)
Mon Mar 16 04:22:43 2009  saving the first 48 matrix rows for later
Mon Mar 16 04:22:43 2009  matrix is 94676 x 94788 (14.0 MB) with weight 4666638 (49.23/col)
Mon Mar 16 04:22:43 2009  sparse part has weight 3103290 (32.74/col)
Mon Mar 16 04:22:43 2009  matrix includes 64 packed rows
Mon Mar 16 04:22:43 2009  using block size 37915 for processor cache size 1024 kB
Mon Mar 16 04:22:44 2009  commencing Lanczos iteration
Mon Mar 16 04:22:44 2009  memory use: 14.4 MB
Mon Mar 16 04:23:41 2009  lanczos halted after 1498 iterations (dim = 94675)
Mon Mar 16 04:23:42 2009  recovered 16 nontrivial dependencies
Mon Mar 16 04:23:42 2009  prp50 factor: 39630807092145422370870826294127675253372111261851
Mon Mar 16 04:23:42 2009  prp51 factor: 128268102157416318560550976482838943377755476654339
Mon Mar 16 04:23:42 2009  elapsed time 07:29:37

(47·10¹³⁴+43)/9 = 5(2)₁₃₃7_<135> = 641 · 1091 · 13597 · 19179759098013795972018131_<26> · C100

C100 = P35 · P65

P35 = 33140813277130657263276598717234867_<35>

P65 = 86401873769297648431111420569995876592842102131867050272977396093_<65>

Number: 52227_134
N=2863428365382506574459322158320072149516768735261054173117115655009321393116863539484787994769174631
  ( 100 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=33140813277130657263276598717234867 (pp35)
 r2=86401873769297648431111420569995876592842102131867050272977396093 (pp65)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 10.58 hours.
Scaled time: 4.98 units (timescale=0.471).
Factorization parameters were as follows:
name: 52227_134
n: 2863428365382506574459322158320072149516768735261054173117115655009321393116863539484787994769174631
m: 1000000000000000000000000000
deg: 5
c5: 47
c0: 430
skew: 1.56
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1565001)
Primes: RFBsize:102146, AFBsize:102377, largePrimes:3399888 encountered
Relations: rels:3402913, finalFF:274311
Max relations in full relation-set: 28
Initial matrix: 204588 x 274311 with sparse part having weight 26498437.
Pruned matrix : 185448 x 186534 with weight 15077134.
Total sieving time: 9.64 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.71 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 10.58 hours.
 --------- CPU info (if available) ----------

(47·10¹¹⁶+43)/9 = 5(2)₁₁₅7_<117> = 53 · 311 · C113

C113 = P55 · P58

P55 = 3685081937763363023441186298874982289878764245745070221_<55>

P58 = 8597495180320429810468301518681351153843577630984803856789_<58>

Number: 52227_116
N=31682474199006383681503501924541783790706923631755276480144526009963126992793922357715356562653777966524432580369
  ( 113 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=3685081937763363023441186298874982289878764245745070221 (pp55)
 r2=8597495180320429810468301518681351153843577630984803856789 (pp58)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.54 hours.
Scaled time: 1.20 units (timescale=0.473).
Factorization parameters were as follows:
name: 52227_116
n: 31682474199006383681503501924541783790706923631755276480144526009963126992793922357715356562653777966524432580369
m: 100000000000000000000000
deg: 5
c5: 470
c0: 43
skew: 0.62
type: snfs
lss: 1
rlim: 640000
alim: 640000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 640000/640000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [320000, 570001)
Primes: RFBsize:52074, AFBsize:52431, largePrimes:1376744 encountered
Relations: rels:1402615, finalFF:193849
Max relations in full relation-set: 28
Initial matrix: 104572 x 193849 with sparse part having weight 9381540.
Pruned matrix : 77739 x 78325 with weight 2885815.
Total sieving time: 2.42 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,640000,640000,25,25,45,45,2.2,2.2,50000
total time: 2.54 hours.
 --------- CPU info (if available) ----------

(47·10¹³²+43)/9 = 5(2)₁₃₁7_<133> = 313 · 541 · 389985959115019_<15> · C113

C113 = P44 · P70

P44 = 66805162715275047378310258081346195204829497_<44>

P70 = 1183735708075989040372436812349988192444720219615958206238555847039933_<70>

Number: 52227_132
N=79079656589897770829755883230016693801070150647426375600966191633835688276797963739134622541280218760533415303701
  ( 113 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=66805162715275047378310258081346195204829497 (pp44)
 r2=1183735708075989040372436812349988192444720219615958206238555847039933 (pp70)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 8.20 hours.
Scaled time: 3.87 units (timescale=0.472).
Factorization parameters were as follows:
name: 52227_132
n: 79079656589897770829755883230016693801070150647426375600966191633835688276797963739134622541280218760533415303701
m: 200000000000000000000000000
deg: 5
c5: 1175
c0: 344
skew: 0.78
type: snfs
lss: 1
rlim: 1220000
alim: 1220000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1220000/1220000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [610000, 1285001)
Primes: RFBsize:94358, AFBsize:94703, largePrimes:3084901 encountered
Relations: rels:3026470, finalFF:247939
Max relations in full relation-set: 28
Initial matrix: 189128 x 247939 with sparse part having weight 21305585.
Pruned matrix : 172342 x 173351 with weight 11877184.
Total sieving time: 7.47 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.53 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1220000,1220000,26,26,47,47,2.3,2.3,75000
total time: 8.20 hours.
 --------- CPU info (if available) ----------

Mar 16, 2009 (3rd)

By Erik Branger / GGNFS,Msieve / Mar 16, 2009

(47·10¹³⁸+43)/9 = 5(2)₁₃₇7_<139> = 13109 · 35591 · C131

C131 = P41 · P90

P41 = 12110497390862521623462778958590913065727_<41>

P90 = 924237560545730707810965451625528143183388041524274755116745709326870820529485298305483679_<90>

Number: 52227_138
N=11192976565526213593774731826873141752598428254938857864208351985208269040250801302155933442685237411336000086672694960933452769633
  ( 131 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=12110497390862521623462778958590913065727
 r2=924237560545730707810965451625528143183388041524274755116745709326870820529485298305483679
Version: 
Total time: 9.42 hours.
Scaled time: 8.22 units (timescale=0.872).
Factorization parameters were as follows:
n: 11192976565526213593774731826873141752598428254938857864208351985208269040250801302155933442685237411336000086672694960933452769633
m: 5000000000000000000000000000
deg: 5
c5: 376
c0: 1075
skew: 1.23
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 301018 x 301266
Total sieving time: 9.42 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 9.42 hours.
 --------- CPU info (if available) ----------

Mar 16, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.2 / Mar 16, 2009

(47·10¹⁷³+43)/9 = 5(2)₁₇₂7_<174> = C174

C174 = P29 · C145

P29 = 90388236299737203736595896523_<29>

C145 = [5777546322405015660288908414817858932872526998188643108740269812721019661590310819817117987276322539822666494675788815649610583379222590816956249_<145>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4040459943
Step 1 took 11205ms
********** Factor found in step 1: 90388236299737203736595896523
Found probable prime factor of 29 digits: 90388236299737203736595896523
Composite cofactor has 145 digits

Mar 16, 2009

By Ignacio Santos / GGNFS, Msieve / Mar 16, 2009

(5·10¹⁷⁹+1)/3 = 1(6)₁₇₈7_<180> = 107 · 3251 · C174

C174 = P59 · P115

P59 = 56945100399310037342624160677944917077499834609175255165571_<59>

P115 = 8413789442005456821614991149706287245459928630228872132857739495389538113846090243571030134274400462207636702323561_<115>

Number: 16667_179
N=479124084513655515532723695848198158055369495702736085997023681187001171937510720401390993042160044692694603433786488892466348719924183404866559151222101802368981123469318331
  ( 174 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=56945100399310037342624160677944917077499834609175255165571 (pp59)
 r2=8413789442005456821614991149706287245459928630228872132857739495389538113846090243571030134274400462207636702323561 (pp115)
Version: Msieve-1.39
Total time: 94.34 hours.
Scaled time: 164.05 units (timescale=1.739).
Factorization parameters were as follows:
n: 479124084513655515532723695848198158055369495702736085997023681187001171937510720401390993042160044692694603433786488892466348719924183404866559151222101802368981123469318331
m: 1000000000000000000000000000000000000
deg: 5
c5: 1
c0: 2
skew: 1.15
type: snfs
lss: 1
rlim: 7000000
alim: 7000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7000000/7000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3500000, 5100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1232775 x 1233023
Total sieving time: 94.34 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,53,53,2.5,2.5,100000
total time: 94.34 hours.
 --------- CPU info (if available) ----------

(47·10¹³⁷+43)/9 = 5(2)₁₃₆7_<138> = 31 · 149 · 32621 · 51973 · 128113 · C120

C120 = P51 · P70

P51 = 225137369694189736044300833591348660134434473007233_<51>

P70 = 2312019757258537421611817790983585370931405479576855830076562217781769_<70>

Number: 52227_137
N=520522046830186152910240975750485609199636284388609452902752302842431586706848237660180276152553860197687119043952535177
  ( 120 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=225137369694189736044300833591348660134434473007233 (pp51)
 r2=2312019757258537421611817790983585370931405479576855830076562217781769 (pp70)
Version: Msieve-1.39
Total time: 5.48 hours.
Scaled time: 14.08 units (timescale=2.571).
Factorization parameters were as follows:
n: 520522046830186152910240975750485609199636284388609452902752302842431586706848237660180276152553860197687119043952535177
m: 2000000000000000000000000000
deg: 5
c5: 1175
c0: 344
skew: 0.78
type: snfs
lss: 1
rlim: 1480000
alim: 1480000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1480000/1480000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [740000, 1640001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 235565 x 235813
Total sieving time: 5.48 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1480000,1480000,26,26,48,48,2.3,2.3,75000
total time: 5.48 hours.
 --------- CPU info (if available) ----------

(47·10¹⁴²+7)/9 = 5(2)₁₄₁3_<143> = 23 · 4567 · 5156969 · C131

C131 = P58 · P74

P58 = 5096739469024961520866987421681254104278729943636216958479_<58>

P74 = 18915139382309534187342328756837372102811459581455292795741652706009590153_<74>

Number: 52223_142
N=96405537451925433914025982196964859702746930465175341349339857626698320278573835356653181875433714404584241620469192691147008257287
  ( 131 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=5096739469024961520866987421681254104278729943636216958479 (pp58)
 r2=18915139382309534187342328756837372102811459581455292795741652706009590153 (pp74)
Version: Msieve-1.39
Total time: 9.63 hours.
Scaled time: 24.66 units (timescale=2.560).
Factorization parameters were as follows:
n: 96405537451925433914025982196964859702746930465175341349339857626698320278573835356653181875433714404584241620469192691147008257287
m: 50000000000000000000000000000
deg: 5
c5: 188
c0: 875
skew: 1.36
type: snfs
lss: 1
rlim: 1880000
alim: 1880000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1880000/1880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [940000, 2540001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 319979 x 320227
Total sieving time: 9.63 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1880000,1880000,26,26,49,49,2.3,2.3,100000
total time: 9.63 hours.
 --------- CPU info (if available) ----------

(47·10¹⁶³+43)/9 = 5(2)₁₆₂7_<164> = 3 · 19 · 59 · 39097 · C156

C156 = P51 · P106

P51 = 307031513422353026269894950420686124016927088828921_<51>

P106 = 1293606215378519849799542839583733138204875126738568274252542589532440363745910647106817207149014577563617_<106>

Number: 52227_163
N=397177874080229317051149764073089318013554005934812637198388942769447745098210464469279064246630105665903019528647062188207604864641024185378483205906967257
  ( 156 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=307031513422353026269894950420686124016927088828921 (pp51)
 r2=1293606215378519849799542839583733138204875126738568274252542589532440363745910647106817207149014577563617 (pp106)
Version: Msieve-1.39
Total time: 58.14 hours.
Scaled time: 150.06 units (timescale=2.581).
Factorization parameters were as follows:
n: 397177874080229317051149764073089318013554005934812637198388942769447745098210464469279064246630105665903019528647062188207604864641024185378483205906967257
m: 500000000000000000000000000000000
deg: 5
c5: 376
c0: 1075
skew: 1.23
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 5150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 810291 x 810539
Total sieving time: 58.14 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 58.14 hours.
 --------- CPU info (if available) ----------

Mar 15, 2009 (10th)

By Andreas Tete / Yafu v1.06 / Mar 15, 2009

(47·10¹¹¹+43)/9 = 5(2)₁₁₀7_<112> = 1583 · 8483699246273473787_<19> · C90

C90 = P32 · P59

P32 = 20563788999704702751348942468709_<32>

P59 = 18909760596300166302687932434463976442247508762236338683643_<59>

03/15/09 06:39:02 v1.06 @ LAPPIE, starting SIQS on c90: 388856326937246800236647155286316443867200551015387592401267281897787797733872823777626887
03/15/09 06:39:03 v1.06 @ LAPPIE, ==== sieve params ====
03/15/09 06:39:03 v1.06 @ LAPPIE, n = 90 digits, 301 bits
03/15/09 06:39:03 v1.06 @ LAPPIE, factor base: 65244 primes (max prime = 1730863)
03/15/09 06:39:03 v1.06 @ LAPPIE, single large prime cutoff: 190394930 (110 * pmax)
03/15/09 06:39:03 v1.06 @ LAPPIE, double large prime range from 43 to 50 bits
03/15/09 06:39:03 v1.06 @ LAPPIE, double large prime cutoff: 800533817759177
03/15/09 06:39:03 v1.06 @ LAPPIE, using 10 large prime slices of factor base
03/15/09 06:39:03 v1.06 @ LAPPIE, buckets hold 1024 elements
03/15/09 06:39:03 v1.06 @ LAPPIE, sieve interval: 18 blocks of size 32768
03/15/09 06:39:03 v1.06 @ LAPPIE, polynomial A has ~ 12 factors
03/15/09 06:39:03 v1.06 @ LAPPIE, using multiplier of 7
03/15/09 06:39:03 v1.06 @ LAPPIE, using small prime variation correction of 19 bits
03/15/09 06:39:03 v1.06 @ LAPPIE, trial factoring cutoff at 100 bits
03/15/09 06:39:03 v1.06 @ LAPPIE, ==== sieving started ====
03/15/09 07:56:06 v1.06 @ LAPPIE, sieve time = 1510.8310, relation time = 761.0720, poly_time = 2338.4970
03/15/09 07:56:06 v1.06 @ LAPPIE, 65309 relations found: 19538 full + 45771 from 717255 partial, using 573435 polys (280 A polys)
03/15/09 07:56:06 v1.06 @ LAPPIE, trial division touched 17037504 sieve locations out of 676451450880
03/15/09 07:56:06 v1.06 @ LAPPIE, ==== post processing stage (msieve-1.38) ====
03/15/09 07:56:07 v1.06 @ LAPPIE, begin with 736793 relations
03/15/09 07:56:07 v1.06 @ LAPPIE, reduce to 146259 relations in 9 passes
03/15/09 07:56:10 v1.06 @ LAPPIE, recovered 146259 relations
03/15/09 07:56:10 v1.06 @ LAPPIE, recovered 129211 polynomials
03/15/09 07:56:10 v1.06 @ LAPPIE, attempting to build 65309 cycles
03/15/09 07:56:10 v1.06 @ LAPPIE, found 65309 cycles in 5 passes
03/15/09 07:56:10 v1.06 @ LAPPIE, distribution of cycle lengths:
03/15/09 07:56:10 v1.06 @ LAPPIE,    length 1 : 19538
03/15/09 07:56:10 v1.06 @ LAPPIE,    length 2 : 15375
03/15/09 07:56:10 v1.06 @ LAPPIE,    length 3 : 12259
03/15/09 07:56:10 v1.06 @ LAPPIE,    length 4 : 7991
03/15/09 07:56:10 v1.06 @ LAPPIE,    length 5 : 4760
03/15/09 07:56:10 v1.06 @ LAPPIE,    length 6 : 2682
03/15/09 07:56:10 v1.06 @ LAPPIE,    length 7 : 1421
03/15/09 07:56:10 v1.06 @ LAPPIE,    length 9+: 1283
03/15/09 07:56:10 v1.06 @ LAPPIE, largest cycle: 16 relations
03/15/09 07:56:10 v1.06 @ LAPPIE, matrix is 65244 x 65309 (14.4 MB) with weight 3502635 (53.63/col)
03/15/09 07:56:10 v1.06 @ LAPPIE, sparse part has weight 3502635 (53.63/col)
03/15/09 07:56:11 v1.06 @ LAPPIE, filtering completed in 3 passes
03/15/09 07:56:11 v1.06 @ LAPPIE, matrix is 60115 x 60179 (13.4 MB) with weight 3274208 (54.41/col)
03/15/09 07:56:11 v1.06 @ LAPPIE, sparse part has weight 3274208 (54.41/col)
03/15/09 07:56:11 v1.06 @ LAPPIE, saving the first 48 matrix rows for later
03/15/09 07:56:11 v1.06 @ LAPPIE, matrix is 60067 x 60179 (8.5 MB) with weight 2518371 (41.85/col)
03/15/09 07:56:11 v1.06 @ LAPPIE, sparse part has weight 1869106 (31.06/col)
03/15/09 07:56:11 v1.06 @ LAPPIE, matrix includes 64 packed rows
03/15/09 07:56:11 v1.06 @ LAPPIE, using block size 24071 for processor cache size 3072 kB
03/15/09 07:56:11 v1.06 @ LAPPIE, commencing Lanczos iteration
03/15/09 07:56:11 v1.06 @ LAPPIE, memory use: 8.6 MB
03/15/09 07:56:30 v1.06 @ LAPPIE, lanczos halted after 952 iterations (dim = 60065)
03/15/09 07:56:30 v1.06 @ LAPPIE, recovered 17 nontrivial dependencies
03/15/09 07:56:32 v1.06 @ LAPPIE, prp32 = 20563788999704702751348942468709
03/15/09 07:56:34 v1.06 @ LAPPIE, prp59 = 18909760596300166302687932434463976442247508762236338683643
03/15/09 07:56:34 v1.06 @ LAPPIE, Lanczos elapsed time = 23.7060 seconds.
03/15/09 07:56:34 v1.06 @ LAPPIE, Sqrt elapsed time = 4.7680 seconds.
03/15/09 07:56:34 v1.06 @ LAPPIE, Total elapsed time = 4652.3250 seconds.

Mar 15, 2009 (9th)

By Markus Tervooren / Msieve / Mar 15, 2009

(47·10¹⁴⁸+7)/9 = 5(2)₁₄₇3_<149> = 4603 · 9239 · C142

C142 = P51 · P91

P51 = 150977405811707391544441629014942915254146978114697_<51>

P91 = 8133499563790653802159123230440166841774559689885450265413877571628391523856582549817248627_<91>

N=1227974664311766589355733242444396647490170147725325989585003427865148305779162556968586001779105369927197797636322777822494344543088171771019
  ( 142 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=150977405811707391544441629014942915254146978114697 (pp51)
 r2=8133499563790653802159123230440166841774559689885450265413877571628391523856582549817248627 (pp91)
Version: Msieve-1.39
Total time: 15.16 hours.
Scaled time: 23.14 units (timescale=1.526).
Factorization parameters were as follows:
n: 1227974664311766589355733242444396647490170147725325989585003427865148305779162556968586001779105369927197797636322777822494344543088171771019
m: 500000000000000000000000000000
deg: 5
c5: 376
c0: 175
skew: 0.86
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4

Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 346131 x 346379
Total sieving time: 15.16 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 15.16 hours.
 --------- CPU info (if available) ----------

Mar 15, 2009 (8th)

By Serge Batalov / GMP-ECM 6.2.2 / Mar 15, 2009

(47·10¹⁸⁹+43)/9 = 5(2)₁₈₈7_<190> = 4229 · 15527 · 16249 · 35311 · 55829 · 20581049 · 606170051 · 1410339719_<10> · 12297067394789855226919_<23> · C122

C122 = P30 · P92

P30 = 981354875644372438893894308249_<30>

P92 = 11692846518522856896650066130971974113304536609575734325101988145505082809852763906711273609_<92>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3996468663
Step 1 took 6425ms
Step 2 took 6668ms
********** Factor found in step 2: 981354875644372438893894308249
Found probable prime factor of 30 digits: 981354875644372438893894308249
Probable prime cofactor has 92 digits

(47·10¹³⁵+43)/9 = 5(2)₁₃₄7_<136> = 1009 · 1436749 · C127

C127 = P28 · P100

P28 = 1224497256592206800729962339_<28>

P100 = 2941883444553664147916566056863280701237761715183346787691176035860224740326839623028029463639854373_<100>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1675325719
Step 1 took 6537ms
Step 2 took 6712ms
********** Factor found in step 2: 1224497256592206800729962339
Found probable prime factor of 28 digits: 1224497256592206800729962339
Probable prime cofactor has 100 digits

(47·10¹⁷²+43)/9 = 5(2)₁₇₁7_<173> = 3 · 7 · 2423 · 64373 · 106530477041_<12> · 30832106241816221_<17> · C136

C136 = P37 · P100

P37 = 2223523490790922978933773329717835559_<37>

P100 = 2183032004907169798835967219091617895808587877255565369566738265988864330167127921846207946304885847_<100>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4024211974
Step 1 took 8060ms
Step 2 took 7553ms
********** Factor found in step 2: 2223523490790922978933773329717835559
Found probable prime factor of 37 digits: 2223523490790922978933773329717835559
Probable prime cofactor 2183032004907169798835967219091617895808587877255565369566738265988864330167127921846207946304885847 has 100 digits

(47·10¹⁶⁴+43)/9 = 5(2)₁₆₃7_<165> = 21031 · 56099 · C156

C156 = P34 · C122

P34 = 9480603531462587241575906463236513_<34>

C122 = [46687897862988976253887223591929792850820668664171354728982099424768530856044160419085192929785748509473936291264991452391_<122>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3007815294
Step 1 took 9252ms
Step 2 took 8645ms
********** Factor found in step 2: 9480603531462587241575906463236513
Found probable prime factor of 34 digits: 9480603531462587241575906463236513
Composite cofactor has 122 digits

(47·10¹⁶⁹+43)/9 = 5(2)₁₆₈7_<170> = 3 · 8572033 · C163

C163 = P34 · C129

P34 = 2460206087289861850132545179847589_<34>

C129 = [825427190163644852254913733459514842316359767509942803406052438727183699044270460684675686871923852679575050581068620849873014557_<129>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1783504632
Step 1 took 9136ms
Step 2 took 8777ms
********** Factor found in step 2: 2460206087289861850132545179847589
Found probable prime factor of 34 digits: 2460206087289861850132545179847589
Composite cofactor has 129 digits

Mar 15, 2009 (7th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Mar 15, 2009

(47·10¹⁴⁶+7)/9 = 5(2)₁₄₅3_<147> = 43943 · 2497759601_<10> · 72190476728398314067_<20> · C113

C113 = P32 · P81

P32 = 85624867478828930787372533109107_<32>

P81 = 769724280521484580060958723080328755146417996214229835475972442189748684927038369_<81>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 65907539514889062053452502588117361920303710604156293441563097996941129629342441926458247231633200554053052326483 (113 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=1394535338
Step 1 took 31217ms
Step 2 took 14063ms
********** Factor found in step 2: 85624867478828930787372533109107
Found probable prime factor of 32 digits: 85624867478828930787372533109107
Probable prime cofactor 769724280521484580060958723080328755146417996214229835475972442189748684927038369 has 81 digits

(47·10¹³¹-11)/9 = 5(2)₁₃₀1_<132> = 7 · C131

C131 = P49 · P83

P49 = 2026351164998001359133074021408059324775297164471_<49>

P83 = 36816508358386235661569433453134759579938638148610938541997940810668852410721162893_<83>

Number: n
N=74603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603
  ( 131 digits)
SNFS difficulty: 132 digits.
Divisors found:

Mon Mar 16 01:01:43 2009  prp49 factor: 2026351164998001359133074021408059324775297164471
Mon Mar 16 01:01:43 2009  prp83 factor: 36816508358386235661569433453134759579938638148610938541997940810668852410721162893
Mon Mar 16 01:01:43 2009  elapsed time 00:21:16 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.42 hours.
Scaled time: 7.73 units (timescale=1.748).
Factorization parameters were as follows:
name: KA_5_2_130_1
n: 74603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603
deg: 5
c5: 470
c0: -11
m: 100000000000000000000000000
skew: 0.47
type: snfs
rlim: 900000
alim: 900000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [450000, 950329)
Primes: RFBsize:71274, AFBsize:71211, largePrimes:8837000 encountered
Relations: rels:8087219, finalFF:150682
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 727414 hash collisions in 8727469 relations
Msieve: matrix is 170628 x 170876 (44.1 MB)

Total sieving time: 4.23 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,900000,900000,28,28,56,56,2.5,2.5,50000
total time: 4.42 hours.
 --------- CPU info (if available) ----------

Mar 15, 2009 (6th)

By Max Dettweiler / GGNFS, msieve v1.40beta2 / Mar 15, 2009

(47·10¹⁵⁷+7)/9 = 5(2)₁₅₆3_<158> = 53 · 421 · 7753 · 11813 · 861740186150432041_<18> · 241830508061251464811661998926787_<33> · C96

C96 = P42 · P54

P42 = 353857639571532254488773357157059114181483_<42>

P54 = 346538414823540919935905899613289637969994899089486299_<54>

Number: 52223_157
N=122625265490318673039471791592719193179089888733075612849378008814899208570958452107536328001417
  ( 96 digits)
Divisors found:
 r1=353857639571532254488773357157059114181483 (pp42)
 r2=346538414823540919935905899613289637969994899089486299 (pp54)
Version: Msieve-1.40
Total time: 6.12 hours.
Scaled time: 10.00 units (timescale=1.634).
Factorization parameters were as follows:
name: 52223_157
n:  122625265490318673039471791592719193179089888733075612849378008814899208570958452107536328001417
m:  6416193915203397720025
deg: 4
c4: 72355248
c3: -272460385524
c2: -509605734721730048
c1: 1140845574484152871
c0: 281369533074014834402142
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.934
# E(F1,F2) = 3.706629e-05
# GGNFS version 0.77.1-20060722-prescott polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1237065719.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1380001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 178331 x 178579
Polynomial selection time: 0.17 hours.
Total sieving time: 5.96 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 6.12 hours.
 --------- CPU info (if available) ----------
[    0.371546] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456482] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004011] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.13 BogoMIPS (lpj=8800268)
[    0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800829)
[    0.460049] Total of 2 processors activated (8800.54 BogoMIPS).

Mar 15, 2009 (5th)

By Sinkiti Sibata / GGNFS, Msieve / Mar 15, 2009

(47·10¹²⁷+7)/9 = 5(2)₁₂₆3_<128> = 197083 · 10577279383829_<14> · C110

C110 = P48 · P63

P48 = 111720058899756669513508290883342780785552558577_<48>

P63 = 224233787317142184660331278856736740012475797164269565267779257_<63>

Number: 52223_127
N=25051411926386634933371128325976038352163784425090994680862630687952591764836059175251741466149949475198037289
  ( 110 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=111720058899756669513508290883342780785552558577 (pp48)
 r2=224233787317142184660331278856736740012475797164269565267779257 (pp63)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 6.24 hours.
Scaled time: 2.95 units (timescale=0.472).
Factorization parameters were as follows:
name: 52223_127
n: 25051411926386634933371128325976038352163784425090994680862630687952591764836059175251741466149949475198037289
m: 50000000000000000000000000
deg: 5
c5: 188
c0: 875
skew: 1.36
type: snfs
lss: 1
rlim: 1060000
alim: 1060000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1060000/1060000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [530000, 1080001)
Primes: RFBsize:82832, AFBsize:82708, largePrimes:2783700 encountered
Relations: rels:2679599, finalFF:202916
Max relations in full relation-set: 28
Initial matrix: 165607 x 202916 with sparse part having weight 16321093.
Pruned matrix : 155684 x 156576 with weight 10102232.
Total sieving time: 5.69 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1060000,1060000,26,26,47,47,2.3,2.3,50000
total time: 6.24 hours.
 --------- CPU info (if available) ----------

(47·10¹³⁸+7)/9 = 5(2)₁₃₇3_<139> = 3 · C139

C139 = P38 · P101

P38 = 74888297967594832839979980338219968859_<38>

P101 = 23244495975779587331338347767981862919991270902971405226871275122113539942555509695342001780626474399_<101>

Number: 52223_138
N=1740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741
  ( 139 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=74888297967594832839979980338219968859
 r2=23244495975779587331338347767981862919991270902971405226871275122113539942555509695342001780626474399
Version: 
Total time: 5.23 hours.
Scaled time: 13.40 units (timescale=2.564).
Factorization parameters were as follows:
name: 52223_138
n: 1740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741
m: 5000000000000000000000000000
deg: 5
c5: 376
c0: 175
skew: 0.86
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1485001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 217288 x 217536
Total sieving time: 5.23 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 5.23 hours.
 --------- CPU info (if available) ----------

(47·10¹⁹³+7)/9 = 5(2)₁₉₂3_<194> = 29 · 61 · 23761 · 37326449201_<11> · 96950219421558950849098121_<26> · 2433677934669052310957101691_<28> · 86827052202846906758072160839_<29> · C94

C94 = P46 · P48

P46 = 4220483980270647555621065653971504476779218067_<46>

P48 = 384961155431091348987210023432906809484810914729_<48>

Sun Mar 15 13:30:35 2009  Msieve v. 1.39
Sun Mar 15 13:30:35 2009  random seeds: 2a5d9f80 e0541b20
Sun Mar 15 13:30:35 2009  factoring 1624722389523399828043595125130484644425963577835363151624918075220481108987769453839633208843 (94 digits)
Sun Mar 15 13:30:36 2009  searching for 15-digit factors
Sun Mar 15 13:30:38 2009  commencing quadratic sieve (94-digit input)
Sun Mar 15 13:30:38 2009  using multiplier of 43
Sun Mar 15 13:30:38 2009  using 32kb Intel Core sieve core
Sun Mar 15 13:30:38 2009  sieve interval: 36 blocks of size 32768
Sun Mar 15 13:30:38 2009  processing polynomials in batches of 6
Sun Mar 15 13:30:38 2009  using a sieve bound of 1987889 (74118 primes)
Sun Mar 15 13:30:38 2009  using large prime bound of 256437681 (27 bits)
Sun Mar 15 13:30:38 2009  using double large prime bound of 1368255814560987 (42-51 bits)
Sun Mar 15 13:30:38 2009  using trial factoring cutoff of 51 bits
Sun Mar 15 13:30:38 2009  polynomial 'A' values have 12 factors
Sun Mar 15 16:13:11 2009  74514 relations (18880 full + 55634 combined from 1019526 partial), need 74214
Sun Mar 15 16:13:13 2009  begin with 1038406 relations
Sun Mar 15 16:13:13 2009  reduce to 189554 relations in 9 passes
Sun Mar 15 16:13:14 2009  attempting to read 189554 relations
Sun Mar 15 16:13:17 2009  recovered 189554 relations
Sun Mar 15 16:13:17 2009  recovered 171469 polynomials
Sun Mar 15 16:13:17 2009  attempting to build 74514 cycles
Sun Mar 15 16:13:17 2009  found 74514 cycles in 5 passes
Sun Mar 15 16:13:17 2009  distribution of cycle lengths:
Sun Mar 15 16:13:17 2009     length 1 : 18880
Sun Mar 15 16:13:17 2009     length 2 : 13503
Sun Mar 15 16:13:17 2009     length 3 : 12691
Sun Mar 15 16:13:17 2009     length 4 : 10168
Sun Mar 15 16:13:17 2009     length 5 : 7464
Sun Mar 15 16:13:17 2009     length 6 : 4933
Sun Mar 15 16:13:17 2009     length 7 : 3032
Sun Mar 15 16:13:17 2009     length 9+: 3843
Sun Mar 15 16:13:17 2009  largest cycle: 19 relations
Sun Mar 15 16:13:17 2009  matrix is 74118 x 74514 (19.6 MB) with weight 4839013 (64.94/col)
Sun Mar 15 16:13:17 2009  sparse part has weight 4839013 (64.94/col)
Sun Mar 15 16:13:19 2009  filtering completed in 3 passes
Sun Mar 15 16:13:19 2009  matrix is 69918 x 69981 (18.5 MB) with weight 4557257 (65.12/col)
Sun Mar 15 16:13:19 2009  sparse part has weight 4557257 (65.12/col)
Sun Mar 15 16:13:19 2009  saving the first 48 matrix rows for later
Sun Mar 15 16:13:19 2009  matrix is 69870 x 69981 (12.2 MB) with weight 3653003 (52.20/col)
Sun Mar 15 16:13:19 2009  sparse part has weight 2769154 (39.57/col)
Sun Mar 15 16:13:19 2009  matrix includes 64 packed rows
Sun Mar 15 16:13:19 2009  using block size 27992 for processor cache size 1024 kB
Sun Mar 15 16:13:19 2009  commencing Lanczos iteration
Sun Mar 15 16:13:19 2009  memory use: 11.4 MB
Sun Mar 15 16:13:52 2009  lanczos halted after 1106 iterations (dim = 69866)
Sun Mar 15 16:13:53 2009  recovered 14 nontrivial dependencies
Sun Mar 15 16:13:53 2009  prp46 factor: 4220483980270647555621065653971504476779218067
Sun Mar 15 16:13:53 2009  prp48 factor: 384961155431091348987210023432906809484810914729
Sun Mar 15 16:13:53 2009  elapsed time 02:43:18

(47·10¹¹⁴+43)/9 = 5(2)₁₁₃7_<115> = 17 · 1129 · C111

C111 = P45 · P67

P45 = 217690804652865617561647456806370878599153369_<45>

P67 = 1249891747297204550590383589450639722047981968436979229406865298531_<67>

Number: 52227_114
N=272089940198104633054875330705060293972918367228792904820623259637483573293503997406461846622321795562039400939
  ( 111 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=217690804652865617561647456806370878599153369 (pp45)
 r2=1249891747297204550590383589450639722047981968436979229406865298531 (pp67)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.61 hours.
Scaled time: 1.23 units (timescale=0.472).
Factorization parameters were as follows:
name: 52227_114
n: 272089940198104633054875330705060293972918367228792904820623259637483573293503997406461846622321795562039400939
m: 100000000000000000000000
deg: 5
c5: 47
c0: 430
skew: 1.56
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 560001)
Primes: RFBsize:50612, AFBsize:50883, largePrimes:1253203 encountered
Relations: rels:1214381, finalFF:134219
Max relations in full relation-set: 28
Initial matrix: 101560 x 134219 with sparse part having weight 6656102.
Pruned matrix : 89680 x 90251 with weight 3329314.
Total sieving time: 2.47 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 2.61 hours.
 --------- CPU info (if available) ----------

(47·10¹²¹+43)/9 = 5(2)₁₂₀7_<122> = 3³ · 181 · 197 · 3079 · 668861027 · 934380757 · C95

C95 = P45 · P50

P45 = 587455999345399754749625762418451209379317133_<45>

P50 = 47984610496102341660255252672803946541711790573741_<50>

Sun Mar 15 17:34:01 2009  Msieve v. 1.39
Sun Mar 15 17:34:01 2009  random seeds: ba2193c0 b2b2aacf
Sun Mar 15 17:34:01 2009  factoring 28188847312187559423374635049668712587940909163633526270956401395328262084066106415596861204553 (95 digits)
Sun Mar 15 17:34:01 2009  searching for 15-digit factors
Sun Mar 15 17:34:03 2009  commencing quadratic sieve (95-digit input)
Sun Mar 15 17:34:03 2009  using multiplier of 17
Sun Mar 15 17:34:03 2009  using 32kb Intel Core sieve core
Sun Mar 15 17:34:03 2009  sieve interval: 36 blocks of size 32768
Sun Mar 15 17:34:03 2009  processing polynomials in batches of 6
Sun Mar 15 17:34:03 2009  using a sieve bound of 2128183 (78401 primes)
Sun Mar 15 17:34:03 2009  using large prime bound of 310714718 (28 bits)
Sun Mar 15 17:34:03 2009  using double large prime bound of 1933086450144842 (43-51 bits)
Sun Mar 15 17:34:03 2009  using trial factoring cutoff of 51 bits
Sun Mar 15 17:34:03 2009  polynomial 'A' values have 12 factors
Sun Mar 15 20:43:29 2009  78536 relations (19778 full + 58758 combined from 1150950 partial), need 78497
Sun Mar 15 20:43:30 2009  begin with 1170728 relations
Sun Mar 15 20:43:31 2009  reduce to 202017 relations in 10 passes
Sun Mar 15 20:43:31 2009  attempting to read 202017 relations
Sun Mar 15 20:43:34 2009  recovered 202017 relations
Sun Mar 15 20:43:34 2009  recovered 184087 polynomials
Sun Mar 15 20:43:35 2009  attempting to build 78536 cycles
Sun Mar 15 20:43:35 2009  found 78536 cycles in 5 passes
Sun Mar 15 20:43:35 2009  distribution of cycle lengths:
Sun Mar 15 20:43:35 2009     length 1 : 19778
Sun Mar 15 20:43:35 2009     length 2 : 14088
Sun Mar 15 20:43:35 2009     length 3 : 13458
Sun Mar 15 20:43:35 2009     length 4 : 10557
Sun Mar 15 20:43:35 2009     length 5 : 7781
Sun Mar 15 20:43:35 2009     length 6 : 5251
Sun Mar 15 20:43:35 2009     length 7 : 3225
Sun Mar 15 20:43:35 2009     length 9+: 4398
Sun Mar 15 20:43:35 2009  largest cycle: 17 relations
Sun Mar 15 20:43:35 2009  matrix is 78401 x 78536 (21.2 MB) with weight 5255274 (66.92/col)
Sun Mar 15 20:43:35 2009  sparse part has weight 5255274 (66.92/col)
Sun Mar 15 20:43:36 2009  filtering completed in 3 passes
Sun Mar 15 20:43:36 2009  matrix is 74350 x 74414 (20.3 MB) with weight 5015728 (67.40/col)
Sun Mar 15 20:43:36 2009  sparse part has weight 5015728 (67.40/col)
Sun Mar 15 20:43:36 2009  saving the first 48 matrix rows for later
Sun Mar 15 20:43:36 2009  matrix is 74302 x 74414 (14.2 MB) with weight 4104596 (55.16/col)
Sun Mar 15 20:43:36 2009  sparse part has weight 3285109 (44.15/col)
Sun Mar 15 20:43:36 2009  matrix includes 64 packed rows
Sun Mar 15 20:43:36 2009  using block size 29765 for processor cache size 1024 kB
Sun Mar 15 20:43:37 2009  commencing Lanczos iteration
Sun Mar 15 20:43:37 2009  memory use: 12.8 MB
Sun Mar 15 20:44:17 2009  lanczos halted after 1176 iterations (dim = 74298)
Sun Mar 15 20:44:18 2009  recovered 15 nontrivial dependencies
Sun Mar 15 20:44:18 2009  prp45 factor: 587455999345399754749625762418451209379317133
Sun Mar 15 20:44:18 2009  prp50 factor: 47984610496102341660255252672803946541711790573741
Sun Mar 15 20:44:18 2009  elapsed time 03:10:17

(47·10¹¹⁵+43)/9 = 5(2)₁₁₄7_<116> = 3 · 67 · 109 · 191 · C110

C110 = P51 · P59

P51 = 289307599580437389286466005391800602139333155100951_<51>

P59 = 43135971538668027066686811497458559892059332937372918510383_<59>

Number: 52227_115
N=12479564381422113272969945943040984668430321188672665832235198048429790674425132185802870517536297144906674233
  ( 110 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=289307599580437389286466005391800602139333155100951 (pp51)
 r2=43135971538668027066686811497458559892059332937372918510383 (pp59)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 2.07 hours.
Scaled time: 0.97 units (timescale=0.472).
Factorization parameters were as follows:
name: 52227_115
n: 12479564381422113272969945943040984668430321188672665832235198048429790674425132185802870517536297144906674233
m: 100000000000000000000000
deg: 5
c5: 47
c0: 43
skew: 0.98
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 510001)
Primes: RFBsize:50612, AFBsize:50513, largePrimes:1250618 encountered
Relations: rels:1223349, finalFF:143869
Max relations in full relation-set: 28
Initial matrix: 101190 x 143869 with sparse part having weight 6594746.
Pruned matrix : 83890 x 84459 with weight 2840891.
Total sieving time: 1.95 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 2.07 hours.
 --------- CPU info (if available) ----------

Mar 15, 2009 (4th)

By Erik Branger / GGNFS, Msieve / Mar 15, 2009

(47·10¹³³+7)/9 = 5(2)₁₃₂3_<134> = 17 · 61 · 2447 · C128

C128 = P42 · P86

P42 = 670530294355163812218807659151808165983773_<42>

P86 = 30691931400014721397861209168400013999985859919109854327608444234510209403027930283209_<86>

Number: 52223_133
N=20579869795980366103623322527150212163132161603121064236735759419745754537062178048188509505557243542748396072817884659988367557
  ( 128 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=670530294355163812218807659151808165983773
 r2=30691931400014721397861209168400013999985859919109854327608444234510209403027930283209
Version: 
Total time: 3.32 hours.
Scaled time: 3.44 units (timescale=1.036).
Factorization parameters were as follows:
n: 20579869795980366103623322527150212163132161603121064236735759419745754537062178048188509505557243542748396072817884659988367557
m: 500000000000000000000000000
deg: 5
c5: 376
c0: 175
skew: 0.86
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 175412 x 175660
Total sieving time: 3.32 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 3.32 hours.
 --------- CPU info (if available) ----------

(47·10¹³¹+43)/9 = 5(2)₁₃₀7_<132> = 11137491919_<11> · C122

C122 = P59 · P64

P59 = 39950370666748923637428313257142978450538278038369002709049_<59>

P64 = 1173673052829063384478836643948244815409866910460348090878975717_<64>

Number: 52227_131
N=46888673502095873639414330175481424941649129130310637419751579010974833661939667282305143033004091755626280533171287163133
  ( 122 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=39950370666748923637428313257142978450538278038369002709049
 r2=1173673052829063384478836643948244815409866910460348090878975717
Version: 
Total time: 3.31 hours.
Scaled time: 3.18 units (timescale=0.961).
Factorization parameters were as follows:
n: 46888673502095873639414330175481424941649129130310637419751579010974833661939667282305143033004091755626280533171287163133
m: 100000000000000000000000000
deg: 5
c5: 470
c0: 43
skew: 0.62
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 168382 x 168630
Total sieving time: 3.31 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 3.31 hours.
 --------- CPU info (if available) ----------

Mar 15, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Mar 15, 2009

(47·10¹⁴⁰+7)/9 = 5(2)₁₃₉3_<141> = 1103 · 1485277 · 894342431 · 283548934196313789203440276497841_<33> · C91

C91 = P34 · P57

P34 = 1911449618135293346702987304200387_<34>

P57 = 657624023197298791172408414280655129548713829126953741129_<57>

Number: xx
N=1257015188017072067989007346481096231837401079833480219711434479996912229920252505539616923
  ( 91 digits)
Divisors found:
 r1=1911449618135293346702987304200387 (pp34)
 r2=657624023197298791172408414280655129548713829126953741129 (pp57)
Version: Msieve-1.39
Total time: 2.18 hours.
Scaled time: 2.62 units (timescale=1.205).
Factorization parameters were as follows:
name: xx
n:  1257015188017072067989007346481096231837401079833480219711434479996912229920252505539616923
m:  546290656101251286969
deg: 4
c4: 14113848
c3: -68846950066
c2: -56128707678443779
c1: 262207139052200188
c0: 7295248138280862827356
skew: 1635.250
type: gnfs
# adj. I(F,S) = 52.887
# E(F1,F2) = 1.611276e-004
# GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=58.00000000, seed=1237044911.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 700000
alim: 700000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.4
alambda: 2.4
qintsize: 40000

type: gnfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [350000, 750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 117271 x 117519
Polynomial selection time: 0.17 hours.
Total sieving time: 2.01 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,90,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000
total time: 2.18 hours.
 --------- CPU info (if available) ----------

(38·10¹⁶⁶+61)/9 = 4(2)₁₆₅9_<167> = 11 · 563 · 4153 · 243527 · 2877547 · C148

C148 = P41 · P108

P41 = 21542209814132096929259164948657660906663_<41>

P108 = 108747249169588185424876695250126633643543443939403426766972201603072209923897950037118523330042709677118583_<108>

Number: 42229_166
N=2342656058320971136078914378894172103407965837435963776301999121838755344379699057145088347325698602189976417552725256631608747785795775281145818529
  ( 148 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=21542209814132096929259164948657660906663 (pp41)
 r2=108747249169588185424876695250126633643543443939403426766972201603072209923897950037118523330042709677118583 (pp108)
Version: Msieve-1.39
Total time: 44.29 hours.
Scaled time: 114.32 units (timescale=2.581).
Factorization parameters were as follows:
n: 2342656058320971136078914378894172103407965837435963776301999121838755344379699057145088347325698602189976417552725256631608747785795775281145818529
m: 1000000000000000000000000000000000
deg: 5
c5: 380
c0: 61
skew: 0.69
type: snfs
lss: 1
rlim: 4300000
alim: 4300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4300000/4300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2150000, 4350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 831110 x 831358
Total sieving time: 44.29 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,4300000,4300000,27,27,51,51,2.4,2.4,100000
total time: 44.29 hours.
 --------- CPU info (if available) ----------

Mar 15, 2009 (2nd)

Factorizations of 522...227 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 15, 2009

By Ignacio Santos / GGNFS, Msieve / Mar 15, 2009

(47·10¹³⁹+7)/9 = 5(2)₁₃₈3_<140> = 712139226103_<12> · C128

C128 = P51 · P77

P51 = 924167590475255281190980833502221704983289143438697_<51>

P77 = 79348679913887986573832937048156352419037224563313906740755084949360325692353_<77>

Number: 52223_139
N=73331478323410147266499510383342895161258683453862402218627955193839501880292089862428301297353485747455249979776189823737184041
  ( 128 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=924167590475255281190980833502221704983289143438697 (pp51)
 r2=79348679913887986573832937048156352419037224563313906740755084949360325692353 (pp77)
Version: Msieve-1.39
Total time: 6.56 hours.
Scaled time: 7.86 units (timescale=1.198).
Factorization parameters were as follows:
n: 73331478323410147266499510383342895161258683453862402218627955193839501880292089862428301297353485747455249979776189823737184041
m: 10000000000000000000000000000
deg: 5
c5: 47
c0: 70
skew: 1.08
type: snfs
lss: 1
rlim: 1610000
alim: 1610000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1610000/1610000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [805000, 2005001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 283781 x 284029
Total sieving time: 6.56 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000
total time: 6.56 hours.
 --------- CPU info (if available) ----------

Mar 14, 2009 (8th)

By Robert Backstrom / GGNFS, Msieve / Mar 14, 2009

(47·10¹⁶⁹-11)/9 = 5(2)₁₆₈1_<170> = 3² · 7727 · 969869 · 6303598959291446191404704491_<28> · 2723550519870143340321040847893_<31> · C101

C101 = P49 · P52

P49 = 5805251729809190300376404710785985342337985768647_<49>

P52 = 7768618262293985963268696684274056390156286740861383_<52>

Number: n
N=45098784605409428064742625617997210424985502259284439385429485124528215712007524190417355036134458801
  ( 101 digits)
Divisors found:

Sat Mar 14 05:34:03 2009  prp49 factor: 5805251729809190300376404710785985342337985768647
Sat Mar 14 05:34:03 2009  prp52 factor: 7768618262293985963268696684274056390156286740861383
Sat Mar 14 05:34:03 2009  elapsed time 00:16:37 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.16 hours.
Scaled time: 5.77 units (timescale=1.829).
Factorization parameters were as follows:
n: 45098784605409428064742625617997210424985502259284439385429485124528215712007524190417355036134458801
skew: 32984.96
Y0: -31305207112067097170
Y1:  26298819041
c0:  26248303229749943875156701
c1: -3897369683786665875900
c2:  71120558524893231
c3:  1928967252970
c4: -38352050
c5:  1500
type: gnfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved  special-q in [900000, 1500181)
Primes: RFBsize:135072, AFBsize:134791, largePrimes:3688710 encountered
Relations: rels:3527827, finalFF:290551
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 225974 hash collisions in 3737360 relations
Msieve: matrix is 226443 x 226690 (61.6 MB)

Total sieving time: 3.09 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 3.16 hours.
 --------- CPU info (if available) ----------

(47·10¹³⁷-11)/9 = 5(2)₁₃₆1_<138> = 7 · 225949 · 5060791 · 7599924193_<10> · 259123385897011_<15> · C101

C101 = P50 · P51

P50 = 59735147037019557046749771013459511227068774912011_<50>

P51 = 554603588668536543331375075752887783477078375203489_<51>

Number: n
N=33129326916373743879818593308170668459850957394530166149302667433219613956117071489960973800195206379
  ( 101 digits)
Divisors found:
 r1=59735147037019557046749771013459511227068774912011 (pp50)
 r2=554603588668536543331375075752887783477078375203489 (pp51)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.78 hours.
Scaled time: 12.41 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_5_2_136_1
n: 33129326916373743879818593308170668459850957394530166149302667433219613956117071489960973800195206379
skew: 15026.39
# norm 5.20e+13
c5: 9000
c4: -68441619
c3: -6377284134589
c2: 18276659793282929
c1: 683527944422973233418
c0: -1557233758004421869608896
# alpha -5.25
Y1: 24649527023
Y0: -20568130175978555333
# Murphy_E 2.90e-09
# M 10810837796529747267112602995107017395615473595624487260735474662472120610519955415167163896302648703
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved  special-q in [900000, 900000)
Primes: RFBsize:135072, AFBsize:134636, largePrimes:4037346 encountered
Relations: rels:4161508, finalFF:490593
Max relations in full relation-set: 28
Initial matrix: 269787 x 490593 with sparse part having weight 44061731.
Pruned matrix : 169019 x 170431 with weight 14515096.
Total sieving time: 6.37 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.20 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 6.78 hours.
 --------- CPU info (if available) ----------

Mar 14, 2009 (7th)

By matsui / GGNFS / Mar 14, 2009

6·10¹⁹⁸+1 = 6(0)₁₉₇1_<199> = 7 · 83 · 827 · C194

C194 = P97 · P97

P97 = 1671913865053753682774008058984727775285847092318926307764219314568321887709471774615950144902657_<97>

P97 = 7468883908162308115227893005644186201669945225303700140432172123968956930897287431172882486068439_<97>

N=12487330562533429624526782202223993573187203816128219910216093255384640999652435966009486208784004562038098845546289493784431212498985404391794158843007198946069300522178539689939582132294942423
  ( 194 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=1671913865053753682774008058984727775285847092318926307764219314568321887709471774615950144902657 (pp97)
 r2=7468883908162308115227893005644186201669945225303700140432172123968956930897287431172882486068439 (pp97)
Version: GGNFS-0.77.1-20060722-nocona

Two P97s are the largest nice-split in our tables so far. Congratulations!

Mar 14, 2009 (6th)

By Sinkiti Sibata / GGNFS, Msieve / Mar 14, 2009

(46·10¹⁴⁹+71)/9 = 5(1)₁₄₈9_<150> = 3² · 7 · 19 · 29 · 199 · 15557131706506123_<17> · 49266879156806711_<17> · C110

C110 = P43 · P68

P43 = 3717593605046269974941029954521038665650971_<43>

P68 = 25967109193812927293021015198828053542275514600080287790314157459599_<68>

Number: 51119_149
N=96535159080457141562553599924179572078378688482304099085018154453390575429391121077991157384943851790967620629
  ( 110 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=3717593605046269974941029954521038665650971 (pp43)
 r2=25967109193812927293021015198828053542275514600080287790314157459599 (pp68)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 35.80 hours.
Scaled time: 16.90 units (timescale=0.472).
Factorization parameters were as follows:
name: 51119_149
n: 96535159080457141562553599924179572078378688482304099085018154453390575429391121077991157384943851790967620629
m: 1000000000000000000000000000000
deg: 5
c5: 23
c0: 355
skew: 1.73
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 2050001)
Primes: RFBsize:169511, AFBsize:169527, largePrimes:7020669 encountered
Relations: rels:7047587, finalFF:505189
Max relations in full relation-set: 28
Initial matrix: 339103 x 505189 with sparse part having weight 53942190.
Pruned matrix : 286006 x 287765 with weight 27710283.
Total sieving time: 32.65 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 2.73 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 35.80 hours.
 --------- CPU info (if available) ----------

(47·10¹⁰⁶+7)/9 = 5(2)₁₀₅3_<107> = 102552171005093_<15> · C93

C93 = P33 · P60

P33 = 586131916604674594186662435865517_<33>

P60 = 868790611576412906071918691609898995245693401683366767021583_<60>

Sat Mar 14 14:24:25 2009  Msieve v. 1.39
Sat Mar 14 14:24:25 2009  random seeds: e23c4660 a3ab0f61
Sat Mar 14 14:24:25 2009  factoring 509225906291430287531211482278866257672652842930993643159194275834613445437410934426824453411 (93 digits)
Sat Mar 14 14:24:26 2009  searching for 15-digit factors
Sat Mar 14 14:24:27 2009  commencing quadratic sieve (93-digit input)
Sat Mar 14 14:24:28 2009  using multiplier of 1
Sat Mar 14 14:24:28 2009  using 32kb Intel Core sieve core
Sat Mar 14 14:24:28 2009  sieve interval: 36 blocks of size 32768
Sat Mar 14 14:24:28 2009  processing polynomials in batches of 6
Sat Mar 14 14:24:28 2009  using a sieve bound of 1923133 (71628 primes)
Sat Mar 14 14:24:28 2009  using large prime bound of 232699093 (27 bits)
Sat Mar 14 14:24:28 2009  using double large prime bound of 1148762820023984 (42-51 bits)
Sat Mar 14 14:24:28 2009  using trial factoring cutoff of 51 bits
Sat Mar 14 14:24:28 2009  polynomial 'A' values have 12 factors
Sat Mar 14 17:06:34 2009  71866 relations (17567 full + 54299 combined from 972710 partial), need 71724
Sat Mar 14 17:06:35 2009  begin with 990277 relations
Sat Mar 14 17:06:36 2009  reduce to 186074 relations in 11 passes
Sat Mar 14 17:06:36 2009  attempting to read 186074 relations
Sat Mar 14 17:06:39 2009  recovered 186074 relations
Sat Mar 14 17:06:39 2009  recovered 168654 polynomials
Sat Mar 14 17:06:39 2009  attempting to build 71866 cycles
Sat Mar 14 17:06:39 2009  found 71866 cycles in 6 passes
Sat Mar 14 17:06:39 2009  distribution of cycle lengths:
Sat Mar 14 17:06:39 2009     length 1 : 17567
Sat Mar 14 17:06:39 2009     length 2 : 12827
Sat Mar 14 17:06:39 2009     length 3 : 12187
Sat Mar 14 17:06:39 2009     length 4 : 9710
Sat Mar 14 17:06:39 2009     length 5 : 7313
Sat Mar 14 17:06:39 2009     length 6 : 4822
Sat Mar 14 17:06:39 2009     length 7 : 3160
Sat Mar 14 17:06:39 2009     length 9+: 4280
Sat Mar 14 17:06:39 2009  largest cycle: 19 relations
Sat Mar 14 17:06:40 2009  matrix is 71628 x 71866 (17.9 MB) with weight 4415802 (61.44/col)
Sat Mar 14 17:06:40 2009  sparse part has weight 4415802 (61.44/col)
Sat Mar 14 17:06:41 2009  filtering completed in 3 passes
Sat Mar 14 17:06:41 2009  matrix is 68211 x 68275 (17.1 MB) with weight 4214479 (61.73/col)
Sat Mar 14 17:06:41 2009  sparse part has weight 4214479 (61.73/col)
Sat Mar 14 17:06:41 2009  saving the first 48 matrix rows for later
Sat Mar 14 17:06:41 2009  matrix is 68163 x 68275 (9.7 MB) with weight 3197837 (46.84/col)
Sat Mar 14 17:06:41 2009  sparse part has weight 2134685 (31.27/col)
Sat Mar 14 17:06:41 2009  matrix includes 64 packed rows
Sat Mar 14 17:06:41 2009  using block size 27310 for processor cache size 1024 kB
Sat Mar 14 17:06:41 2009  commencing Lanczos iteration
Sat Mar 14 17:06:41 2009  memory use: 10.1 MB
Sat Mar 14 17:07:09 2009  lanczos halted after 1080 iterations (dim = 68162)
Sat Mar 14 17:07:09 2009  recovered 17 nontrivial dependencies
Sat Mar 14 17:07:10 2009  prp33 factor: 586131916604674594186662435865517
Sat Mar 14 17:07:10 2009  prp60 factor: 868790611576412906071918691609898995245693401683366767021583
Sat Mar 14 17:07:10 2009  elapsed time 02:42:45

(47·10¹⁶⁵-11)/9 = 5(2)₁₆₄1_<166> = C166

C166 = P40 · P63 · P64

P40 = 5918524479803075086436339126178823754311_<40>

P63 = 519179504524486311724334410233223760285302400037254392850689843_<63>

P64 = 1699512489917835059576268585912961688023355579409275026948322377_<64>

Number: 52221_165
N=5222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
  ( 166 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=5918524479803075086436339126178823754311
 r2=519179504524486311724334410233223760285302400037254392850689843
 r3=1699512489917835059576268585912961688023355579409275026948322377
Version: 
Total time: 44.30 hours.
Scaled time: 113.57 units (timescale=2.564).
Factorization parameters were as follows:
name: 52221_165
n: 5222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 1000000000000000000000000000000000
deg: 5
c5: 47
c0: -11
skew: 0.75
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 751824 x 752072
Total sieving time: 44.30 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 44.30 hours.
 --------- CPU info (if available) ----------

(47·10¹²⁴+7)/9 = 5(2)₁₂₃3_<125> = 103 · 11887 · 14394089 · C112

C112 = P37 · P76

P37 = 2785752717121406456107181322074188931_<37>

P76 = 1063699890799604316061313992156606964334667038811968046342270980758586143477_<76>

Number: 52223_124
N=2963204860996741060096307919041764536362963095353592541342576306410981071514265999823483457395547611649971253087
  ( 112 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=2785752717121406456107181322074188931 (pp37)
 r2=1063699890799604316061313992156606964334667038811968046342270980758586143477 (pp76)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 4.64 hours.
Scaled time: 2.18 units (timescale=0.471).
Factorization parameters were as follows:
name: 52223_124
n: 2963204860996741060096307919041764536362963095353592541342576306410981071514265999823483457395547611649971253087
m: 10000000000000000000000000
deg: 5
c5: 47
c0: 70
skew: 1.08
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 850001)
Primes: RFBsize:71274, AFBsize:71085, largePrimes:2493548 encountered
Relations: rels:2351487, finalFF:160090
Max relations in full relation-set: 28
Initial matrix: 142424 x 160090 with sparse part having weight 12470984.
Pruned matrix : 137621 x 138397 with weight 9162565.
Total sieving time: 4.22 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 4.64 hours.
 --------- CPU info (if available) ----------

(47·10¹¹¹+7)/9 = 5(2)₁₁₀3_<112> = 3 · 167 · 1100719420842443_<16> · C94

C94 = P32 · P62

P32 = 99354390761686984015872318744119_<32>

P62 = 95313392755558649228750245113021824453060736428646393675802319_<62>

Sat Mar 14 17:15:47 2009  Msieve v. 1.39
Sat Mar 14 17:15:47 2009  random seeds: 99cf8800 54b6b3f0
Sat Mar 14 17:15:47 2009  factoring 9469804068657919367648212382115094366701990833108454850429643038325714139839345127949787811961 (94 digits)
Sat Mar 14 17:15:48 2009  searching for 15-digit factors
Sat Mar 14 17:15:49 2009  commencing quadratic sieve (94-digit input)
Sat Mar 14 17:15:49 2009  using multiplier of 1
Sat Mar 14 17:15:49 2009  using 32kb Intel Core sieve core
Sat Mar 14 17:15:49 2009  sieve interval: 36 blocks of size 32768
Sat Mar 14 17:15:49 2009  processing polynomials in batches of 6
Sat Mar 14 17:15:49 2009  using a sieve bound of 2092589 (77647 primes)
Sat Mar 14 17:15:49 2009  using large prime bound of 297147638 (28 bits)
Sat Mar 14 17:15:49 2009  using double large prime bound of 1783816197254578 (42-51 bits)
Sat Mar 14 17:15:49 2009  using trial factoring cutoff of 51 bits
Sat Mar 14 17:15:49 2009  polynomial 'A' values have 12 factors
Sat Mar 14 20:51:17 2009  77940 relations (18705 full + 59235 combined from 1144313 partial), need 77743
Sat Mar 14 20:51:19 2009  begin with 1163018 relations
Sat Mar 14 20:51:20 2009  reduce to 204434 relations in 11 passes
Sat Mar 14 20:51:20 2009  attempting to read 204434 relations
Sat Mar 14 20:51:23 2009  recovered 204434 relations
Sat Mar 14 20:51:23 2009  recovered 188189 polynomials
Sat Mar 14 20:51:23 2009  attempting to build 77940 cycles
Sat Mar 14 20:51:23 2009  found 77940 cycles in 6 passes
Sat Mar 14 20:51:23 2009  distribution of cycle lengths:
Sat Mar 14 20:51:23 2009     length 1 : 18705
Sat Mar 14 20:51:23 2009     length 2 : 13510
Sat Mar 14 20:51:23 2009     length 3 : 13074
Sat Mar 14 20:51:23 2009     length 4 : 10635
Sat Mar 14 20:51:23 2009     length 5 : 8000
Sat Mar 14 20:51:23 2009     length 6 : 5524
Sat Mar 14 20:51:24 2009     length 7 : 3607
Sat Mar 14 20:51:24 2009     length 9+: 4885
Sat Mar 14 20:51:24 2009  largest cycle: 20 relations
Sat Mar 14 20:51:24 2009  matrix is 77647 x 77940 (20.2 MB) with weight 4978462 (63.88/col)
Sat Mar 14 20:51:24 2009  sparse part has weight 4978462 (63.88/col)
Sat Mar 14 20:51:25 2009  filtering completed in 3 passes
Sat Mar 14 20:51:25 2009  matrix is 74172 x 74236 (19.3 MB) with weight 4757980 (64.09/col)
Sat Mar 14 20:51:25 2009  sparse part has weight 4757980 (64.09/col)
Sat Mar 14 20:51:25 2009  saving the first 48 matrix rows for later
Sat Mar 14 20:51:25 2009  matrix is 74124 x 74236 (12.0 MB) with weight 3724349 (50.17/col)
Sat Mar 14 20:51:25 2009  sparse part has weight 2705848 (36.45/col)
Sat Mar 14 20:51:25 2009  matrix includes 64 packed rows
Sat Mar 14 20:51:25 2009  using block size 29694 for processor cache size 1024 kB
Sat Mar 14 20:51:26 2009  commencing Lanczos iteration
Sat Mar 14 20:51:26 2009  memory use: 11.8 MB
Sat Mar 14 20:52:02 2009  lanczos halted after 1173 iterations (dim = 74120)
Sat Mar 14 20:52:02 2009  recovered 14 nontrivial dependencies
Sat Mar 14 20:52:03 2009  prp32 factor: 99354390761686984015872318744119
Sat Mar 14 20:52:03 2009  prp62 factor: 95313392755558649228750245113021824453060736428646393675802319
Sat Mar 14 20:52:03 2009  elapsed time 03:36:16

Mar 14, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.2, msieve-1.40 qs, GMP-ECM 6.2.1 / Mar 14, 2009

(47·10¹⁵²+7)/9 = 5(2)₁₅₁3_<153> = 1952695607832913_<16> · 283524340410277072904211677_<27> · C111

C111 = P36 · P76

P36 = 339373340987111439213032822853497251_<36>

P76 = 2779410708331052353653724618917632167285726758443818868201468908679417755673_<76>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1946158246
Step 1 took 5372ms
Step 2 took 3256ms
********** Factor found in step 2: 339373340987111439213032822853497251
Found probable prime factor of 36 digits: 339373340987111439213032822853497251
Probable prime cofactor has 76 digits

(47·10¹³⁴+7)/9 = 5(2)₁₃₃3_<135> = 3799661 · 18715250221_<11> · C118

C118 = P34 · P85

P34 = 4525990818863841521810589260294153_<34>

P85 = 1622561588863687464350670473498891981365744075605523527865925442743054930210085773311_<85>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1946389392
Step 1 took 6456ms
Step 2 took 6709ms
********** Factor found in step 2: 4525990818863841521810589260294153
Found probable prime factor of 34 digits: 4525990818863841521810589260294153
Probable prime cofactor has 85 digits

(47·10¹⁸⁶+7)/9 = 5(2)₁₈₅3_<187> = 3³ · 23 · 67 · 283 · 432814036485059_<15> · C166

C166 = P28 · P138

P28 = 4840591880169166213085470327_<28>

P138 = 211691151514429896660769178295263694791289185531220177711932718691581543566221485464975234795208195314453290424266620986638735069610692831_<138>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3938707912
Step 1 took 9141ms
Step 2 took 9192ms
********** Factor found in step 2: 4840591880169166213085470327
Found probable prime factor of 28 digits: 4840591880169166213085470327
Probable prime cofactor has 138 digits

(47·10¹³⁷+7)/9 = 5(2)₁₃₆3_<138> = 13² · 19 · 29 · 97 · 109 · 197 · 229937 · 47675357 · C114

C114 = P34 · P37 · P43

P34 = 6422170386514943990059678887791069_<34>

P37 = 4358789346295655325743077570815223087_<37>

P43 = 8774089653393861131013655175773030008711191_<43>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=480940633
Step 1 took 5329ms
Step 2 took 6460ms
********** Factor found in step 2: 6422170386514943990059678887791069
Found probable prime factor of 34 digits: 6422170386514943990059678887791069
Composite cofactor has 80 digits

Sat Mar 14 00:21:33 2009  Msieve v. 1.40
Sat Mar 14 00:21:33 2009  random seeds: 8e3810e2 83902929
Sat Mar 14 00:21:33 2009  factoring 38244408504656100974238958952130843351545315858136955428199482775131044018466617 (80 digits)
Sat Mar 14 00:21:34 2009  searching for 15-digit factors
Sat Mar 14 00:21:34 2009  commencing quadratic sieve (80-digit input)
Sat Mar 14 00:21:34 2009  using multiplier of 2
Sat Mar 14 00:21:34 2009  using 64kb Opteron sieve core
Sat Mar 14 00:21:34 2009  sieve interval: 6 blocks of size 65536
Sat Mar 14 00:21:34 2009  processing polynomials in batches of 17
Sat Mar 14 00:21:34 2009  using a sieve bound of 1252877 (48647 primes)
Sat Mar 14 00:21:34 2009  using large prime bound of 125287700 (26 bits)
Sat Mar 14 00:21:34 2009  using trial factoring cutoff of 27 bits
Sat Mar 14 00:21:34 2009  polynomial 'A' values have 10 factors
Sat Mar 14 00:26:42 2009  49083 relations (25890 full + 23193 combined from 258044 partial), need 48743
Sat Mar 14 00:26:42 2009  begin with 283934 relations
Sat Mar 14 00:26:42 2009  reduce to 69404 relations in 2 passes
Sat Mar 14 00:26:42 2009  attempting to read 69404 relations
Sat Mar 14 00:26:43 2009  recovered 69404 relations
Sat Mar 14 00:26:43 2009  recovered 54668 polynomials
Sat Mar 14 00:26:43 2009  attempting to build 49083 cycles
Sat Mar 14 00:26:43 2009  found 49083 cycles in 1 passes
Sat Mar 14 00:26:43 2009  distribution of cycle lengths:
Sat Mar 14 00:26:43 2009     length 1 : 25890
Sat Mar 14 00:26:43 2009     length 2 : 23193
Sat Mar 14 00:26:43 2009  largest cycle: 2 relations
Sat Mar 14 00:26:43 2009  matrix is 48647 x 49083 (7.2 MB) with weight 1506848 (30.70/col)
Sat Mar 14 00:26:43 2009  sparse part has weight 1506848 (30.70/col)
Sat Mar 14 00:26:43 2009  filtering completed in 3 passes
Sat Mar 14 00:26:43 2009  matrix is 33410 x 33472 (5.4 MB) with weight 1150563 (34.37/col)
Sat Mar 14 00:26:43 2009  sparse part has weight 1150563 (34.37/col)
Sat Mar 14 00:26:43 2009  saving the first 48 matrix rows for later
Sat Mar 14 00:26:43 2009  matrix is 33362 x 33472 (3.6 MB) with weight 845758 (25.27/col)
Sat Mar 14 00:26:43 2009  sparse part has weight 616640 (18.42/col)
Sat Mar 14 00:26:43 2009  matrix includes 64 packed rows
Sat Mar 14 00:26:43 2009  using block size 13388 for processor cache size 6144 kB
Sat Mar 14 00:26:43 2009  commencing Lanczos iteration
Sat Mar 14 00:26:43 2009  memory use: 3.6 MB
Sat Mar 14 00:26:45 2009  lanczos halted after 529 iterations (dim = 33361)
Sat Mar 14 00:26:45 2009  recovered 17 nontrivial dependencies
Sat Mar 14 00:26:45 2009  prp37 factor: 4358789346295655325743077570815223087
Sat Mar 14 00:26:45 2009  prp43 factor: 8774089653393861131013655175773030008711191
Sat Mar 14 00:26:45 2009  elapsed time 00:05:12

(47·10¹⁴⁰+7)/9 = 5(2)₁₃₉3_<141> = 1103 · 1485277 · 894342431 · C123

C123 = P33 · C91

P33 = 283548934196313789203440276497841_<33>

C91 = [1257015188017072067989007346481096231837401079833480219711434479996912229920252505539616923_<91>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2255321493
Step 1 took 6393ms
Step 2 took 6728ms
********** Factor found in step 2: 283548934196313789203440276497841
Found probable prime factor of 33 digits: 283548934196313789203440276497841
Composite cofactor has 91 digits

(47·10¹⁵⁷+7)/9 = 5(2)₁₅₆3_<158> = 53 · 421 · 7753 · 11813 · 861740186150432041_<18> · C128

C128 = P33 · C96

P33 = 241830508061251464811661998926787_<33>

C96 = [122625265490318673039471791592719193179089888733075612849378008814899208570958452107536328001417_<96>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3844973302
Step 1 took 6400ms
Step 2 took 7389ms
********** Factor found in step 2: 241830508061251464811661998926787
Found probable prime factor of 33 digits: 241830508061251464811661998926787
Composite cofactor has 96 digits

(47·10¹⁵³+7)/9 = 5(2)₁₅₂3_<154> = 3 · 67 · 107 · 193 · C148

C148 = P32 · P38 · P79

P32 = 13570844613002159206276004364691_<32>

P38 = 15817293669014247931825045270010627021_<38>

P79 = 5861100234609922300221141974629455706532441454493876553268835399948265889446243_<79>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2000005749
Step 1 took 7681ms
Step 2 took 7924ms
********** Factor found in step 2: 15817293669014247931825045270010627021
Found probable prime factor of 38 digits: 15817293669014247931825045270010627021

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2056501203
Step 1 took 7769ms
Step 2 took 8460ms
********** Factor found in step 2: 13570844613002159206276004364691
Found probable prime factor of 32 digits: 13570844613002159206276004364691

(47·10¹⁹⁰+7)/9 = 5(2)₁₈₉3_<191> = 14419 · 295837 · 75219844079669_<14> · 21189621711595422727_<20> · C148

C148 = P33 · P116

P33 = 316337110404787322260442929286567_<33>

P116 = 24280741272539150477959519296127039083963060012467775306321450629307336526410616631121968182054636945330923198095621_<116>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2071500620
Step 1 took 7669ms
Step 2 took 8472ms
********** Factor found in step 2: 316337110404787322260442929286567
Found probable prime factor of 33 digits: 316337110404787322260442929286567
Probable prime cofactor has 116 digits

Mar 14, 2009 (4th)

By Wataru Sakai / GMP-ECM / Mar 14, 2009

(5·10¹⁷⁶+1)/3 = 1(6)₁₇₅7_<177> = 43 · 502769 · 26728601 · 90499058006410250891821665501032497487_<38> · C124

C124 = P49 · P76

P49 = 2725754774355785969760441380232560871052705129783_<49>

P76 = 1169242880077307275718954778478639891947328564280437102540201756848172409281_<76>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=3476594416
Step 1 took 521560ms
Step 2 took 144786ms
********** Factor found in step 2: 2725754774355785969760441380232560871052705129783
Found probable prime factor of 49 digits: 2725754774355785969760441380232560871052705129783
Probable prime cofactor 1169242880077307275718954778478639891947328564280437102540201756848172409281 has 76 digits

Mar 14, 2009 (3rd)

By Tyler Cadigan / GGNFS, Msieve / Mar 13, 2009

(10¹⁸⁶+53)/9 = (1)₁₈₅7_<186> = 3 · 23 · 29 · 229 · 40306300676599127_<17> · C163

C163 = P67 · P97

P67 = 1169319768458061656957638542309755826295782876079702955713679861317_<67>

P97 = 5144802260188377367236157788169330632323206741118039994276567261208535262981380543018891749384547_<97>

Number: 11117_186
N=6015918987645985707374326771781404241768501075705916328537600681329537905805438980542336186668469369633194704138210533713686971145820624763164643448184023062868399
  ( 163 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=1169319768458061656957638542309755826295782876079702955713679861317 (pp67)
 r2=5144802260188377367236157788169330632323206741118039994276567261208535262981380543018891749384547 (pp97)
Version: Msieve-1.39
Total time: 208.74 hours.
Scaled time: 527.49 units (timescale=2.527).
Factorization parameters were as follows:
n: 6015918987645985707374326771781404241768501075705916328537600681329537905805438980542336186668469369633194704138210533713686971145820624763164643448184023062868399
m: 10000000000000000000000000000000000000
deg: 5
c5: 10
c0: 53
skew: 1.40
type: snfs
lss: 1
rlim: 8800000
alim: 8800000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 8800000/8800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4400000, 7400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1494341 x 1494588
Total sieving time: 208.74 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,8800000,8800000,28,28,54,54,2.5,2.5,100000
total time: 208.74 hours.
 --------- CPU info (if available) ----------

Mar 14, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Mar 13, 2009

(34·10¹⁶⁶+11)/9 = 3(7)₁₆₅9_<167> = 3 · 7 · 31626402448477_<14> · C152

C152 = P67 · P85

P67 = 7433469121613363106548924286466391259517809872867192997109258626823_<67>

P85 = 7652014390216588291222042775069211091736777411099684795795933848178270670770807272469_<85>

Number: 37779_166
N=56881012687816116882509529469225512722853884217827165715545764590324915101749318460398051179992115444952447748972611232406682686285021225138144952835987
  ( 152 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=7433469121613363106548924286466391259517809872867192997109258626823 (pp67)
 r2=7652014390216588291222042775069211091736777411099684795795933848178270670770807272469 (pp85)
Version: Msieve-1.39
Total time: 52.08 hours.
Scaled time: 133.90 units (timescale=2.571).
Factorization parameters were as follows:
n: 56881012687816116882509529469225512722853884217827165715545764590324915101749318460398051179992115444952447748972611232406682686285021225138144952835987
m: 2000000000000000000000000000000000
deg: 5
c5: 85
c0: 88
skew: 1.01
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 4850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 851783 x 852031
Total sieving time: 52.08 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000
total time: 52.08 hours.
 --------- CPU info (if available) ----------

By Ignacio Santos / GGNFS, Msieve / Mar 14, 2009

(47·10¹⁵⁶-11)/9 = 5(2)₁₅₅1_<157> = 394379920267_<12> · 2919127164391_<13> · C133

C133 = P43 · P90

P43 = 7273499550758919787884339332474160728899697_<43>

P90 = 623654589879613371292973321974587414376379766723300320931456522981021853230936509414590769_<90>

Number: 52221_156
N=4536151379318106219337955194636765662118353139712989327151999232488671237829986338239190025532845797040103540422941405561898903096993
  ( 133 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=7273499550758919787884339332474160728899697 (pp43)
 r2=623654589879613371292973321974587414376379766723300320931456522981021853230936509414590769 (pp90)
Version: Msieve-1.39
Total time: 25.98 hours.
Scaled time: 66.81 units (timescale=2.571).
Factorization parameters were as follows:
n: 4536151379318106219337955194636765662118353139712989327151999232488671237829986338239190025532845797040103540422941405561898903096993
m: 20000000000000000000000000000000
deg: 5
c5: 235
c0: -176
skew: 0.94
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1550000, 2950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 598154 x 598402
Total sieving time: 25.98 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000
total time: 25.98 hours.
 --------- CPU info (if available) ----------

(46·10¹⁷³+71)/9 = 5(1)₁₇₂9_<174> = 3 · 7² · C172

C172 = P33 · P52 · P89

P33 = 126509766445013568298328610136223_<33>

P52 = 1180604026176186007639458182676328295836124161667627_<52>

P89 = 23279286946766512066852874314714772481738009363765283757882378099668313192812207895727137_<89>

Number: 51119_173
N=3476946334089191232048374905517762660619803476946334089191232048374905517762660619803476946334089191232048374905517762660619803476946334089191232048374905517762660619803477
  ( 172 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=126509766445013568298328610136223 (pp33)
 r2=1180604026176186007639458182676328295836124161667627 (pp52)
 r3=23279286946766512066852874314714772481738009363765283757882378099668313192812207895727137 (pp89)
Version: Msieve-1.39
Total time: 99.49 hours.
Scaled time: 172.62 units (timescale=1.735).
Factorization parameters were as follows:
n: 3476946334089191232048374905517762660619803476946334089191232048374905517762660619803476946334089191232048374905517762660619803476946334089191232048374905517762660619803477
m: 50000000000000000000000000000000000
deg: 5
c5: 368
c0: 1775
skew: 1.37
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3000000, 8300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1409394 x 1409641
Total sieving time: 99.49 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,53,53,2.5,2.5,100000
total time: 99.49 hours.
 --------- CPU info (if available) ----------

(47·10¹²⁵+7)/9 = 5(2)₁₂₄3_<126> = 13 · 414971 · C119

C119 = P51 · P69

P51 = 249262664540884389477543315300142196556005259225137_<51>

P69 = 388362256356922383654110336587870767762061470294935602486273863612673_<69>

Number: 52223_125
N=96804210826636490116588725889134833374310349809842545479493603579383067588267469704967746999599827869755165879473361201
  ( 119 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=249262664540884389477543315300142196556005259225137 (pp51)
 r2=388362256356922383654110336587870767762061470294935602486273863612673 (pp69)
Version: Msieve-1.39
Total time: 1.68 hours.
Scaled time: 2.01 units (timescale=1.198).
Factorization parameters were as follows:
n: 96804210826636490116588725889134833374310349809842545479493603579383067588267469704967746999599827869755165879473361201
m: 10000000000000000000000000
deg: 5
c5: 47
c0: 7
skew: 0.68
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 110741 x 110989
Total sieving time: 1.68 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 1.68 hours.
 --------- CPU info (if available) ----------

(47·10¹³⁰+7)/9 = 5(2)₁₂₉3_<131> = 88793 · C126

C126 = P47 · P80

P47 = 30602062129474609741231985600401032056090268883_<47>

P80 = 19218784915527384809400907508899151102992419244502866884919413944562822687207517_<80>

Number: 52223_130
N=588134450037978469273729035196718460038766819706758665910851330873179442323406374626628475467911009000959785368466232948793511
  ( 126 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=30602062129474609741231985600401032056090268883 (pp47)
 r2=19218784915527384809400907508899151102992419244502866884919413944562822687207517 (pp80)
Version: Msieve-1.39
Total time: 2.20 hours.
Scaled time: 2.64 units (timescale=1.203).
Factorization parameters were as follows:
n: 588134450037978469273729035196718460038766819706758665910851330873179442323406374626628475467911009000959785368466232948793511
m: 100000000000000000000000000
deg: 5
c5: 47
c0: 7
skew: 0.68
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 153635 x 153878
Total sieving time: 2.20 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 2.20 hours.
 --------- CPU info (if available) ----------

(47·10¹³⁵+7)/9 = 5(2)₁₃₄3_<136> = 3 · 2593 · C132

C132 = P38 · P44 · P51

P38 = 41772283146786978635729672887661947099_<38>

P44 = 33809349590802576044638725167462602354959817_<44>

P51 = 475342392548263571865729455529900570409279608682439_<51>

Number: 52223_135
N=671323077802059676336575680964419876876490837154161488908885746525545985630829441087829055434146062761566039622345060061990258673637
  ( 132 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=41772283146786978635729672887661947099 (pp38)
 r2=33809349590802576044638725167462602354959817 (pp44)
 r3=475342392548263571865729455529900570409279608682439 (pp51)
Version: Msieve-1.39
Total time: 3.33 hours.
Scaled time: 3.98 units (timescale=1.195).
Factorization parameters were as follows:
n: 671323077802059676336575680964419876876490837154161488908885746525545985630829441087829055434146062761566039622345060061990258673637
m: 1000000000000000000000000000
deg: 5
c5: 47
c0: 7
skew: 0.68
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1265001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 183120 x 183368
Total sieving time: 3.33 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 3.33 hours.
 --------- CPU info (if available) ----------

Mar 14, 2009

Factorizations of 522...223 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 13, 2009 (4th)

By Max Dettweiler / GGNFS, msieve v1.40beta2 / Mar 13, 2009

(46·10¹⁶¹+71)/9 = 5(1)₁₆₀9_<162> = 3 · 7 · 467 · 1549693919876341_<16> · C143

C143 = P41 · P103

P41 = 16992883783519846308764066577664900740967_<41>

P103 = 1979092671373367048595934073451965110198678986743029049601958788254140099138182740089543592879492970011_<103>

Thu Mar 12 16:04:04 2009  Msieve v. 1.40
Thu Mar 12 16:04:04 2009  random seeds: 30e12317 790c577c
Thu Mar 12 16:04:04 2009  factoring 33630491761463461278107881750538416295896144123471294761109199342706343370308250905348604392930090333968989529496276747314290683246581410140637 (143 digits)
Thu Mar 12 16:04:05 2009  no P-1/P+1/ECM available, skipping
Thu Mar 12 16:04:05 2009  commencing number field sieve (143-digit input)
Thu Mar 12 16:04:05 2009  R0: -100000000000000000000000000000000
Thu Mar 12 16:04:05 2009  R1:  1
Thu Mar 12 16:04:05 2009  A0:  71
Thu Mar 12 16:04:05 2009  A1:  0
Thu Mar 12 16:04:05 2009  A2:  0
Thu Mar 12 16:04:05 2009  A3:  0
Thu Mar 12 16:04:05 2009  A4:  0
Thu Mar 12 16:04:05 2009  A5:  460
Thu Mar 12 16:04:05 2009  skew 0.69, size 1.255037e-11, alpha 1.174105, combined = 3.813267e-10
Thu Mar 12 16:04:05 2009  
Thu Mar 12 16:04:05 2009  commencing relation filtering
Thu Mar 12 16:04:05 2009  commencing duplicate removal, pass 1
Thu Mar 12 16:04:05 2009  error -9 reading relation 13
Thu Mar 12 16:05:33 2009  found 919606 hash collisions in 9599998 relations
Thu Mar 12 16:05:58 2009  added 1921 free relations
Thu Mar 12 16:05:58 2009  commencing duplicate removal, pass 2
Thu Mar 12 16:06:06 2009  found 831756 duplicates and 8770163 unique relations
Thu Mar 12 16:06:06 2009  memory use: 50.6 MB
Thu Mar 12 16:06:06 2009  reading rational ideals above 3735552
Thu Mar 12 16:06:06 2009  reading algebraic ideals above 3735552
Thu Mar 12 16:06:06 2009  commencing singleton removal, pass 1
Thu Mar 12 16:07:27 2009  relations with 0 large ideals: 98865
Thu Mar 12 16:07:27 2009  relations with 1 large ideals: 729844
Thu Mar 12 16:07:27 2009  relations with 2 large ideals: 2341536
Thu Mar 12 16:07:27 2009  relations with 3 large ideals: 3355712
Thu Mar 12 16:07:27 2009  relations with 4 large ideals: 1836344
Thu Mar 12 16:07:27 2009  relations with 5 large ideals: 58253
Thu Mar 12 16:07:27 2009  relations with 6 large ideals: 349609
Thu Mar 12 16:07:27 2009  relations with 7+ large ideals: 0
Thu Mar 12 16:07:27 2009  8770163 relations and about 9159306 large ideals
Thu Mar 12 16:07:27 2009  commencing singleton removal, pass 2
Thu Mar 12 16:08:52 2009  found 3682975 singletons
Thu Mar 12 16:08:52 2009  current dataset: 5087188 relations and about 4419395 large ideals
Thu Mar 12 16:08:52 2009  commencing singleton removal, pass 3
Thu Mar 12 16:09:40 2009  found 986850 singletons
Thu Mar 12 16:09:40 2009  current dataset: 4100338 relations and about 3355585 large ideals
Thu Mar 12 16:09:40 2009  commencing singleton removal, pass 4
Thu Mar 12 16:10:19 2009  found 294336 singletons
Thu Mar 12 16:10:19 2009  current dataset: 3806002 relations and about 3052506 large ideals
Thu Mar 12 16:10:19 2009  commencing singleton removal, final pass
Thu Mar 12 16:10:59 2009  memory use: 66.6 MB
Thu Mar 12 16:10:59 2009  commencing in-memory singleton removal
Thu Mar 12 16:11:00 2009  begin with 3806002 relations and 3220753 unique ideals
Thu Mar 12 16:11:05 2009  reduce to 3206585 relations and 2607067 ideals in 15 passes
Thu Mar 12 16:11:05 2009  max relations containing the same ideal: 49
Thu Mar 12 16:11:06 2009  reading rational ideals above 720000
Thu Mar 12 16:11:06 2009  reading algebraic ideals above 720000
Thu Mar 12 16:11:06 2009  commencing singleton removal, final pass
Thu Mar 12 16:11:48 2009  keeping 2822482 ideals with weight <= 20, new excess is 327745
Thu Mar 12 16:11:50 2009  memory use: 92.0 MB
Thu Mar 12 16:11:51 2009  commencing in-memory singleton removal
Thu Mar 12 16:11:51 2009  begin with 3208506 relations and 2822482 unique ideals
Thu Mar 12 16:11:55 2009  reduce to 3206205 relations and 2810646 ideals in 9 passes
Thu Mar 12 16:11:55 2009  max relations containing the same ideal: 20
Thu Mar 12 16:11:58 2009  relations with 0 large ideals: 25956
Thu Mar 12 16:11:58 2009  relations with 1 large ideals: 178840
Thu Mar 12 16:11:58 2009  relations with 2 large ideals: 602522
Thu Mar 12 16:11:58 2009  relations with 3 large ideals: 1016724
Thu Mar 12 16:11:58 2009  relations with 4 large ideals: 888209
Thu Mar 12 16:11:58 2009  relations with 5 large ideals: 373815
Thu Mar 12 16:11:58 2009  relations with 6 large ideals: 110612
Thu Mar 12 16:11:58 2009  relations with 7+ large ideals: 9527
Thu Mar 12 16:11:58 2009  commencing 2-way merge
Thu Mar 12 16:12:01 2009  reduce to 1833929 relation sets and 1438640 unique ideals
Thu Mar 12 16:12:01 2009  ignored 270 oversize relation sets
Thu Mar 12 16:12:01 2009  commencing full merge
Thu Mar 12 16:12:25 2009  memory use: 100.4 MB
Thu Mar 12 16:12:25 2009  found 818948 cycles, need 770840
Thu Mar 12 16:12:25 2009  weight of 770840 cycles is about 54088079 (70.17/cycle)
Thu Mar 12 16:12:25 2009  distribution of cycle lengths:
Thu Mar 12 16:12:25 2009  1 relations: 95092
Thu Mar 12 16:12:25 2009  2 relations: 85980
Thu Mar 12 16:12:25 2009  3 relations: 85852
Thu Mar 12 16:12:25 2009  4 relations: 78763
Thu Mar 12 16:12:25 2009  5 relations: 70763
Thu Mar 12 16:12:25 2009  6 relations: 61917
Thu Mar 12 16:12:25 2009  7 relations: 52224
Thu Mar 12 16:12:25 2009  8 relations: 44948
Thu Mar 12 16:12:25 2009  9 relations: 38437
Thu Mar 12 16:12:25 2009  10+ relations: 156864
Thu Mar 12 16:12:25 2009  heaviest cycle: 21 relations
Thu Mar 12 16:12:26 2009  commencing cycle optimization
Thu Mar 12 16:12:28 2009  start with 4639290 relations
Thu Mar 12 16:12:36 2009  pruned 124918 relations
Thu Mar 12 16:12:36 2009  memory use: 123.4 MB
Thu Mar 12 16:12:36 2009  distribution of cycle lengths:
Thu Mar 12 16:12:36 2009  1 relations: 95092
Thu Mar 12 16:12:36 2009  2 relations: 88075
Thu Mar 12 16:12:36 2009  3 relations: 89333
Thu Mar 12 16:12:36 2009  4 relations: 80965
Thu Mar 12 16:12:36 2009  5 relations: 72987
Thu Mar 12 16:12:36 2009  6 relations: 62789
Thu Mar 12 16:12:36 2009  7 relations: 52906
Thu Mar 12 16:12:36 2009  8 relations: 44508
Thu Mar 12 16:12:36 2009  9 relations: 38326
Thu Mar 12 16:12:36 2009  10+ relations: 145859
Thu Mar 12 16:12:36 2009  heaviest cycle: 21 relations
Thu Mar 12 16:12:38 2009  RelProcTime: 466
Thu Mar 12 16:12:38 2009  
Thu Mar 12 16:12:38 2009  commencing linear algebra
Thu Mar 12 16:12:39 2009  read 770840 cycles
Thu Mar 12 16:12:41 2009  cycles contain 2614730 unique relations
Thu Mar 12 16:13:03 2009  read 2614730 relations
Thu Mar 12 16:13:08 2009  using 20 quadratic characters above 134215832
Thu Mar 12 16:13:25 2009  building initial matrix
Thu Mar 12 16:14:20 2009  memory use: 279.4 MB
Thu Mar 12 16:14:21 2009  read 770840 cycles
Thu Mar 12 16:14:25 2009  matrix is 769966 x 770840 (217.9 MB) with weight 67686320 (87.81/col)
Thu Mar 12 16:14:25 2009  sparse part has weight 51726666 (67.10/col)
Thu Mar 12 16:14:46 2009  filtering completed in 3 passes
Thu Mar 12 16:14:46 2009  matrix is 758782 x 758981 (215.4 MB) with weight 66834112 (88.06/col)
Thu Mar 12 16:14:46 2009  sparse part has weight 51142090 (67.38/col)
Thu Mar 12 16:14:56 2009  read 758981 cycles
Thu Mar 12 16:14:56 2009  matrix is 758782 x 758981 (215.4 MB) with weight 66834112 (88.06/col)
Thu Mar 12 16:14:56 2009  sparse part has weight 51142090 (67.38/col)
Thu Mar 12 16:14:56 2009  saving the first 48 matrix rows for later
Thu Mar 12 16:14:57 2009  matrix is 758734 x 758981 (202.7 MB) with weight 53035025 (69.88/col)
Thu Mar 12 16:14:57 2009  sparse part has weight 48576287 (64.00/col)
Thu Mar 12 16:14:57 2009  matrix includes 64 packed rows
Thu Mar 12 16:14:57 2009  using block size 65536 for processor cache size 2048 kB
Thu Mar 12 16:15:02 2009  commencing Lanczos iteration (2 threads)
Thu Mar 12 16:15:02 2009  memory use: 209.4 MB
Thu Mar 12 17:28:24 2009  lanczos halted after 12001 iterations (dim = 758732)
Thu Mar 12 17:28:26 2009  recovered 37 nontrivial dependencies
Thu Mar 12 17:28:26 2009  BLanczosTime: 7786
Thu Mar 12 17:28:26 2009  
Thu Mar 12 17:28:26 2009  commencing square root phase
Thu Mar 12 17:28:26 2009  reading relations for dependency 1
Thu Mar 12 17:28:27 2009  read 379915 cycles
Thu Mar 12 17:28:28 2009  cycles contain 1582369 unique relations
Thu Mar 12 17:28:48 2009  read 1582369 relations
Thu Mar 12 17:28:58 2009  multiplying 1298358 relations
Thu Mar 12 17:30:51 2009  multiply complete, coefficients have about 39.09 million bits
Thu Mar 12 17:30:52 2009  initial square root is modulo 409691
Thu Mar 12 17:34:41 2009  reading relations for dependency 2
Thu Mar 12 17:34:42 2009  read 379636 cycles
Thu Mar 12 17:34:43 2009  cycles contain 1581643 unique relations
Thu Mar 12 17:35:04 2009  read 1581643 relations
Thu Mar 12 17:35:13 2009  multiplying 1297484 relations
Thu Mar 12 17:37:06 2009  multiply complete, coefficients have about 39.06 million bits
Thu Mar 12 17:37:07 2009  initial square root is modulo 406331
Thu Mar 12 17:40:54 2009  sqrtTime: 668
Thu Mar 12 17:40:54 2009  prp41 factor: 16992883783519846308764066577664900740967
Thu Mar 12 17:40:54 2009  prp103 factor: 1979092671373367048595934073451965110198678986743029049601958788254140099138182740089543592879492970011
Thu Mar 12 17:40:54 2009  elapsed time 01:36:50

Mar 13, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Mar 13, 2009

(47·10¹⁵³-11)/9 = 5(2)₁₅₂1_<154> = 43 · 71 · 2441 · 17898373 · 8263935083818247538581_<22> · C118

C118 = P57 · P62

P57 = 226172031937598581999049537050152677114695575507414403739_<57>

P62 = 20946979782671921817910823270603751543852860787070098351507811_<62>

Number: 52221_153
N=4737620980402705705626055815487932594604850839169072620739338386990968212221775269943468270813335695462747750166105329
  ( 118 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=226172031937598581999049537050152677114695575507414403739 (pp57)
 r2=20946979782671921817910823270603751543852860787070098351507811 (pp62)
Version: Msieve-1.39
Total time: 17.16 hours.
Scaled time: 44.12 units (timescale=2.571).
Factorization parameters were as follows:
n: 4737620980402705705626055815487932594604850839169072620739338386990968212221775269943468270813335695462747750166105329
m: 5000000000000000000000000000000
deg: 5
c5: 376
c0: -275
skew: 0.94
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 473115 x 473363
Total sieving time: 17.16 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 17.16 hours.
 --------- CPU info (if available) ----------

(47·10¹⁶⁷-11)/9 = 5(2)₁₆₆1_<168> = 7 · 11821 · C163

C163 = P72 · P92

P72 = 142395689927785736847713012883930874539337535506768450256382601505671667_<72>

P92 = 44320662851452234004074288506988846359535994616193319803200659596263235671600926965502726029_<92>

Number: 52221_167
N=6311071364789324352813059352269232989984195465965197798376040487536976835682528940290550983385768936906742506945535454121868130835223297789916519296436393128720343
  ( 163 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=142395689927785736847713012883930874539337535506768450256382601505671667 (pp72)
 r2=44320662851452234004074288506988846359535994616193319803200659596263235671600926965502726029 (pp92)
Version: Msieve-1.39
Total time: 49.16 hours.
Scaled time: 85.29 units (timescale=1.735).
Factorization parameters were as follows:
n: 6311071364789324352813059352269232989984195465965197798376040487536976835682528940290550983385768936906742506945535454121868130835223297789916519296436393128720343
m: 2000000000000000000000000000000000
deg: 5
c5: 1175
c0: -88
skew: 0.60
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 5050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 914933 x 915181
Total sieving time: 49.16 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000
total time: 49.16 hours.
 --------- CPU info (if available) ----------

Mar 13, 2009 (2nd)

By Serge Batalov / Msieve-1.40 / Mar 13, 2009

(47·10¹⁵⁰-11)/9 = 5(2)₁₄₉1_<151> = C151

C151 = P43 · P108

P43 = 5988111156090505828245750143728185640174571_<43>

P108 = 872098410683425902866041654560780729494484106633726077490895857353439091643504043220735089594598475864322151_<108>

SNFS difficulty: 151 digits.
Divisors found:
 r1=5988111156090505828245750143728185640174571 (pp43)
 r2=872098410683425902866041654560780729494484106633726077490895857353439091643504043220735089594598475864322151 (pp108)
Version: Msieve-1.40
Total time: 4.93 hours.
Scaled time: 14.93 units (timescale=3.028).
Factorization parameters were as follows:
n: 5222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 1000000000000000000000000000000
deg: 5
c5: 47
c0: -11
skew: 0.75
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1200000, 1800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 435666 x 435914
Total sieving time: 4.93 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,51,51,2.5,2.5,100000
total time: 4.93 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU1: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU2: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU3: AMD Phenom(tm) II X4 940 Processor stepping 02
Memory: 8173900k/9175040k available (2699k kernel code, 213168k reserved, 3164k data, 788k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 6413.63 BogoMIPS (lpj=12827264)
Calibrating delay using timer specific routine.. 6413.75 BogoMIPS (lpj=12827519)
Calibrating delay using timer specific routine.. 6413.73 BogoMIPS (lpj=12827464)
Calibrating delay using timer specific routine.. 6413.70 BogoMIPS (lpj=12827407)
Total of 4 processors activated (25654.82 BogoMIPS).

Mar 13, 2009

By Serge Batalov / PFGW / Mar 13, 2009

(19·10⁵⁶⁵⁴⁴-1)/9 = 2(1)₅₆₅₄₄_<56545> is PRP.

It's the largest unprovable near-repdigit PRP so far in our tables. Congratulations!

Mar 12, 2009 (7th)

By Sinkiti Sibata / Msieve, GGNFS / Mar 12, 2009

(46·10¹⁹⁵+53)/9 = 5(1)₁₉₄7_<196> = 7 · 17 · 8171 · 218664548357_<12> · 383029520353_<12> · 1317758454923_<13> · 36851587108333_<14> · 333880318201853_<15> · 920693601912765731333_<21> · C106

C106 = P53 · P54

P53 = 32929899691477187500923347753881273778706767921810279_<53>

P54 = 127671560463196479694817849115602475215226567268386757_<54>

Thu Mar 12 07:10:59 2009  Msieve v. 1.39
Thu Mar 12 07:10:59 2009  random seeds: 0238fc48 25b627af
Thu Mar 12 07:10:59 2009  factoring 4204211679507424846451086882635743171490086993932991463923317493021943202107350324813720870968483350075203 (106 digits)
Thu Mar 12 07:11:00 2009  searching for 15-digit factors
Thu Mar 12 07:11:02 2009  commencing quadratic sieve (106-digit input)
Thu Mar 12 07:11:02 2009  using multiplier of 2
Thu Mar 12 07:11:02 2009  using 32kb Intel Core sieve core
Thu Mar 12 07:11:02 2009  sieve interval: 40 blocks of size 32768
Thu Mar 12 07:11:02 2009  processing polynomials in batches of 6
Thu Mar 12 07:11:02 2009  using a sieve bound of 4380851 (153831 primes)
Thu Mar 12 07:11:02 2009  using large prime bound of 657127650 (29 bits)
Thu Mar 12 07:11:02 2009  using double large prime bound of 7443368346761550 (45-53 bits)
Thu Mar 12 07:11:02 2009  using trial factoring cutoff of 53 bits
Thu Mar 12 07:11:02 2009  polynomial 'A' values have 14 factors
Thu Mar 12 07:11:06 2009  restarting with 28225 full and 1742777 partial relations
Thu Mar 12 15:40:24 2009  154260 relations (37055 full + 117205 combined from 2278358 partial), need 153927
Thu Mar 12 15:40:27 2009  begin with 2315413 relations
Thu Mar 12 15:40:29 2009  reduce to 404849 relations in 10 passes
Thu Mar 12 15:40:29 2009  attempting to read 404849 relations
Thu Mar 12 15:40:38 2009  recovered 404849 relations
Thu Mar 12 15:40:38 2009  recovered 395853 polynomials
Thu Mar 12 15:40:39 2009  attempting to build 154260 cycles
Thu Mar 12 15:40:39 2009  found 154260 cycles in 6 passes
Thu Mar 12 15:40:39 2009  distribution of cycle lengths:
Thu Mar 12 15:40:39 2009     length 1 : 37055
Thu Mar 12 15:40:39 2009     length 2 : 26623
Thu Mar 12 15:40:39 2009     length 3 : 25681
Thu Mar 12 15:40:39 2009     length 4 : 21146
Thu Mar 12 15:40:39 2009     length 5 : 15928
Thu Mar 12 15:40:39 2009     length 6 : 10746
Thu Mar 12 15:40:39 2009     length 7 : 7172
Thu Mar 12 15:40:39 2009     length 9+: 9909
Thu Mar 12 15:40:39 2009  largest cycle: 20 relations
Thu Mar 12 15:40:40 2009  matrix is 153831 x 154260 (42.4 MB) with weight 10493401 (68.02/col)
Thu Mar 12 15:40:40 2009  sparse part has weight 10493401 (68.02/col)
Thu Mar 12 15:40:43 2009  filtering completed in 3 passes
Thu Mar 12 15:40:43 2009  matrix is 147388 x 147451 (40.7 MB) with weight 10068967 (68.29/col)
Thu Mar 12 15:40:43 2009  sparse part has weight 10068967 (68.29/col)
Thu Mar 12 15:40:43 2009  saving the first 48 matrix rows for later
Thu Mar 12 15:40:43 2009  matrix is 147340 x 147451 (22.6 MB) with weight 7695468 (52.19/col)
Thu Mar 12 15:40:43 2009  sparse part has weight 5029748 (34.11/col)
Thu Mar 12 15:40:43 2009  matrix includes 64 packed rows
Thu Mar 12 15:40:43 2009  using block size 43690 for processor cache size 1024 kB
Thu Mar 12 15:40:44 2009  commencing Lanczos iteration
Thu Mar 12 15:40:44 2009  memory use: 23.5 MB
Thu Mar 12 15:43:17 2009  lanczos halted after 2331 iterations (dim = 147339)
Thu Mar 12 15:43:17 2009  recovered 17 nontrivial dependencies
Thu Mar 12 15:43:19 2009  prp53 factor: 32929899691477187500923347753881273778706767921810279
Thu Mar 12 15:43:19 2009  prp54 factor: 127671560463196479694817849115602475215226567268386757
Thu Mar 12 15:43:19 2009  elapsed time 08:32:20

(44·10¹⁸⁰+1)/9 = 4(8)₁₇₉9_<181> = C181

C181 = P83 · P99

P83 = 29998628377250006041227482776218252221391624699072260154192585502404897950350750219_<83>

P99 = 162970414093881199747897196519081791013520831322884381372253453463024642558226884272512371979865931_<99>

Number: 48889_180
N=4888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
  ( 181 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=29998628377250006041227482776218252221391624699072260154192585502404897950350750219
 r2=162970414093881199747897196519081791013520831322884381372253453463024642558226884272512371979865931
Version: 
Total time: 141.87 hours.
Scaled time: 363.75 units (timescale=2.564).
Factorization parameters were as follows:
name: 48889_180
n: 4888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
m: 2000000000000000000000000000000000000
deg: 5
c5: 11
c0: 8
skew: 0.94
type: snfs
lss: 1
rlim: 7700000
alim: 7700000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7700000/7700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3850000, 5750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1429172 x 1429420
Total sieving time: 141.87 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,7700000,7700000,28,28,53,53,2.5,2.5,100000
total time: 141.87 hours.
 --------- CPU info (if available) ----------

(46·10¹⁴⁸+53)/9 = 5(1)₁₄₇7_<149> = 3 · 11 · 2073601 · 362810318840012022254398567_<27> · C115

C115 = P44 · P72

P44 = 10580955501994082609495759629247655155837933_<44>

P72 = 194568114473872391604919830308514587164898854724487789394376603300161559_<72>

Number: 51117_148
N=2058716561354934581684959442841534654116623410836174062651661961139069179305115649044521621779174803752300920617547
  ( 115 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=10580955501994082609495759629247655155837933 (pp44)
 r2=194568114473872391604919830308514587164898854724487789394376603300161559 (pp72)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 33.00 hours.
Scaled time: 15.57 units (timescale=0.472).
Factorization parameters were as follows:
name: 51117_148
n: 2058716561354934581684959442841534654116623410836174062651661961139069179305115649044521621779174803752300920617547
m: 500000000000000000000000000000
deg: 5
c5: 368
c0: 1325
skew: 1.29
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1950001)
Primes: RFBsize:169511, AFBsize:169721, largePrimes:6941653 encountered
Relations: rels:6938774, finalFF:502200
Max relations in full relation-set: 28
Initial matrix: 339299 x 502200 with sparse part having weight 52499115.
Pruned matrix : 282610 x 284370 with weight 26631670.
Total sieving time: 29.86 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 2.72 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 33.00 hours.
 --------- CPU info (if available) ----------

Mar 12, 2009 (6th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Mar 12, 2009

4·10¹⁸²+1 = 4(0)₁₈₁1_<183> = 1160317 · 413745536263432081_<18> · C159

C159 = P47 · P113

P47 = 30385872315370452048023578488339493475461704437_<47>

P113 = 27420685405397558932205897020211411740511536898793314180500096877831147046352018738909437880962687052207823325649_<113>

Number: 40001_182
N=833201445528352286593335902417911384428222650575473822308179231186649593623908068306499385466741863296259737804523328217318371498449825845169438315839239204613
  ( 159 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=30385872315370452048023578488339493475461704437
 r2=27420685405397558932205897020211411740511536898793314180500096877831147046352018738909437880962687052207823325649
Version: 
Total time: 87.22 hours.
Scaled time: 208.02 units (timescale=2.385).
Factorization parameters were as follows:
n: 833201445528352286593335902417911384428222650575473822308179231186649593623908068306499385466741863296259737804523328217318371498449825845169438315839239204613
m: 2000000000000000000000000000000000000
deg: 5
c5: 25
c0: 2
skew: 0.60
type: snfs
lss: 1
rlim: 6600000
alim: 6600000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6600000/6600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3300000, 5600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 18344751
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1254004 x 1254252
Total sieving time: 80.75 hours.
Total relation processing time: 2.24 hours.
Matrix solve time: 3.90 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,6600000,6600000,28,28,53,53,2.5,2.5,100000
total time: 87.22 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Mar 12, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.2 / Mar 12, 2009

(47·10¹⁴⁰-11)/9 = 5(2)₁₃₉1_<141> = 19 · 103 · 647 · 2255083 · 84974721827_<11> · C118

C118 = P31 · P87

P31 = 4818450292839103564887902613193_<31>

P87 = 446684185015450509131514437747403540032672941709118393224734479146379724274632078862423_<87>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=614797269
Step 1 took 6497ms
Step 2 took 6556ms
********** Factor found in step 2: 4818450292839103564887902613193
Found probable prime factor of 31 digits: 4818450292839103564887902613193
Probable prime cofactor 446684185015450509131514437747403540032672941709118393224734479146379724274632078862423 has
 87 digits

(47·10¹⁷⁷-11)/9 = 5(2)₁₇₆1_<178> = 17 · 491 · 476994724582963119809_<21> · C154

C154 = P38 · C116

P38 = 29336523767341974250914648586797711269_<38>

C116 = [44709798057885060980656834282070292023087303425981948741349201177796626681785466973031767603121232173890091368733483_<116>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2578320307
Step 1 took 7724ms
Step 2 took 7937ms
********** Factor found in step 2: 29336523767341974250914648586797711269
Found probable prime factor of 38 digits: 29336523767341974250914648586797711269
Composite cofactor has 116 digits

(47·10¹⁷⁹-11)/9 = 5(2)₁₇₈1_<180> = 7 · 23 · 5322059 · 919996412717_<12> · 29156504009218880992100765849_<29> · C131

C131 = P34 · P97

P34 = 3072254686607955376409364861872723_<34>

P97 = 7395558714522408519984500388661316649969956019249487652617042960649999491932991242793231406163481_<97>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1973163813
Step 1 took 6428ms
Step 2 took 7081ms
********** Factor found in step 2: 3072254686607955376409364861872723
Found probable prime factor of 34 digits: 3072254686607955376409364861872723
Probable prime cofactor 7395558714522408519984500388661316649969956019249487652617042960649999491932991242793231406163481 has 97 digits

(47·10¹⁹⁷-11)/9 = 5(2)₁₉₆1_<198> = 7 · 373 · 1404797 · C189

C189 = P37 · P152

P37 = 5163985378115699491845176569607097011_<37>

P152 = 27570833888524445160516755860685768710081216469115014628752510615388153394577264288236432164511019626347857612199983283847920376203939402113270533430633_<152>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3665488111
Step 1 took 10545ms
Step 2 took 9945ms
********** Factor found in step 2: 5163985378115699491845176569607097011
Found probable prime factor of 37 digits: 5163985378115699491845176569607097011
Probable prime cofactor has 152 digits

Mar 12, 2009 (4th)

By Robert Backstrom / GMP-ECM, GGNFS / Mar 12, 2009

(46·10¹⁷¹+17)/9 = 5(1)₁₇₀3_<172> = 263 · 970249022030821397_<18> · 19026574647719725580906261568180313_<35> · C118

C118 = P39 · P79

P39 = 630342612127198618772322707546108783051_<39>

P79 = 1670086954568573035831635264946570628527344374543767768165202474247383904070241_<79>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 1052726973422312414369679920117417355319166283649319053416903491099269688020426323445565576922947838234591638134285291 (118 digits)
Using B1=10000000, B2=22329304695, polynomial Dickson(12), sigma=2297428923
Step 1 took 115620ms
Step 2 took 43491ms
********** Factor found in step 2: 630342612127198618772322707546108783051
Found probable prime factor of 39 digits: 630342612127198618772322707546108783051
Probable prime cofactor 1670086954568573035831635264946570628527344374543767768165202474247383904070241 has 79 digits

(47·10²⁰⁰-11)/9 = 5(2)₁₉₉1_<201> = 379 · 165247 · 3640480496159251_<16> · 1381752074574568323937_<22> · 400063996400046574075489_<24> · 2207360148890597730653248989359101_<34> · C100

C100 = P47 · P53

P47 = 19655714323899734215684139076568893767821207919_<47>

P53 = 95499747359901403850988662561208824995212239981906401_<53>

Number: n
N=1877115752110819849830579533457599023919068731916339392275250841391975474365193648865172520217989519
  ( 100 digits)
Divisors found:
 r1=19655714323899734215684139076568893767821207919 (pp47)
 r2=95499747359901403850988662561208824995212239981906401 (pp53)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.05 hours.
Scaled time: 7.38 units (timescale=1.823).
Factorization parameters were as follows:
name: n
n: 1877115752110819849830579533457599023919068731916339392275250841391975474365193648865172520217989519
skew: 2212.04
# norm 2.08e+13
c5: 81840
c4: 1870972448
c3: -1317042875282
c2: -6858498513143125
c1: 4671328310322123114
c0: 3377541918769261871349
# alpha -4.84
Y1: 1908640651
Y0: -7449113266076813386
# Murphy_E 3.46e-09
# M 874845903364873350744744798599273379445262588134333452794906208939213299236812744033704378092847643
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: RFBsize:135072, AFBsize:135011, largePrimes:3962908 encountered
Relations: rels:4028871, finalFF:449210
Max relations in full relation-set: 48
Initial matrix: 270165 x 449210 with sparse part having weight 38385272.
Pruned matrix : 169771 x 171185 with weight 13681875.
Total sieving time: 3.70 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.20 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 4.05 hours.
 --------- CPU info (if available) ----------

Mar 12, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Mar 12, 2009

(47·10¹⁰⁵-11)/9 = 5(2)₁₀₄1_<106> = C106

C106 = P49 · P58

P49 = 4727963546619759731766917175356370990122850807563_<49>

P58 = 1104539442981922084666125317770203910599526816212631418567_<58>

Number: 52221_105
N=5222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
  ( 106 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=4727963546619759731766917175356370990122850807563 (pp49)
 r2=1104539442981922084666125317770203910599526816212631418567 (pp58)
Version: Msieve-1.39
Total time: 0.39 hours.
Scaled time: 0.47 units (timescale=1.196).
Factorization parameters were as follows:
n: 5222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 200000000000000000000000000
deg: 4
c4: 235
c0: -88
skew: 0.78
type: snfs
lss: 1
rlim: 430000
alim: 430000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2Factor base limits: 430000/430000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [215000, 295001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 40222 x 40453
Total sieving time: 0.39 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107,4,0,0,0,0,0,0,0,0,430000,430000,25,25,44,44,2.2,2.2,20000
total time: 0.39 hours.
 --------- CPU info (if available) ----------

(47·10¹¹⁰-11)/9 = 5(2)₁₀₉1_<111> = 21773 · 272269 · C101

C101 = P48 · P54

P48 = 216910834226941566211301968179911755666633923569_<48>

P54 = 406123046208282273526869154596718542736108868487201557_<54>

Number: 52221_110
N=88092488751825245839141850043708474345184733484139123482124413214805496243909062730162730403835796933
  ( 101 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=216910834226941566211301968179911755666633923569 (pp48)
 r2=406123046208282273526869154596718542736108868487201557 (pp54)
Version: Msieve-1.39
Total time: 0.71 hours.
Scaled time: 0.85 units (timescale=1.198).
Factorization parameters were as follows:
n: 88092488751825245839141850043708474345184733484139123482124413214805496243909062730162730403835796933
m: 10000000000000000000000
deg: 5
c5: 47
c0: -11
skew: 0.75
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [255000, 405001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 48196 x 48427
Total sieving time: 0.71 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.71 hours.
 --------- CPU info (if available) ----------

(47·10¹²⁵-11)/9 = 5(2)₁₂₄1_<126> = 7 · 61 · 3299 · 285497 · 32485493 · C107

C107 = P48 · P59

P48 = 739186659997327189314836263152927554553245196443_<48>

P59 = 54075435562763884561227665822779541333185768077925461195059_<59>

Number: 52221_125
N=39971840601540122795462405359026089084329468172411782611476635366212541263283110174683000066457789995975137
  ( 107 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=739186659997327189314836263152927554553245196443 (pp48)
 r2=54075435562763884561227665822779541333185768077925461195059 (pp59)
Version: Msieve-1.39
Total time: 1.35 hours.
Scaled time: 1.62 units (timescale=1.197).
Factorization parameters were as follows:
n: 39971840601540122795462405359026089084329468172411782611476635366212541263283110174683000066457789995975137
m: 10000000000000000000000000
deg: 5
c5: 47
c0: -11
skew: 0.75
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 117698 x 117937
Total sieving time: 1.35 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 1.35 hours.
 --------- CPU info (if available) ----------

(47·10¹²³-11)/9 = 5(2)₁₂₂1_<124> = 572549 · 35307465251_<11> · 167535992353_<12> · C97

C97 = P45 · P52

P45 = 213931892963841771830937155726601487835244691_<45>

P52 = 7207630115544321559557722525529973748657968318948273_<52>

Number: 52221_123
N=1541941954401590302360835451795037441318811896762871211954952005084360128665956851129690726868643
  ( 97 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=213931892963841771830937155726601487835244691 (pp45)
 r2=7207630115544321559557722525529973748657968318948273 (pp52)
Version: Msieve-1.39
Total time: 1.32 hours.
Scaled time: 1.58 units (timescale=1.198).
Factorization parameters were as follows:
n: 1541941954401590302360835451795037441318811896762871211954952005084360128665956851129690726868643
m: 5000000000000000000000000
deg: 5
c5: 376
c0: -275
skew: 0.94
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 690001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 129286 x 129534
Total sieving time: 1.32 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 1.32 hours.
 --------- CPU info (if available) ----------

(47·10¹²⁷-11)/9 = 5(2)₁₂₆1_<128> = 3 · 27992513 · C120

C120 = P42 · P78

P42 = 773971033907263552982623116836469574628753_<42>

P78 = 803465989309873832290717161694379700388955748501632241534778895093776564980863_<78>

Number: 52221_127
N=621859402455485415239689534391121204709538132835998233077802175439104285042482874167367803219646889416731088323774553839
  ( 120 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=773971033907263552982623116836469574628753 (pp42)
 r2=803465989309873832290717161694379700388955748501632241534778895093776564980863 (pp78)
Version: Msieve-1.39
Total time: 2.10 hours.
Scaled time: 2.52 units (timescale=1.197).
Factorization parameters were as follows:
n: 621859402455485415239689534391121204709538132835998233077802175439104285042482874167367803219646889416731088323774553839
m: 20000000000000000000000000
deg: 5
c5: 1175
c0: -88
skew: 0.60
type: snfs
lss: 1
rlim: 1010000
alim: 1010000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1010000/1010000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [505000, 905001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 138680 x 138928
Total sieving time: 2.10 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1010000,1010000,26,26,47,47,2.3,2.3,50000
total time: 2.10 hours.
 --------- CPU info (if available) ----------

(46·10¹⁵³+71)/9 = 5(1)₁₅₂9_<154> = 67 · 167907469285391491_<18> · C135

C135 = P40 · P95

P40 = 7133083920115793161754192878302086398429_<40>

P95 = 63693214863059925710776140780854555073194599184277823947866274871020184275904123806802758151363_<95>

Number: 51119_153
N=454329046760172996815214720499930206896377654307005578295605754041686616968350140341961416219894897211617500385463382812242770707408727
  ( 135 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=7133083920115793161754192878302086398429 (pp40)
 r2=63693214863059925710776140780854555073194599184277823947866274871020184275904123806802758151363 (pp95)
Version: Msieve-1.39
Total time: 25.06 hours.
Scaled time: 64.43 units (timescale=2.571).
Factorization parameters were as follows:
n: 454329046760172996815214720499930206896377654307005578295605754041686616968350140341961416219894897211617500385463382812242770707408727
m: 5000000000000000000000000000000
deg: 5
c5: 368
c0: 1775
skew: 1.37
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 523197 x 523445
Total sieving time: 25.06 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 25.06 hours.
 --------- CPU info (if available) ----------

(47·10¹³⁸-11)/9 = 5(2)₁₃₇1_<139> = 69383 · 2943852115113191436936232499_<28> · C107

C107 = P31 · P76

P31 = 3445662944462953372813157292509_<31>

P76 = 7420163804356413285723061705356166490106356012527781697564305483421044156957_<76>

Number: 52221_138
N=25567383462516148887418148093946022278181522749536079967073271232486321862137511716451779062548888556335113
  ( 107 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=3445662944462953372813157292509 (pp31)
 r2=7420163804356413285723061705356166490106356012527781697564305483421044156957 (pp76)
Version: Msieve-1.39
Total time: 4.53 hours.
Scaled time: 5.43 units (timescale=1.199).
Factorization parameters were as follows:
n: 25567383462516148887418148093946022278181522749536079967073271232486321862137511716451779062548888556335113
m: 5000000000000000000000000000
deg: 5
c5: 376
c0: -275
skew: 0.94
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1585001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 235266 x 235514
Total sieving time: 4.53 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 4.53 hours.
 --------- CPU info (if available) ----------

(47·10¹²¹-11)/9 = 5(2)₁₂₀1_<122> = 3 · 3691 · 1909757 · 74109151212795992011_<20> · C92

C92 = P35 · P57

P35 = 79379976514831063632425217374113177_<35>

P57 = 419787142593259868022055127950287131578980559640947153163_<57>

Wed Mar 11 22:42:37 2009  
Wed Mar 11 22:42:37 2009  
Wed Mar 11 22:42:37 2009  Msieve v. 1.40
Wed Mar 11 22:42:37 2009  random seeds: d2ddc4a8 0ca4d5a3
Wed Mar 11 22:42:37 2009  factoring 33322693520281007205858432921805287015651697127047237999398735204667991282155230129915528851 (92 digits)
Wed Mar 11 22:42:38 2009  searching for 15-digit factors
Wed Mar 11 22:42:39 2009  commencing quadratic sieve (92-digit input)
Wed Mar 11 22:42:39 2009  using multiplier of 3
Wed Mar 11 22:42:39 2009  using 32kb Intel Core sieve core
Wed Mar 11 22:42:39 2009  sieve interval: 36 blocks of size 32768
Wed Mar 11 22:42:39 2009  processing polynomials in batches of 6
Wed Mar 11 22:42:39 2009  using a sieve bound of 1805081 (68235 primes)
Wed Mar 11 22:42:39 2009  using large prime bound of 196753829 (27 bits)
Wed Mar 11 22:42:39 2009  using double large prime bound of 849301085385043 (42-50 bits)
Wed Mar 11 22:42:39 2009  using trial factoring cutoff of 50 bits
Wed Mar 11 22:42:39 2009  polynomial 'A' values have 12 factors
Thu Mar 12 00:12:42 2009  68477 relations (17462 full + 51015 combined from 857491 partial), need 68331
Thu Mar 12 00:12:43 2009  begin with 874953 relations
Thu Mar 12 00:12:44 2009  reduce to 172235 relations in 12 passes
Thu Mar 12 00:12:44 2009  attempting to read 172235 relations
Thu Mar 12 00:12:45 2009  recovered 172235 relations
Thu Mar 12 00:12:45 2009  recovered 152549 polynomials
Thu Mar 12 00:12:46 2009  attempting to build 68477 cycles
Thu Mar 12 00:12:46 2009  found 68477 cycles in 5 passes
Thu Mar 12 00:12:46 2009  distribution of cycle lengths:
Thu Mar 12 00:12:46 2009     length 1 : 17462
Thu Mar 12 00:12:46 2009     length 2 : 12684
Thu Mar 12 00:12:46 2009     length 3 : 11864
Thu Mar 12 00:12:46 2009     length 4 : 9303
Thu Mar 12 00:12:46 2009     length 5 : 6763
Thu Mar 12 00:12:46 2009     length 6 : 4296
Thu Mar 12 00:12:46 2009     length 7 : 2696
Thu Mar 12 00:12:46 2009     length 9+: 3409
Thu Mar 12 00:12:46 2009  largest cycle: 18 relations
Thu Mar 12 00:12:46 2009  matrix is 68235 x 68477 (16.9 MB) with weight 4154283 (60.67/col)
Thu Mar 12 00:12:46 2009  sparse part has weight 4154283 (60.67/col)
Thu Mar 12 00:12:46 2009  filtering completed in 3 passes
Thu Mar 12 00:12:46 2009  matrix is 64316 x 64379 (16.0 MB) with weight 3934154 (61.11/col)
Thu Mar 12 00:12:46 2009  sparse part has weight 3934154 (61.11/col)
Thu Mar 12 00:12:46 2009  saving the first 48 matrix rows for later
Thu Mar 12 00:12:46 2009  matrix is 64268 x 64379 (9.5 MB) with weight 3027732 (47.03/col)
Thu Mar 12 00:12:46 2009  sparse part has weight 2093212 (32.51/col)
Thu Mar 12 00:12:46 2009  matrix includes 64 packed rows
Thu Mar 12 00:12:46 2009  using block size 25751 for processor cache size 4096 kB
Thu Mar 12 00:12:47 2009  commencing Lanczos iteration
Thu Mar 12 00:12:47 2009  memory use: 9.6 MB
Thu Mar 12 00:13:04 2009  lanczos halted after 1018 iterations (dim = 64266)
Thu Mar 12 00:13:04 2009  recovered 16 nontrivial dependencies
Thu Mar 12 00:13:04 2009  prp35 factor: 79379976514831063632425217374113177
Thu Mar 12 00:13:04 2009  prp57 factor: 419787142593259868022055127950287131578980559640947153163
Thu Mar 12 00:13:04 2009  elapsed time 01:30:27

(47·10¹⁴¹-11)/9 = 5(2)₁₄₀1_<142> = 52342943 · 73148720929412482777607_<23> · C112

C112 = P36 · P76

P36 = 392991753933664432111486782642856073_<36>

P76 = 3470619774205893994555452494039320050463535188041950431210437525856898810477_<76>

Number: 52221_141
N=1363924952302032704411362231222452808718178922616558200506126938401445710984766595384909799427910544275615476821
  ( 112 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=392991753933664432111486782642856073 (pp36)
 r2=3470619774205893994555452494039320050463535188041950431210437525856898810477 (pp76)
Version: Msieve-1.39
Total time: 6.65 hours.
Scaled time: 7.93 units (timescale=1.192).
Factorization parameters were as follows:
n: 1363924952302032704411362231222452808718178922616558200506126938401445710984766595384909799427910544275615476821
m: 20000000000000000000000000000
deg: 5
c5: 235
c0: -176
skew: 0.94
type: snfs
lss: 1
rlim: 1750000
alim: 1750000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1750000/1750000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [875000, 2075001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 305735 x 305983
Total sieving time: 6.65 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1750000,1750000,26,26,48,48,2.3,2.3,100000
total time: 6.65 hours.
 --------- CPU info (if available) ----------

(46·10¹⁵⁶+71)/9 = 5(1)₁₅₅9_<157> = 13 · 12791 · 14542537 · 4407263369_<10> · 1097910141634106723759003_<25> · C111

C111 = P43 · P69

P43 = 2715484761041453250674567065722056986464791_<43>

P69 = 160858540162485163688402882005891457614428281179133660553932660406097_<69>

Number: 51119_156
N=436808914494603035272948990060886924872748227290197848685460751713925847982802181671282981837615851006452230727
  ( 111 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=2715484761041453250674567065722056986464791 (pp43)
 r2=160858540162485163688402882005891457614428281179133660553932660406097 (pp69)
Version: Msieve-1.39
Total time: 27.31 hours.
Scaled time: 70.23 units (timescale=2.571).
Factorization parameters were as follows:
n: 436808914494603035272948990060886924872748227290197848685460751713925847982802181671282981837615851006452230727
m: 10000000000000000000000000000000
deg: 5
c5: 460
c0: 71
skew: 0.69
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 3000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 542240 x 542488
Total sieving time: 27.31 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 27.31 hours.
 --------- CPU info (if available) ----------

(46·10¹⁶³+71)/9 = 5(1)₁₆₂9_<164> = C164

C164 = P49 · P115

P49 = 7541934798456785863129669147390842480985292538523_<49>

P115 = 6776922961674152159210898254957167446794903963445963850920375427234007766800528046684857758168998176148283384837853_<115>

Number: 51119_163
N=51111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119
  ( 164 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=7541934798456785863129669147390842480985292538523 (pp49)
 r2=6776922961674152159210898254957167446794903963445963850920375427234007766800528046684857758168998176148283384837853 (pp115)
Version: Msieve-1.39
Total time: 48.64 hours.
Scaled time: 84.59 units (timescale=1.739).
Factorization parameters were as follows:
n: 51111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119
m: 500000000000000000000000000000000
deg: 5
c5: 368
c0: 1775
skew: 1.37
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 862475 x 862723
Total sieving time: 48.64 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 48.64 hours.
 --------- CPU info (if available) ----------

(47·10¹⁵²-11)/9 = 5(2)₁₅₁1_<153> = 105707097157561_<15> · C139

C139 = P60 · P80

P60 = 131389417429374689747949086527324232738423508338228019362549_<60>

P80 = 37600257118637648059825623678721994185204133889456608930817885145174309666005889_<80>

Number: 52221_152
N=4940275878012499147589824021265307849742946323735234697706010297652630964917861993303997069328761719581734393133552513562136273904660051061
  ( 139 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=131389417429374689747949086527324232738423508338228019362549 (pp60)
 r2=37600257118637648059825623678721994185204133889456608930817885145174309666005889 (pp80)
Version: Msieve-1.39
Total time: 16.75 hours.
Scaled time: 42.87 units (timescale=2.560).
Factorization parameters were as follows:
n: 4940275878012499147589824021265307849742946323735234697706010297652630964917861993303997069328761719581734393133552513562136273904660051061
m: 2000000000000000000000000000000
deg: 5
c5: 1175
c0: -88
skew: 0.60
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 524524 x 524772
Total sieving time: 16.75 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 16.75 hours.
 --------- CPU info (if available) ----------

Mar 12, 2009 (2nd)

By Serge Batalov / PFGW / Mar 12, 2009

(55·10⁵⁶⁴⁵³-1)/9 = 6(1)₅₆₄₅₃_<56454> is PRP.

It's the largest unprovable near-repdigit PRP so far in our tables. Congratulations!

Mar 12, 2009

Factorizations of 522...221 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 11, 2009 (4th)

By Serge Batalov / Msieve-1.40b2, GMP-ECM 6.2.2 / Mar 11, 2009

(46·10¹⁵⁴+53)/9 = 5(1)₁₅₃7_<155> = 3 · 11 · C154

C154 = P33 · P121

P33 = 852516063533571245521819271819209_<33>

P121 = 1816765237715145703759492901073027105339922842612605998891568224247917184885659921290464520661996160310348489261441512261_<121>

SNFS difficulty: 156 digits.
Divisors found:
 r1=852516063533571245521819271819209 (pp33)
 r2=1816765237715145703759492901073027105339922842612605998891568224247917184885659921290464520661996160310348489261441512261 (pp121)
Version: Msieve-1.40b2
Total time: 6.85 hours.
Scaled time: 19.46 units (timescale=2.840).
Factorization parameters were as follows:
n: 1548821548821548821548821548821548821548821548821548821548821548821548821548821548821548821548821548821548821548821548821548821548821548821548821548821549
m: 10000000000000000000000000000000
deg: 5
c5: 23
c0: 265
skew: 1.63
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 445234 x 445482
Total sieving time: 6.85 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 6.85 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Phenom(tm) II X4 940 Processor stepping 02
...
Calibrating delay using timer specific routine.. 6012.92 BogoMIPS (lpj=12025858)
Total of 4 processors activated (24051.44 BogoMIPS).

(46·10¹⁸²+71)/9 = 5(1)₁₈₁9_<183> = 3 · 58733 · 1774823 · 25827526641592153_<17> · 465844686356268889049_<21> · 117845274305787930833478395083_<30> · C106

C106 = P42 · P64

P42 = 120741530617798527131119236048256983443581_<42>

P64 = 9546936235292443702002424002293228582932021131309767346381629137_<64>

Divisors found:
 r1=120741530617798527131119236048256983443581 (pp42)
 r2=9546936235292443702002424002293228582932021131309767346381629137 (pp64)
Version: Msieve-1.40b2
Total time: 4.09 hours.
Scaled time: 11.61 units (timescale=2.840).
Factorization parameters were as follows:
name: g106
n: 1152711693759732794797020856846100225412145841268368099985008497977318506429012851894590630051823105219597
skew: 16026.11
# norm 4.89e+14
c5: 39780
c4: 2017627500
c3: -35388693634601
c2: -489589232804229509
c1: 3381677356890778647529
c0: -84010979717976372460179
# alpha -5.92
Y1: 158309817083
Y0: -123710210749591011442
# Murphy_E 1.68e-09
# M 892813726663633194563281820820942635632008401814611827374918494568458312093080093548243109977242039588608
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 283578 x 283826
Total sieving time: 4.09 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 4.09 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU1: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU2: AMD Phenom(tm) II X4 940 Processor stepping 02
CPU3: AMD Phenom(tm) II X4 940 Processor stepping 02
Memory: 3529040k/4980736k available (2699k kernel code, 139436k reserved, 3164k data, 788k init)
Calibrating delay loop (skipped), value calculated using timer frequency.. 6012.79 BogoMIPS (lpj=12025596)
Calibrating delay using timer specific routine.. 6012.90 BogoMIPS (lpj=12025808)
Calibrating delay using timer specific routine.. 6012.93 BogoMIPS (lpj=12025873)
Calibrating delay using timer specific routine.. 6012.86 BogoMIPS (lpj=12025737)
Total of 4 processors activated (24051.50 BogoMIPS).

(46·10¹⁷²+71)/9 = 5(1)₁₇₁9_<173> = 197 · 23563 · 46883601728218168478809_<23> · 1269359887331725771628730353_<28> · C117

C117 = P34 · P83

P34 = 1955938999159069482043304901345331_<34>

P83 = 94592666598604770978903820599325507097005874985563292774803682806961506334518555867_<83>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1592344803
Step 1 took 7368ms
Step 2 took 7085ms
********** Factor found in step 2: 1955938999159069482043304901345331
Found probable prime factor of 34 digits: 1955938999159069482043304901345331
Probable prime cofactor 94592666598604770978903820599325507097005874985563292774803682806961506334518555867 has 83 digits

(46·10¹⁸⁸+71)/9 = 5(1)₁₈₇9_<189> = 3 · 10889 · 36749 · 5256173899_<10> · 29420718373331819_<17> · C154

C154 = P35 · P120

P35 = 13826404143888325933007602257630223_<35>

P120 = 199126150836918433734212739176738106376290382162007550285895120053233146782672635111439257595447412165879529697928622711_<120>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3930800050
Step 1 took 8356ms
Step 2 took 8449ms
********** Factor found in step 2: 13826404143888325933007602257630223
Found probable prime factor of 35 digits: 13826404143888325933007602257630223
Probable prime cofactor 199126150836918433734212739176738106376290382162007550285895120053233146782672635111439257595447412165879529697928622711 has 120 digits

Mar 11, 2009 (3rd)

By Sinkiti Sibata / GGNFS / Mar 11, 2009

(46·10¹⁴⁴+17)/9 = 5(1)₁₄₃3_<145> = 7² · 53 · 1409177477_<10> · 244959711137861_<15> · C118

C118 = P54 · P65

P54 = 137650711667873379471304368018035611255346407634131777_<54>

P65 = 41419471879750193306941692642248802022013014694168758886515974941_<65>

Number: 51113_144
N=5701419781155083271333386525485811005817385766910918648397290166476505121632518945836340115783145510877303515223800157
  ( 118 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=137650711667873379471304368018035611255346407634131777 (pp54)
 r2=41419471879750193306941692642248802022013014694168758886515974941 (pp65)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 16.67 hours.
Scaled time: 7.84 units (timescale=0.470).
Factorization parameters were as follows:
name: 51113_144
n: 5701419781155083271333386525485811005817385766910918648397290166476505121632518945836340115783145510877303515223800157
m: 100000000000000000000000000000
deg: 5
c5: 23
c0: 85
skew: 1.30
type: snfs
lss: 1
rlim: 1930000
alim: 1930000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1930000/1930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [965000, 2165001)
Primes: RFBsize:144125, AFBsize:143987, largePrimes:4038730 encountered
Relations: rels:4137598, finalFF:378490
Max relations in full relation-set: 28
Initial matrix: 288177 x 378490 with sparse part having weight 34073323.
Pruned matrix : 255568 x 257072 with weight 19711452.
Total sieving time: 14.69 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 1.70 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000
total time: 16.67 hours.
 --------- CPU info (if available) ----------

Mar 11, 2009 (2nd)

By Max Dettweiler / GGNFS, msieve 1.40beta2, Yafu v1.06 / Mar 11, 2009

(46·10¹⁰¹+71)/9 = 5(1)₁₀₀9_<102> = 3 · 7 · 1163 · 37277 · C93

C93 = P30 · P63

P30 = 910268395208904786366326084731_<30>

P63 = 616745365847203538452641773299137697957859556570687989939496119_<63>

Number: 93snfs
N=561403814422262839080338689536646105016417937847801158082802893349651531081065464852239658989
  ( 93 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=910268395208904786366326084731 (pp30)
 r2=616745365847203538452641773299137697957859556570687989939496119 (pp63)
Version: Msieve-1.40
Total time: 0.37 hours.
Scaled time: 0.60 units (timescale=1.617).
Factorization parameters were as follows:
n: 561403814422262839080338689536646105016417937847801158082802893349651531081065464852239658989
m: 20000000000000000000000000
deg: 4
c4: 115
c0: 284
skew: 1.25
type: snfs
lss: 1
rlim: 370000
alim: 370000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2
Factor base limits: 370000/370000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [185000, 235001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 36202 x 36442
Total sieving time: 0.37 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103,4,0,0,0,0,0,0,0,0,370000,370000,25,25,43,43,2.2,2.2,10000
total time: 0.37 hours.
 --------- CPU info (if available) ----------
[    0.371493] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004011] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.12 BogoMIPS (lpj=8800240)
[    0.004000] Calibrating delay using timer specific routine.. 4400.40 BogoMIPS (lpj=8800805)
[    0.460053] Total of 2 processors activated (8800.52 BogoMIPS).

(46·10¹⁴⁶+71)/9 = 5(1)₁₄₅9_<147> = 3 · 593 · 3659 · 7188543623_<10> · 230211757577_<12> · 24148169986644262188264915023_<29> · C91

C91 = P42 · P49

P42 = 611134958113531502328771287835413519939267_<42>

P49 = 3215046068556093932138125748101914783298678553189_<49>

03/10/09 12:15:11 v1.06 @ Core2Duo, starting SIQS on c91: 1964827044440102596080671481043079945118991673870403606934075870005358155177051070709172463
03/10/09 12:15:12 v1.06 @ Core2Duo, ==== sieve params ====
03/10/09 12:15:12 v1.06 @ Core2Duo, n = 91 digits, 302 bits
03/10/09 12:15:12 v1.06 @ Core2Duo, factor base: 67412 primes (max prime = 1793819)
03/10/09 12:15:12 v1.06 @ Core2Duo, single large prime cutoff: 215258280 (120 * pmax)
03/10/09 12:15:12 v1.06 @ Core2Duo, double large prime range from 43 to 50 bits
03/10/09 12:15:12 v1.06 @ Core2Duo, double large prime cutoff: 998453303834859
03/10/09 12:15:12 v1.06 @ Core2Duo, using 10 large prime slices of factor base
03/10/09 12:15:12 v1.06 @ Core2Duo, buckets hold 1024 elements
03/10/09 12:15:12 v1.06 @ Core2Duo, sieve interval: 22 blocks of size 32768
03/10/09 12:15:12 v1.06 @ Core2Duo, polynomial A has ~ 12 factors
03/10/09 12:15:12 v1.06 @ Core2Duo, using multiplier of 3
03/10/09 12:15:12 v1.06 @ Core2Duo, using small prime variation correction of 21 bits
03/10/09 12:15:12 v1.06 @ Core2Duo, trial factoring cutoff at 97 bits
03/10/09 12:15:12 v1.06 @ Core2Duo, ==== sieving started ====
03/10/09 13:57:06 v1.06 @ Core2Duo, sieve time = 2433.0100, relation time = 1022.4100, poly_time = 2401.3600
03/10/09 13:57:06 v1.06 @ Core2Duo, 67491 relations found: 18551 full + 48940 from 829029 partial, using 522557 polys (255 A polys)
03/10/09 13:57:06 v1.06 @ Core2Duo, trial division touched 29391370 sieve locations out of 753418502144
03/10/09 13:57:06 v1.06 @ Core2Duo, ==== post processing stage (msieve-1.38) ====
03/10/09 13:57:07 v1.06 @ Core2Duo, begin with 847580 relations
03/10/09 13:57:07 v1.06 @ Core2Duo, reduce to 160926 relations in 10 passes
03/10/09 13:57:08 v1.06 @ Core2Duo, failed to read relation 52007
03/10/09 13:57:10 v1.06 @ Core2Duo, recovered 160925 relations
03/10/09 13:57:10 v1.06 @ Core2Duo, recovered 138434 polynomials
03/10/09 13:57:10 v1.06 @ Core2Duo, attempting to build 67490 cycles
03/10/09 13:57:10 v1.06 @ Core2Duo, found 67490 cycles in 5 passes
03/10/09 13:57:10 v1.06 @ Core2Duo, distribution of cycle lengths:
03/10/09 13:57:10 v1.06 @ Core2Duo,    length 1 : 18551
03/10/09 13:57:10 v1.06 @ Core2Duo,    length 2 : 14074
03/10/09 13:57:10 v1.06 @ Core2Duo,    length 3 : 12387
03/10/09 13:57:10 v1.06 @ Core2Duo,    length 4 : 8750
03/10/09 13:57:10 v1.06 @ Core2Duo,    length 5 : 6007
03/10/09 13:57:10 v1.06 @ Core2Duo,    length 6 : 3475
03/10/09 13:57:10 v1.06 @ Core2Duo,    length 7 : 2016
03/10/09 13:57:10 v1.06 @ Core2Duo,    length 9+: 2230
03/10/09 13:57:10 v1.06 @ Core2Duo, largest cycle: 18 relations
03/10/09 13:57:11 v1.06 @ Core2Duo, matrix is 67412 x 67490 (15.9 MB) with weight 3888400 (57.61/col)
03/10/09 13:57:11 v1.06 @ Core2Duo, sparse part has weight 3888400 (57.61/col)
03/10/09 13:57:11 v1.06 @ Core2Duo, filtering completed in 3 passes
03/10/09 13:57:11 v1.06 @ Core2Duo, matrix is 63087 x 63151 (15.0 MB) with weight 3679787 (58.27/col)
03/10/09 13:57:11 v1.06 @ Core2Duo, sparse part has weight 3679787 (58.27/col)
03/10/09 13:57:11 v1.06 @ Core2Duo, saving the first 48 matrix rows for later
03/10/09 13:57:12 v1.06 @ Core2Duo, matrix is 63039 x 63151 (9.5 MB) with weight 2844451 (45.04/col)
03/10/09 13:57:12 v1.06 @ Core2Duo, sparse part has weight 2117659 (33.53/col)
03/10/09 13:57:12 v1.06 @ Core2Duo, matrix includes 64 packed rows
03/10/09 13:57:12 v1.06 @ Core2Duo, using block size 25260 for processor cache size 2048 kB
03/10/09 13:57:12 v1.06 @ Core2Duo, commencing Lanczos iteration
03/10/09 13:57:12 v1.06 @ Core2Duo, memory use: 9.4 MB
03/10/09 13:57:33 v1.06 @ Core2Duo, lanczos halted after 998 iterations (dim = 63038)
03/10/09 13:57:33 v1.06 @ Core2Duo, recovered 17 nontrivial dependencies
03/10/09 13:57:36 v1.06 @ Core2Duo, prp42 = 611134958113531502328771287835413519939267
03/10/09 13:57:36 v1.06 @ Core2Duo, prp49 = 3215046068556093932138125748101914783298678553189
03/10/09 13:57:36 v1.06 @ Core2Duo, Lanczos elapsed time = 26.3700 seconds.
03/10/09 13:57:36 v1.06 @ Core2Duo, Sqrt elapsed time = 3.3200 seconds.
03/10/09 13:57:36 v1.06 @ Core2Duo, Total elapsed time = 1615.5627 seconds.

(46·10¹⁴⁰+71)/9 = 5(1)₁₃₉9_<141> = 3² · 446998291 · C132

C132 = P54 · P78

P54 = 170709216132860956637096332810026479832037334714407579_<54>

P78 = 744234814445627626849250096187520695493006138311265255510571169683581844890519_<78>

Number: c132-snfs
N=127047741792798316217254001664158763991314954393841571660035996551025121160452319171820107600344546858211866086955852492935198843501
  ( 132 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=170709216132860956637096332810026479832037334714407579 (pp54)
 r2=744234814445627626849250096187520695493006138311265255510571169683581844890519 (pp78)
Version: Msieve-1.40
Total time: 3.79 hours.
Scaled time: 5.29 units (timescale=1.397).
Factorization parameters were as follows:
n: 127047741792798316217254001664158763991314954393841571660035996551025121160452319171820107600344546858211866086955852492935198843501
m: 10000000000000000000000000000
deg: 5
c5: 46
c0: 71
skew: 1.09
type: snfs
lss: 1
rlim: 1610000
alim: 1610000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1610000/1610000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [805000, 1605001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 240599 x 240847
Total sieving time: 3.79 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000
total time: 3.79 hours.
 --------- CPU info (if available) ----------

(46·10¹³¹+71)/9 = 5(1)₁₃₀9_<132> = 3³ · 7² · 19 · 139 · 173 · 10733 · 2958650081_<10> · 530919129224999_<15> · C95

C95 = P38 · P58

P38 = 24836285458873298928376313085558197539_<38>

P58 = 2019348256878070729579299955784787789740821226032796066657_<58>

Number: c95-snfs
N=50153109748701971208896012917889902994802688403405049385816511415632634298926030804541817357123
  ( 95 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=24836285458873298928376313085558197539 (pp38)
 r2=2019348256878070729579299955784787789740821226032796066657 (pp58)
Version: Msieve-1.40
Total time: 3.76 hours.
Scaled time: 6.01 units (timescale=1.598).
Factorization parameters were as follows:
n: 50153109748701971208896012917889902994802688403405049385816511415632634298926030804541817357123
m: 100000000000000000000000000
deg: 5
c5: 460
c0: 71
skew: 0.69
type: snfs
lss: 1
rlim: 1140000
alim: 1140000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1140000/1140000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [570000, 1120001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 186854 x 187102
Total sieving time: 3.76 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1140000,1140000,26,26,47,47,2.3,2.3,50000
total time: 3.76 hours.
 --------- CPU info (if available) ----------
[    0.371493] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004011] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.12 BogoMIPS (lpj=8800240)
[    0.004000] Calibrating delay using timer specific routine.. 4400.40 BogoMIPS (lpj=8800805)
[    0.460053] Total of 2 processors activated (8800.52 BogoMIPS).

(46·10¹³⁵+71)/9 = 5(1)₁₃₄9_<136> = 57719 · 7913196622413294944729351989_<28> · C104

C104 = P34 · P70

P34 = 4073095510555953166009954261289693_<34>

P70 = 2747387848474171759521012098472172516349340423226028190381151990067113_<70>

Number: c104-snfs
N=11190373111376128317290326404384020441398937771609307971986652839947006576393671485775642513777005166309
  ( 104 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=4073095510555953166009954261289693 (pp34)
 r2=2747387848474171759521012098472172516349340423226028190381151990067113 (pp70)
Version: Msieve-1.40
Total time: 4.42 hours.
Scaled time: 7.21 units (timescale=1.630).
Factorization parameters were as follows:
n: 11190373111376128317290326404384020441398937771609307971986652839947006576393671485775642513777005166309
m: 1000000000000000000000000000
deg: 5
c5: 46
c0: 71
skew: 1.09
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1265001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 178456 x 178704
Total sieving time: 4.42 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 4.42 hours.
 --------- CPU info (if available) ----------
[    0.371493] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004011] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.12 BogoMIPS (lpj=8800240)
[    0.004000] Calibrating delay using timer specific routine.. 4400.40 BogoMIPS (lpj=8800805)
[    0.460053] Total of 2 processors activated (8800.52 BogoMIPS).

Mar 11, 2009

By Ignacio Santos / GGNFS, Msieve / Mar 11, 2009

(46·10¹⁰⁴+71)/9 = 5(1)₁₀₃9_<105> = 3³ · C104

C104 = P35 · P69

P35 = 46397742154740265377875973078126593_<35>

P69 = 407994878050965040134414999083253246694580794853731611179624305780829_<69>

Number: 51119_104
N=18930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485597
  ( 104 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=46397742154740265377875973078126593 (pp35)
 r2=407994878050965040134414999083253246694580794853731611179624305780829 (pp69)
Version: Msieve-1.39
Total time: 0.31 hours.
Scaled time: 0.36 units (timescale=1.139).
Factorization parameters were as follows:
n: 18930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485597
m: 100000000000000000000000000
deg: 4
c4: 46
c0: 71
skew: 1.11
type: snfs
lss: 1
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [200000, 260001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 38758 x 38990
Total sieving time: 0.31 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105,4,0,0,0,0,0,0,0,0,400000,400000,25,25,44,44,2.2,2.2,20000
total time: 0.31 hours.
 --------- CPU info (if available) ----------

5·10¹⁷⁷+9 = 5(0)₁₇₆9_<178> = 361873 · C173

C173 = P47 · P126

P47 = 59065588279102023578540722642848366939231685729_<47>

P126 = 233926428229777021792526147696670859387164608180601153770469223624167359153947326848196873305595620698830254470527744319418777_<126>

Number: 50009_177
N=13817002097420918388495411373603446513003180673882826295413031643698203513387293332191127826613204079884379326448781754925070397625686359579189384120948509559983751205533433
  ( 173 digits)
SNFS difficulty: 178 digits.
Divisors found:
 r1=59065588279102023578540722642848366939231685729 (pp47)
 r2=233926428229777021792526147696670859387164608180601153770469223624167359153947326848196873305595620698830254470527744319418777 (pp126)
Version: Msieve-1.39
Total time: 100.42 hours.
Scaled time: 174.63 units (timescale=1.739).
Factorization parameters were as follows:
n: 13817002097420918388495411373603446513003180673882826295413031643698203513387293332191127826613204079884379326448781754925070397625686359579189384120948509559983751205533433
m: 200000000000000000000000000000000000
deg: 5
c5: 125
c0: 72
skew: 0.90
type: snfs
lss: 1
rlim: 6600000
alim: 6600000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6600000/6600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3300000, 8400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1405205 x 1405453
Total sieving time: 100.42 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,178,5,0,0,0,0,0,0,0,0,6600000,6600000,28,28,53,53,2.5,2.5,100000
total time: 100.42 hours.
 --------- CPU info (if available) ----------

(46·10¹²¹+71)/9 = 5(1)₁₂₀9_<122> = 29 · 701233933 · C112

C112 = P50 · P62

P50 = 46009683390482676142661469113136711350972508440317_<50>

P62 = 54626723951423242493762457044144963710391442346120152601866451_<62>

Number: 51119_121
N=2513358273664280143428310555211316635939192846588905490712504526036387538687321885693404474919042021725138104967
  ( 112 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=46009683390482676142661469113136711350972508440317 (pp50)
 r2=54626723951423242493762457044144963710391442346120152601866451 (pp62)
Version: Msieve-1.39
Total time: 1.85 hours.
Scaled time: 2.22 units (timescale=1.203).
Factorization parameters were as follows:
n: 2513358273664280143428310555211316635939192846588905490712504526036387538687321885693404474919042021725138104967
m: 1000000000000000000000000
deg: 5
c5: 460
c0: 71
skew: 0.69
type: snfs
lss: 1
rlim: 780000
alim: 780000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 780000/780000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [390000, 790001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 98393 x 98630
Total sieving time: 1.85 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,780000,780000,25,25,46,46,2.2,2.2,50000
total time: 1.85 hours.
 --------- CPU info (if available) ----------

(46·10¹²⁸+71)/9 = 5(1)₁₂₇9_<129> = 3 · 186475951384166345773_<21> · C108

C108 = P43 · P66

P43 = 1370699867468772090856264595932743748201541_<43>

P66 = 666544064106153667875823113158516179177104168930788199356268868261_<66>

Number: 51119_128
N=913631860332401561017826634196444054068347171953019310974100172516873181398679747654830915258945166206190201
  ( 108 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1370699867468772090856264595932743748201541 (pp43)
 r2=666544064106153667875823113158516179177104168930788199356268868261 (pp66)
Version: Msieve-1.39
Total time: 3.01 hours.
Scaled time: 3.60 units (timescale=1.197).
Factorization parameters were as follows:
n: 913631860332401561017826634196444054068347171953019310974100172516873181398679747654830915258945166206190201
m: 50000000000000000000000000
deg: 5
c5: 368
c0: 1775
skew: 1.37
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 1135001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 167666 x 167914
Total sieving time: 3.01 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 3.01 hours.
 --------- CPU info (if available) ----------

(46·10¹²⁹+71)/9 = 5(1)₁₂₈9_<130> = 412876198061_<12> · C119

C119 = P37 · P40 · P42

P37 = 8538467243791808437910109352246048481_<37>

P40 = 1856651886231892063895947145518138484891_<40>

P42 = 780881394845341467663468221315394520530449_<42>

Number: 51119_129
N=12379282543083229215318036156147492197131000724546780647582298971878710416303799076634055246353614555139699826550886379
  ( 119 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=8538467243791808437910109352246048481 (pp37)
 r2=1856651886231892063895947145518138484891 (pp40)
 r3=780881394845341467663468221315394520530449 (pp42)
Version: Msieve-1.39
Total time: 2.65 hours.
Scaled time: 3.17 units (timescale=1.198).
Factorization parameters were as follows:
n: 12379282543083229215318036156147492197131000724546780647582298971878710416303799076634055246353614555139699826550886379
m: 100000000000000000000000000
deg: 5
c5: 23
c0: 355
skew: 1.73
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 1040001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 163702 x 163950
Total sieving time: 2.65 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 2.65 hours.
 --------- CPU info (if available) ----------

(46·10¹⁴³+71)/9 = 5(1)₁₄₂9_<144> = 3 · 7 · 19079 · C139

C139 = P59 · P80

P59 = 97048476889694747931582548591254566855340946171026940283703_<59>

P80 = 13144730780789614385948948986670127604676454170169609999833165175217833747435347_<80>

Number: 51119_143
N=1275676101400720091427151545606391248196374251198927544647970246796181069465832818209777169890383371173768993361215175775687332896830249941
  ( 139 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=97048476889694747931582548591254566855340946171026940283703 (pp59)
 r2=13144730780789614385948948986670127604676454170169609999833165175217833747435347 (pp80)
Version: Msieve-1.39
Total time: 9.57 hours.
Scaled time: 11.48 units (timescale=1.200).
Factorization parameters were as follows:
n: 1275676101400720091427151545606391248196374251198927544647970246796181069465832818209777169890383371173768993361215175775687332896830249941
m: 50000000000000000000000000000
deg: 5
c5: 368
c0: 1775
skew: 1.37
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [950000, 2650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 360745 x 360993
Total sieving time: 9.57 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 9.57 hours.
 --------- CPU info (if available) ----------

(46·10¹⁶³+17)/9 = 5(1)₁₆₂3_<164> = 181 · 214087 · 10207247 · 5373228193_<10> · 524720358470069_<15> · C125

C125 = P40 · P86

P40 = 2901428838271710072989478722772703305541_<40>

P86 = 15796566642975477222426106514151356215220954988925611533724771019602789181077878704181_<86>

Number: 51113_163
N=45832614003609986015505277560643422175904489813533037778187090635645628988225589864451526185487048322758261220754908397166921
  ( 125 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=2901428838271710072989478722772703305541 (pp40)
 r2=15796566642975477222426106514151356215220954988925611533724771019602789181077878704181 (pp86)
Version: Msieve-1.39
Total time: 42.88 hours.
Scaled time: 110.25 units (timescale=2.571).
Factorization parameters were as follows:
n: 45832614003609986015505277560643422175904489813533037778187090635645628988225589864451526185487048322758261220754908397166921
m: 500000000000000000000000000000000
deg: 5
c5: 368
c0: 425
skew: 1.03
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 762163 x 762411
Total sieving time: 42.88 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 42.88 hours.
 --------- CPU info (if available) ----------

(46·10¹⁴⁴+71)/9 = 5(1)₁₄₃9_<145> = 13 · 241 · 137273 · 2139989681_<10> · C127

C127 = P48 · P80

P48 = 500082844191092308756949487823356333584022932113_<48>

P80 = 11104938743856477054517868159608136536088822909774673995551781412181151757616147_<80>

Number: 51119_144
N=5553389351595602956412071273642650455228243831370613711217333031056967390411741311451239092475845957096412679705356650093628611
  ( 127 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=500082844191092308756949487823356333584022932113 (pp48)
 r2=11104938743856477054517868159608136536088822909774673995551781412181151757616147 (pp80)
Version: Msieve-1.39
Total time: 8.25 hours.
Scaled time: 9.95 units (timescale=1.207).
Factorization parameters were as follows:
n: 5553389351595602956412071273642650455228243831370613711217333031056967390411741311451239092475845957096412679705356650093628611
m: 100000000000000000000000000000
deg: 5
c5: 23
c0: 355
skew: 1.73
type: snfs
lss: 1
rlim: 1930000
alim: 1930000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1930000/1930000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [965000, 2465001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 319483 x 319731
Total sieving time: 8.25 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1930000,1930000,26,26,49,49,2.3,2.3,100000
total time: 8.25 hours.
 --------- CPU info (if available) ----------

(46·10¹⁵⁰+71)/9 = 5(1)₁₄₉9_<151> = 13 · 1947223 · 38390909 · C136

C136 = P41 · P96

P41 = 42538139961910785733246934292034615902317_<41>

P96 = 123637264648317163042355890662940623511699502455330354446549884735561640038234169014759390237077_<96>

Number: 51119_150
N=5259299268117919981353554263166022581820714930286677440908229002432500590164069557166613950508425935153269996940771900328189140903607409
  ( 136 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=42538139961910785733246934292034615902317 (pp41)
 r2=123637264648317163042355890662940623511699502455330354446549884735561640038234169014759390237077 (pp96)
Version: Msieve-1.39
Total time: 11.95 hours.
Scaled time: 14.33 units (timescale=1.199).
Factorization parameters were as follows:
n: 5259299268117919981353554263166022581820714930286677440908229002432500590164069557166613950508425935153269996940771900328189140903607409
m: 1000000000000000000000000000000
deg: 5
c5: 46
c0: 71
skew: 1.09
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 354651 x 354899
Total sieving time: 11.95 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 11.95 hours.
 --------- CPU info (if available) ----------

(44·10¹⁷⁷-17)/9 = 4(8)₁₇₆7_<178> = 3 · 18191 · C173

C173 = P43 · P131

P43 = 2461339886774522358152390757453165420172103_<43>

P131 = 36396594389213756106769747898329596555265057158903246811091893445667012912315124913287462349109779266801430409018816915629171603573_<131>

Number: 48887_177
N=89584389512925602200518367853863428598187544919445309748206785203102063087770305625288858755957870904822694169074247134826542225805597802739246310242956936376759366149724019
  ( 173 digits)
SNFS difficulty: 178 digits.
Divisors found:
 r1=2461339886774522358152390757453165420172103 (pp43)
 r2=36396594389213756106769747898329596555265057158903246811091893445667012912315124913287462349109779266801430409018816915629171603573 (pp131)
Version: Msieve-1.39
Total time: 105.06 hours.
Scaled time: 182.70 units (timescale=1.739).
Factorization parameters were as follows:
n: 89584389512925602200518367853863428598187544919445309748206785203102063087770305625288858755957870904822694169074247134826542225805597802739246310242956936376759366149724019
m: 200000000000000000000000000000000000
deg: 5
c5: 275
c0: -34
skew: 0.66
type: snfs
lss: 1
rlim: 6700000
alim: 6700000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6700000/6700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3350000, 8650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1424087 x 1424335
Total sieving time: 105.06 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,178,5,0,0,0,0,0,0,0,0,6700000,6700000,28,28,53,53,2.5,2.5,100000
total time: 105.06 hours.
 --------- CPU info (if available) ----------

(46·10¹⁶²+71)/9 = 5(1)₁₆₁9_<163> = 13 · C162

C162 = P65 · P97

P65 = 57800249016433959471978077093391209607071442449632919182640852059_<65>

P97 = 6802088223713498538731821213822390527250157537497199065944202659052719853731469736697689689346257_<97>

Number: 51119_162
N=393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393163
  ( 162 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=57800249016433959471978077093391209607071442449632919182640852059 (pp65)
 r2=6802088223713498538731821213822390527250157537497199065944202659052719853731469736697689689346257 (pp97)
Version: Msieve-1.39
Total time: 43.47 hours.
Scaled time: 111.28 units (timescale=2.560).
Factorization parameters were as follows:
n: 393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393162393163
m: 200000000000000000000000000000000
deg: 5
c5: 575
c0: 284
skew: 0.87
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 4200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 749577 x 749825
Total sieving time: 43.47 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 43.47 hours.
 --------- CPU info (if available) ----------

Mar 10, 2009 (5th)

By Max Dettweiler / GGNFS, msieve 1.40beta2 / Mar 10, 2009

(46·10¹⁴³+53)/9 = 5(1)₁₄₂7_<144> = 167 · 37118570924934461_<17> · 1129812302800707336140404313_<28> · C98

C98 = P42 · P57

P42 = 142378625024556480860219230295193029828263_<42>

P57 = 512573925015667689031096840646605437504778974894108140489_<57>

Number: c98-2
N=72979570667170880800269840951809789385404819622537142712477547587739621926706887797224141946840607
  ( 98 digits)
Divisors found:
 r1=142378625024556480860219230295193029828263 (pp42)
 r2=512573925015667689031096840646605437504778974894108140489 (pp57)
Version: Msieve-1.39
Total time: 2.25 hours.
Scaled time: 3.17 units (timescale=1.404).
Factorization parameters were as follows:
n: 72979570667170880800269840951809789385404819622537142712477547587739621926706887797224141946840607
Y0: -9466360392364189172
Y1:  5116167023
c0:  53504203757430072580740345
c1: -1917373529601613998914
c2: -91409190740534357
c3:  774922611166
c4:  60938008
c5:  960
skew: 39491.60
type: gnfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 211356 x 211604
Total sieving time: 2.25 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 2.25 hours.
 --------- CPU info (if available) ----------

(46·10¹⁶⁰+17)/9 = 5(1)₁₅₉3_<161> = 79 · 1933 · 65599 · 210773 · 404690413 · 13770380053_<11> · 1861888931832967_<16> · C112

C112 = P47 · P65

P47 = 69421810469250964905352073912281382114825982371_<47>

P65 = 33606681669793526544589443702103712368855493759521473358763489429_<65>

Number: 51113_160
N=2333036685380856739826065847758746702938037939625502537307957298158902603241338377544987477719833473532798856159
  ( 112 digits)
Divisors found:
 r1=69421810469250964905352073912281382114825982371 (pp47)
 r2=33606681669793526544589443702103712368855493759521473358763489429 (pp65)
Version: Msieve-1.40beta2
Total time: 22.62 hours.
Scaled time: 36.91 units (timescale=1.632).
Factorization parameters were as follows:
n: 2333036685380856739826065847758746702938037939625502537307957298158902603241338377544987477719833473532798856159
Y0: -3076877135434206027874
Y1:  294082766161
c0: -51400975692427172720771409
c1:  63166927505729826659688
c2: -278627879419892472
c3: -51454969560080
c4:  88080333
c5:  8460
skew: 49144.96
type: gnfs
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 385651 x 385899
Total sieving time: 22.62 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 22.62 hours.
 --------- CPU info (if available) ----------
[    0.367147] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.452481] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.13 BogoMIPS (lpj=8800276)
[    0.004000] Calibrating delay using timer specific routine.. 4400.40 BogoMIPS (lpj=8800811)
[    0.456049] Total of 2 processors activated (8800.54 BogoMIPS).

(46·10¹⁷⁶+53)/9 = 5(1)₁₇₅7_<177> = 11 · 3028560721_<10> · 3604539157_<10> · 495781041989729909690483821_<27> · 379434690236893159237540439461513_<33> · C98

C98 = P41 · P58

P41 = 17207130506967340177607673105985067756831_<41>

P58 = 1314925662121152539307720963217751339151597375268076893777_<58>

Number: c98-1
N=22626097475079112950538412361578435764788431930006107071944439400234866205055016590621131653140687
  ( 98 digits)
Divisors found:
 r1=17207130506967340177607673105985067756831 (pp41)
 r2=1314925662121152539307720963217751339151597375268076893777 (pp58)
Version: Msieve-1.40beta2
Total time: 3.93 hours.
Scaled time: 6.39 units (timescale=1.625).
Factorization parameters were as follows:
n: 22626097475079112950538412361578435764788431930006107071944439400234866205055016590621131653140687

Y0: -6604835464427066740

Y1:  9414325037

c0: -20535393666216700134369

c1:  23023711095567736083

c2: -8222964854909011

c3:  405478485133

c4:  78897468

c5:  1800

skew: 10007.05

type: gnfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 159895 x 160143
Total sieving time: 3.93 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 3.93 hours.
 --------- CPU info (if available) ----------
[    0.367147] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.452481] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.13 BogoMIPS (lpj=8800276)
[    0.004000] Calibrating delay using timer specific routine.. 4400.40 BogoMIPS (lpj=8800811)
[    0.456049] Total of 2 processors activated (8800.54 BogoMIPS).

Mar 10, 2009 (4th)

By Sinkiti Sibata / GGNFS, Msieve / Mar 10, 2009

(46·10¹⁴³+17)/9 = 5(1)₁₄₂3_<144> = 3 · 179 · 6733 · 24169183 · C130

C130 = P39 · P92

P39 = 139623054636055338710939135384408668661_<39>

P92 = 41890285173377352541316306659022432235174853079005378363036811052955504759851453668960732831_<92>

Number: 51113_143
N=5848849575482404980903607610112559837740405564754665231895575593151694941823586596327909534403255257458667454847960312051623509291
  ( 130 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=139623054636055338710939135384408668661 (pp39)
 r2=41890285173377352541316306659022432235174853079005378363036811052955504759851453668960732831 (pp92)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 19.94 hours.
Scaled time: 9.39 units (timescale=0.471).
Factorization parameters were as follows:
name: 51113_143
n: 5848849575482404980903607610112559837740405564754665231895575593151694941823586596327909534403255257458667454847960312051623509291
m: 50000000000000000000000000000
deg: 5
c5: 368
c0: 425
skew: 1.03
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [950000, 2450001)
Primes: RFBsize:142029, AFBsize:142512, largePrimes:4151889 encountered
Relations: rels:4321208, finalFF:386100
Max relations in full relation-set: 28
Initial matrix: 284608 x 386100 with sparse part having weight 39663465.
Pruned matrix : 250533 x 252020 with weight 23269867.
Total sieving time: 17.80 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.83 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 19.94 hours.
 --------- CPU info (if available) ----------

(46·10¹⁶²+53)/9 = 5(1)₁₆₁7_<163> = 11 · 11215279 · 13426327 · 248887681753_<12> · 2317578175073617_<16> · 32185135718630441_<17> · C105

C105 = P36 · P69

P36 = 644922593370834891407360750242576241_<36>

P69 = 257723845874142713268164872256040302227306103279377599115103092063039_<69>

Mon Mar 09 07:58:40 2009  Msieve v. 1.39
Mon Mar 09 07:58:40 2009  random seeds: 1d3debe0 a1696c50
Mon Mar 09 07:58:40 2009  factoring 166211931054657464690785485770816308830203049067739149906327056881572343337683955416814248719378935656399 (105 digits)
Mon Mar 09 07:58:41 2009  searching for 15-digit factors
Mon Mar 09 07:58:43 2009  commencing quadratic sieve (105-digit input)
Mon Mar 09 07:58:43 2009  using multiplier of 2
Mon Mar 09 07:58:43 2009  using 32kb Intel Core sieve core
Mon Mar 09 07:58:43 2009  sieve interval: 36 blocks of size 32768
Mon Mar 09 07:58:43 2009  processing polynomials in batches of 6
Mon Mar 09 07:58:43 2009  using a sieve bound of 3877483 (137428 primes)
Mon Mar 09 07:58:43 2009  using large prime bound of 581622450 (29 bits)
Mon Mar 09 07:58:43 2009  using double large prime bound of 5975222047534050 (44-53 bits)
Mon Mar 09 07:58:43 2009  using trial factoring cutoff of 53 bits
Mon Mar 09 07:58:43 2009  polynomial 'A' values have 14 factors
Tue Mar 10 22:29:55 2009  137524 relations (31697 full + 105827 combined from 2070007 partial), need 137524
Tue Mar 10 22:29:58 2009  begin with 2101704 relations
Tue Mar 10 22:30:00 2009  reduce to 366393 relations in 11 passes
Tue Mar 10 22:30:00 2009  attempting to read 366393 relations
Tue Mar 10 22:30:09 2009  recovered 366393 relations
Tue Mar 10 22:30:09 2009  recovered 360266 polynomials
Tue Mar 10 22:30:10 2009  attempting to build 137524 cycles
Tue Mar 10 22:30:10 2009  found 137524 cycles in 7 passes
Tue Mar 10 22:30:10 2009  distribution of cycle lengths:
Tue Mar 10 22:30:10 2009     length 1 : 31697
Tue Mar 10 22:30:10 2009     length 2 : 23149
Tue Mar 10 22:30:10 2009     length 3 : 23173
Tue Mar 10 22:30:10 2009     length 4 : 18839
Tue Mar 10 22:30:10 2009     length 5 : 14434
Tue Mar 10 22:30:10 2009     length 6 : 10125
Tue Mar 10 22:30:10 2009     length 7 : 6672
Tue Mar 10 22:30:10 2009     length 9+: 9435
Tue Mar 10 22:30:10 2009  largest cycle: 24 relations
Tue Mar 10 22:30:11 2009  matrix is 137428 x 137524 (39.8 MB) with weight 9887948 (71.90/col)
Tue Mar 10 22:30:11 2009  sparse part has weight 9887948 (71.90/col)
Tue Mar 10 22:30:13 2009  filtering completed in 3 passes
Tue Mar 10 22:30:13 2009  matrix is 132629 x 132693 (38.7 MB) with weight 9601925 (72.36/col)
Tue Mar 10 22:30:13 2009  sparse part has weight 9601925 (72.36/col)
Tue Mar 10 22:30:13 2009  saving the first 48 matrix rows for later
Tue Mar 10 22:30:14 2009  matrix is 132581 x 132693 (24.2 MB) with weight 7667651 (57.78/col)
Tue Mar 10 22:30:14 2009  sparse part has weight 5548870 (41.82/col)
Tue Mar 10 22:30:14 2009  matrix includes 64 packed rows
Tue Mar 10 22:30:14 2009  using block size 43690 for processor cache size 1024 kB
Tue Mar 10 22:30:15 2009  commencing Lanczos iteration
Tue Mar 10 22:30:15 2009  memory use: 23.3 MB
Tue Mar 10 22:32:26 2009  lanczos halted after 2098 iterations (dim = 132578)
Tue Mar 10 22:32:27 2009  recovered 16 nontrivial dependencies
Tue Mar 10 22:32:30 2009  prp36 factor: 644922593370834891407360750242576241
Tue Mar 10 22:32:30 2009  prp69 factor: 257723845874142713268164872256040302227306103279377599115103092063039
Tue Mar 10 22:32:30 2009  elapsed time 38:33:50

Mar 10, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Mar 10, 2009

(44·10²⁰²-17)/9 = 4(8)₂₀₁7_<203> = 19 · C202

C202 = P58 · P144

P58 = 2891584018994382557518753539240993661489392732788328409241_<58>

P144 = 889858084116654916807069578355138652152689469299026049021329528371839912902115848416237708291106981386858036660316985335361448495359121966080853_<144>

Number: n
N=2573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573
  ( 202 digits)
SNFS difficulty: 203 digits.
Divisors found:

Tue Mar 10 07:53:12 2009  prp58 factor: 2891584018994382557518753539240993661489392732788328409241
Tue Mar 10 07:53:12 2009  prp144 factor: 889858084116654916807069578355138652152689469299026049021329528371839912902115848416237708291106981386858036660316985335361448495359121966080853
Tue Mar 10 07:53:12 2009  elapsed time 17:11:08 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 85.73 hours.
Scaled time: 172.75 units (timescale=2.015).
Factorization parameters were as follows:
name: KA_4_8_201_7
n: 2573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573099415204678362573
deg: 5
c5: 275
c0: -34
m: 20000000000000000000000000000000000000000
skew: 0.66
type: snfs
rlim: 12000000
alim: 12000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [6000000, 25599990)
Primes: RFBsize:788060, AFBsize:788250, largePrimes:33189330 encountered
Relations: rels:25821250, finalFF:119729
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 6931779 hash collisions in 42735830 relations
Msieve: matrix is 3220003 x 3220251 (873.3 MB)

Total sieving time: 85.01 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,203,5,0,0,0,0,0,0,0,0,12000000,12000000,29,29,58,58,2.5,2.5,100000
total time: 85.73 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368976k/3407296k available (2745k kernel code, 36940k reserved, 1424k data, 412k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830498)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454)
Total of 4 processors activated (22643.71 BogoMIPS).

Mar 10, 2009 (2nd)

By Ignacio Santos / Msieve, Yafu 1.06, GGNFS / Mar 10, 2009

(46·10¹³⁶+53)/9 = 5(1)₁₃₅7_<137> = 3 · 11 · 35083 · 9683850720145068769_<19> · 1356173883615136264781_<22> · C91

C91 = P28 · P64

P28 = 1093686932178979004947141309_<28>

P64 = 3073605843053092781133130455435874869768958447225792163177835103_<64>

Mon Mar 09 19:01:21 2009  
Mon Mar 09 19:01:21 2009  
Mon Mar 09 19:01:21 2009  Msieve v. 1.40
Mon Mar 09 19:01:21 2009  random seeds: b3e6df80 516fea8b
Mon Mar 09 19:01:21 2009  factoring 3361562545216121472298202857987577242590374665871039124930644519950592605605373751241569827 (91 digits)
Mon Mar 09 19:01:22 2009  searching for 15-digit factors
Mon Mar 09 19:01:23 2009  commencing quadratic sieve (91-digit input)
Mon Mar 09 19:01:23 2009  using multiplier of 3
Mon Mar 09 19:01:23 2009  using 32kb Intel Core sieve core
Mon Mar 09 19:01:23 2009  sieve interval: 36 blocks of size 32768
Mon Mar 09 19:01:23 2009  processing polynomials in batches of 6
Mon Mar 09 19:01:23 2009  using a sieve bound of 1679009 (63529 primes)
Mon Mar 09 19:01:23 2009  using large prime bound of 154468828 (27 bits)
Mon Mar 09 19:01:23 2009  using double large prime bound of 549431410063824 (42-49 bits)
Mon Mar 09 19:01:23 2009  using trial factoring cutoff of 49 bits
Mon Mar 09 19:01:23 2009  polynomial 'A' values have 12 factors
Mon Mar 09 20:22:24 2009  64117 relations (16634 full + 47483 combined from 727403 partial), need 63625
Mon Mar 09 20:22:25 2009  begin with 744037 relations
Mon Mar 09 20:22:25 2009  reduce to 159247 relations in 10 passes
Mon Mar 09 20:22:25 2009  attempting to read 159247 relations
Mon Mar 09 20:22:27 2009  recovered 159247 relations
Mon Mar 09 20:22:27 2009  recovered 139681 polynomials
Mon Mar 09 20:22:27 2009  attempting to build 64117 cycles
Mon Mar 09 20:22:27 2009  found 64117 cycles in 5 passes
Mon Mar 09 20:22:27 2009  distribution of cycle lengths:
Mon Mar 09 20:22:27 2009     length 1 : 16634
Mon Mar 09 20:22:27 2009     length 2 : 12079
Mon Mar 09 20:22:27 2009     length 3 : 11154
Mon Mar 09 20:22:27 2009     length 4 : 8516
Mon Mar 09 20:22:27 2009     length 5 : 6276
Mon Mar 09 20:22:27 2009     length 6 : 3898
Mon Mar 09 20:22:27 2009     length 7 : 2491
Mon Mar 09 20:22:27 2009     length 9+: 3069
Mon Mar 09 20:22:27 2009  largest cycle: 17 relations
Mon Mar 09 20:22:28 2009  matrix is 63529 x 64117 (16.0 MB) with weight 3926651 (61.24/col)
Mon Mar 09 20:22:28 2009  sparse part has weight 3926651 (61.24/col)
Mon Mar 09 20:22:28 2009  filtering completed in 3 passes
Mon Mar 09 20:22:28 2009  matrix is 59791 x 59855 (14.9 MB) with weight 3663215 (61.20/col)
Mon Mar 09 20:22:28 2009  sparse part has weight 3663215 (61.20/col)
Mon Mar 09 20:22:28 2009  saving the first 48 matrix rows for later
Mon Mar 09 20:22:28 2009  matrix is 59743 x 59855 (9.6 MB) with weight 2901903 (48.48/col)
Mon Mar 09 20:22:28 2009  sparse part has weight 2165890 (36.19/col)
Mon Mar 09 20:22:28 2009  matrix includes 64 packed rows
Mon Mar 09 20:22:28 2009  using block size 23942 for processor cache size 4096 kB
Mon Mar 09 20:22:29 2009  commencing Lanczos iteration
Mon Mar 09 20:22:29 2009  memory use: 9.3 MB
Mon Mar 09 20:22:44 2009  lanczos halted after 946 iterations (dim = 59741)
Mon Mar 09 20:22:44 2009  recovered 17 nontrivial dependencies
Mon Mar 09 20:22:45 2009  prp28 factor: 1093686932178979004947141309
Mon Mar 09 20:22:45 2009  prp64 factor: 3073605843053092781133130455435874869768958447225792163177835103
Mon Mar 09 20:22:45 2009  elapsed time 01:21:24

(46·10¹³⁹+53)/9 = 5(1)₁₃₈7_<140> = 3 · 22397 · 389727889 · 74127510042103036208845291422325007_<35> · C92

C92 = P44 · P48

P44 = 87679135327818129083845195790361427454587883_<44>

P48 = 300308110768732222706837801807141690286149914543_<48>

03/09/09 19:06:23 v1.06 @ IGNACIO1, starting SIQS on c92: 26330755484133069354472838342356404140621472902394058726689606504726770947356086733733282469
03/09/09 19:06:24 v1.06 @ IGNACIO1, ==== sieve params ====
03/09/09 19:06:24 v1.06 @ IGNACIO1, n = 92 digits, 307 bits
03/09/09 19:06:24 v1.06 @ IGNACIO1, factor base: 71746 primes (max prime = 1926293)
03/09/09 19:06:24 v1.06 @ IGNACIO1, single large prime cutoff: 231155160 (120 * pmax)
03/09/09 19:06:24 v1.06 @ IGNACIO1, double large prime range from 43 to 51 bits
03/09/09 19:06:24 v1.06 @ IGNACIO1, double large prime cutoff: 1135079986864172
03/09/09 19:06:24 v1.06 @ IGNACIO1, using 10 large prime slices of factor base
03/09/09 19:06:24 v1.06 @ IGNACIO1, buckets hold 1024 elements
03/09/09 19:06:24 v1.06 @ IGNACIO1, sieve interval: 22 blocks of size 32768
03/09/09 19:06:24 v1.06 @ IGNACIO1, polynomial A has ~ 12 factors
03/09/09 19:06:24 v1.06 @ IGNACIO1, using multiplier of 5
03/09/09 19:06:24 v1.06 @ IGNACIO1, using small prime variation correction of 18 bits
03/09/09 19:06:24 v1.06 @ IGNACIO1, trial factoring cutoff at 101 bits
03/09/09 19:06:24 v1.06 @ IGNACIO1, ==== sieving started ====
03/09/09 20:55:52 v1.06 @ IGNACIO1, sieve time = 2156.7930, relation time = 1121.8380, poly_time = 3280.0710
03/09/09 20:55:52 v1.06 @ IGNACIO1, 71836 relations found: 19691 full + 52145 from 892722 partial, using 715821 polys (349 A polys)
03/09/09 20:55:52 v1.06 @ IGNACIO1, trial division touched 26420759 sieve locations out of 1032064991232
03/09/09 20:55:52 v1.06 @ IGNACIO1, ==== post processing stage (msieve-1.38) ====
03/09/09 20:55:53 v1.06 @ IGNACIO1, begin with 912413 relations
03/09/09 20:55:53 v1.06 @ IGNACIO1, reduce to 172190 relations in 11 passes
03/09/09 20:55:55 v1.06 @ IGNACIO1, failed to read relation 80418
03/09/09 20:55:56 v1.06 @ IGNACIO1, failed to read relation 129039
03/09/09 20:55:56 v1.06 @ IGNACIO1, recovered 172188 relations
03/09/09 20:55:56 v1.06 @ IGNACIO1, recovered 152900 polynomials
03/09/09 20:55:57 v1.06 @ IGNACIO1, attempting to build 71834 cycles
03/09/09 20:55:57 v1.06 @ IGNACIO1, found 71834 cycles in 5 passes
03/09/09 20:55:57 v1.06 @ IGNACIO1, distribution of cycle lengths:
03/09/09 20:55:57 v1.06 @ IGNACIO1,    length 1 : 19691
03/09/09 20:55:57 v1.06 @ IGNACIO1,    length 2 : 14772
03/09/09 20:55:57 v1.06 @ IGNACIO1,    length 3 : 13092
03/09/09 20:55:57 v1.06 @ IGNACIO1,    length 4 : 9227
03/09/09 20:55:57 v1.06 @ IGNACIO1,    length 5 : 6460
03/09/09 20:55:57 v1.06 @ IGNACIO1,    length 6 : 3873
03/09/09 20:55:57 v1.06 @ IGNACIO1,    length 7 : 2212
03/09/09 20:55:57 v1.06 @ IGNACIO1,    length 9+: 2507
03/09/09 20:55:57 v1.06 @ IGNACIO1, largest cycle: 18 relations
03/09/09 20:55:57 v1.06 @ IGNACIO1, matrix is 71746 x 71834 (17.3 MB) with weight 4246484 (59.12/col)
03/09/09 20:55:57 v1.06 @ IGNACIO1, sparse part has weight 4246484 (59.12/col)
03/09/09 20:55:57 v1.06 @ IGNACIO1, filtering completed in 3 passes
03/09/09 20:55:57 v1.06 @ IGNACIO1, matrix is 67142 x 67206 (16.3 MB) with weight 4015995 (59.76/col)
03/09/09 20:55:57 v1.06 @ IGNACIO1, sparse part has weight 4015995 (59.76/col)
03/09/09 20:55:57 v1.06 @ IGNACIO1, saving the first 48 matrix rows for later
03/09/09 20:55:57 v1.06 @ IGNACIO1, matrix is 67094 x 67206 (11.1 MB) with weight 3229491 (48.05/col)
03/09/09 20:55:57 v1.06 @ IGNACIO1, sparse part has weight 2496296 (37.14/col)
03/09/09 20:55:57 v1.06 @ IGNACIO1, matrix includes 64 packed rows
03/09/09 20:55:57 v1.06 @ IGNACIO1, using block size 26882 for processor cache size 4096 kB
03/09/09 20:55:58 v1.06 @ IGNACIO1, commencing Lanczos iteration
03/09/09 20:55:58 v1.06 @ IGNACIO1, memory use: 10.5 MB
03/09/09 20:56:21 v1.06 @ IGNACIO1, lanczos halted after 1063 iterations (dim = 67091)
03/09/09 20:56:21 v1.06 @ IGNACIO1, recovered 16 nontrivial dependencies
03/09/09 20:56:22 v1.06 @ IGNACIO1, prp48 = 300308110768732222706837801807141690286149914543
03/09/09 20:56:23 v1.06 @ IGNACIO1, prp44 = 87679135327818129083845195790361427454587883
03/09/09 20:56:23 v1.06 @ IGNACIO1, Lanczos elapsed time = 29.6310 seconds.
03/09/09 20:56:23 v1.06 @ IGNACIO1, Sqrt elapsed time = 1.9950 seconds.
03/09/09 20:56:23 v1.06 @ IGNACIO1, Total elapsed time = 6600.2490 seconds.

(46·10¹⁶³+53)/9 = 5(1)₁₆₂7_<164> = 3 · 17 · 19 · C161

C161 = P50 · P112

P50 = 19681554786229512498521615841720531903117438305569_<50>

P112 = 2679983632879134839217655504863995441112610536764554382163896252409598726595514228780873486445695938122612848197_<112>

Number: 51117_163
N=52746244696709092993922715284944387111569774108473798876275656461414975346863891755532622405687421167297328288040362343767916523334479990826740052746244696709093
  ( 161 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=19681554786229512498521615841720531903117438305569 (pp50)
 r2=2679983632879134839217655504863995441112610536764554382163896252409598726595514228780873486445695938122612848197 (pp112)
Version: Msieve-1.39
Total time: 35.35 hours.
Scaled time: 61.47 units (timescale=1.739).
Factorization parameters were as follows:
n: 52746244696709092993922715284944387111569774108473798876275656461414975346863891755532622405687421167297328288040362343767916523334479990826740052746244696709093
m: 500000000000000000000000000000000
deg: 5
c5: 368
c0: 1325
skew: 1.29
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 757733 x 757981
Total sieving time: 35.35 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 35.35 hours.
 --------- CPU info (if available) ----------

(46·10¹⁶¹+53)/9 = 5(1)₁₆₀7_<162> = 167281501 · C154

C154 = P32 · P123

P32 = 29304073293056004611600603550341_<32>

P123 = 104265207929804161640682601999886440675679347982672371444289866714737148563122388946690763349474640988083937818479288943037_<123>

Number: 51117_161
N=3055395295090705284328546950993171152326706532308740529002732412779528509318619224436006890631087242044242005642399819876742444528346927680372207510925617
  ( 154 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=29304073293056004611600603550341 (pp32)
 r2=104265207929804161640682601999886440675679347982672371444289866714737148563122388946690763349474640988083937818479288943037 (pp123)
Version: Msieve-1.39
Total time: 35.10 hours.
Scaled time: 90.25 units (timescale=2.571).
Factorization parameters were as follows:
n: 3055395295090705284328546950993171152326706532308740529002732412779528509318619224436006890631087242044242005642399819876742444528346927680372207510925617
m: 200000000000000000000000000000000
deg: 5
c5: 115
c0: 424
skew: 1.30
type: snfs
lss: 1
rlim: 3700000
alim: 3700000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3700000/3700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1850000, 3650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 666390 x 666638
Total sieving time: 35.10 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,51,51,2.4,2.4,100000
total time: 35.10 hours.
 --------- CPU info (if available) ----------

(44·10¹⁶³+1)/9 = 4(8)₁₆₂9_<164> = 7 · 5068012901506364190633732107_<28> · C136

C136 = P41 · P95

P41 = 42566000178928534066137272811737382493561_<41>

P95 = 32375133858060673452433631534485078300706599193409229345003393728689063018119668175725228319301_<95>

Number: 48889_163
N=1378079953595045867594053404080634834157078864784978858028996260948676240385650162839972747333355597162475697307787418612773224484520861
  ( 136 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=42566000178928534066137272811737382493561 (pp41)
 r2=32375133858060673452433631534485078300706599193409229345003393728689063018119668175725228319301 (pp95)
Version: Msieve-1.39
Total time: 28.88 hours.
Scaled time: 74.24 units (timescale=2.571).
Factorization parameters were as follows:
n: 1378079953595045867594053404080634834157078864784978858028996260948676240385650162839972747333355597162475697307787418612773224484520861
m: 1000000000000000000000000000000000
deg: 5
c5: 11
c0: 25
skew: 1.18
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 3450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 659068 x 659316
Total sieving time: 28.88 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 28.88 hours.
 --------- CPU info (if available) ----------

Mar 10, 2009

Factorizations of 511...119 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 9, 2009 (8th)

By Andreas Tete / Msieve 1.40beta2 / Mar 9, 2009

(31·10¹⁶⁸+41)/9 = 3(4)₁₆₇9_<169> = 1303 · 312340090511_<12> · 29368458645403_<14> · 7717403667575857_<16> · C125

C125 = P58 · P68

P58 = 3199531318649953244341022926800550296567933036062498357291_<58>

P68 = 11671006212528191652002268221699814254356844004459282877277697877073_<68>

Mon Mar 09 07:15:26 2009  
Mon Mar 09 07:15:26 2009  
Mon Mar 09 07:15:26 2009  Msieve v. 1.40
Mon Mar 09 07:15:26 2009  random seeds: ade51018 e14bc1bb
Mon Mar 09 07:15:26 2009  factoring 37341749897142121501044346885341085486989665803866127120929436699947381633311322080195902338164347592550563750975260551289243 (125 digits)
Mon Mar 09 07:15:27 2009  searching for 15-digit factors
Mon Mar 09 07:15:29 2009  commencing number field sieve (125-digit input)
Mon Mar 09 07:15:29 2009  R0: -1088114432624936520075342
Mon Mar 09 07:15:29 2009  R1:  34737124470091
Mon Mar 09 07:15:29 2009  A0: -71496577573595625906473163785
Mon Mar 09 07:15:29 2009  A1:  35064141251845164949397623
Mon Mar 09 07:15:29 2009  A2: -776953222852106819385
Mon Mar 09 07:15:29 2009  A3: -2160258613523839
Mon Mar 09 07:15:29 2009  A4:  18360593834
Mon Mar 09 07:15:29 2009  A5:  24480
Mon Mar 09 07:15:29 2009  skew 181474.42, size 5.173726e-012, alpha -6.170813, combined = 1.493559e-010
Mon Mar 09 07:15:29 2009  
Mon Mar 09 07:15:29 2009  commencing relation filtering
Mon Mar 09 07:15:29 2009  commencing duplicate removal, pass 1
Mon Mar 09 07:17:02 2009  found 1491858 hash collisions in 9245826 relations
Mon Mar 09 07:17:25 2009  added 58666 free relations
Mon Mar 09 07:17:25 2009  commencing duplicate removal, pass 2
Mon Mar 09 07:17:40 2009  found 1497815 duplicates and 7806676 unique relations
Mon Mar 09 07:17:40 2009  memory use: 65.3 MB
Mon Mar 09 07:17:40 2009  reading rational ideals above 7405568
Mon Mar 09 07:17:40 2009  reading algebraic ideals above 7405568
Mon Mar 09 07:17:40 2009  commencing singleton removal, pass 1
Mon Mar 09 07:19:02 2009  relations with 0 large ideals: 263246
Mon Mar 09 07:19:02 2009  relations with 1 large ideals: 1611965
Mon Mar 09 07:19:02 2009  relations with 2 large ideals: 3137880
Mon Mar 09 07:19:02 2009  relations with 3 large ideals: 2223928
Mon Mar 09 07:19:02 2009  relations with 4 large ideals: 502682
Mon Mar 09 07:19:02 2009  relations with 5 large ideals: 12488
Mon Mar 09 07:19:02 2009  relations with 6 large ideals: 54487
Mon Mar 09 07:19:02 2009  relations with 7+ large ideals: 0
Mon Mar 09 07:19:02 2009  7806676 relations and about 7357141 large ideals
Mon Mar 09 07:19:02 2009  commencing singleton removal, pass 2
Mon Mar 09 07:20:24 2009  found 3492596 singletons
Mon Mar 09 07:20:24 2009  current dataset: 4314080 relations and about 3200149 large ideals
Mon Mar 09 07:20:24 2009  commencing singleton removal, pass 3
Mon Mar 09 07:21:13 2009  found 697808 singletons
Mon Mar 09 07:21:13 2009  current dataset: 3616272 relations and about 2461138 large ideals
Mon Mar 09 07:21:13 2009  commencing singleton removal, pass 4
Mon Mar 09 07:21:56 2009  found 183238 singletons
Mon Mar 09 07:21:56 2009  current dataset: 3433034 relations and about 2274326 large ideals
Mon Mar 09 07:21:56 2009  commencing singleton removal, final pass
Mon Mar 09 07:22:39 2009  memory use: 50.7 MB
Mon Mar 09 07:22:39 2009  commencing in-memory singleton removal
Mon Mar 09 07:22:39 2009  begin with 3433034 relations and 2394020 unique ideals
Mon Mar 09 07:22:41 2009  reduce to 3078894 relations and 2033836 ideals in 11 passes
Mon Mar 09 07:22:41 2009  max relations containing the same ideal: 26
Mon Mar 09 07:22:42 2009  reading rational ideals above 720000
Mon Mar 09 07:22:42 2009  reading algebraic ideals above 720000
Mon Mar 09 07:22:42 2009  commencing singleton removal, final pass
Mon Mar 09 07:23:28 2009  keeping 2804566 ideals with weight <= 20, new excess is 247608
Mon Mar 09 07:23:32 2009  memory use: 91.6 MB
Mon Mar 09 07:23:32 2009  commencing in-memory singleton removal
Mon Mar 09 07:23:33 2009  begin with 3082211 relations and 2804566 unique ideals
Mon Mar 09 07:23:37 2009  reduce to 3031265 relations and 2737239 ideals in 10 passes
Mon Mar 09 07:23:37 2009  max relations containing the same ideal: 20
Mon Mar 09 07:23:40 2009  relations with 0 large ideals: 4169
Mon Mar 09 07:23:40 2009  relations with 1 large ideals: 43318
Mon Mar 09 07:23:40 2009  relations with 2 large ideals: 218635
Mon Mar 09 07:23:40 2009  relations with 3 large ideals: 583081
Mon Mar 09 07:23:40 2009  relations with 4 large ideals: 887820
Mon Mar 09 07:23:40 2009  relations with 5 large ideals: 779594
Mon Mar 09 07:23:40 2009  relations with 6 large ideals: 389468
Mon Mar 09 07:23:40 2009  relations with 7+ large ideals: 125180
Mon Mar 09 07:23:40 2009  commencing 2-way merge
Mon Mar 09 07:23:43 2009  reduce to 1807463 relation sets and 1513482 unique ideals
Mon Mar 09 07:23:43 2009  ignored 45 oversize relation sets
Mon Mar 09 07:23:43 2009  commencing full merge
Mon Mar 09 07:24:18 2009  memory use: 140.6 MB
Mon Mar 09 07:24:18 2009  found 877039 cycles, need 841682
Mon Mar 09 07:24:18 2009  weight of 841682 cycles is about 59272709 (70.42/cycle)
Mon Mar 09 07:24:18 2009  distribution of cycle lengths:
Mon Mar 09 07:24:18 2009  1 relations: 98931
Mon Mar 09 07:24:18 2009  2 relations: 100305
Mon Mar 09 07:24:18 2009  3 relations: 99032
Mon Mar 09 07:24:18 2009  4 relations: 88140
Mon Mar 09 07:24:18 2009  5 relations: 78635
Mon Mar 09 07:24:18 2009  6 relations: 67756
Mon Mar 09 07:24:18 2009  7 relations: 57401
Mon Mar 09 07:24:18 2009  8 relations: 47966
Mon Mar 09 07:24:18 2009  9 relations: 40843
Mon Mar 09 07:24:18 2009  10+ relations: 162673
Mon Mar 09 07:24:18 2009  heaviest cycle: 20 relations
Mon Mar 09 07:24:18 2009  commencing cycle optimization
Mon Mar 09 07:24:20 2009  start with 4988347 relations
Mon Mar 09 07:24:34 2009  pruned 149444 relations
Mon Mar 09 07:24:34 2009  memory use: 129.3 MB
Mon Mar 09 07:24:34 2009  distribution of cycle lengths:
Mon Mar 09 07:24:34 2009  1 relations: 98931
Mon Mar 09 07:24:34 2009  2 relations: 103120
Mon Mar 09 07:24:34 2009  3 relations: 103173
Mon Mar 09 07:24:34 2009  4 relations: 90861
Mon Mar 09 07:24:34 2009  5 relations: 80983
Mon Mar 09 07:24:34 2009  6 relations: 68708
Mon Mar 09 07:24:34 2009  7 relations: 57891
Mon Mar 09 07:24:34 2009  8 relations: 47807
Mon Mar 09 07:24:34 2009  9 relations: 40685
Mon Mar 09 07:24:34 2009  10+ relations: 149523
Mon Mar 09 07:24:34 2009  heaviest cycle: 20 relations
Mon Mar 09 07:24:35 2009  RelProcTime: 534
Mon Mar 09 07:24:35 2009  
Mon Mar 09 07:24:35 2009  commencing linear algebra
Mon Mar 09 07:24:35 2009  read 841682 cycles
Mon Mar 09 07:24:37 2009  cycles contain 2673765 unique relations
Mon Mar 09 07:25:09 2009  read 2673765 relations
Mon Mar 09 07:25:14 2009  using 20 quadratic characters above 134216838
Mon Mar 09 07:25:30 2009  building initial matrix
Mon Mar 09 07:26:13 2009  memory use: 307.6 MB
Mon Mar 09 07:26:14 2009  read 841682 cycles
Mon Mar 09 07:26:15 2009  matrix is 841349 x 841682 (241.5 MB) with weight 80038905 (95.09/col)
Mon Mar 09 07:26:15 2009  sparse part has weight 56569614 (67.21/col)
Mon Mar 09 07:26:32 2009  filtering completed in 3 passes
Mon Mar 09 07:26:32 2009  matrix is 837333 x 837533 (240.7 MB) with weight 79742206 (95.21/col)
Mon Mar 09 07:26:32 2009  sparse part has weight 56405744 (67.35/col)
Mon Mar 09 07:26:35 2009  read 837533 cycles
Mon Mar 09 07:26:36 2009  matrix is 837333 x 837533 (240.7 MB) with weight 79742206 (95.21/col)
Mon Mar 09 07:26:36 2009  sparse part has weight 56405744 (67.35/col)
Mon Mar 09 07:26:36 2009  saving the first 48 matrix rows for later
Mon Mar 09 07:26:37 2009  matrix is 837285 x 837533 (230.5 MB) with weight 63294546 (75.57/col)
Mon Mar 09 07:26:37 2009  sparse part has weight 55403246 (66.15/col)
Mon Mar 09 07:26:37 2009  matrix includes 64 packed rows
Mon Mar 09 07:26:37 2009  using block size 65536 for processor cache size 3072 kB
Mon Mar 09 07:26:43 2009  commencing Lanczos iteration
Mon Mar 09 07:26:43 2009  memory use: 229.4 MB
Mon Mar 09 09:11:21 2009  lanczos halted after 13243 iterations (dim = 837285)
Mon Mar 09 09:11:23 2009  recovered 30 nontrivial dependencies
Mon Mar 09 09:11:23 2009  BLanczosTime: 6361
Mon Mar 09 09:11:23 2009  
Mon Mar 09 09:11:23 2009  commencing square root phase
Mon Mar 09 09:11:23 2009  reading relations for dependency 1
Mon Mar 09 09:11:24 2009  read 418665 cycles
Mon Mar 09 09:11:25 2009  cycles contain 1638314 unique relations
Mon Mar 09 09:11:47 2009  read 1638314 relations
Mon Mar 09 09:11:57 2009  multiplying 1333398 relations
Mon Mar 09 09:15:37 2009  multiply complete, coefficients have about 61.72 million bits
Mon Mar 09 09:15:40 2009  initial square root is modulo 726184289
Mon Mar 09 09:22:06 2009  sqrtTime: 613
Mon Mar 09 09:22:06 2009  prp58 factor: 3199531318649953244341022926800550296567933036062498357291
Mon Mar 09 09:22:06 2009  prp68 factor: 11671006212528191652002268221699814254356844004459282877277697877073
#Mon Mar 09 09:22:06 2009  elapsed time 02:06:40

Total time: 119.2 hours.

Mar 9, 2009 (7th)

By Jo Yeong Uk / GMP-ECM / Mar 9, 2009

(46·10¹⁹³+17)/9 = 5(1)₁₉₂3_<194> = C194

C194 = P36 · C159

P36 = 217410993050638873355737846333375723_<36>

C159 = [235089819488596087295387233793131386382105303301089051036631344503098791738232356187656689122842975052128957602428239192437050778955177424652359127571338331931_<159>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 51111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113 (194 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1525602877
Step 1 took 22444ms
Step 2 took 8829ms
********** Factor found in step 2: 217410993050638873355737846333375723
Found probable prime factor of 36 digits: 217410993050638873355737846333375723
Composite cofactor 235089819488596087295387233793131386382105303301089051036631344503098791738232356187656689122842975052128957602428239192437050778955177424652359127571338331931 has 159 digits

Mar 9, 2009 (6th)

By Serge Batalov / GMP-ECM 6.2.2 / Mar 9, 2009

(46·10¹⁶⁵+53)/9 = 5(1)₁₆₄7_<166> = 7 · 4253 · 4844406113_<10> · 4523158715685319_<16> · C136

C136 = P29 · C108

P29 = 10446812610506949093142876229_<29>

C108 = [749990434194342913627839994778316141735461561144432665049318858824500331417760967267346175218968089628592429_<108>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=143967436
Step 1 took 11117ms
********** Factor found in step 1: 10446812610506949093142876229
Found probable prime factor of 29 digits: 10446812610506949093142876229
Composite cofactor 749990434194342913627839994778316141735461561144432665049318858824500331417760967267346175218968089628592
429 has 108 digits

(46·10¹⁷⁰+53)/9 = 5(1)₁₆₉7_<171> = 11 · 19387 · 1665479 · 1794248597877849317_<19> · C141

C141 = P31 · C111

P31 = 5408617979271676407647398602101_<31>

C111 = [148287294893707759450826773884287490623864556110591552787817847024979548974477424569602377450628469980051583867_<111>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=79750547
Step 1 took 10712ms
Step 2 took 9745ms
********** Factor found in step 2: 5408617979271676407647398602101
Found probable prime factor of 31 digits: 5408617979271676407647398602101
Composite cofactor 148287294893707759450826773884287490623864556110591552787817847024979548974477424569602377450628469980051
583867 has 111 digits

(46·10¹⁶⁶+53)/9 = 5(1)₁₆₅7_<167> = 3 · 11 · 2929337 · C159

C159 = P29 · C131

P29 = 16036699817919812260473949319_<29>

C131 = [32969855616823691466101238160783310004651583931458204036145062340110338667916054195949780242413798330360782553087497224960254295683_<131>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3914349354
Step 1 took 12984ms
Step 2 took 11077ms
********** Factor found in step 2: 16036699817919812260473949319
Found probable prime factor of 29 digits: 16036699817919812260473949319
Composite cofactor has 131 digits

Mar 9, 2009 (5th)

By Max Dettweiler / GGNFS (sieving), msieve-140beta2 (postprocessing) / Mar 9, 2009

(46·10¹⁴⁵+53)/9 = 5(1)₁₄₄7_<146> = 3 · 19 · 47653 · 1435121 · 404405147141_<12> · C122

C122 = P55 · P68

P55 = 1301015403308368069679292029098359067832886330689235907_<55>

P68 = 24920834858529572925651828244003251158782838939266717456699645961551_<68>

Number: 51117_145
N=32422390014251090047405979420912278617048780624947206533054875806767396646879580371495665058985390191313647208718490611757
  ( 122 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1301015403308368069679292029098359067832886330689235907 (pp55)
 r2=24920834858529572925651828244003251158782838939266717456699645961551 (pp68)
Version: Msieve-1.40beta2
Total time: 7.75 hours.
Scaled time: 12.73 units (timescale=1.642).
Factorization parameters were as follows:
n: 32422390014251090047405979420912278617048780624947206533054875806767396646879580371495665058985390191313647208718490611757
m: 100000000000000000000000000000
deg: 5
c5: 46
c0: 53
skew: 1.03
type: snfs
lss: 1
rlim: 1950000
alim: 1950000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1950000/1950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [975000, 1975001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 279389 x 279637
Total sieving time: 7.75 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000
total time: 7.75 hours.
 --------- CPU info (if available) ----------
[    0.371537] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.13 BogoMIPS (lpj=8800276)
[    0.004000] Calibrating delay using timer specific routine.. 4400.40 BogoMIPS (lpj=8800811)
[    0.460049] Total of 2 processors activated (8800.54 BogoMIPS).

Mar 9, 2009 (4th)

By Sinkiti Sibata / GGNFS / Mar 9, 2009

(46·10¹⁴²+17)/9 = 5(1)₁₄₁3_<143> = 199 · 373 · 8836327 · 30944437944034327607351_<23> · C109

C109 = P46 · P63

P46 = 3253898913398857863840646050922281096920564879_<46>

P63 = 773918056022581270276301143282161876126995043437065725389072093_<63>

Number: 51113_142
N=2518251121551633601419087702525546323870542114736815313608600828242439007408590192176793239962892307214821747
  ( 109 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=3253898913398857863840646050922281096920564879 (pp46)
 r2=773918056022581270276301143282161876126995043437065725389072093 (pp63)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 15.98 hours.
Scaled time: 7.53 units (timescale=0.471).
Factorization parameters were as follows:
name: 51113_142
n: 2518251121551633601419087702525546323870542114736815313608600828242439007408590192176793239962892307214821747
m: 20000000000000000000000000000
deg: 5
c5: 575
c0: 68
skew: 0.65
type: snfs
lss: 1
rlim: 1780000
alim: 1780000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1780000/1780000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [890000, 2090001)
Primes: RFBsize:133671, AFBsize:133292, largePrimes:3844978 encountered
Relations: rels:3887227, finalFF:322419
Max relations in full relation-set: 28
Initial matrix: 267030 x 322419 with sparse part having weight 29853912.
Pruned matrix : 247373 x 248772 with weight 20147298.
Total sieving time: 14.09 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 1.62 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1780000,1780000,26,26,49,49,2.3,2.3,100000
total time: 15.98 hours.
 --------- CPU info (if available) ----------

Mar 9, 2009 (3rd)

By Robert Backstrom / GMP-ECM / Mar 9, 2009

(14·10²⁰⁴-17)/3 = 4(6)₂₀₃1_<205> = 47 · 22571 · 24527 · 116818569354037_<15> · 278275966685165104601346551_<27> · 10382326534732513036533810389_<29> · C126

C126 = P41 · P86

P41 = 49351688284424227009747656018018277788269_<41>

P86 = 10767860236981571264712003983278864892088044356372016005085807037138655167068407215317_<86>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 531412081905760891258313848288852999676582475963092517114464340668350919020889228921749982581663250527798455996226636019716273 (126 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=3154146542
Step 1 took 38963ms
Step 2 took 15980ms
********** Factor found in step 2: 49351688284424227009747656018018277788269
Found probable prime factor of 41 digits: 49351688284424227009747656018018277788269
Probable prime cofactor 10767860236981571264712003983278864892088044356372016005085807037138655167068407215317 has 86 digits

(46·10¹⁵¹+53)/9 = 5(1)₁₅₀7_<152> = 3² · 29 · 3639913 · 523471288572563_<15> · 926549273118053965459_<21> · C108

C108 = P35 · P73

P35 = 32146023557560743005476615795064849_<35>

P73 = 3450604360129407926878446661028474159406037561413177599498500341434877193_<73>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 110923209048541761045506758771335276930568084266286353957676501456575706096911007045699418647710773786088857 (108 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=3172833204
Step 1 took 31683ms
Step 2 took 13907ms
********** Factor found in step 2: 32146023557560743005476615795064849
Found probable prime factor of 35 digits: 32146023557560743005476615795064849
Probable prime cofactor 3450604360129407926878446661028474159406037561413177599498500341434877193 has 73 digits

(46·10¹⁵³+17)/9 = 5(1)₁₅₂3_<154> = 937 · 6301 · 1168853512068217384515790254569897_<34> · C114

C114 = P45 · P70

P45 = 196490224292758436049630492490170845480502019_<45>

P70 = 3769339166967671013328223086443654127269835499673885309638515657941743_<70>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 740638298352956917629241927420886535153044207773338129179800117727688945646884036097074009882338060886955895879117 (114 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=1271141060
Step 1 took 31279ms
Step 2 took 14671ms
********** Factor found in step 2: 196490224292758436049630492490170845480502019
Found probable prime factor of 45 digits: 196490224292758436049630492490170845480502019
Probable prime cofactor 3769339166967671013328223086443654127269835499673885309638515657941743 has 70 digits

(46·10¹⁵⁵+53)/9 = 5(1)₁₅₄7_<156> = 8694331 · 120263232533603_<15> · C135

C135 = P40 · P95

P40 = 6101604350504945071703086087387533827909_<40>

P95 = 80112859990158471449995653126153528876347931825122100676739917892233937272907061694672355442841_<95>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 488816975047344480420714150543104820075654662965054212542775479303930556384979153820933164864013988575435626337025233349492623580049469 (135 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=2831832470
Step 1 took 39028ms
Step 2 took 16267ms
********** Factor found in step 2: 6101604350504945071703086087387533827909
Found probable prime factor of 40 digits: 6101604350504945071703086087387533827909
Probable prime cofactor 80112859990158471449995653126153528876347931825122100676739917892233937272907061694672355442841 has 95 digits

Mar 9, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Mar 9, 2009

(46·10¹⁴⁹+17)/9 = 5(1)₁₄₈3_<150> = 3 · 182809683463050359_<18> · C132

C132 = P66 · P67

P66 = 196402249692752872132715270377448801991427612454686894648603854373_<66>

P67 = 4745133252295663327826221303086537424769467238293624817207646507953_<67>

Number: 51113_149
N=931954845842757379712167151150040856218413162686610932846537310731272241905042886757291832003286399733437061941542968128409598328469
  ( 132 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=196402249692752872132715270377448801991427612454686894648603854373 (pp66)
 r2=4745133252295663327826221303086537424769467238293624817207646507953 (pp67)
Version: Msieve-1.39
Total time: 13.09 hours.
Scaled time: 33.66 units (timescale=2.571).
Factorization parameters were as follows:
n: 931954845842757379712167151150040856218413162686610932846537310731272241905042886757291832003286399733437061941542968128409598328469
m: 1000000000000000000000000000000
deg: 5
c5: 23
c0: 85
skew: 1.30
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 357966 x 358214
Total sieving time: 13.09 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 13.09 hours.
 --------- CPU info (if available) ----------

(46·10¹⁰¹+53)/9 = 5(1)₁₀₀7_<102> = 131 · C100

C100 = P46 · P55

P46 = 1051366045249180782192749418420461357285312957_<46>

P55 = 3710992525229035182238005631475257690538237143563716251_<55>

Number: 51117_101
N=3901611535199321458863443596268023748939779474130619168787107718405428329092451229855810008481764207
  ( 100 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=1051366045249180782192749418420461357285312957 (pp46)
 r2=3710992525229035182238005631475257690538237143563716251 (pp55)
Version: Msieve-1.39
Total time: 0.31 hours.
Scaled time: 0.36 units (timescale=1.187).
Factorization parameters were as follows:
n: 3901611535199321458863443596268023748939779474130619168787107718405428329092451229855810008481764207
m: 20000000000000000000000000
deg: 4
c4: 115
c0: 212
skew: 1.17
type: snfs
lss: 1
rlim: 370000
alim: 370000
lpbr: 25
lpba: 25
mfbr: 43
mfba: 43
rlambda: 2.2
alambda: 2.2Factor base limits: 370000/370000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [185000, 245001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 39096 x 39344
Total sieving time: 0.31 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103,4,0,0,0,0,0,0,0,0,370000,370000,25,25,43,43,2.2,2.2,10000
total time: 0.31 hours.
 --------- CPU info (if available) ----------

(46·10¹⁰⁵+53)/9 = 5(1)₁₀₄7_<106> = 7 · C105

C105 = P42 · P64

P42 = 162116180279236321466962628363259874093861_<42>

P64 = 4503922612172772491525277627009783736239098637189147106166898671_<64>

Number: 51117_105
N=730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158731
  ( 105 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=162116180279236321466962628363259874093861 (pp42)
 r2=4503922612172772491525277627009783736239098637189147106166898671 (pp64)
Version: Msieve-1.39
Total time: 0.48 hours.
Scaled time: 0.57 units (timescale=1.185).
Factorization parameters were as follows:
n: 730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158731
m: 200000000000000000000000000
deg: 4
c4: 115
c0: 212
skew: 1.17
type: snfs
lss: 1
rlim: 430000
alim: 430000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 430000/430000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [215000, 315001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 42475 x 42706
Total sieving time: 0.48 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107,4,0,0,0,0,0,0,0,0,430000,430000,25,25,44,44,2.2,2.2,20000
total time: 0.48 hours.
 --------- CPU info (if available) ----------

(46·10¹¹⁷+53)/9 = 5(1)₁₁₆7_<118> = 7² · 197807 · 13400317261_<11> · C101

C101 = P29 · P73

P29 = 37154143007493125814082790629_<29>

P73 = 1059144601138791998487927996098498231586938131803254324761721580375436051_<73>

Number: 51117_117
N=39351609976324944510715763909123822322422147274612099562749814149650216428995341890016476920811566079
  ( 101 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=37154143007493125814082790629 (pp29)
 r2=1059144601138791998487927996098498231586938131803254324761721580375436051 (pp73)
Version: Msieve-1.39
Total time: 1.18 hours.
Scaled time: 1.41 units (timescale=1.194).
Factorization parameters were as follows:
n: 39351609976324944510715763909123822322422147274612099562749814149650216428995341890016476920811566079
m: 200000000000000000000000
deg: 5
c5: 575
c0: 212
skew: 0.82
type: snfs
lss: 1
rlim: 680000
alim: 680000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 680000/680000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [340000, 590001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 72296 x 72542
Total sieving time: 1.18 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,680000,680000,25,25,45,45,2.2,2.2,50000
total time: 1.18 hours.
 --------- CPU info (if available) ----------

(46·10¹¹⁹+53)/9 = 5(1)₁₁₈7_<120> = 44004769 · C113

C113 = P34 · P79

P34 = 2299987638111194800868753964704987_<34>

P79 = 5049984846279583185486306417912232813427855410859885830255590638230699819958039_<79>

Number: 51117_119
N=11614902719091903677783449132777202196223575474538023619919720771880682094050104231000760647354179068889354040493
  ( 113 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=2299987638111194800868753964704987 (pp34)
 r2=5049984846279583185486306417912232813427855410859885830255590638230699819958039 (pp79)
Version: Msieve-1.39
Total time: 0.99 hours.
Scaled time: 1.18 units (timescale=1.197).
Factorization parameters were as follows:
n: 11614902719091903677783449132777202196223575474538023619919720771880682094050104231000760647354179068889354040493
m: 1000000000000000000000000
deg: 5
c5: 23
c0: 265
skew: 1.63
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 570001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 76768 x 77005
Total sieving time: 0.99 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 0.99 hours.
 --------- CPU info (if available) ----------

(46·10¹²³+53)/9 = 5(1)₁₂₂7_<124> = 7 · 29 · 1447 · C119

C119 = P43 · P76

P43 = 4381846120736352361081456772199148603930499_<43>

P76 = 3970942797979298014223135734108633716505660790785836094432416623786964706763_<76>

Number: 51117_123
N=17400060294991543948958814435543935341375943811422685669045557518736271446992796753300053826708260376015302974767264737
  ( 119 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=4381846120736352361081456772199148603930499 (pp43)
 r2=3970942797979298014223135734108633716505660790785836094432416623786964706763 (pp76)
Version: Msieve-1.39
Total time: 1.61 hours.
Scaled time: 1.94 units (timescale=1.202).
Factorization parameters were as follows:
n: 17400060294991543948958814435543935341375943811422685669045557518736271446992796753300053826708260376015302974767264737
m: 5000000000000000000000000
deg: 5
c5: 368
c0: 1325
skew: 1.29
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 740001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 111404 x 111652
Total sieving time: 1.61 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 1.61 hours.
 --------- CPU info (if available) ----------

(46·10¹²⁶+53)/9 = 5(1)₁₂₅7_<127> = 11 · 29303 · 1095503 · C116

C116 = P29 · P34 · P54

P29 = 22951036736328310483109547343_<29>

P34 = 2309389485245674100787978593428487_<34>

P54 = 273084775309771947450739812234858862933212157629549863_<54>

Number: 51117_126
N=14474280371439186954052991391897505152047200545966590968214180692694363767671954878797501982661887134634256255224383
  ( 116 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=22951036736328310483109547343 (pp29)
 r2=2309389485245674100787978593428487 (pp34)
 r3=273084775309771947450739812234858862933212157629549863 (pp54)
Version: Msieve-1.39
Total time: 2.36 hours.
Scaled time: 2.82 units (timescale=1.193).
Factorization parameters were as follows:
n: 14474280371439186954052991391897505152047200545966590968214180692694363767671954878797501982661887134634256255224383
m: 20000000000000000000000000
deg: 5
c5: 115
c0: 424
skew: 1.30
type: snfs
lss: 1
rlim: 970000
alim: 970000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 970000/970000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [485000, 835001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 137624 x 137872
Total sieving time: 2.36 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,970000,970000,26,26,47,47,2.3,2.3,50000
total time: 2.36 hours.
 --------- CPU info (if available) ----------

(46·10¹²⁷+53)/9 = 5(1)₁₂₆7_<128> = 3 · 19 · 1920011 · 46326801803_<11> · C110

C110 = P38 · P72

P38 = 91721246203875859269650966930388504827_<38>

P72 = 109909310516648039879605703572736508047398488711402133692683632228955591_<72>

Number: 51117_127
N=10081018929995717084531629906985375658680279384835188006477904963900095345058949423977762182884447646272137757
  ( 110 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=91721246203875859269650966930388504827 (pp38)
 r2=109909310516648039879605703572736508047398488711402133692683632228955591 (pp72)
Version: Msieve-1.39
Total time: 1.89 hours.
Scaled time: 2.25 units (timescale=1.192).
Factorization parameters were as follows:
n: 10081018929995717084531629906985375658680279384835188006477904963900095345058949423977762182884447646272137757
m: 20000000000000000000000000
deg: 5
c5: 575
c0: 212
skew: 0.82
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 148735 x 148983
Total sieving time: 1.89 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 1.89 hours.
 --------- CPU info (if available) ----------

(46·10¹³²+53)/9 = 5(1)₁₃₁7_<133> = 11 · 10508293 · 348100629696191_<15> · C111

C111 = P32 · P79

P32 = 16249156839947455989159436879759_<32>

P79 = 7817264810862193227507798014636507921023443527299739490009654804228203145655691_<79>

Number: 51117_132
N=127023961971101962933194516572132634935878613282066905551848043549985581772021811459751701479613930969181058469
  ( 111 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=16249156839947455989159436879759 (pp32)
 r2=7817264810862193227507798014636507921023443527299739490009654804228203145655691 (pp79)
Version: Msieve-1.39
Total time: 2.84 hours.
Scaled time: 3.40 units (timescale=1.195).
Factorization parameters were as follows:
n: 127023961971101962933194516572132634935878613282066905551848043549985581772021811459751701479613930969181058469
m: 200000000000000000000000000
deg: 5
c5: 575
c0: 212
skew: 0.82
type: snfs
lss: 1
rlim: 1210000
alim: 1210000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1210000/1210000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [605000, 1130001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 176344 x 176592
Total sieving time: 2.84 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1210000,1210000,26,26,47,47,2.3,2.3,75000
total time: 2.84 hours.
 --------- CPU info (if available) ----------

(46·10¹³³+53)/9 = 5(1)₁₃₂7_<134> = 3⁷ · 659 · 7691 · 14851 · 337078854520259_<15> · C105

C105 = P42 · P64

P42 = 284006308075259780796263372870612103890893_<42>

P64 = 3243270108864037332056686357910502399618877853861850651186350747_<64>

Number: 51117_133
N=921109169709321114107770234761017212288149670987861927693816180198512855050548520942752864928652517047071
  ( 105 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=284006308075259780796263372870612103890893 (pp42)
 r2=3243270108864037332056686357910502399618877853861850651186350747 (pp64)
Version: Msieve-1.39
Total time: 3.32 hours.
Scaled time: 3.97 units (timescale=1.198).
Factorization parameters were as follows:
n: 921109169709321114107770234761017212288149670987861927693816180198512855050548520942752864928652517047071
m: 500000000000000000000000000
deg: 5
c5: 368
c0: 1325
skew: 1.29
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 188774 x 189022
Total sieving time: 3.32 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 3.32 hours.
 --------- CPU info (if available) ----------

(46·10¹⁵¹+17)/9 = 5(1)₁₅₀3_<152> = 9883 · 18356749 · C141

C141 = P64 · P77

P64 = 8172175016707545457583974190335930691504416901869276777808732983_<64>

P77 = 34474112793907433702099859827871212701283307072048202180063531357502611064033_<77>

Number: 51113_151
N=281728483297528288628543635323252275165617448625794641793103989907614506221161628367059228669427524783995179771689025780827272937745212100439
  ( 141 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=8172175016707545457583974190335930691504416901869276777808732983 (pp64)
 r2=34474112793907433702099859827871212701283307072048202180063531357502611064033 (pp77)
Version: Msieve-1.39
Total time: 18.05 hours.
Scaled time: 46.41 units (timescale=2.571).
Factorization parameters were as follows:
n: 281728483297528288628543635323252275165617448625794641793103989907614506221161628367059228669427524783995179771689025780827272937745212100439
m: 2000000000000000000000000000000
deg: 5
c5: 115
c0: 136
skew: 1.03
type: snfs
lss: 1
rlim: 2500000
alim: 2500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1250000, 2250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 484060 x 484308
Total sieving time: 18.05 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000
total time: 18.05 hours.
 --------- CPU info (if available) ----------

(46·10¹⁴⁰+53)/9 = 5(1)₁₃₉7_<141> = 11 · 47 · 107 · 3793 · 331307 · 35317276157668117_<17> · C111

C111 = P55 · P56

P55 = 5098238417384787350273120921414830381099413431566691293_<55>

P56 = 40833838266530485664218230832533871115304766142842709953_<56>

Number: 51117_140
N=208180642979702751743044581507404564446557630316631281934749627910209055736595897807415521997315736741889539229
  ( 111 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=5098238417384787350273120921414830381099413431566691293 (pp55)
 r2=40833838266530485664218230832533871115304766142842709953 (pp56)
Version: Msieve-1.39
Total time: 4.18 hours.
Scaled time: 5.02 units (timescale=1.201).
Factorization parameters were as follows:
n: 208180642979702751743044581507404564446557630316631281934749627910209055736595897807415521997315736741889539229
m: 10000000000000000000000000000
deg: 5
c5: 46
c0: 53
skew: 1.03
type: snfs
lss: 1
rlim: 1610000
alim: 1610000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1610000/1610000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [805000, 1505001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 211578 x 211826
Total sieving time: 4.18 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000
total time: 4.18 hours.
 --------- CPU info (if available) ----------

(46·10¹⁵⁹+53)/9 = 5(1)₁₅₈7_<160> = 7² · 11497 · C154

C154 = P63 · P92

P63 = 146206979062345930258847590663260807771848228702899166301406463_<63>

P92 = 62053546445206031125688035764078006914277054585201952605461595095457720445664741389665548203_<92>

Number: 51117_159
N=9072661565858548922453792047102103141566852597059234815668170953400640648245613516056737269724508631552705161969690604489744638106322520890296334822235989
  ( 154 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=146206979062345930258847590663260807771848228702899166301406463 (pp63)
 r2=62053546445206031125688035764078006914277054585201952605461595095457720445664741389665548203 (pp92)
Version: Msieve-1.39
Total time: 22.23 hours.
Scaled time: 57.14 units (timescale=2.571).
Factorization parameters were as follows:
n: 9072661565858548922453792047102103141566852597059234815668170953400640648245613516056737269724508631552705161969690604489744638106322520890296334822235989
m: 100000000000000000000000000000000
deg: 5
c5: 23
c0: 265
skew: 1.63
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 585594 x 585842
Total sieving time: 22.23 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 22.23 hours.
 --------- CPU info (if available) ----------

(13·10¹⁶⁶+11)/3 = 4(3)₁₆₅7_<167> = 7 · 7039 · 1594049 · 195875087561731_<15> · 30727426106161913_<17> · C125

C125 = P59 · P67

P59 = 30522543014935933535828931337221102964882591495905606382609_<59>

P67 = 3003207391500507654404750316309514446820381495431181608193686383603_<67>

Number: 43337_166
N=91665526789847785397159889897757673029427981309456458068846002562248947844791517560634814045955028451056130736972331961960227
  ( 125 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=30522543014935933535828931337221102964882591495905606382609 (pp59)
 r2=3003207391500507654404750316309514446820381495431181608193686383603 (pp67)
Version: Msieve-1.39
Total time: 39.29 hours.
Scaled time: 68.33 units (timescale=1.739).
Factorization parameters were as follows:
n: 91665526789847785397159889897757673029427981309456458068846002562248947844791517560634814045955028451056130736972331961960227
m: 1000000000000000000000000000000000
deg: 5
c5: 130
c0: 11
skew: 0.61
type: snfs
lss: 1
rlim: 4300000
alim: 4300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4300000/4300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2150000, 4350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 765171 x 765419
Total sieving time: 39.29 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,4300000,4300000,27,27,51,51,2.4,2.4,100000
total time: 39.29 hours.
 --------- CPU info (if available) ----------

(46·10¹⁶⁰+53)/9 = 5(1)₁₅₉7_<161> = 3³ · 11 · 229 · C156

C156 = P31 · P49 · P77

P31 = 3497829786460425219596265083453_<31>

P49 = 3711630603234302531527368993031032123750398751737_<49>

P77 = 57884191535844480051940302137313331900332209124470821556366740038336486224669_<77>

Number: 51117_160
N=751490319661110539324998325483526842090646069297209520402145341495171674696177364784836885758768340039567599004765428831416216180893521990077060431257423009
  ( 156 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=3497829786460425219596265083453 (pp31)
 r2=3711630603234302531527368993031032123750398751737 (pp49)
 r3=57884191535844480051940302137313331900332209124470821556366740038336486224669 (pp77)
Version: Msieve-1.39
Total time: 22.23 hours.
Scaled time: 57.16 units (timescale=2.571).
Factorization parameters were as follows:
n: 751490319661110539324998325483526842090646069297209520402145341495171674696177364784836885758768340039567599004765428831416216180893521990077060431257423009
m: 100000000000000000000000000000000
deg: 5
c5: 46
c0: 53
skew: 1.03
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 2850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 637029 x 637277
Total sieving time: 22.23 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 22.23 hours.
 --------- CPU info (if available) ----------

Mar 9, 2009

By Serge Batalov / PFGW / Mar 9, 2009

(19·10⁵³⁰⁴⁹-1)/9 = 2(1)₅₃₀₄₉_<53050> is PRP.

Mar 8, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Mar 8, 2009

4·10¹⁷⁸+1 = 4(0)₁₇₇1_<179> = 13 · 566167021042476149422414249581680453_<36> · C142

C142 = P67 · P75

P67 = 6061095723787709816177996585617442722607441719998843595973408858077_<67>

P75 = 896645819043518706309661143084647289327440781070529452934200366627156144117_<75>

Number: 40001_178
N=5434656139556799894979519578367289662179199394390968777423929565472413299191034750588773051949376501146939751768504380636817182877903411483009
  ( 142 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=6061095723787709816177996585617442722607441719998843595973408858077
 r2=896645819043518706309661143084647289327440781070529452934200366627156144117
Version: 
Total time: 59.57 hours.
Scaled time: 142.08 units (timescale=2.385).
Factorization parameters were as follows:
n: 5434656139556799894979519578367289662179199394390968777423929565472413299191034750588773051949376501146939751768504380636817182877903411483009
m: 1000000000000000000000000000000000000
deg: 5
c5: 1
c0: 25
skew: 1.90
type: snfs
lss: 1
rlim: 5200000
alim: 5200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 5200000/5200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [2600000, 4200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 17171844
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1152624 x 1152872
Total sieving time: 54.31 hours.
Total relation processing time: 1.46 hours.
Matrix solve time: 3.25 hours.
Time per square root: 0.55 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,53,53,2.5,2.5,100000
total time: 59.57 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Mar 8, 2009 (6th)

By Robert Backstrom / GMP-ECM / Mar 8, 2009

(44·10¹³²-53)/9 = 4(8)₁₃₁3_<133> = C133

C133 = P46 · P88

P46 = 1110220553312655297808882682723776743181104103_<46>

P88 = 4403529437733352862117465895923540771817098994724462891230371415746741912312872108706261_<88>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 4888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883 (133 digits)
Using B1=20000000, B2=59950304286, polynomial Dickson(12), sigma=2504866877
Step 1 took 257030ms
Step 2 took 84305ms
********** Factor found in step 2: 1110220553312655297808882682723776743181104103
Found probable prime factor of 46 digits: 1110220553312655297808882682723776743181104103
Probable prime cofactor 4403529437733352862117465895923540771817098994724462891230371415746741912312872108706261 has 88 digits

Mar 8, 2009 (5th)

By Sinkiti Sibata / GGNFS / Mar 8, 2009

(44·10¹⁵⁴+1)/9 = 4(8)₁₅₃9_<155> = 113 · 2099 · 13442499459349_<14> · C137

C137 = P31 · P106

P31 = 8332570143318425779243813301039_<31>

P106 = 1840179884800480883378157296911883995857869467338990022378628791144496792021799871577494763177951771934377_<106>

Number: 48889_154
N=15333427966423627234645482187688620560689563067187928456403538018817446826320562875885755637186001325087230224620697300802742730853917703
  ( 137 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=8332570143318425779243813301039 (pp31)
 r2=1840179884800480883378157296911883995857869467338990022378628791144496792021799871577494763177951771934377 (pp106)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 46.89 hours.
Scaled time: 22.13 units (timescale=0.472).
Factorization parameters were as follows:
name: 48889_154
n: 15333427966423627234645482187688620560689563067187928456403538018817446826320562875885755637186001325087230224620697300802742730853917703
m: 10000000000000000000000000000000
deg: 5
c5: 22
c0: 5
skew: 0.74
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2500001)
Primes: RFBsize:203362, AFBsize:203168, largePrimes:8086929 encountered
Relations: rels:8238652, finalFF:570345
Max relations in full relation-set: 28
Initial matrix: 406596 x 570345 with sparse part having weight 62465658.
Pruned matrix : 347207 x 349303 with weight 35844249.
Total sieving time: 41.39 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 4.99 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 46.89 hours.
 --------- CPU info (if available) ----------

Mar 8, 2009 (4th)

By Max Dettweiler / GGNFS (sieving), msieve v1.40beta2 (postprocessing) / Mar 8, 2009

(46·10¹⁵⁰+17)/9 = 5(1)₁₄₉3_<151> = 7 · 13597 · 93765122431_<11> · 12927026782792133527436421144607_<32> · C104

C104 = P42 · P63

P42 = 215277725831553129790685239591654012757177_<42>

P63 = 205795139875606871141235190127379148672452160595173895881524083_<63>

Sat Mar  7 17:47:25 2009  Msieve v. 1.40
Sat Mar  7 17:47:25 2009  random seeds: 5be9bc6a a4db309b
Sat Mar  7 17:47:25 2009  factoring 44303109699607022872926009371300736105651392884345897886736800768893549967713945190056822343455756593691 (104 digits)
Sat Mar  7 17:47:26 2009  no P-1/P+1/ECM available, skipping
Sat Mar  7 17:47:26 2009  commencing number field sieve (104-digit input)
Sat Mar  7 17:47:26 2009  R0: -205803718671706643940
Sat Mar  7 17:47:26 2009  R1:  45109791671
Sat Mar  7 17:47:26 2009  A0: -16910212684373235259751719
Sat Mar  7 17:47:26 2009  A1: -671274074771843691581
Sat Mar  7 17:47:26 2009  A2:  68600220111545809
Sat Mar  7 17:47:26 2009  A3:  630091046276
Sat Mar  7 17:47:26 2009  A4: -16543905
Sat Mar  7 17:47:26 2009  A5:  120
Sat Mar  7 17:47:26 2009  skew 49338.29, size 6.783315e-10, alpha -4.664099, combined = 2.157279e-09
Sat Mar  7 17:47:26 2009  
Sat Mar  7 17:47:26 2009  commencing relation filtering
Sat Mar  7 17:47:26 2009  commencing duplicate removal, pass 1
Sat Mar  7 17:48:04 2009  found 350324 hash collisions in 4485313 relations
Sat Mar  7 17:48:21 2009  added 608 free relations
Sat Mar  7 17:48:21 2009  commencing duplicate removal, pass 2
Sat Mar  7 17:48:25 2009  found 333640 duplicates and 4152281 unique relations
Sat Mar  7 17:48:25 2009  memory use: 40.3 MB
Sat Mar  7 17:48:25 2009  reading rational ideals above 1638400
Sat Mar  7 17:48:25 2009  reading algebraic ideals above 1638400
Sat Mar  7 17:48:25 2009  commencing singleton removal, pass 1
Sat Mar  7 17:49:00 2009  relations with 0 large ideals: 46830
Sat Mar  7 17:49:00 2009  relations with 1 large ideals: 383631
Sat Mar  7 17:49:00 2009  relations with 2 large ideals: 1185742
Sat Mar  7 17:49:00 2009  relations with 3 large ideals: 1588216
Sat Mar  7 17:49:00 2009  relations with 4 large ideals: 815270
Sat Mar  7 17:49:00 2009  relations with 5 large ideals: 98913
Sat Mar  7 17:49:00 2009  relations with 6 large ideals: 33676
Sat Mar  7 17:49:00 2009  relations with 7+ large ideals: 3
Sat Mar  7 17:49:00 2009  4152281 relations and about 4324405 large ideals
Sat Mar  7 17:49:00 2009  commencing singleton removal, pass 2
Sat Mar  7 17:49:38 2009  found 1958944 singletons
Sat Mar  7 17:49:38 2009  current dataset: 2193337 relations and about 1929600 large ideals
Sat Mar  7 17:49:38 2009  commencing singleton removal, pass 3
Sat Mar  7 17:49:58 2009  found 473190 singletons
Sat Mar  7 17:49:58 2009  current dataset: 1720147 relations and about 1414479 large ideals
Sat Mar  7 17:49:58 2009  commencing singleton removal, final pass
Sat Mar  7 17:50:17 2009  memory use: 33.3 MB
Sat Mar  7 17:50:17 2009  commencing in-memory singleton removal
Sat Mar  7 17:50:17 2009  begin with 1720147 relations and 1452587 unique ideals
Sat Mar  7 17:50:19 2009  reduce to 1355162 relations and 1074705 ideals in 15 passes
Sat Mar  7 17:50:19 2009  max relations containing the same ideal: 53
Sat Mar  7 17:50:20 2009  reading rational ideals above 720000
Sat Mar  7 17:50:20 2009  reading algebraic ideals above 720000
Sat Mar  7 17:50:20 2009  commencing singleton removal, final pass
Sat Mar  7 17:50:36 2009  keeping 1159198 ideals with weight <= 20, new excess is 167390
Sat Mar  7 17:50:37 2009  memory use: 33.9 MB
Sat Mar  7 17:50:37 2009  commencing in-memory singleton removal
Sat Mar  7 17:50:37 2009  begin with 1355770 relations and 1159198 unique ideals
Sat Mar  7 17:50:38 2009  reduce to 1352754 relations and 1153168 ideals in 10 passes
Sat Mar  7 17:50:38 2009  max relations containing the same ideal: 20
Sat Mar  7 17:50:39 2009  relations with 0 large ideals: 20819
Sat Mar  7 17:50:39 2009  relations with 1 large ideals: 135377
Sat Mar  7 17:50:39 2009  relations with 2 large ideals: 361336
Sat Mar  7 17:50:39 2009  relations with 3 large ideals: 468155
Sat Mar  7 17:50:39 2009  relations with 4 large ideals: 285605
Sat Mar  7 17:50:39 2009  relations with 5 large ideals: 71003
Sat Mar  7 17:50:39 2009  relations with 6 large ideals: 10069
Sat Mar  7 17:50:39 2009  relations with 7+ large ideals: 390
Sat Mar  7 17:50:39 2009  commencing 2-way merge
Sat Mar  7 17:50:40 2009  reduce to 747235 relation sets and 547805 unique ideals
Sat Mar  7 17:50:40 2009  ignored 156 oversize relation sets
Sat Mar  7 17:50:40 2009  commencing full merge
Sat Mar  7 17:50:48 2009  memory use: 34.0 MB
Sat Mar  7 17:50:48 2009  found 311219 cycles, need 292005
Sat Mar  7 17:50:48 2009  weight of 292005 cycles is about 20642731 (70.69/cycle)
Sat Mar  7 17:50:48 2009  distribution of cycle lengths:
Sat Mar  7 17:50:48 2009  1 relations: 35474
Sat Mar  7 17:50:48 2009  2 relations: 29215
Sat Mar  7 17:50:48 2009  3 relations: 29093
Sat Mar  7 17:50:48 2009  4 relations: 26887
Sat Mar  7 17:50:48 2009  5 relations: 24684
Sat Mar  7 17:50:48 2009  6 relations: 21474
Sat Mar  7 17:50:48 2009  7 relations: 19536
Sat Mar  7 17:50:48 2009  8 relations: 16873
Sat Mar  7 17:50:48 2009  9 relations: 14629
Sat Mar  7 17:50:48 2009  10+ relations: 74140
Sat Mar  7 17:50:48 2009  heaviest cycle: 21 relations
Sat Mar  7 17:50:48 2009  commencing cycle optimization
Sat Mar  7 17:50:49 2009  start with 1939747 relations
Sat Mar  7 17:50:53 2009  pruned 57961 relations
Sat Mar  7 17:50:53 2009  memory use: 50.5 MB
Sat Mar  7 17:50:53 2009  distribution of cycle lengths:
Sat Mar  7 17:50:53 2009  1 relations: 35474
Sat Mar  7 17:50:53 2009  2 relations: 30041
Sat Mar  7 17:50:53 2009  3 relations: 30255
Sat Mar  7 17:50:53 2009  4 relations: 27709
Sat Mar  7 17:50:53 2009  5 relations: 25469
Sat Mar  7 17:50:53 2009  6 relations: 22072
Sat Mar  7 17:50:53 2009  7 relations: 19928
Sat Mar  7 17:50:53 2009  8 relations: 16959
Sat Mar  7 17:50:53 2009  9 relations: 14701
Sat Mar  7 17:50:53 2009  10+ relations: 69397
Sat Mar  7 17:50:53 2009  heaviest cycle: 21 relations
Sat Mar  7 17:50:53 2009  RelProcTime: 191
Sat Mar  7 17:50:53 2009  
Sat Mar  7 17:50:53 2009  commencing linear algebra
Sat Mar  7 17:50:54 2009  read 292005 cycles
Sat Mar  7 17:50:54 2009  cycles contain 1060412 unique relations
Sat Mar  7 17:51:04 2009  read 1060412 relations
Sat Mar  7 17:51:05 2009  using 20 quadratic characters above 67107098
Sat Mar  7 17:51:12 2009  building initial matrix
Sat Mar  7 17:51:34 2009  memory use: 114.4 MB
Sat Mar  7 17:51:34 2009  read 292005 cycles
Sat Mar  7 17:51:36 2009  matrix is 291468 x 292005 (82.3 MB) with weight 27886129 (95.50/col)
Sat Mar  7 17:51:36 2009  sparse part has weight 19524201 (66.86/col)
Sat Mar  7 17:51:43 2009  filtering completed in 3 passes
Sat Mar  7 17:51:43 2009  matrix is 287466 x 287666 (81.2 MB) with weight 27492798 (95.57/col)
Sat Mar  7 17:51:43 2009  sparse part has weight 19277016 (67.01/col)
Sat Mar  7 17:51:47 2009  read 287666 cycles
Sat Mar  7 17:51:47 2009  matrix is 287466 x 287666 (81.2 MB) with weight 27492798 (95.57/col)
Sat Mar  7 17:51:47 2009  sparse part has weight 19277016 (67.01/col)
Sat Mar  7 17:51:47 2009  saving the first 48 matrix rows for later
Sat Mar  7 17:51:47 2009  matrix is 287418 x 287666 (78.4 MB) with weight 21745986 (75.59/col)
Sat Mar  7 17:51:47 2009  sparse part has weight 18816033 (65.41/col)
Sat Mar  7 17:51:47 2009  matrix includes 64 packed rows
Sat Mar  7 17:51:47 2009  using block size 65536 for processor cache size 2048 kB
Sat Mar  7 17:51:49 2009  commencing Lanczos iteration
Sat Mar  7 17:51:49 2009  memory use: 76.1 MB
Sat Mar  7 18:04:53 2009  lanczos halted after 4547 iterations (dim = 287417)
Sat Mar  7 18:04:54 2009  recovered 33 nontrivial dependencies
Sat Mar  7 18:04:54 2009  BLanczosTime: 819
Sat Mar  7 18:04:54 2009  
Sat Mar  7 18:04:54 2009  commencing square root phase
Sat Mar  7 18:04:54 2009  reading relations for dependency 1
Sat Mar  7 18:04:54 2009  read 144047 cycles
Sat Mar  7 18:04:55 2009  cycles contain 647455 unique relations
Sat Mar  7 18:05:01 2009  read 647455 relations
Sat Mar  7 18:05:04 2009  multiplying 527798 relations
Sat Mar  7 18:05:53 2009  multiply complete, coefficients have about 18.48 million bits
Sat Mar  7 18:05:54 2009  initial square root is modulo 204107
Sat Mar  7 18:07:25 2009  sqrtTime: 137
Sat Mar  7 18:07:25 2009  prp42 factor: 215277725831553129790685239591654012757177
Sat Mar  7 18:07:25 2009  prp63 factor: 205795139875606871141235190127379148672452160595173895881524083
Sat Mar  7 18:07:25 2009  elapsed time 00:20:00

Mar 8, 2009 (3rd)

By Tyler Cadigan / GGNFS, Msieve / Mar 8, 2009

(10¹⁹⁴+53)/9 = (1)₁₉₃7_<194> = 17 · 1329533 · C186

C186 = P74 · P113

P74 = 25299773945108783709147719647499992506518778128599196990273018706302023747_<74>

P113 = 19430895096918866733182687120277920415164945096409546688245140181892747950729635954281219412653480029348815900651_<113>

Number: 11117_194
N=491597253503169959195805688300332925882781712300976053073704699368394373907366726915351264254667355827024407690569064082744981137388803220693507158975949631810617231371559925933794759297
  ( 186 digits)
SNFS difficulty: 194 digits.
Divisors found:
 r1=25299773945108783709147719647499992506518778128599196990273018706302023747 (pp74)
 r2=19430895096918866733182687120277920415164945096409546688245140181892747950729635954281219412653480029348815900651 (pp113)
Version: Msieve-1.39
Total time: 499.32 hours.
Scaled time: 1277.26 units (timescale=2.558).
Factorization parameters were as follows:
n: 491597253503169959195805688300332925882781712300976053073704699368394373907366726915351264254667355827024407690569064082744981137388803220693507158975949631810617231371559925933794759297
m: 500000000000000000000000000000000000000
deg: 5
c5: 16
c0: 265
skew: 1.75
type: snfs
lss: 1
rlim: 12300000
alim: 12300000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 12300000/12300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6150000, 13150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1793514 x 1793762
Total sieving time: 499.32 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,194,5,0,0,0,0,0,0,0,0,12300000,12300000,28,28,55,55,2.5,2.5,100000
total time: 499.32 hours.
 --------- CPU info (if available) ----------

Mar 8, 2009 (2nd)

By Serge Batalov / GMP-ECM, Msieve / Mar 8, 2009

(46·10¹⁹⁶+17)/9 = 5(1)₁₉₅3_<197> = 53 · 34319 · 810389 · C185

C185 = P32 · C153

P32 = 46638014411653612788414145080653_<32>

C153 = [743483334775093414308085926936551688757350932685493179334475707140726021929978120094874282079886030617190668431423415363905819287792994902061667650047227_<153>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=213234464
Step 1 took 15805ms
Step 2 took 12860ms
********** Factor found in step 2: 46638014411653612788414145080653
Found probable prime factor of 32 digits: 46638014411653612788414145080653
Composite cofactor  has 153 digits

(46·10¹⁵³+17)/9 = 5(1)₁₅₂3_<154> = 937 · 6301 · C147

C147 = P34 · C114

P34 = 1168853512068217384515790254569897_<34>

C114 = [740638298352956917629241927420886535153044207773338129179800117727688945646884036097074009882338060886955895879117_<114>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3675542085
Step 1 took 10717ms
Step 2 took 10124ms
********** Factor found in step 2: 1168853512068217384515790254569897
Found probable prime factor of 34 digits: 1168853512068217384515790254569897
Composite cofactor  has 114 digits

(46·10¹⁸⁰+17)/9 = 5(1)₁₇₉3_<181> = 7 · 47 · 389 · 73665373 · C168

C168 = P34 · P134

P34 = 8104568488111348562614408845397543_<34>

P134 = 66892362423519288858149215229470409647792932927990440248147057831515216094067576405705120507840562693982861619178921972432842900479207_<134>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3582017823
Step 1 took 13133ms
Step 2 took 11373ms
********** Factor found in step 2: 8104568488111348562614408845397543
Found probable prime factor of 34 digits: 8104568488111348562614408845397543
Probable prime cofactor  has 134 digits

(44·10¹⁶⁶+1)/9 = 4(8)₁₆₅9_<167> = 47 · 59 · 587 · 296627 · C156

C156 = P55 · P101

P55 = 2937281513117464590091985435058991865462100989285797601_<55>

P101 = 34471957438172422129150819718021939069550799090932442883442048563826723794482089824148538350124767557_<101>

SNFS difficulty: 168 digits.
Divisors found:
 r1=2937281513117464590091985435058991865462100989285797601 (pp55)
 r2=34471957438172422129150819718021939069550799090932442883442048563826723794482089824148538350124767557 (pp101)
Version: Msieve-1.39
Total time: 30.00 hours.
Scaled time: x units (timescale=3.543).
Factorization parameters were as follows:
n: 101253843304115930376530093063534683573706849408114924995162372570713821635391260017879929438836832145342326795629939482980889279584171294606970491473230757
m: 2000000000000000000000000000000000
deg: 5
c5: 55
c0: 4
skew: 0.59
type: snfs
lss: 1
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2250000, 3850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 707238 x 707486
Total sieving time: 28.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.50 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000
total time: 30.00 hours.
 --------- CPU info (if available) ----------
[    0.295427] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 3.20GHz stepping 0b  * 4

Mar 8, 2009

Factorizations of 511...117 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 7, 2009 (5th)

By Robert Backstrom / GMP-ECM / Mar 7, 2009

(13·10¹⁷⁰+11)/3 = 4(3)₁₆₉7_<171> = 1499 · 567902254172162219_<18> · 1373651784966490440402937717_<28> · C123

C123 = P41 · P82

P41 = 75419873015009426887961716945954103895361_<41>

P82 = 4913426010328832983926082517300597573047085667748765160896669600454929105984112621_<82>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 370569965767644980357356235399428856137811078710645235253822530344840763763076823444886948979877902193136601912075023451181 (123 digits)
Using B1=20000000, B2=59950304286, polynomial Dickson(12), sigma=139757922
Step 1 took 231729ms
Step 2 took 76758ms
********** Factor found in step 2: 75419873015009426887961716945954103895361
Found probable prime factor of 41 digits: 75419873015009426887961716945954103895361
Probable prime cofactor 4913426010328832983926082517300597573047085667748765160896669600454929105984112621 has 82 digits

Mar 7, 2009 (4th)

By Max Dettweiler / GMP-ECM 6.2.1, GGNFS msieve v1.40-beta2 / Mar 7, 2009

(35·10¹⁶⁸-53)/9 = 3(8)₁₆₇3_<169> = 55865683 · 167058817 · 49490597625208871233348177_<26> · C127

C127 = P39 · P89

P39 = 569618098720578477422424600101143173899_<39>

P89 = 14781024690642080932758969397118873168017503155014627158552385373431832745996639435957011_<89>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 8419539181425468806006365315094861322014249606974102335052229082073286916817362732334516441385931952781233787411201237061255889 (127 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2713672085
Step 1 took 11893ms
Step 2 took 6988ms
********** Factor found in step 2: 569618098720578477422424600101143173899
Found probable prime factor of 39 digits: 569618098720578477422424600101143173899
Probable prime cofactor 14781024690642080932758969397118873168017503155014627158552385373431832745996639435957011 has 89 digits

(46·10¹¹³+17)/9 = 5(1)₁₁₂3_<114> = 3 · 61 · 5399 · 1320331 · 2982873143_<10> · C93

C93 = P34 · P59

P34 = 4412416030289271351015581005697119_<34>

P59 = 29768492848110394115729558818954963316995218350789392555507_<59>

Number: 51113_113
N=131350975040553830349733335037245342075215762201405132631282575232890983280795267893437484333
  ( 93 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=4412416030289271351015581005697119 (pp34)
 r2=29768492848110394115729558818954963316995218350789392555507 (pp59)
Version: GGNFS-0.77.1-20060722-prescott
Total time: 1.28 hours.
Scaled time: 2.07 units (timescale=1.621).
Factorization parameters were as follows:
n: 131350975040553830349733335037245342075215762201405132631282575232890983280795267893437484333
m: 50000000000000000000000
deg: 5
c5: 368
c0: 425
skew: 1.03
type: snfs
lss: 1
rlim: 600000
alim: 600000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [300000, 500001)
Primes: RFBsize:49098, AFBsize:49246, largePrimes:1245641 encountered
Relations: rels:1220739, finalFF:145520
Max relations in full relation-set: 32
Initial matrix: 98411 x 145520 with sparse part having weight 6465754.
Pruned matrix : 79822 x 80378 with weight 2618257.
Total sieving time: 1.21 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000
total time: 1.28 hours.
 --------- CPU info (if available) ----------
[    0.371537] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.13 BogoMIPS (lpj=8800276)
[    0.004000] Calibrating delay using timer specific routine.. 4400.40 BogoMIPS (lpj=8800811)
[    0.460049] Total of 2 processors activated (8800.54 BogoMIPS).

(46·10¹²⁶+17)/9 = 5(1)₁₂₅3_<127> = 7 · 29 · 613 · 320189773 · 22998881309715211_<17> · C97

C97 = P37 · P61

P37 = 2718013478775412943759161342874328001_<37>

P61 = 2052074083338351936368477625152429496333705580464085045253489_<61>

Fri Mar  6 15:36:55 2009  Msieve v. 1.40
Fri Mar  6 15:36:55 2009  random seeds: 0ccba1c4 88d7ca1a
Fri Mar  6 15:36:55 2009  factoring 5577565017959340603130194616039714070499780268304544574590233529387927501354604569332715575645489 (97 digits)
Fri Mar  6 15:36:56 2009  no P-1/P+1/ECM available, skipping
Fri Mar  6 15:36:56 2009  commencing number field sieve (97-digit input)
Fri Mar  6 15:36:56 2009  R0: -20000000000000000000000000
Fri Mar  6 15:36:56 2009  R1:  1
Fri Mar  6 15:36:56 2009  A0:  136
Fri Mar  6 15:36:56 2009  A1:  0
Fri Mar  6 15:36:56 2009  A2:  0
Fri Mar  6 15:36:56 2009  A3:  0
Fri Mar  6 15:36:56 2009  A4:  0
Fri Mar  6 15:36:56 2009  A5:  115
Fri Mar  6 15:36:56 2009  skew 1.03, size 2.597754e-09, alpha 1.172882, combined = 7.517651e-09
Fri Mar  6 15:36:56 2009  
Fri Mar  6 15:36:56 2009  commencing relation filtering
Fri Mar  6 15:36:56 2009  commencing duplicate removal, pass 1
Fri Mar  6 15:37:31 2009  found 374913 hash collisions in 3892578 relations
Fri Mar  6 15:37:40 2009  added 31511 free relations
Fri Mar  6 15:37:40 2009  commencing duplicate removal, pass 2
Fri Mar  6 15:37:43 2009  found 377312 duplicates and 3546777 unique relations
Fri Mar  6 15:37:43 2009  memory use: 40.3 MB
Fri Mar  6 15:37:43 2009  reading rational ideals above 1114112
Fri Mar  6 15:37:43 2009  reading algebraic ideals above 1114112
Fri Mar  6 15:37:43 2009  commencing singleton removal, pass 1
Fri Mar  6 15:38:14 2009  relations with 0 large ideals: 60150
Fri Mar  6 15:38:14 2009  relations with 1 large ideals: 530121
Fri Mar  6 15:38:14 2009  relations with 2 large ideals: 1484931
Fri Mar  6 15:38:14 2009  relations with 3 large ideals: 1111827
Fri Mar  6 15:38:14 2009  relations with 4 large ideals: 202778
Fri Mar  6 15:38:14 2009  relations with 5 large ideals: 0
Fri Mar  6 15:38:14 2009  relations with 6 large ideals: 156970
Fri Mar  6 15:38:14 2009  relations with 7+ large ideals: 0
Fri Mar  6 15:38:14 2009  3546777 relations and about 3528629 large ideals
Fri Mar  6 15:38:14 2009  commencing singleton removal, pass 2
Fri Mar  6 15:38:47 2009  found 1578884 singletons
Fri Mar  6 15:38:47 2009  current dataset: 1967893 relations and about 1377042 large ideals
Fri Mar  6 15:38:47 2009  commencing singleton removal, pass 3
Fri Mar  6 15:39:04 2009  found 317709 singletons
Fri Mar  6 15:39:04 2009  current dataset: 1650184 relations and about 1044914 large ideals
Fri Mar  6 15:39:04 2009  commencing singleton removal, final pass
Fri Mar  6 15:39:20 2009  memory use: 26.4 MB
Fri Mar  6 15:39:20 2009  commencing in-memory singleton removal
Fri Mar  6 15:39:21 2009  begin with 1650184 relations and 1068111 unique ideals
Fri Mar  6 15:39:21 2009  reduce to 1549980 relations and 966655 ideals in 7 passes
Fri Mar  6 15:39:21 2009  max relations containing the same ideal: 23
Fri Mar  6 15:39:22 2009  reading rational ideals above 557056
Fri Mar  6 15:39:22 2009  reading algebraic ideals above 557056
Fri Mar  6 15:39:22 2009  commencing singleton removal, final pass
Fri Mar  6 15:39:43 2009  keeping 1178944 ideals with weight <= 20, new excess is 140370
Fri Mar  6 15:39:44 2009  memory use: 34.0 MB
Fri Mar  6 15:39:44 2009  commencing in-memory singleton removal
Fri Mar  6 15:39:44 2009  begin with 1580117 relations and 1178944 unique ideals
Fri Mar  6 15:39:44 2009  reduce to 1549968 relations and 999952 ideals in 2 passes
Fri Mar  6 15:39:44 2009  max relations containing the same ideal: 20
Fri Mar  6 15:39:45 2009  removing 534828 relations and 341235 ideals in 193593 cliques
Fri Mar  6 15:39:45 2009  commencing in-memory singleton removal
Fri Mar  6 15:39:45 2009  begin with 1015140 relations and 999952 unique ideals
Fri Mar  6 15:39:46 2009  reduce to 948043 relations and 582060 ideals in 6 passes
Fri Mar  6 15:39:46 2009  max relations containing the same ideal: 19
Fri Mar  6 15:39:46 2009  removing 426135 relations and 234333 ideals in 191802 cliques
Fri Mar  6 15:39:46 2009  commencing in-memory singleton removal
Fri Mar  6 15:39:47 2009  begin with 521908 relations and 582060 unique ideals
Fri Mar  6 15:39:47 2009  reduce to 470591 relations and 289788 ideals in 7 passes
Fri Mar  6 15:39:47 2009  max relations containing the same ideal: 14
Fri Mar  6 15:39:47 2009  removing 63694 relations and 45721 ideals in 17973 cliques
Fri Mar  6 15:39:47 2009  commencing in-memory singleton removal
Fri Mar  6 15:39:47 2009  begin with 406897 relations and 289788 unique ideals
Fri Mar  6 15:39:47 2009  reduce to 400558 relations and 237472 ideals in 6 passes
Fri Mar  6 15:39:47 2009  max relations containing the same ideal: 14
Fri Mar  6 15:39:48 2009  relations with 0 large ideals: 36310
Fri Mar  6 15:39:48 2009  relations with 1 large ideals: 112733
Fri Mar  6 15:39:48 2009  relations with 2 large ideals: 146048
Fri Mar  6 15:39:48 2009  relations with 3 large ideals: 81988
Fri Mar  6 15:39:48 2009  relations with 4 large ideals: 20059
Fri Mar  6 15:39:48 2009  relations with 5 large ideals: 2184
Fri Mar  6 15:39:48 2009  relations with 6 large ideals: 1234
Fri Mar  6 15:39:48 2009  relations with 7+ large ideals: 2
Fri Mar  6 15:39:48 2009  commencing 2-way merge
Fri Mar  6 15:39:48 2009  reduce to 310081 relation sets and 146995 unique ideals
Fri Mar  6 15:39:48 2009  commencing full merge
Fri Mar  6 15:39:49 2009  memory use: 10.3 MB
Fri Mar  6 15:39:49 2009  found 163405 cycles, need 142070
Fri Mar  6 15:39:49 2009  weight of 142070 cycles is about 7188564 (50.60/cycle)
Fri Mar  6 15:39:49 2009  distribution of cycle lengths:
Fri Mar  6 15:39:49 2009  1 relations: 36324
Fri Mar  6 15:39:49 2009  2 relations: 17964
Fri Mar  6 15:39:49 2009  3 relations: 14416
Fri Mar  6 15:39:49 2009  4 relations: 12395
Fri Mar  6 15:39:49 2009  5 relations: 11292
Fri Mar  6 15:39:49 2009  6 relations: 9710
Fri Mar  6 15:39:49 2009  7 relations: 8514
Fri Mar  6 15:39:49 2009  8 relations: 7597
Fri Mar  6 15:39:49 2009  9 relations: 6625
Fri Mar  6 15:39:49 2009  10+ relations: 17233
Fri Mar  6 15:39:49 2009  heaviest cycle: 16 relations
Fri Mar  6 15:39:49 2009  matrix can improve, retrying
Fri Mar  6 15:39:50 2009  reading rational ideals above 557056
Fri Mar  6 15:39:50 2009  reading algebraic ideals above 557056
Fri Mar  6 15:39:50 2009  commencing singleton removal, final pass
Fri Mar  6 15:40:11 2009  keeping 1188055 ideals with weight <= 25, new excess is 131259
Fri Mar  6 15:40:12 2009  memory use: 34.0 MB
Fri Mar  6 15:40:12 2009  commencing in-memory singleton removal
Fri Mar  6 15:40:12 2009  begin with 1580117 relations and 1188055 unique ideals
Fri Mar  6 15:40:12 2009  reduce to 1549968 relations and 1009063 ideals in 2 passes
Fri Mar  6 15:40:12 2009  max relations containing the same ideal: 25
Fri Mar  6 15:40:13 2009  removing 536286 relations and 341964 ideals in 194322 cliques
Fri Mar  6 15:40:13 2009  commencing in-memory singleton removal
Fri Mar  6 15:40:13 2009  begin with 1013682 relations and 1009063 unique ideals
Fri Mar  6 15:40:14 2009  reduce to 946319 relations and 590094 ideals in 6 passes
Fri Mar  6 15:40:14 2009  max relations containing the same ideal: 23
Fri Mar  6 15:40:15 2009  removing 425142 relations and 233773 ideals in 191369 cliques
Fri Mar  6 15:40:15 2009  commencing in-memory singleton removal
Fri Mar  6 15:40:15 2009  begin with 521177 relations and 590094 unique ideals
Fri Mar  6 15:40:15 2009  reduce to 469861 relations and 298399 ideals in 7 passes
Fri Mar  6 15:40:15 2009  max relations containing the same ideal: 17
Fri Mar  6 15:40:15 2009  removing 66868 relations and 47667 ideals in 19201 cliques
Fri Mar  6 15:40:15 2009  commencing in-memory singleton removal
Fri Mar  6 15:40:15 2009  begin with 402993 relations and 298399 unique ideals
Fri Mar  6 15:40:15 2009  reduce to 396019 relations and 243465 ideals in 6 passes
Fri Mar  6 15:40:15 2009  max relations containing the same ideal: 16
Fri Mar  6 15:40:16 2009  relations with 0 large ideals: 29445
Fri Mar  6 15:40:16 2009  relations with 1 large ideals: 99567
Fri Mar  6 15:40:16 2009  relations with 2 large ideals: 143008
Fri Mar  6 15:40:16 2009  relations with 3 large ideals: 90693
Fri Mar  6 15:40:16 2009  relations with 4 large ideals: 27334
Fri Mar  6 15:40:16 2009  relations with 5 large ideals: 4613
Fri Mar  6 15:40:16 2009  relations with 6 large ideals: 1354
Fri Mar  6 15:40:16 2009  relations with 7+ large ideals: 5
Fri Mar  6 15:40:16 2009  commencing 2-way merge
Fri Mar  6 15:40:16 2009  reduce to 306024 relation sets and 153470 unique ideals
Fri Mar  6 15:40:16 2009  commencing full merge
Fri Mar  6 15:40:18 2009  memory use: 10.4 MB
Fri Mar  6 15:40:18 2009  found 155708 cycles, need 135959
Fri Mar  6 15:40:18 2009  weight of 135959 cycles is about 7629747 (56.12/cycle)
Fri Mar  6 15:40:18 2009  distribution of cycle lengths:
Fri Mar  6 15:40:18 2009  1 relations: 29610
Fri Mar  6 15:40:18 2009  2 relations: 15266
Fri Mar  6 15:40:18 2009  3 relations: 13262
Fri Mar  6 15:40:18 2009  4 relations: 11881
Fri Mar  6 15:40:18 2009  5 relations: 10947
Fri Mar  6 15:40:18 2009  6 relations: 9907
Fri Mar  6 15:40:18 2009  7 relations: 8930
Fri Mar  6 15:40:18 2009  8 relations: 7882
Fri Mar  6 15:40:18 2009  9 relations: 6920
Fri Mar  6 15:40:18 2009  10+ relations: 21354
Fri Mar  6 15:40:18 2009  heaviest cycle: 16 relations
Fri Mar  6 15:40:18 2009  matrix can improve, retrying
Fri Mar  6 15:40:18 2009  reading rational ideals above 557056
Fri Mar  6 15:40:18 2009  reading algebraic ideals above 557056
Fri Mar  6 15:40:18 2009  commencing singleton removal, final pass
Fri Mar  6 15:40:38 2009  keeping 1192907 ideals with weight <= 30, new excess is 126407
Fri Mar  6 15:40:39 2009  memory use: 34.0 MB
Fri Mar  6 15:40:39 2009  commencing in-memory singleton removal
Fri Mar  6 15:40:39 2009  begin with 1580117 relations and 1192907 unique ideals
Fri Mar  6 15:40:40 2009  reduce to 1549968 relations and 1013915 ideals in 2 passes
Fri Mar  6 15:40:40 2009  max relations containing the same ideal: 30
Fri Mar  6 15:40:40 2009  removing 537062 relations and 342352 ideals in 194710 cliques
Fri Mar  6 15:40:41 2009  commencing in-memory singleton removal
Fri Mar  6 15:40:41 2009  begin with 1012906 relations and 1013915 unique ideals
Fri Mar  6 15:40:41 2009  reduce to 945360 relations and 594342 ideals in 6 passes
Fri Mar  6 15:40:41 2009  max relations containing the same ideal: 27
Fri Mar  6 15:40:42 2009  removing 424587 relations and 233454 ideals in 191133 cliques
Fri Mar  6 15:40:42 2009  commencing in-memory singleton removal
Fri Mar  6 15:40:42 2009  begin with 520773 relations and 594342 unique ideals
Fri Mar  6 15:40:42 2009  reduce to 469516 relations and 303031 ideals in 7 passes
Fri Mar  6 15:40:42 2009  max relations containing the same ideal: 18
Fri Mar  6 15:40:42 2009  removing 68492 relations and 48640 ideals in 19852 cliques
Fri Mar  6 15:40:42 2009  commencing in-memory singleton removal
Fri Mar  6 15:40:43 2009  begin with 401024 relations and 303031 unique ideals
Fri Mar  6 15:40:43 2009  reduce to 393653 relations and 246703 ideals in 6 passes
Fri Mar  6 15:40:43 2009  max relations containing the same ideal: 16
Fri Mar  6 15:40:43 2009  relations with 0 large ideals: 26105
Fri Mar  6 15:40:43 2009  relations with 1 large ideals: 91713
Fri Mar  6 15:40:43 2009  relations with 2 large ideals: 139422
Fri Mar  6 15:40:43 2009  relations with 3 large ideals: 95927
Fri Mar  6 15:40:43 2009  relations with 4 large ideals: 32101
Fri Mar  6 15:40:43 2009  relations with 5 large ideals: 6784
Fri Mar  6 15:40:43 2009  relations with 6 large ideals: 1585
Fri Mar  6 15:40:43 2009  relations with 7+ large ideals: 16
Fri Mar  6 15:40:43 2009  commencing 2-way merge
Fri Mar  6 15:40:43 2009  reduce to 303906 relation sets and 156956 unique ideals
Fri Mar  6 15:40:43 2009  commencing full merge
Fri Mar  6 15:40:45 2009  memory use: 10.6 MB
Fri Mar  6 15:40:45 2009  found 151966 cycles, need 133107
Fri Mar  6 15:40:45 2009  weight of 133107 cycles is about 7916211 (59.47/cycle)
Fri Mar  6 15:40:45 2009  distribution of cycle lengths:
Fri Mar  6 15:40:45 2009  1 relations: 26429
Fri Mar  6 15:40:45 2009  2 relations: 14052
Fri Mar  6 15:40:45 2009  3 relations: 12599
Fri Mar  6 15:40:45 2009  4 relations: 11271
Fri Mar  6 15:40:45 2009  5 relations: 10883
Fri Mar  6 15:40:45 2009  6 relations: 9895
Fri Mar  6 15:40:45 2009  7 relations: 8963
Fri Mar  6 15:40:45 2009  8 relations: 7951
Fri Mar  6 15:40:45 2009  9 relations: 7092
Fri Mar  6 15:40:45 2009  10+ relations: 23972
Fri Mar  6 15:40:45 2009  heaviest cycle: 16 relations
Fri Mar  6 15:40:45 2009  matrix can improve, retrying
Fri Mar  6 15:40:45 2009  reading rational ideals above 557056
Fri Mar  6 15:40:45 2009  reading algebraic ideals above 557056
Fri Mar  6 15:40:45 2009  commencing singleton removal, final pass
Fri Mar  6 15:41:06 2009  keeping 1197503 ideals with weight <= 35, new excess is 121811
Fri Mar  6 15:41:07 2009  memory use: 34.0 MB
Fri Mar  6 15:41:07 2009  commencing in-memory singleton removal
Fri Mar  6 15:41:07 2009  begin with 1580117 relations and 1197503 unique ideals
Fri Mar  6 15:41:08 2009  reduce to 1549968 relations and 1018511 ideals in 2 passes
Fri Mar  6 15:41:08 2009  max relations containing the same ideal: 35
Fri Mar  6 15:41:08 2009  removing 537798 relations and 342720 ideals in 195078 cliques
Fri Mar  6 15:41:09 2009  commencing in-memory singleton removal
Fri Mar  6 15:41:09 2009  begin with 1012170 relations and 1018511 unique ideals
Fri Mar  6 15:41:09 2009  reduce to 944493 relations and 598396 ideals in 6 passes
Fri Mar  6 15:41:09 2009  max relations containing the same ideal: 30
Fri Mar  6 15:41:10 2009  removing 424150 relations and 233182 ideals in 190968 cliques
Fri Mar  6 15:41:10 2009  commencing in-memory singleton removal
Fri Mar  6 15:41:10 2009  begin with 520343 relations and 598396 unique ideals
Fri Mar  6 15:41:10 2009  reduce to 469090 relations and 307347 ideals in 7 passes
Fri Mar  6 15:41:10 2009  max relations containing the same ideal: 20
Fri Mar  6 15:41:11 2009  removing 69957 relations and 49515 ideals in 20442 cliques
Fri Mar  6 15:41:11 2009  commencing in-memory singleton removal
Fri Mar  6 15:41:11 2009  begin with 399133 relations and 307347 unique ideals
Fri Mar  6 15:41:11 2009  reduce to 391449 relations and 249810 ideals in 6 passes
Fri Mar  6 15:41:11 2009  max relations containing the same ideal: 19
Fri Mar  6 15:41:11 2009  relations with 0 large ideals: 23355
Fri Mar  6 15:41:11 2009  relations with 1 large ideals: 84028
Fri Mar  6 15:41:11 2009  relations with 2 large ideals: 134661
Fri Mar  6 15:41:11 2009  relations with 3 large ideals: 100205
Fri Mar  6 15:41:11 2009  relations with 4 large ideals: 37834
Fri Mar  6 15:41:11 2009  relations with 5 large ideals: 9201
Fri Mar  6 15:41:11 2009  relations with 6 large ideals: 2124
Fri Mar  6 15:41:11 2009  relations with 7+ large ideals: 41
Fri Mar  6 15:41:11 2009  commencing 2-way merge
Fri Mar  6 15:41:11 2009  reduce to 301917 relation sets and 160278 unique ideals
Fri Mar  6 15:41:11 2009  commencing full merge
Fri Mar  6 15:41:13 2009  memory use: 10.7 MB
Fri Mar  6 15:41:13 2009  found 147593 cycles, need 130011
Fri Mar  6 15:41:13 2009  weight of 130011 cycles is about 8359711 (64.30/cycle)
Fri Mar  6 15:41:13 2009  distribution of cycle lengths:
Fri Mar  6 15:41:13 2009  1 relations: 23765
Fri Mar  6 15:41:13 2009  2 relations: 12632
Fri Mar  6 15:41:13 2009  3 relations: 11596
Fri Mar  6 15:41:13 2009  4 relations: 10671
Fri Mar  6 15:41:13 2009  5 relations: 10244
Fri Mar  6 15:41:13 2009  6 relations: 9368
Fri Mar  6 15:41:13 2009  7 relations: 8683
Fri Mar  6 15:41:13 2009  8 relations: 7701
Fri Mar  6 15:41:13 2009  9 relations: 7179
Fri Mar  6 15:41:13 2009  10+ relations: 28172
Fri Mar  6 15:41:13 2009  heaviest cycle: 18 relations
Fri Mar  6 15:41:13 2009  commencing cycle optimization
Fri Mar  6 15:41:14 2009  start with 765303 relations
Fri Mar  6 15:41:15 2009  pruned 66696 relations
Fri Mar  6 15:41:15 2009  memory use: 17.0 MB
Fri Mar  6 15:41:15 2009  distribution of cycle lengths:
Fri Mar  6 15:41:15 2009  1 relations: 23765
Fri Mar  6 15:41:15 2009  2 relations: 13466
Fri Mar  6 15:41:15 2009  3 relations: 12785
Fri Mar  6 15:41:15 2009  4 relations: 11950
Fri Mar  6 15:41:15 2009  5 relations: 11544
Fri Mar  6 15:41:15 2009  6 relations: 10687
Fri Mar  6 15:41:15 2009  7 relations: 9475
Fri Mar  6 15:41:15 2009  8 relations: 8477
Fri Mar  6 15:41:15 2009  9 relations: 7342
Fri Mar  6 15:41:15 2009  10+ relations: 20520
Fri Mar  6 15:41:15 2009  heaviest cycle: 17 relations
Fri Mar  6 15:41:16 2009  RelProcTime: 221
Fri Mar  6 15:41:16 2009  
Fri Mar  6 15:41:16 2009  commencing linear algebra
Fri Mar  6 15:41:16 2009  read 130011 cycles
Fri Mar  6 15:41:16 2009  cycles contain 333059 unique relations
Fri Mar  6 15:41:19 2009  read 333059 relations
Fri Mar  6 15:41:20 2009  using 20 quadratic characters above 66514674
Fri Mar  6 15:41:22 2009  building initial matrix
Fri Mar  6 15:41:30 2009  memory use: 36.3 MB
Fri Mar  6 15:41:30 2009  read 130011 cycles
Fri Mar  6 15:41:31 2009  matrix is 129812 x 130011 (31.6 MB) with weight 10123002 (77.86/col)
Fri Mar  6 15:41:31 2009  sparse part has weight 7368844 (56.68/col)
Fri Mar  6 15:41:33 2009  filtering completed in 2 passes
Fri Mar  6 15:41:33 2009  matrix is 129413 x 129612 (31.5 MB) with weight 10104954 (77.96/col)
Fri Mar  6 15:41:33 2009  sparse part has weight 7358402 (56.77/col)
Fri Mar  6 15:41:34 2009  read 129612 cycles
Fri Mar  6 15:41:34 2009  matrix is 129413 x 129612 (31.5 MB) with weight 10104954 (77.96/col)
Fri Mar  6 15:41:34 2009  sparse part has weight 7358402 (56.77/col)
Fri Mar  6 15:41:34 2009  saving the first 48 matrix rows for later
Fri Mar  6 15:41:34 2009  matrix is 129365 x 129612 (29.4 MB) with weight 7655401 (59.06/col)
Fri Mar  6 15:41:34 2009  sparse part has weight 6916344 (53.36/col)
Fri Mar  6 15:41:34 2009  matrix includes 64 packed rows
Fri Mar  6 15:41:34 2009  using block size 51844 for processor cache size 2048 kB
Fri Mar  6 15:41:35 2009  commencing Lanczos iteration
Fri Mar  6 15:41:35 2009  memory use: 29.3 MB
Fri Mar  6 15:43:37 2009  lanczos halted after 2047 iterations (dim = 129362)
Fri Mar  6 15:43:38 2009  recovered 36 nontrivial dependencies
Fri Mar  6 15:43:38 2009  BLanczosTime: 132
Fri Mar  6 15:43:38 2009  
Fri Mar  6 15:43:38 2009  commencing square root phase
Fri Mar  6 15:43:38 2009  reading relations for dependency 1
Fri Mar  6 15:43:38 2009  read 64856 cycles
Fri Mar  6 15:43:38 2009  cycles contain 211230 unique relations
Fri Mar  6 15:43:44 2009  read 211230 relations
Fri Mar  6 15:43:45 2009  multiplying 166240 relations
Fri Mar  6 15:43:54 2009  multiply complete, coefficients have about 4.36 million bits
Fri Mar  6 15:43:54 2009  initial square root is modulo 104231
Fri Mar  6 15:44:13 2009  sqrtTime: 27
Fri Mar  6 15:44:13 2009  prp37 factor: 2718013478775412943759161342874328001
Fri Mar  6 15:44:13 2009  prp61 factor: 2052074083338351936368477625152429496333705580464085045253489
Fri Mar  6 15:44:13 2009  elapsed time 00:07:18

(46·10¹⁴⁵+17)/9 = 5(1)₁₄₄3_<146> = 157 · 491 · 10795901819827_<14> · 1187111663117279_<16> · C113

C113 = P42 · P72

P42 = 151187449087050159689435421843968531441609_<42>

P72 = 342190493465467590083868747754619291085634754952297946010802975078867067_<72>

Number: 51113_145
N=51734907808882951637333473963353371587253719697383137652805531581141899550195669462548918187805945701871983590803
  ( 113 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=151187449087050159689435421843968531441609 (pp42)
 r2=342190493465467590083868747754619291085634754952297946010802975078867067 (pp72)
Version: Msieve-1.40beta2
Total time: 8.92 hours.
Scaled time: 14.67 units (timescale=1.644).
Factorization parameters were as follows:
n: 51734907808882951637333473963353371587253719697383137652805531581141899550195669462548918187805945701871983590803
m: 100000000000000000000000000000
deg: 5
c5: 46
c0: 17
skew: 0.82
type: snfs
lss: 1
rlim: 1950000
alim: 1950000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3

Factor base limits: 1950000/1950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [975000, 2175001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 332083 x 332331
Total sieving time: 8.92 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000
total time: 8.92 hours.
 --------- CPU info (if available) ----------
[    0.371537] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.456480] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004010] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.13 BogoMIPS (lpj=8800276)
[    0.004000] Calibrating delay using timer specific routine.. 4400.40 BogoMIPS (lpj=8800811)
[    0.460049] Total of 2 processors activated (8800.54 BogoMIPS).

Mar 7, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.40 / Mar 7, 2009

(46·10¹¹⁰+17)/9 = 5(1)₁₀₉3_<111> = 3³ · 19 · 24709 · 648502445425889_<15> · C89

C89 = P33 · P57

P33 = 509413598709906626667570172159511_<33>

P57 = 122056422191446221014247383030211096456944262433194285491_<57>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2686212401
Step 1 took 5805ms
Step 2 took 6368ms
********** Factor found in step 2: 509413598709906626667570172159511
Found probable prime factor of 33 digits: 509413598709906626667570172159511
Probable prime cofactor 122056422191446221014247383030211096456944262433194285491 has 57 digits

(46·10¹³⁸+17)/9 = 5(1)₁₃₇3_<139> = 7 · 1709 · 931540693 · C126

C126 = P28 · P99

P28 = 2995443894178877333175966911_<28>

P99 = 153113046879406592655362075559329006950987502421523034157252675103445336866089598291005284520872737_<99>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1492474375
Step 1 took 8777ms
Step 2 took 8525ms
********** Factor found in step 2: 2995443894178877333175966911
Found probable prime factor of 28 digits: 2995443894178877333175966911
Probable prime cofactor  has 99 digits

(44·10¹⁵⁶+1)/9 = 4(8)₁₅₅9_<157> = C157

C157 = P53 · P105

P53 = 47642835071258058596160680423741344870035443171703557_<53>

P105 = 102615406526012027575384100100642854238249884773756740758595557060587802504484698285306807742770051495077_<105>

SNFS difficulty: 158 digits.
Divisors found:
 r1=47642835071258058596160680423741344870035443171703557 (pp53)
 r2=102615406526012027575384100100642854238249884773756740758595557060587802504484698285306807742770051495077 (pp105)
Version: Msieve-1.40
Total time: 8.26 hours.
Scaled time: 25.72 units (timescale=3.543).
Factorization parameters were as follows:
n: 4888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
m: 20000000000000000000000000000000
deg: 5
c5: 55
c0: 4
skew: 0.59
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1500000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 456648 x 456896
Total sieving time: 7.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 1.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,52,52,2.4,2.4,100000
total time: 8.26 hours.
 --------- CPU info (if available) ----------
[    0.296963] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 3.20GHz stepping 0b
[    0.576059] Total of 4 processors activated (25632.11 BogoMIPS).

(44·10¹⁴⁹+1)/9 = 4(8)₁₄₈9_<150> = 3² · 19 · 139 · C146

C146 = P67 · P79

P67 = 2097300725793172414818766211917996426019369864092134123926619108377_<67>

P79 = 9807053607602909688818978170095407278852726104132093533745020732100373184796553_<79>

SNFS difficulty: 151 digits.
Divisors found:
 r1=2097300725793172414818766211917996426019369864092134123926619108377 (pp67)
 r2=9807053607602909688818978170095407278852726104132093533745020732100373184796553 (pp79)
Version: Msieve-1.40
Total time: 6.50 hours.
Scaled time: 23.00 units (timescale=3.536).
Factorization parameters were as follows:
n: 20568340649118132394669060073578564049345319066384319445028772303794391387474815469262017286755391008830362610496398203074966927043160793003024481
m: 1000000000000000000000000000000
deg: 5
c5: 22
c0: 5
skew: 0.74
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1150000, 1950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 316427 x 316675
Total sieving time: 6.50 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000
total time: 6.50 hours.
 --------- CPU info (if available) ----------
[    0.296963] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b

(46·10¹⁹⁵+17)/9 = 5(1)₁₉₄3_<196> = 383 · 1291 · 409523 · 1626467 · 145476985781_<12> · C168

C168 = P31 · P137

P31 = 1352232292703206748131418929363_<31>

P137 = 78889854420261070134295297737329302219952025430485075571736676711205438128918148705492132762635601259166557687516563362370477021572531427_<137>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=979988983 
Step 1 took 13253ms
Step 2 took 11473ms
********** Factor found in step 2: 1352232292703206748131418929363
Found probable prime factor of 31 digits: 1352232292703206748131418929363
Probable prime cofactor 788898544202610701342952977373293022199520254304850755717366767112054381289181487054921327626356012591665576875
16563362370477021572531427 has 137 digits

(46·10¹⁵⁰+17)/9 = 5(1)₁₄₉3_<151> = 7 · 13597 · 93765122431_<11> · C135

C135 = P32 · C104

P32 = 12927026782792133527436421144607_<32>

C104 = [44303109699607022872926009371300736105651392884345897886736800768893549967713945190056822343455756593691_<104>]

Using B1=43000000, B2=582162027730, polynomial Dickson(30), sigma=643304458
Step 1 took 136340ms
Step 2 took 89838ms
********** Factor found in step 2: 12927026782792133527436421144607
Found probable prime factor of 32 digits: 12927026782792133527436421144607
Composite cofactor  has 104 digits

(46·10¹⁹⁷+17)/9 = 5(1)₁₉₆3_<198> = 3 · 857 · 941929 · 579647353553_<12> · 1267710460787_<13> · 245525980953755657_<18> · C148

C148 = P30 · P118

P30 = 130550024777403132153418348493_<30>

P118 = 8960592608030015896461355940957297379276489908903690773678245168039100889919773852994128966768993206114558634605407037_<118>

Using B1=43000000, B2=582162027730, polynomial Dickson(30), sigma=1748386705
Step 1 took 154413ms
Step 2 took 115743ms
********** Factor found in step 2: 130550024777403132153418348493
Found probable prime factor of 30 digits: 130550024777403132153418348493
Probable prime cofactor has 118 digits

(46·10¹⁹²+17)/9 = 5(1)₁₉₁3_<193> = 7 · 384865744381226570291_<21> · C172

C172 = P35 · C137

P35 = 24527637055228679790053330005147297_<35>

C137 = [77348574344711900248143397201902127252238419609437775764473096905398712073855667946645489904090700000217853926771032123860527776171449717_<137>]

Using B1=43000000, B2=582162027730, polynomial Dickson(30), sigma=2994922549
Step 1 took 187100ms
Step 2 took 128392ms
********** Factor found in step 2: 24527637055228679790053330005147297
Found probable prime factor of 35 digits: 24527637055228679790053330005147297
Composite cofactor has 137 digits

Mar 7, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Mar 7, 2009

(46·10¹²⁷+17)/9 = 5(1)₁₂₆3_<128> = C128

C128 = P58 · P70

P58 = 6599238864992473661867771888020943737578620316459510081053_<58>

P70 = 7745000924613357302214301740844777467164561254663784453622295281253021_<70>

Number: 51113_127
N=51111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
  ( 128 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=6599238864992473661867771888020943737578620316459510081053
 r2=7745000924613357302214301740844777467164561254663784453622295281253021
Version: 
Total time: 2.86 hours.
Scaled time: 2.84 units (timescale=0.995).
Factorization parameters were as follows:
n: 51111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
m: 20000000000000000000000000
deg: 5
c5: 575
c0: 68
skew: 0.65
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 132565 x 132813
Total sieving time: 2.86 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 2.86 hours.
 --------- CPU info (if available) ----------

Mar 7, 2009

By Ignacio Santos / GGNFS, Msieve, Yafu 1.06 / Mar 7, 2009

(46·10¹¹²+17)/9 = 5(1)₁₁₁3_<113> = 13109 · 11411987 · C102

C102 = P30 · P72

P30 = 517866767205520783356060520331_<30>

P72 = 659730326748824292543983066756293862349872523611320087213527547002192181_<72>

Number: 51113_112
N=341652411540855550987982852437214566361269865885464620167649342547784989794149585043200330164519731911
  ( 102 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=517866767205520783356060520331 (pp30)
 r2=659730326748824292543983066756293862349872523611320087213527547002192181 (pp72)
Version: Msieve-1.39
Total time: 0.66 hours.
Scaled time: 0.79 units (timescale=1.184).
Factorization parameters were as follows:
n: 341652411540855550987982852437214566361269865885464620167649342547784989794149585043200330164519731911
m: 20000000000000000000000
deg: 5
c5: 575
c0: 68
skew: 0.65
type: snfs
lss: 1
rlim: 560000
alim: 560000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 560000/560000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [280000, 430001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 65804 x 66045
Total sieving time: 0.66 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,114,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000
total time: 0.66 hours.
 --------- CPU info (if available) ----------

(46·10¹¹⁵+17)/9 = 5(1)₁₁₄3_<116> = 43 · 431 · C112

C112 = P40 · P72

P40 = 3149446937547697015940394432710152051321_<40>

P72 = 875659574895009800158875966619714504676290535754462619860371208304102141_<72>

Number: 51113_115
N=2757843366487406847844985221556742627265478395894410570933529979555987217995527497496957379329364437010257978261
  ( 112 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=3149446937547697015940394432710152051321 (pp40)
 r2=875659574895009800158875966619714504676290535754462619860371208304102141 (pp72)
Version: Msieve-1.39
Total time: 1.03 hours.
Scaled time: 2.61 units (timescale=2.544).
Factorization parameters were as follows:
n: 2757843366487406847844985221556742627265478395894410570933529979555987217995527497496957379329364437010257978261
m: 100000000000000000000000
deg: 5
c5: 46
c0: 17
skew: 0.82
type: snfs
lss: 1
rlim: 620000
alim: 620000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 620000/620000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [310000, 510001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 61649 x 61881
Total sieving time: 1.03 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000
total time: 1.03 hours.
 --------- CPU info (if available) ----------

(46·10¹¹⁶+17)/9 = 5(1)₁₁₅3_<117> = 3 · 257 · 131251 · C109

C109 = P35 · P75

P35 = 30361717830758145620260372150707551_<35>

P75 = 166353515614767575628006317055974058159089119918491151110217499030179553903_<75>

Number: 51113_116
N=5050778501250192301528964311329771609977887153703816742322552335724886835633236616744409621852067574993621553
  ( 109 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=30361717830758145620260372150707551 (pp35)
 r2=166353515614767575628006317055974058159089119918491151110217499030179553903 (pp75)
Version: Msieve-1.39
Total time: 1.26 hours.
Scaled time: 1.51 units (timescale=1.192).
Factorization parameters were as follows:
n: 5050778501250192301528964311329771609977887153703816742322552335724886835633236616744409621852067574993621553
m: 200000000000000000000000
deg: 5
c5: 115
c0: 136
skew: 1.03
type: snfs
lss: 1
rlim: 660000
alim: 660000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 660000/660000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [330000, 630001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 76182 x 76425
Total sieving time: 1.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,660000,660000,25,25,45,45,2.2,2.2,50000
total time: 1.26 hours.
 --------- CPU info (if available) ----------

(46·10¹¹⁸+17)/9 = 5(1)₁₁₇3_<119> = 53 · 1933 · 16733728229_<11> · C104

C104 = P46 · P59

P46 = 2016015307475000907731963844200174382199696883_<46>

P59 = 14788395673150931151082918084560210578584532965509326765191_<59>

Number: 51113_118
N=29813632050069347490532431275832226137066203213154862026980704247830053064634704339885126599399115599653
  ( 104 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=2016015307475000907731963844200174382199696883 (pp46)
 r2=14788395673150931151082918084560210578584532965509326765191 (pp59)
Version: Msieve-1.39
Total time: 1.54 hours.
Scaled time: 3.93 units (timescale=2.552).
Factorization parameters were as follows:
n: 29813632050069347490532431275832226137066203213154862026980704247830053064634704339885126599399115599653
m: 500000000000000000000000
deg: 5
c5: 368
c0: 425
skew: 1.03
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 665001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 79366 x 79598
Total sieving time: 1.54 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 1.54 hours.
 --------- CPU info (if available) ----------

(46·10¹²²+17)/9 = 5(1)₁₂₁3_<123> = 3 · 1327 · 1709759869_<10> · C110

C110 = P44 · P67

P44 = 34049764786873379485800962656346734204740599_<44>

P67 = 2205331644498568848091937648557874956117764055165157741281702138583_<67>

Number: 51113_122
N=75091023772224931608850193272260239506670593186929340447367012240320458339626335158324329345270161515064431217
  ( 110 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=34049764786873379485800962656346734204740599 (pp44)
 r2=2205331644498568848091937648557874956117764055165157741281702138583 (pp67)
Version: Msieve-1.39
Total time: 1.60 hours.
Scaled time: 1.87 units (timescale=1.168).
Factorization parameters were as follows:
n: 75091023772224931608850193272260239506670593186929340447367012240320458339626335158324329345270161515064431217
m: 2000000000000000000000000
deg: 5
c5: 575
c0: 68
skew: 0.65
type: snfs
lss: 1
rlim: 820000
alim: 820000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 820000/820000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [410000, 760001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 93359 x 93597
Total sieving time: 1.60 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,46,46,2.2,2.2,50000
total time: 1.60 hours.
 --------- CPU info (if available) ----------

(46·10¹²⁴+17)/9 = 5(1)₁₂₃3_<125> = 811 · 24151811 · 990028579567_<12> · C103

C103 = P41 · P62

P41 = 60690029957183105131052218040318610567451_<41>

P62 = 43428985360115019825925624610794271374784635308137098147997509_<62>

Number: 51113_124
N=2635706422515447056256903802271865338169561795700607621402887842394171988138136389923500327521824479559
  ( 103 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=60690029957183105131052218040318610567451 (pp41)
 r2=43428985360115019825925624610794271374784635308137098147997509 (pp62)
Version: Msieve-1.39
Total time: 1.50 hours.
Scaled time: 3.84 units (timescale=2.556).
Factorization parameters were as follows:
n: 2635706422515447056256903802271865338169561795700607621402887842394171988138136389923500327521824479559
m: 10000000000000000000000000
deg: 5
c5: 23
c0: 85
skew: 1.30
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 695001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 131110 x 131358
Total sieving time: 1.50 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 1.50 hours.
 --------- CPU info (if available) ----------

(46·10¹³⁰+17)/9 = 5(1)₁₂₉3_<131> = 197 · 8263 · 4085874223_<10> · 14325620117_<11> · 2861354203786141573_<19> · C87

C87 = P41 · P47

P41 = 13747478299743188012769630624319808854561_<41>

P47 = 13636981603296597526680098271187326870062608421_<47>

Fri Mar 06 18:22:58 2009  
Fri Mar 06 18:22:58 2009  
Fri Mar 06 18:22:58 2009  Msieve v. 1.40
Fri Mar 06 18:22:58 2009  random seeds: 0010f447 0021e88e
Fri Mar 06 18:22:58 2009  factoring 187474108665317042616501734125735600581889023212579579612019036645896104785475882858181 (87 digits)
Fri Mar 06 18:22:59 2009  searching for 15-digit factors
Fri Mar 06 18:23:00 2009  commencing quadratic sieve (87-digit input)
Fri Mar 06 18:23:00 2009  using multiplier of 5
Fri Mar 06 18:23:00 2009  using 32kb Intel Core sieve core
Fri Mar 06 18:23:00 2009  sieve interval: 19 blocks of size 32768
Fri Mar 06 18:23:00 2009  processing polynomials in batches of 11
Fri Mar 06 18:23:00 2009  using a sieve bound of 1478933 (56333 primes)
Fri Mar 06 18:23:00 2009  using large prime bound of 118314640 (26 bits)
Fri Mar 06 18:23:00 2009  using double large prime bound of 339992380628560 (41-49 bits)
Fri Mar 06 18:23:00 2009  using trial factoring cutoff of 49 bits
Fri Mar 06 18:23:00 2009  polynomial 'A' values have 11 factors
Fri Mar 06 18:48:15 2009  56602 relations (16793 full + 39809 combined from 580979 partial), need 56429
Fri Mar 06 18:48:15 2009  begin with 597772 relations
Fri Mar 06 18:48:15 2009  reduce to 131917 relations in 11 passes
Fri Mar 06 18:48:15 2009  attempting to read 131917 relations
Fri Mar 06 18:48:17 2009  recovered 131917 relations
Fri Mar 06 18:48:17 2009  recovered 104390 polynomials
Fri Mar 06 18:48:17 2009  attempting to build 56602 cycles
Fri Mar 06 18:48:17 2009  found 56602 cycles in 5 passes
Fri Mar 06 18:48:17 2009  distribution of cycle lengths:
Fri Mar 06 18:48:17 2009     length 1 : 16793
Fri Mar 06 18:48:17 2009     length 2 : 11564
Fri Mar 06 18:48:17 2009     length 3 : 10042
Fri Mar 06 18:48:17 2009     length 4 : 7084
Fri Mar 06 18:48:17 2009     length 5 : 4903
Fri Mar 06 18:48:17 2009     length 6 : 2853
Fri Mar 06 18:48:17 2009     length 7 : 1626
Fri Mar 06 18:48:17 2009     length 9+: 1737
Fri Mar 06 18:48:17 2009  largest cycle: 17 relations
Fri Mar 06 18:48:17 2009  matrix is 56333 x 56602 (12.7 MB) with weight 3113120 (55.00/col)
Fri Mar 06 18:48:17 2009  sparse part has weight 3113120 (55.00/col)
Fri Mar 06 18:48:18 2009  filtering completed in 3 passes
Fri Mar 06 18:48:18 2009  matrix is 50734 x 50797 (11.6 MB) with weight 2826636 (55.65/col)
Fri Mar 06 18:48:18 2009  sparse part has weight 2826636 (55.65/col)
Fri Mar 06 18:48:18 2009  saving the first 48 matrix rows for later
Fri Mar 06 18:48:18 2009  matrix is 50686 x 50797 (7.4 MB) with weight 2216417 (43.63/col)
Fri Mar 06 18:48:18 2009  sparse part has weight 1642296 (32.33/col)
Fri Mar 06 18:48:18 2009  matrix includes 64 packed rows
Fri Mar 06 18:48:18 2009  using block size 20318 for processor cache size 4096 kB
Fri Mar 06 18:48:18 2009  commencing Lanczos iteration
Fri Mar 06 18:48:18 2009  memory use: 7.3 MB
Fri Mar 06 18:48:28 2009  lanczos halted after 803 iterations (dim = 50680)
Fri Mar 06 18:48:29 2009  recovered 14 nontrivial dependencies
Fri Mar 06 18:48:29 2009  prp41 factor: 13747478299743188012769630624319808854561
Fri Mar 06 18:48:29 2009  prp47 factor: 13636981603296597526680098271187326870062608421
Fri Mar 06 18:48:29 2009  elapsed time 00:25:02

(46·10¹²⁸+17)/9 = 5(1)₁₂₇3_<129> = 3² · 19 · 67 · 241 · 40813 · 34543871077489_<14> · C105

C105 = P32 · P34 · P39

P32 = 86754520556469833455200256325953_<32>

P34 = 5542838338358103983727907338142633_<34>

P39 = 273044552898454950594350745066450950693_<39>

Number: 51113_128
N=131297919127251267690339352393994188785077492024334806689386353399493233465038256753629303186449568944557
  ( 105 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=86754520556469833455200256325953 (pp32)
 r2=5542838338358103983727907338142633 (pp34)
 r3=273044552898454950594350745066450950693 (pp39)
Version: Msieve-1.39
Total time: 2.08 hours.
Scaled time: 2.43 units (timescale=1.170).
Factorization parameters were as follows:
n: 131297919127251267690339352393994188785077492024334806689386353399493233465038256753629303186449568944557
m: 50000000000000000000000000
deg: 5
c5: 368
c0: 425
skew: 1.03
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 935001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 161969 x 162217
Total sieving time: 2.08 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 2.08 hours.
 --------- CPU info (if available) ----------

(46·10¹²⁵+17)/9 = 5(1)₁₂₄3_<126> = 3 · 3463 · 4965509 · 596347207 · 3713495999_<10> · 14359326067_<11> · C87

C87 = P38 · P50

P38 = 25918694903313710763660728913817190897_<38>

P50 = 12021217799467288439523031407236435366656415114659_<50>

Fri Mar 06 18:53:23 2009  
Fri Mar 06 18:53:23 2009  
Fri Mar 06 18:53:23 2009  Msieve v. 1.40
Fri Mar 06 18:53:23 2009  random seeds: 0010f447 0021e88e
Fri Mar 06 18:53:23 2009  factoring 311574276510676870408699248115153667418766226787058099189185771886362891194019546059123 (87 digits)
Fri Mar 06 18:53:24 2009  searching for 15-digit factors
Fri Mar 06 18:53:25 2009  commencing quadratic sieve (87-digit input)
Fri Mar 06 18:53:25 2009  using multiplier of 11
Fri Mar 06 18:53:25 2009  using 32kb Intel Core sieve core
Fri Mar 06 18:53:25 2009  sieve interval: 20 blocks of size 32768
Fri Mar 06 18:53:25 2009  processing polynomials in batches of 11
Fri Mar 06 18:53:25 2009  using a sieve bound of 1489637 (56445 primes)
Fri Mar 06 18:53:25 2009  using large prime bound of 119170960 (26 bits)
Fri Mar 06 18:53:25 2009  using double large prime bound of 344434582165760 (42-49 bits)
Fri Mar 06 18:53:25 2009  using trial factoring cutoff of 49 bits
Fri Mar 06 18:53:25 2009  polynomial 'A' values have 11 factors
Fri Mar 06 19:26:01 2009  56840 relations (16048 full + 40792 combined from 593695 partial), need 56541
Fri Mar 06 19:26:02 2009  begin with 609743 relations
Fri Mar 06 19:26:02 2009  reduce to 135618 relations in 10 passes
Fri Mar 06 19:26:02 2009  attempting to read 135618 relations
Fri Mar 06 19:26:03 2009  recovered 135618 relations
Fri Mar 06 19:26:03 2009  recovered 113425 polynomials
Fri Mar 06 19:26:03 2009  attempting to build 56840 cycles
Fri Mar 06 19:26:03 2009  found 56840 cycles in 4 passes
Fri Mar 06 19:26:03 2009  distribution of cycle lengths:
Fri Mar 06 19:26:03 2009     length 1 : 16048
Fri Mar 06 19:26:03 2009     length 2 : 11289
Fri Mar 06 19:26:03 2009     length 3 : 10080
Fri Mar 06 19:26:03 2009     length 4 : 7357
Fri Mar 06 19:26:03 2009     length 5 : 5026
Fri Mar 06 19:26:03 2009     length 6 : 3101
Fri Mar 06 19:26:03 2009     length 7 : 1809
Fri Mar 06 19:26:03 2009     length 9+: 2130
Fri Mar 06 19:26:03 2009  largest cycle: 18 relations
Fri Mar 06 19:26:04 2009  matrix is 56445 x 56840 (13.2 MB) with weight 3235525 (56.92/col)
Fri Mar 06 19:26:04 2009  sparse part has weight 3235525 (56.92/col)
Fri Mar 06 19:26:04 2009  filtering completed in 3 passes
Fri Mar 06 19:26:04 2009  matrix is 51747 x 51811 (12.1 MB) with weight 2966797 (57.26/col)
Fri Mar 06 19:26:04 2009  sparse part has weight 2966797 (57.26/col)
Fri Mar 06 19:26:04 2009  saving the first 48 matrix rows for later
Fri Mar 06 19:26:04 2009  matrix is 51699 x 51811 (8.0 MB) with weight 2357180 (45.50/col)
Fri Mar 06 19:26:04 2009  sparse part has weight 1788183 (34.51/col)
Fri Mar 06 19:26:04 2009  matrix includes 64 packed rows
Fri Mar 06 19:26:04 2009  using block size 20724 for processor cache size 4096 kB
Fri Mar 06 19:26:04 2009  commencing Lanczos iteration
Fri Mar 06 19:26:04 2009  memory use: 7.7 MB
Fri Mar 06 19:26:16 2009  lanczos halted after 819 iterations (dim = 51697)
Fri Mar 06 19:26:16 2009  recovered 16 nontrivial dependencies
Fri Mar 06 19:26:16 2009  prp38 factor: 25918694903313710763660728913817190897
Fri Mar 06 19:26:16 2009  prp50 factor: 12021217799467288439523031407236435366656415114659
Fri Mar 06 19:26:16 2009  elapsed time 00:32:30

(46·10¹⁶⁴+17)/9 = 5(1)₁₆₃3_<165> = 3³ · 19² · 352973 · 764777593 · 140476876586885601519484471_<27> · 23192450523982436626071140623501_<32> · C89

C89 = P32 · P57

P32 = 63196433917841945793059806729903_<32>

P57 = 943460367647408648898474271030755521492481831856147907147_<57>

03/06/09 19:22:06 v1.06 @ IGNACIO1, starting SIQS on c89: 59623330778132327923866078409993846933798124893348604036533381388770126581603759352316741
03/06/09 19:22:06 v1.06 @ IGNACIO1, ==== sieve params ====
03/06/09 19:22:06 v1.06 @ IGNACIO1, n = 89 digits, 298 bits
03/06/09 19:22:06 v1.06 @ IGNACIO1, factor base: 63461 primes (max prime = 1684867)
03/06/09 19:22:06 v1.06 @ IGNACIO1, single large prime cutoff: 185335370 (110 * pmax)
03/06/09 19:22:06 v1.06 @ IGNACIO1, double large prime range from 43 to 50 bits
03/06/09 19:22:06 v1.06 @ IGNACIO1, double large prime cutoff: 762649442103813
03/06/09 19:22:06 v1.06 @ IGNACIO1, using 10 large prime slices of factor base
03/06/09 19:22:06 v1.06 @ IGNACIO1, buckets hold 1024 elements
03/06/09 19:22:06 v1.06 @ IGNACIO1, sieve interval: 18 blocks of size 32768
03/06/09 19:22:06 v1.06 @ IGNACIO1, polynomial A has ~ 12 factors
03/06/09 19:22:06 v1.06 @ IGNACIO1, using multiplier of 5
03/06/09 19:22:06 v1.06 @ IGNACIO1, using small prime variation correction of 22 bits
03/06/09 19:22:06 v1.06 @ IGNACIO1, trial factoring cutoff at 99 bits
03/06/09 19:22:06 v1.06 @ IGNACIO1, ==== sieving started ====
03/06/09 20:10:54 v1.06 @ IGNACIO1, sieve time = 964.0200, relation time = 483.0980, poly_time = 1477.0580
03/06/09 20:10:54 v1.06 @ IGNACIO1, 63569 relations found: 22378 full + 41191 from 525403 partial, using 390919 polys (217 A polys)
03/06/09 20:10:54 v1.06 @ IGNACIO1, trial division touched 13057043 sieve locations out of 461146816512
03/06/09 20:10:54 v1.06 @ IGNACIO1, ==== post processing stage (msieve-1.38) ====
03/06/09 20:10:55 v1.06 @ IGNACIO1, begin with 547781 relations
03/06/09 20:10:55 v1.06 @ IGNACIO1, reduce to 123657 relations in 8 passes
03/06/09 20:10:57 v1.06 @ IGNACIO1, recovered 123657 relations
03/06/09 20:10:57 v1.06 @ IGNACIO1, recovered 105947 polynomials
03/06/09 20:10:57 v1.06 @ IGNACIO1, attempting to build 63569 cycles
03/06/09 20:10:57 v1.06 @ IGNACIO1, found 63569 cycles in 4 passes
03/06/09 20:10:57 v1.06 @ IGNACIO1, distribution of cycle lengths:
03/06/09 20:10:57 v1.06 @ IGNACIO1,    length 1 : 22378
03/06/09 20:10:57 v1.06 @ IGNACIO1,    length 2 : 19249
03/06/09 20:10:57 v1.06 @ IGNACIO1,    length 3 : 11557
03/06/09 20:10:57 v1.06 @ IGNACIO1,    length 4 : 5805
03/06/09 20:10:57 v1.06 @ IGNACIO1,    length 5 : 2681
03/06/09 20:10:57 v1.06 @ IGNACIO1,    length 6 : 1160
03/06/09 20:10:57 v1.06 @ IGNACIO1,    length 7 : 465
03/06/09 20:10:57 v1.06 @ IGNACIO1,    length 9+: 274
03/06/09 20:10:57 v1.06 @ IGNACIO1, largest cycle: 13 relations
03/06/09 20:10:57 v1.06 @ IGNACIO1, matrix is 63461 x 63569 (12.2 MB) with weight 2951178 (46.42/col)
03/06/09 20:10:57 v1.06 @ IGNACIO1, sparse part has weight 2951178 (46.42/col)
03/06/09 20:10:58 v1.06 @ IGNACIO1, filtering completed in 3 passes
03/06/09 20:10:58 v1.06 @ IGNACIO1, matrix is 55505 x 55569 (10.9 MB) with weight 2647033 (47.64/col)
03/06/09 20:10:58 v1.06 @ IGNACIO1, sparse part has weight 2647033 (47.64/col)
03/06/09 20:10:58 v1.06 @ IGNACIO1, saving the first 48 matrix rows for later
03/06/09 20:10:58 v1.06 @ IGNACIO1, matrix is 55457 x 55569 (6.8 MB) with weight 1941756 (34.94/col)
03/06/09 20:10:58 v1.06 @ IGNACIO1, sparse part has weight 1446471 (26.03/col)
03/06/09 20:10:58 v1.06 @ IGNACIO1, matrix includes 64 packed rows
03/06/09 20:10:58 v1.06 @ IGNACIO1, using block size 22227 for processor cache size 4096 kB
03/06/09 20:10:58 v1.06 @ IGNACIO1, commencing Lanczos iteration
03/06/09 20:10:58 v1.06 @ IGNACIO1, memory use: 7.2 MB
03/06/09 20:11:12 v1.06 @ IGNACIO1, lanczos halted after 878 iterations (dim = 55457)
03/06/09 20:11:12 v1.06 @ IGNACIO1, recovered 18 nontrivial dependencies
03/06/09 20:11:13 v1.06 @ IGNACIO1, prp32 = 63196433917841945793059806729903
03/06/09 20:11:16 v1.06 @ IGNACIO1, prp57 = 943460367647408648898474271030755521492481831856147907147
03/06/09 20:11:16 v1.06 @ IGNACIO1, Lanczos elapsed time = 17.9010 seconds.
03/06/09 20:11:16 v1.06 @ IGNACIO1, Sqrt elapsed time = 4.0970 seconds.
03/06/09 20:11:16 v1.06 @ IGNACIO1, Total elapsed time = 2950.5970 seconds.
03/06/09 20:11:16 v1.06 @ IGNACIO1, 
03/06/09 20:11:16 v1.06 @ IGNACIO1,

(44·10¹⁷⁵+1)/9 = 4(8)₁₇₄9_<176> = 7 · C175

C175 = P38 · P54 · P84

P38 = 35442986267229399162633261670157472131_<38>

P54 = 371307805068356206321839822265856301084971076882538433_<54>

P84 = 530698355873105582302138603830762439466162476705852733800413550935202519189328196949_<84>

Number: 48889_175
N=6984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984127
  ( 175 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=35442986267229399162633261670157472131 (pp38)
 r2=371307805068356206321839822265856301084971076882538433 (pp54)
 r3=530698355873105582302138603830762439466162476705852733800413550935202519189328196949 (pp84)
Version: Msieve-1.39
Total time: 59.27 hours.
Scaled time: 103.06 units (timescale=1.739).
Factorization parameters were as follows:
n: 6984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984127
m: 200000000000000000000000000000000000
deg: 5
c5: 11
c0: 8
skew: 0.94
type: snfs
lss: 1
rlim: 6400000
alim: 6400000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6400000/6400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3200000, 6100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1243658 x 1243905
Total sieving time: 59.27 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,6400000,6400000,28,28,53,53,2.5,2.5,100000
total time: 59.27 hours.
 --------- CPU info (if available) ----------

Mar 6, 2009 (6th)

By Ignacio Santos / GGNFS, Msieve / Mar 6, 2009

(44·10¹⁵⁸+1)/9 = 4(8)₁₅₇9_<159> = 3² · C158

C158 = P61 · P97

P61 = 9848360416398149225067186080579760654382657351109622344230129_<61>

P97 = 5515739205063319279332955934402176085731630867337489498620965400737434071245588770985154056282049_<97>

Number: 48889_158
N=54320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654321
  ( 158 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=9848360416398149225067186080579760654382657351109622344230129 (pp61)
 r2=5515739205063319279332955934402176085731630867337489498620965400737434071245588770985154056282049 (pp97)
Version: Msieve-1.39
Total time: 18.21 hours.
Scaled time: 31.66 units (timescale=1.739).
Factorization parameters were as follows:
n: 54320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654321
m: 100000000000000000000000000000000
deg: 5
c5: 11
c0: 25
skew: 1.18
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 526161 x 526409
Total sieving time: 18.21 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 18.21 hours.
 --------- CPU info (if available) ----------

(35·10¹⁶⁵+1)/9 = 3(8)₁₆₄9_<166> = 397 · 9902507529972705094099711_<25> · C138

C138 = P46 · P93

P46 = 7969168206574953146277054418993341701964192859_<46>

P93 = 124130027950451329601018911129048488882630366948490024869787253847677630490858463394940065113_<93>

Number: 38889_165
N=989213072223997029324437268621781087584043847236369906456237869412242320118933081610072849568352041473013475415066713491512284727949628067
  ( 138 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=7969168206574953146277054418993341701964192859 (pp46)
 r2=124130027950451329601018911129048488882630366948490024869787253847677630490858463394940065113 (pp93)
Version: Msieve-1.39
Total time: 38.30 hours.
Scaled time: 98.85 units (timescale=2.581).
Factorization parameters were as follows:
n: 989213072223997029324437268621781087584043847236369906456237869412242320118933081610072849568352041473013475415066713491512284727949628067
m: 1000000000000000000000000000000000
deg: 5
c5: 35
c0: 1
skew: 0.49
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 722039 x 722287
Total sieving time: 38.30 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 38.30 hours.
 --------- CPU info (if available) ----------

(43·10¹⁶⁵+11)/9 = 4(7)₁₆₄9_<166> = 3⁴ · 44357 · 32757690414695357_<17> · C143

C143 = P42 · P102

P42 = 311620381809285671492200011861477753236249_<42>

P102 = 130268565846521345031874733901498664011189946967186605113219925825056610344851701278521564348131570859_<102>

Number: 47779_165
N=40594340226841052848893161107437392322771902721395587847436530558355802823372594879027855716908914037237639106806282387269815916653335310867891
  ( 143 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=311620381809285671492200011861477753236249 (pp42)
 r2=130268565846521345031874733901498664011189946967186605113219925825056610344851701278521564348131570859 (pp102)
Version: Msieve-1.39
Total time: 43.69 hours.
Scaled time: 112.29 units (timescale=2.570).
Factorization parameters were as follows:
n: 40594340226841052848893161107437392322771902721395587847436530558355802823372594879027855716908914037237639106806282387269815916653335310867891
m: 1000000000000000000000000000000000
deg: 5
c5: 43
c0: 11
skew: 0.76
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 749830 x 750078
Total sieving time: 43.69 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 43.69 hours.
 --------- CPU info (if available) ----------

Mar 6, 2009 (5th)

By Robert Backstrom / GMP-ECM / Mar 6, 2009

(13·10¹⁶⁹+17)/3 = 4(3)₁₆₈9_<170> = 7² · 113 · 6143 · 165463 · 64817842125068594359353753328875377_<35> · C123

C123 = P49 · P74

P49 = 4490825067022399399420148296361555083596606512629_<49>

P74 = 26451204777688322705232514006591186691207302878522084165834979925093494151_<74>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 118787733468585373018803001626199942041486879025646793084250872377023430370450048163478120248088756637535072725204319132979 (123 digits)
Using B1=20000000, B2=59950304286, polynomial Dickson(12), sigma=2331681453
Step 1 took 231773ms
Step 2 took 76796ms
********** Factor found in step 2: 4490825067022399399420148296361555083596606512629
Found probable prime factor of 49 digits: 4490825067022399399420148296361555083596606512629
Probable prime cofactor 26451204777688322705232514006591186691207302878522084165834979925093494151 has 74 digits

Mar 6, 2009 (4th)

By Jo Yeong Uk / GMP-ECM 6.2.1, GGNFS, Msieve v1.39

(44·10¹⁶¹+1)/9 = 4(8)₁₆₀9_<162> = 3 · 31 · 146383 · 62455187 · 35234957627963_<14> · C134

C134 = P35 · P39 · P62

P35 = 10721680065653804531622153413577899_<35>

P39 = 100644272567173590767194450322889930527_<39>

P62 = 15123154865058221644757828838829835138556742249437823869848087_<62>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 16319028784686495073441410728477763729850335981284337339121317606455778849483709735073921300370763471261381354479505089192348146685251 (134 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3824567271
Step 1 took 3925ms
Step 2 took 2391ms
********** Factor found in step 2: 10721680065653804531622153413577899
Found probable prime factor of 35 digits: 10721680065653804531622153413577899
Composite cofactor 1522058920314497003594731912903917548980500574915904153188245724469760275415729343658461101473851849 has 100 digits

Number: 48889_161
N=1522058920314497003594731912903917548980500574915904153188245724469760275415729343658461101473851849
  ( 100 digits)
Divisors found:
 r1=100644272567173590767194450322889930527
 r2=15123154865058221644757828838829835138556742249437823869848087
Version: 
Total time: 2.53 hours.
Scaled time: 6.05 units (timescale=2.387).
Factorization parameters were as follows:
name: 48889_161
n: 1522058920314497003594731912903917548980500574915904153188245724469760275415729343658461101473851849
skew: 4608.20
# norm 8.74e+13
c5: 120960
c4: -2251381788
c3: -7275030022098
c2: 39890601536605384
c1: 12293703365155763303
c0: -119863409440619186752761
# alpha -6.24
Y1: 9469641071
Y0: -6606329861627734912
# Murphy_E 3.63e-09
# M 147994836345165664546504426837728667798585326610074997195026692594517836550201728327005161694661867
type: gnfs
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [600000, 1050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4272446
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 174732 x 174980
Polynomial selection time: 0.17 hours.
Total sieving time: 1.92 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,26,26,49,49,2.5,2.5,50000
total time: 2.53 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Mar 6, 2009 (3rd)

By Sinkiti Sibata / GGNFS, Msieve / Mar 6, 2009

(44·10¹³³+1)/9 = 4(8)₁₃₂9_<134> = 7 · 167 · 1438837 · 375241913 · 4189304017_<10> · C107

C107 = P42 · P65

P42 = 475289440566006397290321440921632356329911_<42>

P65 = 38902066629120643950031096910524820921090037036621244084069980523_<65>

Number: 48889_133
N=18489741485016257135346283032261676060769126256758607819178488418225259325848314110850542595306213532323453
  ( 107 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=475289440566006397290321440921632356329911 (pp42)
 r2=38902066629120643950031096910524820921090037036621244084069980523 (pp65)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 5.19 hours.
Scaled time: 2.45 units (timescale=0.472).
Factorization parameters were as follows:
name: 48889_133
n: 18489741485016257135346283032261676060769126256758607819178488418225259325848314110850542595306213532323453
m: 1000000000000000000000000000
deg: 5
c5: 11
c0: 25
skew: 1.18
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1025001)
Primes: RFBsize:100021, AFBsize:99949, largePrimes:2903136 encountered
Relations: rels:2787872, finalFF:227347
Max relations in full relation-set: 28
Initial matrix: 200036 x 227347 with sparse part having weight 14910802.
Pruned matrix : 186194 x 187258 with weight 9969896.
Total sieving time: 4.50 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.53 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 5.19 hours.
 --------- CPU info (if available) ----------

4·10¹⁷⁶+9 = 4(0)₁₇₅9_<177> = 5949217 · 260808949 · 37078796641_<11> · 25253318745384671209_<20> · C132

C132 = P47 · P85

P47 = 30659586774476168038113800824694868364850678869_<47>

P85 = 8979813218286857062544785990149537754786720685038107462329302196640845737147656966793_<85>

Number: 40009_176
N=275317362584653997775606639924754580390675306209828825216020217427536840717775925177388698131497326405770200711260894351163439797117
  ( 132 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=30659586774476168038113800824694868364850678869
 r2=8979813218286857062544785990149537754786720685038107462329302196640845737147656966793
Version: 
Total time: 80.41 hours.
Scaled time: 206.18 units (timescale=2.564).
Factorization parameters were as follows:
name: 40009_176
n: 275317362584653997775606639924754580390675306209828825216020217427536840717775925177388698131497326405770200711260894351163439797117
m: 200000000000000000000000000000000000
deg: 5
c5: 5
c0: 36
skew: 1.48
type: snfs
lss: 1
rlim: 6300000
alim: 6300000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6300000/6300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3150000, 6150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1237352 x 1237600
Total sieving time: 80.41 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,6300000,6300000,28,28,53,53,2.5,2.5,100000
total time: 80.41 hours.
 --------- CPU info (if available) ----------

Mar 6, 2009 (2nd)

By Max Dettweiler / GGNFS, Msieve / Mar 6, 2009

(44·10¹⁵⁵+1)/9 = 4(8)₁₅₄9_<156> = 3 · 67 · 414433 · 11481317 · 7836538053022379_<16> · C125

C125 = P36 · P89

P36 = 747721133841090078198137225206595801_<36>

P89 = 87237692433773177153894343644156201159419193259335438153340217639240104716819068675807631_<89>

Number: 48889_155
N=65229466300261165037466919710830889605772008462449035695061304084027061958672194500187578471781399630589280305316461848357431
  ( 125 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=747721133841090078198137225206595801 (pp36)
 r2=87237692433773177153894343644156201159419193259335438153340217639240104716819068675807631 (pp89)
Version: Msieve-1.39
Total time: 19.81 hours.
Scaled time: 32.49 units (timescale=1.640).
Factorization parameters were as follows:
n: 65229466300261165037466919710830889605772008462449035695061304084027061958672194500187578471781399630589280305316461848357431
m: 20000000000000000000000000000000
deg: 5
c5: 11
c0: 8
skew: 0.94
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 417069 x 417317
Total sieving time: 19.81 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 19.81 hours.
 --------- CPU info (if available) ----------
[    0.367604] CPU0: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.452480] CPU1: Intel(R) Core(TM)2 Duo CPU     E4500  @ 2.20GHz stepping 0d
[    0.004000] Memory: 2036264k/2070528k available (2576k kernel code, 32096k reserved, 1165k data, 424k init, 1152180k highmem)
[    0.004011] Calibrating delay loop (skipped), value calculated using timer frequency.. 4400.12 BogoMIPS (lpj=8800252)
[    0.004000] Calibrating delay using timer specific routine.. 4400.41 BogoMIPS (lpj=8800821)
[    0.456049] Total of 2 processors activated (8800.53 BogoMIPS).

Mar 6, 2009

Factorizations of 511...113 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 5, 2009 (6th)

By Erik Branger / GGNFS, Msieve / Mar 5, 2009

(44·10¹⁵³+1)/9 = 4(8)₁₅₂9_<154> = 197914564441789163_<18> · C137

C137 = P54 · P83

P54 = 514376085519544118671517084473390831428830178432400813_<54>

P83 = 48023260529503490148502526990560189158732046641053517542997206357039491897439290231_<83>

Number: 48889_153
N=24702016765051234823956342110814867364739946009553963035599813443028417579906934494458521408693453087791090127424365104513052832027357803
  ( 137 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=514376085519544118671517084473390831428830178432400813
 r2=48023260529503490148502526990560189158732046641053517542997206357039491897439290231
Version: 
Total time: 18.83 hours.
Scaled time: 18.72 units (timescale=0.994).
Factorization parameters were as follows:
n: 24702016765051234823956342110814867364739946009553963035599813443028417579906934494458521408693453087791090127424365104513052832027357803
m: 10000000000000000000000000000000
deg: 5
c5: 11
c0: 25
skew: 1.18
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 427579 x 427827
Total sieving time: 18.83 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 18.83 hours.
 --------- CPU info (if available) ----------

(44·10¹³⁷+1)/9 = 4(8)₁₃₆9_<138> = 3 · 29 · 66085433 · C128

C128 = P62 · P67

P62 = 12240016285778463240974206995369762183863435353214459015510897_<62>

P67 = 6947094057530157592362535638508766194233043079469194501342993730647_<67>

Number: 48889_137
N=85032544403003913164511408344638894700587909343810261464472220252022999799189906695559056297867704674071987039169362400711360359
  ( 128 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=12240016285778463240974206995369762183863435353214459015510897
 r2=6947094057530157592362535638508766194233043079469194501342993730647
Version: 
Total time: 7.58 hours.
Scaled time: 5.98 units (timescale=0.789).
Factorization parameters were as follows:
n: 85032544403003913164511408344638894700587909343810261464472220252022999799189906695559056297867704674071987039169362400711360359
m: 5000000000000000000000000000
deg: 5
c5: 176
c0: 125
skew: 0.93
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 220979 x 221227
Total sieving time: 7.58 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 7.58 hours.
 --------- CPU info (if available) ----------

Mar 5, 2009 (5th)

By Serge Batalov / Msieve-1.40-beta2 / Mar 5, 2009

(44·10¹⁷³-71)/9 = 4(8)₁₇₂1_<174> = 37 · 73 · 2731 · 732227884459_<12> · C155

C155 = P78 · P78

P78 = 222196801234260691724485672982075026225893236567024475775850854282288166181119_<78>

P78 = 407361345743615648080243275018852929330785456412776829217583991628992578941731_<78>

SNFS difficulty: 174 digits.
Divisors found:
 r1=222196801234260691724485672982075026225893236567024475775850854282288166181119 (pp78)
 r2=407361345743615648080243275018852929330785456412776829217583991628992578941731 (pp78)
Version: Msieve-1.40-beta2
Total time: 60 hours.
Scaled time: 212.58 units (timescale=3.543).
Factorization parameters were as follows:
n: 90514387970715113812688616286590075454506183274898175753627866482315868310183245520287337553072997967662130006545915774082545876796675105196971760693376989
m: 20000000000000000000000000000000000
deg: 5
c5: 1375
c0: -71
skew: 0.55
type: snfs
lss: 1
rlim: 5700000
alim: 5700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5700000/5700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2850000, 7350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1141060 x 1141308
Total sieving time: 12.78 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 4.00 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,5700000,5700000,27,27,52,52,2.4,2.4,100000
total time: 60 hours.
 --------- CPU info (if available) ----------
[    0.292369] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 3.20GHz stepping 0b
...
[    0.572059] Total of 4 processors activated (25632.32 BogoMIPS).

Two P78s are the largest nice-split in our tables so far. Congratulations!

Mar 5, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Mar 5, 2009

(43·10¹⁷⁰+11)/9 = 4(7)₁₆₉9_<171> = 149 · 43721 · 37026599 · 20473164376070342916391015551218974069_<38> · C119

C119 = P55 · P65

P55 = 5324442344231370954185372841291055123494530955146799973_<55>

P65 = 18170909541081505556029517454042696276539506167164178844597564177_<65>

Number: 47779_170
N=96749960193732196416730950508919877162205494953720763444526510277302946135275614100297949828619793715079692652049367221
  ( 119 digits)
Divisors found:
 r1=5324442344231370954185372841291055123494530955146799973
 r2=18170909541081505556029517454042696276539506167164178844597564177
Version: 
Total time: 27.68 hours.
Scaled time: 66.03 units (timescale=2.386).
Factorization parameters were as follows:
name: 47779_170
n: 96749960193732196416730950508919877162205494953720763444526510277302946135275614100297949828619793715079692652049367221
skew: 42050.23
# norm 5.50e+16
c5: 49320
c4: -16877363589
c3: -1588772230851617
c2: 32193214923300171239
c1: -106734972629034058898608
c0: -916756717234030448522178740
# alpha -6.26
Y1: 5211415765969
Y0: -72198419571172764114417
# Murphy_E 3.19e-10
# M 47608540711978897969945260508855639284228098998401519360740790972855619763105283292526184099468468137325584232810097265
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2000000, 4000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9998130
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 623445 x 623693
Polynomial selection time: 2.34 hours.
Total sieving time: 23.19 hours.
Total relation processing time: 0.98 hours.
Matrix solve time: 0.90 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,52,52,2.4,2.4,100000
total time: 27.68 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(44·10¹⁴⁷+1)/9 = 4(8)₁₄₆9_<148> = 5595133 · 14976155783_<11> · C131

C131 = P58 · P73

P58 = 7555590219918819923651901826599066098972117404756182938387_<58>

P73 = 7722021524322947254908061786740476987835591485377922556867885562685104073_<73>

Number: 48889_147
N=58344430307177078103853004340775132563588429062398214023891731755851726496979978562384892952305723706132625607061463371516041750251
  ( 131 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=7555590219918819923651901826599066098972117404756182938387
 r2=7722021524322947254908061786740476987835591485377922556867885562685104073
Version: 
Total time: 5.59 hours.
Scaled time: 13.25 units (timescale=2.368).
Factorization parameters were as follows:
n: 58344430307177078103853004340775132563588429062398214023891731755851726496979978562384892952305723706132625607061463371516041750251
m: 200000000000000000000000000000
deg: 5
c5: 275
c0: 2
skew: 0.37
type: snfs
lss: 1
rlim: 1650000
alim: 1650000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 1650000/1650000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [825000, 1350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6253725
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 338846 x 339094
Total sieving time: 5.05 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1650000,1650000,27,27,49,49,2.4,2.4,75000
total time: 5.59 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(44·10¹⁵⁹+1)/9 = 4(8)₁₅₈9_<160> = 137153502420783237145181837_<27> · C134

C134 = P35 · P100

P35 = 10034706405889569576221889023898823_<35>

P100 = 3552209685768254673703247578789347277682520409617762582884450556424003928454425456401610252003607739_<100>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 35645381288841680184701319432383484371971244729826037624397820402415032840173903602698503344578660426775445228295677509218587715791197 (134 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3634558091
Step 1 took 3938ms
Step 2 took 908ms
********** Factor found in step 2: 10034706405889569576221889023898823
Found probable prime factor of 35 digits: 10034706405889569576221889023898823
Probable prime cofactor 3552209685768254673703247578789347277682520409617762582884450556424003928454425456401610252003607739 has 100 digits

Mar 5, 2009 (3rd)

By Sinkiti Sibata / GGNFS, Msieve / Mar 5, 2009

(44·10¹⁸²-17)/9 = 4(8)₁₈₁7_<183> = 151 · 33461 · 174367 · 215153 · 5911494629717278475537_<22> · 17463721528733402417637979_<26> · C119

C119 = P47 · P72

P47 = 72877725369541962550839612773055856131488302427_<47>

P72 = 342810168865540864323295835420733036947062052146446962992986050323840027_<72>

Number: 48887_182
N=24983225340469191671372170853204405349769299221541164669012057215760689735949602870419904715442180144321430758143845529
  ( 119 digits)
Divisors found:
 r1=72877725369541962550839612773055856131488302427 (pp47)
 r2=342810168865540864323295835420733036947062052146446962992986050323840027 (pp72)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 95.07 hours.
Scaled time: 44.88 units (timescale=0.472).
Factorization parameters were as follows:
name: 48887_182
n: 24983225340469191671372170853204405349769299221541164669012057215760689735949602870419904715442180144321430758143845529
skew: 81326.26
# norm 1.26e+16
c5: 3780
c4: -3360621385
c3: 88313684980337
c2: 12766101140945879133
c1: 404173228402249633623216
c0: 5564546065439014650337853721
# alpha -5.38
Y1: 2018118572789
Y0: -92051958728877970629458
# Murphy_E 3.33e-10
# M 2326006205974630919379109454394760739892900571011807746130185695075112583263297487941486171691873020998230039209907902
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4230001)
Primes: RFBsize:315948, AFBsize:316780, largePrimes:7704127 encountered
Relations: rels:7813822, finalFF:775045
Max relations in full relation-set: 28
Initial matrix: 632807 x 775045 with sparse part having weight 64821840.
Pruned matrix : 515175 x 518403 with weight 40831694.
Total sieving time: 81.22 hours.
Total relation processing time: 0.83 hours.
Matrix solve time: 12.57 hours.
Time per square root: 0.46 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 95.07 hours.
 --------- CPU info (if available) ----------

(44·10¹⁵⁷+1)/9 = 4(8)₁₅₆9_<158> = 7 · 199 · 1871 · 18733765663_<11> · 475139979542655439_<18> · 111097128739710702376187_<24> · C101

C101 = P42 · P59

P42 = 448350774135273865432868518969449532379539_<42>

P59 = 42307547057122291786168886739490857260394637940501717287063_<59>

Wed Mar 04 20:58:06 2009  Msieve v. 1.39
Wed Mar 04 20:58:06 2009  random seeds: 90f10f5c a26ba651
Wed Mar 04 20:58:06 2009  factoring 18968621474825307162382576287788700571514677901865873275118921187359881407482695541073616281930603957 (101 digits)
Wed Mar 04 20:58:07 2009  searching for 15-digit factors
Wed Mar 04 20:58:09 2009  commencing quadratic sieve (101-digit input)
Wed Mar 04 20:58:09 2009  using multiplier of 1
Wed Mar 04 20:58:09 2009  using 32kb Intel Core sieve core
Wed Mar 04 20:58:09 2009  sieve interval: 36 blocks of size 32768
Wed Mar 04 20:58:09 2009  processing polynomials in batches of 6
Wed Mar 04 20:58:09 2009  using a sieve bound of 2895371 (105000 primes)
Wed Mar 04 20:58:09 2009  using large prime bound of 434305650 (28 bits)
Wed Mar 04 20:58:09 2009  using double large prime bound of 3532090588924500 (43-52 bits)
Wed Mar 04 20:58:09 2009  using trial factoring cutoff of 52 bits
Wed Mar 04 20:58:09 2009  polynomial 'A' values have 13 factors
Thu Mar 05 07:38:25 2009  105133 relations (25969 full + 79164 combined from 1562397 partial), need 105096
Thu Mar 05 07:38:27 2009  begin with 1588366 relations
Thu Mar 05 07:38:28 2009  reduce to 273626 relations in 11 passes
Thu Mar 05 07:38:28 2009  attempting to read 273626 relations
Thu Mar 05 07:38:33 2009  recovered 273626 relations
Thu Mar 05 07:38:33 2009  recovered 262620 polynomials
Thu Mar 05 07:38:33 2009  attempting to build 105133 cycles
Thu Mar 05 07:38:34 2009  found 105133 cycles in 6 passes
Thu Mar 05 07:38:34 2009  distribution of cycle lengths:
Thu Mar 05 07:38:34 2009     length 1 : 25969
Thu Mar 05 07:38:34 2009     length 2 : 18366
Thu Mar 05 07:38:34 2009     length 3 : 17604
Thu Mar 05 07:38:34 2009     length 4 : 14295
Thu Mar 05 07:38:34 2009     length 5 : 10532
Thu Mar 05 07:38:34 2009     length 6 : 7408
Thu Mar 05 07:38:34 2009     length 7 : 4675
Thu Mar 05 07:38:34 2009     length 9+: 6284
Thu Mar 05 07:38:34 2009  largest cycle: 19 relations
Thu Mar 05 07:38:34 2009  matrix is 105000 x 105133 (28.3 MB) with weight 7004619 (66.63/col)
Thu Mar 05 07:38:34 2009  sparse part has weight 7004619 (66.63/col)
Thu Mar 05 07:38:36 2009  filtering completed in 3 passes
Thu Mar 05 07:38:36 2009  matrix is 100178 x 100242 (27.2 MB) with weight 6734418 (67.18/col)
Thu Mar 05 07:38:36 2009  sparse part has weight 6734418 (67.18/col)
Thu Mar 05 07:38:36 2009  saving the first 48 matrix rows for later
Thu Mar 05 07:38:36 2009  matrix is 100130 x 100242 (16.4 MB) with weight 5307533 (52.95/col)
Thu Mar 05 07:38:36 2009  sparse part has weight 3704219 (36.95/col)
Thu Mar 05 07:38:36 2009  matrix includes 64 packed rows
Thu Mar 05 07:38:36 2009  using block size 40096 for processor cache size 1024 kB
Thu Mar 05 07:38:37 2009  commencing Lanczos iteration
Thu Mar 05 07:38:37 2009  memory use: 16.2 MB
Thu Mar 05 07:39:48 2009  lanczos halted after 1584 iterations (dim = 100129)
Thu Mar 05 07:39:48 2009  recovered 16 nontrivial dependencies
Thu Mar 05 07:39:50 2009  prp42 factor: 448350774135273865432868518969449532379539
Thu Mar 05 07:39:50 2009  prp59 factor: 42307547057122291786168886739490857260394637940501717287063
Thu Mar 05 07:39:50 2009  elapsed time 10:41:44

(44·10¹²⁶+1)/9 = 4(8)₁₂₅9_<127> = 509 · 12841 · 3553095281152037_<16> · C105

C105 = P35 · P70

P35 = 43521265142965607939995083695342551_<35>

P70 = 4837101196041471624016224793481902477753259738852941541678317678476263_<70>

Number: 48889_126
N=210516763676276950698136815053296181646950051888481831521398162638508208518541145810777388154911507366913
  ( 105 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=43521265142965607939995083695342551 (pp35)
 r2=4837101196041471624016224793481902477753259738852941541678317678476263 (pp70)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.26 hours.
Scaled time: 1.54 units (timescale=0.472).
Factorization parameters were as follows:
name: 48889_126
n: 210516763676276950698136815053296181646950051888481831521398162638508208518541145810777388154911507366913
m: 20000000000000000000000000
deg: 5
c5: 55
c0: 4
skew: 0.59
type: snfs
lss: 1
rlim: 960000
alim: 960000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 960000/960000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [480000, 730001)
Primes: RFBsize:75618, AFBsize:75696, largePrimes:2683272 encountered
Relations: rels:2701674, finalFF:313626
Max relations in full relation-set: 28
Initial matrix: 151381 x 313626 with sparse part having weight 22104515.
Pruned matrix : 104189 x 105009 with weight 5480480.
Total sieving time: 3.01 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,960000,960000,26,26,47,47,2.3,2.3,50000
total time: 3.26 hours.
 --------- CPU info (if available) ----------

(44·10¹³⁶+1)/9 = 4(8)₁₃₅9_<137> = 8713 · 13931 · 21121 · 196681 · 155441215959456973505639_<24> · C96

C96 = P38 · P58

P38 = 63545509271969160839589261705139727353_<38>

P58 = 9815947500455591675226778421185762174956963827834493969589_<58>

Thu Mar 05 07:47:34 2009  Msieve v. 1.39
Thu Mar 05 07:47:34 2009  random seeds: 301109d8 a9663a24
Thu Mar 05 07:47:34 2009  factoring 623759382903363309442819325262807299780625921424957644014837575765133655544083293853710133467917 (96 digits)
Thu Mar 05 07:47:35 2009  searching for 15-digit factors
Thu Mar 05 07:47:37 2009  commencing quadratic sieve (96-digit input)
Thu Mar 05 07:47:37 2009  using multiplier of 37
Thu Mar 05 07:47:37 2009  using 32kb Intel Core sieve core
Thu Mar 05 07:47:37 2009  sieve interval: 36 blocks of size 32768
Thu Mar 05 07:47:37 2009  processing polynomials in batches of 6
Thu Mar 05 07:47:37 2009  using a sieve bound of 2296643 (84706 primes)
Thu Mar 05 07:47:37 2009  using large prime bound of 344496450 (28 bits)
Thu Mar 05 07:47:37 2009  using double large prime bound of 2327729440990800 (43-52 bits)
Thu Mar 05 07:47:37 2009  using trial factoring cutoff of 52 bits
Thu Mar 05 07:47:37 2009  polynomial 'A' values have 13 factors
Thu Mar 05 12:58:34 2009  84852 relations (21193 full + 63659 combined from 1272611 partial), need 84802
Thu Mar 05 12:58:35 2009  begin with 1293804 relations
Thu Mar 05 12:58:36 2009  reduce to 220822 relations in 11 passes
Thu Mar 05 12:58:36 2009  attempting to read 220822 relations
Thu Mar 05 12:58:40 2009  recovered 220822 relations
Thu Mar 05 12:58:40 2009  recovered 207250 polynomials
Thu Mar 05 12:58:41 2009  attempting to build 84852 cycles
Thu Mar 05 12:58:41 2009  found 84852 cycles in 6 passes
Thu Mar 05 12:58:41 2009  distribution of cycle lengths:
Thu Mar 05 12:58:41 2009     length 1 : 21193
Thu Mar 05 12:58:41 2009     length 2 : 15024
Thu Mar 05 12:58:41 2009     length 3 : 14112
Thu Mar 05 12:58:41 2009     length 4 : 11403
Thu Mar 05 12:58:41 2009     length 5 : 8579
Thu Mar 05 12:58:41 2009     length 6 : 5646
Thu Mar 05 12:58:41 2009     length 7 : 3635
Thu Mar 05 12:58:41 2009     length 9+: 5260
Thu Mar 05 12:58:41 2009  largest cycle: 20 relations
Thu Mar 05 12:58:41 2009  matrix is 84706 x 84852 (23.0 MB) with weight 5702238 (67.20/col)
Thu Mar 05 12:58:41 2009  sparse part has weight 5702238 (67.20/col)
Thu Mar 05 12:58:43 2009  filtering completed in 3 passes
Thu Mar 05 12:58:43 2009  matrix is 80736 x 80800 (22.1 MB) with weight 5469628 (67.69/col)
Thu Mar 05 12:58:43 2009  sparse part has weight 5469628 (67.69/col)
Thu Mar 05 12:58:43 2009  saving the first 48 matrix rows for later
Thu Mar 05 12:58:43 2009  matrix is 80688 x 80800 (14.4 MB) with weight 4400241 (54.46/col)
Thu Mar 05 12:58:43 2009  sparse part has weight 3289200 (40.71/col)
Thu Mar 05 12:58:43 2009  matrix includes 64 packed rows
Thu Mar 05 12:58:43 2009  using block size 32320 for processor cache size 1024 kB
Thu Mar 05 12:58:44 2009  commencing Lanczos iteration
Thu Mar 05 12:58:44 2009  memory use: 13.5 MB
Thu Mar 05 12:59:30 2009  lanczos halted after 1277 iterations (dim = 80687)
Thu Mar 05 12:59:31 2009  recovered 17 nontrivial dependencies
Thu Mar 05 12:59:31 2009  prp38 factor: 63545509271969160839589261705139727353
Thu Mar 05 12:59:31 2009  prp58 factor: 9815947500455591675226778421185762174956963827834493969589
Thu Mar 05 12:59:31 2009  elapsed time 05:11:57

(44·10¹²⁹+1)/9 = 4(8)₁₂₈9_<130> = 5953 · 672367679 · C118

C118 = P58 · P60

P58 = 1728160936759207317423250449466784351977326069208277330599_<58>

P60 = 706778405413566726875860515905167801632878263168590878384353_<60>

Number: 48889_129
N=1221426831180688279002960012848720777457743423346284193353725933058191571678564724627024589146425316248590692769717447
  ( 118 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1728160936759207317423250449466784351977326069208277330599 (pp58)
 r2=706778405413566726875860515905167801632878263168590878384353 (pp60)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 5.53 hours.
Scaled time: 2.60 units (timescale=0.471).
Factorization parameters were as follows:
name: 48889_129
n: 1221426831180688279002960012848720777457743423346284193353725933058191571678564724627024589146425316248590692769717447
m: 100000000000000000000000000
deg: 5
c5: 22
c0: 5
skew: 0.74
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
 Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 990001)
Primes: RFBsize:84270, AFBsize:84259, largePrimes:2900239 encountered
Relations: rels:2881979, finalFF:279784
Max relations in full relation-set: 28
Initial matrix: 168595 x 279784 with sparse part having weight 23071610.
Pruned matrix : 139231 x 140137 with weight 8439977.
Total sieving time: 5.09 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 5.53 hours.
 --------- CPU info (if available) ----------

Mar 5, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Mar 5, 2009

(38·10¹⁶⁵+43)/9 = 4(2)₁₆₄7_<166> = 3 · 89 · 6323 · 210361 · 487730764733_<12> · 1769013090477089_<16> · C128

C128 = P43 · P85

P43 = 9624864893143538828693818535656088289049661_<43>

P85 = 1431645782459834913814885047641598665244275971770173259132088449280057432040679887011_<85>

Number: 42227_165
N=13779397231014677003271297836843222436382621372327834819315841451944209363898472323132704806248632749606937926483332518047853271
  ( 128 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=9624864893143538828693818535656088289049661 (pp43)
 r2=1431645782459834913814885047641598665244275971770173259132088449280057432040679887011 (pp85)
Version: Msieve-1.39
Total time: 50.19 hours.
Scaled time: 129.05 units (timescale=2.571).
Factorization parameters were as follows:
n: 13779397231014677003271297836843222436382621372327834819315841451944209363898472323132704806248632749606937926483332518047853271
m: 1000000000000000000000000000000000
deg: 5
c5: 38
c0: 43
skew: 1.03
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 800481 x 800729
Total sieving time: 50.19 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 50.19 hours.
 --------- CPU info (if available) ----------

(8·10¹⁷⁷-53)/9 = (8)₁₇₆3_<177> = 125399 · C172

C172 = P49 · P124

P49 = 4281919116316707152351160271644136591660758660269_<49>

P124 = 1655445718495538671619999369350006699248872472048836636523424165681830716062409891277817279130004176653121465148247908459193_<124>

Number: 88883_177
N=7088484668050693298103564533121387641758617603720036753793003842844750666982104234394922518432275288390568416724925150032208302210455337673258071347370305097240718736902917
  ( 172 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=4281919116316707152351160271644136591660758660269 (pp49)
 r2=1655445718495538671619999369350006699248872472048836636523424165681830716062409891277817279130004176653121465148247908459193 (pp124)
Version: Msieve-1.39
Total time: 82.71 hours.
Scaled time: 143.82 units (timescale=1.739).
Factorization parameters were as follows:
n: 7088484668050693298103564533121387641758617603720036753793003842844750666982104234394922518432275288390568416724925150032208302210455337673258071347370305097240718736902917
m: 200000000000000000000000000000000000
deg: 5
c5: 25
c0: -53
skew: 1.16
type: snfs
lss: 1
rlim: 6500000
alim: 6500000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6500000/6500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3250000, 7350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1293708 x 1293956
Total sieving time: 82.71 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,6500000,6500000,28,28,53,53,2.5,2.5,100000
total time: 82.71 hours.
 --------- CPU info (if available) ----------

Mar 5, 2009

By Robert Backstrom / GGNFS, GMP-ECM, Msieve / Mar 5, 2009

(44·10¹¹³+1)/9 = 4(8)₁₁₂9_<114> = 3³ · 19 · 71 · 16335531151_<11> · C99

C99 = P42 · P58

P42 = 388108802120652459580690750421457618243901_<42>

P58 = 2117130850233126729863891430790043326178467398399902760293_<58>

Number: n
N=821677118216657280176438291640989826544716440836332482465075702032722614207146795471847445212222993
  ( 99 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=388108802120652459580690750421457618243901 (pp42)
 r2=2117130850233126729863891430790043326178467398399902760293 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.28 hours.
Scaled time: 2.31 units (timescale=1.803).
Factorization parameters were as follows:
name: KA_4_8_112_9
n: 821677118216657280176438291640989826544716440836332482465075702032722614207146795471847445212222993
deg: 5
c5: 11
c0: 25
m: 100000000000000000000000
skew: 1.18
type: snfs
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [250000, 330001)
Primes: RFBsize:41538, AFBsize:41278, largePrimes:5238750 encountered
Relations: rels:4744123, finalFF:291634
Max relations in full relation-set: 48
Initial matrix: 82882 x 291634 with sparse part having weight 36298120.
Pruned matrix : 59122 x 59600 with weight 4271825.
Total sieving time: 1.13 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.5,2.5,50000
total time: 1.28 hours.
 --------- CPU info (if available) ----------

(13·10¹⁶⁶-7)/3 = 4(3)₁₆₅1_<167> = 41 · 254713 · 1160429 · 720322706891_<12> · 7895407570994760379_<19> · C123

C123 = P39 · P85

P39 = 314414705694017135605799681084992228187_<39>

P85 = 1999696316636496215730131756790259309249856000129855091108599659958985721872494604581_<85>

GMP-ECM 6.0 [powered by GMP 4.1.4] [ECM]
Input number is 628733928872674059655935066886932148706683298336978421071876163430726051438205282807890104870440171098852917012474687524647 (123 digits)
Using B1=20000000, B2=59950304286, polynomial Dickson(12), sigma=583429813
Step 1 took 231640ms
Step 2 took 77316ms
********** Factor found in step 2: 314414705694017135605799681084992228187
Found probable prime factor of 39 digits: 314414705694017135605799681084992228187
Probable prime cofactor 1999696316636496215730131756790259309249856000129855091108599659958985721872494604581 has 85 digits

(44·10¹²⁴+1)/9 = 4(8)₁₂₃9_<125> = 23 · 89 · 395851 · C116

C116 = P53 · P63

P53 = 65607094660330748342507041418685412456239437054398433_<53>

P63 = 919622888886411805956840633746774726304291375836858991352861589_<63>

Number: n
N=60333785922977645087382713158145034367621150985678689491667920138777832729104385222146722853596300475841613507490037
  ( 116 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=65607094660330748342507041418685412456239437054398433 (pp53)
 r2=919622888886411805956840633746774726304291375836858991352861589 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.19 hours.
Scaled time: 4.00 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_8_123_9
n: 60333785922977645087382713158145034367621150985678689491667920138777832729104385222146722853596300475841613507490037
deg: 5
c5: 22
c0: 5
m: 10000000000000000000000000
skew: 0.74
type: snfs
rlim: 700000
alim: 700000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [350000, 590001)
Primes: RFBsize:56543, AFBsize:56389, largePrimes:6813290 encountered
Relations: rels:6080771, finalFF:209465
Max relations in full relation-set: 48
Initial matrix: 112998 x 209465 with sparse part having weight 32083107.
Pruned matrix : 100471 x 101099 with weight 10250707.
Total sieving time: 1.94 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.07 hours.
Total square root time: 0.06 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,700000,700000,28,28,56,56,2.5,2.5,50000
total time: 2.19 hours.
 --------- CPU info (if available) ----------

(44·10¹⁸⁴+1)/9 = 4(8)₁₈₃9_<185> = 3634092589279_<13> · 31874480460293_<14> · 149186643169434870150225958130677_<33> · 13539580767694393280067652642610347_<35> · C93

C93 = P38 · P55

P38 = 23803194133008155288609041813708681643_<38>

P55 = 8778102876478133886827822003867357150158400139814099111_<55>

Thu Mar 05 02:37:46 2009  
Thu Mar 05 02:37:46 2009  
Thu Mar 05 02:37:46 2009  Msieve v. 1.39
Thu Mar 05 02:37:46 2009  random seeds: 6d768a74 eabf09d4
Thu Mar 05 02:37:46 2009  factoring 208946886888326328200126038007985057407936209148615529834458396285284634094860013715548319373 (93 digits)
Thu Mar 05 02:37:46 2009  searching for 15-digit factors
Thu Mar 05 02:37:47 2009  commencing quadratic sieve (93-digit input)
Thu Mar 05 02:37:48 2009  using multiplier of 5
Thu Mar 05 02:37:48 2009  using 64kb Opteron sieve core
Thu Mar 05 02:37:48 2009  sieve interval: 18 blocks of size 65536
Thu Mar 05 02:37:48 2009  processing polynomials in batches of 6
Thu Mar 05 02:37:48 2009  using a sieve bound of 1884133 (70588 primes)
Thu Mar 05 02:37:48 2009  using large prime bound of 220443561 (27 bits)
Thu Mar 05 02:37:48 2009  using double large prime bound of 1042162145233209 (42-50 bits)
Thu Mar 05 02:37:48 2009  using trial factoring cutoff of 50 bits
Thu Mar 05 02:37:48 2009  polynomial 'A' values have 12 factors
Thu Mar 05 02:37:48 2009  restarting with 83 full and 5203 partial relations
Thu Mar 05 05:53:01 2009  70935 relations (17619 full + 53316 combined from 931366 partial), need 70684
Thu Mar 05 05:53:03 2009  begin with 948985 relations
Thu Mar 05 05:53:03 2009  reduce to 181597 relations in 10 passes
Thu Mar 05 05:53:03 2009  attempting to read 181597 relations
Thu Mar 05 05:53:07 2009  recovered 181597 relations
Thu Mar 05 05:53:07 2009  recovered 164521 polynomials
Thu Mar 05 05:53:07 2009  attempting to build 70935 cycles
Thu Mar 05 05:53:07 2009  found 70935 cycles in 7 passes
Thu Mar 05 05:53:08 2009  distribution of cycle lengths:
Thu Mar 05 05:53:08 2009     length 1 : 17619
Thu Mar 05 05:53:08 2009     length 2 : 12717
Thu Mar 05 05:53:08 2009     length 3 : 12181
Thu Mar 05 05:53:08 2009     length 4 : 9544
Thu Mar 05 05:53:08 2009     length 5 : 7136
Thu Mar 05 05:53:08 2009     length 6 : 4883
Thu Mar 05 05:53:08 2009     length 7 : 2947
Thu Mar 05 05:53:08 2009     length 9+: 3908
Thu Mar 05 05:53:08 2009  largest cycle: 20 relations
Thu Mar 05 05:53:08 2009  matrix is 70588 x 70935 (17.3 MB) with weight 4242075 (59.80/col)
Thu Mar 05 05:53:08 2009  sparse part has weight 4242075 (59.80/col)
Thu Mar 05 05:53:10 2009  filtering completed in 3 passes
Thu Mar 05 05:53:10 2009  matrix is 66977 x 67041 (16.4 MB) with weight 4020997 (59.98/col)
Thu Mar 05 05:53:10 2009  sparse part has weight 4020997 (59.98/col)
Thu Mar 05 05:53:10 2009  saving the first 48 matrix rows for later
Thu Mar 05 05:53:11 2009  matrix is 66929 x 67041 (9.0 MB) with weight 3004074 (44.81/col)
Thu Mar 05 05:53:11 2009  sparse part has weight 1961779 (29.26/col)
Thu Mar 05 05:53:11 2009  matrix includes 64 packed rows
Thu Mar 05 05:53:11 2009  using block size 21845 for processor cache size 512 kB
Thu Mar 05 05:53:11 2009  commencing Lanczos iteration
Thu Mar 05 05:53:11 2009  memory use: 9.6 MB
Thu Mar 05 05:53:52 2009  lanczos halted after 1060 iterations (dim = 66927)
Thu Mar 05 05:53:52 2009  recovered 17 nontrivial dependencies
Thu Mar 05 05:53:53 2009  prp38 factor: 23803194133008155288609041813708681643
Thu Mar 05 05:53:53 2009  prp55 factor: 8778102876478133886827822003867357150158400139814099111
Thu Mar 05 05:53:53 2009  elapsed time 03:16:07

(35·10²⁰²-17)/9 = 3(8)₂₀₁7_<203> = 37 · C202

C202 = P47 · P55 · P100

P47 = 36118644455111721394476564262279362183697261549_<47>

P55 = 3293898399544187326777054807794959505060276762759732491_<55>

P100 = 8834503942940752249432849357854950544490744137172844219578502235694939623388905000315383980972142789_<100>

Number: n
N=1051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051
  ( 202 digits)
SNFS difficulty: 204 digits.
Divisors found:

Thu Mar  5 21:30:11 2009  prp47 factor: 36118644455111721394476564262279362183697261549
Thu Mar  5 21:30:11 2009  prp55 factor: 3293898399544187326777054807794959505060276762759732491
Thu Mar  5 21:30:11 2009  prp100 factor: 8834503942940752249432849357854950544490744137172844219578502235694939623388905000315383980972142789
Thu Mar  5 21:30:11 2009  elapsed time 19:52:44 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20050930-k8
Total time: 97.20 hours.
Scaled time: 195.76 units (timescale=2.014).
Factorization parameters were as follows:
name: KA_3_8_201_7
n: 1051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051
deg: 5
c5: 28
c0: -425
m: 50000000000000000000000000000000000000000
skew: 1.72
type: snfs
rlim: 12000000
alim: 12000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [6000000, 30099990)
Primes: RFBsize:788060, AFBsize:788064, largePrimes:34129443 encountered
Relations: rels:27304088, finalFF:124994
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 7075499 hash collisions in 42646710 relations
Msieve: matrix is 3340828 x 3341073 (911.0 MB)

Total sieving time: 96.34 hours.
Total relation processing time: 0.86 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,204,5,0,0,0,0,0,0,0,0,12000000,12000000,29,29,58,58,2.5,2.5,100000
total time: 97.20 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368976k/3407296k available (2745k kernel code, 36940k reserved, 1424k data, 412k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830498)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454)
Total of 4 processors activated (22643.71 BogoMIPS).

Mar 4, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.2, Msieve / Mar 4, 2009

(44·10¹⁴⁶+1)/9 = 4(8)₁₄₅9_<147> = 3 · 23 · 31 · C144

C144 = P36 · P109

P36 = 156337413536843385713359958798964493_<36>

P109 = 1461963263796163962865030542478007762086954023549779035977892379429908347870832965015267111700485435552397607_<109>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=4255872709
Step 1 took 3561ms
Step 2 took 3080ms
********** Factor found in step 2: 156337413536843385713359958798964493
Found probable prime factor of 36 digits: 156337413536843385713359958798964493
Probable prime cofactor has 109 digits

(44·10¹⁵⁹+1)/9 = 4(8)₁₅₈9_<160> = C160

C160 = P27 · C134

P27 = 137153502420783237145181837_<27>

C134 = [35645381288841680184701319432383484371971244729826037624397820402415032840173903602698503344578660426775445228295677509218587715791197_<134>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1407227653
Step 1 took 4596ms
Step 2 took 3469ms
********** Factor found in step 2: 137153502420783237145181837
Found probable prime factor of 27 digits: 137153502420783237145181837
Composite cofactor 35645381288841680184701319432383484371971244729826037624397820402415032840173903602698503344578660426775445228295677509218587715791197 has 134 digits

(44·10¹⁸⁷+1)/9 = 4(8)₁₈₆9_<188> = 7 · 233 · 188701 · 297924401 · C171

C171 = P30 · P142

P30 = 526456192270207306192497814231_<30>

P142 = 1012776676261249602907425802562598136206196450536507964244738758587615890319638376087347271113370719438937571302723714882211006597740928373749_<142>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=2745248539
Step 1 took 4424ms
Step 2 took 3652ms
********** Factor found in step 2: 526456192270207306192497814231
Found probable prime factor of 30 digits: 526456192270207306192497814231
Probable prime cofactor has 142 digits

(43·10¹⁷¹+11)/9 = 4(7)₁₇₀9_<172> = 3 · 355093 · 448570037 · C157

C157 = P35 · C123

P35 = 19956188840224140440597442401083283_<35>

C123 = [501019598579825057644595959540665425580414504347777059326970261905824979340160312991495080272365020643529680147710715868931_<123>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=708918991
Step 1 took 13081ms
Step 2 took 11069ms
********** Factor found in step 2: 19956188840224140440597442401083283
Found probable prime factor of 35 digits: 19956188840224140440597442401083283
Composite cofactor  has 123 digits

(44·10¹²¹+1)/9 = 4(8)₁₂₀9_<122> = 7 · C121

C121 = P43 · P79

P43 = 4128872157334460592498795153932340323839073_<43>

P79 = 1691533842170553966100917485120791742004368907555220632245540146694891547578399_<79>

SNFS difficulty: 123 digits.
Divisors found:
 r1=4128872157334460592498795153932340323839073 (pp43)
 r2=1691533842170553966100917485120791742004368907555220632245540146694891547578399 (pp79)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=3.532).
Factorization parameters were as follows:
n: 6984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984127
m: 2000000000000000000000000
deg: 5
c5: 55
c0: 4
skew: 0.59
type: snfs
lss: 1
rlim: 790000
alim: 790000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 790000/790000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [395000, 595001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 75391 x 75629
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,790000,790000,25,25,46,46,2.2,2.2,50000
total time: 1.00 hours.
 --------- CPU info (if available) ----------
[    0.292369] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 3.20GHz stepping 0b

Mar 4, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Mar 4, 2009

(44·10¹⁶⁸-17)/9 = 4(8)₁₆₇7_<169> = 3 · 83 · 162391 · C162

C162 = P73 · P89

P73 = 1715819497950141258159881096879952789398002521580423107736772458539641033_<73>

P89 = 70465617988301484346048053599489955072455045833762809942425229784950721301400075466556321_<89>

Number: 48887_168
N=120906281279433895687407867181020672745576189613869605779656584448499366331553749501491723837270466397711193534571781318644627067337002965372185489657428017119593
  ( 162 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=1715819497950141258159881096879952789398002521580423107736772458539641033 (pp73)
 r2=70465617988301484346048053599489955072455045833762809942425229784950721301400075466556321 (pp89)
Version: Msieve-1.39
Total time: 51.54 hours.
Scaled time: 89.43 units (timescale=1.735).
Factorization parameters were as follows:
n: 120906281279433895687407867181020672745576189613869605779656584448499366331553749501491723837270466397711193534571781318644627067337002965372185489657428017119593
m: 10000000000000000000000000000000000
deg: 5
c5: 11
c0: -425
skew: 2.08
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 938725 x 938973
Total sieving time: 51.54 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 51.54 hours.
 --------- CPU info (if available) ----------

Mar 4, 2009

Factorizations of 488...889 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 3, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Mar 3, 2009

(43·10¹⁷⁶-61)/9 = 4(7)₁₇₅1_<177> = 3 · 19 · 41 · 24481 · 10017223 · 58378057 · 81878593 · 11026136010248736668361127139_<29> · C119

C119 = P57 · P63

P57 = 103405039411964640209554971522786871674702176896591854287_<57>

P63 = 152969793589021182262675715827594600644346714549363121584949737_<63>

Number: 47771_176
N=15817847534912831302529090682116843282045429442306500676740679450683592836514865749211284047570846181272431088522972519
  ( 119 digits)
Divisors found:
 r1=103405039411964640209554971522786871674702176896591854287
 r2=152969793589021182262675715827594600644346714549363121584949737
Version: 
Total time: 23.71 hours.
Scaled time: 56.56 units (timescale=2.385).
Factorization parameters were as follows:
name: 47771_176
n: 15817847534912831302529090682116843282045429442306500676740679450683592836514865749211284047570846181272431088522972519
skew: 52926.37
# norm 1.01e+16
c5: 16200
c4: 1296699318
c3: 321549041620995
c2: -6027505071870800284
c1: -432965756555996210893964
c0: 1395208670446382882234889360
# alpha -5.84
Y1: 778142714723
Y0: -62795191321863803995807
# Murphy_E 3.59e-10
# M 10039002453100207941900866177830567936876972703857384985376185758164620211110620218550257430073029486337315331444330562
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2000000, 3700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9461334
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 641774 x 642022
Polynomial selection time: 2.29 hours.
Total sieving time: 19.58 hours.
Total relation processing time: 0.78 hours.
Matrix solve time: 0.94 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,52,52,2.4,2.4,100000
total time: 23.71 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Mar 3, 2009 (2nd)

By Wataru Sakai / Msieve / Mar 3, 2009

4·10¹⁹⁸+1 = 4(0)₁₉₇1_<199> = 601 · C196

C196 = P60 · P136

P60 = 929931633094791878075356891588302829966299262696914473414281_<60>

P136 = 7157057364649085307661377430067986943422261055343880321564902746003515911775225750122658781467332419066410898034428685018858357725799521_<136>

Number: 40001_198
N=6655574043261231281198003327787021630615640599001663893510815307820299500831946755407653910149750415973377703826955074875207986688851913477537437603993344425956738768718801996672212978369384359401
  ( 196 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=929931633094791878075356891588302829966299262696914473414281
 r2=7157057364649085307661377430067986943422261055343880321564902746003515911775225750122658781467332419066410898034428685018858357725799521
Version: 
Total time: 598.43 hours.
Scaled time: 1065.20 units (timescale=1.780).
Factorization parameters were as follows:
n: 6655574043261231281198003327787021630615640599001663893510815307820299500831946755407653910149750415973377703826955074875207986688851913477537437603993344425956738768718801996672212978369384359401
m: 10000000000000000000000000000000000000000
deg: 5
c5: 1
c0: 25
skew: 1.90
type: snfs
lss: 1
rlim: 15100000
alim: 15100000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
Factor base limits: 15100000/15100000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [7550000, 13250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2568959 x 2569207
Total sieving time: 598.43 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,200,5,0,0,0,0,0,0,0,0,15100000,15100000,29,29,56,56,2.6,2.6,100000
total time: 598.43 hours.
 --------- CPU info (if available) ----------

Mar 3, 2009

By Ignacio Santos / GGNFS, Msieve / Mar 3, 3009

(44·10¹⁶⁷-53)/9 = 4(8)₁₆₆3_<168> = 3 · 307261 · C162

C162 = P60 · P103

P60 = 240176965948327227964428493955389903582874479604862156178867_<60>

P103 = 2208259555617665688706709242812968313599814381853752897676508469902040009732755649720367881553125991303_<103>

Number: 48883_167
N=530373080094652308503073813347489472998405144040288103478680870539908946996081386713455215477925812136792378345976101630089607737275355359004113645932815954393701
  ( 162 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=240176965948327227964428493955389903582874479604862156178867 (pp60)
 r2=2208259555617665688706709242812968313599814381853752897676508469902040009732755649720367881553125991303 (pp103)
Version: Msieve-1.39
Total time: 59.50 hours.
Scaled time: 152.96 units (timescale=2.571).
Factorization parameters were as follows:
n: 530373080094652308503073813347489472998405144040288103478680870539908946996081386713455215477925812136792378345976101630089607737275355359004113645932815954393701
m: 2000000000000000000000000000000000
deg: 5
c5: 275
c0: -106
skew: 0.83
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2300000, 5300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 954960 x 955207
Total sieving time: 59.50 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000
total time: 59.50 hours.
 --------- CPU info (if available) ----------

(82·10¹⁷⁵+71)/9 = 9(1)₁₇₄9_<176> = 3 · 11 · 11587 · C171

C171 = P44 · P127

P44 = 67882709654942508757821179425567338626971537_<44>

P127 = 3510162534540666290452358492207298441872470977033021534083805522851039632888388673042910115047458152439653047100048042698309397_<127>

Number: 91119_175
N=238279344173881154980663050051157412855868021139446012148178368943018981855609110291081465673681087506926809593591331746160433482432274181648480431599444286075855938633189
  ( 171 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=67882709654942508757821179425567338626971537 (pp44)
 r2=3510162534540666290452358492207298441872470977033021534083805522851039632888388673042910115047458152439653047100048042698309397 (pp127)
Version: Msieve-1.39
Total time: 103.46 hours.
Scaled time: 179.91 units (timescale=1.739).
Factorization parameters were as follows:
n: 238279344173881154980663050051157412855868021139446012148178368943018981855609110291081465673681087506926809593591331746160433482432274181648480431599444286075855938633189
m: 100000000000000000000000000000000000
deg: 5
c5: 82
c0: 71
skew: 0.97
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3100000, 7200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1309125 x 1309372
Total sieving time: 103.46 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,53,53,2.5,2.5,100000
total time: 103.46 hours.
 --------- CPU info (if available) ----------

Mar 2, 2009 (7th)

By Ignacio Santos / GGNFS, Msieve / Mar 2, 2009

(37·10¹⁶⁴+71)/9 = 4(1)₁₆₃9_<165> = 25679 · 311393 · 21601121 · 1772064851_<10> · C139

C139 = P41 · P98

P41 = 82984091017440112507642480432701193756559_<41>

P98 = 16185328543252187405293423598335473778264384560401110207473315740112040289602442795258184152320693_<98>

Number: 41119_164
N=1343124776980410906357398666493863766817267437319229096291062496515901520488286342007374944355498394269625371902195894299234123782340175387
  ( 139 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=82984091017440112507642480432701193756559 (pp41)
 r2=16185328543252187405293423598335473778264384560401110207473315740112040289602442795258184152320693 (pp98)
Version: Msieve-1.39
Total time: 56.70 hours.
Scaled time: 145.14 units (timescale=2.560).
Factorization parameters were as follows:
n: 1343124776980410906357398666493863766817267437319229096291062496515901520488286342007374944355498394269625371902195894299234123782340175387
m: 500000000000000000000000000000000
deg: 5
c5: 592
c0: 355
skew: 0.90
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 5050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 879398 x 879646
Total sieving time: 56.70 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 56.70 hours.
 --------- CPU info (if available) ----------

Mar 2, 2009 (6th)

By Serge Batalov / GMP-ECM 6.2.2 / Mar 2, 2009

4·10²⁴⁸+9 = 4(0)₂₄₇9_<249> = 109 · 157 · C245

C245 = P33 · C213

P33 = 222437485156209239721584649092089_<33>

C213 = [105081403472507701127044472851803774228799733560932737552951993501629404537657221649279921860005838295301318857627808513987051312269821710093470836004276067692676649441223404038410980976203789322509492454610415737_<213>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=566428965
Step 1 took 8529ms
Step 2 took 7536ms
********** Factor found in step 2: 222437485156209239721584649092089
Found probable prime factor of 33 digits: 222437485156209239721584649092089
Composite cofactor has 213 digits

Mar 2, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Mar 2, 2009

(38·10¹⁶⁴+43)/9 = 4(2)₁₆₃7_<165> = 7 · 389 · 396166847 · 20688385777365387708581_<23> · C131

C131 = P57 · P74

P57 = 278000081592423342777657256468034862164665053267856254599_<57>

P74 = 68052453504218272772299858954858072418262676712033906643921164158593661093_<74>

Number: 42227_164
N=18918587626737275661569539886981494068926834123091527789688832596833492556859843815321929442379184020868294757891620228514128616707
  ( 131 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=278000081592423342777657256468034862164665053267856254599
 r2=68052453504218272772299858954858072418262676712033906643921164158593661093
Version: 
Total time: 20.33 hours.
Scaled time: 48.51 units (timescale=2.386).
Factorization parameters were as follows:
n: 18918587626737275661569539886981494068926834123091527789688832596833492556859843815321929442379184020868294757891620228514128616707
m: 1000000000000000000000000000000000
deg: 5
c5: 19
c0: 215
skew: 1.62
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2300000, 3900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9569371
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 734818 x 735066
Total sieving time: 18.27 hours.
Total relation processing time: 0.77 hours.
Matrix solve time: 1.22 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,51,51,2.4,2.4,100000
total time: 20.33 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Mar 2, 2009 (4th)

By Sinkiti Sibata / Msieve / Mar 2, 2009

(44·10¹⁴⁰-17)/9 = 4(8)₁₃₉7_<141> = 257 · 6422477429_<10> · C129

C129 = P36 · P94

P36 = 266764282411297588607226035777225117_<36>

P94 = 1110316455753766733474915862488653783239958544991715616798611308282107315182967999730716957687_<94>

Number: 48887_140
N=296192772568608832293367334345646759490235757131489254311000126113016125270223391900385945493158354999363664877502236977162624379
  ( 129 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=266764282411297588607226035777225117
 r2=1110316455753766733474915862488653783239958544991715616798611308282107315182967999730716957687
Version: 
Total time: 5.36 hours.
Scaled time: 13.75 units (timescale=2.564).
Factorization parameters were as follows:
name: 48887_140
n: 296192772568608832293367334345646759490235757131489254311000126113016125270223391900385945493158354999363664877502236977162624379
m: 10000000000000000000000000000
deg: 5
c5: 44
c0: -17
skew: 0.83
type: snfs
lss: 1
rlim: 1610000
alim: 1610000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1610000/1610000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [805000, 1505001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 205151 x 205399
Total sieving time: 5.36 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000
total time: 5.36 hours.
 --------- CPU info (if available) ----------

(44·10¹⁴¹-17)/9 = 4(8)₁₄₀7_<142> = 3 · 3581871731_<10> · C132

C132 = P29 · P46 · P58

P29 = 24511862298614659295884030627_<29>

P46 = 1935713272129890223796790170669706733402120501_<46>

P58 = 9588740089602400047209894490431903419856559262055026071217_<58>

Number: 48887_141
N=454965937368914015315873864169266543070866216239062087628293585488427315665265968070934706966375628047198105997623628926546177772559
  ( 132 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=24511862298614659295884030627
 r2=1935713272129890223796790170669706733402120501
 r3=9588740089602400047209894490431903419856559262055026071217
Version: 
Total time: 6.73 hours.
Scaled time: 17.25 units (timescale=2.564).
Factorization parameters were as follows:
name: 48887_141
n: 454965937368914015315873864169266543070866216239062087628293585488427315665265968070934706966375628047198105997623628926546177772559
m: 20000000000000000000000000000
deg: 5
c5: 55
c0: -68
skew: 1.04
type: snfs
lss: 1
rlim: 1710000
alim: 1710000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1710000/1710000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [855000, 1755001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 282968 x 283216
Total sieving time: 6.73 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1710000,1710000,26,26,48,48,2.3,2.3,100000
total time: 6.73 hours.
 --------- CPU info (if available) ----------

Mar 2, 2009 (3rd)

By Sinkiti Sibata / Msieve / Mar 2, 2009

(44·10¹⁴⁴-17)/9 = 4(8)₁₄₃7_<145> = 3 · 42920959 · C137

C137 = P58 · P79

P58 = 5881370882122551087199960681673227889956880044401651746057_<58>

P79 = 6455664145439386864235246041474399945467845376843360134375006180876717813506283_<79>

Number: 48887_144
N=37968155129749771658867865222434327006291486395484071770848121767960255259665321775071000385374185829110426671259363744170525864289976131
  ( 137 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=5881370882122551087199960681673227889956880044401651746057
 r2=6455664145439386864235246041474399945467845376843360134375006180876717813506283
Version: 
Total time: 7.87 hours.
Scaled time: 20.17 units (timescale=2.564).
Factorization parameters were as follows:
name: 48887_144
n: 37968155129749771658867865222434327006291486395484071770848121767960255259665321775071000385374185829110426671259363744170525864289976131
m: 100000000000000000000000000000
deg: 5
c5: 22
c0: -85
skew: 1.31
type: snfs
lss: 1
rlim: 1920000
alim: 1920000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1920000/1920000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [960000, 1960001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 302720 x 302968
Total sieving time: 7.87 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1920000,1920000,26,26,49,49,2.3,2.3,100000
total time: 7.87 hours.
 --------- CPU info (if available) ----------

Mar 2, 2009 (2nd)

By Serge Batalov / Msieve-1.39 / Mar 2, 2009

(44·10¹⁶⁹-17)/9 = 4(8)₁₆₈7_<170> = 31 · 71 · C167

C167 = P76 · P91

P76 = 9950279730184416324167097807141707833908720539115456322172137682732648571133_<76>

P91 = 2232311694114726941128124192221372005745626339904571066213105265608109389955468274136910139_<91>

SNFS difficulty: 171 digits.
Divisors found:
 r1=9950279730184416324167097807141707833908720539115456322172137682732648571133 (pp76)
 r2=2232311694114726941128124192221372005745626339904571066213105265608109389955468274136910139 (pp91)
Version: Msieve-1.39
Total time: 32.00 hours.
Scaled time: 0.00 units (timescale=3.538).
Factorization parameters were as follows:
n: 22212125801403402493815942248472916351153516078550153970417487000858195769599676914533797768690999040840022212125801403402493815942248472916351153516078550153970417487
m: 10000000000000000000000000000000000
deg: 5
c5: 22
c0: -85
skew: 1.31
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 855369 x 855617
Total sieving time: 31.00 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.70 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 32.00 hours.
 --------- CPU info (if available) ----------
[    0.293509] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
[    0.384446] CPU1: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
[    0.476479] CPU2: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
[    0.568475] CPU3: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b
[    0.004000] Memory: 4045172k/4718592k available (3116k kernel code, 147592k reserved, 1575k data, 540k init)
[    0.004000] Calibrating delay loop (skipped), value calculated using timer frequency.. 6407.98 BogoMIPS (lpj=12815976)
[    0.004000] Calibrating delay using timer specific routine.. 6408.03 BogoMIPS (lpj=12816069)
[    0.004000] Calibrating delay using timer specific routine.. 6408.09 BogoMIPS (lpj=12816188)
[    0.004000] Calibrating delay using timer specific routine.. 6407.99 BogoMIPS (lpj=12815998)
[    0.572060] Total of 4 processors activated (25632.11 BogoMIPS).

(44·10¹³³-17)/9 = 4(8)₁₃₂7_<134> = 313 · 61970431833043_<14> · 383323733230232520362011_<24> · C94

C94 = P38 · P57

P38 = 33566362962259841077602448108183136191_<38>

P57 = 195889569350056287572634065511059531775558430638559368593_<57>

SNFS difficulty: 136 digits.
Divisors found:
 r1=33566362962259841077602448108183136191 (pp38)
 r2=195889569350056287572634065511059531775558430638559368593 (pp57)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=3.532).
Factorization parameters were as follows:
n: 6575300385324759940584283097591155889806485826685800730459825284734913656000610932535487049263
m: 1000000000000000000000000000
c5: 11
c0: -425
skew: 2.08
type: snfs
lss: 1
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved rational special-q in [500000, 1625001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 134734 x 134982
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 0.00 hours.
 --------- CPU info (if available) ----------
[    0.293509] CPU0: Intel(R) Core(TM)2 Quad CPU    Q6600  @ 2.40GHz stepping 0b

Mar 2, 2009

Factorizations of 400...009 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Mar 1, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Mar 1, 2009

(44·10¹⁶²-17)/9 = 4(8)₁₆₁7_<163> = 3 · 1493 · 238969207 · C151

C151 = P34 · P117

P34 = 4990620217664536348150795739736133_<34>

P117 = 915235043598425178251463651557081130210364541733311841146729064706626965210952206645736477433022202095713997208394163_<117>

Number: 48887_162
N=4567590512497384077516115001239745760937417663633887663029203124762414552467670989470663188144500170348913456350212534440575296661544690719878277391679
  ( 151 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=4990620217664536348150795739736133 (pp34)
 r2=915235043598425178251463651557081130210364541733311841146729064706626965210952206645736477433022202095713997208394163 (pp117)
Version: Msieve-1.39
Total time: 36.56 hours.
Scaled time: 93.99 units (timescale=2.571).
Factorization parameters were as follows:
n: 4567590512497384077516115001239745760937417663633887663029203124762414552467670989470663188144500170348913456350212534440575296661544690719878277391679
m: 200000000000000000000000000000000
deg: 5
c5: 275
c0: -34
skew: 0.66
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 3800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 695201 x 695449
Total sieving time: 36.56 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 36.56 hours.
 --------- CPU info (if available) ----------

(4·10¹⁷⁶+41)/9 = (4)₁₇₅9_<176> = 7 · 13267 · C171

C171 = P63 · P109

P63 = 458635566321274600833783985784889081388813133607071962664716819_<63>

P109 = 1043467632893450375012608605725506256081011775877522672352252150556117313829232637468736945319284152674730559_<109>

Number: 44449_176
N=478571368750007477677636718866838713073732294354891777067099295184016673426487250260522288863285320660763488833135324429513017739444211140902178815799076596543996860571821
  ( 171 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=458635566321274600833783985784889081388813133607071962664716819 (pp63)
 r2=1043467632893450375012608605725506256081011775877522672352252150556117313829232637468736945319284152674730559 (pp109)
Version: Msieve-1.39
Total time: 111.09 hours.
Scaled time: 192.73 units (timescale=1.735).
Factorization parameters were as follows:
n: 478571368750007477677636718866838713073732294354891777067099295184016673426487250260522288863285320660763488833135324429513017739444211140902178815799076596543996860571821
m: 100000000000000000000000000000000000
deg: 5
c5: 40
c0: 41
skew: 1.00
type: snfs
lss: 1
rlim: 6100000
alim: 6100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6100000/6100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3050000, 7550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1367987 x 1368235
Total sieving time: 111.09 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6100000,6100000,28,28,53,53,2.5,2.5,100000
total time: 111.09 hours.
 --------- CPU info (if available) ----------

Mar 1, 2009 (3rd)

By 10metreh / YAFU 1.06 / Mar 1, 2009

(44·10¹²²-17)/9 = 4(8)₁₂₁7_<123> = 163 · 595078871 · 40277836111526983476473_<23> · C90

C90 = P41 · P49

P41 = 25055727059552303768450318768856332883833_<41>

P49 = 4994303060252602682538203448316349125497740032091_<49>

02/28/09 16:06:27 v1.06 @ CORE2, starting SIQS on c90: 125135894330376016809008922839988182095396611945786965309120924112043026937092615995084803
02/28/09 16:06:27 v1.06 @ CORE2, ==== sieve params ====
02/28/09 16:06:27 v1.06 @ CORE2, n = 90 digits, 299 bits
02/28/09 16:06:27 v1.06 @ CORE2, factor base: 64055 primes (max prime = 1703573)
02/28/09 16:06:27 v1.06 @ CORE2, single large prime cutoff: 187393030 (110 * pmax)
02/28/09 16:06:27 v1.06 @ CORE2, double large prime range from 43 to 50 bits
02/28/09 16:06:27 v1.06 @ CORE2, double large prime cutoff: 777958052091382
02/28/09 16:06:27 v1.06 @ CORE2, using 10 large prime slices of factor base
02/28/09 16:06:27 v1.06 @ CORE2, buckets hold 1024 elements
02/28/09 16:06:27 v1.06 @ CORE2, sieve interval: 18 blocks of size 32768
02/28/09 16:06:27 v1.06 @ CORE2, polynomial A has ~ 12 factors
02/28/09 16:06:27 v1.06 @ CORE2, using multiplier of 7
02/28/09 16:06:27 v1.06 @ CORE2, using small prime variation correction of 20 bits
02/28/09 16:06:27 v1.06 @ CORE2, trial factoring cutoff at 98 bits
02/28/09 16:06:27 v1.06 @ CORE2, ==== sieving started ====
02/28/09 16:59:39 v1.06 @ CORE2, starting SIQS on c90: 125135894330376016809008922839988182095396611945786965309120924112043026937092615995084803
02/28/09 16:59:42 v1.06 @ CORE2, sieve time = 0.0000, relation time = 0.0000, poly_time = 0.0000
02/28/09 16:59:42 v1.06 @ CORE2, 162915 relations found: 28176 full + 134739 from 1080440 partial, using 0 polys (0 A polys)
02/28/09 16:59:42 v1.06 @ CORE2, trial division touched 0 sieve locations out of 0
02/28/09 16:59:42 v1.06 @ CORE2, ==== post processing stage (msieve-1.38) ====
02/28/09 16:59:43 v1.06 @ CORE2, begin with 1108615 relations
02/28/09 16:59:44 v1.06 @ CORE2, reduce to 367689 relations in 8 passes
02/28/09 16:59:50 v1.06 @ CORE2, recovered 367689 relations
02/28/09 16:59:50 v1.06 @ CORE2, recovered 283808 polynomials
02/28/09 16:59:50 v1.06 @ CORE2, attempting to build 162914 cycles
02/28/09 16:59:50 v1.06 @ CORE2, found 162914 cycles in 4 passes
02/28/09 16:59:50 v1.06 @ CORE2, distribution of cycle lengths:
02/28/09 16:59:50 v1.06 @ CORE2, length 1 : 28176
02/28/09 16:59:50 v1.06 @ CORE2, length 2 : 31519
02/28/09 16:59:50 v1.06 @ CORE2, length 3 : 35187
02/28/09 16:59:50 v1.06 @ CORE2, length 4 : 27750
02/28/09 16:59:50 v1.06 @ CORE2, length 5 : 18776
02/28/09 16:59:50 v1.06 @ CORE2, length 6 : 10969
02/28/09 16:59:50 v1.06 @ CORE2, length 7 : 5645
02/28/09 16:59:50 v1.06 @ CORE2, length 9+: 4892
02/28/09 16:59:50 v1.06 @ CORE2, largest cycle: 16 relations
02/28/09 16:59:51 v1.06 @ CORE2, matrix is 64055 x 162914 (42.0 MB) with weight 10348892 (63.52/col)
02/28/09 16:59:51 v1.06 @ CORE2, sparse part has weight 10348892 (63.52/col)
02/28/09 16:59:52 v1.06 @ CORE2, filtering completed in 4 passes
02/28/09 16:59:52 v1.06 @ CORE2, matrix is 50671 x 50732 (8.3 MB) with weight 1983932 (39.11/col)
02/28/09 16:59:52 v1.06 @ CORE2, sparse part has weight 1983932 (39.11/col)
02/28/09 16:59:52 v1.06 @ CORE2, saving the first 48 matrix rows for later
02/28/09 16:59:52 v1.06 @ CORE2, matrix is 50623 x 50732 (5.4 MB) with weight 1481298 (29.20/col)
02/28/09 16:59:52 v1.06 @ CORE2, sparse part has weight 1115306 (21.98/col)
02/28/09 16:59:52 v1.06 @ CORE2, matrix includes 64 packed rows
02/28/09 16:59:52 v1.06 @ CORE2, using block size 20292 for processor cache size 2048 kB
02/28/09 16:59:52 v1.06 @ CORE2, commencing Lanczos iteration
02/28/09 16:59:52 v1.06 @ CORE2, memory use: 6.0 MB
02/28/09 17:00:02 v1.06 @ CORE2, lanczos halted after 803 iterations (dim = 50620)
02/28/09 17:00:02 v1.06 @ CORE2, recovered 16 nontrivial dependencies
02/28/09 17:00:03 v1.06 @ CORE2, prp41 = 25055727059552303768450318768856332883833
02/28/09 17:00:05 v1.06 @ CORE2, prp49 = 4994303060252602682538203448316349125497740032091
02/28/09 17:00:05 v1.06 @ CORE2, Lanczos elapsed time = 20.5940 seconds.
02/28/09 17:00:05 v1.06 @ CORE2, Sqrt elapsed time = 3.0940 seconds.
02/28/09 17:00:05 v1.06 @ CORE2, Total elapsed time = 25.9070 seconds.
02/28/09 17:00:05 v1.06 @ CORE2,
02/28/09 17:00:05 v1.06 @ CORE2,

Mar 1, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Mar 1, 2009

(44·10¹⁵⁹-17)/9 = 4(8)₁₅₈7_<160> = 3 · 73259 · 8285839 · C148

C148 = P42 · P106

P42 = 290815744390341441958304938177196752945577_<42>

P106 = 9231526502197941525313298896072190111031909233636542906339087491666606405324372762984243973766232005206577_<106>

Number: 48887_159
N=2684673251595859366296733447750095450469216783402820386480815643103167145413834896839154922072085461200253423223343640531863431760230894225123459929
  ( 148 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=290815744390341441958304938177196752945577
 r2=9231526502197941525313298896072190111031909233636542906339087491666606405324372762984243973766232005206577
Version: 
Total time: 14.41 hours.
Scaled time: 34.38 units (timescale=2.385).
Factorization parameters were as follows:
n: 2684673251595859366296733447750095450469216783402820386480815643103167145413834896839154922072085461200253423223343640531863431760230894225123459929
m: 100000000000000000000000000000000
deg: 5
c5: 22
c0: -85
skew: 1.31
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9261785
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 585964 x 586212
Total sieving time: 13.00 hours.
Total relation processing time: 0.56 hours.
Matrix solve time: 0.79 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 14.41 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(44·10¹⁷⁶-17)/9 = 4(8)₁₇₅7_<177> = 43 · 659 · 98196426949_<11> · 24146313277163821_<17> · 192280009873992323_<18> · 40080386376207456114952753675681_<32> · C96

C96 = P39 · P58

P39 = 117784917298517583845267164230914271179_<39>

P58 = 8015932728867754668581789667849717412702585687637176051847_<58>

Number: 48887_176
N=944155973540168858103069780436959607055778687934293351044551531753237918863965710505962721817613
  ( 96 digits)
Divisors found:
 r1=117784917298517583845267164230914271179
 r2=8015932728867754668581789667849717412702585687637176051847
Version: 
Total time: 2.00 hours.
Scaled time: 4.78 units (timescale=2.390).
Factorization parameters were as follows:
name: 48887_176
n: 944155973540168858103069780436959607055778687934293351044551531753237918863965710505962721817613
skew: 6105.86
# norm 3.37e+13
c5: 39060
c4: 174496312
c3: 560423064979
c2: -7334819794986332
c1: -65750106517620250884
c0: 81566268293500715958840
# alpha -6.16
Y1: 65268841
Y0: -1890872683509586427
# Murphy_E 4.98e-09
# M 840741212225823904974665603171945511566543766752601403677445864058164547642630522023787412990490
type: gnfs
rlim: 800000
alim: 800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 40000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [400000, 800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3835605
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 138694 x 138942
Polynomial selection time: 0.10 hours.
Total sieving time: 1.55 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,95,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,800000,800000,26,26,48,48,2.5,2.5,40000
total time: 2.00 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(44·10¹⁶⁰-17)/9 = 4(8)₁₅₉7_<161> = 109 · 55763 · 92761 · 369517186744001_<15> · C135

C135 = P52 · P83

P52 = 4076131018922486931816494926997155938069156975906851_<52>

P83 = 57569086606996077921238443496515686998345474130400656285165932035408929446980022051_<83>

Number: 48887_160
N=234659139649811819090670862727260288441828499203678824064334192951265228686681364538703535838427708550772283462309773126403735701971401
  ( 135 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=4076131018922486931816494926997155938069156975906851
 r2=57569086606996077921238443496515686998345474130400656285165932035408929446980022051
Version: 
Total time: 13.39 hours.
Scaled time: 31.94 units (timescale=2.386).
Factorization parameters were as follows:
n: 234659139649811819090670862727260288441828499203678824064334192951265228686681364538703535838427708550772283462309773126403735701971401
m: 100000000000000000000000000000000
deg: 5
c5: 44
c0: -17
skew: 0.83
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9215084
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 563969 x 564217
Total sieving time: 12.02 hours.
Total relation processing time: 0.51 hours.
Matrix solve time: 0.72 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 13.39 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Mar 1, 2009

By Sinkiti Sibata / Msieve / Mar 1, 2009

(44·10¹³⁴-17)/9 = 4(8)₁₃₃7_<135> = 43 · 71 · 38083 · 336296610392441169560118324067_<30> · C98

C98 = P40 · P58

P40 = 3105462461647958049658077091153892526461_<40>

P58 = 4026275015098169845103596818850013238999514021557153176599_<58>

Sat Feb 28 08:04:13 2009  Msieve v. 1.39
Sat Feb 28 08:04:13 2009  random seeds: 9dcc2490 61e55782
Sat Feb 28 08:04:13 2009  factoring 12503445919658431989941459603443090426080626858741127995674854088135216176777303913162591813486139 (98 digits)
Sat Feb 28 08:04:14 2009  searching for 15-digit factors
Sat Feb 28 08:04:15 2009  commencing quadratic sieve (98-digit input)
Sat Feb 28 08:04:15 2009  using multiplier of 35
Sat Feb 28 08:04:15 2009  using 32kb Intel Core sieve core
Sat Feb 28 08:04:15 2009  sieve interval: 36 blocks of size 32768
Sat Feb 28 08:04:15 2009  processing polynomials in batches of 6
Sat Feb 28 08:04:15 2009  using a sieve bound of 2426387 (89412 primes)
Sat Feb 28 08:04:15 2009  using large prime bound of 363958050 (28 bits)
Sat Feb 28 08:04:15 2009  using double large prime bound of 2569758932207550 (43-52 bits)
Sat Feb 28 08:04:16 2009  using trial factoring cutoff of 52 bits
Sat Feb 28 08:04:16 2009  polynomial 'A' values have 13 factors
Sat Feb 28 14:28:13 2009  89726 relations (21966 full + 67760 combined from 1333140 partial), need 89508
Sat Feb 28 14:28:14 2009  begin with 1355106 relations
Sat Feb 28 14:28:16 2009  reduce to 233233 relations in 12 passes
Sat Feb 28 14:28:16 2009  attempting to read 233233 relations
Sat Feb 28 14:28:20 2009  recovered 233233 relations
Sat Feb 28 14:28:20 2009  recovered 220850 polynomials
Sat Feb 28 14:28:20 2009  attempting to build 89726 cycles
Sat Feb 28 14:28:20 2009  found 89726 cycles in 6 passes
Sat Feb 28 14:28:20 2009  distribution of cycle lengths:
Sat Feb 28 14:28:20 2009     length 1 : 21966
Sat Feb 28 14:28:20 2009     length 2 : 15756
Sat Feb 28 14:28:20 2009     length 3 : 15335
Sat Feb 28 14:28:20 2009     length 4 : 11979
Sat Feb 28 14:28:20 2009     length 5 : 9100
Sat Feb 28 14:28:20 2009     length 6 : 6366
Sat Feb 28 14:28:20 2009     length 7 : 3889
Sat Feb 28 14:28:20 2009     length 9+: 5335
Sat Feb 28 14:28:20 2009  largest cycle: 19 relations
Sat Feb 28 14:28:21 2009  matrix is 89412 x 89726 (24.1 MB) with weight 5966964 (66.50/col)
Sat Feb 28 14:28:21 2009  sparse part has weight 5966964 (66.50/col)
Sat Feb 28 14:28:22 2009  filtering completed in 3 passes
Sat Feb 28 14:28:22 2009  matrix is 85303 x 85367 (23.1 MB) with weight 5701830 (66.79/col)
Sat Feb 28 14:28:22 2009  sparse part has weight 5701830 (66.79/col)
Sat Feb 28 14:28:23 2009  saving the first 48 matrix rows for later
Sat Feb 28 14:28:23 2009  matrix is 85255 x 85367 (13.7 MB) with weight 4447958 (52.10/col)
Sat Feb 28 14:28:23 2009  sparse part has weight 3084971 (36.14/col)
Sat Feb 28 14:28:23 2009  matrix includes 64 packed rows
Sat Feb 28 14:28:23 2009  using block size 34146 for processor cache size 1024 kB
Sat Feb 28 14:28:23 2009  commencing Lanczos iteration
Sat Feb 28 14:28:23 2009  memory use: 13.6 MB
Sat Feb 28 14:29:11 2009  lanczos halted after 1350 iterations (dim = 85253)
Sat Feb 28 14:29:11 2009  recovered 18 nontrivial dependencies
Sat Feb 28 14:29:12 2009  prp40 factor: 3105462461647958049658077091153892526461
Sat Feb 28 14:29:12 2009  prp58 factor: 4026275015098169845103596818850013238999514021557153176599
Sat Feb 28 14:29:12 2009  elapsed time 06:24:59

(44·10¹⁵¹-17)/9 = 4(8)₁₅₀7_<152> = 59 · 250813 · C145

C145 = P35 · P111

P35 = 28010092649606243627127076612342517_<35>

P111 = 117948810979765038663230411677791182952456300022271405308145892823160288837963818959566692105287562931657362133_<111>

Number: 48887_151
N=3303757123454112912191849656705471021045586119288473132078811156214153531284999411668433163074960830017318520097313968120680961708381218101708761
  ( 145 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=28010092649606243627127076612342517
 r2=117948810979765038663230411677791182952456300022271405308145892823160288837963818959566692105287562931657362133
Version: 
Total time: 17.12 hours.
Scaled time: 43.88 units (timescale=2.564).
Factorization parameters were as follows:
name: 48887_151
n: 3303757123454112912191849656705471021045586119288473132078811156214153531284999411668433163074960830017318520097313968120680961708381218101708761
m: 2000000000000000000000000000000
deg: 5
c5: 55
c0: -68
skew: 1.04
type: snfs
lss: 1
rlim: 2500000
alim: 2500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1250000, 2050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 389657 x 389905
Total sieving time: 17.12 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000
total time: 17.12 hours.
 --------- CPU info (if available) ----------

(44·10¹³⁶-17)/9 = 4(8)₁₃₅7_<137> = 127 · 199 · 202624700755326247138439253739_<30> · C103

C103 = P48 · P56

P48 = 144246135426363968879630879600082913331749818833_<48>

P56 = 66184576863078841433464131617341216284110059499927568637_<56>

Sat Feb 28 18:46:57 2009  Msieve v. 1.39
Sat Feb 28 18:46:57 2009  random seeds: 53201200 d3923666
Sat Feb 28 18:46:57 2009  factoring 9546869437328265947016345739376682205270945391780931469957305312715675153214382295432221052946922740621 (103 digits)
Sat Feb 28 18:46:58 2009  searching for 15-digit factors
Sat Feb 28 18:47:00 2009  commencing quadratic sieve (103-digit input)
Sat Feb 28 18:47:00 2009  using multiplier of 1
Sat Feb 28 18:47:00 2009  using 32kb Intel Core sieve core
Sat Feb 28 18:47:00 2009  sieve interval: 36 blocks of size 32768
Sat Feb 28 18:47:00 2009  processing polynomials in batches of 6
Sat Feb 28 18:47:00 2009  using a sieve bound of 3575521 (127255 primes)
Sat Feb 28 18:47:00 2009  using large prime bound of 536328150 (28 bits)
Sat Feb 28 18:47:00 2009  using double large prime bound of 5163867185235900 (44-53 bits)
Sat Feb 28 18:47:00 2009  using trial factoring cutoff of 53 bits
Sat Feb 28 18:47:00 2009  polynomial 'A' values have 13 factors
Sun Mar 01 20:21:08 2009  127447 relations (29752 full + 97695 combined from 1921537 partial), need 127351
Sun Mar 01 20:21:10 2009  begin with 1951289 relations
Sun Mar 01 20:21:12 2009  reduce to 339333 relations in 11 passes
Sun Mar 01 20:21:12 2009  attempting to read 339333 relations
Sun Mar 01 20:21:19 2009  recovered 339333 relations
Sun Mar 01 20:21:19 2009  recovered 331700 polynomials
Sun Mar 01 20:21:20 2009  attempting to build 127447 cycles
Sun Mar 01 20:21:20 2009  found 127447 cycles in 6 passes
Sun Mar 01 20:21:20 2009  distribution of cycle lengths:
Sun Mar 01 20:21:20 2009     length 1 : 29752
Sun Mar 01 20:21:20 2009     length 2 : 21238
Sun Mar 01 20:21:20 2009     length 3 : 21332
Sun Mar 01 20:21:20 2009     length 4 : 17539
Sun Mar 01 20:21:20 2009     length 5 : 13310
Sun Mar 01 20:21:20 2009     length 6 : 9286
Sun Mar 01 20:21:20 2009     length 7 : 6125
Sun Mar 01 20:21:20 2009     length 9+: 8865
Sun Mar 01 20:21:20 2009  largest cycle: 21 relations
Sun Mar 01 20:21:21 2009  matrix is 127255 x 127447 (37.7 MB) with weight 9380272 (73.60/col)
Sun Mar 01 20:21:21 2009  sparse part has weight 9380272 (73.60/col)
Sun Mar 01 20:21:23 2009  filtering completed in 3 passes
Sun Mar 01 20:21:23 2009  matrix is 122522 x 122586 (36.5 MB) with weight 9079411 (74.07/col)
Sun Mar 01 20:21:23 2009  sparse part has weight 9079411 (74.07/col)
Sun Mar 01 20:21:23 2009  saving the first 48 matrix rows for later
Sun Mar 01 20:21:23 2009  matrix is 122474 x 122586 (26.6 MB) with weight 7676124 (62.62/col)
Sun Mar 01 20:21:23 2009  sparse part has weight 6248906 (50.98/col)
Sun Mar 01 20:21:23 2009  matrix includes 64 packed rows
Sun Mar 01 20:21:24 2009  using block size 43690 for processor cache size 1024 kB
Sun Mar 01 20:21:25 2009  commencing Lanczos iteration
Sun Mar 01 20:21:25 2009  memory use: 23.5 MB
Sun Mar 01 20:23:29 2009  lanczos halted after 1939 iterations (dim = 122472)
Sun Mar 01 20:23:30 2009  recovered 15 nontrivial dependencies
Sun Mar 01 20:23:31 2009  prp48 factor: 144246135426363968879630879600082913331749818833
Sun Mar 01 20:23:31 2009  prp56 factor: 66184576863078841433464131617341216284110059499927568637
Sun Mar 01 20:23:31 2009  elapsed time 25:36:34

February 2009

Feb 28, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 28, 2009

(38·10¹⁶⁴+61)/9 = 4(2)₁₆₃9_<165> = 3 · 11 · 13 · 727 · 800001649 · 1032237454763_<13> · 4846862823541547_<16> · C123

C123 = P49 · P75

P49 = 1424218554316875399625038392232057599399988443713_<49>

P75 = 237487918334757094139099263647007383687709373624089339742165459109156850759_<75>

Number: 42229_164
N=338234699718451915584474464557708031138343751984940684675044970600595111547260673187174469507135439903150655763704612828167
  ( 123 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=1424218554316875399625038392232057599399988443713
 r2=237487918334757094139099263647007383687709373624089339742165459109156850759
Version: 
Total time: 20.50 hours.
Scaled time: 48.82 units (timescale=2.382).
Factorization parameters were as follows:
n: 338234699718451915584474464557708031138343751984940684675044970600595111547260673187174469507135439903150655763704612828167
m: 1000000000000000000000000000000000
deg: 5
c5: 19
c0: 305
skew: 1.74
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2300000, 3900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9507815
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 752528 x 752776
Total sieving time: 18.30 hours.
Total relation processing time: 0.77 hours.
Matrix solve time: 1.26 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,51,51,2.4,2.4,100000
total time: 20.50 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 28, 2009 (6th)

By Robert Backstrom / GGNFS, Msieve / Feb 28, 2009

(44·10¹²⁵-17)/9 = 4(8)₁₂₄7_<126> = 7 · 211 · 4453417 · C116

C116 = P43 · P74

P43 = 1602043501271566697868732461382414268534571_<43>

P74 = 46394019911217396269265065640038665422658070408067883179766258176382621433_<74>

Number: n
N=74325238096629497479463277119643411178173653499498587019630169598148762753958763910702546007032640075828840366060243
  ( 116 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=1602043501271566697868732461382414268534571 (pp43)
 r2=46394019911217396269265065640038665422658070408067883179766258176382621433 (pp74)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.59 hours.
Scaled time: 2.91 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_8_124_7
n: 74325238096629497479463277119643411178173653499498587019630169598148762753958763910702546007032640075828840366060243
deg: 5
c5: 44
c0: -17
m: 10000000000000000000000000
skew: 0.83
type: snfs
rlim: 700000
alim: 700000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [350000, 530001)
Primes: RFBsize:56543, AFBsize:56739, largePrimes:6408695 encountered
Relations: rels:5600306, finalFF:171999
Max relations in full relation-set: 48
Initial matrix: 113350 x 171999 with sparse part having weight 23574962.
Pruned matrix : 102616 x 103246 with weight 9631499.
Total sieving time: 1.30 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.06 hours.
Total square root time: 0.14 hours, sqrts: 7.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,700000,700000,28,28,56,56,2.5,2.5,50000
total time: 1.59 hours.
 --------- CPU info (if available) ----------

(44·10¹¹⁸-17)/9 = 4(8)₁₁₇7_<119> = C119

C119 = P52 · P67

P52 = 5119206635006373557156560747475490922102229350311527_<52>

P67 = 9550090936860184163762019684239003669175453223403396936392071157681_<67>

Number: n
N=48888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
  ( 119 digits)
SNFS difficulty: 121 digits.
Divisors found:

Sat Feb 28 16:08:16 2009  prp52 factor: 5119206635006373557156560747475490922102229350311527
Sat Feb 28 16:08:16 2009  prp67 factor: 9550090936860184163762019684239003669175453223403396936392071157681
Sat Feb 28 16:08:16 2009  elapsed time 00:11:05 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.61 hours.
Scaled time: 2.82 units (timescale=1.751).
Factorization parameters were as follows:
name: KA_4_8_117_7
n: 48888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
deg: 5
c5: 11
c0: -425
m: 1000000000000000000000000
skew: 2.08
type: snfs
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [250000, 413089)
Primes: RFBsize:41538, AFBsize:41413, largePrimes:5166760 encountered
Relations: rels:4518399, finalFF:83995
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 274027 hash collisions in 4762437 relations
Msieve: matrix is 98251 x 98499 (25.3 MB)

Total sieving time: 1.52 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.5,2.5,50000
total time: 1.61 hours.
 --------- CPU info (if available) ----------

(44·10¹²⁶-17)/9 = 4(8)₁₂₅7_<127> = 3 · 47653 · 71147 · C117

C117 = P45 · P72

P45 = 597361534589012167168440041910515739916420567_<45>

P72 = 804645930508513497385460242371516277261563191572489892715193841447820557_<72>

Number: n
N=480664527849369266189969060980799482078884937664464172800653847852361236391117647744931659139661111090766438760195819
  ( 117 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=597361534589012167168440041910515739916420567 (pp45)
 r2=804645930508513497385460242371516277261563191572489892715193841447820557 (pp72)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.93 hours.
Scaled time: 3.52 units (timescale=1.823).
Factorization parameters were as follows:
name: KA_4_8_125_7
n: 480664527849369266189969060980799482078884937664464172800653847852361236391117647744931659139661111090766438760195819
deg: 5
c5: 440
c0: -17
m: 10000000000000000000000000
skew: 0.52
type: snfs
rlim: 700000
alim: 700000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [350000, 610001)
Primes: RFBsize:56543, AFBsize:56804, largePrimes:6699266 encountered
Relations: rels:5887799, finalFF:149506
Max relations in full relation-set: 48
Initial matrix: 113414 x 149506 with sparse part having weight 22406191.
Pruned matrix : 107903 x 108534 with weight 12662178.
Total sieving time: 1.69 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.09 hours.
Total square root time: 0.04 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,700000,700000,28,28,56,56,2.5,2.5,50000
total time: 1.93 hours.
 --------- CPU info (if available) ----------

(55·10¹⁸⁹-1)/9 = 6(1)₁₈₉_<190> = 3 · 7 · C189

C189 = P44 · P146

P44 = 10804513265786317319460462777997312080002291_<44>

P146 = 26933678903129430985310353961003134949691654361236458943029562303853859698336539161768227604516361368354018288214754655403161113549617827609433001_<146>

Number: n
N=291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291
  ( 189 digits)
SNFS difficulty: 191 digits.
Divisors found:

Sat Feb 28 20:23:31 2009  prp44 factor: 10804513265786317319460462777997312080002291
Sat Feb 28 20:23:31 2009  prp146 factor: 26933678903129430985310353961003134949691654361236458943029562303853859698336539161768227604516361368354018288214754655403161113549617827609433001
Sat Feb 28 20:23:31 2009  elapsed time 05:43:31 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 25.68 hours.
Scaled time: 51.74 units (timescale=2.015).
Factorization parameters were as follows:
name: KA_6_1_189
n: 291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291005291
deg: 5
c5: 11
c0: -2
m: 100000000000000000000000000000000000000
skew: 0.71
type: snfs
rlim: 9000000
alim: 9000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [4500000, 12000091)
Primes: RFBsize:602489, AFBsize:603256, largePrimes:35249275 encountered
Relations: rels:31811549, finalFF:766356
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 3439632 hash collisions in 33747700 relations
Msieve: matrix is 1996963 x 1997209 (545.6 MB)

Total sieving time: 24.93 hours.
Total relation processing time: 0.74 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,9000000,9000000,29,29,58,58,2.5,2.5,100000
total time: 25.68 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368976k/3407296k available (2745k kernel code, 36940k reserved, 1424k data, 412k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830498)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454)
Total of 4 processors activated (22643.71 BogoMIPS).

Feb 28, 2009 (5th)

By Wataru Sakai / Msieve / Feb 28, 2009

5·10¹⁹⁵-7 = 4(9)₁₉₄3_<196> = 103 · C194

C194 = P40 · P155

P40 = 1538107507489534601481055687712361944471_<40>

P155 = 31560660801675883119225896760035021175119702951582155400620760556441646547154939591760010210551656217315637522354907153165554249169443274017081188872379961_<155>

Number: 49993_195
N=48543689320388349514563106796116504854368932038834951456310679611650485436893203883495145631067961165048543689320388349514563106796116504854368932038834951456310679611650485436893203883495145631
  ( 194 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=1538107507489534601481055687712361944471
 r2=31560660801675883119225896760035021175119702951582155400620760556441646547154939591760010210551656217315637522354907153165554249169443274017081188872379961
Version: 
Total time: 490.56 hours.
Scaled time: 960.02 units (timescale=1.957).
Factorization parameters were as follows:
n: 48543689320388349514563106796116504854368932038834951456310679611650485436893203883495145631067961165048543689320388349514563106796116504854368932038834951456310679611650485436893203883495145631
m: 1000000000000000000000000000000000000000
deg: 5
c5: 5
c0: -7
skew: 1.07
type: snfs
lss: 1
rlim: 12800000
alim: 12800000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 12800000/12800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6400000, 12100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2209599 x 2209846
Total sieving time: 490.56 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,12800000,12800000,28,28,55,55,2.5,2.5,100000
total time: 490.56 hours.
 --------- CPU info (if available) ----------

Feb 28, 2009 (4th)

By Sinkiti Sibata / GGNFS, Msieve / Feb 28, 2009

(44·10¹⁶⁴-53)/9 = 4(8)₁₆₃3_<165> = 3 · 7 · 107 · 191 · 2011 · 74353 · 977464297 · 8323776453036833_<16> · 9095888398974523051_<19> · C108

C108 = P46 · P62

P46 = 7862625727717047507506747886063428866231417793_<46>

P62 = 13092697172411652719473407661621196298322843061510254562777291_<62>

Number: 48883_164
N=102942977633012101180739550347858143335187192258265597979941494870078161661437989140125181736468106633738763
  ( 108 digits)
Divisors found:
 r1=7862625727717047507506747886063428866231417793 (pp46)
 r2=13092697172411652719473407661621196298322843061510254562777291 (pp62)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 21.84 hours.
Scaled time: 10.31 units (timescale=0.472).
Factorization parameters were as follows:
name: 48883_164
n: 102942977633012101180739550347858143335187192258265597979941494870078161661437989140125181736468106633738763
skew: 20692.37
# norm 1.34e+15
c5: 27600
c4: 3288080556
c3: -66558113477159
c2: -1080970303183105211
c1: 9820381395717295647051
c0: 99797268987273415522565403
# alpha -6.18
Y1: 172874243003
Y0: -326837632365735623162
# Murphy_E 1.34e-09
# M 29593209732172111755289090560667936426206250818983003423088700963706017810763694749058577282903162950489239
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2450001)
Primes: RFBsize:183072, AFBsize:183778, largePrimes:4450675 encountered
Relations: rels:4527310, finalFF:452352
Max relations in full relation-set: 28
Initial matrix: 366925 x 452352 with sparse part having weight 32939034.
Pruned matrix : 301955 x 303853 with weight 19313258.
Polynomial selection time: 1.24 hours.
Total sieving time: 17.66 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 2.44 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 21.84 hours.
 --------- CPU info (if available) ----------

(44·10¹⁵¹-53)/9 = 4(8)₁₅₀3_<152> = 89 · 3828689299_<10> · C141

C141 = P61 · P81

P61 = 1223424440156560969442482741818564284725731966756254692657813_<61>

P81 = 117271609007689616091476396520146862786413933843883272607744325347034802241242981_<81>

Number: 48883_151
N=143472952596491781054853177023595303753457066690313745153344570376869567149465397211683238998531186432590885097236794256571770660035621060553
  ( 141 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=1223424440156560969442482741818564284725731966756254692657813
 r2=117271609007689616091476396520146862786413933843883272607744325347034802241242981
Version: 
Total time: 20.66 hours.
Scaled time: 52.98 units (timescale=2.564).
Factorization parameters were as follows:
name: 48883_151
n: 143472952596491781054853177023595303753457066690313745153344570376869567149465397211683238998531186432590885097236794256571770660035621060553
m: 2000000000000000000000000000000
deg: 5
c5: 55
c0: -212
skew: 1.31
type: snfs
lss: 1
rlim: 2500000
alim: 2500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1250000, 2250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 441545 x 441793
Total sieving time: 20.66 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000
total time: 20.66 hours.
 --------- CPU info (if available) ----------

Feb 28, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.1 / Feb 28, 2009

(44·10¹⁴⁶-17)/9 = 4(8)₁₄₅7_<147> = 29437746451_<11> · 39356253678142543_<17> · C120

C120 = P39 · P82

P39 = 145977862620685020006575147046184107331_<39>

P82 = 2890712197147550381221784038267660221257757249803464957889274361683240563824349089_<82>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=695496723
Step 1 took 13197ms
Step 2 took 11773ms
********** Factor found in step 2: 145977862620685020006575147046184107331
Found probable prime factor of 39 digits: 145977862620685020006575147046184107331
Probable prime cofactor 2890712197147550381221784038267660221257757249803464957889274361683240563824349089 has 82 digits

(44·10¹⁹⁷-17)/9 = 4(8)₁₉₆7_<198> = 7 · 43 · 179 · C193

C193 = P30 · P164

P30 = 180192366370524429277382033171_<30>

P164 = 50356350969832803448648096347995128791247155483945461392799207399795166974995809400922218508687516833945192101225665458371976955557885982556232271977569349459988443_<164>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4228587319
Step 1 took 26145ms
Step 2 took 18697ms
********** Factor found in step 2: 180192366370524429277382033171
Found probable prime factor of 30 digits: 180192366370524429277382033171
Probable prime cofactor  has 164 digits

(44·10¹⁷⁰-17)/9 = 4(8)₁₆₉7_<171> = 523 · 26393 · 5248786129_<10> · C154

C154 = P29 · C126

P29 = 67204076825777480647940943101_<29>

C126 = [100407284951808774048499368281072908226415208673026207174570944509767601913362756510328274963943649362315407074660910461389377_<126>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=910978272
Step 1 took 15253ms
Step 2 took 12953ms
********** Factor found in step 2: 67204076825777480647940943101
Found probable prime factor of 29 digits: 67204076825777480647940943101
Composite cofactor has 126 digits

(44·10¹⁶⁶-17)/9 = 4(8)₁₆₅7_<167> = 19 · 177636367 · 493973401 · C149

C149 = P35 · P115

P35 = 10130025607661052751984594948001591_<35>

P115 = 2894746758907489244526766490846737550788329151477578304420727802540456057343393197016694224714405763736055795654909_<115>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2251914498
Step 1 took 14833ms
Step 2 took 13428ms
********** Factor found in step 2: 10130025607661052751984594948001591
Found probable prime factor of 35 digits: 10130025607661052751984594948001591
Probable prime cofactor  has 115 digits

(44·10¹⁷⁶-17)/9 = 4(8)₁₇₅7_<177> = 43 · 659 · 98196426949_<11> · 24146313277163821_<17> · 192280009873992323_<18> · C128

C128 = P32 · C96

P32 = 40080386376207456114952753675681_<32>

C96 = [944155973540168858103069780436959607055778687934293351044551531753237918863965710505962721817613_<96>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4011473568
Step 1 took 13833ms
Step 2 took 12244ms
********** Factor found in step 2: 40080386376207456114952753675681
Found probable prime factor of 32 digits: 40080386376207456114952753675681
Composite cofactor has 96 digits

Feb 28, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Feb 28, 2009

(44·10¹⁰⁴-17)/9 = 4(8)₁₀₃7_<105> = 1453 · 5568533287_<10> · C92

C92 = P43 · P50

P43 = 5335076764314319996463585618733855222723227_<43>

P50 = 11325648007691200306292519178705980717619362257871_<50>

Number: 48887_104
N=60423201526636093683096215646055084505807396854920856177881774149911269616988042460035269717
  ( 92 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=5335076764314319996463585618733855222723227 (pp43)
 r2=11325648007691200306292519178705980717619362257871 (pp50)
Version: GGNFS-0.77.1-VC8(Sat
Total time: 0.40 hours.
Scaled time: 0.48 units (timescale=1.201).
Factorization parameters were as follows:
n: 60423201526636093683096215646055084505807396854920856177881774149911269616988042460035269717
m: 100000000000000000000000000
deg: 4
c4: 44
c0: -17
skew: 0.79
type: snfs
lss: 1
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [200000, 280001)
Primes: RFBsize:33860, AFBsize:33817, largePrimes:1146791 encountered
Relations: rels:1124713, finalFF:144310
Max relations in full relation-set: 32
Initial matrix: 67743 x 144310 with sparse part having weight 5929428.
Pruned matrix : 44033 x 44435 with weight 1341953.
Total sieving time: 0.37 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,105,4,0,0,0,0,0,0,0,0,400000,400000,25,25,44,44,2.2,2.2,20000
total time: 0.40 hours.
 --------- CPU info (if available) ----------

(44·10¹⁰⁵-17)/9 = 4(8)₁₀₄7_<106> = 3 · 671323 · 2473609 · C93

C93 = P34 · P60

P34 = 2460362561262722710018034351313961_<34>

P60 = 398866188750874688871780951536826630692272742500588933046327_<60>

Number: 48887_105
N=981355437756202646545847788660158742199717984732887942496510975874151466019670362386934871247
  ( 93 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=2460362561262722710018034351313961 (pp34)
 r2=398866188750874688871780951536826630692272742500588933046327 (pp60)
Version: GGNFS-0.77.1-VC8(Sat
Total time: 0.43 hours.
Scaled time: 0.48 units (timescale=1.123).
Factorization parameters were as follows:
n: 981355437756202646545847788660158742199717984732887942496510975874151466019670362386934871247
m: 200000000000000000000000000
deg: 4
c4: 55
c0: -34
skew: 0.89
type: snfs
lss: 1
rlim: 420000
alim: 420000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 420000/420000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [210000, 290001)
Primes: RFBsize:35390, AFBsize:35562, largePrimes:1153944 encountered
Relations: rels:1133793, finalFF:148449
Max relations in full relation-set: 32
Initial matrix: 71018 x 148449 with sparse part having weight 5955462.
Pruned matrix : 45383 x 45802 with weight 1386381.
Total sieving time: 0.39 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,106,4,0,0,0,0,0,0,0,0,420000,420000,25,25,44,44,2.2,2.2,20000
total time: 0.43 hours.
 --------- CPU info (if available) ----------

(44·10¹⁰⁷-17)/9 = 4(8)₁₀₆7_<108> = 7 · 151 · 2591167 · 9364636130953_<13> · C86

C86 = P37 · P50

P37 = 1684619316590834232011834229283191761_<37>

P50 = 11314805483343756222966792594459489946735699966481_<50>

Fri Feb 27 16:38:55 2009  
Fri Feb 27 16:38:55 2009  
Fri Feb 27 16:38:55 2009  Msieve v. 1.39
Fri Feb 27 16:38:55 2009  random seeds: a52dbf50 a353c414
Fri Feb 27 16:38:55 2009  factoring 19061139880708782409319760633568622394892870084200765718273837254648507553224395363041 (86 digits)
Fri Feb 27 16:38:55 2009  searching for 15-digit factors
Fri Feb 27 16:38:56 2009  commencing quadratic sieve (86-digit input)
Fri Feb 27 16:38:57 2009  using multiplier of 19
Fri Feb 27 16:38:57 2009  using 32kb Intel Core sieve core
Fri Feb 27 16:38:57 2009  sieve interval: 14 blocks of size 32768
Fri Feb 27 16:38:57 2009  processing polynomials in batches of 15
Fri Feb 27 16:38:57 2009  using a sieve bound of 1446187 (55333 primes)
Fri Feb 27 16:38:57 2009  using large prime bound of 115694960 (26 bits)
Fri Feb 27 16:38:57 2009  using double large prime bound of 326562213825440 (41-49 bits)
Fri Feb 27 16:38:57 2009  using trial factoring cutoff of 49 bits
Fri Feb 27 16:38:57 2009  polynomial 'A' values have 11 factors
Fri Feb 27 17:10:54 2009  55640 relations (15993 full + 39647 combined from 576459 partial), need 55429
Fri Feb 27 17:10:55 2009  begin with 592452 relations
Fri Feb 27 17:10:55 2009  reduce to 131325 relations in 9 passes
Fri Feb 27 17:10:55 2009  attempting to read 131325 relations
Fri Feb 27 17:10:56 2009  recovered 131325 relations
Fri Feb 27 17:10:56 2009  recovered 112086 polynomials
Fri Feb 27 17:10:56 2009  attempting to build 55640 cycles
Fri Feb 27 17:10:56 2009  found 55640 cycles in 5 passes
Fri Feb 27 17:10:56 2009  distribution of cycle lengths:
Fri Feb 27 17:10:56 2009     length 1 : 15993
Fri Feb 27 17:10:56 2009     length 2 : 11214
Fri Feb 27 17:10:56 2009     length 3 : 9830
Fri Feb 27 17:10:56 2009     length 4 : 7059
Fri Feb 27 17:10:56 2009     length 5 : 4878
Fri Feb 27 17:10:56 2009     length 6 : 3028
Fri Feb 27 17:10:56 2009     length 7 : 1708
Fri Feb 27 17:10:56 2009     length 9+: 1930
Fri Feb 27 17:10:56 2009  largest cycle: 17 relations
Fri Feb 27 17:10:57 2009  matrix is 55333 x 55640 (12.7 MB) with weight 3100185 (55.72/col)
Fri Feb 27 17:10:57 2009  sparse part has weight 3100185 (55.72/col)
Fri Feb 27 17:10:57 2009  filtering completed in 3 passes
Fri Feb 27 17:10:57 2009  matrix is 50382 x 50446 (11.6 MB) with weight 2837645 (56.25/col)
Fri Feb 27 17:10:57 2009  sparse part has weight 2837645 (56.25/col)
Fri Feb 27 17:10:57 2009  saving the first 48 matrix rows for later
Fri Feb 27 17:10:57 2009  matrix is 50334 x 50446 (7.3 MB) with weight 2211621 (43.84/col)
Fri Feb 27 17:10:57 2009  sparse part has weight 1613234 (31.98/col)
Fri Feb 27 17:10:57 2009  matrix includes 64 packed rows
Fri Feb 27 17:10:57 2009  using block size 20178 for processor cache size 4096 kB
Fri Feb 27 17:10:57 2009  commencing Lanczos iteration
Fri Feb 27 17:10:57 2009  memory use: 7.2 MB
Fri Feb 27 17:11:08 2009  lanczos halted after 797 iterations (dim = 50328)
Fri Feb 27 17:11:08 2009  recovered 16 nontrivial dependencies
Fri Feb 27 17:11:08 2009  prp37 factor: 1684619316590834232011834229283191761
Fri Feb 27 17:11:08 2009  prp50 factor: 11314805483343756222966792594459489946735699966481
Fri Feb 27 17:11:08 2009  elapsed time 00:32:13

(44·10¹¹⁰-17)/9 = 4(8)₁₀₉7_<111> = 217003 · 1687573343_<10> · C97

C97 = P45 · P52

P45 = 981851775139662680653913806484673951169790561_<45>

P52 = 1359677287156986953147563312834625938221211913279323_<52>

Number: 48887_110
N=1335001558012168518348363004668761307750965113758421449552209044664630372326427757870752601870203
  ( 97 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=981851775139662680653913806484673951169790561 (pp45)
 r2=1359677287156986953147563312834625938221211913279323 (pp52)
Version: GGNFS-0.77.1-VC8(Sat
Total time: 0.54 hours.
Scaled time: 0.64 units (timescale=1.191).
Factorization parameters were as follows:
n: 1335001558012168518348363004668761307750965113758421449552209044664630372326427757870752601870203
m: 10000000000000000000000
deg: 5
c5: 44
c0: -17
skew: 0.83
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [255000, 355001)
Primes: RFBsize:42291, AFBsize:42417, largePrimes:1164161 encountered
Relations: rels:1141095, finalFF:142153
Max relations in full relation-set: 32
Initial matrix: 84776 x 142153 with sparse part having weight 5736914.
Pruned matrix : 60886 x 61373 with weight 1839283.
Total sieving time: 0.49 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.54 hours.
 --------- CPU info (if available) ----------

(44·10¹¹⁴-17)/9 = 4(8)₁₁₃7_<115> = 3 · 335809 · 2932883 · 23406287 · C95

C95 = P44 · P52

P44 = 26447950848946508125891246620051919927934567_<44>

P52 = 2672866621436084828667546678655921370908295550092983_<52>

Number: 48887_114
N=70691845029531284698770512690565030169046872661552376667469972646495013880968365567935989843361
  ( 95 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=26447950848946508125891246620051919927934567 (pp44)
 r2=2672866621436084828667546678655921370908295550092983 (pp52)
Version: GGNFS-0.77.1-VC8(Sat
Total time: 0.77 hours.
Scaled time: 0.91 units (timescale=1.180).
Factorization parameters were as follows:
n: 70691845029531284698770512690565030169046872661552376667469972646495013880968365567935989843361
m: 100000000000000000000000
deg: 5
c5: 22
c0: -85
skew: 1.31
type: snfs
lss: 1
rlim: 610000
alim: 610000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 610000/610000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [305000, 455001)
Primes: RFBsize:49861, AFBsize:49685, largePrimes:1196972 encountered
Relations: rels:1159168, finalFF:133478
Max relations in full relation-set: 32
Initial matrix: 99612 x 133478 with sparse part having weight 5722621.
Pruned matrix : 82459 x 83021 with weight 2662959.
Total sieving time: 0.70 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000
total time: 0.77 hours.
 --------- CPU info (if available) ----------

(44·10¹⁹¹-17)/9 = 4(8)₁₉₀7_<192> = 7 · 751 · 1229217511_<10> · 555335785751_<12> · 17600056050845750873641_<23> · 809722687213904864836267331_<27> · 3959130287390886271927035127231_<31> · C88

C88 = P36 · P53

P36 = 144550996278661975016517134044638733_<36>

P53 = 16703848779271170927251535893830201636903983700639807_<53>

Fri Feb 27 17:57:37 2009  
Fri Feb 27 17:57:37 2009  
Fri Feb 27 17:57:37 2009  Msieve v. 1.39
Fri Feb 27 17:57:37 2009  random seeds: 358661f0 a7325abd
Fri Feb 27 17:57:37 2009  factoring 2414557982731759402829396316481997213725995106766293870774234544362028453002350273844531 (88 digits)
Fri Feb 27 17:57:37 2009  searching for 15-digit factors
Fri Feb 27 17:57:39 2009  commencing quadratic sieve (88-digit input)
Fri Feb 27 17:57:39 2009  using multiplier of 1
Fri Feb 27 17:57:39 2009  using 32kb Intel Core sieve core
Fri Feb 27 17:57:39 2009  sieve interval: 25 blocks of size 32768
Fri Feb 27 17:57:39 2009  processing polynomials in batches of 9
Fri Feb 27 17:57:39 2009  using a sieve bound of 1517671 (57486 primes)
Fri Feb 27 17:57:39 2009  using large prime bound of 121413680 (26 bits)
Fri Feb 27 17:57:39 2009  using double large prime bound of 356189977465520 (42-49 bits)
Fri Feb 27 17:57:39 2009  using trial factoring cutoff of 49 bits
Fri Feb 27 17:57:39 2009  polynomial 'A' values have 11 factors
Fri Feb 27 18:32:02 2009  57591 relations (16453 full + 41138 combined from 603248 partial), need 57582
Fri Feb 27 18:32:02 2009  begin with 619701 relations
Fri Feb 27 18:32:03 2009  reduce to 136773 relations in 9 passes
Fri Feb 27 18:32:03 2009  attempting to read 136773 relations
Fri Feb 27 18:32:04 2009  recovered 136773 relations
Fri Feb 27 18:32:04 2009  recovered 109875 polynomials
Fri Feb 27 18:32:04 2009  attempting to build 57591 cycles
Fri Feb 27 18:32:04 2009  found 57591 cycles in 5 passes
Fri Feb 27 18:32:04 2009  distribution of cycle lengths:
Fri Feb 27 18:32:04 2009     length 1 : 16453
Fri Feb 27 18:32:04 2009     length 2 : 11427
Fri Feb 27 18:32:04 2009     length 3 : 10253
Fri Feb 27 18:32:04 2009     length 4 : 7428
Fri Feb 27 18:32:04 2009     length 5 : 5066
Fri Feb 27 18:32:04 2009     length 6 : 3145
Fri Feb 27 18:32:04 2009     length 7 : 1772
Fri Feb 27 18:32:04 2009     length 9+: 2047
Fri Feb 27 18:32:04 2009  largest cycle: 16 relations
Fri Feb 27 18:32:04 2009  matrix is 57486 x 57591 (13.1 MB) with weight 3193032 (55.44/col)
Fri Feb 27 18:32:04 2009  sparse part has weight 3193032 (55.44/col)
Fri Feb 27 18:32:05 2009  filtering completed in 3 passes
Fri Feb 27 18:32:05 2009  matrix is 52712 x 52775 (12.1 MB) with weight 2967477 (56.23/col)
Fri Feb 27 18:32:05 2009  sparse part has weight 2967477 (56.23/col)
Fri Feb 27 18:32:05 2009  saving the first 48 matrix rows for later
Fri Feb 27 18:32:05 2009  matrix is 52664 x 52775 (7.4 MB) with weight 2253771 (42.71/col)
Fri Feb 27 18:32:05 2009  sparse part has weight 1629875 (30.88/col)
Fri Feb 27 18:32:05 2009  matrix includes 64 packed rows
Fri Feb 27 18:32:05 2009  using block size 21110 for processor cache size 4096 kB
Fri Feb 27 18:32:05 2009  commencing Lanczos iteration
Fri Feb 27 18:32:05 2009  memory use: 7.5 MB
Fri Feb 27 18:32:16 2009  lanczos halted after 834 iterations (dim = 52660)
Fri Feb 27 18:32:16 2009  recovered 14 nontrivial dependencies
Fri Feb 27 18:32:17 2009  prp36 factor: 144550996278661975016517134044638733
Fri Feb 27 18:32:17 2009  prp53 factor: 16703848779271170927251535893830201636903983700639807
Fri Feb 27 18:32:17 2009  elapsed time 00:34:40

(44·10¹²³-17)/9 = 4(8)₁₂₂7_<124> = 3 · 4026625162490093161507_<22> · C102

C102 = P45 · P58

P45 = 145178383648848147018910389708774434246239763_<45>

P58 = 2787698185156916726878264114124424897244941552415044169669_<58>

Number: 48887_123
N=404713516621908573560883803475538757792929116276848385070404870112011575428570816498677996319826348447
  ( 102 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=145178383648848147018910389708774434246239763 (pp45)
 r2=2787698185156916726878264114124424897244941552415044169669 (pp58)
Version: Msieve-1.39
Total time: 1.60 hours.
Scaled time: 1.91 units (timescale=1.196).
Factorization parameters were as follows:
n: 404713516621908573560883803475538757792929116276848385070404870112011575428570816498677996319826348447
m: 10000000000000000000000000
deg: 5
c5: 11
c0: -425
skew: 2.08
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 740001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 109885 x 110130
Total sieving time: 1.60 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 1.60 hours.
 --------- CPU info (if available) ----------

(44·10¹⁶³-53)/9 = 4(8)₁₆₂3_<164> = 30585951059_<11> · C154

C154 = P46 · P108

P46 = 3409381221648677307546535609243234419019084991_<46>

P108 = 468826997834597142439467798015574281037728660247030807287630943512703579760743270536065940594634112718677407_<108>

Number: 48883_163
N=1598409962619200596193855594467257493982145487120616427743983492682436548094421930883169039497314160954071802200907617979095677885648999229600476844498337
  ( 154 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=3409381221648677307546535609243234419019084991 (pp46)
 r2=468826997834597142439467798015574281037728660247030807287630943512703579760743270536065940594634112718677407 (pp108)
Version: Msieve-1.39
Total time: 43.07 hours.
Scaled time: 110.73 units (timescale=2.571).
Factorization parameters were as follows:
n: 1598409962619200596193855594467257493982145487120616427743983492682436548094421930883169039497314160954071802200907617979095677885648999229600476844498337
m: 1000000000000000000000000000000000
deg: 5
c5: 11
c0: -1325
skew: 2.61
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 809954 x 810202
Total sieving time: 43.07 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 43.07 hours.
 --------- CPU info (if available) ----------

(32·10¹⁶⁵+31)/9 = 3(5)₁₆₄9_<166> = 345912299 · 1961284511_<10> · C148

C148 = P50 · P99

P50 = 46393037881197844769329919028092780602515119298841_<50>

P99 = 112966079015722151503179720005482232418100365053255767820984303808963205364486267061134585021699491_<99>

Number: 35559_165
N=5240839583066786717102808797593959640532192845212103667267982451818208133709752857084047933147048892935211822889041927310853330956386924574126589931
  ( 148 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=46393037881197844769329919028092780602515119298841 (pp50)
 r2=112966079015722151503179720005482232418100365053255767820984303808963205364486267061134585021699491 (pp99)
Version: Msieve-1.39
Total time: 32.66 hours.
Scaled time: 84.30 units (timescale=2.581).
Factorization parameters were as follows:
n: 5240839583066786717102808797593959640532192845212103667267982451818208133709752857084047933147048892935211822889041927310853330956386924574126589931
m: 2000000000000000000000000000000000
deg: 5
c5: 1
c0: 31
skew: 1.99
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 3700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 760137 x 760385
Total sieving time: 32.66 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 32.66 hours.
 --------- CPU info (if available) ----------

(44·10¹³⁹-17)/9 = 4(8)₁₃₈7_<140> = 31 · 47 · C137

C137 = P42 · P96

P42 = 247241610213621214642616779079680643653573_<42>

P96 = 135715375271042152313074475367181093008863209189025885597583020412222531793776330579073842334267_<96>

Number: 48887_139
N=33554487912758331426828338290246320445359566842065126210630671852360253183863341721955311522916190040417905894913444673225043849614885991
  ( 137 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=247241610213621214642616779079680643653573 (pp42)
 r2=135715375271042152313074475367181093008863209189025885597583020412222531793776330579073842334267 (pp96)
Version: Msieve-1.39
Total time: 3.89 hours.
Scaled time: 4.63 units (timescale=1.189).
Factorization parameters were as follows:
n: 33554487912758331426828338290246320445359566842065126210630671852360253183863341721955311522916190040417905894913444673225043849614885991
m: 10000000000000000000000000000
deg: 5
c5: 22
c0: -85
skew: 1.31
type: snfs
lss: 1
rlim: 1590000
alim: 1590000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1590000/1590000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [795000, 1495001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 221252 x 221500
Total sieving time: 3.89 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1590000,1590000,26,26,48,48,2.3,2.3,100000
total time: 3.89 hours.
 --------- CPU info (if available) ----------

Feb 28, 2009

By Serge Batalov / PFGW / Feb 28, 2009

(35·10⁵⁶⁸⁹⁸-17)/9 = 3(8)₅₆₈₉₇7_<56899> is PRP.

Feb 27, 2009 (6th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 27, 2009

(43·10¹⁸⁵+11)/9 = 4(7)₁₈₄9_<186> = C186

C186 = P76 · P110

P76 = 6092161031711376573217867290800843504998437328608501888921342869012660587079_<76>

P110 = 78425008021096752968798242838308148647291250676054244791585916514921983250238038209750337111800904899951773301_<110>

Number: 47779_185
N=477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
  ( 186 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=6092161031711376573217867290800843504998437328608501888921342869012660587079
 r2=78425008021096752968798242838308148647291250676054244791585916514921983250238038209750337111800904899951773301
Version: 
Total time: 142.37 hours.
Scaled time: 339.83 units (timescale=2.387).
Factorization parameters were as follows:
n: 477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
m: 10000000000000000000000000000000000000
deg: 5
c5: 43
c0: 11
skew: 0.76
type: snfs
lss: 1
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 8100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 20439229
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1810029 x 1810277
Total sieving time: 129.27 hours.
Total relation processing time: 3.92 hours.
Matrix solve time: 8.89 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000
total time: 142.37 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 27, 2009 (5th)

By Sinkiti Sibata / GGNFS, Msieve / Feb 27, 2009

(44·10¹⁴³-53)/9 = 4(8)₁₄₂3_<144> = 3² · 471671 · 5072605471_<10> · C128

C128 = P52 · P76

P52 = 3166361761003036680303142908682110958372709395350709_<52>

P76 = 7170292373088502235906232820143055411742367312635436307677957012591149333623_<76>

Number: 48883_143
N=22703739585359152834153630462313097456102458702056872748467242203681433200574940099692377148680851774990929417252110879730588707
  ( 128 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=3166361761003036680303142908682110958372709395350709 (pp52)
 r2=7170292373088502235906232820143055411742367312635436307677957012591149333623 (pp76)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 19.94 hours.
Scaled time: 9.41 units (timescale=0.472).
Factorization parameters were as follows:
name: 48883_143
n: 22703739585359152834153630462313097456102458702056872748467242203681433200574940099692377148680851774990929417252110879730588707
m: 100000000000000000000000000000
deg: 5
c5: 11
c0: -1325
skew: 2.61
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [950000, 2450001)
Primes: RFBsize:142029, AFBsize:142523, largePrimes:4104424 encountered
Relations: rels:4229370, finalFF:348448
Max relations in full relation-set: 28
Initial matrix: 284618 x 348448 with sparse part having weight 35413561.
Pruned matrix : 262138 x 263625 with weight 24173663.
Total sieving time: 17.49 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.14 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 19.94 hours.
 --------- CPU info (if available) ----------

(44·10¹⁵³-53)/9 = 4(8)₁₅₂3_<154> = 17 · 1283 · 4019 · C146

C146 = P63 · P84

P63 = 200326200647338176783717118787364154206526143935667093756398611_<63>

P84 = 278406152648363885257167153873463163169044380062157145420913892618617561178604359417_<84>

Number: 48883_153
N=55772046796889604611565433373184869108095366970314153076733218930415322606287422908723895375387076542638241231242160565438609419535425162563569787
  ( 146 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=200326200647338176783717118787364154206526143935667093756398611
 r2=278406152648363885257167153873463163169044380062157145420913892618617561178604359417
Version: 
Total time: 21.35 hours.
Scaled time: 54.53 units (timescale=2.554).
Factorization parameters were as follows:
name: 48883_153
n: 55772046796889604611565433373184869108095366970314153076733218930415322606287422908723895375387076542638241231242160565438609419535425162563569787
m: 10000000000000000000000000000000
deg: 5
c5: 11
c0: -1325
skew: 2.61
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 556380 x 556627
Total sieving time: 21.35 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 21.35 hours.
 --------- CPU info (if available) ----------

Feb 27, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Feb 27, 2009

(44·10¹⁶¹-53)/9 = 4(8)₁₆₀3_<162> = 3³ · 127 · 557 · 809 · C153

C153 = P69 · P85

P69 = 270753400153194627352563532766388049026002628614359930789354579172611_<69>

P85 = 1168597750273654958778265117257632928376975109003170721228878788746067186593553414889_<85>

Number: 48883_161
N=316401814297965907394291797154972600399998639673545127845303781978003377261891752987666719911842619277112628571479923032120541297983200838818775228405179
  ( 153 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=270753400153194627352563532766388049026002628614359930789354579172611 (pp69)
 r2=1168597750273654958778265117257632928376975109003170721228878788746067186593553414889 (pp85)
Version: Msieve-1.39
Total time: 38.09 hours.
Scaled time: 97.94 units (timescale=2.571).
Factorization parameters were as follows:
n: 316401814297965907394291797154972600399998639673545127845303781978003377261891752987666719911842619277112628571479923032120541297983200838818775228405179
m: 200000000000000000000000000000000
deg: 5
c5: 55
c0: -212
skew: 1.31
type: snfs
lss: 1
rlim: 3700000
alim: 3700000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3700000/3700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1850000, 3850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 695008 x 695256
Total sieving time: 38.09 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,51,51,2.4,2.4,100000
total time: 38.09 hours.
 --------- CPU info (if available) ----------

(44·10¹⁷¹-53)/9 = 4(8)₁₇₀3_<172> = C172

C172 = P59 · P113

P59 = 75059015380479339613706194125465158146139625871231697571901_<59>

P113 = 65133933133905008261265014533189153316103348018734416649842781849800236873376647775219658789236125956277334331183_<113>

Number: 48883_171
N=4888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
  ( 172 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=75059015380479339613706194125465158146139625871231697571901 (pp59)
 r2=65133933133905008261265014533189153316103348018734416649842781849800236873376647775219658789236125956277334331183 (pp113)
Version: Msieve-1.39
Total time: 84.05 hours.
Scaled time: 146.16 units (timescale=1.739).
Factorization parameters were as follows:
n: 4888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883
m: 20000000000000000000000000000000000
deg: 5
c5: 55
c0: -212
skew: 1.31
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5400000/5400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2700000, 7100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1078148 x 1078396
Total sieving time: 84.05 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,5400000,5400000,27,27,52,52,2.4,2.4,100000
total time: 84.05 hours.
 --------- CPU info (if available) ----------

Feb 27, 2009 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Feb 27, 2009

(44·10¹⁴¹-53)/9 = 4(8)₁₄₀3_<142> = 39161 · 123787 · 171881 · 6897173 · 269695261837_<12> · 6199736064021385889457145645067_<31> · C78

C78 = P31 · P47

P31 = 8369302132878724900360524015317_<31>

P47 = 60792023715215966066345455742641376351243291791_<47>

GMP-ECM 6.2.1 [powered by GMP 4.1.4] [ECM]
Input number is 508786813741771010621372438944508866566847913331596410044410894001651984362747 (78 digits)
Using B1=452000, B2=347971482, polynomial Dickson(3), sigma=880082943
Step 1 took 3437ms
Step 2 took 1875ms
********** Factor found in step 2: 8369302132878724900360524015317
Found probable prime factor of 31 digits: 8369302132878724900360524015317
Probable prime cofactor 60792023715215966066345455742641376351243291791 has 47 digits

(43·10¹⁷⁹-61)/9 = 4(7)₁₇₈1_<180> = 3² · 7 · C178

C178 = P38 · P45 · P96

P38 = 90888011291841593728293037617292729219_<38>

P45 = 509748305905847001126736992629137395340449583_<45>

P96 = 163690322664170779588161072669009425584870041615565614512563841959454808119330543582803439622121_<96>

Number: n
N=7583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917
  ( 178 digits)
SNFS difficulty: 181 digits.
Divisors found:

Fri Feb 27 08:19:29 2009  prp38 factor: 90888011291841593728293037617292729219
Fri Feb 27 08:19:29 2009  prp45 factor: 509748305905847001126736992629137395340449583
Fri Feb 27 08:19:29 2009  prp96 factor: 163690322664170779588161072669009425584870041615565614512563841959454808119330543582803439622121
Fri Feb 27 08:19:29 2009  elapsed time 03:37:09 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20050930-k8
Total time: 8.15 hours.
Scaled time: 16.43 units (timescale=2.016).
Factorization parameters were as follows:
name: KA_4_7_178_1
n: 7583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917107583774250440917
deg: 5
c5: 43
c0: -610
m: 1000000000000000000000000000000000000
skew: 1.70
type: snfs
rlim: 8000000
alim: 8000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [4000000, 5599990)
Primes: RFBsize:539777, AFBsize:539266, largePrimes:30064188 encountered
Relations: rels:23614284, finalFF:235540
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 3257735 hash collisions in 34545968 relations
Msieve: matrix is 1564511 x 1564759 (427.1 MB)

Total sieving time: 7.71 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,8000000,8000000,29,29,58,58,2.5,2.5,100000
total time: 8.15 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368976k/3407296k available (2745k kernel code, 36940k reserved, 1424k data, 412k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830498)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454)
Total of 4 processors activated (22643.71 BogoMIPS).

Feb 27, 2009 (2nd)

Factorizations of 488...887 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Feb 27, 2009

By Serge Batalov / PFGW / Feb 27, 2009

(61·10⁵²⁷⁶³-7)/9 = 6(7)₅₂₇₆₃_<52764> is PRP.

(76·10⁴⁰⁷⁴³-31)/9 = 8(4)₄₀₇₄₂1_<40744> is PRP.

Feb 26, 2009 (7th)

By matsui / GGNFS / Feb 26, 2009

(86·10¹⁸¹+31)/9 = 9(5)₁₈₀9_<182> = 3³ · 11 · 38219 · C175

C175 = P53 · P123

P53 = 32928690580332125411741090087710651306629243139878707_<53>

P123 = 255649949770519847347395270618009705435442504020620821952131412204032479590771377721477095985577060681219537413453936952959_<123>

N=8418218092870897903880335538818376034304121264940636341132313176468061618263234097127070662630346440900237586586145040200760014348950625555339324814077046096605885076424744013
  ( 175 digits)
SNFS difficulty: 183 digits.
Divisors found:
 r1=32928690580332125411741090087710651306629243139878707 (pp53)
 r2=255649949770519847347395270618009705435442504020620821952131412204032479590771377721477095985577060681219537413453936952959 (pp123)
Version: GGNFS-0.77.1-20060722-nocona

Feb 26, 2009 (6th)

By Robert Backstrom / Msieve, GGNFS / Feb 26, 2009

(44·10¹¹⁰-53)/9 = 4(8)₁₀₉3_<111> = 3 · 7² · 73 · 233 · 761 · 60433935059_<11> · C91

C91 = P40 · P51

P40 = 5206728456358460814368918326710497623619_<40>

P51 = 816551520937130805126208331277646872665420305239041_<51>

Thu Feb 26 12:33:30 2009  
Thu Feb 26 12:33:30 2009  
Thu Feb 26 12:33:30 2009  Msieve v. 1.39
Thu Feb 26 12:33:30 2009  random seeds: 1c0eaa08 647b5fed
Thu Feb 26 12:33:30 2009  factoring 4251562040146140473214122361854652982848323985713055697350360731657598250913534246242509379 (91 digits)
Thu Feb 26 12:33:30 2009  searching for 15-digit factors
Thu Feb 26 12:33:31 2009  commencing quadratic sieve (91-digit input)
Thu Feb 26 12:33:32 2009  using multiplier of 3
Thu Feb 26 12:33:32 2009  using 64kb Opteron sieve core
Thu Feb 26 12:33:32 2009  sieve interval: 18 blocks of size 65536
Thu Feb 26 12:33:32 2009  processing polynomials in batches of 6
Thu Feb 26 12:33:32 2009  using a sieve bound of 1719869 (64602 primes)
Thu Feb 26 12:33:32 2009  using large prime bound of 165107424 (27 bits)
Thu Feb 26 12:33:32 2009  using double large prime bound of 619412223763104 (42-50 bits)
Thu Feb 26 12:33:32 2009  using trial factoring cutoff of 50 bits
Thu Feb 26 12:33:32 2009  polynomial 'A' values have 12 factors
Thu Feb 26 14:20:01 2009  64779 relations (16935 full + 47844 combined from 763205 partial), need 64698
Thu Feb 26 14:20:02 2009  begin with 780140 relations
Thu Feb 26 14:20:03 2009  reduce to 161345 relations in 11 passes
Thu Feb 26 14:20:03 2009  attempting to read 161345 relations
Thu Feb 26 14:20:04 2009  recovered 161345 relations
Thu Feb 26 14:20:04 2009  recovered 140533 polynomials
Thu Feb 26 14:20:05 2009  attempting to build 64779 cycles
Thu Feb 26 14:20:05 2009  found 64779 cycles in 6 passes
Thu Feb 26 14:20:05 2009  distribution of cycle lengths:
Thu Feb 26 14:20:05 2009     length 1 : 16935
Thu Feb 26 14:20:05 2009     length 2 : 12091
Thu Feb 26 14:20:05 2009     length 3 : 11203
Thu Feb 26 14:20:05 2009     length 4 : 8860
Thu Feb 26 14:20:05 2009     length 5 : 6186
Thu Feb 26 14:20:05 2009     length 6 : 4047
Thu Feb 26 14:20:05 2009     length 7 : 2466
Thu Feb 26 14:20:05 2009     length 9+: 2991
Thu Feb 26 14:20:05 2009  largest cycle: 21 relations
Thu Feb 26 14:20:06 2009  matrix is 64602 x 64779 (16.1 MB) with weight 3955790 (61.07/col)
Thu Feb 26 14:20:06 2009  sparse part has weight 3955790 (61.07/col)
Thu Feb 26 14:20:07 2009  filtering completed in 3 passes
Thu Feb 26 14:20:07 2009  matrix is 60649 x 60713 (15.2 MB) with weight 3741452 (61.63/col)
Thu Feb 26 14:20:07 2009  sparse part has weight 3741452 (61.63/col)
Thu Feb 26 14:20:08 2009  saving the first 48 matrix rows for later
Thu Feb 26 14:20:08 2009  matrix is 60601 x 60713 (9.7 MB) with weight 2963658 (48.81/col)
Thu Feb 26 14:20:08 2009  sparse part has weight 2177748 (35.87/col)
Thu Feb 26 14:20:08 2009  matrix includes 64 packed rows
Thu Feb 26 14:20:08 2009  using block size 21845 for processor cache size 512 kB
Thu Feb 26 14:20:08 2009  commencing Lanczos iteration
Thu Feb 26 14:20:08 2009  memory use: 9.4 MB
Thu Feb 26 14:20:43 2009  lanczos halted after 960 iterations (dim = 60599)
Thu Feb 26 14:20:43 2009  recovered 16 nontrivial dependencies
Thu Feb 26 14:20:44 2009  prp40 factor: 5206728456358460814368918326710497623619
Thu Feb 26 14:20:44 2009  prp51 factor: 816551520937130805126208331277646872665420305239041
Thu Feb 26 14:20:44 2009  elapsed time 01:47:14

(44·10¹²⁵-53)/9 = 4(8)₁₂₄3_<126> = 3² · 71 · 571 · 30429810494761178782216697_<26> · C95

C95 = P41 · P55

P41 = 21359195843830967403453380962112507429977_<41>

P55 = 2061527132411459461397036590954458932353735933027377703_<55>

Thu Feb 26 12:35:45 2009  
Thu Feb 26 12:35:45 2009  
Thu Feb 26 12:35:45 2009  Msieve v. 1.39
Thu Feb 26 12:35:45 2009  random seeds: 4e3e03e0 16ce5ef6
Thu Feb 26 12:35:45 2009  factoring 44032561758547617341803247676823990868053192972587863182516175908299645509602916744544203602831 (95 digits)
Thu Feb 26 12:35:45 2009  searching for 15-digit factors
Thu Feb 26 12:35:46 2009  commencing quadratic sieve (95-digit input)
Thu Feb 26 12:35:46 2009  using multiplier of 1
Thu Feb 26 12:35:46 2009  using 64kb Opteron sieve core
Thu Feb 26 12:35:46 2009  sieve interval: 18 blocks of size 65536
Thu Feb 26 12:35:46 2009  processing polynomials in batches of 6
Thu Feb 26 12:35:46 2009  using a sieve bound of 2162071 (79710 primes)
Thu Feb 26 12:35:46 2009  using large prime bound of 324310650 (28 bits)
Thu Feb 26 12:35:46 2009  using double large prime bound of 2087998231332900 (43-51 bits)
Thu Feb 26 12:35:46 2009  using trial factoring cutoff of 51 bits
Thu Feb 26 12:35:46 2009  polynomial 'A' values have 12 factors
Thu Feb 26 14:29:17 2009  79910 relations (20477 full + 59433 combined from 1182055 partial), need 79806
Thu Feb 26 14:29:19 2009  begin with 1202532 relations
Thu Feb 26 14:29:20 2009  reduce to 204460 relations in 10 passes
Thu Feb 26 14:29:20 2009  attempting to read 204460 relations
Thu Feb 26 14:29:23 2009  recovered 204460 relations
Thu Feb 26 14:29:23 2009  recovered 182671 polynomials
Thu Feb 26 14:29:23 2009  attempting to build 79910 cycles
Thu Feb 26 14:29:23 2009  found 79910 cycles in 5 passes
Thu Feb 26 14:29:24 2009  distribution of cycle lengths:
Thu Feb 26 14:29:24 2009     length 1 : 20477
Thu Feb 26 14:29:24 2009     length 2 : 14443
Thu Feb 26 14:29:24 2009     length 3 : 13675
Thu Feb 26 14:29:24 2009     length 4 : 10718
Thu Feb 26 14:29:24 2009     length 5 : 7849
Thu Feb 26 14:29:24 2009     length 6 : 5123
Thu Feb 26 14:29:24 2009     length 7 : 3277
Thu Feb 26 14:29:24 2009     length 9+: 4348
Thu Feb 26 14:29:24 2009  largest cycle: 21 relations
Thu Feb 26 14:29:24 2009  matrix is 79710 x 79910 (21.1 MB) with weight 5207940 (65.17/col)
Thu Feb 26 14:29:24 2009  sparse part has weight 5207940 (65.17/col)
Thu Feb 26 14:29:25 2009  filtering completed in 3 passes
Thu Feb 26 14:29:25 2009  matrix is 75065 x 75129 (20.0 MB) with weight 4934428 (65.68/col)
Thu Feb 26 14:29:25 2009  sparse part has weight 4934428 (65.68/col)
Thu Feb 26 14:29:25 2009  saving the first 48 matrix rows for later
Thu Feb 26 14:29:25 2009  matrix is 75017 x 75129 (13.0 MB) with weight 3925757 (52.25/col)
Thu Feb 26 14:29:25 2009  sparse part has weight 2952697 (39.30/col)
Thu Feb 26 14:29:25 2009  matrix includes 64 packed rows
Thu Feb 26 14:29:25 2009  using block size 30051 for processor cache size 1024 kB
Thu Feb 26 14:29:26 2009  commencing Lanczos iteration
Thu Feb 26 14:29:26 2009  memory use: 12.2 MB
Thu Feb 26 14:30:04 2009  lanczos halted after 1188 iterations (dim = 75016)
Thu Feb 26 14:30:04 2009  recovered 17 nontrivial dependencies
Thu Feb 26 14:30:05 2009  prp41 factor: 21359195843830967403453380962112507429977
Thu Feb 26 14:30:05 2009  prp55 factor: 2061527132411459461397036590954458932353735933027377703
Thu Feb 26 14:30:05 2009  elapsed time 01:54:20

(37·10²⁰⁵+17)/9 = 4(1)₂₀₄3_<206> = C206

C206 = P53 · P75 · P79

P53 = 38708903282648616349050646735593058494904684196090851_<53>

P75 = 523279404482581894105023739895022302701579043553621531881177081933138648717_<75>

P79 = 2029619869509639122374709122919684913926210413942382626800386423565291654417839_<79>

Number: n
N=41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
  ( 206 digits)
SNFS difficulty: 206 digits.
Divisors found:

Thu Feb 26 18:48:16 2009  prp53 factor: 38708903282648616349050646735593058494904684196090851
Thu Feb 26 18:48:16 2009  prp75 factor: 523279404482581894105023739895022302701579043553621531881177081933138648717
Thu Feb 26 18:48:16 2009  prp79 factor: 2029619869509639122374709122919684913926210413942382626800386423565291654417839
Thu Feb 26 18:48:16 2009  elapsed time 16:58:34 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20050930-k8
Total time: 111.52 hours.
Scaled time: 224.70 units (timescale=2.015).
Factorization parameters were as follows:
name: KA_4_1_204_3
n: 41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
deg: 5
c5: 37
c0: 17
m: 100000000000000000000000000000000000000000
skew: 0.86
type: snfs
rlim: 11000000
alim: 11000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [5500000, 32599990)
Primes: RFBsize:726517, AFBsize:727428, largePrimes:36880338 encountered
Relations: rels:31940379, finalFF:85284
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 8266595 hash collisions in 45511633 relations
Msieve: matrix is 3184069 x 3184317 (863.6 MB)

Total sieving time: 110.22 hours.
Total relation processing time: 1.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,11000000,11000000,29,29,58,58,2.5,2.5,100000
total time: 111.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3368976k/3407296k available (2745k kernel code, 36940k reserved, 1424k data, 412k init, 2489792k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.99 BogoMIPS (lpj=2830498)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458)
Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830454)
Total of 4 processors activated (22643.71 BogoMIPS).

Feb 26, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.1 / Feb 26, 2009

(44·10²⁰⁰-53)/9 = 4(8)₁₉₉3_<201> = 3 · 7 · 23 · 490151 · 603522709 · 12983684697563_<14> · 485460576989519_<15> · C156

C156 = P34 · C122

P34 = 7046882295480502467634870497200027_<34>

C122 = [77035442509364829592824984655079160994427570285601319384761126720874299891224577489225266938170642713438522459468169082381_<122>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2540175551
Step 1 took 32875ms
********** Factor found in step 1: 7046882295480502467634870497200027
Found probable prime factor of 34 digits: 7046882295480502467634870497200027
Composite cofactor has 122 digits

(44·10²⁰⁴-53)/9 = 4(8)₂₀₃3_<205> = 31 · 131 · C202

C202 = P35 · C167

P35 = 75956254527312360496911296790966809_<35>

C167 = [15849429573449204111210382410071127103818486388678547282497647139185547003406911430474426852551951533584065408618982135342664560514133979604513938702039208944975046567_<167>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=100595225
Step 1 took 63234ms
Step 2 took 31359ms
********** Factor found in step 2: 75956254527312360496911296790966809
Found probable prime factor of 35 digits: 75956254527312360496911296790966809
Composite cofactor has 167 digits

(44·10¹⁹²-53)/9 = 4(8)₁₉₁3_<193> = 696457 · 8169034619_<10> · 363391761793_<12> · 8428473113059_<13> · C153

C153 = P30 · P124

P30 = 133396886663428373837032220609_<30>

P124 = 2103175169457846601552806103544676440988572210079484013420789074998367704348399128910180822984955341604439165177509040355947_<124>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2020511789
Step 1 took 29469ms
********** Factor found in step 1: 133396886663428373837032220609
Found probable prime factor of 30 digits: 133396886663428373837032220609
Probable prime cofactor has 124 digits

Feb 26, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Feb 26, 2009

(4·10¹⁹⁰+41)/9 = (4)₁₈₉9_<190> = 3² · C189

C189 = P40 · P150

P40 = 2948837566996825795307130730192425607301_<40>

P150 = 167465026226166064292399776036696947548186926080316744399282734221869926819933052095255866949131779342147271334939590492205749388252413890515966641861_<150>

Number: 44449_190
N=493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827161
  ( 189 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=2948837566996825795307130730192425607301 (pp40)
 r2=167465026226166064292399776036696947548186926080316744399282734221869926819933052095255866949131779342147271334939590492205749388252413890515966641861 (pp150)
Version: Msieve-1.39
Total time: 258.26 hours.
Scaled time: 449.12 units (timescale=1.739).
Factorization parameters were as follows:
n: 493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827161
m: 100000000000000000000000000000000000000
deg: 5
c5: 4
c0: 41
skew: 1.59
type: snfs
lss: 1
rlim: 10500000
alim: 10500000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10500000/10500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5250000, 9550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1923959 x 1924207
Total sieving time: 258.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,10500000,10500000,28,28,54,54,2.5,2.5,100000
total time: 258.26 hours.
 --------- CPU info (if available) ----------

(43·10¹⁶³+11)/9 = 4(7)₁₆₂9_<164> = 7 · 52419239 · 1739922117943453_<16> · C140

C140 = P68 · P73

P68 = 30725208977326294282026917154259056299124533303220352723575950353573_<68>

P73 = 2435636872107711589373030968932924793282530963776468209854648002649046067_<73>

Number: 47779_163
N=74835451888390795421193860921480029591140239303958107726711659068218174860236715990676357673712284630905548931915876695279066763919815047391
  ( 140 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=30725208977326294282026917154259056299124533303220352723575950353573 (pp68)
 r2=2435636872107711589373030968932924793282530963776468209854648002649046067 (pp73)
Version: Msieve-1.39
Total time: 46.46 hours.
Scaled time: 119.46 units (timescale=2.571).
Factorization parameters were as follows:
n: 74835451888390795421193860921480029591140239303958107726711659068218174860236715990676357673712284630905548931915876695279066763919815047391
m: 500000000000000000000000000000000
deg: 5
c5: 344
c0: 275
skew: 0.96
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 4450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 764035 x 764282
Total sieving time: 46.46 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 46.46 hours.
 --------- CPU info (if available) ----------

(44·10¹⁵⁶-53)/9 = 4(8)₁₅₅3_<157> = 23 · 54439171 · C148

C148 = P68 · P81

P68 = 22678645829390954202749404051050551174900006487478899476556840123289_<68>

P81 = 172168505322445876370816162423063654892260575030429034434333933237155428621798959_<81>

Number: 48883_156
N=3904548555183361474972152974898301500498034441516456316616201170811593739854587975847222604768148422814799459053584850965755880391863655682531856151
  ( 148 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=22678645829390954202749404051050551174900006487478899476556840123289 (pp68)
 r2=172168505322445876370816162423063654892260575030429034434333933237155428621798959 (pp81)
Version: Msieve-1.39
Total time: 25.70 hours.
Scaled time: 66.08 units (timescale=2.571).
Factorization parameters were as follows:
n: 3904548555183361474972152974898301500498034441516456316616201170811593739854587975847222604768148422814799459053584850965755880391863655682531856151
m: 20000000000000000000000000000000
deg: 5
c5: 55
c0: -212
skew: 1.31
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 569817 x 570065
Total sieving time: 25.70 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 25.70 hours.
 --------- CPU info (if available) ----------

(44·10¹³⁵-53)/9 = 4(8)₁₃₄3_<136> = 1097 · 7356997 · 4215858307_<10> · C117

C117 = P42 · P75

P42 = 332560041044241248900484291976845162767167_<42>

P75 = 432062813561467316727657432335915267712627225383416457686955661487805189323_<75>

Number: 48883_135
N=143686827011691925346526157094251099188322446463017116723156638837921518214692501721207858184843360138281649003357941
  ( 117 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=332560041044241248900484291976845162767167 (pp42)
 r2=432062813561467316727657432335915267712627225383416457686955661487805189323 (pp75)
Version: Msieve-1.39
Total time: 3.60 hours.
Scaled time: 9.25 units (timescale=2.571).
Factorization parameters were as follows:
n: 143686827011691925346526157094251099188322446463017116723156638837921518214692501721207858184843360138281649003357941
m: 1000000000000000000000000000
deg: 5
c5: 44
c0: -53
skew: 1.04
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1265001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 190904 x 191152
Total sieving time: 3.60 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 3.60 hours.
 --------- CPU info (if available) ----------

Feb 26, 2009 (3rd)

By Sinkiti Sibata / GGNFS, Msieve / Feb 26, 2009

(44·10¹³⁹-71)/9 = 4(8)₁₃₈1_<140> = 1559 · 3121 · 30390539151758346199_<20> · C114

C114 = P31 · P83

P31 = 6461651849899623748232000554729_<31>

P83 = 51166807863622394221848695179553706577606524639170306964578149461210274319629978249_<83>

Number: 48881_139
N=330622098685434258936754116359866216587190321981358794573361525938189338670519776376487359516392275259786204089521
  ( 114 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=6461651849899623748232000554729 (pp31)
 r2=51166807863622394221848695179553706577606524639170306964578149461210274319629978249 (pp83)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 11.95 hours.
Scaled time: 5.65 units (timescale=0.473).
Factorization parameters were as follows:
name: 48881_139
n: 330622098685434258936754116359866216587190321981358794573361525938189338670519776376487359516392275259786204089521
m: 10000000000000000000000000000
deg: 5
c5: 22
c0: -355
skew: 1.74
type: snfs
lss: 1
rlim: 1590000
alim: 1590000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1590000/1590000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [795000, 1695001)
Primes: RFBsize:120451, AFBsize:120405, largePrimes:3586520 encountered
Relations: rels:3542114, finalFF:272496
Max relations in full relation-set: 28
Initial matrix: 240922 x 272496 with sparse part having weight 24250856.
Pruned matrix : 230443 x 231711 with weight 18069601.
Total sieving time: 10.45 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.28 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1590000,1590000,26,26,48,48,2.3,2.3,100000
total time: 11.95 hours.
 --------- CPU info (if available) ----------

(31·10¹⁹¹+23)/9 = 3(4)₁₉₀7_<192> = 479 · C189

C189 = P75 · P114

P75 = 721654199380406659494358792402938501466495953581632403259971904944621801459_<75>

P114 = 996447743020499121699374464603815726961346486644180235752675167236186326151725810337002716980797888594745956623227_<114>

Number: 34447_191
N=719090698213871491533286940385061470656460218046856877754581303641846439341220134539549988401762932034330781721178380886105311992577128276501971700301554163767107399675249362096961261888193
  ( 189 digits)
SNFS difficulty: 192 digits.
Divisors found:
 r1=721654199380406659494358792402938501466495953581632403259971904944621801459
 r2=996447743020499121699374464603815726961346486644180235752675167236186326151725810337002716980797888594745956623227
Version: 
Total time: 366.43 hours.
Scaled time: 935.87 units (timescale=2.554).
Factorization parameters were as follows:
name: 34447_191
n: 719090698213871491533286940385061470656460218046856877754581303641846439341220134539549988401762932034330781721178380886105311992577128276501971700301554163767107399675249362096961261888193
m: 100000000000000000000000000000000000000
deg: 5
c5: 310
c0: 23
skew: 0.59
type: snfs
lss: 1
rlim: 11300000
alim: 11300000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 11300000/11300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [5650000, 10350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2016938 x 2017186
Total sieving time: 366.43 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,192,5,0,0,0,0,0,0,0,0,11300000,11300000,28,28,55,55,2.5,2.5,100000
total time: 366.43 hours.
 --------- CPU info (if available) ----------

Feb 26, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Feb 26, 2009

(44·10¹²⁸-53)/9 = 4(8)₁₂₇3_<129> = 3 · 7 · 109 · 613 · 11383 · C119

C119 = P41 · P79

P41 = 11596514298237038639067575234023927441349_<41>

P79 = 2639488026190419162144058720175270446979675692915179501209940086668045827264157_<79>

Number: 48883_128
N=30608860635742654933980094618371424703761115776636432481511316570990030268286904377930692261821975632452045301747427793
  ( 119 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=11596514298237038639067575234023927441349
 r2=2639488026190419162144058720175270446979675692915179501209940086668045827264157
Version: 
Total time: 2.71 hours.
Scaled time: 2.57 units (timescale=0.950).
Factorization parameters were as follows:
n: 30608860635742654933980094618371424703761115776636432481511316570990030268286904377930692261821975632452045301747427793
m: 100000000000000000000000000
deg: 5
c5: 11
c0: -1325
skew: 2.61
type: snfs
lss: 1
rlim: 1070000
alim: 1070000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1070000/1070000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [535000, 935001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 164487 x 164734
Total sieving time: 2.71 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000
total time: 2.71 hours.
 --------- CPU info (if available) ----------

(44·10¹²⁴-53)/9 = 4(8)₁₂₃3_<125> = 27857387 · 27098180189257291_<17> · C101

C101 = P33 · P69

P33 = 105879858460003669738444647465173_<33>

P69 = 611668775478348043887642134207958264068062222551430503567302962499263_<69>

Number: 48883_124
N=64763403372051254345862180645606745671444139005957866904918665429237488531590248316682524769830667499
  ( 101 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=105879858460003669738444647465173
 r2=611668775478348043887642134207958264068062222551430503567302962499263
Version: 
Total time: 2.66 hours.
Scaled time: 2.09 units (timescale=0.787).
Factorization parameters were as follows:
n: 64763403372051254345862180645606745671444139005957866904918665429237488531590248316682524769830667499
m: 10000000000000000000000000
deg: 5
c5: 22
c0: -265
skew: 1.64
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 695001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 114200 x 114440
Total sieving time: 2.66 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 2.66 hours.
 --------- CPU info (if available) ----------

(44·10¹²⁹-53)/9 = 4(8)₁₂₈3_<130> = 19 · 31 · 1904637519067_<13> · C115

C115 = P45 · P71

P45 = 105441685305072759250343963660885215379364893_<45>

P71 = 41330456138185682306653571302025199180323207767883057670613596493709137_<71>

Number: 48883_129
N=4357952949637687480439860834487236713464822412626922260738831005387602493757440039797623836283296431890596931127341
  ( 115 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=105441685305072759250343963660885215379364893
 r2=41330456138185682306653571302025199180323207767883057670613596493709137
Version: 
Total time: 2.55 hours.
Scaled time: 2.54 units (timescale=0.997).
Factorization parameters were as follows:
n: 4357952949637687480439860834487236713464822412626922260738831005387602493757440039797623836283296431890596931127341
m: 100000000000000000000000000
deg: 5
c5: 22
c0: -265
skew: 1.64
type: snfs
lss: 1
rlim: 1080000
alim: 1080000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3Factor base limits: 1080000/1080000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [540000, 890001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 138240 x 138488
Total sieving time: 2.55 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000
total time: 2.55 hours.
 --------- CPU info (if available) ----------

Feb 26, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Feb 26, 2009

(44·10¹⁶²-71)/9 = 4(8)₁₆₁1_<163> = 3 · 61 · 21602829725909_<14> · 13890992668947677_<17> · C131

C131 = P55 · P77

P55 = 2919528487754485360741130920221825593218288436977792273_<55>

P77 = 30493160198018619499137574747553107457658730557098544861937924757079677957063_<77>

Number: 48881_162
N=89025649879776563556284994705112048537492877537816182828421619511054800970064111601633295089238610188889885975117868575212627174199
  ( 131 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=2919528487754485360741130920221825593218288436977792273
 r2=30493160198018619499137574747553107457658730557098544861937924757079677957063
Version: 
Total time: 23.99 hours.
Scaled time: 57.03 units (timescale=2.377).
Factorization parameters were as follows:
n: 89025649879776563556284994705112048537492877537816182828421619511054800970064111601633295089238610188889885975117868575212627174199
m: 200000000000000000000000000000000
deg: 5
c5: 275
c0: -142
skew: 0.88
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 4100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9810253
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 738638 x 738886
Total sieving time: 21.56 hours.
Total relation processing time: 0.93 hours.
Matrix solve time: 1.17 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 23.99 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(44·10¹⁴¹-53)/9 = 4(8)₁₄₀3_<142> = 39161 · 123787 · 171881 · 6897173 · 269695261837_<12> · C109

C109 = P31 · C78

P31 = 6199736064021385889457145645067_<31>

C78 = [508786813741771010621372438944508866566847913331596410044410894001651984362747_<78>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 3154343958053389376334984624566041695442685230963101653023859921211386889423050385418406800432231574239119049 (109 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1434853449
Step 1 took 3287ms
Step 2 took 1989ms
********** Factor found in step 2: 6199736064021385889457145645067
Found probable prime factor of 31 digits: 6199736064021385889457145645067
Composite cofactor 508786813741771010621372438944508866566847913331596410044410894001651984362747 has 78 digits

(44·10¹¹¹-53)/9 = 4(8)₁₁₀3_<112> = 19 · 107 · C109

C109 = P47 · P63

P47 = 15072748997352795060939680449363695294889116749_<47>

P63 = 159543943113817436805969360550316504075555966470480954857298799_<63>

Number: 48883_111
N=2404765808602503142591681696452970432311307864677269497731868612340820899601027490845493796797289173088484451
  ( 109 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=15072748997352795060939680449363695294889116749
 r2=159543943113817436805969360550316504075555966470480954857298799
Version: 
Total time: 0.55 hours.
Scaled time: 1.31 units (timescale=2.380).
Factorization parameters were as follows:
n: 2404765808602503142591681696452970432311307864677269497731868612340820899601027490845493796797289173088484451
m: 20000000000000000000000
deg: 5
c5: 55
c0: -212
skew: 1.31
type: snfs
lss: 1
rlim: 400000
alim: 400000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [200000, 400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 1137031
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 51705 x 51933
Total sieving time: 0.50 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,400000,400000,25,25,45,45,2.2,2.2,25000
total time: 0.55 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 25, 2009 (7th)

By Robert Backstrom / GGNFS, Msieve / Feb 25, 2009

(44·10¹⁴⁸-71)/9 = 4(8)₁₄₇1_<149> = 7 · C148

C148 = P45 · P104

P45 = 473996607386740060872943445846528011842562499_<45>

P104 = 14734550575440180609780035105536363694945692984151226981094395946180645394713692742435856565307183185517_<104>

Number: n
N=6984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126983
  ( 148 digits)
SNFS difficulty: 151 digits.
Divisors found:

Wed Feb 25 16:18:01 2009  prp45 factor: 473996607386740060872943445846528011842562499
Wed Feb 25 16:18:01 2009  prp104 factor: 14734550575440180609780035105536363694945692984151226981094395946180645394713692742435856565307183185517
Wed Feb 25 16:18:01 2009  elapsed time 01:34:40 (Msieve 1.39 - dependency 6)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 22.68 hours.
Scaled time: 39.73 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_4_8_147_1
n: 6984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126983
deg: 5
c5: 11
c0: -1775
m: 1000000000000000000000000000000
skew: 2.76
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [1000000, 1788991)
Primes: RFBsize:148933, AFBsize:149372, largePrimes:13961450 encountered
Relations: rels:13132793, finalFF:269448
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1051593 hash collisions in 14069728 relations
Msieve: matrix is 367270 x 367518 (97.5 MB)

Total sieving time: 22.02 hours.
Total relation processing time: 0.65 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,56,56,2.5,2.5,100000
total time: 22.68 hours.
 --------- CPU info (if available) ----------

Feb 25, 2009 (6th)

By Sinkiti Sibata / GGNFS / Feb 25, 2009

(44·10¹³⁶-71)/9 = 4(8)₁₃₅1_<137> = 7 · 41 · 45481 · 3280681 · C124

C124 = P34 · P90

P34 = 2744064447066890196809404077767207_<34>

P90 = 416044662604396313993951723092527975044912145201118051288551518737312394333927471726272169_<90>

Number: 48881_136
N=1141653367044663660491761682722608073379051329153751902242675265147625385123173999076345161864440171891051539400931104961983
  ( 124 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=2744064447066890196809404077767207 (pp34)
 r2=416044662604396313993951723092527975044912145201118051288551518737312394333927471726272169 (pp90)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 9.29 hours.
Scaled time: 4.39 units (timescale=0.472).
Factorization parameters were as follows:
name: 48881_136
n: 1141653367044663660491761682722608073379051329153751902242675265147625385123173999076345161864440171891051539400931104961983
m: 2000000000000000000000000000
deg: 5
c5: 55
c0: -284
skew: 1.39
type: snfs
lss: 1
rlim: 1410000
alim: 1410000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1410000/1410000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [705000, 1455001)
Primes: RFBsize:107805, AFBsize:108301, largePrimes:3367603 encountered
Relations: rels:3384708, finalFF:322308
Max relations in full relation-set: 28
Initial matrix: 216173 x 322308 with sparse part having weight 27607988.
Pruned matrix : 185337 x 186481 with weight 12402631.
Total sieving time: 8.46 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1410000,1410000,26,26,48,48,2.3,2.3,75000
total time: 9.29 hours.
 --------- CPU info (if available) ----------

(44·10¹³⁷-71)/9 = 4(8)₁₃₆1_<138> = 37 · C137

C137 = P33 · P104

P33 = 340868543207612725222075573719347_<33>

P104 = 38763369270966856217289969579602950513973542633663421837299638535905817359925420336650549634976872218479_<104>

Number: 48881_137
N=13213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213
  ( 137 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=340868543207612725222075573719347 (pp33)
 r2=38763369270966856217289969579602950513973542633663421837299638535905817359925420336650549634976872218479 (pp104)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 11.13 hours.
Scaled time: 4.76 units (timescale=0.428).
Factorization parameters were as follows:
name: 48881_137
n: 13213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213213
m: 2000000000000000000000000000
deg: 5
c5: 275
c0: -142
skew: 0.88
type: snfs
lss: 1
rlim: 1450000
alim: 1450000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1450000/1450000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [725000, 1625001)
Primes: RFBsize:110630, AFBsize:110661, largePrimes:3552440 encountered
Relations: rels:3600847, finalFF:325726
Max relations in full relation-set: 28
Initial matrix: 221357 x 325726 with sparse part having weight 30493824.
Pruned matrix : 191788 x 192958 with weight 14833527.
Total sieving time: 10.14 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.75 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000
total time: 11.13 hours.
 --------- CPU info (if available) ----------

Feb 25, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Feb 25, 2009

(44·10¹⁵⁷-71)/9 = 4(8)₁₅₆1_<158> = 73 · C156

C156 = P57 · P100

P57 = 266760531775608133956050583465012094689794027545223607047_<57>

P100 = 2510531832574284225993222640708878791275251483907369761442063478864181134791112368628433935088415951_<100>

Number: 48881_157
N=669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697
  ( 156 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=266760531775608133956050583465012094689794027545223607047 (pp57)
 r2=2510531832574284225993222640708878791275251483907369761442063478864181134791112368628433935088415951 (pp100)
Version: Msieve-1.39
Total time: 26.26 hours.
Scaled time: 67.52 units (timescale=2.571).
Factorization parameters were as follows:
n: 669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697
m: 20000000000000000000000000000000
deg: 5
c5: 275
c0: -142
skew: 0.88
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1550000, 2950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 538218 x 538466
Total sieving time: 26.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000
total time: 26.26 hours.
 --------- CPU info (if available) ----------

(44·10¹⁶³-71)/9 = 4(8)₁₆₂1_<164> = 40293606533484649013_<20> · C145

C145 = P70 · P75

P70 = 2090142133341823514836371166394869125392607600423305654469844115347859_<70>

P75 = 580494629132693000760167098993643357602606695180416440687702991593086018143_<75>

Number: 48881_163
N=1213316282528877603116799145583708290172539600829303853559907218216047380074537193956932129439123596354105227950875751697368095787851087630205837
  ( 145 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=2090142133341823514836371166394869125392607600423305654469844115347859 (pp70)
 r2=580494629132693000760167098993643357602606695180416440687702991593086018143 (pp75)
Version: Msieve-1.39
Total time: 42.36 hours.
Scaled time: 108.90 units (timescale=2.571).
Factorization parameters were as follows:
n: 1213316282528877603116799145583708290172539600829303853559907218216047380074537193956932129439123596354105227950875751697368095787851087630205837
m: 200000000000000000000000000000000
deg: 5
c5: 1375
c0: -71
skew: 0.55
type: snfs
lss: 1
rlim: 3900000
alim: 3900000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 3900000/3900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1950000, 4150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 732974 x 733222
Total sieving time: 42.36 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3900000,3900000,27,27,51,51,2.4,2.4,100000
total time: 42.36 hours.
 --------- CPU info (if available) ----------

Feb 25, 2009 (4th)

By Erik Branger / GGNFS, Msieve, GMP-ECM / Feb 25, 2009

(44·10¹⁵⁰-71)/9 = 4(8)₁₄₉1_<151> = 3² · 51197 · 4521741435891364483_<19> · C127

C127 = P57 · P71

P57 = 230042934078513792659027921169867040472521633549158310061_<57>

P71 = 10200196105649887861156671475312764849458021711987665441965423462292219_<71>

Number: 48881_150
N=2346483040319930262471884695240655852973736090122040956860740182038035783923398759608186873543390899886975864020261543389715359
  ( 127 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=230042934078513792659027921169867040472521633549158310061
 r2=10200196105649887861156671475312764849458021711987665441965423462292219
Version: 
Total time: 19.56 hours.
Scaled time: 20.23 units (timescale=1.034).
Factorization parameters were as follows:
n: 2346483040319930262471884695240655852973736090122040956860740182038035783923398759608186873543390899886975864020261543389715359
m: 1000000000000000000000000000000
deg: 5
c5: 44
c0: -71
skew: 1.10
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 2000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 433086 x 433334
Total sieving time: 19.56 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 19.56 hours.
 --------- CPU info (if available) ----------

(44·10¹⁴³-71)/9 = 4(8)₁₄₂1_<144> = 23 · 37 · 199 · 30302636207_<11> · 4307160298747_<13> · C116

C116 = P38 · P79

P38 = 16407153915374855716140672893295921439_<38>

P79 = 1348102242729470640250881292514087976844275396957524728539042720088578215437399_<79>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 22118520990124458332699006534768476475381642269965611325044514221416868763053419753069680858556126450701594126497161 (116 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=853145556
Step 1 took 31309ms
Step 2 took 11544ms
********** Factor found in step 2: 16407153915374855716140672893295921439
Found probable prime factor of 38 digits: 16407153915374855716140672893295921439
Probable prime cofactor 1348102242729470640250881292514087976844275396957524728539042720088578215437399 has 79 digits

(43·10¹⁵⁸+11)/9 = 4(7)₁₅₇9_<159> = 223 · 15507127 · 14607641584687_<14> · C136

C136 = P50 · P87

P50 = 30394270223730515609456784038820180026129302682419_<50>

P87 = 311184469852027455725596184106294444408741498018266638730912165177164854047468063456183_<87>

Number: 47779_158
N=9458224866110844426386379033165601182210899487313783158712396653134358965763386452505542412533445380253027686320324072560877769970946677
  ( 136 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=30394270223730515609456784038820180026129302682419
 r2=311184469852027455725596184106294444408741498018266638730912165177164854047468063456183
Version: 
Total time: 55.26 hours.
Scaled time: 43.27 units (timescale=0.783).
Factorization parameters were as follows:
n: 9458224866110844426386379033165601182210899487313783158712396653134358965763386452505542412533445380253027686320324072560877769970946677
m: 50000000000000000000000000000000
deg: 5
c5: 344
c0: 275
skew: 0.96
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 683237 x 683485
Total sieving time: 55.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 55.26 hours.
 --------- CPU info (if available) ----------

Feb 25, 2009 (3rd)

By Tyler Cadigan / GGNFS, Msieve / Feb 25, 2009

(10¹⁹⁶+53)/9 = (1)₁₉₅7_<196> = 19 · 739 · 1297 · 175039 · 259878475236857_<15> · 1510283330627080248420932638301_<31> · C138

C138 = P60 · P79

P60 = 276770545742713499359339707621751061182650942179447980819891_<60>

P79 = 3208751188163324485416450871925542565808986088227453373291593937334726893986197_<79>

Number: 11117_196
N=888087817500543690374777485610139659656184329191590913987962706355569305479165393738154255599358025085365797320711586900377767369297044527
  ( 138 digits)
Divisors found:
 r1=276770545742713499359339707621751061182650942179447980819891 (pp60)
 r2=3208751188163324485416450871925542565808986088227453373291593937334726893986197 (pp79)
Version: Msieve-1.39
Total time: 949.97 hours.
Scaled time: 2407.23 units (timescale=2.534).
Factorization parameters were as follows:
name: 11117_196
n: 888087817500543690374777485610139659656184329191590913987962706355569305479165393738154255599358025085365797320711586900377767369297044527
skew: 550372.48
# norm 1.41e+19
c5: 111720
c4: 790382198768
c3: -169446067282460132
c2: -364765162766298110614081
c1: 34335070314051591273192601162
c0: 18956319517172044216016560873788003
# alpha 7.114396
Y1: 2556859849182053
Y0: -380242682535105905692270984
type: gnfs
lss: 1
rlim: 12900000
alim: 12900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
qintsize: 1000000
Factor base limits: 12900000/12900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6450000, 20450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1955255 x 1955503
Total sieving time: 949.97 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,137,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12900000,12900000,28,28,55,55,2.5,2.5,60000
total time: 949.97 hours.
 --------- CPU info (if available) ----------

Feb 25, 2009 (2nd)

By Serge Batalov / PFGW / Feb 25, 2009

(76·10³⁵⁴²⁷-31)/9 = 8(4)₃₅₄₂₆1_<35428> is PRP.

Feb 25, 2009

Factorizations of 488...883 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Feb 24, 2009 (6th)

By Wataru Sakai / GMP-ECM / Feb 24, 2009

(43·10¹⁹⁰+11)/9 = 4(7)₁₈₉9_<191> = C191

C191 = P43 · P47 · P50 · P53

P43 = 2296681587052719423860117114229198911432333_<43>

P47 = 15570079985107990077984373269745574874310941497_<47>

P50 = 60119068484720194413645850533910859383261467146867_<50>

P53 = 22223991954571482014953594682406371807911258907638637_<53>

-------
Input number is
47777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779
(191 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=208888904
Step 1 took 73125ms
Step 2 took 24257ms
********** Factor found in step 2: 2296681587052719423860117114229198911432333
Found probable prime factor of 43 digits:
2296681587052719423860117114229198911432333
Composite cofactor
20802961127532676845791180520483094188690819112594979637430646939415754594890399668350082445540467751199882868417289174626988408216248330568874577663
has 149 digits
----------
Input number is
20802961127532676845791180520483094188690819112594979637430646939415754594890399668350082445540467751199882868417289174626988408216248330568874577663
(149 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1301257518
Step 1 took 185301ms
Step 2 took 57413ms
********** Factor found in step 2:
60119068484720194413645850533910859383261467146867
Found probable prime factor of 50 digits:
60119068484720194413645850533910859383261467146867
Composite cofactor
346029332321074431997114693740257714417458796246588353710386771084181929049928930706702480523819589
has 99 digits
----------
Input number is
346029332321074431997114693740257714417458796246588353710386771084181929049928930706702480523819589
(99 digits)
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1827407922
Step 1 took 411700ms
Step 2 took 119590ms
********** Factor found in step 2:
15570079985107990077984373269745574874310941497
Found probable prime factor of 47 digits:
15570079985107990077984373269745574874310941497
Probable prime cofactor
22223991954571482014953594682406371807911258907638637 has 53 digits
----------

Feb 24, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Feb 24, 2009

(7·10¹⁶⁹-43)/9 = (7)₁₆₈3_<169> = 3² · 113 · 49991 · 5632442647674936588605121832519_<31> · C131

C131 = P57 · P75

P57 = 165855014904250974498183632926088661986783788509769529269_<57>

P75 = 163763596475382264171981673046491009331053941417905993150662041160894520369_<75>

Number: 77773_169
N=27161013734198267779787441623856865261526769714349621384721227945530504045181223735394220143911476359430775105460879711466662180261
  ( 131 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=165855014904250974498183632926088661986783788509769529269 (pp57)
 r2=163763596475382264171981673046491009331053941417905993150662041160894520369 (pp75)
Version: Msieve-1.39
Total time: 49.96 hours.
Scaled time: 128.45 units (timescale=2.571).
Factorization parameters were as follows:
n: 27161013734198267779787441623856865261526769714349621384721227945530504045181223735394220143911476359430775105460879711466662180261
m: 5000000000000000000000000000000000
deg: 5
c5: 112
c0: -215
skew: 1.14
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 4850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 908762 x 909010
Total sieving time: 49.96 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 49.96 hours.
 --------- CPU info (if available) ----------

Feb 24, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 24, 2009

(44·10¹⁴⁰-71)/9 = 4(8)₁₃₉1_<141> = 13 · 37 · 18953839044024127688623_<23> · C116

C116 = P48 · P69

P48 = 509123278828127286216988563096938862260588684297_<48>

P69 = 105328269145172653612757075034695759465207254455961930240426228195271_<69>

Number: 48881_140
N=53625073740481772972409824072405535386545820550053849846053767223604814908309704448037052570648052207497954687359487
  ( 116 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=509123278828127286216988563096938862260588684297
 r2=105328269145172653612757075034695759465207254455961930240426228195271
Version: 
Total time: 4.50 hours.
Scaled time: 10.74 units (timescale=2.389).
Factorization parameters were as follows:
n: 53625073740481772972409824072405535386545820550053849846053767223604814908309704448037052570648052207497954687359487
m: 10000000000000000000000000000
deg: 5
c5: 44
c0: -71
skew: 1.10
type: snfs
lss: 1
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [600000, 1100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3360002
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 198140 x 198388
Total sieving time: 4.21 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,48,48,2.3,2.3,50000
total time: 4.50 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(44·10¹⁵³-71)/9 = 4(8)₁₅₂1_<154> = 3 · 29 · 5686565066897115489601_<22> · 480561239432935951772923342469_<30> · C101

C101 = P30 · P71

P30 = 207788945034135538746511370141_<30>

P71 = 98962287285357687567718782537306001105195681542297973648064568489776647_<71>

Number: 48881_153
N=20563269273189518839408618741350859979878540178289245336713437567214603823608381501320185903034897227
  ( 101 digits)
Divisors found:
 r1=207788945034135538746511370141
 r2=98962287285357687567718782537306001105195681542297973648064568489776647
Version: 
Total time: 2.54 hours.
Scaled time: 6.07 units (timescale=2.385).
Factorization parameters were as follows:
name: 48881_153
n: 20563269273189518839408618741350859979878540178289245336713437567214603823608381501320185903034897227
skew: 5676.13
# norm 1.86e+14
c5: 344520
c4: -1637807466
c3: -26734948702069
c2: 70694864340124641
c1: 482804719370645285549
c0: 199362126528802262426345
# alpha -6.87
Y1: 36487728641
Y0: -9019391019254834158
# Murphy_E 3.44e-09
# M 15579905984155218821420874809478929204387125506285712518361026215595714425854941028538745894119301401
type: gnfs
rlim: 1200000
alim: 1200000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [600000, 1050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4083039
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 209301 x 209549
Polynomial selection time: 0.19 hours.
Total sieving time: 1.93 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,26,26,49,49,2.5,2.5,50000
total time: 2.54 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(44·10¹⁵⁵-71)/9 = 4(8)₁₅₄1_<156> = 37 · 97 · 498889679 · 18697682263419627917303_<23> · 440832314293904601752619068922493_<33> · C89

C89 = P39 · P51

P39 = 261205238291645927272402074009059256239_<39>

P51 = 126820397395510759541604069650822061270444804667271_<51>

Tue Feb 24 00:48:15 2009  
Tue Feb 24 00:48:15 2009  
Tue Feb 24 00:48:15 2009  Msieve v. 1.39
Tue Feb 24 00:48:15 2009  random seeds: 5915a884 8e521e17
Tue Feb 24 00:48:15 2009  factoring 33126152121935620473093722297086995034869661998940995868094417359149617683041111125853769 (89 digits)
Tue Feb 24 00:48:16 2009  searching for 15-digit factors
Tue Feb 24 00:48:17 2009  commencing quadratic sieve (89-digit input)
Tue Feb 24 00:48:17 2009  using multiplier of 1
Tue Feb 24 00:48:17 2009  using VC8 32kb sieve core
Tue Feb 24 00:48:17 2009  sieve interval: 32 blocks of size 32768
Tue Feb 24 00:48:17 2009  processing polynomials in batches of 7
Tue Feb 24 00:48:17 2009  using a sieve bound of 1550243 (59000 primes)
Tue Feb 24 00:48:17 2009  using large prime bound of 124019440 (26 bits)
Tue Feb 24 00:48:17 2009  using double large prime bound of 370067932007440 (42-49 bits)
Tue Feb 24 00:48:17 2009  using trial factoring cutoff of 49 bits
Tue Feb 24 00:48:17 2009  polynomial 'A' values have 11 factors
Tue Feb 24 01:44:43 2009  59380 relations (15995 full + 43385 combined from 624990 partial), need 59096
Tue Feb 24 01:44:48 2009  begin with 640985 relations
Tue Feb 24 01:44:48 2009  reduce to 143986 relations in 10 passes
Tue Feb 24 01:44:48 2009  attempting to read 143986 relations
Tue Feb 24 01:44:50 2009  recovered 143986 relations
Tue Feb 24 01:44:50 2009  recovered 118738 polynomials
Tue Feb 24 01:44:50 2009  attempting to build 59380 cycles
Tue Feb 24 01:44:50 2009  found 59380 cycles in 5 passes
Tue Feb 24 01:44:50 2009  distribution of cycle lengths:
Tue Feb 24 01:44:50 2009     length 1 : 15995
Tue Feb 24 01:44:50 2009     length 2 : 11514
Tue Feb 24 01:44:50 2009     length 3 : 10428
Tue Feb 24 01:44:50 2009     length 4 : 7909
Tue Feb 24 01:44:50 2009     length 5 : 5509
Tue Feb 24 01:44:50 2009     length 6 : 3484
Tue Feb 24 01:44:50 2009     length 7 : 2091
Tue Feb 24 01:44:50 2009     length 9+: 2450
Tue Feb 24 01:44:50 2009  largest cycle: 17 relations
Tue Feb 24 01:44:50 2009  matrix is 59000 x 59380 (15.1 MB) with weight 3493763 (58.84/col)
Tue Feb 24 01:44:50 2009  sparse part has weight 3493763 (58.84/col)
Tue Feb 24 01:44:51 2009  filtering completed in 3 passes
Tue Feb 24 01:44:51 2009  matrix is 54792 x 54855 (14.1 MB) with weight 3246248 (59.18/col)
Tue Feb 24 01:44:51 2009  sparse part has weight 3246248 (59.18/col)
Tue Feb 24 01:44:51 2009  saving the first 48 matrix rows for later
Tue Feb 24 01:44:51 2009  matrix is 54744 x 54855 (10.2 MB) with weight 2652281 (48.35/col)
Tue Feb 24 01:44:51 2009  sparse part has weight 2118421 (38.62/col)
Tue Feb 24 01:44:51 2009  matrix includes 64 packed rows
Tue Feb 24 01:44:51 2009  using block size 21942 for processor cache size 4096 kB
Tue Feb 24 01:44:52 2009  commencing Lanczos iteration
Tue Feb 24 01:44:52 2009  memory use: 8.7 MB
Tue Feb 24 01:45:13 2009  lanczos halted after 867 iterations (dim = 54742)
Tue Feb 24 01:45:13 2009  recovered 15 nontrivial dependencies
Tue Feb 24 01:45:13 2009  prp39 factor: 261205238291645927272402074009059256239
Tue Feb 24 01:45:13 2009  prp51 factor: 126820397395510759541604069650822061270444804667271
Tue Feb 24 01:45:13 2009  elapsed time 00:56:58

(44·10¹⁴³-71)/9 = 4(8)₁₄₂1_<144> = 23 · 37 · 199 · 30302636207_<11> · 4307160298747_<13> · C116

C116 = P38 · P79

P38 = 16407153915374855716140672893295921439_<38>

P79 = 1348102242729470640250881292514087976844275396957524728539042720088578215437399_<79>

Number: 48881_143
N=22118520990124458332699006534768476475381642269965611325044514221416868763053419753069680858556126450701594126497161
  ( 116 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=16407153915374855716140672893295921439
 r2=1348102242729470640250881292514087976844275396957524728539042720088578215437399
Version: 
Total time: 5.53 hours.
Scaled time: 13.18 units (timescale=2.384).
Factorization parameters were as follows:
n: 22118520990124458332699006534768476475381642269965611325044514221416868763053419753069680858556126450701594126497161
m: 100000000000000000000000000000
deg: 5
c5: 11
c0: -1775
skew: 2.76
type: snfs
lss: 1
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [750000, 1350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3676723
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 264624 x 264872
Total sieving time: 5.21 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,49,49,2.3,2.3,75000
total time: 5.53 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 24, 2009 (3rd)

By Sinkiti Sibata / Msieve, GGNFS / Feb 24, 2009

(44·10¹⁴⁹-71)/9 = 4(8)₁₄₈1_<150> = 37 · 73 · 61961 · 24126935406859_<14> · 27995820258820794195604377373_<29> · C100

C100 = P43 · P58

P43 = 1823386628589600235665888424988868096924179_<43>

P58 = 2371881789921313843032874446987776090309859711930752765857_<58>

Mon Feb 23 13:53:09 2009  Msieve v. 1.39
Mon Feb 23 13:53:09 2009  random seeds: 79c73e94 b196d9d5
Mon Feb 23 13:53:09 2009  factoring 4324857540337690895886670133751822679873755496465154258190521001152601075515706549500196558668956403 (100 digits)
Mon Feb 23 13:53:10 2009  searching for 15-digit factors
Mon Feb 23 13:53:12 2009  commencing quadratic sieve (100-digit input)
Mon Feb 23 13:53:12 2009  using multiplier of 11
Mon Feb 23 13:53:12 2009  using 32kb Intel Core sieve core
Mon Feb 23 13:53:12 2009  sieve interval: 36 blocks of size 32768
Mon Feb 23 13:53:12 2009  processing polynomials in batches of 6
Mon Feb 23 13:53:12 2009  using a sieve bound of 2711333 (98824 primes)
Mon Feb 23 13:53:12 2009  using large prime bound of 406699950 (28 bits)
Mon Feb 23 13:53:12 2009  using double large prime bound of 3138292436875950 (43-52 bits)
Mon Feb 23 13:53:12 2009  using trial factoring cutoff of 52 bits
Mon Feb 23 13:53:12 2009  polynomial 'A' values have 13 factors
Tue Feb 24 02:43:55 2009  99124 relations (22994 full + 76130 combined from 1499481 partial), need 98920
Tue Feb 24 02:43:58 2009  begin with 1522475 relations
Tue Feb 24 02:43:59 2009  reduce to 263904 relations in 14 passes
Tue Feb 24 02:43:59 2009  attempting to read 263904 relations
Tue Feb 24 02:44:04 2009  recovered 263904 relations
Tue Feb 24 02:44:04 2009  recovered 255780 polynomials
Tue Feb 24 02:44:05 2009  attempting to build 99124 cycles
Tue Feb 24 02:44:05 2009  found 99124 cycles in 6 passes
Tue Feb 24 02:44:05 2009  distribution of cycle lengths:
Tue Feb 24 02:44:05 2009     length 1 : 22994
Tue Feb 24 02:44:05 2009     length 2 : 16653
Tue Feb 24 02:44:05 2009     length 3 : 16437
Tue Feb 24 02:44:05 2009     length 4 : 13818
Tue Feb 24 02:44:05 2009     length 5 : 10262
Tue Feb 24 02:44:05 2009     length 6 : 7282
Tue Feb 24 02:44:05 2009     length 7 : 4731
Tue Feb 24 02:44:05 2009     length 9+: 6947
Tue Feb 24 02:44:05 2009  largest cycle: 22 relations
Tue Feb 24 02:44:05 2009  matrix is 98824 x 99124 (27.6 MB) with weight 6829409 (68.90/col)
Tue Feb 24 02:44:05 2009  sparse part has weight 6829409 (68.90/col)
Tue Feb 24 02:44:07 2009  filtering completed in 3 passes
Tue Feb 24 02:44:07 2009  matrix is 95251 x 95314 (26.6 MB) with weight 6588098 (69.12/col)
Tue Feb 24 02:44:07 2009  sparse part has weight 6588098 (69.12/col)
Tue Feb 24 02:44:07 2009  saving the first 48 matrix rows for later
Tue Feb 24 02:44:08 2009  matrix is 95203 x 95314 (16.3 MB) with weight 5168196 (54.22/col)
Tue Feb 24 02:44:08 2009  sparse part has weight 3703985 (38.86/col)
Tue Feb 24 02:44:08 2009  matrix includes 64 packed rows
Tue Feb 24 02:44:08 2009  using block size 38125 for processor cache size 1024 kB
Tue Feb 24 02:44:08 2009  commencing Lanczos iteration
Tue Feb 24 02:44:08 2009  memory use: 15.9 MB
Tue Feb 24 02:45:13 2009  lanczos halted after 1507 iterations (dim = 95201)
Tue Feb 24 02:45:13 2009  recovered 17 nontrivial dependencies
Tue Feb 24 02:45:15 2009  prp43 factor: 1823386628589600235665888424988868096924179
Tue Feb 24 02:45:15 2009  prp58 factor: 2371881789921313843032874446987776090309859711930752765857
Tue Feb 24 02:45:15 2009  elapsed time 12:52:06

(44·10¹⁵¹-71)/9 = 4(8)₁₅₀1_<152> = 19 · 41 · 40795973 · 53086617357311_<14> · 787828356283625781569_<21> · C107

C107 = P36 · P71

P36 = 425947598878060367961552767720056277_<36>

P71 = 86354023540670324234290958731200652262153362934003180239457072040500101_<71>

Number: 48881_151
N=36782288980608025602558997767137002692332449728901869109100194795392576159672152415241702975132762944183977
  ( 107 digits)
Divisors found:
 r1=425947598878060367961552767720056277 (pp36)
 r2=86354023540670324234290958731200652262153362934003180239457072040500101 (pp71)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 18.41 hours.
Scaled time: 8.71 units (timescale=0.473).
Factorization parameters were as follows:
name: 48881_151
n: 36782288980608025602558997767137002692332449728901869109100194795392576159672152415241702975132762944183977
skew: 12055.98
# norm 7.62e+14
c5: 155700
c4: 1637779484
c3: -13851048219839
c2: -236112434457720744
c1: -3660715319507968407076
c0: 16672546580673607696079200
# alpha -6.72
Y1: 92626107473
Y0: -188221650890861899581
# Murphy_E 1.53e-09
# M 18157611387834815042861964823819336260349267121385750848762299243356676082757506236419679403295869746734284
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:183993, largePrimes:4418375 encountered
Relations: rels:4476604, finalFF:446496
Max relations in full relation-set: 28
Initial matrix: 367151 x 446496 with sparse part having weight 33191043.
Pruned matrix : 303955 x 305854 with weight 19226197.
Total sieving time: 15.49 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 2.39 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 18.41 hours.
 --------- CPU info (if available) ----------

(44·10¹³⁵-71)/9 = 4(8)₁₃₄1_<136> = 3 · 82549 · C131

C131 = P65 · P66

P65 = 38357340097329560078233395558992864916910707708764623785880080749_<65>

P66 = 514669713737333210325188168649284923465893594557365709330203361227_<66>

Number: 48881_135
N=19741361247618137465379709380242396996082685794251046404312949031843264359709137962054411678271446409158555883531352646665975719023
  ( 131 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=38357340097329560078233395558992864916910707708764623785880080749 (pp65)
 r2=514669713737333210325188168649284923465893594557365709330203361227 (pp66)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 9.13 hours.
Scaled time: 4.31 units (timescale=0.472).
Factorization parameters were as follows:
name: 48881_135
n: 19741361247618137465379709380242396996082685794251046404312949031843264359709137962054411678271446409158555883531352646665975719023
m: 1000000000000000000000000000
deg: 5
c5: 44
c0: -71
skew: 1.10
type: snfs
lss: 1
rlim: 1330000
alim: 1330000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1330000/1330000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [665000, 1415001)
Primes: RFBsize:102146, AFBsize:102624, largePrimes:3331762 encountered
Relations: rels:3328059, finalFF:289048
Max relations in full relation-set: 28
Initial matrix: 204836 x 289048 with sparse part having weight 25651418.
Pruned matrix : 181849 x 182937 with weight 12934923.
Total sieving time: 8.30 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.62 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000
total time: 9.13 hours.
 --------- CPU info (if available) ----------

Feb 24, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Feb 24, 2009

(32·10¹⁶⁵+13)/9 = 3(5)₁₆₄7_<166> = 458981 · 630263 · C155

C155 = P44 · P111

P44 = 18681192180063273540908440345016705640959411_<44>

P111 = 657940106077601764355434130314334771812300887403075420900850959415178524121749594369791636050706233899226953629_<111>

Number: 35557_165
N=12291105564606894753648143531039730271512437525537283493091738158472357920721801541135677888602504092366897956430047188487377389072348162342113998368152519
  ( 155 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=18681192180063273540908440345016705640959411
 r2=657940106077601764355434130314334771812300887403075420900850959415178524121749594369791636050706233899226953629
Version: 
Total time: 38.75 hours.
Scaled time: 37.47 units (timescale=0.967).
Factorization parameters were as follows:
n: 12291105564606894753648143531039730271512437525537283493091738158472357920721801541135677888602504092366897956430047188487377389072348162342113998368152519
m: 2000000000000000000000000000000000
deg: 5
c5: 1
c0: 13
skew: 1.67
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 3600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 685665 x 685913
Total sieving time: 38.75 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 38.75 hours.
 --------- CPU info (if available) ----------

(44·10¹⁴⁴-71)/9 = 4(8)₁₄₃1_<145> = 3 · 3861802112461_<13> · C132

C132 = P50 · P83

P50 = 27176738312456067705423924254415620270867506101379_<50>

P83 = 15527500933247063626950184057751950006067441741686919878574402788064647788046405133_<83>

Number: 48881_144
N=421986829509272820353632573560155796304665185167618184592094823146824649144255133281704521784352850104568736051129758745664803978407
  ( 132 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=27176738312456067705423924254415620270867506101379
 r2=15527500933247063626950184057751950006067441741686919878574402788064647788046405133
Version: 
Total time: 9.10 hours.
Scaled time: 9.65 units (timescale=1.060).
Factorization parameters were as follows:
n: 421986829509272820353632573560155796304665185167618184592094823146824649144255133281704521784352850104568736051129758745664803978407
m: 100000000000000000000000000000
deg: 5
c5: 22
c0: -355
skew: 1.74
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2200001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 341023 x 341271
Total sieving time: 9.10 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000
total time: 9.10 hours.
 --------- CPU info (if available) ----------

Feb 24, 2009

By Serge Batalov / PFGW / Feb 23, 2009

(31·10³⁵⁹⁹⁰+23)/9 = 3(4)₃₅₉₈₉7_<35991> is PRP.

(13·10²²⁰⁴⁸-7)/3 = 4(3)₂₂₀₄₇1_<22049> is PRP.

Feb 23, 2009 (6th)

By Sinkiti Sibata / Msieve / Feb 23, 2009

(44·10¹⁴¹-71)/9 = 4(8)₁₄₀1_<142> = 3² · 41 · 73 · 131 · 153953 · 789490181 · 4200148643_<10> · 583003741888800227_<18> · C94

C94 = P46 · P49

P46 = 1689109804305687021321287700092427147181180249_<46>

P49 = 2755883601781023358092221328064703478054177727799_<49>

Mon Feb 23 07:23:14 2009  Msieve v. 1.39
Mon Feb 23 07:23:14 2009  random seeds: df699430 3111daa0
Mon Feb 23 07:23:14 2009  factoring 4654990011293596264643196610177277729826715307937834774996988833394165195376426115665877041951 (94 digits)
Mon Feb 23 07:23:15 2009  searching for 15-digit factors
Mon Feb 23 07:23:17 2009  commencing quadratic sieve (94-digit input)
Mon Feb 23 07:23:17 2009  using multiplier of 39
Mon Feb 23 07:23:17 2009  using 32kb Intel Core sieve core
Mon Feb 23 07:23:17 2009  sieve interval: 36 blocks of size 32768
Mon Feb 23 07:23:17 2009  processing polynomials in batches of 6
Mon Feb 23 07:23:17 2009  using a sieve bound of 2059481 (76413 primes)
Mon Feb 23 07:23:17 2009  using large prime bound of 284208378 (28 bits)
Mon Feb 23 07:23:17 2009  using double large prime bound of 1646441586215862 (42-51 bits)
Mon Feb 23 07:23:17 2009  using trial factoring cutoff of 51 bits
Mon Feb 23 07:23:17 2009  polynomial 'A' values have 12 factors
Mon Feb 23 10:36:21 2009  76733 relations (19105 full + 57628 combined from 1093329 partial), need 76509
Mon Feb 23 10:36:22 2009  begin with 1112434 relations
Mon Feb 23 10:36:23 2009  reduce to 197760 relations in 11 passes
Mon Feb 23 10:36:23 2009  attempting to read 197760 relations
Mon Feb 23 10:36:26 2009  recovered 197760 relations
Mon Feb 23 10:36:26 2009  recovered 180870 polynomials
Mon Feb 23 10:36:27 2009  attempting to build 76733 cycles
Mon Feb 23 10:36:27 2009  found 76733 cycles in 6 passes
Mon Feb 23 10:36:27 2009  distribution of cycle lengths:
Mon Feb 23 10:36:27 2009     length 1 : 19105
Mon Feb 23 10:36:27 2009     length 2 : 13731
Mon Feb 23 10:36:27 2009     length 3 : 13102
Mon Feb 23 10:36:27 2009     length 4 : 10332
Mon Feb 23 10:36:27 2009     length 5 : 7683
Mon Feb 23 10:36:27 2009     length 6 : 5124
Mon Feb 23 10:36:27 2009     length 7 : 3231
Mon Feb 23 10:36:27 2009     length 9+: 4425
Mon Feb 23 10:36:27 2009  largest cycle: 17 relations
Mon Feb 23 10:36:27 2009  matrix is 76413 x 76733 (20.9 MB) with weight 5160119 (67.25/col)
Mon Feb 23 10:36:27 2009  sparse part has weight 5160119 (67.25/col)
Mon Feb 23 10:36:28 2009  filtering completed in 3 passes
Mon Feb 23 10:36:28 2009  matrix is 72426 x 72490 (19.8 MB) with weight 4900322 (67.60/col)
Mon Feb 23 10:36:28 2009  sparse part has weight 4900322 (67.60/col)
Mon Feb 23 10:36:28 2009  saving the first 48 matrix rows for later
Mon Feb 23 10:36:29 2009  matrix is 72378 x 72490 (13.7 MB) with weight 4007388 (55.28/col)
Mon Feb 23 10:36:29 2009  sparse part has weight 3153350 (43.50/col)
Mon Feb 23 10:36:29 2009  matrix includes 64 packed rows
Mon Feb 23 10:36:29 2009  using block size 28996 for processor cache size 1024 kB
Mon Feb 23 10:36:29 2009  commencing Lanczos iteration
Mon Feb 23 10:36:29 2009  memory use: 12.4 MB
Mon Feb 23 10:37:06 2009  lanczos halted after 1146 iterations (dim = 72376)
Mon Feb 23 10:37:06 2009  recovered 18 nontrivial dependencies
Mon Feb 23 10:37:07 2009  prp46 factor: 1689109804305687021321287700092427147181180249
Mon Feb 23 10:37:07 2009  prp49 factor: 2755883601781023358092221328064703478054177727799
Mon Feb 23 10:37:07 2009  elapsed time 03:13:53

Feb 23, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39, yafu-1.06 / Feb 23, 2009

(13·10¹⁷²-7)/3 = 4(3)₁₇₁1_<173> = 289733 · 341083 · 4227751937_<10> · 88169691859_<11> · C142

C142 = P37 · P105

P37 = 3446714640637299830656897972064937911_<37>

P105 = 341294988336445193728905705649852576939546047528827589956637878582237898276169125438517320288890233544833_<105>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1660133444
Step 1 took 26687ms
Step 2 took 17954ms
********** Factor found in step 2: 3446714640637299830656897972064937911
Found probable prime factor of 37 digits: 3446714640637299830656897972064937911
Probable prime cofactor  has 105 digits

(44·10¹²⁴-71)/9 = 4(8)₁₂₃1_<125> = 7² · 197 · 4679 · 31154132951377_<14> · C104

C104 = P32 · P73

P32 = 25396419038491858287986340454153_<32>

P73 = 1368064780176544709535508833324802532043828326786680880921691567406497923_<73>

SNFS difficulty: 126 digits.
Divisors found:
 r1=25396419038491858287986340454153
 r2=1368064780176544709535508833324802532043828326786680880921691567406497923
Version:
Total time: 1.24 hours.
Scaled time: 3.32 units (timescale=2.677).
Factorization parameters were as follows:
n: 34743946429165779062937821146668289023142555909174816609220785749295779247311346548900553474735071224219
m: 10000000000000000000000000
c5: 22
c0: -355
skew: 1.74
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 25
lpba: 25
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 48/48
Sieved rational special-q in [445000, 745001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 113205 x 113450
Total sieving time: 1.24 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,25,25,48,48,2.3,2.3,50000
total time: 1.24 hours.

(44·10¹⁷⁰-71)/9 = 4(8)₁₆₉1_<171> = 13 · 17 · 37 · 222919 · 5364775547_<10> · 4563975737099127801032473103_<28> · 58627240909157056665846947136373_<32> · C93

C93 = P42 · P51

P42 = 629413938427228336143257358605484317506289_<42>

P51 = 296850911885490573747756395058094668056965871611231_<51>

starting SIQS on c93: 186842101575560748251901609180483102105679639113695638170972246212189545448427085736405531759

==== sieve params ====
n = 93 digits, 308 bits
factor base: 74997 primes (max prime = 2013299)
single large prime cutoff: 241595880 (120 * pmax)
double large prime range from 43 to 51 bits
double large prime cutoff: 1229026205170180
using 11 large prime slices of factor base
buckets hold 1024 elements
sieve interval: 22 blocks of size 32768
polynomial A has ~ 12 factors
using multiplier of 2
using small prime variation correction of 20 bits
trial factoring cutoff at 98 bits

==== sieving in progress:   75061 relations needed ====
====      Press ctrl-c to abort and save state     ====
75075 rels found: 19639 full + 55436 from 963672 partial, (1.28 rels/poly, 202.06 rels/sec)
sieve time = 1605.0670, relation time = 962.0480, poly_time = 2294.4940
trial division touched 46335727 sieve locations out of 1106774327296
trial division early aborted 32681170 times
size of relation set in memory = 0 bytes
QS elapsed time = 4866.5470 seconds.

==== post processing stage (msieve-1.38) ====
begin with 983311 relations
reduce to 186463 relations in 11 passes
attempting to read 186463 relations
recovered 186463 relations
recovered 165561 polynomials
attempting to build 75075 cycles
found 75075 cycles in 5 passes
distribution of cycle lengths:
   length 1 : 19639
   length 2 : 14403
   length 3 : 13190
   length 4 : 9949
   length 5 : 7107
   length 6 : 4609
   length 7 : 2701
   length 9+: 3477
largest cycle: 19 relations
matrix is 74997 x 75075 (19.0 MB) with weight 4684698 (62.40/col)
sparse part has weight 4684698 (62.40/col)
filtering completed in 3 passes
matrix is 70882 x 70946 (18.1 MB) with weight 4473451 (63.05/col)
sparse part has weight 4473451 (63.05/col)
saving the first 48 matrix rows for later
matrix is 70834 x 70946 (12.3 MB) with weight 3649716 (51.44/col)
sparse part has weight 2811715 (39.63/col)
matrix includes 64 packed rows
using block size 28378 for processor cache size 4096 kB
commencing Lanczos iteration
memory use: 11.5 MB
lanczos halted after 1122 iterations (dim = 70833)
recovered 17 nontrivial dependencies
Lanczos elapsed time = 26.5630 seconds.
Sqrt elapsed time = 1.5150 seconds.
Total elapsed time = 4894.6250 seconds.

***factors found***

PRP42 = 629413938427228336143257358605484317506289
PRP51 = 296850911885490573747756395058094668056965871611231

Feb 23, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Feb 23, 2009

(37·10¹⁷⁵+17)/9 = 4(1)₁₇₄3_<176> = 23 · 2539 · C171

C171 = P74 · P98

P74 = 23586711719453871087522664522636742344493353264814241528919205959807570277_<74>

P98 = 29847040760283621496854245399203499887235219181116358275700688536486472950381821332414081846863577_<98>

Number: 41113_175
N=703993546091599073772815574620461857819941283132885441223198299760451925802885612464871673392659059730998357982620872837836038000430006868693787542358530594227633459100829
  ( 171 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=23586711719453871087522664522636742344493353264814241528919205959807570277 (pp74)
 r2=29847040760283621496854245399203499887235219181116358275700688536486472950381821332414081846863577 (pp98)
Version: Msieve-1.39
Total time: 77.02 hours.
Scaled time: 133.94 units (timescale=1.739).
Factorization parameters were as follows:
n: 703993546091599073772815574620461857819941283132885441223198299760451925802885612464871673392659059730998357982620872837836038000430006868693787542358530594227633459100829
m: 100000000000000000000000000000000000
deg: 5
c5: 37
c0: 17
skew: 0.86
type: snfs
lss: 1
rlim: 6100000
alim: 6100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6100000/6100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3050000, 6950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1306867 x 1307115
Total sieving time: 77.02 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6100000,6100000,28,28,53,53,2.5,2.5,100000
total time: 77.02 hours.
 --------- CPU info (if available) ----------

Feb 23, 2009 (3rd)

By Erik Branger / GGNFS, Msieve

(44·10¹¹⁸-71)/9 = 4(8)₁₁₇1_<119> = 7 · C118

C118 = P54 · P65

P54 = 416440717606357993741576196275666721789252219034067903_<54>

P65 = 16770999301583074158031570541847272998272867034768728791605138361_<65>

Number: 48881_118
N=6984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126983
  ( 118 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=416440717606357993741576196275666721789252219034067903
 r2=16770999301583074158031570541847272998272867034768728791605138361
Version: 
Total time: 1.68 hours.
Scaled time: 1.66 units (timescale=0.989).
Factorization parameters were as follows:
n: 6984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126984126983
m: 200000000000000000000000
deg: 5
c5: 1375
c0: -71
skew: 0.55
type: snfs
lss: 1
rlim: 700000
alim: 700000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [350000, 600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 87398 x 87646
Total sieving time: 1.68 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,700000,700000,25,25,45,45,2.2,2.2,50000
total time: 1.68 hours.
 --------- CPU info (if available) ----------

(44·10¹²⁵-71)/9 = 4(8)₁₂₄1_<126> = 29 · 37 · 73 · 1481 · C118

C118 = P41 · P78

P41 = 12477073105331465445789572500714681458613_<41>

P78 = 337769014512650326216567018186916042346285216264847869760875598543396841692813_<78>

Number: 48881_125
N=4214368686790102824475544972011472419570332450119467343144868288579673570537216715847822445421317865443217046919048369
  ( 118 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=12477073105331465445789572500714681458613
 r2=337769014512650326216567018186916042346285216264847869760875598543396841692813
Version: 
Total time: 2.17 hours.
Scaled time: 2.09 units (timescale=0.965).
Factorization parameters were as follows:
n: 4214368686790102824475544972011472419570332450119467343144868288579673570537216715847822445421317865443217046919048369
m: 10000000000000000000000000
deg: 5
c5: 44
c0: -71
skew: 1.10
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 135095 x 135343
Total sieving time: 2.17 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 2.17 hours.
 --------- CPU info (if available) ----------

Feb 23, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Feb 22, 2009

(44·10¹⁰⁹-71)/9 = 4(8)₁₀₈1_<110> = 73 · C108

C108 = P41 · P68

P41 = 35566845797976201162695764745383432956709_<41>

P68 = 18829637311701547205216682636999200838650523549983041259903340871733_<68>

Number: 48881_109
N=669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697
  ( 108 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=35566845797976201162695764745383432956709
 r2=18829637311701547205216682636999200838650523549983041259903340871733
Version: 
Total time: 0.38 hours.
Scaled time: 0.91 units (timescale=2.379).
Factorization parameters were as follows:
n: 669710806697108066971080669710806697108066971080669710806697108066971080669710806697108066971080669710806697
m: 10000000000000000000000
deg: 5
c5: 22
c0: -355
skew: 1.74
type: snfs
lss: 1
rlim: 320000
alim: 320000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 320000/320000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [160000, 300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 961229
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 43983 x 44216
Total sieving time: 0.34 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,320000,320000,25,25,44,44,2.2,2.2,20000
total time: 0.38 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(44·10¹¹¹-71)/9 = 4(8)₁₁₀1_<112> = 3 · 41 · 619 · 1993 · 891763 · C98

C98 = P43 · P56

P43 = 1351980281510634921679265723748664648148189_<43>

P56 = 26723128574901564786591298311795686272646239432459060663_<56>

Number: 48881_111
N=36129142893540309774385216913572919724754103318722012008593516148461445958436410349932217364589307
  ( 98 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=1351980281510634921679265723748664648148189
 r2=26723128574901564786591298311795686272646239432459060663
Version: 
Total time: 0.41 hours.
Scaled time: 0.98 units (timescale=2.372).
Factorization parameters were as follows:
n: 36129142893540309774385216913572919724754103318722012008593516148461445958436410349932217364589307
m: 20000000000000000000000
deg: 5
c5: 55
c0: -284
skew: 1.39
type: snfs
lss: 1
rlim: 360000
alim: 360000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [180000, 330001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 982594
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 49757 x 49991
Total sieving time: 0.37 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,360000,360000,25,25,45,45,2.2,2.2,25000
total time: 0.41 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(44·10¹⁴²-71)/9 = 4(8)₁₄₁1_<143> = 7 · 601 · 1586766675259_<13> · 603149822923393391_<18> · 10114884012409807074443_<23> · C88

C88 = P32 · P56

P32 = 38857779451858321390658667718439_<32>

P56 = 30893029087204983813564181049616963052872694625767854991_<56>

Sun Feb 22 22:54:09 2009  
Sun Feb 22 22:54:09 2009  
Sun Feb 22 22:54:09 2009  Msieve v. 1.39
Sun Feb 22 22:54:09 2009  random seeds: 012cf744 94063b51
Sun Feb 22 22:54:09 2009  factoring 1200434510870455254743290303365774516525651954915925350818770002948070047475388968879049 (88 digits)
Sun Feb 22 22:54:10 2009  searching for 15-digit factors
Sun Feb 22 22:54:11 2009  commencing quadratic sieve (88-digit input)
Sun Feb 22 22:54:11 2009  using multiplier of 5
Sun Feb 22 22:54:11 2009  using VC8 32kb sieve core
Sun Feb 22 22:54:11 2009  sieve interval: 24 blocks of size 32768
Sun Feb 22 22:54:11 2009  processing polynomials in batches of 9
Sun Feb 22 22:54:11 2009  using a sieve bound of 1500533 (57333 primes)
Sun Feb 22 22:54:11 2009  using large prime bound of 120042640 (26 bits)
Sun Feb 22 22:54:11 2009  using double large prime bound of 348982681131840 (42-49 bits)
Sun Feb 22 22:54:11 2009  using trial factoring cutoff of 49 bits
Sun Feb 22 22:54:11 2009  polynomial 'A' values have 11 factors
Sun Feb 22 23:43:15 2009  57727 relations (15785 full + 41942 combined from 604889 partial), need 57429
Sun Feb 22 23:43:15 2009  begin with 620674 relations
Sun Feb 22 23:43:15 2009  reduce to 139072 relations in 9 passes
Sun Feb 22 23:43:15 2009  attempting to read 139072 relations
Sun Feb 22 23:43:17 2009  recovered 139072 relations
Sun Feb 22 23:43:17 2009  recovered 116567 polynomials
Sun Feb 22 23:43:17 2009  attempting to build 57727 cycles
Sun Feb 22 23:43:17 2009  found 57727 cycles in 5 passes
Sun Feb 22 23:43:17 2009  distribution of cycle lengths:
Sun Feb 22 23:43:17 2009     length 1 : 15785
Sun Feb 22 23:43:17 2009     length 2 : 11179
Sun Feb 22 23:43:17 2009     length 3 : 10318
Sun Feb 22 23:43:17 2009     length 4 : 7571
Sun Feb 22 23:43:17 2009     length 5 : 5283
Sun Feb 22 23:43:17 2009     length 6 : 3301
Sun Feb 22 23:43:17 2009     length 7 : 1998
Sun Feb 22 23:43:17 2009     length 9+: 2292
Sun Feb 22 23:43:17 2009  largest cycle: 19 relations
Sun Feb 22 23:43:17 2009  matrix is 57333 x 57727 (14.5 MB) with weight 3340533 (57.87/col)
Sun Feb 22 23:43:17 2009  sparse part has weight 3340533 (57.87/col)
Sun Feb 22 23:43:18 2009  filtering completed in 3 passes
Sun Feb 22 23:43:18 2009  matrix is 52958 x 53021 (13.4 MB) with weight 3087569 (58.23/col)
Sun Feb 22 23:43:18 2009  sparse part has weight 3087569 (58.23/col)
Sun Feb 22 23:43:18 2009  saving the first 48 matrix rows for later
Sun Feb 22 23:43:18 2009  matrix is 52910 x 53021 (9.2 MB) with weight 2470788 (46.60/col)
Sun Feb 22 23:43:18 2009  sparse part has weight 1876061 (35.38/col)
Sun Feb 22 23:43:18 2009  matrix includes 64 packed rows
Sun Feb 22 23:43:18 2009  using block size 21208 for processor cache size 4096 kB
Sun Feb 22 23:43:18 2009  commencing Lanczos iteration
Sun Feb 22 23:43:18 2009  memory use: 8.0 MB
Sun Feb 22 23:43:37 2009  lanczos halted after 838 iterations (dim = 52908)
Sun Feb 22 23:43:37 2009  recovered 17 nontrivial dependencies
Sun Feb 22 23:43:37 2009  prp32 factor: 38857779451858321390658667718439
Sun Feb 22 23:43:37 2009  prp56 factor: 30893029087204983813564181049616963052872694625767854991
Sun Feb 22 23:43:37 2009  elapsed time 00:49:28

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Feb 23, 2009

(44·10¹³²-71)/9 = 4(8)₁₃₁1_<133> = 3⁵ · 4339 · 15978271 · 93502943 · 105465168068487408287_<21> · C92

C92 = P45 · P48

P45 = 260189102411844591320932191190753612446510353_<45>

P48 = 113099589360575310311511645016805083348433825191_<48>

Sun Feb 22 23:46:51 2009  
Sun Feb 22 23:46:51 2009  
Sun Feb 22 23:46:51 2009  Msieve v. 1.39
Sun Feb 22 23:46:51 2009  random seeds: d93107a4 3bab7459
Sun Feb 22 23:46:51 2009  factoring 29427280638876298352094944415671764174672400927972612484598350746797758877263449175173702423 (92 digits)
Sun Feb 22 23:46:52 2009  searching for 15-digit factors
Sun Feb 22 23:46:52 2009  commencing quadratic sieve (92-digit input)
Sun Feb 22 23:46:53 2009  using multiplier of 2
Sun Feb 22 23:46:53 2009  using VC8 32kb sieve core
Sun Feb 22 23:46:53 2009  sieve interval: 36 blocks of size 32768
Sun Feb 22 23:46:53 2009  processing polynomials in batches of 6
Sun Feb 22 23:46:53 2009  using a sieve bound of 1776617 (67059 primes)
Sun Feb 22 23:46:53 2009  using large prime bound of 186544785 (27 bits)
Sun Feb 22 23:46:53 2009  using double large prime bound of 771630750831045 (42-50 bits)
Sun Feb 22 23:46:53 2009  using trial factoring cutoff of 50 bits
Sun Feb 22 23:46:53 2009  polynomial 'A' values have 12 factors
Mon Feb 23 01:30:43 2009  67582 relations (17465 full + 50117 combined from 829202 partial), need 67155
Mon Feb 23 01:30:44 2009  begin with 846667 relations
Mon Feb 23 01:30:44 2009  reduce to 169150 relations in 10 passes
Mon Feb 23 01:30:44 2009  attempting to read 169150 relations
Mon Feb 23 01:30:46 2009  recovered 169150 relations
Mon Feb 23 01:30:46 2009  recovered 148216 polynomials
Mon Feb 23 01:30:47 2009  attempting to build 67582 cycles
Mon Feb 23 01:30:47 2009  found 67582 cycles in 5 passes
Mon Feb 23 01:30:47 2009  distribution of cycle lengths:
Mon Feb 23 01:30:47 2009     length 1 : 17465
Mon Feb 23 01:30:47 2009     length 2 : 12674
Mon Feb 23 01:30:47 2009     length 3 : 11758
Mon Feb 23 01:30:47 2009     length 4 : 9043
Mon Feb 23 01:30:47 2009     length 5 : 6478
Mon Feb 23 01:30:47 2009     length 6 : 4270
Mon Feb 23 01:30:47 2009     length 7 : 2643
Mon Feb 23 01:30:47 2009     length 9+: 3251
Mon Feb 23 01:30:47 2009  largest cycle: 19 relations
Mon Feb 23 01:30:47 2009  matrix is 67059 x 67582 (17.7 MB) with weight 4108292 (60.79/col)
Mon Feb 23 01:30:47 2009  sparse part has weight 4108292 (60.79/col)
Mon Feb 23 01:30:48 2009  filtering completed in 3 passes
Mon Feb 23 01:30:48 2009  matrix is 63161 x 63225 (16.6 MB) with weight 3844548 (60.81/col)
Mon Feb 23 01:30:48 2009  sparse part has weight 3844548 (60.81/col)
Mon Feb 23 01:30:48 2009  saving the first 48 matrix rows for later
Mon Feb 23 01:30:48 2009  matrix is 63113 x 63225 (10.4 MB) with weight 2947191 (46.61/col)
Mon Feb 23 01:30:48 2009  sparse part has weight 2083604 (32.96/col)
Mon Feb 23 01:30:48 2009  matrix includes 64 packed rows
Mon Feb 23 01:30:48 2009  using block size 25290 for processor cache size 4096 kB
Mon Feb 23 01:30:48 2009  commencing Lanczos iteration
Mon Feb 23 01:30:48 2009  memory use: 9.4 MB
Mon Feb 23 01:31:14 2009  lanczos halted after 999 iterations (dim = 63111)
Mon Feb 23 01:31:14 2009  recovered 17 nontrivial dependencies
Mon Feb 23 01:31:14 2009  prp45 factor: 260189102411844591320932191190753612446510353
Mon Feb 23 01:31:14 2009  prp48 factor: 113099589360575310311511645016805083348433825191
Mon Feb 23 01:31:14 2009  elapsed time 01:44:23

(44·10¹⁵⁵-71)/9 = 4(8)₁₅₄1_<156> = 37 · 97 · 498889679 · 18697682263419627917303_<23> · C122

C122 = P33 · C89

P33 = 440832314293904601752619068922493_<33>

C89 = [33126152121935620473093722297086995034869661998940995868094417359149617683041111125853769_<89>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 14603078303564818279173845988926349653740533214373454335871022413890641803324821089370234331992907488797307054889512926117 (122 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3845036566
Step 1 took 3945ms
Step 2 took 2293ms
********** Factor found in step 2: 440832314293904601752619068922493
Found probable prime factor of 33 digits: 440832314293904601752619068922493
Composite cofactor 33126152121935620473093722297086995034869661998940995868094417359149617683041111125853769 has 89 digits

(44·10¹⁵³-71)/9 = 4(8)₁₅₂1_<154> = 3 · 29 · 5686565066897115489601_<22> · C130

C130 = P30 · C101

P30 = 480561239432935951772923342469_<30>

C101 = [20563269273189518839408618741350859979878540178289245336713437567214603823608381501320185903034897227_<101>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 9881910168717163209631261810317703627882659164497899775880673087419777791936683716199703007690664433555697694512695772842739433463 (130 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1617530254
Step 1 took 3914ms
Step 2 took 2376ms
********** Factor found in step 2: 480561239432935951772923342469
Found probable prime factor of 30 digits: 480561239432935951772923342469
Composite cofactor 20563269273189518839408618741350859979878540178289245336713437567214603823608381501320185903034897227 has 101 digits

(44·10¹⁶⁵-71)/9 = 4(8)₁₆₄1_<166> = 3 · 23² · 73 · 110567 · 93218987047_<11> · C145

C145 = P28 · P117

P28 = 4682812091093777041353233063_<28>

P117 = 874326705316405572786123234035850728935404455548662025784508076079796335019128265791706308917733245997267724658335013_<117>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 4094307667221849768503331020912509608304619865549751287988453380418056262380073505171906009921330949575502129726494033608850944517940838122134819 (145 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2266374876
Step 1 took 4701ms
Step 2 took 2623ms
********** Factor found in step 2: 4682812091093777041353233063
Found probable prime factor of 28 digits: 4682812091093777041353233063
Probable prime cofactor 874326705316405572786123234035850728935404455548662025784508076079796335019128265791706308917733245997267724658335013 has 117 digits

(14·10¹⁶³+1)/3 = 4(6)₁₆₂7_<164> = 541 · 56552399 · 1300505580877_<13> · 6763759569124322149817_<22> · C120

C120 = P41 · P79

P41 = 87626829942236546445549104979905166220049_<41>

P79 = 1978887024576844368225830411346447797924000567626738265413690868084042418013093_<79>

Number: 46667_163
N=173403596777493614657332166591274041874084815925516146203645866528900650934565328260520164469099995823858736379801101557
  ( 120 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=87626829942236546445549104979905166220049
 r2=1978887024576844368225830411346447797924000567626738265413690868084042418013093
Version: 
Total time: 22.87 hours.
Scaled time: 54.51 units (timescale=2.383).
Factorization parameters were as follows:
n: 173403596777493614657332166591274041874084815925516146203645866528900650934565328260520164469099995823858736379801101557
m: 1000000000000000000000000000000000
deg: 5
c5: 7
c0: 50
skew: 1.48
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 3900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9787512
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 725648 x 725896
Total sieving time: 20.43 hours.
Total relation processing time: 0.91 hours.
Matrix solve time: 1.15 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 22.87 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 23, 2009

By Robert Backstrom / GGNFS, Msieve / Feb 22, 2009

(14·10¹⁵⁹-11)/3 = 4(6)₁₅₈3_<160> = 5766037489_<10> · C150

C150 = P54 · P97

P54 = 260455141077573786525035422943583702088538753349314693_<54>

P97 = 3107394444335760734125359606663890296019575646343939677484645823076134984300128089687641614775019_<97>

Number: n
N=809336858383139566622867419699960030326931970224425064723450442114644854447748573538049479488333355625649950862930760710263336733339554370467026054167
  ( 150 digits)
SNFS difficulty: 160 digits.
Divisors found:

Mon Feb 23 00:56:38 2009  prp54 factor: 260455141077573786525035422943583702088538753349314693
Mon Feb 23 00:56:38 2009  prp97 factor: 3107394444335760734125359606663890296019575646343939677484645823076134984300128089687641614775019
Mon Feb 23 00:56:38 2009  elapsed time 02:44:21 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 21.59 hours.
Scaled time: 39.48 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_6_158_3
n: 809336858383139566622867419699960030326931970224425064723450442114644854447748573538049479488333355625649950862930760710263336733339554370467026054167
deg: 5
c5: 7
c0: -55
m: 100000000000000000000000000000000
skew: 1.51
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [2000000, 3200117)
Primes: RFBsize:283146, AFBsize:282788, largePrimes:16763038 encountered
Relations: rels:15061344, finalFF:470776
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1073168 hash collisions in 16406181 relations
Msieve: matrix is 798613 x 798861 (216.7 MB)

Total sieving time: 21.25 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,56,56,2.5,2.5,100000
total time: 21.59 hours.
 --------- CPU info (if available) ----------

Feb 22, 2009 (6th)

By Wataru Sakai / Msieve / Feb 22, 2009

(14·10²⁰⁵-11)/3 = 4(6)₂₀₄3_<206> = C206

C206 = P103 · P104

P103 = 2121306592776648777932591399219834774802781918867930539380539448487074254168075843706510005973451437893_<103>

P104 = 21999020238551709776934090605708851713877528642400823630041963062954447513472170746146025058346596528891_<104>

Number: 46663_205
N=46666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
  ( 206 digits)
SNFS difficulty: 206 digits.
Divisors found:
 r1=2121306592776648777932591399219834774802781918867930539380539448487074254168075843706510005973451437893
 r2=21999020238551709776934090605708851713877528642400823630041963062954447513472170746146025058346596528891
Version: 
Total time: 1093.48 hours.
Scaled time: 1932.19 units (timescale=1.767).
Factorization parameters were as follows:
n: 46666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663
m: 100000000000000000000000000000000000000000
deg: 5
c5: 14
c0: -11
skew: 0.95
type: snfs
lss: 1
rlim: 19100000
alim: 19100000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 19100000/19100000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [9550000, 20850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3269052 x 3269300
Total sieving time: 1093.48 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,19100000,19100000,29,29,56,56,2.6,2.6,100000
total time: 1093.48 hours.
 --------- CPU info (if available) ----------

P103 is the largest prime factor which was found in our tables so far. Congratulations!

5·10¹⁹³-9 = 4(9)₁₉₂1_<194> = 2111 · C191

C191 = P53 · P138

P53 = 46280192363403452945907094423911587820648171502970737_<53>

P138 = 511783895437135635957154567370339647742796615436941073014585973056439262887348563848497984154002794113583812498276542761057932913246823513_<138>

Number: 49991_193
N=23685457129322595926101373756513500710563713879677877783041212695405021316911416390336333491236380862150639507342491710090004737091425864519185220274751302700142112742775935575556608242539081
  ( 191 digits)
SNFS difficulty: 194 digits.
Divisors found:
 r1=46280192363403452945907094423911587820648171502970737
 r2=511783895437135635957154567370339647742796615436941073014585973056439262887348563848497984154002794113583812498276542761057932913246823513
Version: 
Total time: 514.11 hours.
Scaled time: 1035.93 units (timescale=2.015).
Factorization parameters were as follows:
n: 23685457129322595926101373756513500710563713879677877783041212695405021316911416390336333491236380862150639507342491710090004737091425864519185220274751302700142112742775935575556608242539081
m: 500000000000000000000000000000000000000
deg: 5
c5: 8
c0: -45
skew: 1.41
type: snfs
lss: 1
rlim: 12200000
alim: 12200000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 12200000/12200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6100000, 11100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1742550 x 1742798
Total sieving time: 514.11 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,194,5,0,0,0,0,0,0,0,0,12200000,12200000,28,28,55,55,2.5,2.5,100000
total time: 514.11 hours.
 --------- CPU info (if available) ----------

Feb 22, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.1, yafu-1.06 / Feb 22, 2009

(43·10¹⁹⁷+11)/9 = 4(7)₁₉₆9_<198> = 47 · 1321 · 1361 · 132338431180593418567771_<24> · C167

C167 = P42 · P126

P42 = 331708104640154262349394010682175102067601_<42>

P126 = 128802733727568111758695581281046348446516164327418168890927756109284401384948163029643002128681541870249908675847736129947407_<126>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=651099684
Step 1 took 36625ms
Step 2 took 18719ms
********** Factor found in step 2: 331708104640154262349394010682175102067601
Found probable prime factor of 42 digits: 331708104640154262349394010682175102067601
Probable prime cofactor has 126 digits

(2·10¹⁷¹+61)/9 = (2)₁₇₀9_<171> = 461 · 151570609 · 216132972529_<12> · 2335216729459_<13> · C136

C136 = P42 · P45 · P51

P42 = 107307406764746593081378156040526559657763_<42>

P45 = 346004849803017639555116780811604078215096527_<45>

P51 = 169711573352147205928889097569640982156924008532511_<51>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1058474660
Step 1 took 26829ms
Step 2 took 17359ms
********** Factor found in step 2: 346004849803017639555116780811604078215096527
Found probable prime factor of 45 digits: 346004849803017639555116780811604078215096527
Composite cofactor has 92 digits

starting SIQS on c92: 

==== sieve params ====
n = 92 digits, 304 bits
factor base: 71746 primes (max prime = 1927319)
single large prime cutoff: 231278280 (120 * pmax)
double large prime range from 43 to 51 bits
double large prime cutoff: 1136168456955099
using 10 large prime slices of factor base
buckets hold 1024 elements
sieve interval: 22 blocks of size 32768
polynomial A has ~ 12 factors
using multiplier of 1
using small prime variation correction of 19 bits
trial factoring cutoff at 98 bits

==== sieving in progress:   71810 relations needed ====
====      Press ctrl-c to abort and save state     ====
71837 rels found: 19040 full + 52797 from 918502 partial, (1.45 rels/poly, 23
sieve time = 1329.8350, relation time = 831.9500, poly_time = 1843.4930
trial division touched 36530963 sieve locations out of 930211037184
trial division early aborted 24830250 times
size of relation set in memory = 0 bytes
QS elapsed time = 4009.3910 seconds.

==== post processing stage (msieve-1.38) ====
begin with 937542 relations
reduce to 177059 relations in 10 passes
attempting to read 177059 relations
recovered 177059 relations
recovered 154919 polynomials
attempting to build 71837 cycles
found 71837 cycles in 5 passes
distribution of cycle lengths:
   length 1 : 19040
   length 2 : 13960
   length 3 : 12639
   length 4 : 9626
   length 5 : 6569
   length 6 : 4326
   length 7 : 2534
   length 9+: 3143
largest cycle: 19 relations
matrix is 71746 x 71837 (17.5 MB) with weight 4299912 (59.86/col)
sparse part has weight 4299912 (59.86/col)
filtering completed in 4 passes
matrix is 67493 x 67557 (16.6 MB) with weight 4084336 (60.46/col)
sparse part has weight 4084336 (60.46/col)
saving the first 48 matrix rows for later
matrix is 67445 x 67557 (10.9 MB) with weight 3243734 (48.01/col)
sparse part has weight 2463447 (36.46/col)
matrix includes 64 packed rows
using block size 27022 for processor cache size 4096 kB
commencing Lanczos iteration
memory use: 10.6 MB
lanczos halted after 1069 iterations (dim = 67443)
recovered 15 nontrivial dependencies
Lanczos elapsed time = 21.5630 seconds.
Sqrt elapsed time = 2.8590 seconds.
Total elapsed time = 4033.8130 seconds.

***factors found***

PRP51 = 169711573352147205928889097569640982156924008532511
PRP42 = 107307406764746593081378156040526559657763

Feb 22, 2009 (4th)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Feb 22, 2009

(43·10¹⁶⁰+11)/9 = 4(7)₁₅₉9_<161> = 24460091 · 11342534099773_<14> · C141

C141 = P33 · P108

P33 = 554530125227161494702649780672981_<33>

P108 = 310550790918183757138040292450770137837000349722124572567731528164572899124874670393566999702736101247089513_<108>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 172209768977254485464791824792255114721860563702277174648505747761995164855752309554901813150171274613701938489623941891084638103124687548253 (141 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2608419802
Step 1 took 4656ms
Step 2 took 2602ms
********** Factor found in step 2: 554530125227161494702649780672981
Found probable prime factor of 33 digits: 554530125227161494702649780672981
Probable prime cofactor 310550790918183757138040292450770137837000349722124572567731528164572899124874670393566999702736101247089513 has 108 digits

(43·10¹⁵⁷+11)/9 = 4(7)₁₅₆9_<158> = 7 · 19 · 71 · 634793981 · C145

C145 = P60 · P86

P60 = 569398400463786844822991231371199194147265537056016392601101_<60>

P86 = 13998029790680444609644935809592066783975004954562700212966249573206820485535946233113_<86>

Number: 47779_157
N=7970455772457882142378370810311293034070800362661745376018533241192809998167135231459500149657003373220030542303745103840118021642124004966457413
  ( 145 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=569398400463786844822991231371199194147265537056016392601101
 r2=13998029790680444609644935809592066783975004954562700212966249573206820485535946233113
Version: 
Total time: 15.16 hours.
Scaled time: 35.95 units (timescale=2.371).
Factorization parameters were as follows:
n: 7970455772457882142378370810311293034070800362661745376018533241192809998167135231459500149657003373220030542303745103840118021642124004966457413
m: 10000000000000000000000000000000
deg: 5
c5: 4300
c0: 11
skew: 0.3
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1700000, 3000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8611651
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 542033 x 542281
Total sieving time: 13.77 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 0.67 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,50,50,2.4,2.4,100000
total time: 15.16 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 22, 2009 (3rd)

By Erik Branger / GGNFS, Msieve / Feb 22, 2009

(43·10¹⁶⁰-61)/9 = 4(7)₁₅₉1_<161> = 945435727446149_<15> · 153348803163867721_<18> · C129

C129 = P57 · P72

P57 = 507677995989841246989194634726525592636366766426170255699_<57>

P72 = 649120320669006679097042822232948846496567890641704033432611051708405901_<72>

Number: 47771_160
N=329544103553524437142630573737847138140672187662421531344207977931454906200837907178392131176682093632910926826470819616850479799
  ( 129 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=507677995989841246989194634726525592636366766426170255699
 r2=649120320669006679097042822232948846496567890641704033432611051708405901
Version: 
Total time: 56.69 hours.
Scaled time: 44.05 units (timescale=0.777).
Factorization parameters were as follows:
n: 329544103553524437142630573737847138140672187662421531344207977931454906200837907178392131176682093632910926826470819616850479799
m: 100000000000000000000000000000000
deg: 5
c5: 43
c0: -61
skew: 1.07
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 633074 x 633322
Total sieving time: 56.69 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 56.69 hours.
 --------- CPU info (if available) ----------

(43·10¹⁵³+11)/9 = 4(7)₁₅₂9_<154> = 3 · 13956860129130757_<17> · C138

C138 = P55 · P83

P55 = 2390398834710402655240393538570122004850597163918549889_<55>

P83 = 47736062871370708505479132371741318962492341955898192429827608909943783990709854941_<83>

Number: 47779_153
N=114108229061387059407795316515320184476644107180547072391599074615035448306680841601658779924230943441450886744859116513862646670261651549
  ( 138 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=2390398834710402655240393538570122004850597163918549889
 r2=47736062871370708505479132371741318962492341955898192429827608909943783990709854941
Version: 
Total time: 26.00 hours.
Scaled time: 27.27 units (timescale=1.049).
Factorization parameters were as follows:
n: 114108229061387059407795316515320184476644107180547072391599074615035448306680841601658779924230943441450886744859116513862646670261651549
m: 5000000000000000000000000000000
deg: 5
c5: 344
c0: 275
skew: 0.96
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 485116 x 485364
Total sieving time: 26.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 26.00 hours.
 --------- CPU info (if available) ----------

Feb 22, 2009 (2nd)

Factorizations of 488...881 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Feb 22, 2009

By Serge Batalov / PFGW / Feb 22, 2009

(65·10¹²¹⁷⁵-11)/9 = 7(2)₁₂₁₇₄1_<12176> is PRP.

Feb 21, 2009 (8th)

By Ignacio Santos / GGNFS, Msieve / Feb 21, 2009

(11·10¹⁸⁸+43)/9 = 1(2)₁₈₇7_<189> = 1321 · C185

C185 = P44 · P69 · P73

P44 = 32500590808365891660494126460420756674718181_<44>

P69 = 543030414799904978254708147320654776932247308215000344723661626079893_<69>

P73 = 5242421637376962007933603554526722658769614576691122109338592923947287939_<73>

Number: 12227_188
N=92522499789721591386996383211371856337791235595929010009252249978972159138699638321137185633779123559592901000925224997897215913869963832113718563377912355959290100092522499789721591387
  ( 185 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=32500590808365891660494126460420756674718181 (pp44)
 r2=543030414799904978254708147320654776932247308215000344723661626079893 (pp69)
 r3=5242421637376962007933603554526722658769614576691122109338592923947287939 (pp73)
Version: Msieve-1.39
Total time: 320.82 hours.
Scaled time: 557.90 units (timescale=1.739).
Factorization parameters were as follows:
n: 92522499789721591386996383211371856337791235595929010009252249978972159138699638321137185633779123559592901000925224997897215913869963832113718563377912355959290100092522499789721591387
m: 50000000000000000000000000000000000000
deg: 5
c5: 88
c0: 1075
skew: 1.65
type: snfs
lss: 1
rlim: 10400000
alim: 10400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 10400000/10400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5200000, 10500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1944125 x 1944373
Total sieving time: 320.82 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,10400000,10400000,28,28,54,54,2.5,2.5,100000
total time: 320.82 hours.
 --------- CPU info (if available) ----------

Feb 21, 2009 (7th)

By Sinkiti Sibata / GGNFS / Feb 21, 2009

(43·10¹³¹+11)/9 = 4(7)₁₃₀9_<132> = 55001 · 3884083551878620423_<19> · C109

C109 = P41 · P69

P41 = 11966861624006845044170697133053452418829_<41>

P69 = 186890199515821385603655482586900451315521584217335048559569919540337_<69>

Number: 47779_131
N=2236489156488865591889647066020115676177330652039542505529233844200322483485327020696231388249200924483805373
  ( 109 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=11966861624006845044170697133053452418829 (pp41)
 r2=186890199515821385603655482586900451315521584217335048559569919540337 (pp69)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 6.36 hours.
Scaled time: 3.00 units (timescale=0.472).
Factorization parameters were as follows:
name: 47779_131
n: 2236489156488865591889647066020115676177330652039542505529233844200322483485327020696231388249200924483805373
m: 200000000000000000000000000
deg: 5
c5: 215
c0: 176
skew: 0.96
type: snfs
lss: 1
rlim: 1190000
alim: 1190000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1190000/1190000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [595000, 1120001)
Primes: RFBsize:92225, AFBsize:92618, largePrimes:3053285 encountered
Relations: rels:3041735, finalFF:295264
Max relations in full relation-set: 28
Initial matrix: 184910 x 295264 with sparse part having weight 24278213.
Pruned matrix : 153701 x 154689 with weight 9384043.
Total sieving time: 5.84 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.34 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1190000,1190000,26,26,47,47,2.3,2.3,75000
total time: 6.36 hours.
 --------- CPU info (if available) ----------

Feb 21, 2009 (6th)

By Serge Batalov / Msieve / Feb 21, 2009

(43·10¹⁰⁹+11)/9 = 4(7)₁₀₈9_<110> = 7 · 9326851 · 147552919 · C94

C94 = P34 · P60

P34 = 5186641571572763891836425583825171_<34>

P60 = 956222206640134678845241597923401166745068949951938745849003_<60>

Fri Feb 20 19:28:21 2009  Msieve v. 1.39
Fri Feb 20 19:28:21 2009  random seeds: 70e09421 4868b65f
Fri Feb 20 19:28:21 2009  factoring 4959581848620764314873082640202983684038637690697228712941474720772791534728505411094716654513 (94 digits)
Fri Feb 20 19:28:22 2009  searching for 15-digit factors
Fri Feb 20 19:28:23 2009  commencing number field sieve (94-digit input)
Fri Feb 20 19:28:23 2009  R0: -10000000000000000000000
Fri Feb 20 19:28:23 2009  R1:  1
Fri Feb 20 19:28:23 2009  A0:  110
Fri Feb 20 19:28:23 2009  A1:  0
Fri Feb 20 19:28:23 2009  A2:  0
Fri Feb 20 19:28:23 2009  A3:  0
Fri Feb 20 19:28:23 2009  A4:  0
Fri Feb 20 19:28:23 2009  A5:  43
Fri Feb 20 19:28:23 2009  size score = 6.059901e-08, Murphy alpha = 0.621738, combined = 4.925606e-08
Fri Feb 20 19:28:23 2009  
Fri Feb 20 19:28:23 2009  commencing square root phase
Fri Feb 20 19:28:23 2009  reading relations for dependency 1
Fri Feb 20 19:28:23 2009  read 25324 cycles
Fri Feb 20 19:28:23 2009  cycles contain 90261 unique relations
Fri Feb 20 19:28:24 2009  read 90261 relations
Fri Feb 20 19:28:24 2009  multiplying 69680 relations
Fri Feb 20 19:28:27 2009  multiply complete, coefficients have about 1.69 million bits
Fri Feb 20 19:28:27 2009  initial square root is modulo 62099671
Fri Feb 20 19:28:32 2009  Newton iteration failed to converge
Fri Feb 20 19:28:32 2009  algebraic square root failed
Fri Feb 20 19:28:32 2009  reading relations for dependency 2
Fri Feb 20 19:28:32 2009  read 25291 cycles
Fri Feb 20 19:28:32 2009  cycles contain 90029 unique relations
Fri Feb 20 19:28:33 2009  read 90029 relations
Fri Feb 20 19:28:33 2009  multiplying 69474 relations
Fri Feb 20 19:28:36 2009  multiply complete, coefficients have about 1.68 million bits
Fri Feb 20 19:28:36 2009  initial square root is modulo 58919291
Fri Feb 20 19:28:41 2009  prp34 factor: 5186641571572763891836425583825171
Fri Feb 20 19:28:41 2009  prp60 factor: 956222206640134678845241597923401166745068949951938745849003
Fri Feb 20 19:28:41 2009  elapsed time 00:00:20

Feb 21, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 21, 2009

(43·10¹⁴⁸+11)/9 = 4(7)₁₄₇9_<149> = 55434706652456510426180009_<26> · C123

C123 = P36 · P87

P36 = 880473705643800323008781414226040537_<36>

P87 = 978876272798095084184897796318874119497804652497593236125475126377821797059918500810163_<87>

Number: 47779_148
N=861874819277330356327609514781646580120356516383198868090420835498813576559283961722781870003966532142251375809846179577531
  ( 123 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=880473705643800323008781414226040537
 r2=978876272798095084184897796318874119497804652497593236125475126377821797059918500810163
Version: 
Total time: 9.29 hours.
Scaled time: 22.19 units (timescale=2.388).
Factorization parameters were as follows:
n: 861874819277330356327609514781646580120356516383198868090420835498813576559283961722781870003966532142251375809846179577531
m: 1000000000000000000000000000000
deg: 5
c5: 43
c0: 1100
skew: 1.91
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7230844
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 368529 x 368777
Total sieving time: 8.56 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000
total time: 9.29 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 21, 2009 (4th)

By Sinkiti Sibata / GGNFS / Feb 21, 2009

(43·10¹²⁷+11)/9 = 4(7)₁₂₆9_<128> = 7² · 17 · 3823 · 36191 · 222552349 · C109

C109 = P32 · P77

P32 = 44081140412735548636973386146047_<32>

P77 = 42256260316589121143556886855498657765076762677937532780858710902359236274497_<77>

Number: 47779_127
N=1862704144332670156720268853192338984265184891905277609373267801082571490102306484312947988653238917023463359
  ( 109 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=44081140412735548636973386146047 (pp32)
 r2=42256260316589121143556886855498657765076762677937532780858710902359236274497 (pp77)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 4.71 hours.
Scaled time: 2.22 units (timescale=0.472).
Factorization parameters were as follows:
name: 47779_127
n: 1862704144332670156720268853192338984265184891905277609373267801082571490102306484312947988653238917023463359
m: 20000000000000000000000000
deg: 5
c5: 1075
c0: 88
skew: 0.61
type: snfs
lss: 1
rlim: 1010000
alim: 1010000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1010000/1010000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [505000, 905001)
Primes: RFBsize:79251, AFBsize:79252, largePrimes:2661170 encountered
Relations: rels:2570098, finalFF:217499
Max relations in full relation-set: 28
Initial matrix: 158570 x 217499 with sparse part having weight 16509802.
Pruned matrix : 139367 x 140223 with weight 7866099.
Total sieving time: 4.30 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1010000,1010000,26,26,47,47,2.3,2.3,50000
total time: 4.71 hours.
 --------- CPU info (if available) ----------

Feb 21, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Feb 21, 2009

(43·10¹⁵⁹+11)/9 = 4(7)₁₅₈9_<160> = 3 · 17 · 23 · C157

C157 = P50 · P52 · P57

P50 = 11231391656393485544496622672465008980700034909609_<50>

P52 = 3014196135867233202687935157625883361795625141037437_<52>

P57 = 120315852673499043834233788846040848684277725755808369531_<57>

Number: 47779_159
N=4073126835275172871080799469546272615326323766221464431183101259827602538599981055224021975940134507909443970825044993842947807142180543715070569290518139623
  ( 157 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=11231391656393485544496622672465008980700034909609 (pp50)
 r2=3014196135867233202687935157625883361795625141037437 (pp52)
 r3=120315852673499043834233788846040848684277725755808369531 (pp57)
Version: Msieve-1.39
Total time: 30.34 hours.
Scaled time: 77.98 units (timescale=2.570).
Factorization parameters were as follows:
n: 4073126835275172871080799469546272615326323766221464431183101259827602538599981055224021975940134507909443970825044993842947807142180543715070569290518139623
m: 100000000000000000000000000000000
deg: 5
c5: 43
c0: 110
skew: 1.21
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 620461 x 620709
Total sieving time: 30.34 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 30.34 hours.
 --------- CPU info (if available) ----------

Feb 21, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.1 / Feb 21, 2009

(43·10¹⁸⁴+11)/9 = 4(7)₁₈₃9_<185> = 502173835561_<12> · 1764054615755273_<16> · C158

C158 = P35 · P124

P35 = 19779660838974429503159350745426911_<35>

P124 = 2726722849829117633288105012852610477794751506660331369964335151196302306688943733512946151533573442920320969197061013111613_<124>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3925499624
Step 1 took 33172ms
Step 2 took 31609ms
********** Factor found in step 2: 19779660838974429503159350745426911
Found probable prime factor of 35 digits: 19779660838974429503159350745426911
Probable prime cofactor has 124 digits

(43·10¹⁵⁴+11)/9 = 4(7)₁₅₃9_<155> = 61 · 2521 · 6621191 · 847749629250263763887_<21> · C122

C122 = P35 · C88

P35 = 16675085747257594544754493982884013_<35>

C88 = [3319337902489520751226070898363623293975319262802295525732486647927953485243921707385579_<88>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1862379626
Step 1 took 21938ms
Step 2 took 23406ms
********** Factor found in step 2: 16675085747257594544754493982884013
Found probable prime factor of 35 digits: 16675085747257594544754493982884013
Composite cofactor has 88 digits

(43·10¹⁷²+11)/9 = 4(7)₁₇₁9_<173> = 509 · 49201 · 11533729 · C159

C159 = P32 · P127

P32 = 57344023234304788989693444726809_<32>

P127 = 2884538444478075465915083887707291101979033666860029443770170453897934362899979487077169234337132170666443297398816898669830871_<127>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4028011784
Step 1 took 33562ms
Step 2 took 31500ms
********** Factor found in step 2: 57344023234304788989693444726809
Found probable prime factor of 32 digits: 57344023234304788989693444726809
Probable prime cofactor has 127 digits

Feb 21, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Feb 21, 2009

(43·10¹⁴⁶+11)/9 = 4(7)₁₄₅9_<147> = 29 · 5939380283_<10> · 211859631176295106006771_<24> · C113

C113 = P50 · P63

P50 = 15087489785086270771497404761812202993118278003931_<50>

P63 = 867803933596246020684967505127274412556662504314507971740173597_<63>

Number: 47779_146
N=13092982983591046266291176692464995493840491391051995577697638177682986033121860520529575409164790910616588409807
  ( 113 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=15087489785086270771497404761812202993118278003931
 r2=867803933596246020684967505127274412556662504314507971740173597
Version: 
Total time: 6.49 hours.
Scaled time: 15.49 units (timescale=2.388).
Factorization parameters were as follows:
n: 13092982983591046266291176692464995493840491391051995577697638177682986033121860520529575409164790910616588409807
m: 100000000000000000000000000000
deg: 5
c5: 430
c0: 11
skew: 0.48
type: snfs
lss: 1
rlim: 1650000
alim: 1650000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1650000/1650000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [825000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4161154
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 254636 x 254884
Total sieving time: 6.09 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1650000,1650000,26,26,49,49,2.3,2.3,75000
total time: 6.49 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(28·10¹⁹⁴+71)/9 = 3(1)₁₉₃9_<195> = 11² · 41 · 1674922471_<10> · 1474538095136372480044028131_<28> · 267407641043367558042632242380571217_<36> · C119

C119 = P32 · P88

P32 = 12106194029400988433886496553153_<32>

P88 = 7843576659298273046592920579513889096997867755355782782493662806320570224295195937674179_<88>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 94955860921945704007355546974800936804246583000431312236385646536971406882241375331831813631952300999296434499069136387 (119 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=235263376
Step 1 took 11871ms
Step 2 took 5314ms
********** Factor found in step 2: 12106194029400988433886496553153
Found probable prime factor of 32 digits: 12106194029400988433886496553153
Probable prime cofactor 7843576659298273046592920579513889096997867755355782782493662806320570224295195937674179 has 88 digits

(43·10¹⁵⁴+11)/9 = 4(7)₁₅₃9_<155> = 61 · 2521 · 6621191 · 847749629250263763887_<21> · 16675085747257594544754493982884013_<35> · C88

C88 = P40 · P48

P40 = 5636508307787864317600687433160633242081_<40>

P48 = 588899673562664672531521296334719610351148598859_<48>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 55350244148134926631508712649392541668678343419702755748874150275125536746147316396440138150515401329333495269396625848527 (122 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3859335070
Step 1 took 12059ms
********** Factor found in step 1: 5636508307787864317600687433160633242081
Found probable prime factor of 40 digits: 5636508307787864317600687433160633242081
Composite cofactor 9819952553189439735588237898709102832197648043856985505276394036828197492861141167 has 82 digits

Feb 20, 2009 (5th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Feb 20, 2009

(43·10¹²⁵+11)/9 = 4(7)₁₂₄9_<126> = 2351653 · C120

C120 = P34 · P87

P34 = 1266553334462239478412150091931083_<34>

P87 = 160409181960779313344897035534485477224261426249638458525237845325877356661108151236421_<87>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 203166784290785153157280337608387707615782506083073386157642210724872154938580554944874000448951345193265238441971573943 (120 digits)
Using B1=1474000, B2=2140044280, polynomial Dickson(6), sigma=3687375578
Step 1 took 12812ms
Step 2 took 6485ms
********** Factor found in step 2: 1266553334462239478412150091931083
Found probable prime factor of 34 digits: 1266553334462239478412150091931083
Probable prime cofactor 160409181960779313344897035534485477224261426249638458525237845325877356661108151236421 has 87 digits

(41·10²⁰³+31)/9 = 4(5)₂₀₂9_<204> = 3 · 13 · C203

C203 = P93 · P110

P93 = 457387337981603800293347279194388993095518723402417924356630498257271643329743269622387958219_<93>

P110 = 25538336352856119614320678777293019262107045729253609068129147639376452298149730952253210525759589139805192099_<110>

Number: n
N=11680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911681
  ( 203 digits)
SNFS difficulty: 206 digits.
Divisors found:

Fri Feb 20 21:41:51 2009  prp93 factor: 457387337981603800293347279194388993095518723402417924356630498257271643329743269622387958219
Fri Feb 20 21:41:51 2009  prp110 factor: 25538336352856119614320678777293019262107045729253609068129147639376452298149730952253210525759589139805192099
Fri Feb 20 21:41:51 2009  elapsed time 24:43:38 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20050930-k8
Total time: 171.01 hours.
Scaled time: 344.07 units (timescale=2.012).
Factorization parameters were as follows:
name: KA_4_5_202_9
n: 11680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911680911681
deg: 5
c5: 41
c0: 3100
m: 100000000000000000000000000000000000000000
skew: 2.38
type: snfs
rlim: 11000000
alim: 11000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 47599990)
Primes: RFBsize:726517, AFBsize:725685, largePrimes:32641643 encountered
Relations: rels:24382690, finalFF:56661
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 9194383 hash collisions in 46991467 relations
Msieve: matrix is 3662245 x 3662493 (995.4 MB)

Total sieving time: 169.65 hours.
Total relation processing time: 1.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,11000000,11000000,29,29,58,58,2.5,2.5,100000
total time: 171.01 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.92 BogoMIPS (lpj=2830461)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830455)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22643.63 BogoMIPS).

Feb 20, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 20, 2009

(14·10¹⁶¹-11)/3 = 4(6)₁₆₀3_<162> = 2875802551489229275389845286190879_<34> · C129

C129 = P40 · P41 · P49

P40 = 7961407472498715044312651769180597757613_<40>

P41 = 17841291452200529199647842314509698688099_<41>

P49 = 1142435201272643601345229374671734463684938243231_<49>

Number: 46663_161
N=162273542189120096933435105385323543745120089475806304724912872877238918245061625164527994822545703074883859629274728091025656697
  ( 129 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=7961407472498715044312651769180597757613
 r2=17841291452200529199647842314509698688099
 r3=1142435201272643601345229374671734463684938243231
Version: 
Total time: 16.13 hours.
Scaled time: 38.51 units (timescale=2.387).
Factorization parameters were as follows:
n: 162273542189120096933435105385323543745120089475806304724912872877238918245061625164527994822545703074883859629274728091025656697
m: 100000000000000000000000000000000
deg: 5
c5: 140
c0: -11
skew: 0.60
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1800000, 3100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9428208
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 603820 x 604068
Total sieving time: 14.16 hours.
Total relation processing time: 0.61 hours.
Matrix solve time: 0.82 hours.
Time per square root: 0.54 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000
total time: 16.13 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 20, 2009 (3rd)

By Sinkiti Sibata / Msieve, GGNFS / Feb 20, 2009

(43·10¹²⁹+11)/9 = 4(7)₁₂₈9_<130> = 3² · 390307 · 26599219579_<11> · 1064068310384686629507983_<25> · C89

C89 = P38 · P52

P38 = 27140931207690852879667282035137002753_<38>

P52 = 1770573452161694692999975192547293750680635048843173_<52>

Fri Feb 20 06:52:14 2009  Msieve v. 1.39
Fri Feb 20 06:52:14 2009  random seeds: 21016154 f81c930e
Fri Feb 20 06:52:14 2009  factoring 48055012263284266871337658562328737011072592194561029695649063803572406500776859166255269 (89 digits)
Fri Feb 20 06:52:15 2009  searching for 15-digit factors
Fri Feb 20 06:52:16 2009  commencing quadratic sieve (89-digit input)
Fri Feb 20 06:52:16 2009  using multiplier of 1
Fri Feb 20 06:52:16 2009  using 32kb Intel Core sieve core
Fri Feb 20 06:52:16 2009  sieve interval: 32 blocks of size 32768
Fri Feb 20 06:52:16 2009  processing polynomials in batches of 7
Fri Feb 20 06:52:16 2009  using a sieve bound of 1556173 (58969 primes)
Fri Feb 20 06:52:16 2009  using large prime bound of 124493840 (26 bits)
Fri Feb 20 06:52:16 2009  using double large prime bound of 372619898133360 (42-49 bits)
Fri Feb 20 06:52:16 2009  using trial factoring cutoff of 49 bits
Fri Feb 20 06:52:16 2009  polynomial 'A' values have 11 factors
Fri Feb 20 07:59:21 2009  59187 relations (15670 full + 43517 combined from 631081 partial), need 59065
Fri Feb 20 07:59:22 2009  begin with 646751 relations
Fri Feb 20 07:59:23 2009  reduce to 145134 relations in 9 passes
Fri Feb 20 07:59:23 2009  attempting to read 145134 relations
Fri Feb 20 07:59:24 2009  recovered 145134 relations
Fri Feb 20 07:59:24 2009  recovered 123372 polynomials
Fri Feb 20 07:59:25 2009  attempting to build 59187 cycles
Fri Feb 20 07:59:25 2009  found 59187 cycles in 5 passes
Fri Feb 20 07:59:25 2009  distribution of cycle lengths:
Fri Feb 20 07:59:25 2009     length 1 : 15670
Fri Feb 20 07:59:25 2009     length 2 : 11090
Fri Feb 20 07:59:25 2009     length 3 : 10545
Fri Feb 20 07:59:25 2009     length 4 : 7913
Fri Feb 20 07:59:25 2009     length 5 : 5579
Fri Feb 20 07:59:25 2009     length 6 : 3664
Fri Feb 20 07:59:25 2009     length 7 : 2137
Fri Feb 20 07:59:25 2009     length 9+: 2589
Fri Feb 20 07:59:25 2009  largest cycle: 17 relations
Fri Feb 20 07:59:25 2009  matrix is 58969 x 59187 (14.4 MB) with weight 3532633 (59.69/col)
Fri Feb 20 07:59:25 2009  sparse part has weight 3532633 (59.69/col)
Fri Feb 20 07:59:26 2009  filtering completed in 3 passes
Fri Feb 20 07:59:26 2009  matrix is 55025 x 55089 (13.5 MB) with weight 3314938 (60.17/col)
Fri Feb 20 07:59:26 2009  sparse part has weight 3314938 (60.17/col)
Fri Feb 20 07:59:26 2009  saving the first 48 matrix rows for later
Fri Feb 20 07:59:26 2009  matrix is 54977 x 55089 (9.6 MB) with weight 2720133 (49.38/col)
Fri Feb 20 07:59:26 2009  sparse part has weight 2174140 (39.47/col)
Fri Feb 20 07:59:26 2009  matrix includes 64 packed rows
Fri Feb 20 07:59:26 2009  using block size 22035 for processor cache size 1024 kB
Fri Feb 20 07:59:27 2009  commencing Lanczos iteration
Fri Feb 20 07:59:27 2009  memory use: 8.8 MB
Fri Feb 20 07:59:46 2009  lanczos halted after 871 iterations (dim = 54977)
Fri Feb 20 07:59:46 2009  recovered 17 nontrivial dependencies
Fri Feb 20 07:59:47 2009  prp38 factor: 27140931207690852879667282035137002753
Fri Feb 20 07:59:47 2009  prp52 factor: 1770573452161694692999975192547293750680635048843173
Fri Feb 20 07:59:47 2009  elapsed time 01:07:33

(43·10¹⁴²+11)/9 = 4(7)₁₄₁9_<143> = 401 · 1321 · 1867727 · 14366243 · 608193757 · 1383871068526152654861029_<25> · C91

C91 = P35 · P57

P35 = 24378346084486836937126300457149213_<35>

P57 = 163825055878536304330382129043609238283062757523353906131_<57>

Fri Feb 20 08:21:18 2009  Msieve v. 1.39
Fri Feb 20 08:21:18 2009  random seeds: 8f5564e0 c40a7580
Fri Feb 20 08:21:18 2009  factoring 3993783909517352782752855055687311510858077698847215776271767549538611990502412608262524903 (91 digits)
Fri Feb 20 08:21:19 2009  searching for 15-digit factors
Fri Feb 20 08:21:20 2009  commencing quadratic sieve (91-digit input)
Fri Feb 20 08:21:20 2009  using multiplier of 7
Fri Feb 20 08:21:20 2009  using 32kb Intel Core sieve core
Fri Feb 20 08:21:20 2009  sieve interval: 36 blocks of size 32768
Fri Feb 20 08:21:20 2009  processing polynomials in batches of 6
Fri Feb 20 08:21:20 2009  using a sieve bound of 1685933 (63261 primes)
Fri Feb 20 08:21:20 2009  using large prime bound of 155105836 (27 bits)
Fri Feb 20 08:21:20 2009  using double large prime bound of 553516580371368 (42-49 bits)
Fri Feb 20 08:21:20 2009  using trial factoring cutoff of 49 bits
Fri Feb 20 08:21:20 2009  polynomial 'A' values have 12 factors
Fri Feb 20 10:02:11 2009  63847 relations (16461 full + 47386 combined from 729762 partial), need 63357
Fri Feb 20 10:02:12 2009  begin with 746223 relations
Fri Feb 20 10:02:13 2009  reduce to 158830 relations in 11 passes
Fri Feb 20 10:02:13 2009  attempting to read 158830 relations
Fri Feb 20 10:02:15 2009  recovered 158830 relations
Fri Feb 20 10:02:15 2009  recovered 139831 polynomials
Fri Feb 20 10:02:15 2009  attempting to build 63847 cycles
Fri Feb 20 10:02:15 2009  found 63847 cycles in 6 passes
Fri Feb 20 10:02:15 2009  distribution of cycle lengths:
Fri Feb 20 10:02:15 2009     length 1 : 16461
Fri Feb 20 10:02:15 2009     length 2 : 11921
Fri Feb 20 10:02:15 2009     length 3 : 11240
Fri Feb 20 10:02:15 2009     length 4 : 8716
Fri Feb 20 10:02:15 2009     length 5 : 6117
Fri Feb 20 10:02:15 2009     length 6 : 3998
Fri Feb 20 10:02:15 2009     length 7 : 2425
Fri Feb 20 10:02:15 2009     length 9+: 2969
Fri Feb 20 10:02:15 2009  largest cycle: 20 relations
Fri Feb 20 10:02:16 2009  matrix is 63261 x 63847 (15.7 MB) with weight 3848842 (60.28/col)
Fri Feb 20 10:02:16 2009  sparse part has weight 3848842 (60.28/col)
Fri Feb 20 10:02:17 2009  filtering completed in 3 passes
Fri Feb 20 10:02:17 2009  matrix is 59516 x 59580 (14.6 MB) with weight 3588684 (60.23/col)
Fri Feb 20 10:02:17 2009  sparse part has weight 3588684 (60.23/col)
Fri Feb 20 10:02:17 2009  saving the first 48 matrix rows for later
Fri Feb 20 10:02:17 2009  matrix is 59468 x 59580 (8.8 MB) with weight 2770890 (46.51/col)
Fri Feb 20 10:02:17 2009  sparse part has weight 1957825 (32.86/col)
Fri Feb 20 10:02:17 2009  matrix includes 64 packed rows
Fri Feb 20 10:02:17 2009  using block size 23832 for processor cache size 1024 kB
Fri Feb 20 10:02:17 2009  commencing Lanczos iteration
Fri Feb 20 10:02:17 2009  memory use: 8.8 MB
Fri Feb 20 10:02:37 2009  lanczos halted after 942 iterations (dim = 59467)
Fri Feb 20 10:02:37 2009  recovered 17 nontrivial dependencies
Fri Feb 20 10:02:38 2009  prp35 factor: 24378346084486836937126300457149213
Fri Feb 20 10:02:38 2009  prp57 factor: 163825055878536304330382129043609238283062757523353906131
Fri Feb 20 10:02:38 2009  elapsed time 01:41:20

(43·10¹¹⁹+11)/9 = 4(7)₁₁₈9_<120> = 59² · 877169 · 43205687870409677_<17> · C94

C94 = P40 · P55

P40 = 1629543914890988045527593250715973643091_<40>

P55 = 2222448240333959828698516219357710508359559810761141373_<55>

Fri Feb 20 10:12:46 2009  Msieve v. 1.39
Fri Feb 20 10:12:46 2009  random seeds: bc4c5380 61111fb9
Fri Feb 20 10:12:46 2009  factoring 3621577006196388380317543352631061323163065442252020335260657653797868983538297184444095703943 (94 digits)
Fri Feb 20 10:12:47 2009  searching for 15-digit factors
Fri Feb 20 10:12:48 2009  commencing quadratic sieve (94-digit input)
Fri Feb 20 10:12:48 2009  using multiplier of 3
Fri Feb 20 10:12:48 2009  using 32kb Intel Core sieve core
Fri Feb 20 10:12:48 2009  sieve interval: 36 blocks of size 32768
Fri Feb 20 10:12:48 2009  processing polynomials in batches of 6
Fri Feb 20 10:12:48 2009  using a sieve bound of 2017133 (75294 primes)
Fri Feb 20 10:12:48 2009  using large prime bound of 270295822 (28 bits)
Fri Feb 20 10:12:48 2009  using double large prime bound of 1504217873095760 (42-51 bits)
Fri Feb 20 10:12:48 2009  using trial factoring cutoff of 51 bits
Fri Feb 20 10:12:48 2009  polynomial 'A' values have 12 factors
Fri Feb 20 13:30:21 2009  75562 relations (18319 full + 57243 combined from 1073394 partial), need 75390
Fri Feb 20 13:30:23 2009  begin with 1091713 relations
Fri Feb 20 13:30:24 2009  reduce to 197045 relations in 15 passes
Fri Feb 20 13:30:24 2009  attempting to read 197045 relations
Fri Feb 20 13:30:27 2009  recovered 197045 relations
Fri Feb 20 13:30:27 2009  recovered 180850 polynomials
Fri Feb 20 13:30:27 2009  attempting to build 75562 cycles
Fri Feb 20 13:30:27 2009  found 75562 cycles in 6 passes
Fri Feb 20 13:30:27 2009  distribution of cycle lengths:
Fri Feb 20 13:30:27 2009     length 1 : 18319
Fri Feb 20 13:30:27 2009     length 2 : 13159
Fri Feb 20 13:30:27 2009     length 3 : 12641
Fri Feb 20 13:30:27 2009     length 4 : 10177
Fri Feb 20 13:30:27 2009     length 5 : 7828
Fri Feb 20 13:30:27 2009     length 6 : 5356
Fri Feb 20 13:30:27 2009     length 7 : 3413
Fri Feb 20 13:30:27 2009     length 9+: 4669
Fri Feb 20 13:30:27 2009  largest cycle: 20 relations
Fri Feb 20 13:30:28 2009  matrix is 75294 x 75562 (19.7 MB) with weight 4853868 (64.24/col)
Fri Feb 20 13:30:28 2009  sparse part has weight 4853868 (64.24/col)
Fri Feb 20 13:30:29 2009  filtering completed in 3 passes
Fri Feb 20 13:30:29 2009  matrix is 71919 x 71983 (18.8 MB) with weight 4643042 (64.50/col)
Fri Feb 20 13:30:29 2009  sparse part has weight 4643042 (64.50/col)
Fri Feb 20 13:30:29 2009  saving the first 48 matrix rows for later
Fri Feb 20 13:30:29 2009  matrix is 71871 x 71983 (11.6 MB) with weight 3613430 (50.20/col)
Fri Feb 20 13:30:29 2009  sparse part has weight 2611838 (36.28/col)
Fri Feb 20 13:30:29 2009  matrix includes 64 packed rows
Fri Feb 20 13:30:29 2009  using block size 28793 for processor cache size 1024 kB
Fri Feb 20 13:30:29 2009  commencing Lanczos iteration
Fri Feb 20 13:30:29 2009  memory use: 11.4 MB
Fri Feb 20 13:31:02 2009  lanczos halted after 1139 iterations (dim = 71869)
Fri Feb 20 13:31:03 2009  recovered 16 nontrivial dependencies
Fri Feb 20 13:31:04 2009  prp40 factor: 1629543914890988045527593250715973643091
Fri Feb 20 13:31:04 2009  prp55 factor: 2222448240333959828698516219357710508359559810761141373
Fri Feb 20 13:31:04 2009  elapsed time 03:18:18

(43·10¹³²+11)/9 = 4(7)₁₃₁9_<133> = 3 · 139 · 1617060083_<10> · 5214396783389_<13> · C109

C109 = P50 · P59

P50 = 50541247719731333587997428474350383605813549419067_<50>

P59 = 26885226523835445887875722827790004920957495463615810581103_<59>

Number: 47779_132
N=1358812893742258597789747014238676024239796240176713828444379631747797948175870514261049944549847657338090901
  ( 109 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=50541247719731333587997428474350383605813549419067 (pp50)
 r2=26885226523835445887875722827790004920957495463615810581103 (pp59)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 7.22 hours.
Scaled time: 3.41 units (timescale=0.472).
Factorization parameters were as follows:
naqme: 47779_132
n: 1358812893742258597789747014238676024239796240176713828444379631747797948175870514261049944549847657338090901
m: 200000000000000000000000000
deg: 5
c5: 1075
c0: 88
skew: 0.61
type: snfs
lss: 1
rlim: 1220000
alim: 1220000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1220000/1220000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [610000, 1210001)
Primes: RFBsize:94358, AFBsize:94464, largePrimes:3034738 encountered
Relations: rels:2961930, finalFF:243551
Max relations in full relation-set: 28
Initial matrix: 188889 x 243551 with sparse part having weight 19965553.
Pruned matrix : 172717 x 173725 with weight 11107596.
Total sieving time: 6.54 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.50 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1220000,1220000,26,26,47,47,2.3,2.3,75000
total time: 7.22 hours.
 --------- CPU info (if available) ----------

(43·10¹²⁰+11)/9 = 4(7)₁₁₉9_<121> = 3² · 93827 · C115

C115 = P31 · P84

P31 = 7038155769238927850882817067061_<31>

P84 = 803890195150983067956507741009808847217713781424351512089994883241101368694024928773_<84>

Number: 47779_120
N=5657904414836499062432606792616882107824658121125733504544152509734556124898634695033030977552987919584599289446153
  ( 115 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=7038155769238927850882817067061 (pp31)
 r2=803890195150983067956507741009808847217713781424351512089994883241101368694024928773 (pp84)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.25 hours.
Scaled time: 1.53 units (timescale=0.472).
Factorization parameters were as follows:
name: 47779_120
n: 5657904414836499062432606792616882107824658121125733504544152509734556124898634695033030977552987919584599289446153
m: 1000000000000000000000000
deg: 5
c5: 43
c0: 11
skew: 0.76
type: snfs
lss: 1
rlim: 750000
alim: 750000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 750000/750000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [375000, 675001)
Primes: RFBsize:60238, AFBsize:60292, largePrimes:1430749 encountered
Relations: rels:1457858, finalFF:198259
Max relations in full relation-set: 28
Initial matrix: 120595 x 198259 with sparse part having weight 9889634.
Pruned matrix : 94071 x 94737 with weight 3577001.
Total sieving time: 3.10 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000
total time: 3.25 hours.
 --------- CPU info (if available) ----------

Feb 20, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Feb 20, 2009

4·10¹⁹⁹+9 = 4(0)₁₉₈9_<200> = 7 · 167 · 807609247 · 69410343209_<11> · 3583758997367_<13> · 4408808231743453_<16> · 902378687429809728877943_<24> · C125

C125 = P56 · P70

P56 = 34354547702604499771852060945580290335045785027459957891_<56>

P70 = 1246197671815972306658825990912399156490027586001311061642622929565689_<70>

Number: 40009_199
N=42812557363276487782916934524262511105753525850950546127721797492871267553551320202026578618974150388644911007529878858401899
  ( 125 digits)
Divisors found:
 r1=34354547702604499771852060945580290335045785027459957891
 r2=1246197671815972306658825990912399156490027586001311061642622929565689
Version: 
Total time: 97.56 hours.
Scaled time: 95.51 units (timescale=0.979).
Factorization parameters were as follows:
name: 40009_199
n: 42812557363276487782916934524262511105753525850950546127721797492871267553551320202026578618974150388644911007529878858401899
skew: 65485.13
# norm 6.24e+016
c5: 68820
c4: 15113653308
c3: 959756630908979
c2: -113306794408852250946
c1: -1423181321023806426462144
c0: 147911972968623758768192128
# alpha -5.27
Y1: 21201521590249
Y0: -909433307150304267179703
# Murphy_E 1.49e-010
# M 32842432499441896725282475792804844789405376223120805660169649129695932462276002551250689726016767061919229024782184398833998
type: gnfs
rlim: 8000000
alim: 8000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [4000000, 7600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 942045 x 942293
Total sieving time: 97.56 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,124,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,27,27,51,51,2.5,2.5,100000
total time: 97.56 hours.
 --------- CPU info (if available) ----------

(43·10¹³⁸+11)/9 = 4(7)₁₃₇9_<139> = 3³ · 827 · C135

C135 = P34 · P102

P34 = 1607990073692464275813762654005857_<34>

P102 = 133067901779035413042325512388656807161085244651646675288949326546221468227376511792074081928684625643_<102>

Number: 47779_138
N=213971865187772751926990809161976701947143973208732042535616363373987987719010156199461587074108906703290688242992421415100442374391051
  ( 135 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=1607990073692464275813762654005857
 r2=133067901779035413042325512388656807161085244651646675288949326546221468227376511792074081928684625643
Version: 
Total time: 7.39 hours.
Scaled time: 7.12 units (timescale=0.963).
Factorization parameters were as follows:
n: 213971865187772751926990809161976701947143973208732042535616363373987987719010156199461587074108906703290688242992421415100442374391051
m: 5000000000000000000000000000
deg: 5
c5: 344
c0: 275
skew: 0.96
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1785001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 254465 x 254713
Total sieving time: 7.39 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 7.39 hours.
 --------- CPU info (if available) ----------

(43·10¹³³+11)/9 = 4(7)₁₃₂9_<134> = 7 · 4297 · 655021 · C124

C124 = P62 · P63

P62 = 11346499132520100806728972455098551130381922768598092307243241_<62>

P63 = 213720137275370303790128482759435136117254500175820246299702841_<63>

Number: 47779_133
N=2424975352197066012744415971921744477993322570850246873141852961150303718684874715843679972242569935216148066118330205747681
  ( 124 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=11346499132520100806728972455098551130381922768598092307243241
 r2=213720137275370303790128482759435136117254500175820246299702841
Version: 
Total time: 5.54 hours.
Scaled time: 5.40 units (timescale=0.975).
Factorization parameters were as follows:
n: 2424975352197066012744415971921744477993322570850246873141852961150303718684874715843679972242569935216148066118330205747681
m: 500000000000000000000000000
deg: 5
c5: 344
c0: 275
skew: 0.96
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1325001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 201665 x 201913
Total sieving time: 5.54 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 5.54 hours.
 --------- CPU info (if available) ----------

Feb 20, 2009

By Serge Batalov / GMP-ECM 6.2.1 / Feb 20, 2009

(10²¹⁵+17)/9 = (1)₂₁₄3_<215> = 19 · 8461 · 4461943 · 43154329 · 233686394639_<12> · 3159117892938247_<16> · 10104647752741917108451_<23> · C146

C146 = P33 · P113

P33 = 501928547260793544603300585296669_<33>

P113 = 95867515236356305111343622696905285564256741353453902846428516503461544038617123729098432688474118148620085298703_<113>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=141999233
Step 1 took 30390ms
Step 2 took 29422ms
********** Factor found in step 2: 501928547260793544603300585296669
Found probable prime factor of 33 digits: 501928547260793544603300585296669
Probable prime cofactor 95867515236356305111343622696905285564256741353453902846428516503461544038617123729098432688474118148620085298703 has 113 digits

(10²³⁵+17)/9 = (1)₂₃₄3_<235> = 3 · C234

C234 = P37 · C198

P37 = 1462632956704910743229377279655903083_<37>

C198 = [253221677162778007115933666937499898630720100146308997547782269439806975654231771169379649040305075932932943995847187788035663927744145241864622405151602202392552517630064393035746096398124433056137_<198>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3955205230
Step 1 took 84796ms
Step 2 took 55438ms
********** Factor found in step 2: 1462632956704910743229377279655903083
Found probable prime factor of 37 digits: 1462632956704910743229377279655903083
Composite cofactor has 198 digits

Feb 19, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 19, 2009

(14·10¹⁶⁶-11)/3 = 4(6)₁₆₅3_<167> = 149 · 185903 · 368231 · 9731163539_<10> · 1043796167165768018697691187783_<31> · C114

C114 = P51 · P63

P51 = 494708760820451125848952720900188160753421001266359_<51>

P63 = 910507854449915240799919859053471284297372043363584815488929473_<63>

Number: 46663_166
N=450436212392205245158977097476905739315982037445676265753566615858125703057142741445006681401990315834878238498807
  ( 114 digits)
Divisors found:
 r1=494708760820451125848952720900188160753421001266359
 r2=910507854449915240799919859053471284297372043363584815488929473
Version: 
Total time: 15.97 hours.
Scaled time: 38.13 units (timescale=2.388).
Factorization parameters were as follows:
name: 46663_166
n: 450436212392205245158977097476905739315982037445676265753566615858125703057142741445006681401990315834878238498807
skew: 27512.07
# norm 2.14e+15
c5: 51660
c4: -2900960325
c3: -142057854067848
c2: 1898402704471809028
c1: 36240627074749100550306
c0: -188164729597955528825118040
# alpha -5.15
Y1: 438006036127
Y0: -6138978709709931512157
# Murphy_E 5.94e-10
# M 448558176564726215625748641011569023622740611486017860202758900290125331933431385049191181063798011377365875845011
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1400000, 2520001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9170106
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 539874 x 540122
Polynomial selection time: 1.15 hours.
Total sieving time: 13.07 hours.
Total relation processing time: 0.70 hours.
Matrix solve time: 0.66 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000
total time: 15.97 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 19, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Feb 19, 2009

(14·10¹⁵⁹+1)/3 = 4(6)₁₅₈7_<160> = 13 · 23283681427_<11> · 191171963208617_<15> · 1118699180060677_<16> · C119

C119 = P41 · P79

P41 = 11174819369441197114738866818706428965753_<41>

P79 = 6451099618540499233273736884263980249879617664845365580552739306543961653391721_<79>

Number: 46667_159
N=72089872971461088881510076819431699394836374891179644631331325694824456779438131337001864179041635058446583330602730913
  ( 119 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=11174819369441197114738866818706428965753 (pp41)
 r2=6451099618540499233273736884263980249879617664845365580552739306543961653391721 (pp79)
Version: Msieve-1.39
Total time: 20.77 hours.
Scaled time: 53.41 units (timescale=2.571).
Factorization parameters were as follows:
n: 72089872971461088881510076819431699394836374891179644631331325694824456779438131337001864179041635058446583330602730913
m: 100000000000000000000000000000000
deg: 5
c5: 7
c0: 5
skew: 0.93
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 576094 x 576342
Total sieving time: 20.77 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 20.77 hours.
 --------- CPU info (if available) ----------

(43·10¹⁵⁹-61)/9 = 4(7)₁₅₈1_<160> = 13 · 2689 · 4481225199742768913_<19> · 5783879069787889733681_<22> · C115

C115 = P41 · P75

P41 = 25751251215386511006956956407779078076869_<41>

P75 = 204775258284067508010307871544880791955964544084259425523964948382641441579_<75>

Number: 47771_159
N=5273219118768680122071708571506706716912016856156729728638835595725334023723100878336479878234453392900749134736151
  ( 115 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=25751251215386511006956956407779078076869 (pp41)
 r2=204775258284067508010307871544880791955964544084259425523964948382641441579 (pp75)
Version: Msieve-1.39
Total time: 36.92 hours.
Scaled time: 94.51 units (timescale=2.560).
Factorization parameters were as follows:
n: 5273219118768680122071708571506706716912016856156729728638835595725334023723100878336479878234453392900749134736151
m: 100000000000000000000000000000000
deg: 5
c5: 43
c0: -610
skew: 1.70
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 604530 x 604778
Total sieving time: 36.92 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 36.92 hours.
 --------- CPU info (if available) ----------

Feb 19, 2009

Factorizations of 477...779 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Feb 18, 2009 (5th)

By matsui / GGNFS / Feb 18, 2009

4·10¹⁹⁸+9 = 4(0)₁₉₇9_<199> = 13 · C198

C198 = P87 · P112

P87 = 119161480369370553888738724548996511607859620678122425499095327719568445123612055947061_<87>

P112 = 2582145729799085189864734222137758538649682303628164199071706577153193715726836851292948073706300167943278781913_<112>

N=307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693
  ( 198 digits)
SNFS difficulty: 198 digits.
Divisors found:
 r1=119161480369370553888738724548996511607859620678122425499095327719568445123612055947061 (pp87)
 r2=2582145729799085189864734222137758538649682303628164199071706577153193715726836851292948073706300167943278781913 (pp112)
Version: GGNFS-0.77.1-20060722-nocona

Feb 18, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Feb 18, 2009

(14·10¹⁷⁹+1)/3 = 4(6)₁₇₈7_<180> = 29 · C179

C179 = P38 · P141

P38 = 92675896264996983590750934289457199517_<38>

P141 = 173636885873488126303743651617020492024657710926734399245020902788494883365428374403641911428951894559811517313745583408396839097490999409619_<141>

Number: 46667_179
N=16091954022988505747126436781609195402298850574712643678160919540229885057471264367816091954022988505747126436781609195402298850574712643678160919540229885057471264367816091954023
  ( 179 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=92675896264996983590750934289457199517 (pp38)
 r2=173636885873488126303743651617020492024657710926734399245020902788494883365428374403641911428951894559811517313745583408396839097490999409619 (pp141)
Version: Msieve-1.39
Total time: 120.30 hours.
Scaled time: 307.98 units (timescale=2.560).
Factorization parameters were as follows:
n: 16091954022988505747126436781609195402298850574712643678160919540229885057471264367816091954022988505747126436781609195402298850574712643678160919540229885057471264367816091954023
m: 1000000000000000000000000000000000000
deg: 5
c5: 7
c0: 5
skew: 0.93
type: snfs
lss: 1
rlim: 7200000
alim: 7200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 7200000/7200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3600000, 5400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1311235 x 1311483
Total sieving time: 120.30 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,53,53,2.5,2.5,100000
total time: 120.30 hours.
 --------- CPU info (if available) ----------

(14·10¹⁵⁸-11)/3 = 4(6)₁₅₇3_<159> = 347 · 491 · 125053 · 727032431635420269844340393_<27> · C122

C122 = P36 · P36 · P51

P36 = 234803378827784030361597153387592303_<36>

P36 = 310713995993218869665380397868638747_<36>

P51 = 412936009293891525760838697224581450103900217364471_<51>

Number: 46663_158
N=30126446942224599374723108632407551078384197415597531296302534156777173628577007643433952264201441997937407902630281128611
  ( 122 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=234803378827784030361597153387592303 (pp36)
 r2=310713995993218869665380397868638747 (pp36)
 r3=412936009293891525760838697224581450103900217364471 (pp51)
Version: Msieve-1.39
Total time: 26.56 hours.
Scaled time: 68.55 units (timescale=2.581).
Factorization parameters were as follows:
n: 30126446942224599374723108632407551078384197415597531296302534156777173628577007643433952264201441997937407902630281128611
m: 50000000000000000000000000000000
deg: 5
c5: 112
c0: -275
skew: 1.20
type: snfs
lss: 1
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1650000, 3050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 624870 x 625118
Total sieving time: 26.56 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000
total time: 26.56 hours.
 --------- CPU info (if available) ----------

Feb 18, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 18, 2009

(43·10¹⁴⁸-61)/9 = 4(7)₁₄₇1_<149> = 46769 · 2629210397582974763360451419_<28> · C117

C117 = P44 · P73

P44 = 69658373543494025241174894925771756251923011_<44>

P73 = 5577880312046131909818066047850483955999577280283171864433498801873353451_<73>

Number: 47771_148
N=388546070357410472888762122414019432805997798219949048919437242587685416530014291285085014722220535373757598043160961
  ( 117 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=69658373543494025241174894925771756251923011
 r2=5577880312046131909818066047850483955999577280283171864433498801873353451
Version: 
Total time: 10.24 hours.
Scaled time: 24.17 units (timescale=2.359).
Factorization parameters were as follows:
n: 388546070357410472888762122414019432805997798219949048919437242587685416530014291285085014722220535373757598043160961
m: 1000000000000000000000000000000
deg: 5
c5: 43
c0: -6100
skew: 2.69
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7428740
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 368502 x 368750
Total sieving time: 9.50 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000
total time: 10.24 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(43·10¹⁵⁴-61)/9 = 4(7)₁₅₃1_<155> = 31 · 269 · 1723 · 11717 · 88339 · 102451 · C134

C134 = P36 · P99

P36 = 144998455525129973735485583611764881_<36>

P99 = 216261000622321818515855235227174561862847527613062975417782961788362713610454628027413792585977831_<99>

Number: 47771_154
N=31357511080555835774399090121316456047579255614504315798291457403930937839118791844386060841950607986280672665057609217229883050353111
  ( 134 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=144998455525129973735485583611764881
 r2=216261000622321818515855235227174561862847527613062975417782961788362713610454628027413792585977831
Version: 
Total time: 11.55 hours.
Scaled time: 27.55 units (timescale=2.385).
Factorization parameters were as follows:
n: 31357511080555835774399090121316456047579255614504315798291457403930937839118791844386060841950607986280672665057609217229883050353111
m: 10000000000000000000000000000000
deg: 5
c5: 43
c0: -610
skew: 1.70
type: snfs
lss: 1
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1400000, 2400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7959798
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 536710 x 536958
Total sieving time: 10.25 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 0.65 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000
total time: 11.55 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 18, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Feb 17, 2009

(43·10¹⁴⁵-61)/9 = 4(7)₁₄₄1_<146> = 843901 · 293991666959251_<15> · C126

C126 = P60 · P66

P60 = 918101328123974051862278530274961583258199669722430734090181_<60>

P66 = 209753302917850389604880863916559051862645756212210465413357673241_<66>

Number: 47771_145
N=192574785987268684455780319215148361749984341794729274246592538316541197471849039135275279536004523144463306494469797224546621
  ( 126 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=918101328123974051862278530274961583258199669722430734090181
 r2=209753302917850389604880863916559051862645756212210465413357673241
Version: 
Total time: 15.17 hours.
Scaled time: 11.88 units (timescale=0.783).
Factorization parameters were as follows:
n: 192574785987268684455780319215148361749984341794729274246592538316541197471849039135275279536004523144463306494469797224546621
m: 100000000000000000000000000000
deg: 5
c5: 43
c0: -61
skew: 1.07
type: snfs
lss: 1
rlim: 1950000
alim: 1950000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1950000/1950000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [975000, 2375001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 322228 x 322476
Total sieving time: 15.17 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000
total time: 15.17 hours.
 --------- CPU info (if available) ----------

Feb 18, 2009

Factorizations of 11...113 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Feb 17, 2009 (6th)

By Wataru Sakai / GMP-ECM 6.2.1 / Feb 17, 2009

4·10²⁵⁰+1 = 4(0)₂₄₉1_<251> = 13 · 609367039316849421092272000364917_<33> · C217

C217 = P28 · C190

P28 = 3646063837616479765543282237_<28>

C190 = [1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213_<190>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1542610798
Step 1 took 31294ms
Step 2 took 11523ms
********** Factor found in step 2: 3646063837616479765543282237
Found probable prime factor of 28 digits: 3646063837616479765543282237
Composite cofactor 1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213 has 190 digits

Feb 17, 2009 (5th)

By Sinkiti Sibata / Msieve / Feb 17, 2009

(43·10¹⁴⁰-61)/9 = 4(7)₁₃₉1_<141> = 3 · 19 · 613 · 12014939130369479_<17> · 2807781173984016080101272676799_<31> · C90

C90 = P43 · P47

P43 = 7723640672041417684521576904447403699170337_<43>

P47 = 52478779051999590207042356963788789748797491103_<47>

Mon Feb 16 21:12:07 2009  Msieve v. 1.39
Mon Feb 16 21:12:07 2009  random seeds: 24d6521f 26e401d8
Mon Feb 16 21:12:07 2009  factoring 405327232305099187365298506794707503782075648245778252701956086130956454512842708239011711 (90 digits)
Mon Feb 16 21:12:08 2009  searching for 15-digit factors
Mon Feb 16 21:12:10 2009  commencing quadratic sieve (90-digit input)
Mon Feb 16 21:12:10 2009  using multiplier of 11
Mon Feb 16 21:12:10 2009  using 64kb Pentium 4 sieve core
Mon Feb 16 21:12:10 2009  sieve interval: 18 blocks of size 65536
Mon Feb 16 21:12:10 2009  processing polynomials in batches of 6
Mon Feb 16 21:12:10 2009  using a sieve bound of 1584403 (60000 primes)
Mon Feb 16 21:12:10 2009  using large prime bound of 126752240 (26 bits)
Mon Feb 16 21:12:10 2009  using double large prime bound of 384875318121120 (42-49 bits)
Mon Feb 16 21:12:10 2009  using trial factoring cutoff of 49 bits
Mon Feb 16 21:12:10 2009  polynomial 'A' values have 12 factors
Mon Feb 16 23:51:54 2009  60283 relations (15605 full + 44678 combined from 641499 partial), need 60096
Mon Feb 16 23:51:56 2009  begin with 657104 relations
Mon Feb 16 23:51:57 2009  reduce to 148545 relations in 11 passes
Mon Feb 16 23:51:57 2009  attempting to read 148545 relations
Mon Feb 16 23:52:01 2009  recovered 148545 relations
Mon Feb 16 23:52:01 2009  recovered 130823 polynomials
Mon Feb 16 23:52:01 2009  attempting to build 60283 cycles
Mon Feb 16 23:52:01 2009  found 60283 cycles in 5 passes
Mon Feb 16 23:52:01 2009  distribution of cycle lengths:
Mon Feb 16 23:52:01 2009     length 1 : 15605
Mon Feb 16 23:52:01 2009     length 2 : 11482
Mon Feb 16 23:52:01 2009     length 3 : 10488
Mon Feb 16 23:52:01 2009     length 4 : 8082
Mon Feb 16 23:52:01 2009     length 5 : 5828
Mon Feb 16 23:52:01 2009     length 6 : 3718
Mon Feb 16 23:52:01 2009     length 7 : 2305
Mon Feb 16 23:52:01 2009     length 9+: 2775
Mon Feb 16 23:52:01 2009  largest cycle: 18 relations
Mon Feb 16 23:52:02 2009  matrix is 60000 x 60283 (14.8 MB) with weight 3645163 (60.47/col)
Mon Feb 16 23:52:02 2009  sparse part has weight 3645163 (60.47/col)
Mon Feb 16 23:52:03 2009  filtering completed in 3 passes
Mon Feb 16 23:52:03 2009  matrix is 56611 x 56675 (14.0 MB) with weight 3440546 (60.71/col)
Mon Feb 16 23:52:03 2009  sparse part has weight 3440546 (60.71/col)
Mon Feb 16 23:52:03 2009  saving the first 48 matrix rows for later
Mon Feb 16 23:52:03 2009  matrix is 56563 x 56675 (8.8 MB) with weight 2717635 (47.95/col)
Mon Feb 16 23:52:03 2009  sparse part has weight 1974818 (34.84/col)
Mon Feb 16 23:52:03 2009  matrix includes 64 packed rows
Mon Feb 16 23:52:03 2009  using block size 21845 for processor cache size 512 kB
Mon Feb 16 23:52:04 2009  commencing Lanczos iteration
Mon Feb 16 23:52:04 2009  memory use: 8.6 MB
Mon Feb 16 23:52:34 2009  lanczos halted after 896 iterations (dim = 56562)
Mon Feb 16 23:52:34 2009  recovered 17 nontrivial dependencies
Mon Feb 16 23:52:35 2009  prp43 factor: 7723640672041417684521576904447403699170337
Mon Feb 16 23:52:35 2009  prp47 factor: 52478779051999590207042356963788789748797491103
Mon Feb 16 23:52:35 2009  elapsed time 02:40:28

(43·10¹⁴³-61)/9 = 4(7)₁₄₂1_<144> = 3³ · 7 · 5743 · 432337 · 7595130892169_<13> · 177081686227891007_<18> · C102

C102 = P39 · P64

P39 = 102624840455862064407000833817896986463_<39>

P64 = 7376349985613162477584632245935778321122766520937732169503100401_<64>

Mon Feb 16 07:33:36 2009  Msieve v. 1.39
Mon Feb 16 07:33:36 2009  random seeds: 1efa2ba8 3f80fda9
Mon Feb 16 07:33:36 2009  factoring 756996740420151233386293617974273659264620199260250699674158397990327213454264657595630963113226871663 (102 digits)
Mon Feb 16 07:33:37 2009  searching for 15-digit factors
Mon Feb 16 07:33:39 2009  commencing quadratic sieve (102-digit input)
Mon Feb 16 07:33:40 2009  using multiplier of 2
Mon Feb 16 07:33:40 2009  using 32kb Intel Core sieve core
Mon Feb 16 07:33:40 2009  sieve interval: 36 blocks of size 32768
Mon Feb 16 07:33:40 2009  processing polynomials in batches of 6
Mon Feb 16 07:33:40 2009  using a sieve bound of 3272387 (117500 primes)
Mon Feb 16 07:33:40 2009  using large prime bound of 490858050 (28 bits)
Mon Feb 16 07:33:40 2009  using double large prime bound of 4402715446837350 (44-52 bits)
Mon Feb 16 07:33:40 2009  using trial factoring cutoff of 52 bits
Mon Feb 16 07:33:40 2009  polynomial 'A' values have 13 factors
Tue Feb 17 03:20:09 2009  117796 relations (27579 full + 90217 combined from 1762840 partial), need 117596
Tue Feb 17 03:20:11 2009  begin with 1790419 relations
Tue Feb 17 03:20:13 2009  reduce to 313239 relations in 12 passes
Tue Feb 17 03:20:13 2009  attempting to read 313239 relations
Tue Feb 17 03:20:19 2009  recovered 313239 relations
Tue Feb 17 03:20:19 2009  recovered 305305 polynomials
Tue Feb 17 03:20:20 2009  attempting to build 117796 cycles
Tue Feb 17 03:20:20 2009  found 117795 cycles in 5 passes
Tue Feb 17 03:20:20 2009  distribution of cycle lengths:
Tue Feb 17 03:20:20 2009     length 1 : 27579
Tue Feb 17 03:20:20 2009     length 2 : 19739
Tue Feb 17 03:20:20 2009     length 3 : 19664
Tue Feb 17 03:20:20 2009     length 4 : 15984
Tue Feb 17 03:20:20 2009     length 5 : 12454
Tue Feb 17 03:20:20 2009     length 6 : 8760
Tue Feb 17 03:20:20 2009     length 7 : 5606
Tue Feb 17 03:20:20 2009     length 9+: 8009
Tue Feb 17 03:20:20 2009  largest cycle: 19 relations
Tue Feb 17 03:20:21 2009  matrix is 117500 x 117795 (34.8 MB) with weight 8657234 (73.49/col)
Tue Feb 17 03:20:21 2009  sparse part has weight 8657234 (73.49/col)
Tue Feb 17 03:20:23 2009  filtering completed in 3 passes
Tue Feb 17 03:20:23 2009  matrix is 113209 x 113273 (33.6 MB) with weight 8359768 (73.80/col)
Tue Feb 17 03:20:23 2009  sparse part has weight 8359768 (73.80/col)
Tue Feb 17 03:20:23 2009  saving the first 48 matrix rows for later
Tue Feb 17 03:20:23 2009  matrix is 113161 x 113273 (23.6 MB) with weight 6934256 (61.22/col)
Tue Feb 17 03:20:23 2009  sparse part has weight 5513657 (48.68/col)
Tue Feb 17 03:20:23 2009  matrix includes 64 packed rows
Tue Feb 17 03:20:23 2009  using block size 43690 for processor cache size 1024 kB
Tue Feb 17 03:20:25 2009  commencing Lanczos iteration
Tue Feb 17 03:20:25 2009  memory use: 21.1 MB
Tue Feb 17 03:22:09 2009  lanczos halted after 1791 iterations (dim = 113159)
Tue Feb 17 03:22:10 2009  recovered 16 nontrivial dependencies
Tue Feb 17 03:22:11 2009  prp39 factor: 102624840455862064407000833817896986463
Tue Feb 17 03:22:11 2009  prp64 factor: 7376349985613162477584632245935778321122766520937732169503100401
Tue Feb 17 03:22:11 2009  elapsed time 19:48:35

(43·10¹²⁵-61)/9 = 4(7)₁₂₄1_<126> = 3² · 7 · 167 · 16667869 · 493736484911653679987_<21> · C94

C94 = P44 · P50

P44 = 98302269014734626147638425900634857243929937_<44>

P50 = 56134529111699639152696867219348421245265838793141_<50>

Tue Feb 17 07:51:21 2009  Msieve v. 1.39
Tue Feb 17 07:51:21 2009  random seeds: 4e82ded0 626dabf8
Tue Feb 17 07:51:21 2009  factoring 5518151581753750275625959440828313150369530075974461894895744348308024266777754720900040162117 (94 digits)
Tue Feb 17 07:51:22 2009  searching for 15-digit factors
Tue Feb 17 07:51:23 2009  commencing quadratic sieve (94-digit input)
Tue Feb 17 07:51:24 2009  using multiplier of 13
Tue Feb 17 07:51:24 2009  using 32kb Intel Core sieve core
Tue Feb 17 07:51:24 2009  sieve interval: 36 blocks of size 32768
Tue Feb 17 07:51:24 2009  processing polynomials in batches of 6
Tue Feb 17 07:51:24 2009  using a sieve bound of 2050679 (76471 primes)
Tue Feb 17 07:51:24 2009  using large prime bound of 282993702 (28 bits)
Tue Feb 17 07:51:24 2009  using double large prime bound of 1633797068989626 (42-51 bits)
Tue Feb 17 07:51:24 2009  using trial factoring cutoff of 51 bits
Tue Feb 17 07:51:24 2009  polynomial 'A' values have 12 factors
Tue Feb 17 10:46:01 2009  76683 relations (19245 full + 57438 combined from 1089796 partial), need 76567
Tue Feb 17 10:46:02 2009  begin with 1109041 relations
Tue Feb 17 10:46:04 2009  reduce to 197134 relations in 14 passes
Tue Feb 17 10:46:04 2009  attempting to read 197134 relations
Tue Feb 17 10:46:07 2009  recovered 197134 relations
Tue Feb 17 10:46:07 2009  recovered 178691 polynomials
Tue Feb 17 10:46:07 2009  attempting to build 76683 cycles
Tue Feb 17 10:46:07 2009  found 76682 cycles in 5 passes
Tue Feb 17 10:46:07 2009  distribution of cycle lengths:
Tue Feb 17 10:46:07 2009     length 1 : 19245
Tue Feb 17 10:46:07 2009     length 2 : 13786
Tue Feb 17 10:46:07 2009     length 3 : 12988
Tue Feb 17 10:46:07 2009     length 4 : 10368
Tue Feb 17 10:46:07 2009     length 5 : 7746
Tue Feb 17 10:46:07 2009     length 6 : 5041
Tue Feb 17 10:46:07 2009     length 7 : 3234
Tue Feb 17 10:46:07 2009     length 9+: 4274
Tue Feb 17 10:46:07 2009  largest cycle: 23 relations
Tue Feb 17 10:46:07 2009  matrix is 76471 x 76682 (20.3 MB) with weight 5018304 (65.44/col)
Tue Feb 17 10:46:07 2009  sparse part has weight 5018304 (65.44/col)
Tue Feb 17 10:46:09 2009  filtering completed in 3 passes
Tue Feb 17 10:46:09 2009  matrix is 72546 x 72610 (19.4 MB) with weight 4785339 (65.90/col)
Tue Feb 17 10:46:09 2009  sparse part has weight 4785339 (65.90/col)
Tue Feb 17 10:46:09 2009  saving the first 48 matrix rows for later
Tue Feb 17 10:46:09 2009  matrix is 72498 x 72610 (12.8 MB) with weight 3853848 (53.08/col)
Tue Feb 17 10:46:09 2009  sparse part has weight 2914060 (40.13/col)
Tue Feb 17 10:46:09 2009  matrix includes 64 packed rows
Tue Feb 17 10:46:09 2009  using block size 29044 for processor cache size 1024 kB
Tue Feb 17 10:46:10 2009  commencing Lanczos iteration
Tue Feb 17 10:46:10 2009  memory use: 11.9 MB
Tue Feb 17 10:46:45 2009  lanczos halted after 1148 iterations (dim = 72498)
Tue Feb 17 10:46:45 2009  recovered 18 nontrivial dependencies
Tue Feb 17 10:46:46 2009  prp44 factor: 98302269014734626147638425900634857243929937
Tue Feb 17 10:46:46 2009  prp50 factor: 56134529111699639152696867219348421245265838793141
Tue Feb 17 10:46:46 2009  elapsed time 02:55:25

Feb 17, 2009 (4th)

By Andreas Tete / Msieve-1.39 ECM / Feb 17, 2009

(4·10¹⁹⁹+23)/9 = (4)₁₉₈7_<199> = 7 · 1231 · C195

C195 = P38 · P158

P38 = 14225762137075170435338246532576567317_<38>

P158 = 36256497391523557391150836153499812526265014545716861850062848979279699883581750510325625228713377300801607790879317559258903710821964811855003806638790958123_<158>

Fri Feb 13 18:48:52 2009  Msieve v. 1.39
Fri Feb 13 18:48:52 2009  random seeds: 471c3938 94b24410
Fri Feb 13 18:48:52 2009  factoring 515776307815300504171340889456242827485719443477363867290755999123180276713989142908720487924387193274276946088481425605714801490593529586218457055175170528541771433729191649581576470284837465991 (195 digits)
Fri Feb 13 18:48:55 2009  searching for 15-digit factors
Fri Feb 13 18:48:58 2009  searching for 20-digit factors
Fri Feb 13 18:49:40 2009  searching for 25-digit factors
Fri Feb 13 18:57:51 2009  searching for 30-digit factors
Fri Feb 13 20:15:25 2009  searching for 35-digit factors
Sat Feb 14 07:16:27 2009  searching for 40-digit factors
Mon Feb 16 20:05:38 2009  ECM stage 2 factor found
Mon Feb 16 20:05:39 2009  prp38 factor: 14225762137075170435338246532576567317
Mon Feb 16 20:05:39 2009  prp158 factor: 36256497391523557391150836153499812526265014545716861850062848979279699883581750510325625228713377300801607790879317559258903710821964811855003806638790958123
Mon Feb 16 20:05:39 2009  elapsed time 73:16:47

Feb 17, 2009 (3rd)

By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1 / Feb 17, 2009

(43·10¹⁶⁷-61)/9 = 4(7)₁₆₆1_<168> = 3 · 7 · 1201 · 12893 · C160

C160 = P42 · P58 · P60

P42 = 319763349029725752411560301820144379646161_<42>

P58 = 6014427291190661113921720374543389795594170837747841101189_<58>

P60 = 763988283777773635783075645741983142491685470331316503861583_<60>

SNFS difficulty: 168 digits.
Divisors found:
 r1=319763349029725752411560301820144379646161 (pp42)
 r2=6014427291190661113921720374543389795594170837747841101189 (pp58)
 r3=763988283777773635783075645741983142491685470331316503861583 (pp60)
Version: Msieve-1.39
Total time: 40.84 hours.
Scaled time:  units (timescale=2.949).
Factorization parameters were as follows:
n: 1469297235067544757374446987145317016369300741801669019628303151502780964333241182086023179625663090895049087028637150168413736423357403521235814614745394074107
m: 1000000000000000000000000000000000
deg: 5
c5: 4300
c0: -61
skew: 0.5
type: snfs
lss: 1
rlim: 4700000
alim: 4700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4700000/4700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2350000, 5350001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 959321 x 959569
Total sieving time: 32.84 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 2.00 hours. x 4 cpu
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,200000
total time: 40.84 hours.

4·10²⁰⁹+1 = 4(0)₂₀₈1_<210> = 7 · 19 · C208

C208 = P100 · P108

P100 = 3868312352905881234614717303045694938316220300630823137841921435236696906862947702213074172986063797_<100>

P108 = 777475685161057172420107889087596154100076593781412039785204592057085537200948941303744478811373723078515001_<108>

# well, can't have a p102, but I have more than one p100   :-)
#                                                                      (rest in peace, St. George Carlin!)
SNFS difficulty: 210 digits.
Divisors found:
 r1=3868312352905881234614717303045694938316220300630823137841921435236696906862947702213074172986063797 (pp100)
 r2=777475685161057172420107889087596154100076593781412039785204592057085537200948941303744478811373723078515001 (pp108)
Version: Msieve-1.39
Total time: 1000.01 hours.
Scaled time: 2735.04 units (timescale=2.735).
Factorization parameters were as follows:
n: 3007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518796992481203007518797
m: 1000000000000000000000000000000000000000000
c5: 2
c0: 5
skew: 1.20
type: snfs
lss: 1
rlim: 24000000
alim: 24000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
rlambda: 2.6
alambda: 2.6
Factor base limits: 24000000/24000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 57/57
Sieved rational special-q in [12000000, 28800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: 50191195 relations (45865473 unique relations and about 35456933 large ideals)
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 3128545 x 3128793
Total sieving time: 900.01 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 29.10 hours. * 4 cpu
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,210,5,0,0,0,0,0,0,0,0,24000000,24000000,29,29,57,57,2.6,2.6,200000
total time: 1000.01 hours.

# quintic was faster than sextic; tested both; sieved on one side to minimize redundant relations

4·10²¹¹+1 = 4(0)₂₁₀1_<212> = 41 · 59 · 148721 · C204

C204 = P43 · C161

P43 = 1332356352410729241381459477648619855405009_<43>

C161 = [83450977684793282694551706981476556088621921512009377560353348583288515960273808416054497177857020031325682869956011963367750061419815803842510520381026012953211_<161>]

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1854358772
Step 1 took 267563ms
Step 2 took 91155ms
********** Factor found in step 2: 1332356352410729241381459477648619855405009
Found probable prime factor of 43 digits: 1332356352410729241381459477648619855405009
Composite cofactor has 161 digits

(64·10³³¹-1)/9 = 7(1)₃₃₁_<332> = 1627 · 5507 · 10546009 · 145180731511060009_<18> · 623478735428331443_<18> · C283

C283 = P38 · P246

P38 = 23456386816454549108790357240236910413_<38>

P246 = 354449980168239535745303077765553350378792474439978401690941252988338747486305028374580076545491280877079036161017542178942829000740483344638466667222237280561425839512652267467737233102180796563105230664353426524559063796193515087840859358054081_<246>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=3294908386
Step 1 took 111556ms
Step 2 took 60526ms
********** Factor found in step 2: 23456386816454549108790357240236910413
Found probable prime factor of 38 digits: 23456386816454549108790357240236910413
Probable prime cofactor 354449980168239535745303077765553350378792474439978401690941252988338747486305028374580076545491280877079036161017542178942829000740483344638466667222237280561425839512652267467737233102180796563105230664353426524559063796193515087840859358054081 has 246 digits

(64·10³³⁹-1)/9 = 7(1)₃₃₉_<340> = 13 · 31 · 157 · 3837923 · 34741013129584239530947685332231348396862921255411672754594954962184841471111675073557581361932830161869671_<107> · C222

C222 = P43 · C180

P43 = 1601837752074052763584458486041045553597079_<43>

C180 = [526229880308897806430105246913759491169408945893819869505892057808030029041536086980688560962160211962119608854022769551651299899931637375167849847544953178072548577431851592405163_<180>]

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1474824190
Step 1 took 318827ms
Step 2 took 101271ms
********** Factor found in step 2: 1601837752074052763584458486041045553597079
Found probable prime factor of 43 digits: 1601837752074052763584458486041045553597079
Composite cofactor has 180 digits

5·10¹⁹³-1 = 4(9)₁₉₃_<194> = 7 · 8839 · C189

C189 = P42 · C148

P42 = 107516249752971035684650211176390698878497_<42>

C148 = [7516137612365669741489365283749544184373803307710159983061153726053943367711447968803833931459424804091388388814143702729443123989730707737970742479_<148>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3184635571
Step 1 took 16335ms
Step 2 took 17245ms
********** Factor found in step 2: 107516249752971035684650211176390698878497
Found probable prime factor of 42 digits: 107516249752971035684650211176390698878497
Composite cofactor has 148 digits

(35·10²⁰⁴-71)/9 = 3(8)₂₀₃1_<205> = 61 · 67 · C201

C201 = P37 · C165

P37 = 3902505814693479946914232122945187201_<37>

C165 = [243824497793396457157695281071537524590427598565699673829660810250881151190575939082501252646909037808114080747612376446679162713152731850998085293276833764395008663_<165>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3483678870
Step 1 took 18399ms
Step 2 took 18677ms
********** Factor found in step 2: 3902505814693479946914232122945187201
Found probable prime factor of 37 digits: 3902505814693479946914232122945187201
Composite cofactor has 165 digits

Feb 17, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Feb 16, 2009

(38·10¹⁷¹+61)/9 = 4(2)₁₇₀9_<172> = 131 · C170

C170 = P56 · P115

P56 = 19656586353109644988628428880782557935174813548674463961_<56>

P115 = 1639689791881402852262937784707669473345717597586097018290930889928565528828480997000727743404647721038578540516319_<115>

Number: 42229_171
N=32230703986429177268871925360474978795589482612383375742154368108566581849024597116200169635284139100932994062765055131467345207803223070398642917726887192536047497879559
  ( 170 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=19656586353109644988628428880782557935174813548674463961 (pp56)
 r2=1639689791881402852262937784707669473345717597586097018290930889928565528828480997000727743404647721038578540516319 (pp115)
Version: Msieve-1.39
Total time: 63.58 hours.
Scaled time: 110.57 units (timescale=1.739).
Factorization parameters were as follows:
n: 32230703986429177268871925360474978795589482612383375742154368108566581849024597116200169635284139100932994062765055131467345207803223070398642917726887192536047497879559
m: 10000000000000000000000000000000000
deg: 5
c5: 380
c0: 61
skew: 0.69
type: snfs
lss: 1
rlim: 5300000
alim: 5300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2650000, 5950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 984707 x 984955
Total sieving time: 63.58 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.4,2.4,100000
total time: 63.58 hours.
 --------- CPU info (if available) ----------

(41·10¹⁷³+31)/9 = 4(5)₁₇₂9_<174> = 3² · 13³ · C170

C170 = P43 · P57 · P71

P43 = 3029238009120866184274345315387011894129521_<43>

P57 = 679776460891127365680164499381757723798582319378637295351_<57>

P71 = 11188432898523632839484220414481435452661059309668165398028722268040373_<71>

Number: 45559_173
N=23039273532370179312980101934737043218305545721719291739015604893316924875110279449529942626589569390358344993453474715802131975701995425861303573335131520535859786352883
  ( 170 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=3029238009120866184274345315387011894129521 (pp43)
 r2=679776460891127365680164499381757723798582319378637295351 (pp57)
 r3=11188432898523632839484220414481435452661059309668165398028722268040373 (pp71)
Version: Msieve-1.39
Total time: 113.83 hours.
Scaled time: 292.66 units (timescale=2.571).
Factorization parameters were as follows:
n: 23039273532370179312980101934737043218305545721719291739015604893316924875110279449529942626589569390358344993453474715802131975701995425861303573335131520535859786352883
m: 50000000000000000000000000000000000
deg: 5
c5: 328
c0: 775
skew: 1.19
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3000000, 8400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1341651 x 1341899
Total sieving time: 113.83 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,53,53,2.5,2.5,100000
total time: 113.83 hours.
 --------- CPU info (if available) ----------

By Ignacio Santos / GGNFS, Msieve / Feb 17, 2009

(13·10¹⁷⁵+11)/3 = 4(3)₁₇₄7_<176> = 29 · 61 · C173

C173 = P40 · P40 · P47 · P48

P40 = 1288621095191851780372499073998595818057_<40>

P40 = 7132302930944498108158521532994477253953_<40>

P47 = 26155680541725035222970324444772014948886396049_<47>

P48 = 101899774506178196286892707388314296027824602137_<48>

Number: 43337_175
N=24495948746938006406632749199170906350103636706237045411720369323534953834558130770680233653664970793291878650838515168645185603919351799510081025061239871867345016016581873
  ( 173 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=1288621095191851780372499073998595818057 (pp40)
 r2=7132302930944498108158521532994477253953 (pp40)
 r3=26155680541725035222970324444772014948886396049 (pp47)
 r4=101899774506178196286892707388314296027824602137 (pp48)
Version: Msieve-1.39
Total time: 66.16 hours.
Scaled time: 115.05 units (timescale=1.739).
Factorization parameters were as follows:
n: 24495948746938006406632749199170906350103636706237045411720369323534953834558130770680233653664970793291878650838515168645185603919351799510081025061239871867345016016581873
m: 100000000000000000000000000000000000
deg: 5
c5: 13
c0: 11
skew: 0.97
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3000000, 6300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1195582 x 1195828
Total sieving time: 66.16 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,53,53,2.5,2.5,100000
total time: 66.16 hours.
 --------- CPU info (if available) ----------

Feb 17, 2009

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Feb 16, 2009

(35·10¹⁶⁵-17)/9 = 3(8)₁₆₄7_<166> = 13 · 29 · 200041 · 6591395639_<10> · 10664333440055130067457_<23> · C126

C126 = P39 · P88

P39 = 109280386502103256471935743911750090597_<39>

P88 = 6712925841213146837839103821365744689243652680605247737247853841651220452334798552144461_<88>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 733591130487729320041466339475378877828506230498071346123108945591659364833598799646116043576499629418508345462979745381733217 (126 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2491864470
Step 1 took 11843ms
Step 2 took 5342ms
********** Factor found in step 2: 109280386502103256471935743911750090597
Found probable prime factor of 39 digits: 109280386502103256471935743911750090597
Probable prime cofactor 6712925841213146837839103821365744689243652680605247737247853841651220452334798552144461 has 88 digits

(43·10¹²⁴-61)/9 = 4(7)₁₂₃1_<125> = 31 · 163 · 6389 · 41959 · C113

C113 = P44 · P69

P44 = 57670739452665100371167339196616006651255717_<44>

P69 = 611593851386938504114770827406703530934017650552297959822029434697721_<69>

Number: 47771_124
N=35271069654188110604310693579449758929093792694822280641027184497713020658439788776775525020655692211494968120957
  ( 113 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=57670739452665100371167339196616006651255717
 r2=611593851386938504114770827406703530934017650552297959822029434697721
Version: 
Total time: 1.00 hours.
Scaled time: 2.33 units (timescale=2.335).
Factorization parameters were as follows:
n: 35271069654188110604310693579449758929093792694822280641027184497713020658439788776775525020655692211494968120957
m: 10000000000000000000000000
deg: 5
c5: 43
c0: -610
skew: 1.70
type: snfs
lss: 1
rlim: 800000
alim: 800000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [400000, 680001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2328603
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 127754 x 128002
Total sieving time: 0.87 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,800000,800000,26,26,46,46,2.3,2.3,40000
total time: 1.00 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Feb 17, 2009

(43·10¹⁴²-61)/9 = 4(7)₁₄₁1_<143> = 35768251 · 971975142044493496125235627_<27> · C109

C109 = P49 · P60

P49 = 6359029958009305926862739463303985620388379963359_<49>

P60 = 216113657076574346992381331592346705690321604633547083159597_<60>

Number: 47771_142
N=1374273219684886110425633843081179314367550784801415167464068283959390961846904203558375753774865608809206323
  ( 109 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=6359029958009305926862739463303985620388379963359
 r2=216113657076574346992381331592346705690321604633547083159597
Version: 
Total time: 6.13 hours.
Scaled time: 14.57 units (timescale=2.375).
Factorization parameters were as follows:
n: 1374273219684886110425633843081179314367550784801415167464068283959390961846904203558375753774865608809206323
m: 10000000000000000000000000000
deg: 5
c5: 4300
c0: -61
skew: 0.43
type: snfs
lss: 1
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [750000, 1400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3850387
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 251977 x 252225
Total sieving time: 5.71 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,49,49,2.3,2.3,50000
total time: 6.13 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(43·10¹⁴⁴-61)/9 = 4(7)₁₄₃1_<145> = 502657741 · 2309269179827263_<16> · C121

C121 = P45 · P77

P45 = 110193612870242212645693272924122113622791783_<45>

P77 = 37352750701688809281498611377219784036007829353980004226140370590943237683439_<77>

Number: 47771_144
N=4116034550460564813748098138709870879452440801197676121176679269551367554028928848439137916612448202103176435268764381737
  ( 121 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=110193612870242212645693272924122113622791783
 r2=37352750701688809281498611377219784036007829353980004226140370590943237683439
Version: 
Total time: 6.41 hours.
Scaled time: 14.86 units (timescale=2.319).
Factorization parameters were as follows:
n: 4116034550460564813748098138709870879452440801197676121176679269551367554028928848439137916612448202103176435268764381737
m: 100000000000000000000000000000
deg: 5
c5: 43
c0: -610
skew: 1.70
type: snfs
lss: 1
rlim: 1650000
alim: 1650000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1650000/1650000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [825000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4241738
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 246727 x 246975
Total sieving time: 6.08 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1650000,1650000,26,26,49,49,2.3,2.3,75000
total time: 6.41 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 16, 2009 (7th)

By Robert Backstrom / GGNFS, Msieve / Feb 16, 2009

(43·10¹¹⁹-61)/9 = 4(7)₁₁₈1_<120> = 3 · 7 · 33786569 · 75207302532881_<14> · C97

C97 = P45 · P53

P45 = 686841041276857189302957733169540389755111199_<45>

P53 = 13036058767483538717215947584356676918200426562472841_<53>

Number: n
N=8953700178004697272850078007323773932868947994732885669881369760907449234154980288975464372446359
  ( 97 digits)
SNFS difficulty: 121 digits.
Divisors found:

Mon Feb 16 16:33:14 2009  prp45 factor: 686841041276857189302957733169540389755111199
Mon Feb 16 16:33:14 2009  prp53 factor: 13036058767483538717215947584356676918200426562472841
Mon Feb 16 16:33:14 2009  elapsed time 00:16:20 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 1.96 hours.
Scaled time: 2.57 units (timescale=1.316).
Factorization parameters were as follows:
name: KA_4_7_118_1
n: 8953700178004697272850078007323773932868947994732885669881369760907449234154980288975464372446359
deg: 5
c5: 43
c0: -610
m: 1000000000000000000000000
skew: 1.70
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 480203)
Primes: RFBsize:49098, AFBsize:49047, largePrimes:5511719 encountered
Relations: rels:4688886, finalFF:109219
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 243840 hash collisions in 4898442 relations
Msieve: matrix is 124992 x 125240 (33.4 MB)

Total sieving time: 1.85 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,28,28,56,56,2.5,2.5,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------

Feb 16, 2009 (6th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 16, 2009

4·10¹⁸¹+9 = 4(0)₁₈₀9_<182> = 7 · 4463 · 9013 · 44939 · 54440369 · 646495019927_<12> · 17375472304230114852745301318776299103_<38> · C112

C112 = P47 · P65

P47 = 96680330851377897032675335617773667304146317489_<47>

P65 = 53466443788604542141782787390935555045766340238599979694824022367_<65>

Number: 40009_181
N=5169153474928885848324348321675877484252277469106881063647738317793449445476644541605020599482510225817619276463
  ( 112 digits)
Divisors found:
 r1=96680330851377897032675335617773667304146317489
 r2=53466443788604542141782787390935555045766340238599979694824022367
Version: 
Total time: 11.56 hours.
Scaled time: 27.56 units (timescale=2.384).
Factorization parameters were as follows:
name: 40009_181
n: 5169153474928885848324348321675877484252277469106881063647738317793449445476644541605020599482510225817619276463
skew: 11307.69
# norm 4.27e+15
c5: 81900
c4: 15515914875
c3: -252443578509548
c2: -2026077604162000042
c1: 2623866671835000250456
c0: 6610025439422676503234535
# alpha -5.84
Y1: 426573340633
Y0: -2290994471364759764248
# Murphy_E 7.55e-10
# M 599980959666439027133329231836971032000226273846861958358850094938446921738455534823840668568287349303771514218
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1200000, 2040001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8194253
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 442248 x 442496
Polynomial selection time: 0.87 hours.
Total sieving time: 9.62 hours.
Total relation processing time: 0.56 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000
total time: 11.56 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 16, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39 / Feb 16, 2009

(43·10¹⁴⁰-61)/9 = 4(7)₁₃₉1_<141> = 3 · 19 · 613 · 12014939130369479_<17> · C121

C121 = P31 · C90

P31 = 2807781173984016080101272676799_<31>

C90 = [405327232305099187365298506794707503782075648245778252701956086130956454512842708239011711_<90>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2177330287
Step 1 took 9832ms
Step 2 took 12144ms
********** Factor found in step 2: 2807781173984016080101272676799
Found probable prime factor of 31 digits: 2807781173984016080101272676799
Composite cofactor has 90 digits

(43·10¹⁴²-61)/9 = 4(7)₁₄₁1_<143> = 35768251 · C136

C136 = P27 · C109

P27 = 971975142044493496125235627_<27>

C109 = [1374273219684886110425633843081179314367550784801415167464068283959390961846904203558375753774865608809206323_<109>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3401780523
Step 1 took 12739ms
Step 2 took 13538ms
********** Factor found in step 2: 971975142044493496125235627
Found probable prime factor of 27 digits: 971975142044493496125235627
Composite cofactor has 109 digits

(43·10¹⁹⁰-61)/9 = 4(7)₁₈₉1_<191> = 63793 · 1164937 · 8792622349836405869542771_<25> · C155

C155 = P38 · P117

P38 = 83298832294425500958607625722801434401_<38>

P117 = 877795089404486954963782457552404091105528419858714925670383392791228993400713983819414032809076686946161566570798161_<117>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2603822046
Step 1 took 14402ms
Step 2 took 15584ms
********** Factor found in step 2: 83298832294425500958607625722801434401
Found probable prime factor of 38 digits: 83298832294425500958607625722801434401
Probable prime cofactor has 117 digits

(43·10¹⁷¹-61)/9 = 4(7)₁₇₀1_<172> = 13 · 17 · 41 · C168

C168 = P34 · P134

P34 = 7845455428462107106676257169548517_<34>

P134 = 67209653484714549323117321466492145147605549149413730004693507794615691079450687744110971209177162816167855429388847000741239221795683_<134>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4178244371
Step 1 took 13637ms
Step 2 took 15854ms
********** Factor found in step 2: 7845455428462107106676257169548517
Found probable prime factor of 34 digits: 7845455428462107106676257169548517
Probable prime cofactor has 134 digits

(43·10¹²⁷-61)/9 = 4(7)₁₂₆1_<128> = 3911 · 7397642663_<10> · 524720936425589_<15> · C100

C100 = P33 · P67

P33 = 509054986545985914315609096394579_<33>

P67 = 6182323008851373913280520769101995173342062958201255762686072243637_<67>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3547595471
Step 1 took 8268ms
Step 2 took 10640ms
********** Factor found in step 2: 509054986545985914315609096394579
Found probable prime factor of 33 digits: 509054986545985914315609096394579
Probable prime cofactor 6182323008851373913280520769101995173342062958201255762686072243637 has 67 digits

(43·10¹⁸¹-61)/9 = 4(7)₁₈₀1_<182> = 41 · 4993 · 4637239 · 23447794511_<11> · 2238586197354816928711_<22> · C138

C138 = P39 · P100

P39 = 787520244228026613351141308129216378279_<39>

P100 = 1217540722763297522505208509838978461879989223390529575643052343951874281431929038985853638287595867_<100>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4086981410
Step 1 took 11891ms
Step 2 took 13652ms
********** Factor found in step 2: 787520244228026613351141308129216378279
Found probable prime factor of 39 digits: 787520244228026613351141308129216378279
Probable prime cofactor 1217540722763297522505208509838978461879989223390529575643052343951874281431929038985853638287595867 has 100 digits

(43·10¹⁹³-61)/9 = 4(7)₁₉₂1_<194> = 7194113 · 1121757930540769_<16> · C172

C172 = P35 · P137

P35 = 71199310765325297693532708112008109_<35>

P137 = 83152201696408126546070047639498561500691348762681096052862159690720257463473192817296392702546939875802035388838203099768227067086826327_<137>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1650842304
Step 1 took 13686ms
Step 2 took 15855ms
********** Factor found in step 2: 71199310765325297693532708112008109
Found probable prime factor of 35 digits: 71199310765325297693532708112008109
Probable prime cofactor has 137 digits

(43·10¹⁸⁸-61)/9 = 4(7)₁₈₇1_<189> = 3² · 883 · 66071 · C180

C180 = P32 · C149

P32 = 19525460771553668149596808042841_<32>

C149 = [46602644501345193158597898914670594145834189426831461696667881665565602998778190931880816833841590944874547410124468413046847275701045361362861642463_<149>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=637296109
Step 1 took 16324ms
********** Factor found in step 1: 19525460771553668149596808042841
Found probable prime factor of 32 digits: 19525460771553668149596808042841
Composite cofactor has 149 digits

(43·10¹⁶⁶-61)/9 = 4(7)₁₆₅1_<167> = 41 · 3361 · 56851564871_<11> · 54458529178463_<14> · 1356201014051082287469709_<25> · C113

C113 = P33 · P38 · P43

P33 = 897280718820561928249807356357529_<33>

P38 = 73970249053547678867643207278372778361_<38>

P43 = 1244101359385847412349825255921033918644487_<43>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=59274701
Step 1 took 8344ms
Step 2 took 10793ms
********** Factor found in step 2: 897280718820561928249807356357529
Found probable prime factor of 33 digits: 897280718820561928249807356357529
Composite cofactor has 80 digits
Sun Feb 15 14:10:39 2009
Sun Feb 15 14:10:39 2009  Msieve v. 1.39
Sun Feb 15 14:10:39 2009  random seeds: d29fd19c 3cf57266
Sun Feb 15 14:10:39 2009  factoring 92026487401628360238713977917529420698694663305061074443251871502594085205545807 (80 digits)
Sun Feb 15 14:10:40 2009  searching for 15-digit factors
Sun Feb 15 14:10:40 2009  commencing quadratic sieve (80-digit input)
Sun Feb 15 14:10:40 2009  using multiplier of 7
Sun Feb 15 14:10:40 2009  using 64kb Opteron sieve core
Sun Feb 15 14:10:40 2009  sieve interval: 6 blocks of size 65536
Sun Feb 15 14:10:40 2009  processing polynomials in batches of 17
Sun Feb 15 14:10:40 2009  using a sieve bound of 1301077 (49996 primes)
Sun Feb 15 14:10:40 2009  using large prime bound of 130107700 (26 bits)
Sun Feb 15 14:10:40 2009  using trial factoring cutoff of 27 bits
Sun Feb 15 14:10:40 2009  polynomial 'A' values have 10 factors
Sun Feb 15 14:22:26 2009  50288 relations (26258 full + 24030 combined from 270126 partial), need 50092
Sun Feb 15 14:22:27 2009  begin with 296384 relations
Sun Feb 15 14:22:27 2009  reduce to 71381 relations in 2 passes
Sun Feb 15 14:22:27 2009  attempting to read 71381 relations
Sun Feb 15 14:22:27 2009  recovered 71381 relations
Sun Feb 15 14:22:27 2009  recovered 58949 polynomials
Sun Feb 15 14:22:27 2009  attempting to build 50288 cycles
Sun Feb 15 14:22:27 2009  found 50288 cycles in 1 passes
Sun Feb 15 14:22:27 2009  distribution of cycle lengths:
Sun Feb 15 14:22:27 2009     length 1 : 26258
Sun Feb 15 14:22:27 2009     length 2 : 24030
Sun Feb 15 14:22:27 2009  largest cycle: 2 relations
Sun Feb 15 14:22:27 2009  matrix is 49996 x 50288 (7.4 MB) with weight 1533099 (30.49/col)
Sun Feb 15 14:22:27 2009  sparse part has weight 1533099 (30.49/col)
Sun Feb 15 14:22:28 2009  filtering completed in 3 passes
Sun Feb 15 14:22:28 2009  matrix is 34735 x 34799 (5.6 MB) with weight 1196408 (34.38/col)
Sun Feb 15 14:22:28 2009  sparse part has weight 1196408 (34.38/col)
Sun Feb 15 14:22:28 2009  saving the first 48 matrix rows for later
Sun Feb 15 14:22:28 2009  matrix is 34687 x 34799 (4.2 MB) with weight 930902 (26.75/col)
Sun Feb 15 14:22:28 2009  sparse part has weight 740458 (21.28/col)
Sun Feb 15 14:22:28 2009  matrix includes 64 packed rows
Sun Feb 15 14:22:28 2009  using block size 13919 for processor cache size 1024 kB
Sun Feb 15 14:22:28 2009  commencing Lanczos iteration
Sun Feb 15 14:22:28 2009  memory use: 4.0 MB
Sun Feb 15 14:22:34 2009  lanczos halted after 551 iterations (dim = 34686)
Sun Feb 15 14:22:34 2009  recovered 17 nontrivial dependencies
Sun Feb 15 14:22:34 2009  prp38 factor: 73970249053547678867643207278372778361
Sun Feb 15 14:22:34 2009  prp43 factor: 1244101359385847412349825255921033918644487
Sun Feb 15 14:22:34 2009  elapsed time 00:11:55

Feb 16, 2009 (4th)

By Erik Branger / Msieve, GGNFS / Feb 16, 2009

(43·10¹⁰⁷-61)/9 = 4(7)₁₀₆1_<108> = 3² · 7² · 17 · 541 · 5623 · 14393833 · C91

C91 = P32 · P60

P32 = 14226811194310956229338618806873_<32>

P60 = 102303162456309080732822575209405595505437738286521037113289_<60>

Sun Feb 15 14:55:03 2009  Msieve v. 1.39
Sun Feb 15 14:55:03 2009  random seeds: f5ae9c98 fff75bb0
Sun Feb 15 14:55:03 2009  factoring 1455447776846830371340399960018503553645247165141598369089276272909152778232497473312835297 (91 digits)
Sun Feb 15 14:55:04 2009  searching for 15-digit factors
Sun Feb 15 14:55:06 2009  commencing quadratic sieve (91-digit input)
Sun Feb 15 14:55:06 2009  using multiplier of 1
Sun Feb 15 14:55:06 2009  using 32kb Intel Core sieve core
Sun Feb 15 14:55:06 2009  sieve interval: 36 blocks of size 32768
Sun Feb 15 14:55:06 2009  processing polynomials in batches of 6
Sun Feb 15 14:55:06 2009  using a sieve bound of 1652513 (62308 primes)
Sun Feb 15 14:55:06 2009  using large prime bound of 145421144 (27 bits)
Sun Feb 15 14:55:06 2009  using double large prime bound of 492866721827128 (42-49 bits)
Sun Feb 15 14:55:06 2009  using trial factoring cutoff of 49 bits
Sun Feb 15 14:55:06 2009  polynomial 'A' values have 12 factors
Sun Feb 15 14:55:25 2009  
Sun Feb 15 14:55:25 2009  

Sun Feb 15 16:49:40 2009  
Sun Feb 15 16:49:40 2009  Msieve v. 1.39
Sun Feb 15 16:49:40 2009  random seeds: 2c38db48 15232584
Sun Feb 15 16:49:40 2009  factoring 1455447776846830371340399960018503553645247165141598369089276272909152778232497473312835297 (91 digits)
Sun Feb 15 16:49:41 2009  searching for 15-digit factors
Sun Feb 15 16:49:43 2009  commencing quadratic sieve (91-digit input)
Sun Feb 15 16:49:43 2009  using multiplier of 1
Sun Feb 15 16:49:43 2009  using 32kb Intel Core sieve core
Sun Feb 15 16:49:43 2009  sieve interval: 36 blocks of size 32768
Sun Feb 15 16:49:43 2009  processing polynomials in batches of 6
Sun Feb 15 16:49:43 2009  using a sieve bound of 1652513 (62308 primes)
Sun Feb 15 16:49:43 2009  using large prime bound of 145421144 (27 bits)
Sun Feb 15 16:49:43 2009  using double large prime bound of 492866721827128 (42-49 bits)
Sun Feb 15 16:49:43 2009  using trial factoring cutoff of 49 bits
Sun Feb 15 16:49:43 2009  polynomial 'A' values have 12 factors
Sun Feb 15 16:49:44 2009  restarting with 17030 full and 725896 partial relations
Sun Feb 15 16:49:44 2009  68855 relations (17030 full + 51825 combined from 725896 partial), need 62404
Sun Feb 15 16:49:44 2009  begin with 742926 relations
Sun Feb 15 16:49:45 2009  reduce to 170003 relations in 10 passes
Sun Feb 15 16:49:45 2009  attempting to read 170003 relations

Sun Feb 15 16:49:50 2009  recovered 168835 relations
Sun Feb 15 16:49:50 2009  recovered 142934 polynomials
Sun Feb 15 16:49:51 2009  attempting to build 67691 cycles
Sun Feb 15 16:49:51 2009  found 67691 cycles in 6 passes
Sun Feb 15 16:49:51 2009  distribution of cycle lengths:
Sun Feb 15 16:49:51 2009     length 1 : 16909
Sun Feb 15 16:49:51 2009     length 2 : 12702
Sun Feb 15 16:49:51 2009     length 3 : 12004
Sun Feb 15 16:49:51 2009     length 4 : 9263
Sun Feb 15 16:49:51 2009     length 5 : 6880
Sun Feb 15 16:49:51 2009     length 6 : 4239
Sun Feb 15 16:49:51 2009     length 7 : 2643
Sun Feb 15 16:49:51 2009     length 9+: 3051
Sun Feb 15 16:49:51 2009  largest cycle: 18 relations
Sun Feb 15 16:49:51 2009  matrix is 62308 x 67691 (16.6 MB) with weight 4091641 (60.45/col)
Sun Feb 15 16:49:51 2009  sparse part has weight 4091641 (60.45/col)
Sun Feb 15 16:49:52 2009  filtering completed in 4 passes
Sun Feb 15 16:49:52 2009  matrix is 57681 x 57745 (13.2 MB) with weight 3241565 (56.14/col)
Sun Feb 15 16:49:52 2009  sparse part has weight 3241565 (56.14/col)
Sun Feb 15 16:49:52 2009  saving the first 48 matrix rows for later
Sun Feb 15 16:49:52 2009  matrix is 57633 x 57745 (8.2 MB) with weight 2515473 (43.56/col)
Sun Feb 15 16:49:52 2009  sparse part has weight 1794001 (31.07/col)
Sun Feb 15 16:49:52 2009  matrix includes 64 packed rows
Sun Feb 15 16:49:52 2009  using block size 23098 for processor cache size 2048 kB
Sun Feb 15 16:49:52 2009  commencing Lanczos iteration
Sun Feb 15 16:49:52 2009  memory use: 8.2 MB
Sun Feb 15 16:50:09 2009  lanczos halted after 913 iterations (dim = 57631)
Sun Feb 15 16:50:09 2009  recovered 15 nontrivial dependencies
Sun Feb 15 16:50:10 2009  prp32 factor: 14226811194310956229338618806873
Sun Feb 15 16:50:10 2009  prp60 factor: 102303162456309080732822575209405595505437738286521037113289
Sun Feb 15 16:50:10 2009  elapsed time 00:00:30

(43·10¹²²-61)/9 = 4(7)₁₂₁1_<123> = 3 · 19² · 389 · 41673733 · 17391826414699782103_<20> · C91

C91 = P41 · P50

P41 = 28184184763523821836019790432528482078337_<41>

P50 = 55518128008771743119102762930430142616557897671791_<50>

Sun Feb 15 15:16:02 2009  Msieve v. 1.38
Sun Feb 15 15:16:02 2009  random seeds: 7f02d460 f08de5ca
Sun Feb 15 15:16:02 2009  factoring 1564733177524189700508302751567064458781574081944760784627626700487602371134391481177091567 (91 digits)
Sun Feb 15 15:16:03 2009  searching for 15-digit factors
Sun Feb 15 15:16:05 2009  commencing quadratic sieve (91-digit input)
Sun Feb 15 15:16:05 2009  using multiplier of 7
Sun Feb 15 15:16:05 2009  using 64kb Pentium 4 sieve core
Sun Feb 15 15:16:05 2009  sieve interval: 18 blocks of size 65536
Sun Feb 15 15:16:05 2009  processing polynomials in batches of 6
Sun Feb 15 15:16:05 2009  using a sieve bound of 1645421 (62353 primes)
Sun Feb 15 15:16:05 2009  using large prime bound of 144797048 (27 bits)
Sun Feb 15 15:16:05 2009  using double large prime bound of 489065930136608 (42-49 bits)
Sun Feb 15 15:16:05 2009  using trial factoring cutoff of 49 bits
Sun Feb 15 15:16:05 2009  polynomial 'A' values have 12 factors
Sun Feb 15 17:32:30 2009  62641 relations (16533 full + 46108 combined from 696963 partial), need 62449
Sun Feb 15 17:32:33 2009  begin with 713496 relations
Sun Feb 15 17:32:34 2009  reduce to 154230 relations in 10 passes
Sun Feb 15 17:32:34 2009  attempting to read 154230 relations
Sun Feb 15 17:32:40 2009  recovered 154230 relations
Sun Feb 15 17:32:40 2009  recovered 134193 polynomials
Sun Feb 15 17:32:40 2009  attempting to build 62641 cycles
Sun Feb 15 17:32:40 2009  found 62641 cycles in 5 passes
Sun Feb 15 17:32:40 2009  distribution of cycle lengths:
Sun Feb 15 17:32:40 2009     length 1 : 16533
Sun Feb 15 17:32:40 2009     length 2 : 11802
Sun Feb 15 17:32:40 2009     length 3 : 10893
Sun Feb 15 17:32:40 2009     length 4 : 8380
Sun Feb 15 17:32:40 2009     length 5 : 6072
Sun Feb 15 17:32:40 2009     length 6 : 3885
Sun Feb 15 17:32:40 2009     length 7 : 2327
Sun Feb 15 17:32:40 2009     length 9+: 2749
Sun Feb 15 17:32:40 2009  largest cycle: 17 relations
Sun Feb 15 17:32:40 2009  matrix is 62353 x 62641 (15.4 MB) with weight 3792217 (60.54/col)
Sun Feb 15 17:32:40 2009  sparse part has weight 3792217 (60.54/col)
Sun Feb 15 17:32:41 2009  filtering completed in 3 passes
Sun Feb 15 17:32:41 2009  matrix is 58535 x 58599 (14.5 MB) with weight 3566489 (60.86/col)
Sun Feb 15 17:32:41 2009  sparse part has weight 3566489 (60.86/col)
Sun Feb 15 17:32:42 2009  saving the first 48 matrix rows for later
Sun Feb 15 17:32:42 2009  matrix is 58487 x 58599 (9.2 MB) with weight 2813987 (48.02/col)
Sun Feb 15 17:32:42 2009  sparse part has weight 2071367 (35.35/col)
Sun Feb 15 17:32:42 2009  matrix includes 64 packed rows
Sun Feb 15 17:32:42 2009  using block size 21845 for processor cache size 512 kB
Sun Feb 15 17:32:42 2009  commencing Lanczos iteration
Sun Feb 15 17:32:42 2009  memory use: 9.0 MB
Sun Feb 15 17:33:16 2009  lanczos halted after 926 iterations (dim = 58485)
Sun Feb 15 17:33:16 2009  recovered 16 nontrivial dependencies
Sun Feb 15 17:33:17 2009  prp41 factor: 28184184763523821836019790432528482078337
Sun Feb 15 17:33:17 2009  prp50 factor: 55518128008771743119102762930430142616557897671791
Sun Feb 15 17:33:17 2009  elapsed time 02:17:15

(43·10¹²¹-61)/9 = 4(7)₁₂₀1_<122> = 41 · 937 · 11969 · 25429687427_<11> · C103

C103 = P35 · P68

P35 = 90194248637814352047759031494690479_<35>

P68 = 45302770742221875681422612444030225099879253011075410319280004436519_<68>

Number: 47771_121
N=4086049368305861293153821232230387164334742283566132179392795643464068457934791786218016782912709202601
  ( 103 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=90194248637814352047759031494690479
 r2=45302770742221875681422612444030225099879253011075410319280004436519
Version: 
Total time: 2.37 hours.
Scaled time: 2.36 units (timescale=0.994).
Factorization parameters were as follows:
n: 4086049368305861293153821232230387164334742283566132179392795643464068457934791786218016782912709202601
m: 1000000000000000000000000
deg: 5
c5: 430
c0: -61
skew: 0.68
type: snfs
lss: 1
rlim: 770000
alim: 770000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 770000/770000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [385000, 685001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 86738 x 86983
Total sieving time: 2.37 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,770000,770000,25,25,46,46,2.2,2.2,50000
total time: 2.37 hours.
 --------- CPU info (if available) ----------

Feb 16, 2009 (3rd)

By Serge Batalov / GMP-ECM / Feb 15, 2009

(64·10³¹³-1)/9 = 7(1)₃₁₃_<314> = 21311665559_<11> · C304

C304 = P32 · C272

P32 = 56869355183867970524925233480563_<32>

C272 = [58673469295479689569217613095246308254466564622209413268305902989491810201228240723973260931840271019115647539071466078885025309304572271657870575907588919118705280718254174488336225167199496315865486233581672561101987944769670437830049389779045700170933931843777556163883_<272>]

Input number is (64*10^313-1)/9/21311665559 (304 digits)
Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=586813494
Step 1 took 11294ms
Step 2 took 8312ms
********** Factor found in step 2: 56869355183867970524925233480563
Found probable prime factor of 32 digits: 56869355183867970524925233480563
Composite cofactor has 272 digits

(64·10³²⁹-1)/9 = 7(1)₃₂₉_<330> = 3 · 25391 · 229689721 · 699955539929_<12> · 1124527993523090279_<19> · C287

C287 = P29 · C259

P29 = 40704154126759059654594607763_<29>

C259 = [1268572766450642491152425150378294135396957255234847563295739922893453854657476574671444949567558350482770410510695204806721172358758008154803977106461792779271742602837417211283835274253110616197477675473057655924764392013624354984613370223714600952428428599_<259>]

Input number is (64*10^329-1)/9/17496155117733/699955539929/1124527993523090279 (287 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1652848252
Step 1 took 10096ms
Step 2 took 5695ms
********** Factor found in step 2: 40704154126759059654594607763
Found probable prime factor of 29 digits: 40704154126759059654594607763
Composite cofactor has 259 digits

(64·10³²⁵-1)/9 = 7(1)₃₂₅_<326> = 2351 · 2693 · 559369 · 409481053 · C305

C305 = P37 · C269

P37 = 2055038511900243647232933024391865987_<37>

C269 = [23861421436245432814856204502196893138753855465286917828862029055337849688154013987993558266773941682867659577131547642497160767247096986685566754254247968589257517588732393442403635800292178906992890301105723560177433653333434641150265701045469843517957678137021325403_<269>]

Input number is (64*10^325-1)/9/2351/2693/559369/409481053 (305 digits)
Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4209806395
Step 1 took 34082ms
Step 2 took 25836ms
********** Factor found in step 2: 2055038511900243647232933024391865987
Found probable prime factor of 37 digits: 2055038511900243647232933024391865987
Composite cofactor ((64*10^325-1)/9/2351/2693/559369/409481053)/2055038511900243647232933024391865987 has 269 digits

By Serge Batalov / GMP-ECM, Msieve-1.39 / Feb 16, 2009

(64·10³⁰⁹-1)/9 = 7(1)₃₀₉_<310> = 13 · 31 · 67 · 199 · 2332951 · 1107465757_<10> · 231408998480608427_<18> · 2433987702761838793853_<22> · 5870493298900966567934867_<25> · 9972146931819828646905779951_<28> · C197

C197 = P30 · P42 · P60 · P67

P30 = 175215362685043374193444272439_<30>

P42 = 135881099877537704102527393172637763005001_<42>

P60 = 455143980801337770203718698452650780386906760272814860845717_<60>

P60 = 1433595695421525345160288214513093277763500173335894023645075916027_<67>

Input number is (64*10^309-1)/(4*10^103-1)/3/31/1107465757 (197 digits)
Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1837215423
Step 1 took 6099ms
Step 2 took 5093ms
********** Factor found in step 2: 175215362685043374193444272439
Found probable prime factor of 30 digits: 175215362685043374193444272439
Composite cofactor has 167 digits

Input number is (64*10^309-1)/(4*10^103-1)/3/31/1107465757/175215362685043374193444272439 (167 digits)
Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2067577463
Step 1 took 50538ms
Step 2 took 33888ms
********** Factor found in step 2: 135881099877537704102527393172637763005001
Found probable prime factor of 42 digits: 135881099877537704102527393172637763005001
Composite cofactor ((64*10^309-1)/(4*10^103-1)/3/31/1107465757/175215362685043374193444272439)/135881099877537704102527393172637763005001 has 126 digits

N=652492451673815201209861895168404601709647029326303666607615459828522384455586028292649098275637500812719004235320429694606359
  ( 126 digits)
Divisors found:
 r1=455143980801337770203718698452650780386906760272814860845717 (pp60)
 r2=1433595695421525345160288214513093277763500173335894023645075916027 (pp67)
Version: Msieve-1.39
Total time: 61 hours.
Scaled time: 179.19 units (timescale=2.948).
Factorization parameters were as follows:
name: t
n: 652492451673815201209861895168404601709647029326303666607615459828522384455586028292649098275637500812719004235320429694606359
skew: 208560.13
# norm 3.79e+17
c5: 20520
c4: -39040291878
c3: -1815988380632129
c2: 1418998931057512282898
c1: 52248932385834119347087434
c0: -8322878027540642438038865640480
# alpha -7.33
Y1: 10998909987373
Y0: -1997471249591076947964299
# Murphy_E 1.51e-10
# M 440071143724497757575898699709739009936761701217522723178112120106975840417089773780803036670841879485242795129300641371276230
type: gnfs
rlim: 8000000
alim: 8000000
lpbr: 27
lpba: 27
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 54/54
Sieved algebraic special-q in [4000000, 7500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1019394 x 1019642
Total sieving time: 50.61 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 1.50 hours. x 4 cpus
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,125,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,27,27,54,54,2.5,2.5,200000
total time: 61 hours.

Feb 16, 2009 (2nd)

Factorizations of 711...11 have been extended up to n=350.

Feb 16, 2009

By Serge Batalov / PFGW / Feb 16, 2009

(43·10¹⁵⁹⁵⁵-61)/9 = 4(7)₁₅₉₅₄1_<15956> is PRP.

(43·10¹⁶⁰⁹⁸-61)/9 = 4(7)₁₆₀₉₇1_<16099> is PRP.

Feb 15, 2009 (6th)

By Erik Branger / GGNFS, Msieve / Feb 15, 2009

(85·10¹⁸⁶+41)/9 = 9(4)₁₈₅9_<187> = 7² · 73 · 2963 · 13879 · 15569 · 249311 · 13535091039564671486279847232684736987_<38> · C130

C130 = P60 · P70

P60 = 292843897769971100638716964000406879520058047538234610226607_<60>

P70 = 4173189726567027680792291651364686867194792560382788150602958007405151_<70>

Number: 94449_186
N=1222093145661488304689087334206869992908799364801631751346153045069664958899170583005647688332917002870930209205870065660169052657
  ( 130 digits)
Divisors found:
 r1=292843897769971100638716964000406879520058047538234610226607
 r2=4173189726567027680792291651364686867194792560382788150602958007405151
Version: 
Total time: 270.00 hours.
Factorization parameters were as follows:
name: 94449_186
n: 1222093145661488304689087334206869992908799364801631751346153045069664958899170583005647688332917002870930209205870065660169052657
skew: 510698.00
Y0: -7656719028100712519179654
Y1:  142321670357531
c0:  1167978539070622701566323783130925
c1:  5304559839315764477186444265
c2: -3710644512753648335949
c3: -35176895023575725
c4: -8370219004
c5:  46440
type: gnfs
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [5500000, 13300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1252951 x 1253199
Total sieving time: 99.99 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,129,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,11000000,11000000,27,27,51,51,2.6,2.6,100000
total time: 270.00 hours.
 --------- CPU info (if available) ----------

Feb 15, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 15, 2009

(14·10¹⁵⁴+1)/3 = 4(6)₁₅₃7_<155> = 293 · 7512655541259282306331650654533633_<34> · C119

C119 = P41 · P78

P41 = 54231808989727239423216603755622960161369_<41>

P78 = 390923332769930875603107034278747100755856831370854327511895410945686871799847_<78>

Number: 46667_154
N=21200479512406470387486737841689387728256616761959944459277057188240292447586447134939384922724107131176462502589510543
  ( 119 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=54231808989727239423216603755622960161369
 r2=390923332769930875603107034278747100755856831370854327511895410945686871799847
Version: 
Total time: 8.87 hours.
Scaled time: 21.14 units (timescale=2.384).
Factorization parameters were as follows:
n: 21200479512406470387486737841689387728256616761959944459277057188240292447586447134939384922724107131176462502589510543
m: 10000000000000000000000000000000
deg: 5
c5: 7
c0: 5
skew: 0.93
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1100000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8302757
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 366414 x 366662
Total sieving time: 8.12 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000
total time: 8.87 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(14·10¹⁷⁵-11)/3 = 4(6)₁₇₄3_<176> = 19 · 18637 · 883431433 · 1059339599_<10> · 163183031653807813_<18> · 387506515120886326479029_<24> · C112

C112 = P53 · P59

P53 = 39458651391662737560426731250115138746054521972087131_<53>

P59 = 56438163889499086885495949504388402747909851042790704623549_<59>

Number: 46663_175
N=2226973834101272806078695268331691820297865666351981094067120577496103583990954688153969172760108806003182447919
  ( 112 digits)
Divisors found:
 r1=39458651391662737560426731250115138746054521972087131
 r2=56438163889499086885495949504388402747909851042790704623549
Version: 
Total time: 11.13 hours.
Scaled time: 25.91 units (timescale=2.327).
Factorization parameters were as follows:
name: 46663_175
n: 2226973834101272806078695268331691820297865666351981094067120577496103583990954688153969172760108806003182447919
skew: 18558.79
# norm 2.18e+15
c5: 48300
c4: 154232447
c3: -77704578312477
c2: 1515535832638192026
c1: 6186317058615615263235
c0: -184906614236828287925975
# alpha -5.68
Y1: 1058921340037
Y0: -2151559993028487286086
# Murphy_E 8.38e-10
# M 1641793509583862624017536670586366418670310473889377820970417999873360158999715871821814994386591398598360466243
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1200000, 1980001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8230458
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 408250 x 408498
Polynomial selection time: 0.93 hours.
Total sieving time: 8.99 hours.
Total relation processing time: 0.52 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000
total time: 11.13 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 15, 2009 (4th)

By Sinkiti Sibata / Msieve / Feb 15, 2009

(14·10¹⁴⁷+1)/3 = 4(6)₁₄₆7_<148> = 13 · 71 · 10821683 · 415360308636593_<15> · C124

C124 = P53 · P71

P53 = 59211116240071953560041490929300702713976962338049427_<53>

P71 = 18996869093972672801989286866587901833146301492603126387978691101914233_<71>

Number: 46667_147
N=1124825824120646305023027673995572656480837216059662782981628272312007636368630268568362380512011078237498677112251068794491
  ( 124 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=59211116240071953560041490929300702713976962338049427
 r2=18996869093972672801989286866587901833146301492603126387978691101914233
Version: 
Total time: 14.36 hours.
Scaled time: 27.90 units (timescale=1.943).
Factorization parameters were as follows:
name: 46667_147
n: 1124825824120646305023027673995572656480837216059662782981628272312007636368630268568362380512011078237498677112251068794491
m: 500000000000000000000000000000
deg: 5
c5: 56
c0: 125
skew: 1.17
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1100000, 1600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 318450 x 318698
Total sieving time: 14.36 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,49,49,2.4,2.4,100000
total time: 14.36 hours.
 --------- CPU info (if available) ----------

(14·10¹⁹⁶+1)/3 = 4(6)₁₉₅7_<197> = 19 · 88125623503_<11> · 63724402211023850353_<20> · 174979598539031380917131233_<27> · 300304125643577097155478944475718909_<36> · C103

C103 = P35 · P69

P35 = 36569467023955655702572987728072281_<35>

P69 = 227602936992216342653791484918798807288750684295729520069400243313211_<69>

Sat Feb 14 08:07:36 2009  Msieve v. 1.39
Sat Feb 14 08:07:36 2009  random seeds: 54bcde54 f0c5251e
Sat Feb 14 08:07:36 2009  factoring 8323318098892312395018467980900645024149797138390385911208071430477385229001986137257942282261530204291 (103 digits)
Sat Feb 14 08:07:37 2009  searching for 15-digit factors
Sat Feb 14 08:07:39 2009  commencing quadratic sieve (103-digit input)
Sat Feb 14 08:07:39 2009  using multiplier of 3
Sat Feb 14 08:07:39 2009  using 32kb Intel Core sieve core
Sat Feb 14 08:07:39 2009  sieve interval: 36 blocks of size 32768
Sat Feb 14 08:07:39 2009  processing polynomials in batches of 6
Sat Feb 14 08:07:39 2009  using a sieve bound of 3491867 (125000 primes)
Sat Feb 14 08:07:39 2009  using large prime bound of 523780050 (28 bits)
Sat Feb 14 08:07:39 2009  using double large prime bound of 4948437687597450 (44-53 bits)
Sat Feb 14 08:07:39 2009  using trial factoring cutoff of 53 bits
Sat Feb 14 08:07:39 2009  polynomial 'A' values have 14 factors
Sun Feb 15 10:05:35 2009  125322 relations (29305 full + 96017 combined from 1879366 partial), need 125096
Sun Feb 15 10:05:38 2009  begin with 1908671 relations
Sun Feb 15 10:05:40 2009  reduce to 331728 relations in 12 passes
Sun Feb 15 10:05:40 2009  attempting to read 331728 relations
Sun Feb 15 10:05:47 2009  recovered 331728 relations
Sun Feb 15 10:05:47 2009  recovered 324855 polynomials
Sun Feb 15 10:05:48 2009  attempting to build 125322 cycles
Sun Feb 15 10:05:48 2009  found 125322 cycles in 6 passes
Sun Feb 15 10:05:48 2009  distribution of cycle lengths:
Sun Feb 15 10:05:48 2009     length 1 : 29305
Sun Feb 15 10:05:48 2009     length 2 : 21336
Sun Feb 15 10:05:48 2009     length 3 : 21156
Sun Feb 15 10:05:48 2009     length 4 : 17003
Sun Feb 15 10:05:48 2009     length 5 : 13040
Sun Feb 15 10:05:48 2009     length 6 : 9175
Sun Feb 15 10:05:48 2009     length 7 : 5943
Sun Feb 15 10:05:48 2009     length 9+: 8364
Sun Feb 15 10:05:48 2009  largest cycle: 22 relations
Sun Feb 15 10:05:48 2009  matrix is 125000 x 125322 (36.0 MB) with weight 8946269 (71.39/col)
Sun Feb 15 10:05:48 2009  sparse part has weight 8946269 (71.39/col)
Sun Feb 15 10:05:51 2009  filtering completed in 3 passes
Sun Feb 15 10:05:51 2009  matrix is 120297 x 120361 (34.8 MB) with weight 8630529 (71.71/col)
Sun Feb 15 10:05:51 2009  sparse part has weight 8630529 (71.71/col)
Sun Feb 15 10:05:51 2009  saving the first 48 matrix rows for later
Sun Feb 15 10:05:51 2009  matrix is 120249 x 120361 (22.1 MB) with weight 6954167 (57.78/col)
Sun Feb 15 10:05:51 2009  sparse part has weight 5074835 (42.16/col)
Sun Feb 15 10:05:51 2009  matrix includes 64 packed rows
Sun Feb 15 10:05:51 2009  using block size 43690 for processor cache size 1024 kB
Sun Feb 15 10:05:52 2009  commencing Lanczos iteration
Sun Feb 15 10:05:52 2009  memory use: 21.0 MB
Sun Feb 15 10:07:37 2009  lanczos halted after 1904 iterations (dim = 120247)
Sun Feb 15 10:07:37 2009  recovered 17 nontrivial dependencies
Sun Feb 15 10:07:38 2009  prp35 factor: 36569467023955655702572987728072281
Sun Feb 15 10:07:38 2009  prp69 factor: 227602936992216342653791484918798807288750684295729520069400243313211
Sun Feb 15 10:07:38 2009  elapsed time 26:00:02

Feb 15, 2009 (3rd)

By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1 / Feb 15, 2009

(14·10¹⁷⁰+1)/3 = 4(6)₁₆₉7_<171> = 46743868447870267651_<20> · C151

C151 = P48 · P104

P48 = 104294166814274386903054982107897366760334221897_<48>

P104 = 95724280549876303733349614934130035922104058690830754970637258308603613525009196486295646799077246779761_<104>

SNFS difficulty: 171 digits.
Divisors found:
 r1=104294166814274386903054982107897366760334221897 (pp48)
 r2=95724280549876303733349614934130035922104058690830754970637258308603613525009196486295646799077246779761 (pp104)
Version: Msieve-1.39
Total time: 30.32 hours.
Scaled time:  units (timescale=2.950).
Factorization parameters were as follows:
n: 9983484083845200357518942533658895832376749692236922937893888318516337912293695221613470764610702632769022446093554356116181010244931137412628862626617
m: 10000000000000000000000000000000000
deg: 5
c5: 14
c0: 1
skew: 0.59
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 4500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 883374 x 883621
Total sieving time: 22.32 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 1.60 hours. * 4
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,200000
total time: 30.32 hours.

7·10¹⁹⁵-3 = 6(9)₁₉₄7_<196> = 139 · 3067 · 17876051 · 24527621194063819800299250874272523_<35> · C149

C149 = P38 · P112

P38 = 10810175462712766378399682400374658337_<38>

P112 = 3464253826178025203451630850730623859360665647158270629727669693950603939546671253113435093020109567689734805669_<112>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=705256189
Step 1 took 58911ms
Step 2 took 44658ms
********** Factor found in step 2: 10810175462712766378399682400374658337
Found probable prime factor of 38 digits: 10810175462712766378399682400374658337
probable prime cofactor

(8·10¹⁸¹-53)/9 = (8)₁₈₀3_<181> = 3 · 3373 · 104548979020861334868919_<24> · C154

C154 = P35 · P120

P35 = 12499821320686222156090511981140217_<35>

P120 = 672181074501094515150749049807572101902956191960026465193303607551381843935978711469108196973715165015264234761959682059_<120>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1439701945
Step 1 took 45437ms
Step 2 took 35187ms
********** Factor found in step 2: 12499821320686222156090511981140217
Found probable prime factor of 35 digits: 12499821320686222156090511981140217
Probable prime cofactor has 120 digits

(28·10¹⁹⁰+71)/9 = 3(1)₁₈₉9_<191> = 3 · 11 · 19 · 118571561 · C180

C180 = P41 · C139

P41 = 72948732985607639943348271937061875858767_<41>

C139 = [5736535564946222076701029625873664000242757235671459219099940391735526356194060277001714023463867870843827613222563476713106720501742427331_<139>]

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=2901755410
Step 1 took 59001ms
Step 2 took 44783ms
********** Factor found in step 2: 72948732985607639943348271937061875858767
Found probable prime factor of 41 digits: 72948732985607639943348271937061875858767
Composite cofactor has 139 digits

(8·10¹⁸⁹-53)/9 = (8)₁₈₈3_<189> = 67 · 3715079 · 3805037 · 5562883 · C168

C168 = P39 · P129

P39 = 264803101224449082168597348476311611311_<39>

P129 = 637122209537919103959346621143746198671213839806088223842581849059827407105588908456565553663175429328843741231582163026217491951_<129>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1970532011
Step 1 took 50602ms
Step 2 took 39936ms
********** Factor found in step 2: 264803101224449082168597348476311611311
Found probable prime factor of 39 digits: 264803101224449082168597348476311611311
Probable prime cofactor has 129 digits

Feb 15, 2009 (2nd)

Factorizations of 477...771 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Feb 15, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 15, 2009

(14·10¹⁵³+1)/3 = 4(6)₁₅₂7_<154> = 13² · 9187433068570610519_<19> · 85252816908018269189_<20> · C113

C113 = P54 · P59

P54 = 432646889532735937305204725920593650955996146661358049_<54>

P59 = 81486106008963007311412437866254747504214979242895064015777_<59>

Number: 46667_153
N=35254710304912628291403028187926064483943842176341801575918120849567564630525220153645723046212671844646381939073
  ( 113 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=432646889532735937305204725920593650955996146661358049
 r2=81486106008963007311412437866254747504214979242895064015777
Version: 
Total time: 9.75 hours.
Scaled time: 23.18 units (timescale=2.377).
Factorization parameters were as follows:
n: 35254710304912628291403028187926064483943842176341801575918120849567564630525220153645723046212671844646381939073
m: 10000000000000000000000000000000
deg: 5
c5: 7
c0: 50
skew: 1.48
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1100000, 2000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7765803
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 459979 x 460227
Total sieving time: 8.90 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000
total time: 9.75 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 14, 2009 (5th)

By matsui / GGNFS / Feb 14, 2009

2·10²⁰⁰-3 = 1(9)₁₉₉7_<201> = 3917 · C197

C197 = P52 · P60 · P87

P52 = 1353143889460780219324261867805948229627354629623799_<52>

P60 = 107421636386525513520653234479254640339061189356540018700131_<60>

P87 = 351269691736020689086731151005390507435230742784114223916529804772069637453814458555389_<87>

N=51059484299208577993362267041102884860862905284656624968087822312994638754148583099310696961960684197089609394945111054378350778657135562930814398774572376818994128159305591013530763339290273168241
  ( 197 digits)
SNFS difficulty: 200 digits.
Divisors found:
 r1=1353143889460780219324261867805948229627354629623799 (pp52)
 r2=107421636386525513520653234479254640339061189356540018700131 (pp60)
 r3=351269691736020689086731151005390507435230742784114223916529804772069637453814458555389 (pp87)
Version: GGNFS-0.77.1-20060722-nocona

Feb 14, 2009 (4th)

By Sinkiti Sibata / Msieve / Feb 14, 2009

(14·10¹⁶⁶+1)/3 = 4(6)₁₆₅7_<167> = 227 · 93609576563291_<14> · 6410436491169121721_<19> · 8567432506482975511227306736847_<31> · C101

C101 = P48 · P54

P48 = 105837646301488096064392853135688270797190690443_<48>

P54 = 377817592382338625566553437445757380341481911272332791_<54>

Fri Feb 13 12:23:57 2009  Msieve v. 1.39
Fri Feb 13 12:23:57 2009  random seeds: c697f178 e036b717
Fri Feb 13 12:23:57 2009  factoring 39987324709041758691823561140139597659692108721927001185977095775180330550267978236047812260559216413 (101 digits)
Fri Feb 13 12:23:58 2009  searching for 15-digit factors
Fri Feb 13 12:23:59 2009  commencing quadratic sieve (101-digit input)
Fri Feb 13 12:24:00 2009  using multiplier of 5
Fri Feb 13 12:24:00 2009  using 32kb Intel Core sieve core
Fri Feb 13 12:24:00 2009  sieve interval: 36 blocks of size 32768
Fri Feb 13 12:24:00 2009  processing polynomials in batches of 6
Fri Feb 13 12:24:00 2009  using a sieve bound of 2974607 (107273 primes)
Fri Feb 13 12:24:00 2009  using large prime bound of 446191050 (28 bits)
Fri Feb 13 12:24:00 2009  using double large prime bound of 3707981036623950 (44-52 bits)
Fri Feb 13 12:24:00 2009  using trial factoring cutoff of 52 bits
Fri Feb 13 12:24:00 2009  polynomial 'A' values have 13 factors
Sat Feb 14 03:55:15 2009  107440 relations (25168 full + 82272 combined from 1625467 partial), need 107369
Sat Feb 14 03:55:17 2009  begin with 1650635 relations
Sat Feb 14 03:55:19 2009  reduce to 286005 relations in 11 passes
Sat Feb 14 03:55:19 2009  attempting to read 286005 relations
Sat Feb 14 03:55:25 2009  recovered 286005 relations
Sat Feb 14 03:55:25 2009  recovered 278001 polynomials
Sat Feb 14 03:55:25 2009  attempting to build 107440 cycles
Sat Feb 14 03:55:25 2009  found 107440 cycles in 6 passes
Sat Feb 14 03:55:25 2009  distribution of cycle lengths:
Sat Feb 14 03:55:25 2009     length 1 : 25168
Sat Feb 14 03:55:25 2009     length 2 : 18101
Sat Feb 14 03:55:25 2009     length 3 : 17717
Sat Feb 14 03:55:25 2009     length 4 : 14669
Sat Feb 14 03:55:25 2009     length 5 : 11309
Sat Feb 14 03:55:25 2009     length 6 : 7873
Sat Feb 14 03:55:25 2009     length 7 : 5171
Sat Feb 14 03:55:25 2009     length 9+: 7432
Sat Feb 14 03:55:25 2009  largest cycle: 21 relations
Sat Feb 14 03:55:26 2009  matrix is 107273 x 107440 (30.8 MB) with weight 7645489 (71.16/col)
Sat Feb 14 03:55:26 2009  sparse part has weight 7645489 (71.16/col)
Sat Feb 14 03:55:28 2009  filtering completed in 3 passes
Sat Feb 14 03:55:28 2009  matrix is 103299 x 103363 (29.8 MB) with weight 7398436 (71.58/col)
Sat Feb 14 03:55:28 2009  sparse part has weight 7398436 (71.58/col)
Sat Feb 14 03:55:28 2009  saving the first 48 matrix rows for later
Sat Feb 14 03:55:28 2009  matrix is 103251 x 103363 (19.5 MB) with weight 5997541 (58.02/col)
Sat Feb 14 03:55:28 2009  sparse part has weight 4487591 (43.42/col)
Sat Feb 14 03:55:28 2009  matrix includes 64 packed rows
Sat Feb 14 03:55:28 2009  using block size 41345 for processor cache size 1024 kB
Sat Feb 14 03:55:29 2009  commencing Lanczos iteration
Sat Feb 14 03:55:29 2009  memory use: 18.2 MB
Sat Feb 14 03:56:55 2009  lanczos halted after 1634 iterations (dim = 103249)
Sat Feb 14 03:56:55 2009  recovered 17 nontrivial dependencies
Sat Feb 14 03:56:56 2009  prp48 factor: 105837646301488096064392853135688270797190690443
Sat Feb 14 03:56:56 2009  prp54 factor: 377817592382338625566553437445757380341481911272332791
Sat Feb 14 03:56:56 2009  elapsed time 15:32:59

(14·10¹⁴⁴+1)/3 = 4(6)₁₄₃7_<145> = 34231 · 112734187101659502097272353_<27> · C115

C115 = P53 · P62

P53 = 41860487605074545822214730527238787086921508635630057_<53>

P62 = 28888651782642712901521098516490340221304589902980438590000517_<62>

Number: 46667_144
N=1209293049874629965857509671889586266473728920998546232084066695052908898286693988441135423590198309266664250739469
  ( 115 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=41860487605074545822214730527238787086921508635630057
 r2=28888651782642712901521098516490340221304589902980438590000517
Version: 
Total time: 9.39 hours.
Scaled time: 18.52 units (timescale=1.972).
Factorization parameters were as follows:
name: 46667_144
n: 1209293049874629965857509671889586266473728920998546232084066695052908898286693988441135423590198309266664250739469
m: 100000000000000000000000000000
deg: 5
c5: 7
c0: 5
skew: 0.93
type: snfs
lss: 1
rlim: 1890000
alim: 1890000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1890000/1890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [945000, 1845001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 267507 x 267755
Total sieving time: 9.39 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1890000,1890000,26,26,49,49,2.3,2.3,100000
total time: 9.39 hours.
 --------- CPU info (if available) ----------

Feb 14, 2009 (3rd)

By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1 / Feb 14, 2009

(14·10¹⁶⁵-11)/3 = 4(6)₁₆₄3_<166> = 1187 · C163

C163 = P53 · P110

P53 = 75273344314006455047373618700306263254729554245011119_<53>

P110 = 52229377573155775722074013780922150979377281646505623065824363308585613892793884921603674014013584366953471971_<110>

SNFS difficulty: 166 digits.
Divisors found:
 r1=75273344314006455047373618700306263254729554245011119 (pp53)
 r2=52229377573155775722074013780922150979377281646505623065824363308585613892793884921603674014013584366953471971 (pp110)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.917).
Factorization parameters were as follows:
n: 3931479921370401572591968548160629036787419264251614714967705700645885987082280258354394832912103341757933164841336703173265936534681269306374613872507722549845549
m: 1000000000000000000000000000000000
deg: 5
c5: 14
c0: -11
skew: 0.95
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2050000, 3650001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 739970 x 740218
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,52,52,2.4,2.4,200000
total time: 29.00 hours.

(10¹⁹⁵+17)/9 = (1)₁₉₄3_<195> = 89 · 839 · 46337 · C185

C185 = P39 · P147

P39 = 180219932950749045834203315868394030019_<39>

P147 = 178186495547831158629886584868040389093978707544314165250237649071872527239633949856494301323944055336016195990546166140103456946868516762554689901_<147>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=410370439
Step 1 took 58922ms
Step 2 took 44850ms
********** Factor found in step 2: 180219932950749045834203315868394030019
Found probable prime factor of 39 digits: 180219932950749045834203315868394030019
Probable prime cofactor has 147 digits

(10¹⁹⁹+17)/9 = (1)₁₉₈3_<199> = 3 · 53 · 61 · 5261569 · 14429307007535652733_<20> · 28953978442052238625370216321_<29> · C140

C140 = P44 · P47 · P50

P44 = 22030472258797275743537418347333146628457907_<44>

P47 = 34282597905119932900091785459591793403348759523_<47>

P50 = 69002370162380621152740212076872714098090972363351_<50>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1005177743
Step 1 took 43500ms
Step 2 took 35167ms
********** Factor found in step 2: 34282597905119932900091785459591793403348759523
Found probable prime factor of 47 digits: 34282597905119932900091785459591793403348759523
Composite cofactor has 94 digits

N=1520154801653587145519307402953669982384665387658339424932743614496399400375403119312412966357
  ( 94 digits)
Divisors found:
 r1=22030472258797275743537418347333146628457907 (pp44)
 r2=69002370162380621152740212076872714098090972363351 (pp50)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
name: t
n:  1520154801653587145519307402953669982384665387658339424932743614496399400375403119312412966357
m:  2670485256132997099992
deg: 4
c4: 29890080
c3: -13117314349
c2: -242242966401244948
c1: 324114490938892144
c0: 357487177208619254665813
skew: 1635.250
type: gnfs
# adj. I(F,S) = 53.124
# E(F1,F2) = 6.714689e-05
# GGNFS version 0.77.1-20060722-k8 polyselect.
# Options were:
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1234577083.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 140362 x 140589
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 3.00 hours.

(4·10¹⁹¹+41)/9 = (4)₁₉₀9_<191> = 9445455512599_<13> · 568330868941154509_<18> · 18527367251974270369_<20> · C141

C141 = P39 · P103

P39 = 335732563467571075947367193609809575347_<39>

P103 = 1331024816574415178535198740376933736414450937292699184327359822630102869705402231438438248290257348273_<103>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=152571016
Step 1 took 43365ms
Step 2 took 29504ms
********** Factor found in step 2: 335732563467571075947367193609809575347
Found probable prime factor of 39 digits: 335732563467571075947367193609809575347
Probable prime cofactor has 103 digits

7·10¹⁸⁶-3 = 6(9)₁₈₅7_<187> = 887 · 439823 · 1196059 · 1026017623085007713_<19> · C155

C155 = P32 · P123

P32 = 92337907616891958329226316547999_<32>

P123 = 158346705035860066410666443177431638272396001523007818205086265361406331827017357270653495045419576915774032335665253102209_<123>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2080995158
Step 1 took 52056ms
Step 2 took 32746ms
********** Factor found in step 2: 92337907616891958329226316547999
Found probable prime factor of 32 digits: 92337907616891958329226316547999
Probable prime cofactor 158346705035860066410666443177431638272396001523007818205086265361406331827017357270653495045419576915774032335665253102209 has 123 digits

5·10¹⁸⁴-7 = 4(9)₁₈₃3_<185> = 59 · 2381 · 3823 · 6566081 · 31425551790847_<14> · C156

C156 = P41 · P115

P41 = 80039443926543333426030393619033027817759_<41>

P115 = 5637169435779042518564618258869429332554961926507393446662237475156718430440794073039044584353258208612957374372233_<115>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2736760227
Step 1 took 51483ms
Step 2 took 33748ms
********** Factor found in step 2: 80039443926543333426030393619033027817759
Found probable prime factor of 41 digits: 80039443926543333426030393619033027817759
Probable prime cofactor 5637169435779042518564618258869429332554961926507393446662237475156718430440794073039044584353258208612957374372233 has 115 digits

7·10¹⁹⁵-3 = 6(9)₁₉₄7_<196> = 139 · 3067 · 17876051 · C183

C183 = P35 · C149

P35 = 24527621194063819800299250874272523_<35>

C149 = [37449191708358504951512531418661234354118514299816902412910533299054998461221910284706013330562360986172625399055406703880777217563744499862965712453_<149>]

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=2507872870
Step 1 took 59190ms
Step 2 took 46541ms
********** Factor found in step 2: 24527621194063819800299250874272523
Found probable prime factor of 35 digits: 24527621194063819800299250874272523
Composite cofactor has 149 digits

(4·10¹⁸⁴+41)/9 = (4)₁₈₃9_<184> = 3 · 493859316479_<12> · C172

C172 = P40 · C133

P40 = 1028468656901316025194870592631166453493_<40>

C133 = [2916768192185476209130600299020222703251001859873551312550186038537008789362831619096830736907690865140108164330933656050977865580289_<133>]

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1065531543
Step 1 took 50760ms
Step 2 took 41555ms
********** Factor found in step 2: 1028468656901316025194870592631166453493
Found probable prime factor of 40 digits: 1028468656901316025194870592631166453493
Composite cofactor has 133 digits

8·10¹⁷⁰-7 = 7(9)₁₆₉3_<171> = 13 · 167 · 173 · 3527 · 1164843975864664079_<19> · C144

C144 = P39 · P106

P39 = 267225671577587886263333427818158723483_<39>

P106 = 1940138194737605546964094210184209125694364459325237602677778591219159584108616662614835144171508335314589_<106>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=4243394023
Step 1 took 43630ms
Step 2 took 10886ms
********** Factor found in step 2: 267225671577587886263333427818158723483
Found probable prime factor of 39 digits: 267225671577587886263333427818158723483
Probable prime cofactor has 106 digits

(28·10¹⁹⁴+71)/9 = 3(1)₁₉₃9_<195> = 11² · 41 · 1674922471_<10> · 1474538095136372480044028131_<28> · C155

C155 = P36 · C119

P36 = 267407641043367558042632242380571217_<36>

C119 = [94955860921945704007355546974800936804246583000431312236385646536971406882241375331831813631952300999296434499069136387_<119>]

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=710368225
Step 1 took 55001ms
Step 2 took 37692ms
********** Factor found in step 2: 267407641043367558042632242380571217
Found probable prime factor of 36 digits: 267407641043367558042632242380571217
Composite cofactor has 119 digits

8·10¹⁹⁶-7 = 7(9)₁₉₅3_<197> = 5531 · 358990876536924989546737_<24> · C170

C170 = P36 · P135

P36 = 214605166213413649753799079575549309_<36>

P135 = 187742563889361910433535169521129458961729353440826580401787271210018504832215823551155968418007570578866423270571979403524548052497991_<135>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=1664096161
Step 1 took 50439ms
Step 2 took 41184ms
********** Factor found in step 2: 214605166213413649753799079575549309
Found probable prime factor of 36 digits: 214605166213413649753799079575549309
Probable prime cofactor has 135 digits

(8·10¹⁸²-53)/9 = (8)₁₈₁3_<182> = 157 · 499 · 22385351 · C170

C170 = P38 · P133

P38 = 20927507877603562216772481531959930821_<38>

P133 = 2421953813812902991229062272111059316848736284277459734782495754095937631298254836200644777053879601560333590388382682997464506923911_<133>

Using B1=11000000, B2=96175819756, polynomial Dickson(12), sigma=2787302746
Step 1 took 50683ms
Step 2 took 40992ms
********** Factor found in step 2: 20927507877603562216772481531959930821
Found probable prime factor of 38 digits: 20927507877603562216772481531959930821
Probable prime cofactor has 133 digits

Feb 14, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Feb 14, 2009

(14·10¹⁴³+1)/3 = 4(6)₁₄₂7_<144> = 9020890114447567_<16> · C128

C128 = P45 · P84

P45 = 260954755813331551484629836671841329424589369_<45>

P84 = 198240403140835028113695300828948914392004001895842843502933578491559379460150732429_<84>

Number: 46667_143
N=51731775993953009910301308419212924796902674648198394769006101620615186310053836176840364665870571890912291010439718267916947301
  ( 128 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=260954755813331551484629836671841329424589369
 r2=198240403140835028113695300828948914392004001895842843502933578491559379460150732429
Version: 
Total time: 12.09 hours.
Scaled time: 9.46 units (timescale=0.782).
Factorization parameters were as follows:
n: 51731775993953009910301308419212924796902674648198394769006101620615186310053836176840364665870571890912291010439718267916947301
m: 100000000000000000000000000000
deg: 5
c5: 7
c0: 50
skew: 1.48
type: snfs
lss: 1
rlim: 1900000
alim: 1900000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3

Factor base limits: 1900000/1900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [950000, 2050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 309798 x 310046
Total sieving time: 12.09 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000
total time: 12.09 hours.
 --------- CPU info (if available) ----------

Feb 14, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 14, 2009

(14·10¹⁴⁹+1)/3 = 4(6)₁₄₈7_<150> = 17 · 1433 · 88848637 · 29178780371701_<14> · C124

C124 = P59 · P66

P59 = 52085636918944088812203312210504732508023447832895818013441_<59>

P66 = 141865170733330080376212873778627147222277396429992237445479582291_<66>

Number: 46669_149
N=7389137774260243688053830273352604246508616558218557111613676233755812817641078542381629932217207801812449835065450103573331
  ( 124 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=52085636918944088812203312210504732508023447832895818013441
 r2=141865170733330080376212873778627147222277396429992237445479582291
Version: 
Total time: 5.45 hours.
Scaled time: 12.87 units (timescale=2.360).
Factorization parameters were as follows:
n: 7389137774260243688053830273352604246508616558218557111613676233755812817641078542381629932217207801812449835065450103573331
m: 1000000000000000000000000000000
deg: 5
c5: 7
c0: 5
skew: 0.93
type: snfs
lss: 1
rlim: 1800000
alim: 1800000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [900000, 1400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 6346214
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 348304 x 348552
Total sieving time: 4.98 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,27,27,49,49,2.4,2.4,100000
total time: 5.45 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(14·10¹⁵²+1)/3 = 4(6)₁₅₁7_<153> = 1259 · 4449581879_<10> · 31680660311933_<14> · C127

C127 = P51 · P77

P51 = 164419801792715399978720014469178894785688300264421_<51>

P77 = 15992394807860943672501515269727850107518587694312563080621071031105148189079_<77>

Number: 46667_152
N=2629466384499347241036001490457162666115412103509341476457525842912585465822458952893668770251581037113343323667412465004458259
  ( 127 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=164419801792715399978720014469178894785688300264421
 r2=15992394807860943672501515269727850107518587694312563080621071031105148189079
Version: 
Total time: 7.86 hours.
Scaled time: 18.80 units (timescale=2.392).
Factorization parameters were as follows:
n: 2629466384499347241036001490457162666115412103509341476457525842912585465822458952893668770251581037113343323667412465004458259
m: 2000000000000000000000000000000
deg: 5
c5: 175
c0: 4
skew: 0.47
type: snfs
lss: 1
rlim: 2200000
alim: 2200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1100000, 1800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8279462
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 340575 x 340823
Total sieving time: 7.23 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000
total time: 7.86 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 13, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 13, 2009

(13·10¹⁹⁵+17)/3 = 4(3)₁₉₄9_<196> = C196

C196 = P44 · P49 · P104

P44 = 43038594302076212180404662503389491920977571_<44>

P49 = 6396895104394665782573448096012043723085976503681_<49>

P104 = 15739639826095135291644801789933718287314134718487647918772287020703181372193969444606666771292347715689_<104>

Number: 43339_195
N=4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339
  ( 196 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=43038594302076212180404662503389491920977571
 r2=6396895104394665782573448096012043723085976503681
 r3=15739639826095135291644801789933718287314134718487647918772287020703181372193969444606666771292347715689
Version: 
Total time: 283.07 hours.
Scaled time: 674.00 units (timescale=2.381).
Factorization parameters were as follows:
n: 4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339
m: 1000000000000000000000000000000000000000
deg: 5
c5: 13
c0: 17
skew: 1.06
type: snfs
lss: 1
rlim: 15000000
alim: 15000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 15000000/15000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [7500000, 14100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 23478985
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2445387 x 2445635
Total sieving time: 256.46 hours.
Total relation processing time: 8.45 hours.
Matrix solve time: 17.08 hours.
Time per square root: 1.08 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,15000000,15000000,28,28,55,55,2.5,2.5,100000
total time: 283.07 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 13, 2009 (4th)

By Erik Branger / Msieve / Feb 13, 2009

(14·10¹⁶²+1)/3 = 4(6)₁₆₁7_<163> = 139 · 599 · 37243 · 1143529 · 521121781 · 85455939917603_<14> · 399007013662755691469737714633_<30> · C95

C95 = P42 · P53

P42 = 780810284493164937541387674186542177655467_<42>

P53 = 94856213196199882289140137695997617853942491092295137_<53>

Thu Feb 12 17:48:12 2009  Msieve v. 1.38
Thu Feb 12 17:48:12 2009  random seeds: bd78225c 7d519f38
Thu Feb 12 17:48:12 2009  factoring 74064706811669136267266549263175661936240043622241422381737475862705723444971303591286665563979 (95 digits)
Thu Feb 12 17:48:14 2009  searching for 15-digit factors
Thu Feb 12 17:48:15 2009  commencing quadratic sieve (95-digit input)
Thu Feb 12 17:48:16 2009  using multiplier of 35
Thu Feb 12 17:48:16 2009  using 64kb Pentium 4 sieve core
Thu Feb 12 17:48:16 2009  sieve interval: 18 blocks of size 65536
Thu Feb 12 17:48:16 2009  processing polynomials in batches of 6
Thu Feb 12 17:48:16 2009  using a sieve bound of 2193701 (81176 primes)
Thu Feb 12 17:48:16 2009  using large prime bound of 329055150 (28 bits)
Thu Feb 12 17:48:16 2009  using double large prime bound of 2143303351966200 (43-51 bits)
Thu Feb 12 17:48:16 2009  using trial factoring cutoff of 51 bits
Thu Feb 12 17:48:16 2009  polynomial 'A' values have 12 factors
Fri Feb 13 00:06:21 2009  81352 relations (19911 full + 61441 combined from 1214476 partial), need 81272
Fri Feb 13 00:06:27 2009  begin with 1234387 relations
Fri Feb 13 00:06:29 2009  reduce to 211622 relations in 11 passes
Fri Feb 13 00:06:29 2009  attempting to read 211622 relations
Fri Feb 13 00:06:35 2009  recovered 211622 relations
Fri Feb 13 00:06:35 2009  recovered 196858 polynomials
Fri Feb 13 00:06:35 2009  attempting to build 81352 cycles
Fri Feb 13 00:06:35 2009  found 81352 cycles in 6 passes
Fri Feb 13 00:06:35 2009  distribution of cycle lengths:
Fri Feb 13 00:06:35 2009     length 1 : 19911
Fri Feb 13 00:06:35 2009     length 2 : 14320
Fri Feb 13 00:06:35 2009     length 3 : 13518
Fri Feb 13 00:06:35 2009     length 4 : 11192
Fri Feb 13 00:06:35 2009     length 5 : 8350
Fri Feb 13 00:06:35 2009     length 6 : 5604
Fri Feb 13 00:06:35 2009     length 7 : 3538
Fri Feb 13 00:06:35 2009     length 9+: 4919
Fri Feb 13 00:06:35 2009  largest cycle: 20 relations
Fri Feb 13 00:06:36 2009  matrix is 81176 x 81352 (22.7 MB) with weight 5613162 (69.00/col)
Fri Feb 13 00:06:36 2009  sparse part has weight 5613162 (69.00/col)
Fri Feb 13 00:06:37 2009  filtering completed in 3 passes
Fri Feb 13 00:06:37 2009  matrix is 77351 x 77415 (21.7 MB) with weight 5377028 (69.46/col)
Fri Feb 13 00:06:37 2009  sparse part has weight 5377028 (69.46/col)
Fri Feb 13 00:06:38 2009  saving the first 48 matrix rows for later
Fri Feb 13 00:06:38 2009  matrix is 77303 x 77415 (16.2 MB) with weight 4522122 (58.41/col)
Fri Feb 13 00:06:38 2009  sparse part has weight 3771008 (48.71/col)
Fri Feb 13 00:06:38 2009  matrix includes 64 packed rows
Fri Feb 13 00:06:38 2009  using block size 21845 for processor cache size 512 kB
Fri Feb 13 00:06:40 2009  commencing Lanczos iteration
Fri Feb 13 00:06:40 2009  memory use: 14.1 MB
Fri Feb 13 00:07:51 2009  lanczos halted after 1223 iterations (dim = 77301)
Fri Feb 13 00:07:52 2009  recovered 18 nontrivial dependencies
Fri Feb 13 00:07:53 2009  prp42 factor: 780810284493164937541387674186542177655467
Fri Feb 13 00:07:53 2009  prp53 factor: 94856213196199882289140137695997617853942491092295137
Fri Feb 13 00:07:53 2009  elapsed time 06:19:41

Feb 13, 2009 (3rd)

By Sinkiti Sibata / GGNFS, Msieve / Feb 13, 2009

(14·10¹⁵²-11)/3 = 4(6)₁₅₁3_<153> = 599 · 2039 · 5201159 · 500019643 · 9330687712735106756107_<22> · C110

C110 = P45 · P65

P45 = 203620709236385827266419928602895446827412681_<45>

P65 = 77328562429293032074941586762299177146068262610310551977403790177_<65>

Number: 46663_152
N=15745696726082785761030779523873758778735086950631405227876971911156989281795370993215599311066355391913034537
  ( 110 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=203620709236385827266419928602895446827412681 (pp45)
 r2=77328562429293032074941586762299177146068262610310551977403790177 (pp65)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 45.55 hours.
Scaled time: 21.50 units (timescale=0.472).
Factorization parameters were as follows:
name: 46663_152
n: 15745696726082785761030779523873758778735086950631405227876971911156989281795370993215599311066355391913034537
m: 2000000000000000000000000000000
deg: 5
c5: 175
c0: -44
skew: 0.76
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2400001)
Primes: RFBsize:189880, AFBsize:189466, largePrimes:7918447 encountered
Relations: rels:7927369, finalFF:448114
Max relations in full relation-set: 28
Initial matrix: 379413 x 448114 with sparse part having weight 48120728.
Pruned matrix : 354056 x 356017 with weight 35108498.
Total sieving time: 39.99 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 5.03 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 45.55 hours.
 --------- CPU info (if available) ----------

(14·10¹²⁸+1)/3 = 4(6)₁₂₇7_<129> = C129

C129 = P47 · P82

P47 = 97442427809946115669704136955838175329000474229_<47>

P82 = 4789152704372922037448426573012625124657528365691003679694960030537882336201918623_<82>

Number: 46667_128
N=466666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667
  ( 129 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=97442427809946115669704136955838175329000474229
 r2=4789152704372922037448426573012625124657528365691003679694960030537882336201918623
Version: 
Total time: 3.58 hours.
Scaled time: 7.10 units (timescale=1.985).
Factorization parameters were as follows:
name: 46667_128
n: 466666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667
m: 100000000000000000000000000
deg: 5
c5: 7
c0: 50
skew: 1.48
type: snfs
lss: 1
rlim: 1060000
alim: 1060000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1060000/1060000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [530000, 930001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 139335 x 139583
Total sieving time: 3.58 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1060000,1060000,26,26,47,47,2.3,2.3,50000
total time: 3.58 hours.
 --------- CPU info (if available) ----------

(14·10¹³⁹+1)/3 = 4(6)₁₃₈7_<140> = 47 · 919 · 19207 · 320149 · 14326847864654454928200037_<26> · C101

C101 = P49 · P53

P49 = 1171756816497492817243664472564133432549308489139_<49>

P53 = 10466309853523263277601766588807565342572842167782031_<53>

Fri Feb 13 07:37:47 2009  Msieve v. 1.39
Fri Feb 13 07:37:47 2009  random seeds: d3312254 864c9447
Fri Feb 13 07:37:47 2009  factoring 12263969914440759335266783627234628457014011679040525685138368121008357742749535862197848991282861309 (101 digits)
Fri Feb 13 07:37:48 2009  searching for 15-digit factors
Fri Feb 13 07:37:49 2009  commencing quadratic sieve (101-digit input)
Fri Feb 13 07:37:50 2009  using multiplier of 1
Fri Feb 13 07:37:50 2009  using 32kb Intel Core sieve core
Fri Feb 13 07:37:50 2009  sieve interval: 36 blocks of size 32768
Fri Feb 13 07:37:50 2009  processing polynomials in batches of 6
Fri Feb 13 07:37:50 2009  using a sieve bound of 2823631 (102500 primes)
Fri Feb 13 07:37:50 2009  using large prime bound of 423544650 (28 bits)
Fri Feb 13 07:37:50 2009  using double large prime bound of 3376125230508000 (43-52 bits)
Fri Feb 13 07:37:50 2009  using trial factoring cutoff of 52 bits
Fri Feb 13 07:37:50 2009  polynomial 'A' values have 13 factors
Fri Feb 13 07:37:53 2009  restarting with 15879 full and 1011164 partial relations
Fri Feb 13 11:40:41 2009  102614 relations (24294 full + 78320 combined from 1548059 partial), need 102596
Fri Feb 13 11:40:43 2009  begin with 1572353 relations
Fri Feb 13 11:40:45 2009  reduce to 272541 relations in 10 passes
Fri Feb 13 11:40:45 2009  attempting to read 272541 relations
Fri Feb 13 11:40:50 2009  recovered 272541 relations
Fri Feb 13 11:40:50 2009  recovered 263021 polynomials
Fri Feb 13 11:40:50 2009  attempting to build 102614 cycles
Fri Feb 13 11:40:50 2009  found 102614 cycles in 6 passes
Fri Feb 13 11:40:50 2009  distribution of cycle lengths:
Fri Feb 13 11:40:50 2009     length 1 : 24294
Fri Feb 13 11:40:50 2009     length 2 : 17427
Fri Feb 13 11:40:50 2009     length 3 : 16759
Fri Feb 13 11:40:50 2009     length 4 : 14052
Fri Feb 13 11:40:50 2009     length 5 : 10897
Fri Feb 13 11:40:50 2009     length 6 : 7402
Fri Feb 13 11:40:50 2009     length 7 : 4908
Fri Feb 13 11:40:50 2009     length 9+: 6875
Fri Feb 13 11:40:50 2009  largest cycle: 20 relations
Fri Feb 13 11:40:51 2009  matrix is 102500 x 102614 (27.8 MB) with weight 6875032 (67.00/col)
Fri Feb 13 11:40:51 2009  sparse part has weight 6875032 (67.00/col)
Fri Feb 13 11:40:52 2009  filtering completed in 3 passes
Fri Feb 13 11:40:52 2009  matrix is 98568 x 98631 (26.9 MB) with weight 6647785 (67.40/col)
Fri Feb 13 11:40:52 2009  sparse part has weight 6647785 (67.40/col)
Fri Feb 13 11:40:53 2009  saving the first 48 matrix rows for later
Fri Feb 13 11:40:53 2009  matrix is 98520 x 98631 (15.8 MB) with weight 5180923 (52.53/col)
Fri Feb 13 11:40:53 2009  sparse part has weight 3562677 (36.12/col)
Fri Feb 13 11:40:53 2009  matrix includes 64 packed rows
Fri Feb 13 11:40:53 2009  using block size 39452 for processor cache size 1024 kB
Fri Feb 13 11:40:53 2009  commencing Lanczos iteration
Fri Feb 13 11:40:53 2009  memory use: 15.9 MB
Fri Feb 13 11:42:06 2009  lanczos halted after 1559 iterations (dim = 98516)
Fri Feb 13 11:42:06 2009  recovered 14 nontrivial dependencies
Fri Feb 13 11:42:07 2009  prp49 factor: 1171756816497492817243664472564133432549308489139
Fri Feb 13 11:42:07 2009  prp53 factor: 10466309853523263277601766588807565342572842167782031
Fri Feb 13 11:42:07 2009  elapsed time 04:04:20

(14·10¹⁴²+1)/3 = 4(6)₁₄₁7_<143> = 19 · 631 · 8629 · 82279 · 654047 · 1261759 · 280607091209_<12> · C107

C107 = P51 · P56

P51 = 354652338619270676018346061231933256617627024018009_<51>

P56 = 66755569921628218018055123882044193969712077797446507941_<56>

Number: 46667_142
N=23675018988567691200233651263717779618750621657030298258543712888967462264993398109679892203846411745509469
  ( 107 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=354652338619270676018346061231933256617627024018009
 r2=66755569921628218018055123882044193969712077797446507941
Version: 
Total time: 8.19 hours.
Scaled time: 16.11 units (timescale=1.967).
Factorization parameters were as follows:
name: 46667_142
n: 23675018988567691200233651263717779618750621657030298258543712888967462264993398109679892203846411745509469
m: 50000000000000000000000000000
deg: 5
c5: 56
c0: 125
skew: 1.17
type: snfs
lss: 1
rlim: 1840000
alim: 1840000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1840000/1840000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [920000, 1720001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 278300 x 278548
Total sieving time: 8.19 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1840000,1840000,26,26,49,49,2.3,2.3,100000
total time: 8.19 hours.
 --------- CPU info (if available) ----------

Feb 13, 2009 (2nd)

By Andreas Tete / Msieve-1.39 / Feb 13, 2009

(14·10¹⁷⁵+1)/3 = 4(6)₁₇₄7_<176> = 211 · 128977427 · 674809256778071_<15> · 2798171122344373_<16> · 169183188323265888376647544823_<30> · C106

C106 = P48 · P58

P48 = 645931821966020252623561182000975442691069658013_<48>

P58 = 8310199105822166266834778444707835250551130821474294358883_<58>

Thu Feb 12 22:34:57 2009  Msieve v. 1.39
Thu Feb 12 22:34:57 2009  random seeds: 9db02c00 3ef00dcd
Thu Feb 12 22:34:57 2009  factoring 5367822049324104198459781648285230954004443945514259477635815794499811904007692354910681910349769898679479 (106 digits)
Thu Feb 12 22:34:58 2009  searching for 15-digit factors
Thu Feb 12 22:34:59 2009  commencing number field sieve (106-digit input)
Thu Feb 12 22:34:59 2009  R0: -258172299182433160252
Thu Feb 12 22:34:59 2009  R1:  107981281439
Thu Feb 12 22:34:59 2009  A0: -82194652127860805641635
Thu Feb 12 22:34:59 2009  A1:  7033312543780076998983
Thu Feb 12 22:34:59 2009  A2: -87363472109491385
Thu Feb 12 22:34:59 2009  A3: -17887783854145
Thu Feb 12 22:34:59 2009  A4:  104218002
Thu Feb 12 22:34:59 2009  A5:  4680
Thu Feb 12 22:34:59 2009  skew 24498.05, size 6.764167e-011, alpha -5.840131, combined = 4.738707e-010
Thu Feb 12 22:35:00 2009  
Thu Feb 12 22:35:00 2009  commencing relation filtering
Thu Feb 12 22:35:00 2009  commencing duplicate removal, pass 1
Thu Feb 12 22:35:56 2009  found 323492 hash collisions in 4679360 relations
Thu Feb 12 22:36:09 2009  added 31781 free relations
Thu Feb 12 22:36:09 2009  commencing duplicate removal, pass 2
Thu Feb 12 22:36:16 2009  found 299722 duplicates and 4411418 unique relations
Thu Feb 12 22:36:16 2009  memory use: 43.3 MB
Thu Feb 12 22:36:16 2009  reading rational ideals above 2818048
Thu Feb 12 22:36:16 2009  reading algebraic ideals above 2818048
Thu Feb 12 22:36:16 2009  commencing singleton removal, pass 1
Thu Feb 12 22:37:03 2009  relations with 0 large ideals: 104413
Thu Feb 12 22:37:03 2009  relations with 1 large ideals: 664703
Thu Feb 12 22:37:03 2009  relations with 2 large ideals: 1546652
Thu Feb 12 22:37:03 2009  relations with 3 large ideals: 1511527
Thu Feb 12 22:37:03 2009  relations with 4 large ideals: 528095
Thu Feb 12 22:37:03 2009  relations with 5 large ideals: 25948
Thu Feb 12 22:37:03 2009  relations with 6 large ideals: 30080
Thu Feb 12 22:37:03 2009  relations with 7+ large ideals: 0
Thu Feb 12 22:37:03 2009  4411418 relations and about 4341436 large ideals
Thu Feb 12 22:37:03 2009  commencing singleton removal, pass 2
Thu Feb 12 22:37:51 2009  found 1970017 singletons
Thu Feb 12 22:37:51 2009  current dataset: 2441401 relations and about 1971541 large ideals
Thu Feb 12 22:37:51 2009  commencing singleton removal, pass 3
Thu Feb 12 22:38:24 2009  found 459939 singletons
Thu Feb 12 22:38:24 2009  current dataset: 1981462 relations and about 1477357 large ideals
Thu Feb 12 22:38:24 2009  commencing singleton removal, final pass
Thu Feb 12 22:39:07 2009  memory use: 37.3 MB
Thu Feb 12 22:39:07 2009  commencing in-memory singleton removal
Thu Feb 12 22:39:07 2009  begin with 1981462 relations and 1518445 unique ideals
Thu Feb 12 22:39:09 2009  reduce to 1658341 relations and 1186258 ideals in 16 passes
Thu Feb 12 22:39:09 2009  max relations containing the same ideal: 49
Thu Feb 12 22:39:10 2009  reading rational ideals above 720000
Thu Feb 12 22:39:10 2009  reading algebraic ideals above 720000
Thu Feb 12 22:39:10 2009  commencing singleton removal, final pass
Thu Feb 12 22:39:32 2009  keeping 1441724 ideals with weight <= 20, new excess is 185015
Thu Feb 12 22:39:34 2009  memory use: 46.8 MB
Thu Feb 12 22:39:34 2009  commencing in-memory singleton removal
Thu Feb 12 22:39:34 2009  begin with 1663865 relations and 1441724 unique ideals
Thu Feb 12 22:39:36 2009  reduce to 1646608 relations and 1397747 ideals in 11 passes
Thu Feb 12 22:39:36 2009  max relations containing the same ideal: 20
Thu Feb 12 22:39:37 2009  removing 167614 relations and 150492 ideals in 17122 cliques
Thu Feb 12 22:39:37 2009  commencing in-memory singleton removal
Thu Feb 12 22:39:37 2009  begin with 1478994 relations and 1397747 unique ideals
Thu Feb 12 22:39:38 2009  reduce to 1467517 relations and 1235600 ideals in 7 passes
Thu Feb 12 22:39:38 2009  max relations containing the same ideal: 20
Thu Feb 12 22:39:39 2009  removing 123087 relations and 105965 ideals in 17122 cliques
Thu Feb 12 22:39:39 2009  commencing in-memory singleton removal
Thu Feb 12 22:39:39 2009  begin with 1344430 relations and 1235600 unique ideals
Thu Feb 12 22:39:40 2009  reduce to 1336954 relations and 1122079 ideals in 8 passes
Thu Feb 12 22:39:40 2009  max relations containing the same ideal: 20
Thu Feb 12 22:39:41 2009  relations with 0 large ideals: 16191
Thu Feb 12 22:39:41 2009  relations with 1 large ideals: 109998
Thu Feb 12 22:39:41 2009  relations with 2 large ideals: 306115
Thu Feb 12 22:39:41 2009  relations with 3 large ideals: 427806
Thu Feb 12 22:39:41 2009  relations with 4 large ideals: 318411
Thu Feb 12 22:39:41 2009  relations with 5 large ideals: 125538
Thu Feb 12 22:39:41 2009  relations with 6 large ideals: 29363
Thu Feb 12 22:39:41 2009  relations with 7+ large ideals: 3532
Thu Feb 12 22:39:41 2009  commencing 2-way merge
Thu Feb 12 22:39:42 2009  reduce to 793256 relation sets and 578381 unique ideals
Thu Feb 12 22:39:42 2009  commencing full merge
Thu Feb 12 22:39:52 2009  memory use: 43.3 MB
Thu Feb 12 22:39:52 2009  found 366573 cycles, need 340581
Thu Feb 12 22:39:52 2009  weight of 340581 cycles is about 24093365 (70.74/cycle)
Thu Feb 12 22:39:52 2009  distribution of cycle lengths:
Thu Feb 12 22:39:52 2009  1 relations: 38055
Thu Feb 12 22:39:52 2009  2 relations: 34114
Thu Feb 12 22:39:52 2009  3 relations: 33825
Thu Feb 12 22:39:52 2009  4 relations: 31479
Thu Feb 12 22:39:52 2009  5 relations: 29063
Thu Feb 12 22:39:52 2009  6 relations: 25710
Thu Feb 12 22:39:52 2009  7 relations: 23273
Thu Feb 12 22:39:52 2009  8 relations: 21000
Thu Feb 12 22:39:52 2009  9 relations: 18232
Thu Feb 12 22:39:52 2009  10+ relations: 85830
Thu Feb 12 22:39:52 2009  heaviest cycle: 20 relations
Thu Feb 12 22:39:52 2009  commencing cycle optimization
Thu Feb 12 22:39:52 2009  start with 2233449 relations
Thu Feb 12 22:39:59 2009  pruned 71620 relations
Thu Feb 12 22:39:59 2009  memory use: 56.8 MB
Thu Feb 12 22:39:59 2009  distribution of cycle lengths:
Thu Feb 12 22:39:59 2009  1 relations: 38055
Thu Feb 12 22:39:59 2009  2 relations: 35065
Thu Feb 12 22:39:59 2009  3 relations: 35335
Thu Feb 12 22:39:59 2009  4 relations: 32598
Thu Feb 12 22:39:59 2009  5 relations: 30086
Thu Feb 12 22:39:59 2009  6 relations: 26481
Thu Feb 12 22:39:59 2009  7 relations: 23791
Thu Feb 12 22:39:59 2009  8 relations: 21224
Thu Feb 12 22:39:59 2009  9 relations: 18440
Thu Feb 12 22:39:59 2009  10+ relations: 79506
Thu Feb 12 22:39:59 2009  heaviest cycle: 19 relations
Thu Feb 12 22:40:00 2009  
Thu Feb 12 22:40:00 2009  commencing linear algebra
Thu Feb 12 22:40:00 2009  read 340581 cycles
Thu Feb 12 22:40:00 2009  cycles contain 1166929 unique relations
Thu Feb 12 22:40:14 2009  read 1166929 relations
Thu Feb 12 22:40:16 2009  using 20 quadratic characters above 67107708
Thu Feb 12 22:40:23 2009  building initial matrix
Thu Feb 12 22:40:38 2009  memory use: 137.7 MB
Thu Feb 12 22:40:38 2009  read 340581 cycles
Thu Feb 12 22:40:39 2009  matrix is 340340 x 340581 (96.0 MB) with weight 32664453 (95.91/col)
Thu Feb 12 22:40:39 2009  sparse part has weight 22770201 (66.86/col)
Thu Feb 12 22:40:44 2009  filtering completed in 3 passes
Thu Feb 12 22:40:44 2009  matrix is 338226 x 338426 (95.6 MB) with weight 32510703 (96.06/col)
Thu Feb 12 22:40:44 2009  sparse part has weight 22686610 (67.04/col)
Thu Feb 12 22:40:45 2009  read 338426 cycles
Thu Feb 12 22:40:46 2009  matrix is 338226 x 338426 (95.6 MB) with weight 32510703 (96.06/col)
Thu Feb 12 22:40:46 2009  sparse part has weight 22686610 (67.04/col)
Thu Feb 12 22:40:46 2009  saving the first 48 matrix rows for later
Thu Feb 12 22:40:46 2009  matrix is 338178 x 338426 (92.3 MB) with weight 25662083 (75.83/col)
Thu Feb 12 22:40:46 2009  sparse part has weight 22161269 (65.48/col)
Thu Feb 12 22:40:46 2009  matrix includes 64 packed rows
Thu Feb 12 22:40:46 2009  using block size 65536 for processor cache size 3072 kB
Thu Feb 12 22:40:49 2009  commencing Lanczos iteration
Thu Feb 12 22:40:49 2009  memory use: 90.3 MB
Thu Feb 12 22:57:01 2009  lanczos halted after 5349 iterations (dim = 338176)
Thu Feb 12 22:57:02 2009  recovered 28 nontrivial dependencies
Thu Feb 12 22:57:02 2009  
Thu Feb 12 22:57:02 2009  commencing square root phase
Thu Feb 12 22:57:02 2009  reading relations for dependency 1
Thu Feb 12 22:57:02 2009  read 169394 cycles
Thu Feb 12 22:57:03 2009  cycles contain 719905 unique relations
Thu Feb 12 22:57:12 2009  read 719905 relations
Thu Feb 12 22:57:16 2009  multiplying 582576 relations
Thu Feb 12 22:58:47 2009  multiply complete, coefficients have about 23.47 million bits
Thu Feb 12 22:58:48 2009  initial square root is modulo 5501819
Thu Feb 12 23:00:56 2009  prp48 factor: 645931821966020252623561182000975442691069658013
Thu Feb 12 23:00:56 2009  prp58 factor: 8310199105822166266834778444707835250551130821474294358883
Thu Feb 12 23:00:56 2009  elapsed time 00:25:59

Feb 13, 2009

By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1 / Feb 13, 2009

(14·10¹⁵⁰+1)/3 = 4(6)₁₄₉7_<151> = 233 · 20231 · 9565063 · C138

C138 = P60 · P78

P60 = 278292037251093167192697707757978140015212683389508754823953_<60>

P78 = 371916027933907022212166087325008623133827796688636219284264407757441270101811_<78>

SNFS difficulty: 151 digits.
Divisors found:
 r1=278292037251093167192697707757978140015212683389508754823953 (pp60)
 r2=371916027933907022212166087325008623133827796688636219284264407757441270101811 (pp78)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
n: 103501269100061459963680493576104709397584435573134197614576074461874816345074624925092291323443376939458487404792623379413862577691478883
m: 1000000000000000000000000000000
deg: 5
c5: 14
c0: 1
skew: 0.59
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1150000, 1650001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 324486 x 324734
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,52,52,2.4,2.4,100000
total time: 10.00 hours.

(14·10¹³³+1)/3 = 4(6)₁₃₂7_<134> = 17 · 13769216033340347807_<20> · C114

C114 = P51 · P63

P51 = 447832221926721618206166623088373467276639957980131_<51>

P63 = 445177603722581126154064540081841356282753677680658453973442903_<63>

SNFS difficulty: 135 digits.
Divisors found:
 r1=447832221926721618206166623088373467276639957980131 (pp51)
 r2=445177603722581126154064540081841356282753677680658453973442903 (pp63)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
n: 199364875427097082889189878762010012232418735432546046038860594807740900792360923025260503562375875979319736960293
m: 1000000000000000000000000000
deg: 5
c5: 7
c0: 50
skew: 1.48
type: snfs
lss: 1
rlim: 1290000
alim: 1290000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1290000/1290000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [645000, 1320001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 161579 x 161825
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,49,49,2.3,2.3,75000
total time: 3.00 hours.

(8·10¹⁸⁴+7)/3 = 2(6)₁₈₃9_<185> = 23 · 3331 · 9974131 · 44534953 · 560165357 · C157

C157 = P32 · C126

P32 = 10490142307214064479640205122143_<32>

C126 = [133349862070778274177903595909790086247733391434306851920325896211332328606192378743990711854039144978397117642580702153728441_<126>]

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2422990683
Step 1 took 51122ms
Step 2 took 33274ms
********** Factor found in step 2: 10490142307214064479640205122143
Found probable prime factor of 32 digits: 10490142307214064479640205122143
Composite cofactor has 126 digits

(8·10¹⁹⁵+7)/3 = 2(6)₁₉₄9_<196> = 17 · 15193 · 114861703391_<12> · 190185939589_<12> · C168

C168 = P41 · P128

P41 = 21361646902753773798774688972047426229999_<41>

P128 = 22125234476041939644861842402929543686459937107236436624986438920087136960016791042077082338659824729805893701781682408595537649_<128>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3406529621
Step 1 took 13669ms
Step 2 took 317ms
********** Factor found in step 2: 21361646902753773798774688972047426229999
Found probable prime factor of 41 digits: 21361646902753773798774688972047426229999
Probable prime cofactor has 128 digits

(8·10¹⁸³+7)/3 = 2(6)₁₈₂9_<184> = 566794065586391351689_<21> · C163

C163 = P35 · P129

P35 = 30060400046075892826912630127724553_<35>

P129 = 156512375065718674354721548240702754368556888089823882809533087811465411008217641205470073242329288280820516388264024561842672157_<129>

Using B1=8000000, B2=46840406350, polynomial Dickson(12), sigma=215209419
Step 1 took 36590ms
Step 2 took 28115ms
********** Factor found in step 2: 30060400046075892826912630127724553
Found probable prime factor of 35 digits: 30060400046075892826912630127724553
Probable prime cofactor has 129 digits

(5·10¹⁸⁰+7)/3 = 1(6)₁₇₉9_<181> = 709 · 2644933042766470246966192621_<28> · C150

C150 = P35 · P116

P35 = 31773102888110998286705529243790757_<35>

P116 = 27972301658995088320960956104735130981351338320881303986748486437792405387531996289545564795758198381632115477266953_<116>

Using B1=6000000, B2=35128842850, polynomial Dickson(12), sigma=1855914501
Step 1 took 23790ms
Step 2 took 20738ms
********** Factor found in step 2: 31773102888110998286705529243790757
Found probable prime factor of 35 digits: 31773102888110998286705529243790757
Probable prime cofactor has 116 digits

6·10¹⁸²+1 = 6(0)₁₈₁1_<183> = 197 · 145547 · 1137803 · C170

C170 = P37 · P133

P37 = 3697766213694124457129202150295765873_<37>

P133 = 4973650241959479991177377391777452977902057601073658068611396750923243720787211361706581622604893959178219884712767066984209658142981_<133>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=1250300280
Step 1 took 50747ms
Step 2 took 32902ms
********** Factor found in step 2: 3697766213694124457129202150295765873
Found probable prime factor of 37 digits: 3697766213694124457129202150295765873
Probable prime cofactor has 133 digits

4·10¹⁸¹+9 = 4(0)₁₈₀9_<182> = 7 · 4463 · 9013 · 44939 · 54440369 · 646495019927_<12> · C149

C149 = P38 · C112

P38 = 17375472304230114852745301318776299103_<38>

C112 = [5169153474928885848324348321675877484252277469106881063647738317793449445476644541605020599482510225817619276463_<112>]

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2640071409
Step 1 took 43398ms
Step 2 took 30394ms
********** Factor found in step 2: 17375472304230114852745301318776299103
Found probable prime factor of 38 digits: 17375472304230114852745301318776299103
Composite cofactor has 112 digits

Feb 12, 2009 (5th)

By Sinkiti Sibata / Msieve / Feb 12, 2009

(14·10¹¹²+1)/3 = 4(6)₁₁₁7_<113> = 71 · 79 · 1459060062993079_<16> · C94

C94 = P46 · P49

P46 = 2788605938735191414130857038217899259398483257_<46>

P49 = 2044847961067233264018846952173523758557643519821_<49>

Thu Feb 12 07:47:53 2009  Msieve v. 1.39
Thu Feb 12 07:47:53 2009  random seeds: 626506b0 94752051
Thu Feb 12 07:47:53 2009  factoring 5702275168042634161453697274977310092999593281419143237948608709452904758430079124662216136997 (94 digits)
Thu Feb 12 07:47:54 2009  searching for 15-digit factors
Thu Feb 12 07:47:56 2009  commencing quadratic sieve (94-digit input)
Thu Feb 12 07:47:56 2009  using multiplier of 13
Thu Feb 12 07:47:56 2009  using 32kb Intel Core sieve core
Thu Feb 12 07:47:56 2009  sieve interval: 36 blocks of size 32768
Thu Feb 12 07:47:56 2009  processing polynomials in batches of 6
Thu Feb 12 07:47:56 2009  using a sieve bound of 2055311 (76471 primes)
Thu Feb 12 07:47:56 2009  using large prime bound of 283632918 (28 bits)
Thu Feb 12 07:47:56 2009  using double large prime bound of 1640445722406174 (42-51 bits)
Thu Feb 12 07:47:56 2009  using trial factoring cutoff of 51 bits
Thu Feb 12 07:47:56 2009  polynomial 'A' values have 12 factors
Thu Feb 12 10:18:24 2009  76601 relations (20440 full + 56161 combined from 1076215 partial), need 76567
Thu Feb 12 10:18:25 2009  begin with 1096655 relations
Thu Feb 12 10:18:26 2009  reduce to 192800 relations in 10 passes
Thu Feb 12 10:18:26 2009  attempting to read 192800 relations
Thu Feb 12 10:18:29 2009  recovered 192800 relations
Thu Feb 12 10:18:29 2009  recovered 170944 polynomials
Thu Feb 12 10:18:29 2009  attempting to build 76601 cycles
Thu Feb 12 10:18:30 2009  found 76601 cycles in 6 passes
Thu Feb 12 10:18:30 2009  distribution of cycle lengths:
Thu Feb 12 10:18:30 2009     length 1 : 20440
Thu Feb 12 10:18:30 2009     length 2 : 14239
Thu Feb 12 10:18:30 2009     length 3 : 13100
Thu Feb 12 10:18:30 2009     length 4 : 10074
Thu Feb 12 10:18:30 2009     length 5 : 7275
Thu Feb 12 10:18:30 2009     length 6 : 4693
Thu Feb 12 10:18:30 2009     length 7 : 2891
Thu Feb 12 10:18:30 2009     length 9+: 3889
Thu Feb 12 10:18:30 2009  largest cycle: 20 relations
Thu Feb 12 10:18:30 2009  matrix is 76471 x 76601 (19.9 MB) with weight 4914996 (64.16/col)
Thu Feb 12 10:18:30 2009  sparse part has weight 4914996 (64.16/col)
Thu Feb 12 10:18:31 2009  filtering completed in 3 passes
Thu Feb 12 10:18:31 2009  matrix is 71826 x 71890 (18.9 MB) with weight 4656393 (64.77/col)
Thu Feb 12 10:18:31 2009  sparse part has weight 4656393 (64.77/col)
Thu Feb 12 10:18:31 2009  saving the first 48 matrix rows for later
Thu Feb 12 10:18:31 2009  matrix is 71778 x 71890 (12.7 MB) with weight 3753540 (52.21/col)
Thu Feb 12 10:18:31 2009  sparse part has weight 2886411 (40.15/col)
Thu Feb 12 10:18:31 2009  matrix includes 64 packed rows
Thu Feb 12 10:18:31 2009  using block size 28756 for processor cache size 1024 kB
Thu Feb 12 10:18:32 2009  commencing Lanczos iteration
Thu Feb 12 10:18:32 2009  memory use: 11.8 MB
Thu Feb 12 10:19:07 2009  lanczos halted after 1137 iterations (dim = 71778)
Thu Feb 12 10:19:08 2009  recovered 18 nontrivial dependencies
Thu Feb 12 10:19:09 2009  prp46 factor: 2788605938735191414130857038217899259398483257
Thu Feb 12 10:19:09 2009  prp49 factor: 2044847961067233264018846952173523758557643519821
Thu Feb 12 10:19:09 2009  elapsed time 02:31:16

(14·10¹¹⁹+1)/3 = 4(6)₁₁₈7_<120> = C120

C120 = P36 · P41 · P45

P36 = 342863294583316472753439512436141793_<36>

P41 = 10008884276539516247435781948737347856839_<41>

P45 = 135987853606852843149955196433161787992971421_<45>

Number: 46667_119
N=466666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667
  ( 120 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=342863294583316472753439512436141793
 r2=10008884276539516247435781948737347856839
 r3=135987853606852843149955196433161787992971421
Version: 
Total time: 1.60 hours.
Scaled time: 3.18 units (timescale=1.991).
Factorization parameters were as follows:
name: 46667_119
n: 466666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667
m: 1000000000000000000000000
deg: 5
c5: 7
c0: 5
skew: 0.93
type: snfs
lss: 1
rlim: 720000
alim: 720000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 720000/720000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [360000, 560001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 70783 x 71030
Total sieving time: 1.60 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,720000,720000,25,25,46,46,2.2,2.2,50000
total time: 1.60 hours.
 --------- CPU info (if available) ----------

(14·10¹⁵⁷+1)/3 = 4(6)₁₅₆7_<158> = 1229 · 14639 · 20570610787_<11> · 136089221564531_<15> · 6207025213840049369221560139_<28> · C99

C99 = P47 · P52

P47 = 69640697804905676650210740049288662547179405011_<47>

P52 = 2143512135664749341932732352584032738864120525449489_<52>

Thu Feb 12 11:55:17 2009  Msieve v. 1.39
Thu Feb 12 11:55:17 2009  random seeds: e96394ac 9a5ad5fa
Thu Feb 12 11:55:17 2009  factoring 149275680880976788467660198622530779642196164017610224805481211436514278248616466484962074353989379 (99 digits)
Thu Feb 12 11:55:18 2009  searching for 15-digit factors
Thu Feb 12 11:55:20 2009  commencing quadratic sieve (99-digit input)
Thu Feb 12 11:55:20 2009  using multiplier of 1
Thu Feb 12 11:55:20 2009  using 32kb Intel Core sieve core
Thu Feb 12 11:55:20 2009  sieve interval: 36 blocks of size 32768
Thu Feb 12 11:55:20 2009  processing polynomials in batches of 6
Thu Feb 12 11:55:20 2009  using a sieve bound of 2577401 (94097 primes)
Thu Feb 12 11:55:20 2009  using large prime bound of 386610150 (28 bits)
Thu Feb 12 11:55:20 2009  using double large prime bound of 2864783531160900 (43-52 bits)
Thu Feb 12 11:55:20 2009  using trial factoring cutoff of 52 bits
Thu Feb 12 11:55:20 2009  polynomial 'A' values have 13 factors
Thu Feb 12 18:39:39 2009  94622 relations (23309 full + 71313 combined from 1406727 partial), need 94193
Thu Feb 12 18:39:41 2009  begin with 1430036 relations
Thu Feb 12 18:39:42 2009  reduce to 246673 relations in 12 passes
Thu Feb 12 18:39:42 2009  attempting to read 246673 relations
Thu Feb 12 18:39:46 2009  recovered 246673 relations
Thu Feb 12 18:39:46 2009  recovered 233241 polynomials
Thu Feb 12 18:39:47 2009  attempting to build 94622 cycles
Thu Feb 12 18:39:47 2009  found 94622 cycles in 6 passes
Thu Feb 12 18:39:47 2009  distribution of cycle lengths:
Thu Feb 12 18:39:47 2009     length 1 : 23309
Thu Feb 12 18:39:47 2009     length 2 : 16347
Thu Feb 12 18:39:47 2009     length 3 : 15767
Thu Feb 12 18:39:47 2009     length 4 : 12855
Thu Feb 12 18:39:47 2009     length 5 : 9640
Thu Feb 12 18:39:47 2009     length 6 : 6630
Thu Feb 12 18:39:47 2009     length 7 : 4243
Thu Feb 12 18:39:47 2009     length 9+: 5831
Thu Feb 12 18:39:47 2009  largest cycle: 18 relations
Thu Feb 12 18:39:47 2009  matrix is 94097 x 94622 (25.6 MB) with weight 6321039 (66.80/col)
Thu Feb 12 18:39:47 2009  sparse part has weight 6321039 (66.80/col)
Thu Feb 12 18:39:49 2009  filtering completed in 3 passes
Thu Feb 12 18:39:49 2009  matrix is 89731 x 89795 (24.3 MB) with weight 6003460 (66.86/col)
Thu Feb 12 18:39:49 2009  sparse part has weight 6003460 (66.86/col)
Thu Feb 12 18:39:49 2009  saving the first 48 matrix rows for later
Thu Feb 12 18:39:49 2009  matrix is 89683 x 89795 (14.6 MB) with weight 4679779 (52.12/col)
Thu Feb 12 18:39:49 2009  sparse part has weight 3297305 (36.72/col)
Thu Feb 12 18:39:49 2009  matrix includes 64 packed rows
Thu Feb 12 18:39:49 2009  using block size 35918 for processor cache size 1024 kB
Thu Feb 12 18:39:50 2009  commencing Lanczos iteration
Thu Feb 12 18:39:50 2009  memory use: 14.4 MB
Thu Feb 12 18:40:44 2009  lanczos halted after 1420 iterations (dim = 89681)
Thu Feb 12 18:40:45 2009  recovered 16 nontrivial dependencies
Thu Feb 12 18:40:46 2009  prp47 factor: 69640697804905676650210740049288662547179405011
Thu Feb 12 18:40:46 2009  prp52 factor: 2143512135664749341932732352584032738864120525449489
Thu Feb 12 18:40:46 2009  elapsed time 06:45:29

(14·10¹²²+1)/3 = 4(6)₁₂₁7_<123> = 181 · C121

C121 = P36 · P86

P36 = 233363571794395358732871502584131711_<36>

P86 = 11048291971135058539564418334874354567896531951537936403069323653753099323612883519137_<86>

Number: 46667_122
N=2578268876611418047882136279926335174953959484346224677716390423572744014732965009208103130755064456721915285451197053407
  ( 121 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=233363571794395358732871502584131711
 r2=11048291971135058539564418334874354567896531951537936403069323653753099323612883519137
Version: 
Total time: 1.85 hours.
Scaled time: 3.66 units (timescale=1.979).
Factorization parameters were as follows:
name: 46667_122
n: 2578268876611418047882136279926335174953959484346224677716390423572744014732965009208103130755064456721915285451197053407
m: 5000000000000000000000000
deg: 5
c5: 56
c0: 125
skew: 1.17
type: snfs
lss: 1
rlim: 860000
alim: 860000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 860000/860000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [430000, 630001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 100795 x 101040
Total sieving time: 1.85 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,860000,860000,26,26,46,46,2.3,2.3,50000
total time: 1.85 hours.
 --------- CPU info (if available) ----------

Feb 12, 2009 (4th)

By Erik Branger / GGNFS, Msieve / Feb 12, 2009

(14·10¹⁶⁵-17)/3 = 4(6)₁₆₄1_<166> = 9488819 · 43588177743829_<14> · C146

C146 = P69 · P77

P69 = 192291543504650266312924830780127324976051701536760368444962051931847_<69>

P77 = 58676705241607330640162008428812640085749921181414466216785690293885780591613_<77>

Number: 46661_165
N=11283034218676076335450062104328480022556931502317869197767600548494780149843252727291425682419289464184378251077512205365756428650696865215799211
  ( 146 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=192291543504650266312924830780127324976051701536760368444962051931847
 r2=58676705241607330640162008428812640085749921181414466216785690293885780591613
Version: 
Total time: 64.10 hours.
Scaled time: 49.17 units (timescale=0.767).
Factorization parameters were as follows:
n: 11283034218676076335450062104328480022556931502317869197767600548494780149843252727291425682419289464184378251077512205365756428650696865215799211
m: 1000000000000000000000000000000000
deg: 5
c5: 14
c0: -17
skew: 1.04
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4

Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 3750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 751250 x 751498
Total sieving time: 64.10 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 64.10 hours.
 --------- CPU info (if available) ----------

Feb 12, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Feb 12, 2009

(32·10¹⁹⁶+31)/9 = 3(5)₁₉₅9_<197> = 3 · C197

C197 = P49 · P148

P49 = 3559279910565634648793619648390695211930101119007_<49>

P148 = 3329845404029596513584266686001452221852005046336820091842356487673056284411726044805774754469766724250478115806325903135290063433358994107001192979_<148>

Number: n
N=11851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853
  ( 197 digits)
SNFS difficulty: 197 digits.
Divisors found:

Thu Feb 12 05:19:50 2009  prp49 factor: 3559279910565634648793619648390695211930101119007
Thu Feb 12 05:19:50 2009  prp148 factor: 3329845404029596513584266686001452221852005046336820091842356487673056284411726044805774754469766724250478115806325903135290063433358994107001192979
Thu Feb 12 05:19:50 2009  elapsed time 10:06:12 (Msieve 1.39 - dependency 9)

Version: GGNFS-0.77.1-20050930-k8
Total time: 40.90 hours.
Scaled time: 82.20 units (timescale=2.010).
Factorization parameters were as follows:
name: KA_3_5_195_9
n: 11851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853
deg: 5
c5: 10
c0: 31
m: 2000000000000000000000000000000000000000
skew: 1.25
type: snfs
rlim: 10000000
alim: 10000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 14052713)
Primes: RFBsize:664579, AFBsize:664406, largePrimes:37099223 encountered
Relations: rels:33783957, finalFF:423024
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 5477645 hash collisions in 39908701 relations
Msieve: matrix is 2271192 x 2271440 (617.6 MB)

Total sieving time: 40.07 hours.
Total relation processing time: 0.82 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000
total time: 40.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.96 BogoMIPS (lpj=2830483)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Total of 4 processors activated (22643.68 BogoMIPS).

(14·10¹⁰¹+1)/3 = 4(6)₁₀₀7_<102> = 17 · 97 · C99

C99 = P37 · P62

P37 = 5033234758058990957431315127552236327_<37>

P62 = 56226226564171399584270023372840804616856797530190186799408429_<62>

Number: n
N=282999797857287244794825146553466747523751768748736608045279967657165959167172023448554679603800283
  ( 99 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=5033234758058990957431315127552236327 (pp37)
 r2=56226226564171399584270023372840804616856797530190186799408429 (pp62)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.71 hours.
Scaled time: 1.25 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_4_6_100_7
n: 282999797857287244794825146553466747523751768748736608045279967657165959167172023448554679603800283
deg: 5
c5: 140
c0: 1
m: 100000000000000000000
skew: 0.37
type: snfs
rlim: 400000
alim: 400000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 400000/400000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved algebraic special-q in [200000, 230001)
Primes: RFBsize:33860, AFBsize:33783, largePrimes:4654390 encountered
Relations: rels:3905590, finalFF:116916
Max relations in full relation-set: 28
Initial matrix: 67710 x 116916 with sparse part having weight 9501067.
Pruned matrix : 56212 x 56614 with weight 2878348.
Total sieving time: 0.61 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,400000,400000,29,29,58,58,2.5,2.5,20000
total time: 0.71 hours.
 --------- CPU info (if available) ----------

Feb 12, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39 / Feb 12, 2009

(14·10¹³¹+1)/3 = 4(6)₁₃₀7_<132> = 305947 · 159457726751_<12> · C115

C115 = P35 · P81

P35 = 46554278325090552516893199847461541_<35>

P81 = 205473308908773787368632582384091275114615193757427857138289590570000231197871171_<81>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=871041688
Step 1 took 8145ms
Step 2 took 9102ms
********** Factor found in step 2: 46554278325090552516893199847461541
Found probable prime factor of 35 digits: 46554278325090552516893199847461541
Probable prime cofactor 205473308908773787368632582384091275114615193757427857138289590570000231197871171 has 81 digits

(14·10¹⁶²+1)/3 = 4(6)₁₆₁7_<163> = 139 · 599 · 37243 · 1143529 · 521121781 · 85455939917603_<14> · C125

C125 = P30 · C95

P30 = 399007013662755691469737714633_<30>

C95 = [74064706811669136267266549263175661936240043622241422381737475862705723444971303591286665563979_<95>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=953689393
Step 1 took 9805ms
Step 2 took 10466ms
********** Factor found in step 2: 399007013662755691469737714633
Found probable prime factor of 30 digits: 399007013662755691469737714633
Composite cofactor has 95 digits

(14·10¹²⁹+1)/3 = 4(6)₁₂₈7_<130> = 13 · 89399 · C124

C124 = P35 · P90

P35 = 10192161599110403859711452399948989_<35>

P90 = 393971192375050542532099397791091062168385809913731410123886724602590737694211075449017269_<90>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=76032831
Step 1 took 3242ms
Step 2 took 3943ms
********** Factor found in step 2: 10192161599110403859711452399948989
Found probable prime factor of 35 digits: 10192161599110403859711452399948989
Probable prime cofactor 393971192375050542532099397791091062168385809913731410123886724602590737694211075449017269 has 90 digits

(14·10¹⁵⁴+1)/3 = 4(6)₁₅₃7_<155> = 293 · C153

C153 = P34 · C119

P34 = 7512655541259282306331650654533633_<34>

C119 = [21200479512406470387486737841689387728256616761959944459277057188240292447586447134939384922724107131176462502589510543_<119>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3012614861
Step 1 took 3893ms
Step 2 took 4707ms
********** Factor found in step 2: 7512655541259282306331650654533633
Found probable prime factor of 34 digits: 7512655541259282306331650654533633
Composite cofactor has 119 digits

(14·10¹⁶⁶+1)/3 = 4(6)₁₆₅7_<167> = 227 · 93609576563291_<14> · 6410436491169121721_<19> · C132

C132 = P31 · C101

P31 = 8567432506482975511227306736847_<31>

C101 = [39987324709041758691823561140139597659692108721927001185977095775180330550267978236047812260559216413_<101>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3502152376
Step 1 took 3243ms
Step 2 took 4098ms
********** Factor found in step 2: 8567432506482975511227306736847
Found probable prime factor of 31 digits: 8567432506482975511227306736847
Composite cofactor has 101 digits

(14·10¹⁸⁶+1)/3 = 4(6)₁₈₅7_<187> = 10267 · 13219 · 4164360581_<10> · C169

C169 = P31 · C139

P31 = 1488247983280186098571489708637_<31>

C139 = [5548057925542539633876144788364042228068713112868763687008067831727809467689271994969198458381672917577464003883096593416056508405328606507_<139>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1804857347
Step 1 took 4577ms
Step 2 took 5369ms
********** Factor found in step 2: 1488247983280186098571489708637
Found probable prime factor of 31 digits: 1488247983280186098571489708637
Composite cofactor has 139 digits

(14·10¹⁹³+1)/3 = 4(6)₁₉₂7_<194> = 162042457 · 20695762423014919_<17> · C170

C170 = P33 · P137

P33 = 462119935655791361486982051216493_<33>

P137 = 30112154280186876402133415618899951125050959464703518389615185245091234262257669146945323775268235498034779512356171484421776174648079993_<137>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3931416344
Step 1 took 4596ms
Step 2 took 5150ms
********** Factor found in step 2: 462119935655791361486982051216493
Found probable prime factor of 33 digits: 462119935655791361486982051216493
Probable prime cofactor has 137 digits

(14·10¹⁸⁹+1)/3 = 4(6)₁₈₈7_<190> = 13 · 3089 · C186

C186 = P29 · C158

P29 = 10128992616845406650370872567_<29>

C158 = [11473060026002633862873187847428263852356990812032173801213368823063425357300143024973808939526542988293615478197607055708097005793552950139882721311441146193_<158>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=559243349
Step 1 took 5299ms
Step 2 took 5887ms
********** Factor found in step 2: 10128992616845406650370872567
Found probable prime factor of 29 digits: 10128992616845406650370872567
Composite cofactor has 158 digits

(14·10¹⁹⁸+1)/3 = 4(6)₁₉₇7_<199> = 104241439 · 804275831676937_<15> · C176

C176 = P31 · C146

P31 = 2302547123295387084975840675017_<31>

C146 = [24174240446012188423303584163418618873580884672507283345705373054705879742773704017354755985074043014862200477183294129720127756212163374408552357_<146>]

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=1926129916
Step 1 took 5350ms
Step 2 took 5715ms
********** Factor found in step 2: 2302547123295387084975840675017
Found probable prime factor of 31 digits: 2302547123295387084975840675017
Composite cofactor has 146 digits

(14·10²⁰⁵+1)/3 = 4(6)₂₀₄7_<206> = 211 · 313883 · 166392511157_<12> · C187

C187 = P35 · C152

P35 = 85546395577581480397571844796656383_<35>

C152 = [49501805467225833449350459682062479620662966987145895723889560077810294783203738814482530345222472524750975100610029437647086129084137651615311158833889_<152>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3996907096
Step 1 took 16003ms
Step 2 took 15084ms
********** Factor found in step 2: 85546395577581480397571844796656383
Found probable prime factor of 35 digits: 85546395577581480397571844796656383
Composite cofactor has 152 digits

(14·10¹⁹⁶+1)/3 = 4(6)₁₉₅7_<197> = 19 · 88125623503_<11> · 63724402211023850353_<20> · 174979598539031380917131233_<27> · C139

C139 = P36 · C103

P36 = 300304125643577097155478944475718909_<36>

C103 = [8323318098892312395018467980900645024149797138390385911208071430477385229001986137257942282261530204291_<103>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2390175780
Step 1 took 11879ms
Step 2 took 11261ms
********** Factor found in step 2: 300304125643577097155478944475718909
Found probable prime factor of 36 digits: 300304125643577097155478944475718909
Composite cofactor has 103 digits

(14·10¹⁴⁵+1)/3 = 4(6)₁₄₄7_<146> = 211 · C144

C144 = P52 · P92

P52 = 8052958223086142680681622957815586168218929634167397_<52>

P92 = 27464321831555993887170069360422205207318039121738929888700795651176142159905108128526327701_<92>

SNFS difficulty: 146 digits.
Divisors found:
 r1=8052958223086142680681622957815586168218929634167397 (pp52)
 r2=27464321831555993887170069360422205207318039121738929888700795651176142159905108128526327701 (pp92)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.301).
Factorization parameters were as follows:
n: 221169036334913112164296998420221169036334913112164296998420221169036334913112164296998420221169036334913112164296998420221169036334913112164297
m: 100000000000000000000000000000
deg: 5
c5: 14
c0: 1
skew: 0.59
type: snfs
lss: 1
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [955000, 1755001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 270750 x 270998
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 6.00 hours.

(13·10¹⁷⁴+17)/3 = 4(3)₁₇₃9_<175> = 67 · 2339 · 145679 · 2299821779_<10> · C155

C155 = P37 · P119

P37 = 1541598869214810667584140500809981461_<37>

P119 = 53537064669212941145413465295673500930472498315861866176240448112515332806782940163632147043692072447594155558117056003_<119>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=3498946439
Step 1 took 53500ms
Step 2 took 33290ms
********** Factor found in step 2: 1541598869214810667584140500809981461
Found probable prime factor of 37 digits: 1541598869214810667584140500809981461
Probable prime cofactor has 119 digits

Feb 12, 2009

Factorizations of 466...667 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Feb 11, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.1 / Feb 11, 2009

(10²⁴⁶-7)/3 = (3)₂₄₅1_<246> = 19 · 2573359 · 14760685190666539_<17> · 1961244970676841191_<19> · C204

C204 = P34 · C170

P34 = 3670527667049049608762094305631461_<34>

P38 = 32853358459821858604617750306149758051_<38>

P43 = 1346947706777778949523481608494225806440537_<43>

P91 = 1449864434985030623918793573325434152665912082226603904556877026696713336128758158707403277_<91>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=978534757
Step 1 took 68215ms
Step 2 took 25543ms
********** Factor found in step 2: 3670527667049049608762094305631461
Found probable prime factor of 34 digits: 3670527667049049608762094305631461
Composite cofactor has 170 digits

I temporarily created the _largest_ GNFS. 170 digits.  33331_246

So after some CPUs freed up I've restarted it's cracking and it is finished!

Input number is 64159046974295305520723950792773478735297829893535629441057371436514358427793184945168214366306467643277111078191056438010184481010418240802535657701836153578260482169199 (170 digits)
Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2339262197
Step 1 took 50772ms
Step 2 took 34131ms
********** Factor found in step 2: 1346947706777778949523481608494225806440537
Found probable prime factor of 43 digits: 1346947706777778949523481608494225806440537
Composite cofactor has 128 digits

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=3044812234
Step 1 took 50698ms
Step 2 took 33816ms
********** Factor found in step 2: 32853358459821858604617750306149758051
Found probable prime factor of 38 digits: 32853358459821858604617750306149758051

Done.

Feb 11, 2009

By Robert Backstrom / GGNFS, Msieve / Feb 11, 2009

(14·10¹⁵¹-11)/3 = 4(6)₁₅₀3_<152> = 71 · 8287 · 7636701967_<10> · C137

C137 = P48 · P89

P48 = 248786394540065217850357824605605247924193004817_<48>

P89 = 41746361077843051159101552049861320614361683800694094804506317570285200098139725783800321_<89>

Number: n
N=10385926657724283585795401521825314336224352567336082740302586858895012580247310523831021187057343404423646960236022461931116166519146257
  ( 137 digits)
SNFS difficulty: 152 digits.
Divisors found:

Wed Feb 11 04:04:05 2009  prp48 factor: 248786394540065217850357824605605247924193004817
Wed Feb 11 04:04:05 2009  prp89 factor: 41746361077843051159101552049861320614361683800694094804506317570285200098139725783800321
Wed Feb 11 04:04:05 2009  elapsed time 01:11:10 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 11.77 hours.
Scaled time: 21.53 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_6_150_3
n: 10385926657724283585795401521825314336224352567336082740302586858895012580247310523831021187057343404423646960236022461931116166519146257
deg: 5
c5: 140
c0: -11
m: 1000000000000000000000000000000
skew: 0.60
type: snfs
rlim: 2400000
alim: 2400000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 1900267)
Primes: RFBsize:176302, AFBsize:176359, largePrimes:14958013 encountered
Relations: rels:13357259, finalFF:360294
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 813924 hash collisions in 13880876 relations
Msieve: matrix is 462992 x 463240 (125.6 MB)

Total sieving time: 11.32 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,29,29,58,58,2.5,2.5,100000
total time: 11.77 hours.
 --------- CPU info (if available) ----------

Feb 10, 2009 (5th)

By Wataru Sakai / Msieve / Feb 10, 2009

(38·10¹⁸⁰+43)/9 = 4(2)₁₇₉7_<181> = 3² · C180

C180 = P52 · P61 · P68

P52 = 4095157380675222708692130449535082586017393959914693_<52>

P61 = 4359068972382103688986139651920014643722275960934943125231403_<61>

P68 = 26280537309026180225728609426477728057761054472759357321451829916157_<68>

Number: 42227_180
N=469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135803
  ( 180 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=4095157380675222708692130449535082586017393959914693
 r2=4359068972382103688986139651920014643722275960934943125231403
 r3=26280537309026180225728609426477728057761054472759357321451829916157
Version: 
Total time: 264.64 hours.
Scaled time: 491.96 units (timescale=1.859).
Factorization parameters were as follows:
n: 469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135803
m: 1000000000000000000000000000000000000
deg: 5
c5: 38
c0: 43
skew: 1.03
type: snfs
lss: 1
rlim: 7400000
alim: 7400000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3700000, 6600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1187661 x 1187909
Total sieving time: 264.64 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,53,53,2.5,2.5,100000
total time: 264.64 hours.
 --------- CPU info (if available) ----------

(34·10¹⁹³+11)/9 = 3(7)₁₉₂9_<194> = 3 · 13 · C192

C192 = P65 · P128

P65 = 73872414964991438154457483704634845335532705457402330595616523903_<65>

P128 = 13112620849338994250152717854469097344358167518774155826832299075626325663630475733433075729484006608794021173456736425417519787_<128>

Number: 37779_193
N=968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968661
  ( 192 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=73872414964991438154457483704634845335532705457402330595616523903
 r2=13112620849338994250152717854469097344358167518774155826832299075626325663630475733433075729484006608794021173456736425417519787
Version: 
Total time: 628.47 hours.
Scaled time: 1191.57 units (timescale=1.896).
Factorization parameters were as follows:
n: 968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968660968661
m: 500000000000000000000000000000000000000
deg: 5
c5: 272
c0: 275
skew: 1.00
type: snfs
lss: 1
rlim: 12900000
alim: 12900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 12900000/12900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6450000, 13550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2002769 x 2003017
Total sieving time: 628.47 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,12900000,12900000,28,28,55,55,2.5,2.5,100000
total time: 628.47 hours.
 --------- CPU info (if available) ----------

Feb 10, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.1 / Feb 10, 2009

(10²¹⁴-7)/3 = (3)₂₁₃1_<214> = 199 · 3417523601_<10> · 146381644507781_<15> · 542863066827693324113_<21> · 3626441620130113046137_<22> · C146

C146 = P32 · C115

P32 = 16330057924125944094464094405083_<32>

C115 = [1041522875628824850206331401809802733379697364432095474461905180421216813505211719464595804937315371883591311059963_<115>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2876835942
Step 1 took 9988ms
Step 2 took 9713ms
********** Factor found in step 2: 16330057924125944094464094405083
Found probable prime factor of 32 digits: 16330057924125944094464094405083
Composite cofactor has 115 digits

submitted too soon!!
 http://hpcgi2.nifty.com/m_kamada/f/c.cgi?q=33331_214

Here's the 2nd factor and it is now done.

Input number is 17008128888320931383354727108483414056951585774063347834284200331023442461936324048949309012574574088508559087429890500055997434344403526624991929 (146 digits)
Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=113639890
Step 1 took 10005ms
Step 2 took 9736ms
********** Factor found in step 2: 90101525598690239302205389921070183
Found probable prime factor of 35 digits: 90101525598690239302205389921070183
Probable prime cofactor...

1041522875628824850206331401809802733379697364432095474461905180421216813505211719464595804937315371883591311059963/90101525598690239302205389921070183 is 3-PRP! (0.0003s+0.0002s)

(10²⁰¹-7)/3 = (3)₂₀₀1_<201> = 17 · 179 · 89172847 · 59585840242305315008580382109_<29> · C161

C161 = P30 · P132

P30 = 113651646881442264198543362827_<30>

P132 = 181395019774523320920170919435768269521331834965340563969332201510128587969477158608084691969423902103319185187992483378214882686977_<132>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4223742160
Step 1 took 13927ms
Step 2 took 7230ms
********** Factor found in step 2: 113651646881442264198543362827
Found probable prime factor of 30 digits: 113651646881442264198543362827
Probable prime cofactor has 132 digits

(10²²⁴-7)/3 = (3)₂₂₃1_<224> = 6217 · 41690693165187663091061923_<26> · C195

C195 = P31 · P164

P31 = 1910292367392025446273032520521_<31>

P164 = 67322296392159002608077001735383769255278175908017691909794326083950780784359539151524449036248700307859001497285459431557783174630917455064131629636899687902659521_<164>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=859583623
Step 1 took 15768ms
Step 2 took 7621ms
********** Factor found in step 2: 1910292367392025446273032520521
Found probable prime factor of 31 digits: 1910292367392025446273032520521
Probable prime cofactor has 164 digits

(10²⁴¹-7)/3 = (3)₂₄₀1_<241> = 23 · 2213 · 23014650598801_<14> · 4338308440643575944982309_<25> · C198

C198 = P32 · P167

P32 = 33064576717718812538576350565093_<32>

P167 = 19837261401965769198527981065990686460477593452013812421089201511447713289236940228265964568859059864261224949749765633813634285773219174280863253840646720592135734937_<167>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1448815010
Step 1 took 18365ms
Step 2 took 9100ms
********** Factor found in step 2: 33064576717718812538576350565093
Found probable prime factor of 32 digits: 33064576717718812538576350565093
Probable prime cofactor has 167 digits

(10²⁰³-7)/3 = (3)₂₀₂1_<203> = 61 · 137458709 · 74987928326523863886652073_<26> · C167

C167 = P35 · C133

P35 = 10610358077968123193638709904195047_<35>

C133 = [4996377606594178960305032917299180726132415750204707883244133191273381282972582184700185290354272608872569221264882363056206902082349_<133>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4042664593
Step 1 took 13716ms
Step 2 took 7519ms
********** Factor found in step 2: 10610358077968123193638709904195047
Found probable prime factor of 35 digits: 10610358077968123193638709904195047
Composite cofactor

(10²⁴⁵-7)/3 = (3)₂₄₄1_<245> = 97 · 66751 · 3258371 · 1403863703183_<13> · 2249810655289_<13> · 81791825300240873_<17> · 145142221366577384926667_<24> · C167

C167 = P35 · C133

P35 = 31324445949473317700096188175894333_<35>

C133 = [1345211973340636127176790697467331273618032323820765030845459707299234006881987792073875316307596244915355092769177331580459819511583_<133>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3217281827
Step 1 took 13848ms
Step 2 took 7475ms
********** Factor found in step 2: 31324445949473317700096188175894333
Found probable prime factor of 35 digits: 31324445949473317700096188175894333
Composite cofactor

(10²¹²-7)/3 = (3)₂₁₁1_<212> = 31 · 1093 · 100741 · 10606483 · 31419071 · 50412367 · C180

C180 = P39 · C142

P39 = 160369474887919636204031018406084819503_<39>

C142 = [3624658501922790512467951115480401502972941554455672341416503473005149627879493077221463061699864507739026825856828851938839116595131830375689_<142>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=983877145
Step 1 took 15973ms
Step 2 took 8179ms
********** Factor found in step 2: 160369474887919636204031018406084819503
Found probable prime factor of 39 digits: 160369474887919636204031018406084819503
Composite cofactor has 142 digits

(10²³⁰-7)/3 = (3)₂₂₉1_<230> = 233 · 1297 · 393122956362713113380660433_<27> · C198

C198 = P34 · C164

P34 = 9303129115468200415617210160203863_<34>

C164 = [30159587312927400531121782459578573768168220812002239640548897386508114122444066628011920137122898396501255946521973488448971446636365589871978276114626319714707389_<164>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2889055076
Step 1 took 18352ms
Step 2 took 9099ms
********** Factor found in step 2: 9303129115468200415617210160203863
Found probable prime factor of 34 digits: 9303129115468200415617210160203863
Composite cofactor has 164 digits

(10²³¹-7)/3 = (3)₂₃₀1_<231> = 1499 · 2482112511942529_<16> · C212

C212 = P34 · C179

P34 = 3446466606505865790664327219252139_<34>

C179 = [25994506314096885876158633451155888467704893043048927716803604951844879501178514759167485473233340925526490101735084270552747077029197942597564019662065791324161042138087343728699_<179>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2658315989
Step 1 took 22491ms
Step 2 took 10133ms
********** Factor found in step 2: 3446466606505865790664327219252139
Found probable prime factor of 34 digits: 3446466606505865790664327219252139
Composite cofactor has 179 digits

Feb 10, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 10, 2009

(14·10¹⁹⁵-11)/3 = 4(6)₁₉₄3_<196> = 587 · 797 · 83773 · 1172713 · 178969457 · 846897031831_<12> · 8237203638149_<13> · 201492578685756587_<18> · 80127682289557157831_<20> · C109

C109 = P41 · P69

P41 = 22558276111077612412558862726288421629303_<41>

P69 = 223294318380324094025369972631450077795174647404248745282626852355461_<69>

Number: 46663_195
N=5037134888058223633450405039362530589056135098486725936090357273858295899885946655529213127422826484929673683
  ( 109 digits)
Divisors found:
 r1=22558276111077612412558862726288421629303
 r2=223294318380324094025369972631450077795174647404248745282626852355461
Version: 
Total time: 7.96 hours.
Scaled time: 19.01 units (timescale=2.389).
Factorization parameters were as follows:
name: 46663_195
n: 5037134888058223633450405039362530589056135098486725936090357273858295899885946655529213127422826484929673683
skew: 28245.07
# norm 9.99e+14
c5: 6720
c4: 193258244
c3: 36868640092844
c2: -461046821771144595
c1: -11402140141774968346118
c0: -51999097899030472876385888
# alpha -6.14
Y1: 297120973369
Y0: -943978439869455520635
# Murphy_E 1.16e-09
# M 3864773925994558014424622908664061302157833946497194619583286798249691747731010960060528393480808806337866640
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 51/51
Sieved algebraic special-q in [900000, 1500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 5208950
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 360431 x 360679
Polynomial selection time: 0.58 hours.
Total sieving time: 6.73 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,51,51,2.6,2.6,50000
total time: 7.96 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(14·10¹⁵⁴-11)/3 = 4(6)₁₅₃3_<155> = 17 · 419 · 124219040700783859777_<21> · C131

C131 = P55 · P77

P55 = 1092016169384849798120897210779304049877673274452365493_<55>

P77 = 48297716353085503445307835642388754394984414013051487482307443167425362155721_<77>

Number: 46663_154
N=52741887201932449189966675575636064389669071230243083895140283552082454064592436345514785806933159360295226874178203392830272935453
  ( 131 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=1092016169384849798120897210779304049877673274452365493
 r2=48297716353085503445307835642388754394984414013051487482307443167425362155721
Version: 
Total time: 8.85 hours.
Scaled time: 21.11 units (timescale=2.387).
Factorization parameters were as follows:
n: 52741887201932449189966675575636064389669071230243083895140283552082454064592436345514785806933159360295226874178203392830272935453
m: 10000000000000000000000000000000
deg: 5
c5: 7
c0: -55
skew: 1.51
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8032928
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 414630 x 414878
Total sieving time: 8.09 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 8.85 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 10, 2009 (2nd)

By Sinkiti Sibata / Msieve, GGNFS / Feb 10, 2009

(14·10¹⁴⁵-11)/3 = 4(6)₁₄₄3_<146> = 953 · 19463 · 313037 · 25299178511_<11> · 221211803957189523635743_<24> · C100

C100 = P49 · P51

P49 = 2776588592463035618167267446146966595973892341987_<49>

P51 = 517228173529495948025544277131777941326206753336991_<51>

Mon Feb 09 19:05:19 2009  Msieve v. 1.39
Mon Feb 09 19:05:19 2009  random seeds: 93e85930 5a9aa090
Mon Feb 09 19:05:19 2009  factoring 1436129846322489891861707997659023743610672331253254191596629561333123038998333422561982792429541117 (100 digits)
Mon Feb 09 19:05:20 2009  searching for 15-digit factors
Mon Feb 09 19:05:22 2009  commencing quadratic sieve (100-digit input)
Mon Feb 09 19:05:22 2009  using multiplier of 5
Mon Feb 09 19:05:22 2009  using 32kb Intel Core sieve core
Mon Feb 09 19:05:22 2009  sieve interval: 36 blocks of size 32768
Mon Feb 09 19:05:22 2009  processing polynomials in batches of 6
Mon Feb 09 19:05:22 2009  using a sieve bound of 2665589 (97647 primes)
Mon Feb 09 19:05:22 2009  using large prime bound of 399838350 (28 bits)
Mon Feb 09 19:05:22 2009  using double large prime bound of 3043630695467550 (43-52 bits)
Mon Feb 09 19:05:22 2009  using trial factoring cutoff of 52 bits
Mon Feb 09 19:05:22 2009  polynomial 'A' values have 13 factors
Tue Feb 10 05:05:58 2009  97905 relations (23686 full + 74219 combined from 1461371 partial), need 97743
Tue Feb 10 05:06:00 2009  begin with 1485057 relations
Tue Feb 10 05:06:01 2009  reduce to 256622 relations in 11 passes
Tue Feb 10 05:06:01 2009  attempting to read 256622 relations
Tue Feb 10 05:06:06 2009  recovered 256622 relations
Tue Feb 10 05:06:06 2009  recovered 246902 polynomials
Tue Feb 10 05:06:06 2009  attempting to build 97905 cycles
Tue Feb 10 05:06:06 2009  found 97905 cycles in 7 passes
Tue Feb 10 05:06:06 2009  distribution of cycle lengths:
Tue Feb 10 05:06:06 2009     length 1 : 23686
Tue Feb 10 05:06:06 2009     length 2 : 16873
Tue Feb 10 05:06:06 2009     length 3 : 16230
Tue Feb 10 05:06:06 2009     length 4 : 13475
Tue Feb 10 05:06:06 2009     length 5 : 10092
Tue Feb 10 05:06:06 2009     length 6 : 6934
Tue Feb 10 05:06:06 2009     length 7 : 4403
Tue Feb 10 05:06:06 2009     length 9+: 6212
Tue Feb 10 05:06:06 2009  largest cycle: 27 relations
Tue Feb 10 05:06:07 2009  matrix is 97647 x 97905 (26.2 MB) with weight 6485509 (66.24/col)
Tue Feb 10 05:06:07 2009  sparse part has weight 6485509 (66.24/col)
Tue Feb 10 05:06:09 2009  filtering completed in 3 passes
Tue Feb 10 05:06:09 2009  matrix is 93535 x 93599 (25.2 MB) with weight 6227516 (66.53/col)
Tue Feb 10 05:06:09 2009  sparse part has weight 6227516 (66.53/col)
Tue Feb 10 05:06:09 2009  saving the first 48 matrix rows for later
Tue Feb 10 05:06:09 2009  matrix is 93487 x 93599 (14.8 MB) with weight 4798306 (51.26/col)
Tue Feb 10 05:06:09 2009  sparse part has weight 3306922 (35.33/col)
Tue Feb 10 05:06:09 2009  matrix includes 64 packed rows
Tue Feb 10 05:06:09 2009  using block size 37439 for processor cache size 1024 kB
Tue Feb 10 05:06:10 2009  commencing Lanczos iteration
Tue Feb 10 05:06:10 2009  memory use: 14.9 MB
Tue Feb 10 05:07:16 2009  lanczos halted after 1480 iterations (dim = 93487)
Tue Feb 10 05:07:17 2009  recovered 18 nontrivial dependencies
Tue Feb 10 05:07:20 2009  prp49 factor: 2776588592463035618167267446146966595973892341987
Tue Feb 10 05:07:20 2009  prp51 factor: 517228173529495948025544277131777941326206753336991
Tue Feb 10 05:07:20 2009  elapsed time 10:02:01

(14·10¹²⁴-11)/3 = 4(6)₁₂₃3_<125> = 6481 · 461027756647_<12> · C110

C110 = P41 · P69

P41 = 46900919101739598763136250902750403061951_<41>

P69 = 333009277288341262475781822043827398097001339583286019035504156113359_<69>

Number: 46663_124
N=15618441174229263451452204214107669620027686965986696000061011132240544631265281382536562568528268909055703409
  ( 110 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=46900919101739598763136250902750403061951 (pp41)
 r2=333009277288341262475781822043827398097001339583286019035504156113359 (pp69)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.20 hours.
Scaled time: 1.51 units (timescale=0.472).
Factorization parameters were as follows:
name: 46663_124
n: 15618441174229263451452204214107669620027686965986696000061011132240544631265281382536562568528268909055703409
m: 10000000000000000000000000
deg: 5
c5: 7
c0: -55
skew: 1.51
type: snfs
lss: 1
rlim: 880000
alim: 880000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 880000/880000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [440000, 690001)
Primes: RFBsize:69823, AFBsize:69849, largePrimes:2497100 encountered
Relations: rels:2459152, finalFF:254174
Max relations in full relation-set: 28
Initial matrix: 139737 x 254174 with sparse part having weight 18212629.
Pruned matrix : 105737 x 106499 with weight 5326069.
Total sieving time: 2.96 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000
total time: 3.20 hours.
 --------- CPU info (if available) ----------

(14·10¹²⁵-11)/3 = 4(6)₁₂₄3_<126> = 197 · 373 · C121

C121 = P58 · P64

P58 = 5034932239666512615015060534000743855051033015105258165189_<58>

P64 = 1261357206557626066936205067924634248448443329495853791285540707_<64>

Number: 46663_125
N=6350848065032684185934686063971185295064937421464959195801182165004105369642038985134479207777067087637166977404589848623
  ( 121 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=5034932239666512615015060534000743855051033015105258165189 (pp58)
 r2=1261357206557626066936205067924634248448443329495853791285540707 (pp64)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 3.13 hours.
Scaled time: 1.48 units (timescale=0.472).
Factorization parameters were as follows:
name: 46663_125
n: 6350848065032684185934686063971185295064937421464959195801182165004105369642038985134479207777067087637166977404589848623
m: 10000000000000000000000000
deg: 5
c5: 14
c0: -11
skew: 0.95
type: snfs
lss: 1
rlim: 890000
alim: 890000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 890000/890000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [445000, 695001)
Primes: RFBsize:70555, AFBsize:70714, largePrimes:2555662 encountered
Relations: rels:2542004, finalFF:275929
Max relations in full relation-set: 28
Initial matrix: 141337 x 275929 with sparse part having weight 20282825.
Pruned matrix : 103424 x 104194 with weight 5518508.
Total sieving time: 2.88 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000
total time: 3.13 hours.
 --------- CPU info (if available) ----------

(14·10¹²⁶-11)/3 = 4(6)₁₂₅3_<127> = 8297 · 158364175209281901057565131239_<30> · C94

C94 = P43 · P52

P43 = 3252180732294199220113691787392621500316407_<43>

P52 = 1092079048213714302920212100999726007741012258867823_<52>

Tue Feb 10 07:35:01 2009  Msieve v. 1.39
Tue Feb 10 07:35:01 2009  random seeds: 7830df1c 55440e32
Tue Feb 10 07:35:01 2009  factoring 3551638438742829478396902688411967033383524043930677957142978601586957545196084433786091271961 (94 digits)
Tue Feb 10 07:35:02 2009  searching for 15-digit factors
Tue Feb 10 07:35:03 2009  commencing quadratic sieve (94-digit input)
Tue Feb 10 07:35:03 2009  using multiplier of 1
Tue Feb 10 07:35:03 2009  using 32kb Intel Core sieve core
Tue Feb 10 07:35:03 2009  sieve interval: 36 blocks of size 32768
Tue Feb 10 07:35:03 2009  processing polynomials in batches of 6
Tue Feb 10 07:35:03 2009  using a sieve bound of 2017283 (75294 primes)
Tue Feb 10 07:35:03 2009  using large prime bound of 270315922 (28 bits)
Tue Feb 10 07:35:03 2009  using double large prime bound of 1504419205773942 (42-51 bits)
Tue Feb 10 07:35:03 2009  using trial factoring cutoff of 51 bits
Tue Feb 10 07:35:03 2009  polynomial 'A' values have 12 factors
Tue Feb 10 10:04:55 2009  75815 relations (19619 full + 56196 combined from 1059430 partial), need 75390
Tue Feb 10 10:04:56 2009  begin with 1079049 relations
Tue Feb 10 10:04:57 2009  reduce to 193123 relations in 11 passes
Tue Feb 10 10:04:57 2009  attempting to read 193123 relations
Tue Feb 10 10:05:00 2009  recovered 193123 relations
Tue Feb 10 10:05:00 2009  recovered 172486 polynomials
Tue Feb 10 10:05:00 2009  attempting to build 75815 cycles
Tue Feb 10 10:05:00 2009  found 75815 cycles in 6 passes
Tue Feb 10 10:05:00 2009  distribution of cycle lengths:
Tue Feb 10 10:05:00 2009     length 1 : 19619
Tue Feb 10 10:05:00 2009     length 2 : 13612
Tue Feb 10 10:05:00 2009     length 3 : 12791
Tue Feb 10 10:05:00 2009     length 4 : 10175
Tue Feb 10 10:05:00 2009     length 5 : 7352
Tue Feb 10 10:05:00 2009     length 6 : 4997
Tue Feb 10 10:05:00 2009     length 7 : 3140
Tue Feb 10 10:05:00 2009     length 9+: 4129
Tue Feb 10 10:05:00 2009  largest cycle: 21 relations
Tue Feb 10 10:05:00 2009  matrix is 75294 x 75815 (18.8 MB) with weight 4635779 (61.15/col)
Tue Feb 10 10:05:00 2009  sparse part has weight 4635779 (61.15/col)
Tue Feb 10 10:05:01 2009  filtering completed in 3 passes
Tue Feb 10 10:05:01 2009  matrix is 71133 x 71197 (17.7 MB) with weight 4353762 (61.15/col)
Tue Feb 10 10:05:01 2009  sparse part has weight 4353762 (61.15/col)
Tue Feb 10 10:05:01 2009  saving the first 48 matrix rows for later
Tue Feb 10 10:05:02 2009  matrix is 71085 x 71197 (10.5 MB) with weight 3344583 (46.98/col)
Tue Feb 10 10:05:02 2009  sparse part has weight 2318253 (32.56/col)
Tue Feb 10 10:05:02 2009  matrix includes 64 packed rows
Tue Feb 10 10:05:02 2009  using block size 28478 for processor cache size 1024 kB
Tue Feb 10 10:05:02 2009  commencing Lanczos iteration
Tue Feb 10 10:05:02 2009  memory use: 10.6 MB
Tue Feb 10 10:05:32 2009  lanczos halted after 1125 iterations (dim = 71085)
Tue Feb 10 10:05:32 2009  recovered 17 nontrivial dependencies
Tue Feb 10 10:05:34 2009  prp43 factor: 3252180732294199220113691787392621500316407
Tue Feb 10 10:05:34 2009  prp52 factor: 1092079048213714302920212100999726007741012258867823
Tue Feb 10 10:05:34 2009  elapsed time 02:30:33

(14·10¹²⁷-11)/3 = 4(6)₁₂₆3_<128> = 43 · C127

C127 = P52 · P75

P52 = 3202818108069289937646699055896780108615579936997021_<52>

P75 = 338848876586274922737750506772338476604603843678007719668492077103044148921_<75>

Number: 46663_127
N=1085271317829457364341085271317829457364341085271317829457364341085271317829457364341085271317829457364341085271317829457364341
  ( 127 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=3202818108069289937646699055896780108615579936997021 (pp52)
 r2=338848876586274922737750506772338476604603843678007719668492077103044148921 (pp75)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 5.12 hours.
Scaled time: 2.42 units (timescale=0.472).
Factorization parameters were as follows:
name: 46663_127
n: 1085271317829457364341085271317829457364341085271317829457364341085271317829457364341085271317829457364341085271317829457364341
m: 20000000000000000000000000
deg: 5
c5: 175
c0: -44
skew: 0.76
type: snfs
lss: 1
rlim: 980000
alim: 980000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 980000/980000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [490000, 940001)
Primes: RFBsize:77067, AFBsize:76869, largePrimes:2752811 encountered
Relations: rels:2682505, finalFF:229280
Max relations in full relation-set: 28
Initial matrix: 154003 x 229280 with sparse part having weight 19036918.
Pruned matrix : 135193 x 136027 with weight 8277896.
Total sieving time: 4.71 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,980000,980000,26,26,47,47,2.3,2.3,50000
total time: 5.12 hours.
 --------- CPU info (if available) ----------

Feb 10, 2009

Torbjörn Granlund's web page moved from http://swox.com/~tege/ to https://gmplib.org/~tege/.

Feb 9, 2009

By Robert Backstrom / GGNFS, Msieve

(31·10¹⁹⁶-13)/9 = 3(4)₁₉₅3_<197> = 3 · C197

C197 = P73 · P124

P73 = 1541538682997486108092462038285734433957144793058057857281416009722861673_<73>

P124 = 7448065759307452366876877828005306670204146180497540890101571996285418693550680753007022233010389291838968682804731542510497_<124>

Number: n
N=11481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481
  ( 197 digits)
SNFS difficulty: 197 digits.
Divisors found:

Mon Feb  9 23:38:14 2009  prp73 factor: 1541538682997486108092462038285734433957144793058057857281416009722861673
Mon Feb  9 23:38:14 2009  prp124 factor: 7448065759307452366876877828005306670204146180497540890101571996285418693550680753007022233010389291838968682804731542510497
Mon Feb  9 23:38:14 2009  elapsed time 10:06:08 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20050930-k8
Total time: 44.75 hours.
Scaled time: 89.95 units (timescale=2.010).
Factorization parameters were as follows:
name: KA_3_4_195_3
n: 11481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481
deg: 5
c5: 310
c0: -13
m: 1000000000000000000000000000000000000000
skew: 0.53
type: snfs
rlim: 10000000
alim: 10000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 15503027)
Primes: RFBsize:664579, AFBsize:664376, largePrimes:37285387 encountered
Relations: rels:34226712, finalFF:440225
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 4998041 hash collisions in 37704766 relations
Msieve: matrix is 2492067 x 2492312 (683.2 MB)

Total sieving time: 43.87 hours.
Total relation processing time: 0.88 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000
total time: 44.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.96 BogoMIPS (lpj=2830483)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Total of 4 processors activated (22643.68 BogoMIPS).

Feb 9, 2009 (5th)

Factorizations of 33...331 have been extended up to n=250. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Feb 9, 2009 (4th)

By Sinkiti Sibata / Msieve, GGNFS / Feb 9, 2009

(14·10¹¹³-11)/3 = 4(6)₁₁₂3_<114> = 1061 · 213765728522524457_<18> · C94

C94 = P33 · P61

P33 = 654530224410243311038137953434723_<33>

P61 = 3143573448517984282356294478527718100470179527192788309661953_<61>

Mon Feb 09 07:55:40 2009  Msieve v. 1.39
Mon Feb 09 07:55:40 2009  random seeds: 68aec570 31520c7c
Mon Feb 09 07:55:40 2009  factoring 2057563834708558700370740045678726131547157359320251956209589653345623526539050521743382194019 (94 digits)
Mon Feb 09 07:55:41 2009  searching for 15-digit factors
Mon Feb 09 07:55:42 2009  commencing quadratic sieve (94-digit input)
Mon Feb 09 07:55:43 2009  using multiplier of 19
Mon Feb 09 07:55:43 2009  using 32kb Intel Core sieve core
Mon Feb 09 07:55:43 2009  sieve interval: 36 blocks of size 32768
Mon Feb 09 07:55:43 2009  processing polynomials in batches of 6
Mon Feb 09 07:55:43 2009  using a sieve bound of 1991609 (73895 primes)
Mon Feb 09 07:55:43 2009  using large prime bound of 256917561 (27 bits)
Mon Feb 09 07:55:43 2009  using double large prime bound of 1372868018887893 (42-51 bits)
Mon Feb 09 07:55:43 2009  using trial factoring cutoff of 51 bits
Mon Feb 09 07:55:43 2009  polynomial 'A' values have 12 factors
Mon Feb 09 11:00:34 2009  74091 relations (18064 full + 56027 combined from 1032110 partial), need 73991
Mon Feb 09 11:00:35 2009  begin with 1050174 relations
Mon Feb 09 11:00:36 2009  reduce to 192079 relations in 11 passes
Mon Feb 09 11:00:36 2009  attempting to read 192079 relations
Mon Feb 09 11:00:39 2009  recovered 192079 relations
Mon Feb 09 11:00:39 2009  recovered 176068 polynomials
Mon Feb 09 11:00:40 2009  attempting to build 74091 cycles
Mon Feb 09 11:00:40 2009  found 74091 cycles in 5 passes
Mon Feb 09 11:00:40 2009  distribution of cycle lengths:
Mon Feb 09 11:00:40 2009     length 1 : 18064
Mon Feb 09 11:00:40 2009     length 2 : 13101
Mon Feb 09 11:00:40 2009     length 3 : 12529
Mon Feb 09 11:00:40 2009     length 4 : 9968
Mon Feb 09 11:00:40 2009     length 5 : 7638
Mon Feb 09 11:00:40 2009     length 6 : 5072
Mon Feb 09 11:00:40 2009     length 7 : 3333
Mon Feb 09 11:00:40 2009     length 9+: 4386
Mon Feb 09 11:00:40 2009  largest cycle: 22 relations
Mon Feb 09 11:00:40 2009  matrix is 73895 x 74091 (19.5 MB) with weight 4822373 (65.09/col)
Mon Feb 09 11:00:40 2009  sparse part has weight 4822373 (65.09/col)
Mon Feb 09 11:00:41 2009  filtering completed in 3 passes
Mon Feb 09 11:00:41 2009  matrix is 70504 x 70568 (18.7 MB) with weight 4617367 (65.43/col)
Mon Feb 09 11:00:41 2009  sparse part has weight 4617367 (65.43/col)
Mon Feb 09 11:00:41 2009  saving the first 48 matrix rows for later
Mon Feb 09 11:00:41 2009  matrix is 70456 x 70568 (11.9 MB) with weight 3636187 (51.53/col)
Mon Feb 09 11:00:41 2009  sparse part has weight 2704076 (38.32/col)
Mon Feb 09 11:00:41 2009  matrix includes 64 packed rows
Mon Feb 09 11:00:41 2009  using block size 28227 for processor cache size 1024 kB
Mon Feb 09 11:00:42 2009  commencing Lanczos iteration
Mon Feb 09 11:00:42 2009  memory use: 11.4 MB
Mon Feb 09 11:01:15 2009  lanczos halted after 1116 iterations (dim = 70453)
Mon Feb 09 11:01:15 2009  recovered 16 nontrivial dependencies
Mon Feb 09 11:01:15 2009  prp33 factor: 654530224410243311038137953434723
Mon Feb 09 11:01:15 2009  prp61 factor: 3143573448517984282356294478527718100470179527192788309661953
Mon Feb 09 11:01:15 2009  elapsed time 03:05:35

(14·10¹³⁹-11)/3 = 4(6)₁₃₈3_<140> = 19 · 35603 · 822283639517_<12> · 230069536579690634739859_<24> · C99

C99 = P38 · P61

P38 = 98791777779310242924201001806786296129_<38>

P61 = 3691178247521975388576957842118369003602251665922839419914457_<61>

Number: 46663_139
N=364658061173014811940660341074139620063025883624393215828062415791310764890201996071076685050236953
  ( 99 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=98791777779310242924201001806786296129 (pp38)
 r2=3691178247521975388576957842118369003602251665922839419914457 (pp61)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 9.34 hours.
Scaled time: 4.41 units (timescale=0.472).
Factorization parameters were as follows:
name: 46663_139
n: 364658061173014811940660341074139620063025883624393215828062415791310764890201996071076685050236953
m: 10000000000000000000000000000
deg: 5
c5: 7
c0: -55
skew: 1.51
type: snfs
lss: 1
rlim: 1560000
alim: 1560000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1560000/1560000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [780000, 1480001)
Primes: RFBsize:118376, AFBsize:118000, largePrimes:3519188 encountered
Relations: rels:3532090, finalFF:334834
Max relations in full relation-set: 28
Initial matrix: 236441 x 334834 with sparse part having weight 27429830.
Pruned matrix : 201972 x 203218 with weight 12873741.
Total sieving time: 8.36 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.77 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1560000,1560000,26,26,48,48,2.3,2.3,100000
total time: 9.34 hours.
 --------- CPU info (if available) ----------

(14·10¹³⁰-11)/3 = 4(6)₁₂₉3_<131> = 157 · 191 · 509 · 691 · 2341 · 501145152136659382411_<21> · C97

C97 = P44 · P53

P44 = 55689754421731528313630528731556321420638201_<44>

P53 = 67723232865001450904226740152972125229116778491836821_<53>

Mon Feb 09 12:09:28 2009  Msieve v. 1.39
Mon Feb 09 12:09:28 2009  random seeds: 02d95db0 73bd4a11
Mon Feb 09 12:09:28 2009  factoring 3771490206897668508996417662258181683331035013057624605196952681250925972453955826817274570999021 (97 digits)
Mon Feb 09 12:09:29 2009  searching for 15-digit factors
Mon Feb 09 12:09:31 2009  commencing quadratic sieve (97-digit input)
Mon Feb 09 12:09:31 2009  using multiplier of 1
Mon Feb 09 12:09:31 2009  using 32kb Intel Core sieve core
Mon Feb 09 12:09:31 2009  sieve interval: 36 blocks of size 32768
Mon Feb 09 12:09:31 2009  processing polynomials in batches of 6
Mon Feb 09 12:09:31 2009  using a sieve bound of 2367983 (87059 primes)
Mon Feb 09 12:09:31 2009  using large prime bound of 355197450 (28 bits)
Mon Feb 09 12:09:31 2009  using double large prime bound of 2459493347837550 (43-52 bits)
Mon Feb 09 12:09:31 2009  using trial factoring cutoff of 52 bits
Mon Feb 09 12:09:31 2009  polynomial 'A' values have 12 factors
Mon Feb 09 18:19:31 2009  87388 relations (20335 full + 67053 combined from 1326971 partial), need 87155
Mon Feb 09 18:19:33 2009  begin with 1347306 relations
Mon Feb 09 18:19:34 2009  reduce to 232128 relations in 11 passes
Mon Feb 09 18:19:34 2009  attempting to read 232128 relations
Mon Feb 09 18:19:38 2009  recovered 232128 relations
Mon Feb 09 18:19:38 2009  recovered 219748 polynomials
Mon Feb 09 18:19:38 2009  attempting to build 87388 cycles
Mon Feb 09 18:19:38 2009  found 87388 cycles in 6 passes
Mon Feb 09 18:19:38 2009  distribution of cycle lengths:
Mon Feb 09 18:19:38 2009     length 1 : 20335
Mon Feb 09 18:19:38 2009     length 2 : 14866
Mon Feb 09 18:19:38 2009     length 3 : 14623
Mon Feb 09 18:19:38 2009     length 4 : 11771
Mon Feb 09 18:19:38 2009     length 5 : 9183
Mon Feb 09 18:19:38 2009     length 6 : 6338
Mon Feb 09 18:19:38 2009     length 7 : 4190
Mon Feb 09 18:19:38 2009     length 9+: 6082
Mon Feb 09 18:19:38 2009  largest cycle: 23 relations
Mon Feb 09 18:19:39 2009  matrix is 87059 x 87388 (24.7 MB) with weight 6119422 (70.03/col)
Mon Feb 09 18:19:39 2009  sparse part has weight 6119422 (70.03/col)
Mon Feb 09 18:19:40 2009  filtering completed in 3 passes
Mon Feb 09 18:19:40 2009  matrix is 83556 x 83620 (23.7 MB) with weight 5876520 (70.28/col)
Mon Feb 09 18:19:40 2009  sparse part has weight 5876520 (70.28/col)
Mon Feb 09 18:19:40 2009  saving the first 48 matrix rows for later
Mon Feb 09 18:19:40 2009  matrix is 83508 x 83620 (17.8 MB) with weight 4998471 (59.78/col)
Mon Feb 09 18:19:40 2009  sparse part has weight 4156746 (49.71/col)
Mon Feb 09 18:19:40 2009  matrix includes 64 packed rows
Mon Feb 09 18:19:40 2009  using block size 33448 for processor cache size 1024 kB
Mon Feb 09 18:19:41 2009  commencing Lanczos iteration
Mon Feb 09 18:19:41 2009  memory use: 15.5 MB
Mon Feb 09 18:20:36 2009  lanczos halted after 1322 iterations (dim = 83508)
Mon Feb 09 18:20:36 2009  recovered 17 nontrivial dependencies
Mon Feb 09 18:20:38 2009  prp44 factor: 55689754421731528313630528731556321420638201
Mon Feb 09 18:20:38 2009  prp53 factor: 67723232865001450904226740152972125229116778491836821
Mon Feb 09 18:20:38 2009  elapsed time 06:11:10

Feb 9, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Feb 9, 2009

(10²⁰⁷+53)/9 = (1)₂₀₆7_<207> = 3 · 13³ · 283 · 349 · 551849 · 1122179 · 6118409299921_<13> · 339049922873154043_<18> · 685413813735893660349622719120345198553_<39> · C117

C117 = P57 · P60

P57 = 327597678480587299287372122181103817091004565322392430599_<57>

P60 = 591719762991577707223700158132962999415974935538273550337851_<60>

Number: 11117_207
N=193846020667124193274134252463231803230311020333243374266479905607388867655634000609161657914215087575387961520302749
  ( 117 digits)
Divisors found:
 r1=327597678480587299287372122181103817091004565322392430599
 r2=591719762991577707223700158132962999415974935538273550337851
Version: 
Total time: 19.55 hours.
Scaled time: 46.28 units (timescale=2.367).
Factorization parameters were as follows:
name: 11117_207
n: 193846020667124193274134252463231803230311020333243374266479905607388867655634000609161657914215087575387961520302749
skew: 107858.03
# norm 2.21e+16
c5: 15840
c4: 4785890814
c3: -627266472330572
c2: -53548644060612055049
c1: 2253751019221062026198932
c0: 103688977492581055389939665580
# alpha -6.50
Y1: 4068156942829
Y0: -26153888062927757184623
# Murphy_E 4.29e-10
# M 92835809245172179468634018042921575755769658885494068594739687015821530467670081734141198875134486549057400035496978
type: gnfs
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1650000, 3075001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8802597
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 586758 x 587006
Polynomial selection time: 1.74 hours.
Total sieving time: 15.84 hours.
Total relation processing time: 0.79 hours.
Matrix solve time: 0.78 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3300000,3300000,27,27,52,52,2.4,2.4,75000
total time: 19.55 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(14·10¹⁸⁴-11)/3 = 4(6)₁₈₃3_<185> = C185

C185 = P34 · C151

P34 = 4668890605796314894638351907992049_<34>

C151 = [9995236686147910038267303546468007143025885328917020162545384580246400396068697926861790973608564543295543608436375160287050653974281499069764351921687_<151>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 46666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 (185 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3831152227
Step 1 took 6335ms
Step 2 took 3490ms
********** Factor found in step 2: 4668890605796314894638351907992049
Found probable prime factor of 34 digits: 4668890605796314894638351907992049
Composite cofactor 9995236686147910038267303546468007143025885328917020162545384580246400396068697926861790973608564543295543608436375160287050653974281499069764351921687 has 151 digits

(41·10¹⁶⁴+31)/9 = 4(5)₁₆₃9_<165> = 3³ · 113 · 6295483 · C155

C155 = P53 · P102

P53 = 24644657017319536075637648204817074896826094722424223_<53>

P102 = 962381588209100952662270281234582209105507926978236055510596512465101473662453819049646267537489907601_<102>

Number: 45559_164
N=23717564161196539892251867407341411144763331780835323870934055365940487933694852897012184070156437658761039170173770543157049325016555122847010362994219023
  ( 155 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=24644657017319536075637648204817074896826094722424223
 r2=962381588209100952662270281234582209105507926978236055510596512465101473662453819049646267537489907601
Version: 
Total time: 29.63 hours.
Scaled time: 70.72 units (timescale=2.387).
Factorization parameters were as follows:
n: 23717564161196539892251867407341411144763331780835323870934055365940487933694852897012184070156437658761039170173770543157049325016555122847010362994219023
m: 1000000000000000000000000000000000
deg: 5
c5: 41
c0: 310
skew: 1.50
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2400000, 4800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9931917
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 850619 x 850867
Total sieving time: 26.82 hours.
Total relation processing time: 1.16 hours.
Matrix solve time: 1.55 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000
total time: 29.63 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 9, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Feb 9, 2009

(14·10¹¹²-11)/3 = 4(6)₁₁₁3_<113> = 2771442762173_<13> · C101

C101 = P45 · P56

P45 = 333728983045174223839178403845903215232489713_<45>

P56 = 50455317365568699719447303521559444723728810119559570787_<56>

Number: 46663_112
N=16838401753632761174552519581665125790188915294280208670878619634506695061919163828271280503672814131
  ( 101 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=333728983045174223839178403845903215232489713
 r2=50455317365568699719447303521559444723728810119559570787
Version: 
Total time: 1.63 hours.
Scaled time: 1.59 units (timescale=0.974).
Factorization parameters were as follows:
n: 16838401753632761174552519581665125790188915294280208670878619634506695061919163828271280503672814131
m: 20000000000000000000000
deg: 5
c5: 175
c0: -44
skew: 0.76
type: snfs
lss: 1
rlim: 550000
alim: 550000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2Factor base limits: 550000/550000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [275000, 475001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 61692 x 61912
Total sieving time: 1.63 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,550000,550000,25,25,45,45,2.2,2.2,50000
total time: 1.63 hours.
 --------- CPU info (if available) ----------

Feb 9, 2009

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39 / Feb 9, 2009

(64·10²⁹⁷-1)/9 = 7(1)₂₉₇_<298> = 13 · 293 · 26665813 · 9021099883_<10> · 189256500952289_<15> · 24044752429310032168540061230181910195509606708410951093861793321486277261565258129_<83> · C181

C181 = P47 · P135

P47 = 16442043085323670784303794624712073185907565987_<47>

P135 = 103725436973974982201757157777695270482997614883091416586064114895967077526909040887938629134734812311918176371422582980975507023006683_<135>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=3599812418
Step 1 took 233912ms
********** Factor found in step 1: 16442043085323670784303794624712073185907565987
Found probable prime factor of 47 digits: 16442043085323670784303794624712073185907565987
Probable prime cofactor 103725436973974982201757157777695270482997614883091416586064114895967077526909040887938629134734812311918176371422582980975507023006683 has 135 digits

(14·10¹⁰¹-11)/3 = 4(6)₁₀₀3_<102> = 36876819092879_<14> · C89

C89 = P29 · P60

P29 = 36013266440688616345295431069_<29>

P60 = 351391145736525018235906374578142388376586965484659934737213_<60>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4220053992
Step 1 took 6870ms
********** Factor found in step 1: 36013266440688616345295431069
Found probable prime factor of 29 digits: 36013266440688616345295431069
Probable prime cofactor 351391145736525018235906374578142388376586965484659934737213 has 60 digits

(14·10¹⁵⁷-17)/3 = 4(6)₁₅₆1_<158> = 263 · 787 · 240308225105553793_<18> · C135

C135 = P40 · P96

P40 = 6364827987763412741265319171442647020667_<40>

P96 = 147407979413118889989841788857004121650104020896717420967838755485153730188771108947439999704851_<96>

SNFS difficulty: 158 digits.
Divisors found:
 r1=6364827987763412741265319171442647020667 (pp40)
 r2=147407979413118889989841788857004121650104020896717420967838755485153730188771108947439999704851 (pp96)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 938226432988272075613869989547150629966908036890822199766480366690506401506901213714078973070685006525883063074112294164616654497155617
m: 20000000000000000000000000000000
deg: 5
c5: 175
c0: -68
skew: 0.83
type: snfs
lss: 1
rlim: 3100000
alim: 3100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3100000/3100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1550000, 2950001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 524520 x 524768
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,52,52,2.4,2.4,200000
total time: 22.00 hours.

(14·10¹⁴⁰-11)/3 = 4(6)₁₃₉3_<141> = 37189 · 252319 · 22400846957_<11> · 4769457958706308051_<19> · C102

C102 = P31 · P72

P31 = 1452696818449679082915802292831_<31>

P72 = 320430521352587908644960768758778465953139301183716248884263546526306429_<72>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2525157069
Step 1 took 8338ms
Step 2 took 8976ms
********** Factor found in step 2: 1452696818449679082915802292831
Found probable prime factor of 31 digits: 1452696818449679082915802292831
Probable prime cofactor 320430521352587908644960768758778465953139301183716248884263546526306429 has 72 digits

(14·10¹⁴²-11)/3 = 4(6)₁₄₁3_<143> = 109 · 919249 · 73606566395819363416676910463121_<32> · C103

C103 = P31 · P73

P31 = 3462877103033302539607363495213_<31>

P73 = 1827231102064920444057882406957079321514533690060753527648703282452182191_<73>

)
Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3838477871
Step 1 took 8269ms
Step 2 took 8915ms
********** Factor found in step 2: 3462877103033302539607363495213
Found probable prime factor of 31 digits: 3462877103033302539607363495213
Probable prime cofactor 1827231102064920444057882406957079321514533690060753527648703282452182191 has 73 digits

(14·10¹⁶²-11)/3 = 4(6)₁₆₁3_<163> = 503 · 374518897483_<12> · 189621156269036017_<18> · 7990768929294686986643119_<25> · C107

C107 = P32 · P75

P32 = 34829683178143719100208863012159_<32>

P75 = 469396852263803644050747678050048937489138627551650080432575631558714868691_<75>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1341912022
Step 1 took 8205ms
Step 2 took 8827ms
********** Factor found in step 2: 34829683178143719100208863012159
Found probable prime factor of 32 digits: 34829683178143719100208863012159
Probable prime cofactor has 75 digits

(14·10¹³¹-11)/3 = 4(6)₁₃₀3_<132> = 421 · 6653 · 25669853931265529_<17> · C109

C109 = P28 · P82

P28 = 5441001506811607664968380853_<28>

P82 = 1192902415759760041155529560368665943663030476585120252386859746571997424266723923_<82>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1710825438
Step 1 took 8241ms
Step 2 took 9259ms
********** Factor found in step 2: 5441001506811607664968380853
Found probable prime factor of 28 digits: 5441001506811607664968380853
Probable prime cofactor has 82 digits

(14·10¹²⁸-11)/3 = 4(6)₁₂₇3_<129> = 23 · 631 · 8627 · C121

C121 = P32 · P90

P32 = 18204393101316710103977304775103_<32>

P90 = 204745130990860189227208339461806475665544579666634988381174275691813652333618575353392371_<90>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3648609508
Step 1 took 10038ms
Step 2 took 10265ms
********** Factor found in step 2: 18204393101316710103977304775103
Found probable prime factor of 32 digits: 18204393101316710103977304775103
Probable prime cofactor has 90 digits

(14·10¹²⁶-11)/3 = 4(6)₁₂₅3_<127> = 8297 · C123

C123 = P30 · C94

P30 = 158364175209281901057565131239_<30>

C94 = [3551638438742829478396902688411967033383524043930677957142978601586957545196084433786091271961_<94>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1792202309
Step 1 took 9786ms
********** Factor found in step 1: 158364175209281901057565131239
Found probable prime factor of 30 digits: 158364175209281901057565131239
Composite cofactor has 94 digits

(14·10¹²³-11)/3 = 4(6)₁₂₂3_<124> = C124

C124 = P36 · P89

P36 = 139976468207411466690992179483251259_<36>

P89 = 33338937082994470387437373381084003444503733868280889830350658073276061742343159749441157_<89>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3143898098
Step 1 took 9739ms
Step 2 took 10298ms
********** Factor found in step 2: 139976468207411466690992179483251259
Found probable prime factor of 36 digits: 139976468207411466690992179483251259
Probable prime cofactor has 89 digits

(14·10¹³⁸-11)/3 = 4(6)₁₃₇3_<139> = 17 · 2549 · 3021473437_<10> · C125

C125 = P33 · P93

P33 = 169383648259152212642177349998479_<33>

P93 = 210425205953249123792514702887199157100147468023394362068500007475951252567608738084988271257_<93>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3300486010
Step 1 took 9925ms
Step 2 took 10356ms
********** Factor found in step 2: 169383648259152212642177349998479
Found probable prime factor of 33 digits: 169383648259152212642177349998479
Probable prime cofactor has 93 digits

(14·10¹⁴³-11)/3 = 4(6)₁₄₂3_<144> = 47 · 727 · 8713 · C136

C136 = P31 · P105

P31 = 3245984688652840477417892491523_<31>

P105 = 482903475654005879880195721922667663804795587529937577601033996124366227516537727443752024883915447773773_<105>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3298060385
Step 1 took 12686ms
Step 2 took 11105ms
********** Factor found in step 2: 3245984688652840477417892491523
Found probable prime factor of 31 digits: 3245984688652840477417892491523
Probable prime cofactor has 105 digits

(14·10¹⁴⁶-11)/3 = 4(6)₁₄₅3_<147> = 6607 · 15496067 · C136

C136 = P34 · P102

P34 = 7427355865375387772385083366322131_<34>

P102 = 613686763280137392811487951105655467824258493297675528637383799033626156222044909139765480052040935217_<102>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1885434380
Step 1 took 12242ms
Step 2 took 11012ms
********** Factor found in step 2: 7427355865375387772385083366322131
Found probable prime factor of 34 digits: 7427355865375387772385083366322131
Probable prime cofactor has 102 digits

(14·10¹⁶⁶-11)/3 = 4(6)₁₆₅3_<167> = 149 · 185903 · 368231 · 9731163539_<10> · C144

C144 = P31 · C114

P31 = 1043796167165768018697691187783_<31>

C114 = [450436212392205245158977097476905739315982037445676265753566615858125703057142741445006681401990315834878238498807_<114>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2756841653
Step 1 took 11783ms
Step 2 took 11432ms
********** Factor found in step 2: 1043796167165768018697691187783
Found probable prime factor of 31 digits: 1043796167165768018697691187783
Composite cofactor has 114 digits

(14·10¹⁶¹-11)/3 = 4(6)₁₆₀3_<162> = C162

C162 = P34 · C129

P34 = 2875802551489229275389845286190879_<34>

C129 = [162273542189120096933435105385323543745120089475806304724912872877238918245061625164527994822545703074883859629274728091025656697_<129>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1917313492
Step 1 took 13819ms
Step 2 took 13032ms
********** Factor found in step 2: 2875802551489229275389845286190879
Found probable prime factor of 34 digits: 2875802551489229275389845286190879
Composite cofactor has 129 digits

(14·10¹⁹⁷-11)/3 = 4(6)₁₉₆3_<198> = 8641 · 3267760391131588957807_<22> · C173

C173 = P42 · P45 · P86

P42 = 390172050462673323748290444226800413632453_<42>

P45 = 450278405481663845043229149162313921029509993_<45>

P86 = 94070899340616556671932508249628020480735055023855761777736156380149259767518266558381_<86>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4276860758
Step 1 took 13941ms
********** Factor found in step 1: 450278405481663845043229149162313921029509993
Found probable prime factor of 45 digits: 450278405481663845043229149162313921029509993
Composite cofactor has 128 digits

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=188301114
Step 1 took 13717ms
Step 2 took 13368ms
********** Factor found in step 2: 390172050462673323748290444226800413632453
Found probable prime factor of 42 digits: 390172050462673323748290444226800413632453

(14·10¹¹⁷-11)/3 = 4(6)₁₁₆3_<118> = 16879 · 478517553659149_<15> · C99

C99 = P36 · P64

P36 = 401939126226079394957983105887462761_<36>

P64 = 1437480327483622902238400805844525586589744752604432045435492773_<64>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3372623027
Step 1 took 8298ms
Step 2 took 8669ms
********** Factor found in step 2: 401939126226079394957983105887462761
Found probable prime factor of 36 digits: 401939126226079394957983105887462761
Probable prime cofactor has 64 digits

(14·10¹⁶⁰-11)/3 = 4(6)₁₅₉3_<161> = 29 · 2689 · 1202104864181153_<16> · 158067366782897648179_<21> · 1220582996606484482685652906127_<31> · C91

C91 = P41 · P51

P41 = 13430269913018161973891911460679331665677_<41>

P51 = 192123881081759972441577844435514524860830594438251_<51>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2182111048
Step 1 took 6910ms
********** Factor found in step 1: 13430269913018161973891911460679331665677
Found probable prime factor of 41 digits: 13430269913018161973891911460679331665677
Probable prime cofactor has 51 digits

(14·10¹⁶⁷-11)/3 = 4(6)₁₆₆3_<168> = C168

C168 = P35 · C134

P35 = 19011604170792844575925477496114081_<35>

C134 = [24546411890039112735283532246090593965242266454661597228757806133149530566680832089355587701794240785601818656426814464057750533738823_<134>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1597030230
Step 1 took 13734ms
Step 2 took 13471ms
********** Factor found in step 2: 19011604170792844575925477496114081
Found probable prime factor of 35 digits: 19011604170792844575925477496114081
Composite cofactor has 134 digits

(14·10¹³⁵-11)/3 = 4(6)₁₃₄3_<136> = 97 · C134

C134 = P54 · P81

P54 = 216325011683394660532029937394768546868919821917193331_<54>

P81 = 222396685715430861931979051153696150459754279890786849159256645176706568853454109_<81>

SNFS difficulty: 136 digits.
Divisors found:
 r1=216325011683394660532029937394768546868919821917193331 (pp54)
 r2=222396685715430861931979051153696150459754279890786849159256645176706568853454109 (pp81)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.315).
Factorization parameters were as follows:
n: 48109965635738831615120274914089347079037800687285223367697594501718213058419243986254295532646048109965635738831615120274914089347079
m: 1000000000000000000000000000
deg: 5
c5: 14
c0: -11
skew: 0.95
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [650000, 1250001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 152434 x 152682
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,49,49,2.3,2.3,75000
total time: 4.4 hours.

(14·10¹⁴⁹-11)/3 = 4(6)₁₄₈3_<150> = 6883 · 17477 · C142

C142 = P45 · P97

P45 = 790201431747591512328248467805173945915034069_<45>

P97 = 4909353592223147287834320869080266584236486513036668945791681139340268204613391366624894381757797_<97>

SNFS difficulty: 150 digits.
Divisors found:
 r1=790201431747591512328248467805173945915034069 (pp45)
 r2=4909353592223147287834320869080266584236486513036668945791681139340268204613391366624894381757797 (pp97)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.314).
Factorization parameters were as follows:
n: 3879378237529912534734671158532224275623306421061235339840031566168200646252874061613388020263311523219493339180997249207708347834241361385993
m: 1000000000000000000000000000000
deg: 5
c5: 7
c0: -55
skew: 1.51
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1150000, 1750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 331160 x 331408
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,52,52,2.4,2.4,100000
total time: 12.00 hours.

Feb 8, 2009 (3rd)

Factorizations of 466...663 have been extended up to n=205. I ran experimentally ECM B1=1e6 118 times. I hoped unknown factors have at least 30 digits. ~~However, it seems that too many composite numbers are remaining.~~

Feb 8, 2009 (2nd)

By Wataru Sakai / Msieve / Feb 8, 2009

(13·10²⁰³+17)/3 = 4(3)₂₀₂9_<204> = C204

C204 = P79 · P126

P79 = 2396922217925402921268172480416775195264378139564695797430089284426611931793187_<79>

P126 = 180787398978843102854779581501356388765373471532135050456200490221538733081519619337690684251051702407065124758455082706286697_<126>

Number: 43339_203
N=433333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339
  ( 204 digits)
SNFS difficulty: 205 digits.
Divisors found:
 r1=2396922217925402921268172480416775195264378139564695797430089284426611931793187
 r2=180787398978843102854779581501356388765373471532135050456200490221538733081519619337690684251051702407065124758455082706286697
Version: 
Total time: 1546.99 hours.
Scaled time: 2936.18 units (timescale=1.898).
Factorization parameters were as follows:
n: 433333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339
m: 50000000000000000000000000000000000000000
deg: 5
c5: 104
c0: 425
skew: 1.33
type: snfs
lss: 1
rlim: 18600000
alim: 18600000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 18600000/18600000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [9300000, 25500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3847609 x 3847857
Total sieving time: 1546.99 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,205,5,0,0,0,0,0,0,0,0,18600000,18600000,29,29,56,56,2.6,2.6,100000
total time: 1546.99 hours.
 --------- CPU info (if available) ----------

7·10¹⁸⁰+9 = 7(0)₁₇₉9_<181> = 457 · 10529 · C175

C175 = P79 · P97

P79 = 1161717801790034418750773470371703452693891867991269877836662145444170819572499_<79>

P97 = 1252258735325612009550476834654012397263074865238067762790885431533794609601067164264750550906747_<97>

Number: 70009_180
N=1454771265274838504802719507838411489534063780913110045341063849287359513258473575015176381663813583116174084579985714146175001085882837294433026799172775493671433259354750753
  ( 175 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=1161717801790034418750773470371703452693891867991269877836662145444170819572499
 r2=1252258735325612009550476834654012397263074865238067762790885431533794609601067164264750550906747
Version: 
Total time: 217.89 hours.
Scaled time: 380.44 units (timescale=1.746).
Factorization parameters were as follows:
n: 1454771265274838504802719507838411489534063780913110045341063849287359513258473575015176381663813583116174084579985714146175001085882837294433026799172775493671433259354750753
m: 1000000000000000000000000000000000000
deg: 5
c5: 7
c0: 9
skew: 1.05
type: snfs
lss: 1
rlim: 7200000
alim: 7200000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5Factor base limits: 7200000/7200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3600000, 5800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 942311 x 942559
Total sieving time: 217.89 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,53,53,2.5,2.5,100000
total time: 217.89 hours.
 --------- CPU info (if available) ----------

Feb 8, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 7, 2009

(41·10¹⁶⁷+31)/9 = 4(5)₁₆₆9_<168> = 3 · 13 · 146417 · 3749386087_<10> · 7098948666829_<13> · 3133780391015160839802677_<25> · C114

C114 = P45 · P70

P45 = 101472537403836748368128744496067715026029073_<45>

P70 = 9425707481952324684742027744584472179540783842426196428244301764446471_<70>

Number: 45559_167
N=956450455020031159389268098812021233312805198791307521949393569028884562027532289831015426464963301244570998251383
  ( 114 digits)
Divisors found:
 r1=101472537403836748368128744496067715026029073
 r2=9425707481952324684742027744584472179540783842426196428244301764446471
Version: 
Total time: 13.43 hours.
Scaled time: 32.08 units (timescale=2.388).
Factorization parameters were as follows:
name: 45559_167
n: 956450455020031159389268098812021233312805198791307521949393569028884562027532289831015426464963301244570998251383
skew: 30481.77
# norm 1.70e+15
c5: 43680
c4: 1742174970
c3: -91384218325573
c2: -1454084337276899623
c1: 53164942488116076744005
c0: -63484431654432790325108940
# alpha -5.75
Y1: 1747376151809
Y0: -7380319266821848992667
# Murphy_E 6.77e-10
# M 101155875623595634141182088016873264147289890902546611979436826875341583844862873953881230937014456091194334254487
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1400000, 2310001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9302131
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 450298 x 450546
Polynomial selection time: 1.16 hours.
Total sieving time: 11.15 hours.
Total relation processing time: 0.60 hours.
Matrix solve time: 0.45 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000
total time: 13.43 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 8, 2009

(41·10¹⁶¹+31)/9 = 4(5)₁₆₀9_<162> = 3 · 13 · 151 · 211 · 132211512885134352891187_<24> · C133

C133 = P45 · P88

P45 = 738981477450049648950797460130140636375735769_<45>

P88 = 3752446506855152964198148192252292656497302159234075473588209776069104121023725885264007_<88>

Number: 45559_161
N=2772988463688098795660883458291110182748717211815370475266497074618030888415888309341225266286540888669696576874059611633329438166383
  ( 133 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=738981477450049648950797460130140636375735769
 r2=3752446506855152964198148192252292656497302159234075473588209776069104121023725885264007
Version: 
Total time: 20.57 hours.
Scaled time: 49.11 units (timescale=2.387).
Factorization parameters were as follows:
n: 2772988463688098795660883458291110182748717211815370475266497074618030888415888309341225266286540888669696576874059611633329438166383
m: 100000000000000000000000000000000
deg: 5
c5: 410
c0: 31
skew: 0.60
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 3700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9550539
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 718232 x 718480
Total sieving time: 18.44 hours.
Total relation processing time: 0.79 hours.
Matrix solve time: 1.10 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 20.57 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 7, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 7, 2009

(14·10¹⁶³-17)/3 = 4(6)₁₆₂1_<164> = 1168831 · 6733721 · 1301355036901_<13> · 2440717223838173782958585557_<28> · C112

C112 = P45 · P67

P45 = 533378067555167994638532653261545026277626203_<45>

P67 = 3499866867258391013568251576377228303516047175484132830549381462241_<67>

Number: 46661_163
N=1866752226358640258544889293860773927262146021843474161287748794725834827673734517799791108691807542626556700923
  ( 112 digits)
Divisors found:
 r1=533378067555167994638532653261545026277626203
 r2=3499866867258391013568251576377228303516047175484132830549381462241
Version: 
Total time: 12.19 hours.
Scaled time: 29.10 units (timescale=2.388).
Factorization parameters were as follows:
name: 46661_163
n: 1866752226358640258544889293860773927262146021843474161287748794725834827673734517799791108691807542626556700923
skew: 23720.01
# norm 2.55e+15
c5: 14400
c4: -2094460356
c3: -15775499728857
c2: -1176969688500835859
c1: 2468827411660161501747
c0: 67206418064965898205875705
# alpha -5.63
Y1: 154891682693
Y0: -2645730334848852522966
# Murphy_E 7.89e-10
# M 1361559699571845916487310165643954984042140026411175833540923279969064349616331700765422401167513410905746795998
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1200000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8502252
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 409481 x 409729
Polynomial selection time: 0.87 hours.
Total sieving time: 10.17 hours.
Total relation processing time: 0.61 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000
total time: 12.19 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(41·10¹⁶⁶+31)/9 = 4(5)₁₆₅9_<167> = 3727 · 6079 · 446523649107241_<15> · 282439056897102489148533809233561_<33> · C113

C113 = P48 · P66

P48 = 144729762785463117546069830118601103140161870319_<48>

P66 = 110159699597928074202809633863893697276737851710914857601435993817_<66>

Number: 45559_166
N=15943387191326006946618098390931334098583772565115458602425948433791571117252421966012384908580203304557239817623
  ( 113 digits)
Divisors found:
 r1=144729762785463117546069830118601103140161870319
 r2=110159699597928074202809633863893697276737851710914857601435993817
Version: 
Total time: 12.11 hours.
Scaled time: 28.76 units (timescale=2.375).
Factorization parameters were as follows:
name: 45559_166
n: 15943387191326006946618098390931334098583772565115458602425948433791571117252421966012384908580203304557239817623
skew: 66609.94
# norm 6.86e+15
c5: 10620
c4: -637189443
c3: -279914786507971
c2: 2532966587926767017
c1: 333602027686008373998116
c0: -4735595543010627300655644864
# alpha -6.53
Y1: 410884714789
Y0: -4318090211932266210077
# Murphy_E 7.61e-10
# M 11050356650595640620372840521874159368328391234008289347464790086922844142246216431649260467707320208882737639920
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1200000, 2040001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8427716
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 397846 x 398094
Polynomial selection time: 1.00 hours.
Total sieving time: 9.72 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000
total time: 12.11 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 7, 2009

By Erik Branger / GGNFS, Msieve / Feb 7, 2009

(41·10¹⁵⁹+31)/9 = 4(5)₁₅₈9_<160> = 4057 · C157

C157 = P37 · P120

P37 = 1731585413574630738720683078158942651_<37>

P120 = 648473780046223736657506407721592954100495580810060166742346782078054396205770239313450393164960173160241188816269253837_<120>

Number: 45559_159
N=1122887738613644455399446772382439131268315394517021334867033659244652589488675266343494097992495823405362473639525648399200284830060526387861857420644701887
  ( 157 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=1731585413574630738720683078158942651
 r2=648473780046223736657506407721592954100495580810060166742346782078054396205770239313450393164960173160241188816269253837
Version: 
Total time: 59.12 hours.
Scaled time: 46.88 units (timescale=0.793).
Factorization parameters were as follows:
n: 1122887738613644455399446772382439131268315394517021334867033659244652589488675266343494097992495823405362473639525648399200284830060526387861857420644701887
m: 100000000000000000000000000000000
deg: 5
c5: 41
c0: 310
skew: 1.50
type: snfs
lss: 1
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4

Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1750000, 3450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 660055 x 660303
Total sieving time: 59.12 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000
total time: 59.12 hours.
 --------- CPU info (if available) ----------

(13·10¹⁷⁰+17)/3 = 4(3)₁₆₉9_<171> = 23 · 93239 · 36247012699501949_<17> · 111749476448043512309014281079_<30> · C119

C119 = P52 · P67

P52 = 9982224044582916016268575585641683162100429624915229_<52>

P67 = 4997486439806848026678176052097065941998066363081734935397254369093_<67>

Number: 43339_170
N=49886029301916991974609276945844526763522100914866945557848915315097860285142484809452828704329455042175060930002617297
  ( 119 digits)
Divisors found:
 r1=9982224044582916016268575585641683162100429624915229
 r2=4997486439806848026678176052097065941998066363081734935397254369093
Version: 
Total time: 47.19 hours.
Scaled time: 47.95 units (timescale=1.016).
Factorization parameters were as follows:
name: 43339_170
n: 49886029301916991974609276945844526763522100914866945557848915315097860285142484809452828704329455042175060930002617297
skew: 66614.94
# norm 1.39e+016
c5: 5940
c4: -9717206
c3: 271066779631260
c2: -16839166633651307384
c1: -809108711192551559580945
c0: -3794215600553577222149750975
# alpha -6.07
Y1: 4103857232819
Y0: -96569171293182790941618
# Murphy_E 3.57e-010
# M 12916932973635699386178460139706812150626101346765211629154440786058901502475079559245375928187080673077840138975882646
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3990001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 618297 x 618545
Polynomial selection time: 4.58 hours.
Total sieving time: 42.61 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 47.19 hours.
 --------- CPU info (if available) ----------

Feb 6, 2009 (4th)

By Andreas Tete / Msieve v 1.39 / Feb 6, 2009

(14·10¹⁵⁵-17)/3 = 4(6)₁₅₄1_<156> = 13 · 11093 · 28109 · 611467 · 181767269 · 4633157982779_<13> · 6977436007721_<13> · C107

C107 = P42 · P66

P42 = 140562441090611118741109961262705922783769_<42>

P66 = 227949189434413385400660055310324153026565342740516563531969876557_<66>

Thu Feb 05 23:23:07 2009  
Thu Feb 05 23:23:07 2009  
Thu Feb 05 23:23:07 2009  Msieve v. 1.39
Thu Feb 05 23:23:07 2009  random seeds: 1e3e56b4 f2204d78
Thu Feb 05 23:23:07 2009  factoring 32041094511527285925771939862536179270622749029683467024592163859076668364555480887662733657021368733203333 (107 digits)
Thu Feb 05 23:23:08 2009  searching for 15-digit factors
Thu Feb 05 23:23:10 2009  commencing number field sieve (107-digit input)
Thu Feb 05 23:23:10 2009  R0: -417696951770538278410
Thu Feb 05 23:23:10 2009  R1:  109521462829
Thu Feb 05 23:23:10 2009  A0: -65569852078498172292350013
Thu Feb 05 23:23:10 2009  A1:  6114587653619319208227
Thu Feb 05 23:23:10 2009  A2:  16211690701126034
Thu Feb 05 23:23:10 2009  A3: -7509391818145
Thu Feb 05 23:23:10 2009  A4:  6034581
Thu Feb 05 23:23:10 2009  A5:  2520
Thu Feb 05 23:23:10 2009  skew 34711.60, size 7.223162e-011, alpha -5.300903, combined = 4.227773e-010
Thu Feb 05 23:23:11 2009  
Thu Feb 05 23:23:11 2009  commencing relation filtering
Thu Feb 05 23:23:11 2009  commencing duplicate removal, pass 1
Thu Feb 05 23:23:46 2009  error -15 reading relation 2573525
Thu Feb 05 23:23:53 2009  error -15 reading relation 3299075
Thu Feb 05 23:24:07 2009  found 321328 hash collisions in 4785439 relations
Thu Feb 05 23:24:21 2009  added 31972 free relations
Thu Feb 05 23:24:21 2009  commencing duplicate removal, pass 2
Thu Feb 05 23:24:27 2009  found 295093 duplicates and 4522317 unique relations
Thu Feb 05 23:24:27 2009  memory use: 43.3 MB
Thu Feb 05 23:24:27 2009  reading rational ideals above 2949120
Thu Feb 05 23:24:27 2009  reading algebraic ideals above 2949120
Thu Feb 05 23:24:27 2009  commencing singleton removal, pass 1
Thu Feb 05 23:25:15 2009  relations with 0 large ideals: 114789
Thu Feb 05 23:25:15 2009  relations with 1 large ideals: 709847
Thu Feb 05 23:25:15 2009  relations with 2 large ideals: 1600072
Thu Feb 05 23:25:15 2009  relations with 3 large ideals: 1520566
Thu Feb 05 23:25:15 2009  relations with 4 large ideals: 521434
Thu Feb 05 23:25:15 2009  relations with 5 large ideals: 25444
Thu Feb 05 23:25:15 2009  relations with 6 large ideals: 30165
Thu Feb 05 23:25:15 2009  relations with 7+ large ideals: 0
Thu Feb 05 23:25:15 2009  4522317 relations and about 4381735 large ideals
Thu Feb 05 23:25:15 2009  commencing singleton removal, pass 2
Thu Feb 05 23:26:04 2009  found 1977858 singletons
Thu Feb 05 23:26:04 2009  current dataset: 2544459 relations and about 2016860 large ideals
Thu Feb 05 23:26:04 2009  commencing singleton removal, pass 3
Thu Feb 05 23:26:37 2009  found 454942 singletons
Thu Feb 05 23:26:37 2009  current dataset: 2089517 relations and about 1529923 large ideals
Thu Feb 05 23:26:37 2009  commencing singleton removal, final pass
Thu Feb 05 23:27:05 2009  memory use: 37.3 MB
Thu Feb 05 23:27:05 2009  commencing in-memory singleton removal
Thu Feb 05 23:27:05 2009  begin with 2089517 relations and 1573278 unique ideals
Thu Feb 05 23:27:07 2009  reduce to 1778301 relations and 1253915 ideals in 16 passes
Thu Feb 05 23:27:07 2009  max relations containing the same ideal: 50
Thu Feb 05 23:27:08 2009  reading rational ideals above 720000
Thu Feb 05 23:27:08 2009  reading algebraic ideals above 720000
Thu Feb 05 23:27:08 2009  commencing singleton removal, final pass
Thu Feb 05 23:27:32 2009  keeping 1516991 ideals with weight <= 20, new excess is 189911
Thu Feb 05 23:27:34 2009  memory use: 47.1 MB
Thu Feb 05 23:27:34 2009  commencing in-memory singleton removal
Thu Feb 05 23:27:34 2009  begin with 1782859 relations and 1516991 unique ideals
Thu Feb 05 23:27:36 2009  reduce to 1767800 relations and 1479938 ideals in 9 passes
Thu Feb 05 23:27:36 2009  max relations containing the same ideal: 20
Thu Feb 05 23:27:37 2009  removing 259209 relations and 225427 ideals in 33783 cliques
Thu Feb 05 23:27:37 2009  commencing in-memory singleton removal
Thu Feb 05 23:27:37 2009  begin with 1508591 relations and 1479938 unique ideals
Thu Feb 05 23:27:38 2009  reduce to 1483922 relations and 1229289 ideals in 8 passes
Thu Feb 05 23:27:38 2009  max relations containing the same ideal: 20
Thu Feb 05 23:27:39 2009  removing 192769 relations and 158986 ideals in 33783 cliques
Thu Feb 05 23:27:39 2009  commencing in-memory singleton removal
Thu Feb 05 23:27:39 2009  begin with 1291153 relations and 1229289 unique ideals
Thu Feb 05 23:27:40 2009  reduce to 1273620 relations and 1052357 ideals in 8 passes
Thu Feb 05 23:27:40 2009  max relations containing the same ideal: 20
Thu Feb 05 23:27:41 2009  relations with 0 large ideals: 17696
Thu Feb 05 23:27:41 2009  relations with 1 large ideals: 115178
Thu Feb 05 23:27:41 2009  relations with 2 large ideals: 305321
Thu Feb 05 23:27:41 2009  relations with 3 large ideals: 409159
Thu Feb 05 23:27:41 2009  relations with 4 large ideals: 288047
Thu Feb 05 23:27:41 2009  relations with 5 large ideals: 110539
Thu Feb 05 23:27:41 2009  relations with 6 large ideals: 24923
Thu Feb 05 23:27:41 2009  relations with 7+ large ideals: 2757
Thu Feb 05 23:27:41 2009  commencing 2-way merge
Thu Feb 05 23:27:42 2009  reduce to 773554 relation sets and 552291 unique ideals
Thu Feb 05 23:27:42 2009  commencing full merge
Thu Feb 05 23:27:51 2009  memory use: 41.2 MB
Thu Feb 05 23:27:51 2009  found 360431 cycles, need 332491
Thu Feb 05 23:27:51 2009  weight of 332491 cycles is about 23593800 (70.96/cycle)
Thu Feb 05 23:27:51 2009  distribution of cycle lengths:
Thu Feb 05 23:27:51 2009  1 relations: 35680
Thu Feb 05 23:27:51 2009  2 relations: 32523
Thu Feb 05 23:27:51 2009  3 relations: 32986
Thu Feb 05 23:27:51 2009  4 relations: 30726
Thu Feb 05 23:27:51 2009  5 relations: 28831
Thu Feb 05 23:27:51 2009  6 relations: 26149
Thu Feb 05 23:27:51 2009  7 relations: 23584
Thu Feb 05 23:27:51 2009  8 relations: 21305
Thu Feb 05 23:27:51 2009  9 relations: 18931
Thu Feb 05 23:27:51 2009  10+ relations: 81776
Thu Feb 05 23:27:51 2009  heaviest cycle: 19 relations
Thu Feb 05 23:27:51 2009  commencing cycle optimization
Thu Feb 05 23:27:52 2009  start with 2159557 relations
Thu Feb 05 23:27:58 2009  pruned 72796 relations
Thu Feb 05 23:27:58 2009  memory use: 54.5 MB
Thu Feb 05 23:27:58 2009  distribution of cycle lengths:
Thu Feb 05 23:27:58 2009  1 relations: 35680
Thu Feb 05 23:27:58 2009  2 relations: 33458
Thu Feb 05 23:27:58 2009  3 relations: 34546
Thu Feb 05 23:27:58 2009  4 relations: 31823
Thu Feb 05 23:27:58 2009  5 relations: 30091
Thu Feb 05 23:27:58 2009  6 relations: 26865
Thu Feb 05 23:27:58 2009  7 relations: 24369
Thu Feb 05 23:27:58 2009  8 relations: 21642
Thu Feb 05 23:27:58 2009  9 relations: 19118
Thu Feb 05 23:27:58 2009  10+ relations: 74899
Thu Feb 05 23:27:58 2009  heaviest cycle: 18 relations
Thu Feb 05 23:27:58 2009  
Thu Feb 05 23:27:58 2009  commencing linear algebra
Thu Feb 05 23:27:58 2009  read 332491 cycles
Thu Feb 05 23:27:59 2009  cycles contain 1110974 unique relations
Thu Feb 05 23:28:13 2009  read 1110974 relations
Thu Feb 05 23:28:14 2009  using 20 quadratic characters above 67107810
Thu Feb 05 23:28:21 2009  building initial matrix
Thu Feb 05 23:28:35 2009  memory use: 130.5 MB
Thu Feb 05 23:28:35 2009  read 332491 cycles
Thu Feb 05 23:28:36 2009  matrix is 332253 x 332491 (93.9 MB) with weight 31306746 (94.16/col)
Thu Feb 05 23:28:36 2009  sparse part has weight 22286145 (67.03/col)
Thu Feb 05 23:28:40 2009  filtering completed in 3 passes
Thu Feb 05 23:28:41 2009  matrix is 330616 x 330816 (93.6 MB) with weight 31190739 (94.28/col)
Thu Feb 05 23:28:41 2009  sparse part has weight 22219842 (67.17/col)
Thu Feb 05 23:28:42 2009  read 330816 cycles
Thu Feb 05 23:28:42 2009  matrix is 330616 x 330816 (93.6 MB) with weight 31190739 (94.28/col)
Thu Feb 05 23:28:42 2009  sparse part has weight 22219842 (67.17/col)
Thu Feb 05 23:28:42 2009  saving the first 48 matrix rows for later
Thu Feb 05 23:28:43 2009  matrix is 330568 x 330816 (89.5 MB) with weight 24527269 (74.14/col)
Thu Feb 05 23:28:43 2009  sparse part has weight 21468133 (64.89/col)
Thu Feb 05 23:28:43 2009  matrix includes 64 packed rows
Thu Feb 05 23:28:43 2009  using block size 65536 for processor cache size 3072 kB
Thu Feb 05 23:28:45 2009  commencing Lanczos iteration
Thu Feb 05 23:28:45 2009  memory use: 87.5 MB
Thu Feb 05 23:43:59 2009  lanczos halted after 5229 iterations (dim = 330567)
Thu Feb 05 23:44:00 2009  recovered 30 nontrivial dependencies
Thu Feb 05 23:44:00 2009  
Thu Feb 05 23:44:00 2009  commencing square root phase
Thu Feb 05 23:44:00 2009  reading relations for dependency 1
Thu Feb 05 23:44:00 2009  read 165222 cycles
Thu Feb 05 23:44:01 2009  cycles contain 686041 unique relations
Thu Feb 05 23:44:16 2009  read 686041 relations
Thu Feb 05 23:44:19 2009  multiplying 553752 relations
Thu Feb 05 23:45:48 2009  multiply complete, coefficients have about 21.63 million bits
Thu Feb 05 23:45:49 2009  initial square root is modulo 1629293
Thu Feb 05 23:47:56 2009  reading relations for dependency 2
Thu Feb 05 23:47:56 2009  read 164877 cycles
Thu Feb 05 23:47:56 2009  cycles contain 686198 unique relations
Thu Feb 05 23:48:11 2009  read 686198 relations
Thu Feb 05 23:48:15 2009  multiplying 553800 relations
Thu Feb 05 23:49:43 2009  multiply complete, coefficients have about 21.63 million bits
Thu Feb 05 23:49:44 2009  initial square root is modulo 1629581
Thu Feb 05 23:51:48 2009  reading relations for dependency 3
Thu Feb 05 23:51:49 2009  read 164910 cycles
Thu Feb 05 23:51:49 2009  cycles contain 684575 unique relations
Thu Feb 05 23:51:58 2009  read 684575 relations
Thu Feb 05 23:52:01 2009  multiplying 552312 relations
Thu Feb 05 23:53:30 2009  multiply complete, coefficients have about 21.57 million bits
Thu Feb 05 23:53:31 2009  initial square root is modulo 1571417
Thu Feb 05 23:55:35 2009  prp42 factor: 140562441090611118741109961262705922783769
Thu Feb 05 23:55:35 2009  prp66 factor: 227949189434413385400660055310324153026565342740516563531969876557
Thu Feb 05 23:55:35 2009  elapsed time 00:32:28

Feb 6, 2009 (3rd)

By Sinkiti Sibata / Msieve / Feb 6, 2009

(14·10¹⁴²-17)/3 = 4(6)₁₄₁1_<143> = 23² · 1927327249_<10> · 8660199409527959_<16> · 399129679764332149_<18> · C98

C98 = P38 · P60

P38 = 79231793353124078236648743941235412967_<38>

P60 = 167129935477735101894427739732000701586771138451062866657553_<60>

Thu Feb 05 22:04:54 2009  Msieve v. 1.39
Thu Feb 05 22:04:54 2009  random seeds: 985e3b90 8cf72a5a
Thu Feb 05 22:04:54 2009  factoring 13242004510892868113458993218395334183291843600653289491957333697295603953723418924379752924689751 (98 digits)
Thu Feb 05 22:04:55 2009  searching for 15-digit factors
Thu Feb 05 22:04:56 2009  commencing quadratic sieve (98-digit input)
Thu Feb 05 22:04:57 2009  using multiplier of 19
Thu Feb 05 22:04:57 2009  using 32kb Intel Core sieve core
Thu Feb 05 22:04:57 2009  sieve interval: 36 blocks of size 32768
Thu Feb 05 22:04:57 2009  processing polynomials in batches of 6
Thu Feb 05 22:04:57 2009  using a sieve bound of 2439067 (89290 primes)
Thu Feb 05 22:04:57 2009  using large prime bound of 365860050 (28 bits)
Thu Feb 05 22:04:57 2009  using double large prime bound of 2593981779484650 (43-52 bits)
Thu Feb 05 22:04:57 2009  using trial factoring cutoff of 52 bits
Thu Feb 05 22:04:57 2009  polynomial 'A' values have 13 factors
Fri Feb 06 04:46:34 2009  89401 relations (21588 full + 67813 combined from 1343759 partial), need 89386
Fri Feb 06 04:46:35 2009  begin with 1365347 relations
Fri Feb 06 04:46:37 2009  reduce to 234933 relations in 11 passes
Fri Feb 06 04:46:37 2009  attempting to read 234933 relations
Fri Feb 06 04:46:41 2009  recovered 234933 relations
Fri Feb 06 04:46:41 2009  recovered 223383 polynomials
Fri Feb 06 04:46:41 2009  attempting to build 89401 cycles
Fri Feb 06 04:46:41 2009  found 89401 cycles in 6 passes
Fri Feb 06 04:46:41 2009  distribution of cycle lengths:
Fri Feb 06 04:46:41 2009     length 1 : 21588
Fri Feb 06 04:46:41 2009     length 2 : 15332
Fri Feb 06 04:46:41 2009     length 3 : 15003
Fri Feb 06 04:46:41 2009     length 4 : 12199
Fri Feb 06 04:46:41 2009     length 5 : 9254
Fri Feb 06 04:46:41 2009     length 6 : 6387
Fri Feb 06 04:46:41 2009     length 7 : 4096
Fri Feb 06 04:46:41 2009     length 9+: 5542
Fri Feb 06 04:46:41 2009  largest cycle: 20 relations
Fri Feb 06 04:46:42 2009  matrix is 89290 x 89401 (24.5 MB) with weight 6054518 (67.72/col)
Fri Feb 06 04:46:42 2009  sparse part has weight 6054518 (67.72/col)
Fri Feb 06 04:46:43 2009  filtering completed in 3 passes
Fri Feb 06 04:46:43 2009  matrix is 85516 x 85580 (23.6 MB) with weight 5838893 (68.23/col)
Fri Feb 06 04:46:43 2009  sparse part has weight 5838893 (68.23/col)
Fri Feb 06 04:46:43 2009  saving the first 48 matrix rows for later
Fri Feb 06 04:46:43 2009  matrix is 85468 x 85580 (14.8 MB) with weight 4648295 (54.32/col)
Fri Feb 06 04:46:43 2009  sparse part has weight 3377193 (39.46/col)
Fri Feb 06 04:46:43 2009  matrix includes 64 packed rows
Fri Feb 06 04:46:43 2009  using block size 34232 for processor cache size 1024 kB
Fri Feb 06 04:46:44 2009  commencing Lanczos iteration
Fri Feb 06 04:46:44 2009  memory use: 14.2 MB
Fri Feb 06 04:47:32 2009  lanczos halted after 1354 iterations (dim = 85466)
Fri Feb 06 04:47:32 2009  recovered 17 nontrivial dependencies
Fri Feb 06 04:47:33 2009  prp38 factor: 79231793353124078236648743941235412967
Fri Feb 06 04:47:33 2009  prp60 factor: 167129935477735101894427739732000701586771138451062866657553
Fri Feb 06 04:47:33 2009  elapsed time 06:42:39

(14·10¹²⁷-17)/3 = 4(6)₁₂₆1_<128> = 167 · 7670628211_<10> · 8705215404553_<13> · 2725762211620447_<16> · C88

C88 = P43 · P45

P43 = 5261974045839364868774416996076713797221377_<43>

P45 = 291771713889094533014889494807646277268465479_<45>

Fri Feb 06 07:38:10 2009  Msieve v. 1.39
Fri Feb 06 07:38:10 2009  random seeds: d1fb9c90 fabe24e3
Fri Feb 06 07:38:10 2009  factoring 1535295185794484367616350693774708322882980721452664621333563416031092169180374845344583 (88 digits)
Fri Feb 06 07:38:11 2009  searching for 15-digit factors
Fri Feb 06 07:38:12 2009  commencing quadratic sieve (88-digit input)
Fri Feb 06 07:38:12 2009  using multiplier of 7
Fri Feb 06 07:38:12 2009  using 32kb Intel Core sieve core
Fri Feb 06 07:38:12 2009  sieve interval: 24 blocks of size 32768
Fri Feb 06 07:38:12 2009  processing polynomials in batches of 9
Fri Feb 06 07:38:12 2009  using a sieve bound of 1508383 (57325 primes)
Fri Feb 06 07:38:12 2009  using large prime bound of 120670640 (26 bits)
Fri Feb 06 07:38:12 2009  using double large prime bound of 352275850752880 (42-49 bits)
Fri Feb 06 07:38:12 2009  using trial factoring cutoff of 49 bits
Fri Feb 06 07:38:12 2009  polynomial 'A' values have 11 factors
Fri Feb 06 08:28:48 2009  57685 relations (15938 full + 41747 combined from 607295 partial), need 57421
Fri Feb 06 08:28:49 2009  begin with 623233 relations
Fri Feb 06 08:28:50 2009  reduce to 138855 relations in 10 passes
Fri Feb 06 08:28:50 2009  attempting to read 138855 relations
Fri Feb 06 08:28:51 2009  recovered 138855 relations
Fri Feb 06 08:28:51 2009  recovered 116994 polynomials
Fri Feb 06 08:28:52 2009  attempting to build 57685 cycles
Fri Feb 06 08:28:52 2009  found 57685 cycles in 5 passes
Fri Feb 06 08:28:52 2009  distribution of cycle lengths:
Fri Feb 06 08:28:52 2009     length 1 : 15938
Fri Feb 06 08:28:52 2009     length 2 : 11180
Fri Feb 06 08:28:52 2009     length 3 : 10089
Fri Feb 06 08:28:52 2009     length 4 : 7707
Fri Feb 06 08:28:52 2009     length 5 : 5129
Fri Feb 06 08:28:52 2009     length 6 : 3437
Fri Feb 06 08:28:52 2009     length 7 : 1986
Fri Feb 06 08:28:52 2009     length 9+: 2219
Fri Feb 06 08:28:52 2009  largest cycle: 18 relations
Fri Feb 06 08:28:52 2009  matrix is 57325 x 57685 (13.7 MB) with weight 3362837 (58.30/col)
Fri Feb 06 08:28:52 2009  sparse part has weight 3362837 (58.30/col)
Fri Feb 06 08:28:53 2009  filtering completed in 3 passes
Fri Feb 06 08:28:53 2009  matrix is 53023 x 53087 (12.7 MB) with weight 3111841 (58.62/col)
Fri Feb 06 08:28:53 2009  sparse part has weight 3111841 (58.62/col)
Fri Feb 06 08:28:53 2009  saving the first 48 matrix rows for later
Fri Feb 06 08:28:53 2009  matrix is 52975 x 53087 (8.8 MB) with weight 2527280 (47.61/col)
Fri Feb 06 08:28:53 2009  sparse part has weight 1998012 (37.64/col)
Fri Feb 06 08:28:53 2009  matrix includes 64 packed rows
Fri Feb 06 08:28:53 2009  using block size 21234 for processor cache size 1024 kB
Fri Feb 06 08:28:53 2009  commencing Lanczos iteration
Fri Feb 06 08:28:53 2009  memory use: 8.2 MB
Fri Feb 06 08:29:11 2009  lanczos halted after 840 iterations (dim = 52971)
Fri Feb 06 08:29:11 2009  recovered 15 nontrivial dependencies
Fri Feb 06 08:29:11 2009  prp43 factor: 5261974045839364868774416996076713797221377
Fri Feb 06 08:29:11 2009  prp45 factor: 291771713889094533014889494807646277268465479
Fri Feb 06 08:29:11 2009  elapsed time 00:51:01

Feb 6, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39 / Feb 6, 2009

(14·10¹⁸⁰-17)/3 = 4(6)₁₇₉1_<181> = 1060606468531_<13> · 2463919773272663639_<19> · 434405729906257285262769119_<27> · C124

C124 = P39 · P86

P39 = 161485093949478888156665341696665738479_<39>

P86 = 25456457124730078165396640183259087880093460044467293671285886996120689261101704351329_<86>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=21286820
Step 1 took 7797ms
Step 2 took 8008ms
********** Factor found in step 2: 161485093949478888156665341696665738479
Found probable prime factor of 39 digits: 161485093949478888156665341696665738479
Probable prime cofactor 25456457124730078165396640183259087880093460044467293671285886996120689261101704351329 has 86 digits

(14·10¹²⁹-17)/3 = 4(6)₁₂₈1_<130> = C130

C130 = P41 · P44 · P46

P41 = 30756232585203612651027937491020501863669_<41>

P44 = 21962830987637620960120313531065216680029647_<44>

P46 = 6908524863886151706440987531973173393945771327_<46>

SNFS difficulty: 130 digits.
Divisors found:
 r1=30756232585203612651027937491020501863669 (pp41)
 r2=21962830987637620960120313531065216680029647 (pp44)
 r3=6908524863886151706440987531973173393945771327 (pp46)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.541).
Factorization parameters were as follows:
n: 4666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
m: 100000000000000000000000000
deg: 5
c5: 7
c0: -85
skew: 1.65
type: snfs
lss: 1
rlim: 1060000
alim: 1060000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1060000/1060000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [530000, 1030001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 130792 x 131040
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1060000,1060000,26,26,49,49,2.3,2.3,50000
total time: 2.00 hours.

(14·10¹²⁸-17)/3 = 4(6)₁₂₇1_<129> = C129

C129 = P41 · P89

P41 = 34738831090628376848964014280911856883289_<41>

P89 = 13433574245754085320082529574069024061482425726692517836889920164527496860879649497269549_<89>

SNFS difficulty: 130 digits.
Divisors found:
 r1=34738831090628376848964014280911856883289 (pp41)
 r2=13433574245754085320082529574069024061482425726692517836889920164527496860879649497269549 (pp89)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.530).
Factorization parameters were as follows:
n: 466666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
m: 50000000000000000000000000
deg: 5
c5: 112
c0: -425
skew: 1.31
type: snfs
lss: 1
rlim: 1050000
alim: 1050000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1050000/1050000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [525000, 1025001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 124141 x 124389
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1050000,1050000,26,26,49,49,2.3,2.3,50000
total time: 2.00 hours.

(14·10¹³¹-17)/3 = 4(6)₁₃₀1_<132> = 13 · 41 · C129

C129 = P45 · P85

P45 = 288828715094532057700386432700031725817336707_<45>

P85 = 3031371782837000235560081497627944101257914587605168405618276781202903817139350539931_<85>

SNFS difficulty: 133 digits.
Divisors found:
 r1=288828715094532057700386432700031725817336707 (pp45)
 r2=3031371782837000235560081497627944101257914587605168405618276781202903817139350539931 (pp85)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.714).
Factorization parameters were as follows:
n: 875547217010631644777986241400875547217010631644777986241400875547217010631644777986241400875547217010631644777986241400875547217
m: 200000000000000000000000000
deg: 5
c5: 35
c0: -136
skew: 1.31
type: snfs
lss: 1
rlim: 1160000
alim: 1160000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1160000/1160000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [580000, 1130001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 137843 x 138091
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1160000,1160000,26,26,49,49,2.3,2.3,50000
total time: 2.00 hours.

Feb 6, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Feb 6, 2009

(14·10¹³⁷-17)/3 = 4(6)₁₃₆1_<138> = 13 · 7603 · 304459 · C128

C128 = P55 · P73

P55 = 2818644549300440001732463462728060471607712298207676717_<55>

P73 = 5501857144976582782595579223104339161632838489649970345026741343782422733_<73>

Number: 46661_137
N=15507779652717925762978812460724967482128140727375939557997598641655050637148977744817023024039883436393222293563772349495607561
  ( 128 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=2818644549300440001732463462728060471607712298207676717
 r2=5501857144976582782595579223104339161632838489649970345026741343782422733
Version: 
Total time: 3.11 hours.
Scaled time: 7.42 units (timescale=2.384).
Factorization parameters were as follows:
n: 15507779652717925762978812460724967482128140727375939557997598641655050637148977744817023024039883436393222293563772349495607561
m: 2000000000000000000000000000
deg: 5
c5: 175
c0: -68
skew: 0.83
type: snfs
lss: 1
rlim: 1700000
alim: 1700000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1700000/1700000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [850000, 1600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3895980
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 244627 x 244875
Total sieving time: 2.70 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1700000,1700000,26,26,48,48,2.3,2.3,50000
total time: 3.11 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(14·10¹³²-17)/3 = 4(6)₁₃₁1_<133> = 43 · 242477283479484920079946834362098068307_<39> · C93

C93 = P44 · P49

P44 = 92660912312177449516990491215937950320787587_<44>

P49 = 4830262083843456169427769670141277271595721208103_<49>

Fri Feb 06 00:12:50 2009  
Fri Feb 06 00:12:50 2009  
Fri Feb 06 00:12:50 2009  Msieve v. 1.39
Fri Feb 06 00:12:50 2009  random seeds: 660a05d0 5cd60cef
Fri Feb 06 00:12:50 2009  factoring 447576491395854011724077485504451312282020626085064397979685957809662700075420254722086217461 (93 digits)
Fri Feb 06 00:12:51 2009  searching for 15-digit factors
Fri Feb 06 00:12:52 2009  commencing quadratic sieve (93-digit input)
Fri Feb 06 00:12:53 2009  using multiplier of 1
Fri Feb 06 00:12:53 2009  using VC8 32kb sieve core
Fri Feb 06 00:12:53 2009  sieve interval: 36 blocks of size 32768
Fri Feb 06 00:12:53 2009  processing polynomials in batches of 6
Fri Feb 06 00:12:53 2009  using a sieve bound of 1921417 (71765 primes)
Fri Feb 06 00:12:53 2009  using large prime bound of 232491457 (27 bits)
Fri Feb 06 00:12:53 2009  using double large prime bound of 1146918485979948 (42-51 bits)
Fri Feb 06 00:12:53 2009  using trial factoring cutoff of 51 bits
Fri Feb 06 00:12:53 2009  polynomial 'A' values have 12 factors
Fri Feb 06 02:14:34 2009  72152 relations (18323 full + 53829 combined from 965521 partial), need 71861
Fri Feb 06 02:14:40 2009  begin with 983844 relations
Fri Feb 06 02:14:41 2009  reduce to 184485 relations in 11 passes
Fri Feb 06 02:14:41 2009  attempting to read 184485 relations
Fri Feb 06 02:14:43 2009  recovered 184485 relations
Fri Feb 06 02:14:43 2009  recovered 164103 polynomials
Fri Feb 06 02:14:43 2009  attempting to build 72152 cycles
Fri Feb 06 02:14:43 2009  found 72152 cycles in 6 passes
Fri Feb 06 02:14:43 2009  distribution of cycle lengths:
Fri Feb 06 02:14:43 2009     length 1 : 18323
Fri Feb 06 02:14:43 2009     length 2 : 12755
Fri Feb 06 02:14:43 2009     length 3 : 12311
Fri Feb 06 02:14:43 2009     length 4 : 9774
Fri Feb 06 02:14:43 2009     length 5 : 7136
Fri Feb 06 02:14:43 2009     length 6 : 4780
Fri Feb 06 02:14:43 2009     length 7 : 3028
Fri Feb 06 02:14:43 2009     length 9+: 4045
Fri Feb 06 02:14:43 2009  largest cycle: 23 relations
Fri Feb 06 02:14:44 2009  matrix is 71765 x 72152 (18.7 MB) with weight 4323305 (59.92/col)
Fri Feb 06 02:14:44 2009  sparse part has weight 4323305 (59.92/col)
Fri Feb 06 02:14:45 2009  filtering completed in 3 passes
Fri Feb 06 02:14:45 2009  matrix is 67870 x 67934 (17.6 MB) with weight 4081009 (60.07/col)
Fri Feb 06 02:14:45 2009  sparse part has weight 4081009 (60.07/col)
Fri Feb 06 02:14:45 2009  saving the first 48 matrix rows for later
Fri Feb 06 02:14:45 2009  matrix is 67822 x 67934 (10.4 MB) with weight 3095781 (45.57/col)
Fri Feb 06 02:14:45 2009  sparse part has weight 2042670 (30.07/col)
Fri Feb 06 02:14:45 2009  matrix includes 64 packed rows
Fri Feb 06 02:14:45 2009  using block size 27173 for processor cache size 4096 kB
Fri Feb 06 02:14:45 2009  commencing Lanczos iteration
Fri Feb 06 02:14:45 2009  memory use: 9.8 MB
Fri Feb 06 02:15:08 2009  lanczos halted after 1074 iterations (dim = 67818)
Fri Feb 06 02:15:08 2009  recovered 14 nontrivial dependencies
Fri Feb 06 02:15:08 2009  prp44 factor: 92660912312177449516990491215937950320787587
Fri Feb 06 02:15:08 2009  prp49 factor: 4830262083843456169427769670141277271595721208103
Fri Feb 06 02:15:08 2009  elapsed time 02:02:18

(14·10¹³⁹-17)/3 = 4(6)₁₃₈1_<140> = 110772383 · C132

C132 = P45 · P87

P45 = 867544928525630775815933587141684050103818013_<45>

P87 = 485605175809815527350504843798878617019451230961361043265636180271974040650810199695159_<87>

Number: 46661_139
N=421284307539602778669721916758499875069643185943437423989214592112428119079704791280572763941231332602699958767400234286434613099067
  ( 132 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=867544928525630775815933587141684050103818013
 r2=485605175809815527350504843798878617019451230961361043265636180271974040650810199695159
Version: 
Total time: 3.57 hours.
Scaled time: 8.49 units (timescale=2.380).
Factorization parameters were as follows:
n: 421284307539602778669721916758499875069643185943437423989214592112428119079704791280572763941231332602699958767400234286434613099067
m: 10000000000000000000000000000
deg: 5
c5: 7
c0: -85
skew: 1.65
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [500000, 900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2811844
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 186156 x 186404
Total sieving time: 3.32 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,48,48,2.3,2.3,50000
total time: 3.57 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(41·10¹⁶²+31)/9 = 4(5)₁₆₁9_<163> = 17 · 1291 · 52027 · 826867 · 546491484953_<12> · 22764025382123370395299679_<26> · C111

C111 = P41 · P71

P41 = 25996216458010873554969888938827763682619_<41>

P71 = 14919667159164842307233929961510023909214702259020600485547130499361161_<71>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 387854896951125408943277008177821207312190067820682958920140801813820386612531689968710232347976385056259360659 (111 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=274949117
Step 1 took 3300ms
Step 2 took 2073ms
********** Factor found in step 2: 25996216458010873554969888938827763682619
Found probable prime factor of 41 digits: 25996216458010873554969888938827763682619
Probable prime cofactor 14919667159164842307233929961510023909214702259020600485547130499361161 has 71 digits

(14·10¹⁶¹-17)/3 = 4(6)₁₆₀1_<162> = 13 · 41 · 400827176682167_<15> · 450713539888987849_<18> · 589985397401568359_<18> · C109

C109 = P42 · P68

P42 = 250324450930278353820829206543780882674057_<42>

P68 = 32815367512362198271629357660350079777521673182900499191564513469473_<68>

Number: 46661_161
N=8214488854607361552562394585386053901344629054961773047084840017735290069003506936168427706337309270878561961
  ( 109 digits)
Divisors found:
 r1=250324450930278353820829206543780882674057
 r2=32815367512362198271629357660350079777521673182900499191564513469473
Version: 
Total time: 8.58 hours.
Scaled time: 20.50 units (timescale=2.388).
Factorization parameters were as follows:
name: 46661_161
n: 8214488854607361552562394585386053901344629054961773047084840017735290069003506936168427706337309270878561961
skew: 18354.32
# norm 1.68e+15
c5: 22440
c4: 91497934
c3: -98957537020339
c2: -142166828582838284
c1: 5528770218687941854244
c0: 17899750049926615259981280
# alpha -5.65
Y1: 90997625029
Y0: -817921264128797702543
# Murphy_E 1.11e-09
# M 5826943395806438051439883087651505012647109574972570195839436233128308131774899666095698190388894654990385360
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 51/51
Sieved algebraic special-q in [900000, 1550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 5462762
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 317048 x 317296
Polynomial selection time: 0.58 hours.
Total sieving time: 7.37 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,51,51,2.6,2.6,50000
total time: 8.58 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(41·10¹⁷²+31)/9 = 4(5)₁₇₁9_<173> = 29 · 557 · 521539 · 44450561224585183_<17> · 51805289001007337_<17> · 9858668244709752623_<19> · C111

C111 = P49 · P62

P49 = 4328914463841173098664599202895716455251590868607_<49>

P62 = 55024075942331598058118325165702275379523661514693064001296867_<62>

Number: 45559_172
N=238194518206254381237258429068330575418003725742747954852656581645557520590732261056020564376931006742997754269
  ( 111 digits)
Divisors found:
 r1=4328914463841173098664599202895716455251590868607
 r2=55024075942331598058118325165702275379523661514693064001296867
Version: 
Total time: 9.71 hours.
Scaled time: 23.17 units (timescale=2.387).
Factorization parameters were as follows:
name: 45559_172
n: 238194518206254381237258429068330575418003725742747954852656581645557520590732261056020564376931006742997754269
skew: 29654.94
# norm 2.17e+15
c5: 11400
c4: -4564535842
c3: -33787724348993
c2: 4155617604175931241
c1: 23211893197472624221503
c0: -43709897113678688254743969
# alpha -6.34
Y1: 603982391419
Y0: -1836609473063635500152
# Murphy_E 9.27e-10
# M 94084022461141940107718860003564971933967674203863533458747794154722012115069391269788586720547840715494287834
type: gnfs
rlim: 2100000
alim: 2100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1050000, 1750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8270726
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 356337 x 356585
Polynomial selection time: 0.78 hours.
Total sieving time: 8.03 hours.
Total relation processing time: 0.56 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000
total time: 9.71 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 5, 2009 (8th)

By Sinkiti Sibata / Msieve / Feb 5, 2009

(14·10¹⁰⁸-17)/3 = 4(6)₁₀₇1_<109> = 533723 · 18179547451229_<14> · C90

C90 = P35 · P55

P35 = 69465947887975644559852068056851351_<35>

P55 = 6923661521546369811565028929358579000131701666180044333_<55>

Thu Feb 05 16:45:53 2009  Msieve v. 1.39
Thu Feb 05 16:45:53 2009  random seeds: 37737dfc 756aaded
Thu Feb 05 16:45:53 2009  factoring 480958710449722285681960117310286212508354971043812209689150467311885349813017173570943883 (90 digits)
Thu Feb 05 16:45:54 2009  searching for 15-digit factors
Thu Feb 05 16:45:56 2009  commencing quadratic sieve (90-digit input)
Thu Feb 05 16:45:56 2009  using multiplier of 3
Thu Feb 05 16:45:56 2009  using 32kb Intel Core sieve core
Thu Feb 05 16:45:56 2009  sieve interval: 36 blocks of size 32768
Thu Feb 05 16:45:56 2009  processing polynomials in batches of 6
Thu Feb 05 16:45:56 2009  using a sieve bound of 1583807 (60000 primes)
Thu Feb 05 16:45:56 2009  using large prime bound of 126704560 (26 bits)
Thu Feb 05 16:45:56 2009  using double large prime bound of 384614732789440 (42-49 bits)
Thu Feb 05 16:45:56 2009  using trial factoring cutoff of 49 bits
Thu Feb 05 16:45:56 2009  polynomial 'A' values have 12 factors
Thu Feb 05 18:07:35 2009  60536 relations (16049 full + 44487 combined from 637026 partial), need 60096
Thu Feb 05 18:07:36 2009  begin with 653075 relations
Thu Feb 05 18:07:36 2009  reduce to 147583 relations in 10 passes
Thu Feb 05 18:07:37 2009  attempting to read 147583 relations
Thu Feb 05 18:07:38 2009  recovered 147583 relations
Thu Feb 05 18:07:38 2009  recovered 127631 polynomials
Thu Feb 05 18:07:39 2009  attempting to build 60536 cycles
Thu Feb 05 18:07:39 2009  found 60536 cycles in 5 passes
Thu Feb 05 18:07:39 2009  distribution of cycle lengths:
Thu Feb 05 18:07:39 2009     length 1 : 16049
Thu Feb 05 18:07:39 2009     length 2 : 11747
Thu Feb 05 18:07:39 2009     length 3 : 10567
Thu Feb 05 18:07:39 2009     length 4 : 8067
Thu Feb 05 18:07:39 2009     length 5 : 5731
Thu Feb 05 18:07:39 2009     length 6 : 3589
Thu Feb 05 18:07:39 2009     length 7 : 2197
Thu Feb 05 18:07:39 2009     length 9+: 2589
Thu Feb 05 18:07:39 2009  largest cycle: 17 relations
Thu Feb 05 18:07:39 2009  matrix is 60000 x 60536 (14.8 MB) with weight 3627676 (59.93/col)
Thu Feb 05 18:07:39 2009  sparse part has weight 3627676 (59.93/col)
Thu Feb 05 18:07:40 2009  filtering completed in 3 passes
Thu Feb 05 18:07:40 2009  matrix is 56066 x 56128 (13.7 MB) with weight 3361309 (59.89/col)
Thu Feb 05 18:07:40 2009  sparse part has weight 3361309 (59.89/col)
Thu Feb 05 18:07:40 2009  saving the first 48 matrix rows for later
Thu Feb 05 18:07:40 2009  matrix is 56018 x 56128 (8.6 MB) with weight 2637423 (46.99/col)
Thu Feb 05 18:07:40 2009  sparse part has weight 1924355 (34.29/col)
Thu Feb 05 18:07:40 2009  matrix includes 64 packed rows
Thu Feb 05 18:07:40 2009  using block size 22451 for processor cache size 1024 kB
Thu Feb 05 18:07:40 2009  commencing Lanczos iteration
Thu Feb 05 18:07:40 2009  memory use: 8.4 MB
Thu Feb 05 18:07:59 2009  lanczos halted after 887 iterations (dim = 56014)
Thu Feb 05 18:07:59 2009  recovered 14 nontrivial dependencies
Thu Feb 05 18:08:00 2009  prp35 factor: 69465947887975644559852068056851351
Thu Feb 05 18:08:00 2009  prp55 factor: 6923661521546369811565028929358579000131701666180044333
Thu Feb 05 18:08:00 2009  elapsed time 01:22:07

(14·10¹¹⁹-17)/3 = 4(6)₁₁₈1_<120> = 13 · 59 · 7283 · 4132797668804504093_<19> · C95

C95 = P35 · P60

P35 = 44357599571637221207700789302449841_<35>

P60 = 455710386511529836317128544802766863224130000687759052360477_<60>

Thu Feb 05 18:19:03 2009  Msieve v. 1.39
Thu Feb 05 18:19:03 2009  random seeds: f5622540 4dc7e8cd
Thu Feb 05 18:19:03 2009  factoring 20214218845514468376829031884492141202780645129534194815969814747284526402923001349089943334157 (95 digits)
Thu Feb 05 18:19:04 2009  searching for 15-digit factors
Thu Feb 05 18:19:06 2009  commencing quadratic sieve (95-digit input)
Thu Feb 05 18:19:06 2009  using multiplier of 37
Thu Feb 05 18:19:06 2009  using 32kb Intel Core sieve core
Thu Feb 05 18:19:06 2009  sieve interval: 36 blocks of size 32768
Thu Feb 05 18:19:06 2009  processing polynomials in batches of 6
Thu Feb 05 18:19:06 2009  using a sieve bound of 2128183 (78772 primes)
Thu Feb 05 18:19:06 2009  using large prime bound of 310714718 (28 bits)
Thu Feb 05 18:19:06 2009  using double large prime bound of 1933086450144842 (43-51 bits)
Thu Feb 05 18:19:06 2009  using trial factoring cutoff of 51 bits
Thu Feb 05 18:19:06 2009  polynomial 'A' values have 12 factors
Thu Feb 05 21:54:39 2009  78919 relations (19582 full + 59337 combined from 1161867 partial), need 78868
Thu Feb 05 21:54:42 2009  begin with 1181449 relations
Thu Feb 05 21:54:43 2009  reduce to 204186 relations in 10 passes
Thu Feb 05 21:54:43 2009  attempting to read 204186 relations
Thu Feb 05 21:54:46 2009  recovered 204186 relations
Thu Feb 05 21:54:46 2009  recovered 188215 polynomials
Thu Feb 05 21:54:46 2009  attempting to build 78919 cycles
Thu Feb 05 21:54:46 2009  found 78919 cycles in 6 passes
Thu Feb 05 21:54:46 2009  distribution of cycle lengths:
Thu Feb 05 21:54:46 2009     length 1 : 19582
Thu Feb 05 21:54:46 2009     length 2 : 14025
Thu Feb 05 21:54:46 2009     length 3 : 13434
Thu Feb 05 21:54:46 2009     length 4 : 10578
Thu Feb 05 21:54:46 2009     length 5 : 7884
Thu Feb 05 21:54:46 2009     length 6 : 5442
Thu Feb 05 21:54:46 2009     length 7 : 3407
Thu Feb 05 21:54:46 2009     length 9+: 4567
Thu Feb 05 21:54:46 2009  largest cycle: 21 relations
Thu Feb 05 21:54:46 2009  matrix is 78772 x 78919 (21.5 MB) with weight 5330814 (67.55/col)
Thu Feb 05 21:54:46 2009  sparse part has weight 5330814 (67.55/col)
Thu Feb 05 21:54:48 2009  filtering completed in 3 passes
Thu Feb 05 21:54:48 2009  matrix is 74850 x 74914 (20.6 MB) with weight 5106202 (68.16/col)
Thu Feb 05 21:54:48 2009  sparse part has weight 5106202 (68.16/col)
Thu Feb 05 21:54:48 2009  saving the first 48 matrix rows for later
Thu Feb 05 21:54:48 2009  matrix is 74802 x 74914 (14.8 MB) with weight 4233713 (56.51/col)
Thu Feb 05 21:54:48 2009  sparse part has weight 3424377 (45.71/col)
Thu Feb 05 21:54:48 2009  matrix includes 64 packed rows
Thu Feb 05 21:54:48 2009  using block size 29965 for processor cache size 1024 kB
Thu Feb 05 21:54:49 2009  commencing Lanczos iteration
Thu Feb 05 21:54:49 2009  memory use: 13.2 MB
Thu Feb 05 21:55:29 2009  lanczos halted after 1184 iterations (dim = 74800)
Thu Feb 05 21:55:29 2009  recovered 17 nontrivial dependencies
Thu Feb 05 21:55:33 2009  prp35 factor: 44357599571637221207700789302449841
Thu Feb 05 21:55:33 2009  prp60 factor: 455710386511529836317128544802766863224130000687759052360477
Thu Feb 05 21:55:33 2009  elapsed time 03:36:30

Feb 5, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 5, 2009

(41·10¹⁷¹+31)/9 = 4(5)₁₇₀9_<172> = 2345953 · 225083257862155001821_<21> · 87966517951616456089657749134835387907_<38> · C107

C107 = P47 · P61

P47 = 97527605102358392635059652231653292903706452529_<47>

P61 = 1005619964341110324977300989851086904195026065037215955093281_<61>

Number: 45559_171
N=98075706765307536187489902095252886657188662798627501819296576957833560811191731511967177870879541793357649
  ( 107 digits)
Divisors found:
 r1=97527605102358392635059652231653292903706452529
 r2=1005619964341110324977300989851086904195026065037215955093281
Version: 
Total time: 7.61 hours.
Scaled time: 18.18 units (timescale=2.388).
Factorization parameters were as follows:
name: 45559_171
n: 98075706765307536187489902095252886657188662798627501819296576957833560811191731511967177870879541793357649
skew: 3694.36
# norm 6.81e+14
c5: 262080
c4: 74249556
c3: -78205127191976
c2: -9335641545687925
c1: 102035892536425629126
c0: 59977709598120917721174
# alpha -5.38
Y1: 151806050231
Y0: -206359988591435496625
# Murphy_E 1.41e-09
# M 69217724840439548628410125642110719760392330332550285062401846730483530177346371570195000966628927571656931
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 51/51
Sieved algebraic special-q in [900000, 1450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 5355063
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 299146 x 299394
Polynomial selection time: 0.43 hours.
Total sieving time: 6.26 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.43 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,51,51,2.6,2.6,50000
total time: 7.61 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(14·10¹⁰⁹-17)/3 = 4(6)₁₀₈1_<110> = C110

C110 = P47 · P64

P47 = 20787052726234940370216484139571950095666873157_<47>

P64 = 2244987169718849182365886078043557243840241223173465926322376673_<64>

Number: 46661_109
N=46666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
  ( 110 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=20787052726234940370216484139571950095666873157
 r2=2244987169718849182365886078043557243840241223173465926322376673
Version: 
Total time: 0.35 hours.
Scaled time: 0.82 units (timescale=2.357).
Factorization parameters were as follows:
n: 46666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
m: 10000000000000000000000
deg: 5
c5: 7
c0: -85
skew: 1.65
type: snfs
lss: 1
rlim: 320000
alim: 320000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 320000/320000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [160000, 280001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 943417
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 42297 x 42527
Total sieving time: 0.31 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,320000,320000,25,25,44,44,2.2,2.2,20000
total time: 0.35 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(41·10¹⁵⁸+31)/9 = 4(5)₁₅₇9_<159> = 3 · 313 · 2171717 · 362805067747_<12> · 35153901082644763763_<20> · C119

C119 = P39 · P80

P39 = 221173944223763048794372321041180140113_<39>

P80 = 79193892564994506212021420437914729233141839242031716913696415972933097456063401_<80>

Number: 45559_158
N=17515625577032778123482422833133199922476087253746096807624813956948927100810670967169644831409843544339495714591304313
  ( 119 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=221173944223763048794372321041180140113
 r2=79193892564994506212021420437914729233141839242031716913696415972933097456063401
Version: 
Total time: 23.05 hours.
Scaled time: 55.08 units (timescale=2.390).
Factorization parameters were as follows:
n: 17515625577032778123482422833133199922476087253746096807624813956948927100810670967169644831409843544339495714591304313
m: 100000000000000000000000000000000
deg: 5
c5: 41
c0: 3100
skew: 2.38
type: snfs
lss: 1
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1800000, 3800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9853177
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 686884 x 687132
Total sieving time: 20.86 hours.
Total relation processing time: 0.95 hours.
Matrix solve time: 1.01 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000
total time: 23.05 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797)
Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285)
Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337)
Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Feb 5, 2009 (6th)

By Serge Batalov / GMP-ECM 6.2.1 / Feb 5, 2009

(14·10¹³³-17)/3 = 4(6)₁₃₂1_<134> = 71 · 79 · 37447 · 1134660619_<10> · 1073535220299519023701001_<25> · C93

C93 = P33 · P61

P33 = 115751464003827661828457840765689_<33>

P61 = 1575779834591580964906843212112016937196963642469575467360977_<61>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=805836458
Step 1 took 1800ms
********** Factor found in step 1: 115751464003827661828457840765689
Found probable prime factor of 33 digits: 115751464003827661828457840765689
Probable prime cofactor 1575779834591580964906843212112016937196963642469575467360977 has 61 digits

(14·10¹⁷⁴-17)/3 = 4(6)₁₇₃1_<175> = 43 · 5581 · 2169822149101_<13> · 65388310432339_<14> · 1153785311426014376606166601_<28> · C117

C117 = P30 · P87

P30 = 424978918630483693742771562901_<30>

P87 = 279517920157753837998752384235868465539820566237989946548788294559504855551561157233553_<87>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1507051256
Step 1 took 2796ms
********** Factor found in step 1: 424978918630483693742771562901
Found probable prime factor of 30 digits: 424978918630483693742771562901
Probable prime cofactor has 87 digits

(14·10¹⁶⁹-17)/3 = 4(6)₁₆₈1_<170> = C170

C170 = P30 · C141

P30 = 215880244364499579382801212799_<30>

C141 = [216169232177971192501955249216876153564299586479509590522860815653381675214844760678296009204006289701356974365633658790823919329922476632539_<141>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3927306547
Step 1 took 3572ms
Step 2 took 3373ms
********** Factor found in step 2: 215880244364499579382801212799
Found probable prime factor of 30 digits: 215880244364499579382801212799
Composite cofactor has 141 digits

(14·10¹⁸²-17)/3 = 4(6)₁₈₁1_<183> = 19445673994992446629_<20> · C164

C164 = P35 · P129

P35 = 40139161552591513443366540237002969_<35>

P129 = 597882007272101010985678287128299619443541305065912651420531019621137283657335574509787903281386890063449376162669440326865485161_<129>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3815980854
Step 1 took 4532ms
Step 2 took 4245ms
********** Factor found in step 2: 40139161552591513443366540237002969
Found probable prime factor of 35 digits: 40139161552591513443366540237002969
Probable prime cofactor 597882007272101010985678287128299619443541305065912651420531019621137283657335574509787903281386890063449376162669440326865485161 has 129 digits

(14·10¹⁰⁴-17)/3 = 4(6)₁₀₃1_<105> = 3315197839_<10> · C96

C96 = P37 · P60

P37 = 1048186020905847339687889653549342847_<37>

P60 = 134294728908693501313898247253393131921162318436945997859317_<60>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1343043597
Step 1 took 5472ms
Step 2 took 6340ms
********** Factor found in step 2: 1048186020905847339687889653549342847
Found probable prime factor of 37 digits: 1048186020905847339687889653549342847
Probable prime cofactor has 60 digits

(14·10¹⁴⁵-17)/3 = 4(6)₁₄₄1_<146> = 149 · 17159 · 113217659 · 23804775121_<11> · 10255604759491163_<17> · C105

C105 = P39 · P67

P39 = 153263613785359808010712420969640040613_<39>

P67 = 4308736618824956231372711263088119074543145711353357387045343555331_<67>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=746015315
Step 1 took 8338ms
Step 2 took 9009ms
********** Factor found in step 2: 153263613785359808010712420969640040613
Found probable prime factor of 39 digits: 153263613785359808010712420969640040613
Probable prime cofactor 4308736618824956231372711263088119074543145711353357387045343555331 has 67 digits

(14·10¹⁷³-17)/3 = 4(6)₁₇₂1_<174> = 13 · 859 · 5998697 · 13845991 · C156

C156 = P33 · C124

P33 = 409103341929942277576340139824293_<33>

C124 = [1229861670861254617548494925913918290044304120418280776400992158432398260682671962391119989681635502520909226281982831769953_<124>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1580869394
Step 1 took 10961ms
Step 2 took 10200ms
********** Factor found in step 2: 409103341929942277576340139824293
Found probable prime factor of 33 digits: 409103341929942277576340139824293
Composite cofactor has 124 digits

(14·10¹³²-17)/3 = 4(6)₁₃₁1_<133> = 43 · C132

C132 = P39 · C93

P39 = 242477283479484920079946834362098068307_<39>

C93 = [447576491395854011724077485504451312282020626085064397979685957809662700075420254722086217461_<93>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=456477673
Step 1 took 9730ms
Step 2 took 10894ms
********** Factor found in step 2: 242477283479484920079946834362098068307
Found probable prime factor of 39 digits: 242477283479484920079946834362098068307
Composite cofactor has 93 digits

(14·10¹⁶⁴-17)/3 = 4(6)₁₆₃1_<165> = 23 · 109 · 520607 · 105002844451_<12> · C145

C145 = P34 · P111

P34 = 7375632163441432727253479391156161_<34>

P111 = 461681136379374003491287880045920544178410299268405105269544565799988405783938430548888977576093818499029824699_<111>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2326954712
Step 1 took 9217ms
Step 2 took 9096ms
********** Factor found in step 2: 7375632163441432727253479391156161
Found probable prime factor of 34 digits: 7375632163441432727253479391156161
Probable prime cofactor 461681136379374003491287880045920544178410299268405105269544565799988405783938430548888977576093818499029824699 has 111 digits

Feb 5, 2009 (5th)

By Erik Branger / GGNFS, Msieve / Feb 5, 2009

(13·10¹⁷⁶+17)/3 = 4(3)₁₇₅9_<177> = 97 · 109 · 901097 · 451257280864272805261_<21> · 3965646214566007961499170761_<28> · C119

C119 = P56 · P63

P56 = 59185885698644238019123758994034774471830972650680846983_<56>

P63 = 429433559966094613538911133005929578976819079364002591855166933_<63>

Number: 43339_176
N=25416405595315161978385298359847677774018773093491295116086851158718087605127154500811030786194342648976153229294413139
  ( 119 digits)
Divisors found:
 r1=59185885698644238019123758994034774471830972650680846983
 r2=429433559966094613538911133005929578976819079364002591855166933
Version: 
Total time: 46.43 hours.
Scaled time: 48.89 units (timescale=1.053).
Factorization parameters were as follows:
name: 43339_176
n: 25416405595315161978385298359847677774018773093491295116086851158718087605127154500811030786194342648976153229294413139
skew: 207459.67
Y0: -70807329228647219464816
Y1:  5649748224103
c0: -3986302978437759696767634254043
c1:  48211596676827722611050315
c2:  160152199119492675151
c3: -1985529414860945
c4: -2119259958
c5:  14280
type: gnfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4230001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 606781 x 607029
Total sieving time: 46.43 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 46.43 hours.
 --------- CPU info (if available) ----------

Feb 5, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Feb 5, 2009

(41·10¹⁴⁹+31)/9 = 4(5)₁₄₈9_<150> = 3 · 13 · 89 · 2681561 · 7209187 · 198035972315986749236495057_<27> · C107

C107 = P42 · P65

P42 = 742595156508827118542839675104487894660931_<42>

P65 = 46165395947484115517095878930268133102823135966773754229187847641_<65>

Number: n
N=34282199428913939966287465267724872592788642827752255150950681745921588947521176996927132361852311383213771
  ( 107 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=742595156508827118542839675104487894660931 (pp42)
 r2=46165395947484115517095878930268133102823135966773754229187847641 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 16.56 hours.
Scaled time: 30.28 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_5_148_9
n: 34282199428913939966287465267724872592788642827752255150950681745921588947521176996927132361852311383213771
deg: 5
c5: 41
c0: 310
m: 1000000000000000000000000000000
skew: 1.50
type: snfs
rlim: 2200000
alim: 2200000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [1100000, 1920001)
Primes: RFBsize:162662, AFBsize:163117, largePrimes:14471590 encountered
Relations: rels:13542748, finalFF:378681
Max relations in full relation-set: 48
Initial matrix: 325844 x 378681 with sparse part having weight 60399318.
Pruned matrix : 311607 x 313300 with weight 44312611.
Total sieving time: 14.53 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 1.46 hours.
Total square root time: 0.15 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,56,56,2.5,2.5,100000
total time: 16.56 hours.
 --------- CPU info (if available) ----------

(41·10¹⁴⁷+31)/9 = 4(5)₁₄₆9_<148> = 139 · 587 · 6902943828894011321_<19> · C124

C124 = P44 · P81

P44 = 15790481464166446594690651815180971019684223_<44>

P81 = 512222597526685881224335243996449802720016005174732892674800648867239124059296361_<81>

Number: n
N=8088241431772323359905288451844054603516404793649864842836942168315351908932187004288549805467603217715112449054385793012503
  ( 124 digits)
SNFS difficulty: 148 digits.
Divisors found:

Thu Feb 05 15:47:15 2009  prp44 factor: 15790481464166446594690651815180971019684223
Thu Feb 05 15:47:15 2009  prp81 factor: 512222597526685881224335243996449802720016005174732892674800648867239124059296361
Thu Feb 05 15:47:15 2009  elapsed time 01:37:26 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 17.78 hours.
Scaled time: 31.14 units (timescale=1.751).
Factorization parameters were as follows:
name: KA_4_5_146_9
n: 8088241431772323359905288451844054603516404793649864842836942168315351908932187004288549805467603217715112449054385793012503
deg: 5
c5: 4100
c0: 31
m: 100000000000000000000000000000
skew: 0.38
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2750357)
Primes: RFBsize:148933, AFBsize:148687, largePrimes:14081621 encountered
Relations: rels:13256340, finalFF:301266
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 1857315 hash collisions in 14938253 relations
Msieve: matrix is 390722 x 390970 (102.5 MB)

Total sieving time: 17.15 hours.
Total relation processing time: 0.63 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,56,56,2.5,2.5,100000
total time: 17.78 hours.
 --------- CPU info (if available) ----------

Feb 5, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 5, 2009

(41·10¹⁶⁰+31)/9 = 4(5)₁₅₉9_<161> = 19081 · 121814779271_<12> · 246290541059_<12> · 2928052299134664302694239_<25> · C110

C110 = P48 · P62

P48 = 417031829818786514625003110149835023357335429041_<48>

P62 = 65169511730006841092794775676897877056841471574689193783777149_<62>

Number: 45559_160
N=27177760725161624492666122154903250925655192592760208327964201536452894271617890829840465084241824723446784109
  ( 110 digits)
Divisors found:
 r1=417031829818786514625003110149835023357335429041
 r2=65169511730006841092794775676897877056841471574689193783777149
Version: 
Total time: 9.18 hours.
Scaled time: 21.90 units (timescale=2.386).
Factorization parameters were as follows:
name: 45559_160
n: 27177760725161624492666122154903250925655192592760208327964201536452894271617890829840465084241824723446784109
skew: 33792.95
# norm 2.92e+15
c5: 18240
c4: -2426298761
c3: -129766364201011
c2: 2159625987619716429
c1: 30758043909317759146504
c0: -322864991197159729721686960
# alpha -6.42
Y1: 509338277569
Y0: -1083036769604062843989
# Murphy_E 1.06e-09
# M 4069870747139864016425162783638635230370222738182267958161246223817949573585473063739648028664842912771748600
type: gnfs
rlim: 2100000
alim: 2100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1050000, 1700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8114328
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 357183 x 357431
Polynomial selection time: 0.66 hours.
Total sieving time: 7.64 hours.
Total relation processing time: 0.52 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000
total time: 9.18 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672353)

Feb 5, 2009 (2nd)

Factorizations of 466...661 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Feb 5, 2009

By Robert Backstrom / GGNFS, Msieve / Feb 5, 2009

(37·10²⁰⁴+17)/9 = 4(1)₂₀₃3_<205> = 3 · C205

C205 = P102 · P103

P102 = 153309913352856585802120594537109285957749031611920050232775437965114309133133655034055113177052274147_<102>

P103 = 8938563334885849358263822539007719875728625710335868949963740586159114978519165202551819473673605180193_<103>

Number: n
N=1370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370371
  ( 205 digits)
SNFS difficulty: 206 digits.
Divisors found:

Wed Feb  4 22:20:50 2009  prp102 factor: 153309913352856585802120594537109285957749031611920050232775437965114309133133655034055113177052274147
Wed Feb  4 22:20:50 2009  prp103 factor: 8938563334885849358263822539007719875728625710335868949963740586159114978519165202551819473673605180193
Wed Feb  4 22:20:50 2009  elapsed time 24:31:38 (Msieve 1.39 - dependency 1)

Version: GGNFS-0.77.1-20050930-k8
Total time: 151.50 hours.
Scaled time: 304.66 units (timescale=2.011).
Factorization parameters were as follows:
name: KA_4_1_203_3
n: 1370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370370371
deg: 5
c5: 37
c0: 170
m: 100000000000000000000000000000000000000000
skew: 1.36
type: snfs
rlim: 10000000
alim: 10000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 42599990)
Primes: RFBsize:664579, AFBsize:664455, largePrimes:36623236 encountered
Relations: rels:31037462, finalFF:48980
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 8849123 hash collisions in 45406511 relations
Msieve: matrix is 3743033 x 3743281 (1019.2 MB)

Total sieving time: 150.22 hours.
Total relation processing time: 1.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,206,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000
total time: 151.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.96 BogoMIPS (lpj=2830483)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Total of 4 processors activated (22643.68 BogoMIPS).

P102 is the largest prime factor which was found in our tables so far. Congratulations!

Feb 4, 2009 (2nd)

By Jo Yeong Uk / GGNFS, MSieve v1.39 / Feb 4, 2009

(41·10¹⁵⁴+31)/9 = 4(5)₁₅₃9_<155> = 1283 · 1871 · 987869 · 7992647567_<10> · 17891718779497_<14> · 45579564781601_<14> · C106

C106 = P47 · P60

P47 = 12777040938465543273078312549300380272022438917_<47>

P60 = 230673847391265473660109691575737534480723477975666285649269_<60>

Number: 45559_154
N=2947329191551552118509279124099511833564446263428751552985788903463748077941107615863485422624550238201673
  ( 106 digits)
Divisors found:
 r1=12777040938465543273078312549300380272022438917
 r2=230673847391265473660109691575737534480723477975666285649269
Version: 
Total time: 5.69 hours.
Scaled time: 13.60 units (timescale=2.391).
Factorization parameters were as follows:
name: 45559_154
n: 2947329191551552118509279124099511833564446263428751552985788903463748077941107615863485422624550238201673
skew: 9152.16
# norm 7.12e+14
c5: 45720
c4: -1680847446
c3: 28490701205429
c2: 459015295180056074
c1: -856933538753681074326
c0: 316787297664447954662535
# alpha -6.42
Y1: 133171513343
Y0: -145166836990382843528
# Murphy_E 1.77e-09
# M 1114897154838392718458649305345136319880261944443620690400281399038725591199716555678089018166755566500259
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved algebraic special-q in [750000, 1150001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 4842124
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 255636 x 255884
Polynomial selection time: 0.38 hours.
Total sieving time: 4.60 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000
total time: 5.69 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672353)

(13·10¹⁷⁷+17)/3 = 4(3)₁₇₆9_<178> = C178

C178 = P62 · P117

P62 = 12864649056903134634243503707994331842134704910686309339021097_<62>

P117 = 336840384387172910065381478083455265403401238630972549534291262928443204454411404621225093869459778485857538625090787_<117>

Number: 43339_177
N=4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339
  ( 178 digits)
SNFS difficulty: 178 digits.
Divisors found:
 r1=12864649056903134634243503707994331842134704910686309339021097
 r2=336840384387172910065381478083455265403401238630972549534291262928443204454411404621225093869459778485857538625090787
Version: 
Total time: 88.51 hours.
Scaled time: 211.28 units (timescale=2.387).
Factorization parameters were as follows:
n: 4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339
m: 100000000000000000000000000000000000
deg: 5
c5: 1300
c0: 17
skew: 0.42
type: snfs
lss: 1
rlim: 6000000
alim: 6000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3000000, 5500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 18243247
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1291523 x 1291771
Total sieving time: 82.00 hours.
Total relation processing time: 2.39 hours.
Matrix solve time: 3.79 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
snfs,178,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,53,53,2.5,2.5,100000
total time: 88.51 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672353)

Feb 4, 2009

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39 / Feb 4, 2009

(41·10¹⁹¹+31)/9 = 4(5)₁₉₀9_<192> = 3³ · 13 · 109 · 211 · 15573491 · 19169933 · C171

C171 = P32 · P139

P32 = 39851434970484144828435349156003_<32>

P139 = 4743236095339451124911657751165018729393994052130281112840738761497417153390871883429816815069838248761715721446026550938237187794672084099_<139>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2412366714
Step 1 took 13613ms
Step 2 took 16052ms
********** Factor found in step 2: 39851434970484144828435349156003
Found probable prime factor of 32 digits: 39851434970484144828435349156003
Probable prime cofactor has 139 digits

(41·10¹⁷¹+31)/9 = 4(5)₁₇₀9_<172> = 2345953 · 225083257862155001821_<21> · C145

C145 = P38 · C107

P38 = 87966517951616456089657749134835387907_<38>

C107 = [98075706765307536187489902095252886657188662798627501819296576957833560811191731511967177870879541793357649_<107>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3230988224
Step 1 took 11699ms
Step 2 took 14113ms
********** Factor found in step 2: 87966517951616456089657749134835387907
Found probable prime factor of 38 digits: 87966517951616456089657749134835387907
Composite cofactor has 107 digits

(41·10¹³⁷+31)/9 = 4(5)₁₃₆9_<138> = 3⁴ · 13 · 32410105898003833122953056363_<29> · C107

C107 = P48 · P59

P48 = 252393054615440922847616237510590238393523348029_<48>

P59 = 52887754263971463652272433280462875253408094097265038159789_<59>

SNFS difficulty: 139 digits.
Divisors found:
 r1=252393054615440922847616237510590238393523348029 (pp48)
 r2=52887754263971463652272433280462875253408094097265038159789 (pp59)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.729).
Factorization parameters were as follows:
n: 13348501850434568171603581727123465106200956285391267018621817037449652422929632858882357728590612360205881
m: 2000000000000000000000000000
deg: 5
c5: 1025
c0: 248
skew: 0.75
type: snfs
lss: 1
rlim: 1480000
alim: 1480000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1480000/1480000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [740000, 1790001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 248108 x 248356
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1480000,1480000,26,26,49,49,2.3,2.3,75000
total time: 4.00 hours.

(41·10¹⁴⁴+31)/9 = 4(5)₁₄₃9_<145> = 29 · 3583 · 31883 · C136

C136 = P44 · P92

P44 = 43891407210223167991938940264408438234274231_<44>

P92 = 31329816916985703162968325139908103167161980429416652592213407347484770038268189526368100369_<92>

SNFS difficulty: 146 digits.
Divisors found:
 r1=43891407210223167991938940264408438234274231 (pp44)
 r2=31329816916985703162968325139908103167161980429416652592213407347484770038268189526368100369 (pp92)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.301).
Factorization parameters were as follows:
n: 1375109752125158075603206090777891282120476954822609292629635110157496109652935842053098044646592473679160655521538764646654558878291239
m: 100000000000000000000000000000
deg: 5
c5: 41
c0: 310
skew: 1.50
type: snfs
lss: 1
rlim: 1940000
alim: 1940000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1940000/1940000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [970000, 2470001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 323468 x 323716
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1940000,1940000,26,26,49,49,2.3,2.3,100000
total time: 7.00 hours.

Feb 3, 2009 (4th)

By Robert Backstrom / Msieve, GMP-ECM / Feb 3, 2009

(41·10¹⁵²+31)/9 = 4(5)₁₅₁9_<153> = 3 · 17226924482964131660780603123_<29> · 8255403602793355396207431453373333_<34> · C91

C91 = P38 · P53

P38 = 64454058946572661063597653904314564797_<38>

P53 = 16566232802982385348636217381941028289030910679890111_<53>

Tue Feb 03 15:06:21 2009  
Tue Feb 03 15:06:21 2009  
Tue Feb 03 15:06:21 2009  Msieve v. 1.39
Tue Feb 03 15:06:21 2009  random seeds: 618d5abc 61d4c648
Tue Feb 03 15:06:21 2009  factoring 1067760945606072306357447751924608914188862999876886904348598844862669877874888108749022467 (91 digits)
Tue Feb 03 15:06:22 2009  searching for 15-digit factors
Tue Feb 03 15:06:23 2009  commencing quadratic sieve (91-digit input)
Tue Feb 03 15:06:23 2009  using multiplier of 3
Tue Feb 03 15:06:23 2009  using 64kb Opteron sieve core
Tue Feb 03 15:06:23 2009  sieve interval: 18 blocks of size 65536
Tue Feb 03 15:06:23 2009  processing polynomials in batches of 6
Tue Feb 03 15:06:23 2009  using a sieve bound of 1651693 (62353 primes)
Tue Feb 03 15:06:23 2009  using large prime bound of 145348984 (27 bits)
Tue Feb 03 15:06:23 2009  using double large prime bound of 492426660101728 (42-49 bits)
Tue Feb 03 15:06:23 2009  using trial factoring cutoff of 49 bits
Tue Feb 03 15:06:23 2009  polynomial 'A' values have 12 factors
Tue Feb 03 16:39:43 2009  62529 relations (16520 full + 46009 combined from 694872 partial), need 62449
Tue Feb 03 16:39:43 2009  begin with 711392 relations
Tue Feb 03 16:39:44 2009  reduce to 153393 relations in 9 passes
Tue Feb 03 16:39:44 2009  attempting to read 153393 relations
Tue Feb 03 16:39:46 2009  recovered 153393 relations
Tue Feb 03 16:39:46 2009  recovered 132684 polynomials
Tue Feb 03 16:39:46 2009  attempting to build 62529 cycles
Tue Feb 03 16:39:46 2009  found 62529 cycles in 6 passes
Tue Feb 03 16:39:47 2009  distribution of cycle lengths:
Tue Feb 03 16:39:47 2009     length 1 : 16520
Tue Feb 03 16:39:47 2009     length 2 : 11962
Tue Feb 03 16:39:47 2009     length 3 : 11103
Tue Feb 03 16:39:47 2009     length 4 : 8367
Tue Feb 03 16:39:47 2009     length 5 : 5935
Tue Feb 03 16:39:47 2009     length 6 : 3722
Tue Feb 03 16:39:47 2009     length 7 : 2242
Tue Feb 03 16:39:47 2009     length 9+: 2678
Tue Feb 03 16:39:47 2009  largest cycle: 20 relations
Tue Feb 03 16:39:47 2009  matrix is 62353 x 62529 (15.3 MB) with weight 3758775 (60.11/col)
Tue Feb 03 16:39:47 2009  sparse part has weight 3758775 (60.11/col)
Tue Feb 03 16:39:49 2009  filtering completed in 3 passes
Tue Feb 03 16:39:49 2009  matrix is 58603 x 58667 (14.5 MB) with weight 3556923 (60.63/col)
Tue Feb 03 16:39:49 2009  sparse part has weight 3556923 (60.63/col)
Tue Feb 03 16:39:49 2009  saving the first 48 matrix rows for later
Tue Feb 03 16:39:49 2009  matrix is 58555 x 58667 (9.2 MB) with weight 2801740 (47.76/col)
Tue Feb 03 16:39:49 2009  sparse part has weight 2052873 (34.99/col)
Tue Feb 03 16:39:49 2009  matrix includes 64 packed rows
Tue Feb 03 16:39:49 2009  using block size 21845 for processor cache size 512 kB
Tue Feb 03 16:39:49 2009  commencing Lanczos iteration
Tue Feb 03 16:39:49 2009  memory use: 8.9 MB
Tue Feb 03 16:40:21 2009  lanczos halted after 928 iterations (dim = 58551)
Tue Feb 03 16:40:22 2009  recovered 15 nontrivial dependencies
Tue Feb 03 16:40:22 2009  prp38 factor: 64454058946572661063597653904314564797
Tue Feb 03 16:40:22 2009  prp53 factor: 16566232802982385348636217381941028289030910679890111
Tue Feb 03 16:40:22 2009  elapsed time 01:34:01

(41·10¹⁴⁰+31)/9 = 4(5)₁₃₉9_<141> = 3 · C141

C141 = P34 · P108

P34 = 1199724753870660251498367251866019_<34>

P108 = 126572241976281397788306276290203483556777976494085693561461616930615405285457813403487508172685964660247887_<108>

GMP-ECM 6.2.1 [powered by GMP 4.1.4] [ECM]
Input number is 151851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851851853 (141 digits)
Using B1=298000, B2=172085560, polynomial Dickson(3), sigma=3207482358
Step 1 took 4359ms
Step 2 took 2203ms
********** Factor found in step 2: 1199724753870660251498367251866019
Found probable prime factor of 34 digits: 1199724753870660251498367251866019
Probable prime cofactor 126572241976281397788306276290203483556777976494085693561461616930615405285457813403487508172685964660247887 has 108 digits

Feb 3, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39 / Feb 3, 2009

(41·10¹¹⁷+31)/9 = 4(5)₁₁₆9_<118> = 2579 · 45449651019682374295796358109_<29> · C86

C86 = P35 · P51

P35 = 66632079996950000918850156270835181_<35>

P51 = 583278652312656861739409130860545541746824360450149_<51>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=2416555942
Step 1 took 2262ms
Step 2 took 3014ms
********** Factor found in step 2: 66632079996950000918850156270835181
Found probable prime factor of 35 digits: 66632079996950000918850156270835181
Probable prime cofactor 583278652312656861739409130860545541746824360450149 has 51 digits

(41·10¹³⁵+31)/9 = 4(5)₁₃₄9_<136> = 3023 · 478444886724083_<15> · C118

C118 = P37 · P38 · P44

P37 = 3556372132455003504299125348332795791_<37>

P38 = 81764998487587515297393502595915397367_<38>

P44 = 10831700697889374875547086213253766769996683_<44>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=4009176397
Step 1 took 3337ms
Step 2 took 3839ms
********** Factor found in step 2: 3556372132455003504299125348332795791
Found probable prime factor of 37 digits: 3556372132455003504299125348332795791
Composite cofactor has 81 digits

Mon Feb  2 10:54:20 2009  Msieve v. 1.39
Mon Feb  2 10:54:20 2009  random seeds: c823d20b 086b9660
Mon Feb  2 10:54:20 2009  factoring 885653991180925370649281203219902274025329631298217788923412812505979443216933661 (81 digits)
Mon Feb  2 10:54:21 2009  searching for 15-digit factors
Mon Feb  2 10:54:21 2009  commencing quadratic sieve (81-digit input)
Mon Feb  2 10:54:22 2009  using multiplier of 1
Mon Feb  2 10:54:22 2009  using 64kb Opteron sieve core
Mon Feb  2 10:54:22 2009  sieve interval: 6 blocks of size 65536
Mon Feb  2 10:54:22 2009  processing polynomials in batches of 17
Mon Feb  2 10:54:22 2009  using a sieve bound of 1325939 (50860 primes)
Mon Feb  2 10:54:22 2009  using large prime bound of 127290144 (26 bits)
Mon Feb  2 10:54:22 2009  using trial factoring cutoff of 27 bits
Mon Feb  2 10:54:22 2009  polynomial 'A' values have 10 factors
Mon Feb  2 11:09:51 2009  50979 relations (26425 full + 24554 combined from 272911 partial), need 50956
Mon Feb  2 11:09:51 2009  begin with 299336 relations
Mon Feb  2 11:09:51 2009  reduce to 72500 relations in 2 passes
Mon Feb  2 11:09:51 2009  attempting to read 72500 relations
Mon Feb  2 11:09:51 2009  recovered 72500 relations
Mon Feb  2 11:09:51 2009  recovered 62259 polynomials
Mon Feb  2 11:09:52 2009  attempting to build 50979 cycles
Mon Feb  2 11:09:52 2009  found 50979 cycles in 1 passes
Mon Feb  2 11:09:52 2009  distribution of cycle lengths:
Mon Feb  2 11:09:52 2009     length 1 : 26425
Mon Feb  2 11:09:52 2009     length 2 : 24554
Mon Feb  2 11:09:52 2009  largest cycle: 2 relations
Mon Feb  2 11:09:52 2009  matrix is 50860 x 50979 (7.4 MB) with weight 1539782 (30.20/col)
Mon Feb  2 11:09:52 2009  sparse part has weight 1539782 (30.20/col)
Mon Feb  2 11:09:52 2009  filtering completed in 3 passes
Mon Feb  2 11:09:52 2009  matrix is 36210 x 36273 (5.8 MB) with weight 1231213 (33.94/col)
Mon Feb  2 11:09:52 2009  sparse part has weight 1231213 (33.94/col)
Mon Feb  2 11:09:52 2009  saving the first 48 matrix rows for later
Mon Feb  2 11:09:52 2009  matrix is 36162 x 36273 (4.4 MB) with weight 976497 (26.92/col)
Mon Feb  2 11:09:52 2009  sparse part has weight 791496 (21.82/col)
Mon Feb  2 11:09:52 2009  matrix includes 64 packed rows
Mon Feb  2 11:09:52 2009  using block size 14509 for processor cache size 1024 kB
Mon Feb  2 11:09:52 2009  commencing Lanczos iteration
Mon Feb  2 11:09:52 2009  memory use: 4.2 MB
Mon Feb  2 11:09:59 2009  lanczos halted after 574 iterations (dim = 36159)
Mon Feb  2 11:09:59 2009  recovered 15 nontrivial dependencies
Mon Feb  2 11:09:59 2009  prp38 factor: 81764998487587515297393502595915397367
Mon Feb  2 11:09:59 2009  prp44 factor: 10831700697889374875547086213253766769996683
Mon Feb  2 11:09:59 2009  elapsed time 00:15:39

(41·10²⁰⁴+31)/9 = 4(5)₂₀₃9_<205> = 107 · 131 · 31277 · C197

C197 = P30 · P167

P30 = 230454230267348953158887518549_<30>

P167 = 45089612115818448155796470649616724336674999001543316720183911839357510803560451459077985696357661739476679106474543100464107779255828793471990363456921813665099755799_<167>

Using B1=1000000, B2=2852890960, polynomial Dickson(6), sigma=3108296035
Step 1 took 6098ms
********** Factor found in step 1: 230454230267348953158887518549
Found probable prime factor of 30 digits: 230454230267348953158887518549
Probable prime cofactor has 167 digits

(41·10¹⁹⁸+31)/9 = 4(5)₁₉₇9_<199> = 11491 · 17387 · 56369 · 263821 · 767587 · 1785217112626973_<16> · 9504219627715347490470906977_<28> · C132

C132 = P34 · P37 · P62

P34 = 1177579993328123065167747303985169_<34>

P37 = 5156157608132315031396242239112911579_<37>

P62 = 19389091393505217028537474507543121002110687928310985249625999_<62>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1851117601
Step 1 took 9840ms
Step 2 took 12537ms
********** Factor found in step 2: 1177579993328123065167747303985169
Found probable prime factor of 34 digits: 1177579993328123065167747303985169
Composite cofactor has 98 digits

45559_198

Found extra factor

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=515529071
Step 1 took 9976ms
Step 2 took 2325ms
********** Factor found in step 2: 5156157608132315031396242239112911579
Found probable prime factor of 37 digits: 5156157608132315031396242239112911579
Probable prime cofactor.

(41·10¹⁸⁵+31)/9 = 4(5)₁₈₄9_<186> = 3 · 13 · 23 · 431 · 32561 · 1733946335992663789331_<22> · C155

C155 = P29 · P126

P29 = 34008497648100591013052154037_<29>

P126 = 613692478267694301112861462527973809965834124804709250280401185930469290003364382565567322986277018807383528660445164767960311_<126>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2010483597
Step 1 took 14823ms
Step 2 took 15166ms
********** Factor found in step 2: 34008497648100591013052154037
Found probable prime factor of 29 digits: 34008497648100591013052154037
Probable prime cofactor has 126 digits

(41·10¹²⁰+31)/9 = 4(5)₁₁₉9_<121> = 212243 · C116

C116 = P33 · P39 · P45

P33 = 340372629305350493038858258580227_<33>

P39 = 142707570407913263217126244735561659953_<39>

P45 = 441882019100876445682608173027102980374694223_<45>

SNFS difficulty: 121 digits.
Divisors found:
 r1=340372629305350493038858258580227 (pp33)
 r2=142707570407913263217126244735561659953 (pp39)
 r3=441882019100876445682608173027102980374694223 (pp45)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.725).
Factorization parameters were as follows:
n: 21463867150179537396076928593902062991738505183000407813475853411210525461643284139196843031598477007748456041214813
m: 1000000000000000000000000
deg: 5
c5: 41
c0: 31
skew: 0.95
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 49
mfba: 49
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 49/49
Sieved rational special-q in [370000, 720001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 76551 x 76794
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,49,49,2.2,2.2,50000
total time: 1.00 hours.

(41·10¹⁵⁰+31)/9 = 4(5)₁₄₉9_<151> = 59 · C149

C149 = P46 · P49 · P56

P46 = 1834886255558059164439981705268639491756411363_<46>

P49 = 2810565013910426340429576863390187630819434313763_<49>

P56 = 14972232145499087168765999273668718924452898779323137629_<56>

SNFS difficulty: 151 digits.
Divisors found:
 r1=1834886255558059164439981705268639491756411363 (pp46)
 r2=2810565013910426340429576863390187630819434313763 (pp49)
 r3=14972232145499087168765999273668718924452898779323137629 (pp56)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.900).
Factorization parameters were as follows:
n: 77212806026365348399246704331450094161958568738229755178907721280602636534839924670433145009416195856873822975517890772128060263653483992467043314501
m: 1000000000000000000000000000000
deg: 5
c5: 41
c0: 31
skew: 0.95
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1200000, 1800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 486507 x 486755
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,52,52,2.4,2.4,200000
total time: 12.00 hours.

(41·10¹⁶⁶+31)/9 = 4(5)₁₆₅9_<167> = 3727 · 6079 · 446523649107241_<15> · C145

C145 = P33 · C113

P33 = 282439056897102489148533809233561_<33>

C113 = [15943387191326006946618098390931334098583772565115458602425948433791571117252421966012384908580203304557239817623_<113>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2537698185
Step 1 took 11804ms
Step 2 took 13768ms
********** Factor found in step 2: 282439056897102489148533809233561
Found probable prime factor of 33 digits: 282439056897102489148533809233561
Composite cofactor has 113 digits

(41·10¹⁴⁶+31)/9 = 4(5)₁₄₅9_<147> = 3² · 17² · 327834257 · C135

C135 = P63 · P73

P63 = 168438529842683148308054615040993794916373972406674183409321003_<63>

P73 = 3171795800429727056384870508088370966952792701950555965163582644756292829_<73>

SNFS difficulty: 147 digits.
Divisors found:
 r1=168438529842683148308054615040993794916373972406674183409321003 (pp63)
 r2=3171795800429727056384870508088370966952792701950555965163582644756292829 (pp73)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 534252621585579664145356129183084336477260959704351426118664324429932031453629717985356037374518157303450315183482115567372178327987487
m: 100000000000000000000000000000
deg: 5
c5: 410
c0: 31
skew: 0.60
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 2600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 336386 x 336634
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,200000
total time: 9.00 hours.

Feb 3, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Feb 3, 2009

(41·10¹⁰⁹+31)/9 = 4(5)₁₀₈9_<110> = 7 · C109

C109 = P55 · P55

P55 = 1609234307804789928170154494737947503033525274455224753_<55>

P55 = 4044119912416110926650212851123881732754785808323471729_<55>

Number: 45559_109
N=6507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937
  ( 109 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=1609234307804789928170154494737947503033525274455224753
 r2=4044119912416110926650212851123881732754785808323471729
Version: 
Total time: 0.81 hours.
Scaled time: 0.74 units (timescale=0.919).
Factorization parameters were as follows:
n: 6507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937
m: 10000000000000000000000
deg: 5
c5: 41
c0: 310
skew: 1.50
type: snfs
lss: 1
rlim: 510000
alim: 510000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2Factor base limits: 510000/510000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [255000, 405001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 56531 x 56768
Total sieving time: 0.81 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000
total time: 0.81 hours.
 --------- CPU info (if available) ----------

(41·10¹²¹+31)/9 = 4(5)₁₂₀9_<122> = 7 · 3705469 · 520867280357_<12> · C103

C103 = P50 · P54

P50 = 25085893303696860441801815651838721304018746730029_<50>

P54 = 134413681174714126884752061671698555522359697260204341_<54>

Number: 45559_121
N=3371887264506005865805313674602489526825146226501314368068657627613618458765311747507547885746100855889
  ( 103 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=25085893303696860441801815651838721304018746730029
 r2=134413681174714126884752061671698555522359697260204341
Version: 
Total time: 1.97 hours.
Scaled time: 1.88 units (timescale=0.957).
Factorization parameters were as follows:
n: 3371887264506005865805313674602489526825146226501314368068657627613618458765311747507547885746100855889
m: 1000000000000000000000000
deg: 5
c5: 410
c0: 31
skew: 0.60
type: snfs
lss: 1
rlim: 770000
alim: 770000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 770000/770000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [385000, 735001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 89947 x 90180
Total sieving time: 1.97 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,770000,770000,25,25,46,46,2.2,2.2,50000
total time: 1.97 hours.
 --------- CPU info (if available) ----------

(41·10¹⁴²+31)/9 = 4(5)₁₄₁9_<143> = 153990042194763251_<18> · C126

C126 = P42 · P85

P42 = 187207276255012422729752934399155835081317_<42>

P85 = 1580250675639547341201881408748595868779650270106661112293742173219702816098552534777_<85>

Number: 45559_142
N=295834424786622768934616718704627647167534159440814108027259696373751625241655417932525050790318493612028538924965970265461309
  ( 126 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=187207276255012422729752934399155835081317
 r2=1580250675639547341201881408748595868779650270106661112293742173219702816098552534777
Version: 
Total time: 10.13 hours.
Scaled time: 10.48 units (timescale=1.034).
Factorization parameters were as follows:
n: 295834424786622768934616718704627647167534159440814108027259696373751625241655417932525050790318493612028538924965970265461309
m: 20000000000000000000000000000
deg: 5
c5: 1025
c0: 248
skew: 0.75
type: snfs
lss: 1
rlim: 1790000
alim: 1790000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3Factor base limits: 1790000/1790000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [895000, 2495001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 315955 x 316199
Total sieving time: 10.13 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1790000,1790000,26,26,49,49,2.3,2.3,100000
total time: 10.13 hours.
 --------- CPU info (if available) ----------

(41·10¹³⁴+31)/9 = 4(5)₁₃₃9_<135> = 3 · 883 · 32377 · C127

C127 = P40 · P42 · P46

P40 = 3355064599436787641763869624679045857743_<40>

P42 = 368969902060043715953543653361241381955493_<42>

P46 = 4290727720963025960639081602634475180502286117_<46>

Number: 45559_134
N=5311568463843240783696431311443730078646697133227443199942657861469752424179442702126915376040709373856154541001672707481092983
  ( 127 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=3355064599436787641763869624679045857743
 r2=368969902060043715953543653361241381955493
 r3=4290727720963025960639081602634475180502286117
Version: 
Total time: 7.52 hours.
Scaled time: 5.93 units (timescale=0.789).
Factorization parameters were as follows:
n: 5311568463843240783696431311443730078646697133227443199942657861469752424179442702126915376040709373856154541001672707481092983
m: 1000000000000000000000000000
deg: 5
c5: 41
c0: 310
skew: 1.50
type: snfs
lss: 1
rlim: 1320000
alim: 1320000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3

Factor base limits: 1320000/1320000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [660000, 1410001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 197763 x 198002
Total sieving time: 7.52 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1320000,1320000,26,26,48,48,2.3,2.3,75000
total time: 7.52 hours.
 --------- CPU info (if available) ----------

(41·10¹⁴⁸+31)/9 = 4(5)₁₄₇9_<149> = 383 · 1433 · 808173809 · 8477228183791_<13> · 927160788567923339_<18> · C104

C104 = P42 · P62

P42 = 993961156893056416607626915683869223442657_<42>

P62 = 13146594532571871522060287814049648829068446860402530335788413_<62>

Number: 45559_148
N=13067204310799067675002578708822192265309826867751678543454220556585403784206054853790648961562190533341
  ( 104 digits)
Divisors found:
 r1=993961156893056416607626915683869223442657
 r2=13146594532571871522060287814049648829068446860402530335788413
Version: 
Total time: 6.90 hours.
Scaled time: 6.80 units (timescale=0.986).
Factorization parameters were as follows:
name: 45559_148
n: 13067204310799067675002578708822192265309826867751678543454220556585403784206054853790648961562190533341
skew: 9512.93
# norm 5.22e+014
c5: 135240
c4: -1395252628
c3: -24330005753916
c2: -61135301664736594
c1: -851727712597451983479
c0: 1781714010621733225497320
# alpha -6.83
Y1: 26281209977
Y0: -39538127680531691007
# Murphy_E 2.28e-009
# M 1140871152934581302784860955381968303936443731707518166701881245649768293362391649966531840834781000646
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 239666 x 239914
Total sieving time: 6.90 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 6.90 hours.
 --------- CPU info (if available) ----------

Feb 3, 2009

Factorizations of 455...559 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Feb 2, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.1 / Feb 2, 2009

(10²³⁶+53)/9 = (1)₂₃₅7_<236> = 674701 · 5882643317337888139541_<22> · C208

C208 = P37 · P171

P37 = 6441578044112823884570058936524253053_<37>

P171 = 434591619408805768143625917498820920011217018449056507968046547524309851912068932987925474120037566751443665167098712448762668941244063377529397213814853294257863694748929_<171>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3597231909
Step 1 took 18287ms
Step 2 took 19995ms
********** Factor found in step 2: 6441578044112823884570058936524253053
Found probable prime factor of 37 digits: 6441578044112823884570058936524253053
Probable prime cofactor 434591619408805768143625917498820920011217018449056507968046547524309851912068932987925474120037566751443665167098712448762668941244063377529397213814853294257863694748929 has 171 digits

(10²¹⁸+53)/9 = (1)₂₁₇7_<218> = 12011 · C213

C213 = P33 · C181

P33 = 512897387066005167185285145268987_<33>

C181 = [1803631605744975289400475808506029437291090273290543686553003525106616277961259899167998057470194014633619515672877514719326520302185737901874383150102742811832669066034475554442181_<181>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2633345069
Step 1 took 22257ms
Step 2 took 21658ms
********** Factor found in step 2: 512897387066005167185285145268987
Found probable prime factor of 33 digits: 512897387066005167185285145268987
Composite cofactor has 181 digits

Feb 2, 2009

By Erik Branger / GMP-ECM / Feb 2, 2009

(34·10¹⁶⁴-61)/9 = 3(7)₁₆₃1_<165> = 7 · 23 · 353 · 1011600001_<10> · 1844691721343774408357773_<25> · C127

C127 = P38 · P90

P38 = 10238952342665722552924471286551411529_<38>

P90 = 347894597654053818724629590777249720177493714919264286922036675658099324234379842682033311_<90>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 3562076205650723332723478089195457228089971102211463041322115816197812550131136868037166251702503830534612839535087394847442519 (127 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3670331619
Step 1 took 40404ms
Step 2 took 13244ms
********** Factor found in step 2: 10238952342665722552924471286551411529
Found probable prime factor of 38 digits: 10238952342665722552924471286551411529
Probable prime cofactor 347894597654053818724629590777249720177493714919264286922036675658099324234379842682033311 has 90 digits

Feb 1, 2009 (6th)

By Ignacio Santos / GGNFS, Msieve / Feb 1, 2009

(35·10¹⁹⁰+1)/9 = 3(8)₁₈₉9_<191> = 3 · 18133 · 387285994369780603_<18> · 209624376426807196690783_<24> · 3919701941592254012158021_<25> · C121

C121 = P50 · P71

P50 = 63257351576766423947399512515745629216260427114779_<50>

P71 = 35513787691764778266303377928648484869380394953958769263504184367442221_<71>

Number: 38889_190
N=2246508153840604716035067114927749010950257513841294239081602295716965799348681521884485308054931395687535388799017684159
  ( 121 digits)
Divisors found:
 r1=63257351576766423947399512515745629216260427114779 (pp50)
 r2=35513787691764778266303377928648484869380394953958769263504184367442221 (pp71)
Version: Msieve-1.39
Total time: 47.85 hours.
Scaled time: 123.21 units (timescale=2.575).
Factorization parameters were as follows:
name: 38889_190
n: 2246508153840604716035067114927749010950257513841294239081602295716965799348681521884485308054931395687535388799017684159
skew: 89795.70
# norm 4.84e+016
c5: 57960
c4: 15793821326
c3: -1353809886740391
c2: -110952005119332163476
c1: 4885296725903794475561744
c0: 65659481591859212307474820632
# alpha -6.57
Y1: 3293507150791
Y0: -131121929075933727303169
# Murphy_E 2.78e-010
# M 1162552003123135492243094452700316052253313243880108098060031554406446515399379307476238877588418167574564767225395438595
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 4540001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 625638 x 625886
Polynomial selection time: 5.97 hours.
Total sieving time: 41.88 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 47.85 hours.
 --------- CPU info (if available) ----------

Feb 1, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Feb 1, 2009

(41·10¹⁷⁰-23)/9 = 4(5)₁₆₉3_<171> = 3 · 7741 · 852757 · 1413377533_<10> · 148750380557_<12> · 180901800576639967975769_<24> · C117

C117 = P57 · P61

P57 = 192901592601939758636554313145335370935170023200299215809_<57>

P61 = 3135470797399039833359351146040596545713359677745700369560123_<61>

Number: 45553_170
N=604837310375148778124776070708546525562586241475263243320444004969928838465156382209315580150383458737203131177584507
  ( 117 digits)
Divisors found:
 r1=192901592601939758636554313145335370935170023200299215809
 r2=3135470797399039833359351146040596545713359677745700369560123
Version: 
Total time: 20.73 hours.
Scaled time: 49.11 units (timescale=2.369).
Factorization parameters were as follows:
name: 45553_170
n: 604837310375148778124776070708546525562586241475263243320444004969928838465156382209315580150383458737203131177584507
skew: 85070.85
# norm 1.56e+16
c5: 15720
c4: 354141478
c3: 288449499827863
c2: -2433438192573369533
c1: -1708571568065724032767647
c0: 32726708019292214323410349959
# alpha -6.24
Y1: 2798172666233
Y0: -32887967898160717062940
# Murphy_E 3.92e-10
# M 414115915751592902022938657497943809537832392809746713569400063865266331813947822522717002899585836852504694144087261
type: gnfs
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1650000, 3225001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9178307
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 578724 x 578972
Polynomial selection time: 1.74 hours.
Total sieving time: 17.26 hours.
Total relation processing time: 0.89 hours.
Matrix solve time: 0.71 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3300000,3300000,27,27,52,52,2.4,2.4,75000
total time: 20.73 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673806)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672353)

Feb 1, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.1 / Feb 1, 2009

(10²⁰⁷+53)/9 = (1)₂₀₆7_<207> = 3 · 13³ · 283 · 349 · 551849 · 1122179 · 6118409299921_<13> · 339049922873154043_<18> · C156

C156 = P39 · C117

P39 = 685413813735893660349622719120345198553_<39>

C117 = [193846020667124193274134252463231803230311020333243374266479905607388867655634000609161657914215087575387961520302749_<117>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2452372186
Step 1 took 15004ms
Step 2 took 3165ms
********** Factor found in step 2: 685413813735893660349622719120345198553
Found probable prime factor of 39 digits: 685413813735893660349622719120345198553
Composite cofactor has 117 digits

(10²⁵⁰+53)/9 = (1)₂₄₉7_<250> = 19 · 16744799 · 1282670489_<10> · 1282892248388561_<16> · 316506541719636211_<18> · 24198990469696224316973_<23> · C177

C177 = P31 · P147

P31 = 1952336428161608917887269931907_<31>

P147 = 141933224730094412121746955107189516661928241972823958395563629646112650310877205015050914315308289712595775165605200513388474099048767270249187173_<147>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=617356213
Step 1 took 15993ms
********** Factor found in step 1: 1952336428161608917887269931907
Found probable prime factor of 31 digits: 1952336428161608917887269931907
Probable prime cofactor has 147 digits

(10²¹⁷+53)/9 = (1)₂₁₆7_<217> = 7 · 281 · 14563 · 1305599 · C203

C203 = P32 · C172

P32 = 18593651670229859248063017074413_<32>

C172 = [1597819737685561365333130675782680514858164472226776884815071261197870477464151112602423542579571993529313203161064470366587111467303582456055977186951165047742572925518971_<172>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=747078882
Step 1 took 18290ms
Step 2 took 220ms
********** Factor found in step 2: 18593651670229859248063017074413
Found probable prime factor of 32 digits: 18593651670229859248063017074413
Composite cofactor has 172 digits

(10²²²+53)/9 = (1)₂₂₁7_<222> = 3 · 71 · 151 · 4289 · 60737 · 94781 · C204

C204 = P32 · C172

P32 = 38038740024260123690761310466913_<32>

C172 = [3678274590709306140246941889232418903617930778762751714691175028205559197443108836905780275024765880645406906569791283872756506787257452163015607432724671749967545265118171_<172>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2504251202
Step 1 took 18432ms
Step 2 took 16653ms
********** Factor found in step 2: 38038740024260123690761310466913
Found probable prime factor of 32 digits: 38038740024260123690761310466913
Composite cofactor has 172 digits

(10²²³+53)/9 = (1)₂₂₂7_<223> = 7 · 31 · 47103143 · C213

C213 = P30 · P183

P30 = 832177666653514566119777542327_<30>

P183 = 130626657316830411812762093162086307095861313693375756369803147844839177447021792293586324665117396046889406586142681119113736143908559800043999461524339507535727217655605059442783541_<183>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3480091773
Step 1 took 22570ms
********** Factor found in step 1: 832177666653514566119777542327
Found probable prime factor of 30 digits: 832177666653514566119777542327
Probable prime cofactor has 183 digits

(10²²⁵+53)/9 = (1)₂₂₄7_<225> = 3 · 13 · C223

C223 = P32 · P191

P32 = 31435107881709275231021785937689_<32>

P191 = 90631241340849989373993210775096622109323257490044296493338670472548365542130633364114358541105166361984056494877293836718094400774895621031251966312312387413255954176898968368530708788862627_<191>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=262501054
Step 1 took 22143ms
Step 2 took 18592ms
********** Factor found in step 2: 31435107881709275231021785937689
Found probable prime factor of 32 digits: 31435107881709275231021785937689
Probable prime cofactor has 191 digits

Feb 1, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.1 / Feb 1, 2009

(4·10²⁴¹-1)/3 = 1(3)₂₄₁_<242> = 13 · 3784757 · 4646801 · 183261467 · 52651626410827_<14> · 3917565792818569_<16> · 9984057494986111353041_<22> · C168

C168 = P42 · C126

P42 = 423978422171785937525330791300274672892443_<42>

C126 = [364462821471541316916182370125769150792316542042148094133332048440810743632250528660469332549245321864282313669340167794844431_<126>]

# no GNFS-168 here! :-)
#
Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=1678757752
Step 1 took 50833ms
Step 2 took 34740ms
********** Factor found in step 2: 423978422171785937525330791300274672892443
Found probable prime factor of 42 digits: 423978422171785937525330791300274672892443
Composite cofactor has 126 digits

Feb 1, 2009 (2nd)

By anonymous / Msieve ecm / Feb 1, 2009

(5·10¹⁹⁹-17)/3 = 1(6)₁₉₈1_<200> = 11 · 216509 · C193

C193 = P33 · P161

P33 = 309043692410763708504054591900071_<33>

P161 = 22644369155569801482004116295604415131414902032878438050293139566303788227904437910339217278579371739796569961741957220320246133261615506936781044026479149468109_<161>

Sat Jan 31 22:37:44 2009  Msieve v. 1.39
Sat Jan 31 22:37:44 2009  random seeds: de90e960 74083f1a
Sat Jan 31 22:37:44 2009  factoring 6998099456149698864782302422308149552744465658016595852898269887863853934548455330501342445418673196733231189073671372328702970847177323582461475112588923100264430186050072521304664079329335739 (193 digits)
Sat Jan 31 22:37:46 2009  searching for 15-digit factors
Sat Jan 31 22:37:50 2009  searching for 20-digit factors
Sat Jan 31 22:38:31 2009  searching for 25-digit factors
Sat Jan 31 22:46:43 2009  searching for 30-digit factors
Sun Feb 01 00:04:39 2009  searching for 35-digit factors
Sun Feb 01 00:27:05 2009  ECM stage 2 factor found
Sun Feb 01 00:27:05 2009  prp33 factor: 309043692410763708504054591900071
Sun Feb 01 00:27:05 2009  prp161 factor: 22644369155569801482004116295604415131414902032878438050293139566303788227904437910339217278579371739796569961741957220320246133261615506936781044026479149468109
Sun Feb 01 00:27:05 2009  elapsed time 01:49:21

Feb 1, 2009

Factorizations of 11...117 have been extended up to n=250. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

January 2009

Jan 31, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 31, 2009

(41·10¹⁶¹-23)/9 = 4(5)₁₆₀3_<162> = 3 · 7 · 131 · 1123943 · 309453852605561_<15> · C138

C138 = P44 · P94

P44 = 48715522449375037037112608816998451240059843_<44>

P94 = 9773344594347818728692771659151250188561551518867168822085057404744657355124995709625315835227_<94>

Number: 45553_161
N=476113587991429327991160095841723465002630865947020881182067571272286331325153049728211155687436532750693507773602785210557141607007489361
  ( 138 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=48715522449375037037112608816998451240059843
 r2=9773344594347818728692771659151250188561551518867168822085057404744657355124995709625315835227
Version: 
Total time: 19.15 hours.
Scaled time: 45.82 units (timescale=2.393).
Factorization parameters were as follows:
n: 476113587991429327991160095841723465002630865947020881182067571272286331325153049728211155687436532750693507773602785210557141607007489361
m: 100000000000000000000000000000000
deg: 5
c5: 410
c0: -23
skew: 0.56
type: snfs
lss: 1
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2000000, 3600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9381225
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 740977 x 741225
Total sieving time: 17.03 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 1.11 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000
total time: 19.15 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047104k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804)
Calibrating delay using timer specific routine.. 5604.08 BogoMIPS (lpj=2802042)
Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672376)
Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672350)

Jan 31, 2009

By Serge Batalov / Msieve-1.39 / Jan 31, 2009

(41·10¹⁶⁵-23)/9 = 4(5)₁₆₄3_<166> = C166

C166 = P43 · P48 · P76

P43 = 7048830044955730285803652614749917171590703_<43>

P48 = 217664130389283169762486791539612080217356148339_<48>

P76 = 2969186257631440708130691194440226995175932326438344612604677326089467529109_<76>

SNFS difficulty: 166 digits.
Divisors found:
 r1=7048830044955730285803652614749917171590703 (pp43)
 r2=217664130389283169762486791539612080217356148339 (pp48)
 r3=2969186257631440708130691194440226995175932326438344612604677326089467529109 (pp76)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.294).
Factorization parameters were as follows:
n: 4555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
m: 1000000000000000000000000000000000
deg: 5
c5: 41
c0: -23
skew: 0.89
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2100000, 4100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 773789 x 774037
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,52,52,2.4,2.4,100000
total time: 37.00 hours.

(41·10¹⁷¹+13)/9 = 4(5)₁₇₀7_<172> = 3 · 7² · 17 · 50513 · 40344357139_<11> · C153

C153 = P62 · P92

P62 = 13545655697291753895167415183155062115257968864458197026561047_<62>

P92 = 66037267802058900270285640006155171253032916972658859255631851488321722456468401221793505867_<92>

SNFS difficulty: 172 digits.
Divisors found:
 r1=13545655697291753895167415183155062115257968864458197026561047 (pp62)
 r2=66037267802058900270285640006155171253032916972658859255631851488321722456468401221793505867 (pp92)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.302).
Factorization parameters were as follows:
n: 894518092836540440883213933824080875780792388807894997431695313391332454085486399914701232771571225453111058182290877031803884777922102962656532628162749
m: 10000000000000000000000000000000000
deg: 5
c5: 410
c0: 13
skew: 0.50
type: snfs
lss: 1
rlim: 5600000
alim: 5600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5600000/5600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2800000, 6600001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 982605 x 982853
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000
total time: 50.00 hours.

Jan 30, 2009 (4th)

By Sinkiti Sibata / GGNFS / Jan 30, 2009

(35·10¹⁶⁴+1)/9 = 3(8)₁₆₃9_<165> = 282833 · 347981 · 1195263561592703068137949500679_<31> · C124

C124 = P50 · P74

P50 = 39575882037420828963570411917339240644716762775903_<50>

P74 = 83530607544231245392846006539898621111183905857449706817593594044549213589_<74>

Number: 38889_164
N=3305797470684590126516118944166244859718767479459168848484632525243758609790874378955530593175883268566507494694347289345867
  ( 124 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=39575882037420828963570411917339240644716762775903 (pp50)
 r2=83530607544231245392846006539898621111183905857449706817593594044549213589 (pp74)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 79.80 hours.
Scaled time: 37.75 units (timescale=0.473).
Factorization parameters were as follows:
name: 38889_164
n: 3305797470684590126516118944166244859718767479459168848484632525243758609790874378955530593175883268566507494694347289345867
m: 1000000000000000000000000000000000
deg: 5
c5: 7
c0: 2
skew: 0.78
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 3650001)
Primes: RFBsize:289774, AFBsize:289257, largePrimes:9034055 encountered
Relations: rels:9241991, finalFF:676064
Max relations in full relation-set: 28
Initial matrix: 579096 x 676064 with sparse part having weight 68165626.
Pruned matrix : 516684 x 519643 with weight 51138428.
Total sieving time: 64.49 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 14.61 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 79.80 hours.
 --------- CPU info (if available) ----------

Jan 30, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Jan 30, 2009

(43·10²⁰⁶-7)/9 = 4(7)₂₀₆_<207> = 3 · 73 · 1197999487_<10> · 919272050133022870840781_<24> · 227091512033988664050765336907_<30> · 9979120019997928268416395684139_<31> · C111

C111 = P43 · P69

P43 = 2075634083079828998567220764778928732800821_<43>

P69 = 421150384930020461727145617061926763309795192374704172359381305111733_<69>

Number: 47777_206
N=874154093062940053723423566083923324074453222353223316638756093434022663299154755490033595932211400153439132793
  ( 111 digits)
Divisors found:
 r1=2075634083079828998567220764778928732800821
 r2=421150384930020461727145617061926763309795192374704172359381305111733
Version: 
Total time: 10.14 hours.
Scaled time: 24.15 units (timescale=2.382).
Factorization parameters were as follows:
name: 47777_206
n: 874154093062940053723423566083923324074453222353223316638756093434022663299154755490033595932211400153439132793
skew: 30687.16
# norm 3.99e+15
c5: 113400
c4: 2920482650
c3: -302366368859399
c2: -2625363309198789138
c1: 137037003928894478826152
c0: 801887937814693936058974480
# alpha -6.60
Y1: 274783993297
Y0: -1504508271055678830873
# Murphy_E 8.66e-10
# M 33913588752037023001154899934271482323043432368019170082195613568306518138961385112480392869526368209010001248
type: gnfs
rlim: 2100000
alim: 2100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1050000, 1800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8166464
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 386617 x 386865
Polynomial selection time: 0.76 hours.
Total sieving time: 8.40 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 0.31 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000
total time: 10.14 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360)
Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043)
Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)

(43·10²⁰²-7)/9 = 4(7)₂₀₂_<203> = 7331 · 2224447 · 4264331689_<10> · 3282544923857_<13> · 129162515387784254409797833_<27> · 894140490812561508197748839283473_<33> · C112

C112 = P50 · P63

P50 = 12468621839237019750134274632920275340919814102191_<50>

P63 = 145351091738832752462107761351113457049563025712898988930667003_<63>

Number: 47777_202
N=1812327796811753621163200021922067097052888721647496808031500412932013350729735549051173339843739136511233703573
  ( 112 digits)
Divisors found:
 r1=12468621839237019750134274632920275340919814102191
 r2=145351091738832752462107761351113457049563025712898988930667003
Version: 
Total time: 11.29 hours.
Scaled time: 26.94 units (timescale=2.387).
Factorization parameters were as follows:
name: 47777_202
n: 1812327796811753621163200021922067097052888721647496808031500412932013350729735549051173339843739136511233703573
skew: 54094.49
# norm 4.44e+15
c5: 7680
c4: 3175216088
c3: -75687149631190
c2: -7247399479012978327
c1: 75161386214624790981960
c0: 3589599881379885118000877349
# alpha -6.21
Y1: 937728520817
Y0: -2982385752308822800816
# Murphy_E 7.94e-10
# M 452990686981099005718217834527867984953168050273452541942955949321535635220026936614575740434782683652135110614
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1200000, 2040001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8532087
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 384054 x 384302
Polynomial selection time: 0.87 hours.
Total sieving time: 9.47 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000
total time: 11.29 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360)
Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043)
Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)

(41·10¹⁸³-23)/9 = 4(5)₁₈₂3_<184> = C184

C184 = P35 · P150

P35 = 14589501503902084137302513137370873_<35>

P150 = 312248883509634249005847902099113991658769635405891185299817342330275330744748507088676770238588018801904100842443828422508631356486325904946577765161_<150>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 4555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553 (184 digits)
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3268419040
Step 1 took 6263ms
Step 2 took 3376ms
********** Factor found in step 2: 14589501503902084137302513137370873
Found probable prime factor of 35 digits: 14589501503902084137302513137370873
Probable prime cofactor 312248883509634249005847902099113991658769635405891185299817342330275330744748507088676770238588018801904100842443828422508631356486325904946577765161 has 150 digits

Jan 30, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Jan 30, 2009

(41·10¹⁵¹-23)/9 = 4(5)₁₅₀3_<152> = 383 · 8447 · 19571 · 9230748389_<10> · C131

C131 = P42 · P90

P42 = 124434346315030176296076825378828222961733_<42>

P90 = 626397301816530774964119179790139452924785821296333787068498699938708732827425248548556339_<90>

Number: 45553_151
N=77945338785038671394181877897307420049103361412246789040632117018754521459012051523341323925873080957218788678619520132547991575487
  ( 131 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=124434346315030176296076825378828222961733
 r2=626397301816530774964119179790139452924785821296333787068498699938708732827425248548556339
Version: 
Total time: 22.11 hours.
Scaled time: 43.01 units (timescale=1.945).
Factorization parameters were as follows:
n: 77945338785038671394181877897307420049103361412246789040632117018754521459012051523341323925873080957218788678619520132547991575487
m: 1000000000000000000000000000000
deg: 5
c5: 410
c0: -23
skew: 0.56
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1200000, 2000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 484391 x 484639
Total sieving time: 22.11 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000
total time: 22.11 hours.
 --------- CPU info (if available) ----------

Jan 30, 2009

By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1 / Jan 30, 2009

(41·10¹⁶³-23)/9 = 4(5)₁₆₂3_<164> = 389 · 45851195581_<11> · C151

C151 = P68 · P83

P68 = 29133329337945510299957110140657349252840116046675345541662393249319_<68>

P83 = 87669991230507932658083828877276980219124823060697439168343320477973842654932855143_<83>

SNFS difficulty: 166 digits.
Divisors found:
 r1=29133329337945510299957110140657349252840116046675345541662393249319 (pp68)
 r2=87669991230507932658083828877276980219124823060697439168343320477973842654932855143 (pp83)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 2554118727573182363624568773003137949230779989157913559867837585944130801792176347437384308522371049214854200576158632139427275758913382964941710397617
m: 500000000000000000000000000000000
deg: 5
c5: 328
c0: -575
skew: 1.12
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2050000, 4650001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 782389 x 782637
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,52,52,2.4,2.4,200000
total time: 42.00 hours.

(13·10¹⁶⁹+17)/3 = 4(3)₁₆₈9_<170> = 7² · 113 · 6143 · 165463 · C157

C157 = P35 · C123

P35 = 64817842125068594359353753328875377_<35>

C123 = [118787733468585373018803001626199942041486879025646793084250872377023430370450048163478120248088756637535072725204319132979_<123>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=746734294
Step 1 took 13951ms
Step 2 took 13265ms
********** Factor found in step 2: 64817842125068594359353753328875377
Found probable prime factor of 35 digits: 64817842125068594359353753328875377
Composite cofactor has 123 digits

Jan 29, 2009 (9th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 29, 2009

(13·10¹⁶²+17)/3 = 4(3)₁₆₁9_<163> = 71143 · 1199953693995273725407_<22> · C137

C137 = P52 · P85

P52 = 7529261953382445456022978831409101175220907433308991_<52>

P85 = 6741755973701705171652646158601204512690915622307800010016289079913328347215654722829_<85>

Number: 43339_162
N=50760446751781071257905593169998899590553675465934743310278919667953736415005326576711409469460862032185500165163685445643993256418655539
  ( 137 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=7529261953382445456022978831409101175220907433308991
 r2=6741755973701705171652646158601204512690915622307800010016289079913328347215654722829
Version: 
Total time: 23.65 hours.
Scaled time: 56.53 units (timescale=2.390).
Factorization parameters were as follows:
n: 50760446751781071257905593169998899590553675465934743310278919667953736415005326576711409469460862032185500165163685445643993256418655539
m: 100000000000000000000000000000000
deg: 5
c5: 1300
c0: 17
skew: 0.42
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2100000, 4100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9731766
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 779314 x 779562
Total sieving time: 21.33 hours.
Total relation processing time: 0.94 hours.
Matrix solve time: 1.28 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000
total time: 23.65 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360)
Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043)
Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)

(35·10¹⁶⁴-17)/9 = 3(8)₁₆₃7_<165> = 3² · 227 · 283 · 607 · 721641441052677560056142789_<27> · C130

C130 = P43 · P87

P43 = 2164226505067740336545299545138264786212773_<43>

P87 = 709508928632527276438580379581169517506057775727086708484652773434018533527897889599737_<87>

Number: 38887_164
N=1535538028928731310411299976352496883335984799898135849679037491841562148763146925000134438926258136116973870389355679625086840701
  ( 130 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=2164226505067740336545299545138264786212773
 r2=709508928632527276438580379581169517506057775727086708484652773434018533527897889599737
Version: 
Total time: 20.65 hours.
Scaled time: 49.29 units (timescale=2.387).
Factorization parameters were as follows:
n: 1535538028928731310411299976352496883335984799898135849679037491841562148763146925000134438926258136116973870389355679625086840701
m: 1000000000000000000000000000000000
deg: 5
c5: 7
c0: -34
skew: 1.37
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 3900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9680389
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 723944 x 724192
Total sieving time: 18.70 hours.
Total relation processing time: 0.80 hours.
Matrix solve time: 1.08 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 20.65 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360)
Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043)
Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)

Jan 29, 2009 (8th)

By Serge Batalov / Msieve-1.39, pol51 / Jan 29, 2009

(41·10¹⁵⁸-23)/9 = 4(5)₁₅₇3_<159> = 3² · 89 · C156

C156 = P65 · P92

P65 = 28850941907203007847401689552967354640673245661890210464614317293_<65>

P92 = 19712823566187765936501050571307241754800318770326492415189741533994996509543568798904090021_<92>

SNFS difficulty: 161 digits.
Divisors found:
 r1=28850941907203007847401689552967354640673245661890210464614317293 (pp65)
 r2=19712823566187765936501050571307241754800318770326492415189741533994996509543568798904090021 (pp92)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.952).
Factorization parameters were as follows:
n: 568733527535025662366486336523789707310306561242890830905812179220418920793452628658621167984463864613677347759744763490081842141767235400194201692329033153
m: 50000000000000000000000000000000
c5: 328
c0: -575
skew: 1.12
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1700000, 3500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 613407 x 613655
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,52,52,2.4,2.4,200000
total time: 27.00 hours.

(41·10¹⁷⁸-23)/9 = 4(5)₁₇₇3_<179> = 1183943 · 189287933041368939698424948529_<30> · 1208868416299919985898567336255445891869_<40> · C105

C105 = P48 · P57

P48 = 481911941006296666803436041025635734292586173461_<48>

P57 = 348932085078507959564569166156418142784583065154844041511_<57>

Divisors found:
 r1=481911941006296666803436041025635734292586173461 (pp48)
 r2=348932085078507959564569166156418142784583065154844041511 (pp57)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.528).
Factorization parameters were as follows:
name: 45553_178
n: 168154538399558017254478603113207313708895276072507757115220953746111331152469234868619217627939730539571
skew: 9723.82
# norm 1.94e+14
c5: 45840
c4: 436103556
c3: -14526373230872
c2: -44181904912960523
c1: -101954573143161400030
c0: 412019275248612995904320
# alpha -5.43
Y1: 16582549357
Y0: -81826246411099303959
# Murphy_E 1.94e-09
# M 114387187697216149807785384983138201125110014197248308094008292071209457371172444703697085321264377513011
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2150001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 275264 x 275512
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 6.00 hours.

Jan 29, 2009 (7th)

By Erik Branger / GGNFS, Msieve / Jan 29, 2009

(41·10¹³⁹-23)/9 = 4(5)₁₃₈3_<140> = 4007 · 324829275755121868009_<21> · C116

C116 = P45 · P71

P45 = 773862830377449253413698674936532384941341169_<45>

P71 = 45227528252266932279145332153783269490963211018115404781446254785187599_<71>

Number: 45553_139
N=34999903024275338901522874375799121511839485670661437667979695890714240654775511337191106823261682968866354326963231
  ( 116 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=773862830377449253413698674936532384941341169
 r2=45227528252266932279145332153783269490963211018115404781446254785187599
Version: 
Total time: 9.89 hours.
Scaled time: 20.66 units (timescale=2.088).
Factorization parameters were as follows:
n: 34999903024275338901522874375799121511839485670661437667979695890714240654775511337191106823261682968866354326963231
m: 10000000000000000000000000000
deg: 5
c5: 41
c0: -230
skew: 1.41
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [800000, 1900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 284118 x 284366
Total sieving time: 9.89 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000
total time: 9.89 hours.
 --------- CPU info (if available) ----------

(41·10¹³¹-23)/9 = 4(5)₁₃₀3_<132> = 3² · 7² · 311 · 43711 · C122

C122 = P40 · P83

P40 = 1801364495446163282257831597361756468273_<40>

P83 = 42184220455933837447552299166930194478197239547739286056819295000322534357624766001_<83>

Number: 45553_131
N=75989156997392977105229538608994471183862080258012139504286349375102219420870458470076856934080344251900169694479805586273
  ( 122 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=1801364495446163282257831597361756468273
 r2=42184220455933837447552299166930194478197239547739286056819295000322534357624766001
Version: 
Total time: 4.54 hours.
Scaled time: 3.58 units (timescale=0.789).
Factorization parameters were as follows:
n: 75989156997392977105229538608994471183862080258012139504286349375102219420870458470076856934080344251900169694479805586273
m: 100000000000000000000000000
deg: 5
c5: 410
c0: -23
skew: 0.56
type: snfs
lss: 1
rlim: 1140000
alim: 1140000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3

Factor base limits: 1140000/1140000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [570000, 1020001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 180838 x 181086
Total sieving time: 4.54 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1140000,1140000,26,26,47,47,2.3,2.3,50000
total time: 4.54 hours.
 --------- CPU info (if available) ----------

Jan 29, 2009 (6th)

By Tyler Cadigan / GGNFS, Msieve / Jan 29, 2009

(43·10¹⁷⁸-7)/9 = 4(7)₁₇₈_<179> = 383 · 4354027 · 249604739031097_<15> · C156

C156 = P37 · P49 · P70

P37 = 3673652886587821683140672767941328687_<37>

P49 = 6902107741445885438068266121725096751735112138723_<49>

P70 = 4526925785659940824204341239430806891307484383858194682858972240819401_<70>

Number: 47777_178
N=114784494947366634262426183006958123861511699275635538429018736808936826291842714776329045547599116455771782266887863028084494441647275112045251159350246101
  ( 156 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=3673652886587821683140672767941328687 (pp37)
 r2=6902107741445885438068266121725096751735112138723 (pp49)
 r3=4526925785659940824204341239430806891307484383858194682858972240819401 (pp70)
Version: Msieve-1.39
Total time: 265.08 hours.
Scaled time: 678.60 units (timescale=2.560).
Factorization parameters were as follows:
n: 114784494947366634262426183006958123861511699275635538429018736808936826291842714776329045547599116455771782266887863028084494441647275112045251159350246101
m: 500000000000000000000000000000000000
deg: 5
c5: 344
c0: -175
skew: 0.87
type: snfs
lss: 1
rlim: 7300000
alim: 7300000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 1000000Factor base limits: 7300000/7300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3650000, 7650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1044036 x 1044284
Total sieving time: 265.08 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,7300000,7300000,28,28,53,53,2.5,2.5,100000
total time: 265.08 hours.
 --------- CPU info (if available) ----------

Jan 29, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 29, 2009

(41·10¹⁰³-23)/9 = 4(5)₁₀₂3_<104> = 7990030831_<10> · C94

C94 = P46 · P49

P46 = 1880920131093652155510042425842068306778985389_<46>

P49 = 3031255455185522651922420611150645662026396145867_<49>

Number: 45553_103
N=5701549408145901503037085784626249029245523765558490565924019718661277785944948321258305737263
  ( 94 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=1880920131093652155510042425842068306778985389 (pp46)
 r2=3031255455185522651922420611150645662026396145867 (pp49)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.47 hours.
Scaled time: 1.13 units (timescale=2.392).
Factorization parameters were as follows:
n: 5701549408145901503037085784626249029245523765558490565924019718661277785944948321258305737263
m: 1000000000000000000000
deg: 5
c5: 41
c0: -2300
skew: 2.24
type: snfs
lss: 1
rlim: 240000
alim: 240000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.2
alambda: 2.2
Factor base limits: 240000/240000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved rational special-q in [120000, 260001)
Primes: RFBsize:21221, AFBsize:21090, largePrimes:852509 encountered
Relations: rels:745091, finalFF:50700
Max relations in full relation-set: 28
Initial matrix: 42378 x 50700 with sparse part having weight 2823579.
Pruned matrix : 40967 x 41242 with weight 1775227.
Total sieving time: 0.45 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,106,5,0,0,0,0,0,0,0,0,240000,240000,25,25,44,44,2.2,2.2,20000
total time: 0.47 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360)
Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043)
Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)

(41·10¹²⁹-23)/9 = 4(5)₁₂₈3_<130> = 44029 · 1333136341721_<13> · C113

C113 = P33 · P81

P33 = 245833508742300870269048663236781_<33>

P81 = 315708938586453576137949202042096617259121045616596246935483076636501414393941457_<81>

Number: 45553_129
N=77611836114015463765579271944208630546320167838921160599412055952667076355928840955602283169533935707733843129917
  ( 113 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=245833508742300870269048663236781
 r2=315708938586453576137949202042096617259121045616596246935483076636501414393941457
Version: 
Total time: 1.96 hours.
Scaled time: 4.67 units (timescale=2.389).
Factorization parameters were as follows:
n: 77611836114015463765579271944208630546320167838921160599412055952667076355928840955602283169533935707733843129917
m: 100000000000000000000000000
deg: 5
c5: 41
c0: -230
skew: 1.41
type: snfs
lss: 1
rlim: 1100000
alim: 1100000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1100000/1100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [550000, 1100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3173600
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 166118 x 166366
Total sieving time: 1.72 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360)
Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043)
Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)

Jan 29, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39, pol51 / Jan 29, 2009

(43·10²¹³-7)/9 = 4(7)₂₁₃_<214> = 29 · 3461 · 47701 · 316223 · 600109 · 13162957 · 39284608416614303_<17> · 75505295088633637_<17> · C153

C153 = P37 · P116

P37 = 3526680938895455431728898504444220551_<37>

P116 = 38190540064821716358063950502102091512430090081925348378008427894317449358648344734268599001413164789278233232637447_<116>

Using B1=5000000, B2=11416314010, polynomial Dickson(12), sigma=2511989336
Step 1 took 15349ms
Step 2 took 9332ms
********** Factor found in step 2: 3526680938895455431728898504444220551
Found probable prime factor of 37 digits: 3526680938895455431728898504444220551
Probable prime cofactor 38190540064821716358063950502102091512430090081925348378008427894317449358648344734268599001413164789278233232637447 has 116 digits

(43·10²⁰³-7)/9 = 4(7)₂₀₃_<204> = 3 · 67 · 547 · 2838580823343361_<16> · 70019741574365087_<17> · C167

C167 = P43 · C124

P43 = 2334561165143153784276485597559959244336157_<43>

C124 = [9365167244931605937271157091977652941532850887100421862106964322653891953074392906416380032956187565261989128184595620958209_<124>]

Using B1=5000000, B2=23417929090, polynomial Dickson(12), sigma=3473665096
Step 1 took 22798ms
Step 2 took 19003ms
********** Factor found in step 2: 2334561165143153784276485597559959244336157
Found probable prime factor of 43 digits: 2334561165143153784276485597559959244336157
Composite cofactor 9365167244931605937271157091977652941532850887100421862106964322653891953074392906416380032956187565261989128184595620958209 has 124 digits

(43·10²³⁴-7)/9 = 4(7)₂₃₄_<235> = 8821 · 576493 · 63521290844627070769256161_<26> · 192264712908627279576854165210309221783217_<42> · C158

C158 = P38 · P121

P38 = 41012255466950321646301229829861542741_<38>

P121 = 1875778410670032148125989730595334818323781272326288536827048138746736685097497248156417793124849522779165277155797324877_<121>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=227219622
Step 1 took 50881ms
Step 2 took 33448ms
********** Factor found in step 2: 41012255466950321646301229829861542741
Found probable prime factor of 38 digits: 41012255466950321646301229829861542741
Probable prime cofactor 1875778410670032148125989730595334818323781272326288536827048138746736685097497248156417793124849522779165277155797324877 has 121 digits

(41·10¹⁵⁴-23)/9 = 4(5)₁₅₃3_<155> = 293099 · 105043513 · 152505329 · 27447127457_<11> · 142320476143_<12> · C112

C112 = P32 · P81

P32 = 19133469743565591575826954988903_<32>

P81 = 129811967521642553356376795770261489514163544206752823212917396577776180348802387_<81>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=2312512268
Step 1 took 2290ms
********** Factor found in step 1: 19133469743565591575826954988903
Found probable prime factor of 32 digits: 19133469743565591575826954988903
Probable prime cofactor has 81 digits

(41·10¹⁷⁸-23)/9 = 4(5)₁₇₇3_<179> = 1183943 · 189287933041368939698424948529_<30> · C144

C144 = P40 · C105

P40 = 1208868416299919985898567336255445891869_<40>

C105 = [168154538399558017254478603113207313708895276072507757115220953746111331152469234868619217627939730539571_<105>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=744591357
Step 1 took 3877ms
Step 2 took 3636ms
********** Factor found in step 2: 1208868416299919985898567336255445891869
Found probable prime factor of 40 digits: 1208868416299919985898567336255445891869

(41·10¹⁹⁶-23)/9 = 4(5)₁₉₅3_<197> = 17188148844872638761949_<23> · C175

C175 = P33 · C142

P33 = 292583499806596595725013018613757_<33>

C142 = [9058627697344100435072959011588414226107521095119906981620337036029788299086931609550622788224999995837661941137272253328636031596381018952121_<142>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3690523421
Step 1 took 4610ms
Step 2 took 2451ms
********** Factor found in step 2: 292583499806596595725013018613757
Found probable prime factor of 33 digits: 292583499806596595725013018613757

(43·10²⁴⁹-7)/9 = 4(7)₂₄₉_<250> = 53 · 1103 · 801179 · C240

C240 = P41 · C199

P41 = 25422133258858709804303131627232676780973_<41>

C199 = [4012666034857030268082611148502973012917801084731203623422488400448065571628447168512039491797916152679691062964730175869111228899299131087507442826326840156446022996606392734495211546245324030097309_<199>]

Using B1=5000000, B2=23417929090, polynomial Dickson(12), sigma=907905841
Step 1 took 40103ms
Step 2 took 28475ms
********** Factor found in step 2: 25422133258858709804303131627232676780973
Found probable prime factor of 41 digits: 25422133258858709804303131627232676780973
Composite cofactor has 199 digits

(41·10¹²⁸-23)/9 = 4(5)₁₂₇3_<129> = 3 · 967 · 1217 · 1987 · 4421 · 1581473 · 99039401 · C101

C101 = P32 · P70

P32 = 36815704935774161283902098630699_<32>

P70 = 2547309708588572668816893086055764752839607538779524027891261431143921_<70>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3995894486
Step 1 took 8241ms
Step 2 took 8956ms
********** Factor found in step 2: 36815704935774161283902098630699
Found probable prime factor of 32 digits: 36815704935774161283902098630699
Probable prime cofactor 2547309708588572668816893086055764752839607538779524027891261431143921 has 70 digits

(41·10¹⁷¹-23)/9 = 4(5)₁₇₀3_<172> = 29 · 1253249 · 5380782097_<10> · C155

C155 = P31 · P125

P31 = 1463794900797595489324207413307_<31>

P125 = 15914036422945819678315903115949927673919089268637693940382042994674920656345122295731706640532780037792152348394058778535167_<125>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1832035179
Step 1 took 4149ms
Step 2 took 3431ms
********** Factor found in step 2: 1463794900797595489324207413307
Found probable prime factor of 31 digits: 1463794900797595489324207413307

(41·10¹⁸⁰-23)/9 = 4(5)₁₇₉3_<181> = 283 · 52385059 · 1021842427_<10> · 5329217405573587_<16> · C146

C146 = P31 · P116

P31 = 1236015933287564641565112604157_<31>

P116 = 45653705905749501607668550745050362451412108047028724874923313666054388301773089959197844701598951814422751612491493_<116>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1040011698
Step 1 took 3317ms
Step 2 took 3189ms
********** Factor found in step 2: 1236015933287564641565112604157
Found probable prime factor of 31 digits: 1236015933287564641565112604157

(41·10¹²⁴-23)/9 = 4(5)₁₂₃3_<125> = 17 · 105603271 · C116

C116 = P29 · P43 · P45

P29 = 65888693420744699362403856113_<29>

P43 = 2542943309278235960488509909300823318289419_<43>

P45 = 151449373643723932213841050457974953231496357_<45>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2501097197
Step 1 took 8922ms
Step 2 took 8826ms
********** Factor found in step 2: 65888693420744699362403856113
Found probable prime factor of 29 digits: 65888693420744699362403856113
Composite cofactor has 87 digits

Wed Jan 28 11:15:04 2009  Msieve v. 1.39
Wed Jan 28 11:15:04 2009  random seeds: 275c7966 7c142380
Wed Jan 28 11:15:04 2009  factoring 385127171401687385207501402488493862650469459394203243914566369266391722206958970146583 (87 digits)
Wed Jan 28 11:15:04 2009  searching for 15-digit factors
Wed Jan 28 11:15:05 2009  commencing quadratic sieve (87-digit input)
Wed Jan 28 11:15:05 2009  using multiplier of 3
Wed Jan 28 11:15:05 2009  using 64kb Opteron sieve core
Wed Jan 28 11:15:05 2009  sieve interval: 10 blocks of size 65536
Wed Jan 28 11:15:05 2009  processing polynomials in batches of 11
Wed Jan 28 11:15:05 2009  using a sieve bound of 1483927 (56667 primes)
Wed Jan 28 11:15:05 2009  using large prime bound of 118714160 (26 bits)
Wed Jan 28 11:15:05 2009  using double large prime bound of 342061674768240 (42-49 bits)
Wed Jan 28 11:15:05 2009  using trial factoring cutoff of 49 bits
Wed Jan 28 11:15:05 2009  polynomial 'A' values have 11 factors
Wed Jan 28 11:55:01 2009  56875 relations (15830 full + 41045 combined from 594180 partial), need 56763
Wed Jan 28 11:55:01 2009  begin with 610010 relations
Wed Jan 28 11:55:02 2009  reduce to 136243 relations in 9 passes
Wed Jan 28 11:55:02 2009  attempting to read 136243 relations
Wed Jan 28 11:55:03 2009  recovered 136243 relations
Wed Jan 28 11:55:03 2009  recovered 116276 polynomials
Wed Jan 28 11:55:03 2009  attempting to build 56875 cycles
Wed Jan 28 11:55:03 2009  found 56875 cycles in 5 passes
Wed Jan 28 11:55:03 2009  distribution of cycle lengths:
Wed Jan 28 11:55:03 2009     length 1 : 15830
Wed Jan 28 11:55:03 2009     length 2 : 11102
Wed Jan 28 11:55:03 2009     length 3 : 10213
Wed Jan 28 11:55:03 2009     length 4 : 7378
Wed Jan 28 11:55:03 2009     length 5 : 5089
Wed Jan 28 11:55:03 2009     length 6 : 3212
Wed Jan 28 11:55:03 2009     length 7 : 1901
Wed Jan 28 11:55:03 2009     length 9+: 2150
Wed Jan 28 11:55:03 2009  largest cycle: 18 relations
Wed Jan 28 11:55:03 2009  matrix is 56667 x 56875 (14.0 MB) with weight 3216000 (56.55/col)
Wed Jan 28 11:55:03 2009  sparse part has weight 3216000 (56.55/col)
Wed Jan 28 11:55:04 2009  filtering completed in 3 passes
Wed Jan 28 11:55:04 2009  matrix is 52253 x 52317 (13.0 MB) with weight 2983093 (57.02/col)
Wed Jan 28 11:55:04 2009  sparse part has weight 2983093 (57.02/col)
Wed Jan 28 11:55:04 2009  saving the first 48 matrix rows for later
Wed Jan 28 11:55:04 2009  matrix is 52205 x 52317 (8.6 MB) with weight 2356656 (45.05/col)
Wed Jan 28 11:55:04 2009  sparse part has weight 1732285 (33.11/col)
Wed Jan 28 11:55:04 2009  matrix includes 64 packed rows
Wed Jan 28 11:55:04 2009  using block size 20926 for processor cache size 1024 kB
Wed Jan 28 11:55:04 2009  commencing Lanczos iteration
Wed Jan 28 11:55:04 2009  memory use: 7.7 MB
Wed Jan 28 11:55:18 2009  lanczos halted after 827 iterations (dim = 52203)
Wed Jan 28 11:55:18 2009  recovered 16 nontrivial dependencies
Wed Jan 28 11:55:19 2009  prp43 factor: 2542943309278235960488509909300823318289419
Wed Jan 28 11:55:19 2009  prp45 factor: 151449373643723932213841050457974953231496357
Wed Jan 28 11:55:19 2009  elapsed time 00:40:15

(41·10¹⁴⁰-23)/9 = 4(5)₁₃₉3_<141> = 3² · 17 · 877 · 19246389499_<11> · 32476760901407_<14> · C112

C112 = P38 · P75

P38 = 23113065209519892999049301512692497833_<38>

P75 = 235001589601884725897441826945509931421660229052691677615339453591200234977_<75>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1100794531
Step 1 took 8421ms
Step 2 took 9318ms
********** Factor found in step 2: 23113065209519892999049301512692497833
Found probable prime factor of 38 digits: 23113065209519892999049301512692497833
Probable prime cofactor has 75 digits

(41·10¹⁵⁰-23)/9 = 4(5)₁₄₉3_<151> = 71 · 181 · 461 · 467 · 56663 · C137

C137 = P32 · P49 · P57

P32 = 33408920017609314616108752626191_<32>

P49 = 2321894412504908509073233224243572594876465727407_<49>

P57 = 374612401179637846452271743435694521178321815681110300299_<57>

# I am very grateful to Mr.Erik Branger who kindly released this number
#                                                                            after the factor was found
#
# When I run ECM, I remove numbers (which are reserved by others) periodically - 
# but sometimes an overlap happens: a number is cracked and turns out to be reserved. I usually dismiss such factors. This p49 was a quite a bit lucky... 
# Thank you, Erik!

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4014584566
Step 1 took 11854ms
Step 2 took 11645ms
********** Factor found in step 2: 2321894412504908509073233224243572594876465727407
Found probable prime factor of 49 digits: 2321894412504908509073233224243572594876465727407
Composite cofactor has 89 digits

Wed Jan 28 15:13:15 2009  Msieve v. 1.39
Wed Jan 28 15:13:15 2009  random seeds: dcc1d19f 8003f6d6
Wed Jan 28 15:13:15 2009  factoring 12515395748615094072564422948254398042726817026678117369398473451436798060732256902531109 (89 digits)
Wed Jan 28 15:13:15 2009  searching for 15-digit factors
Wed Jan 28 15:13:16 2009  commencing quadratic sieve (89-digit input)
Wed Jan 28 15:13:16 2009  using multiplier of 1
Wed Jan 28 15:13:16 2009  using 64kb Opteron sieve core
Wed Jan 28 15:13:16 2009  sieve interval: 14 blocks of size 65536
Wed Jan 28 15:13:16 2009  processing polynomials in batches of 8
Wed Jan 28 15:13:16 2009  using a sieve bound of 1537153 (58332 primes)
Wed Jan 28 15:13:16 2009  using large prime bound of 122972240 (26 bits)
Wed Jan 28 15:13:16 2009  using double large prime bound of 364462296550480 (42-49 bits)
Wed Jan 28 15:13:16 2009  using trial factoring cutoff of 49 bits
Wed Jan 28 15:13:16 2009  polynomial 'A' values have 11 factors
Wed Jan 28 15:51:53 2009  58627 relations (16387 full + 42240 combined from 612438 partial), need 58428
Wed Jan 28 15:51:53 2009  begin with 628825 relations
Wed Jan 28 15:51:54 2009  reduce to 140159 relations in 10 passes
Wed Jan 28 15:51:54 2009  attempting to read 140159 relations
Wed Jan 28 15:51:55 2009  recovered 140159 relations
Wed Jan 28 15:51:55 2009  recovered 112789 polynomials
Wed Jan 28 15:51:55 2009  attempting to build 58627 cycles
Wed Jan 28 15:51:55 2009  found 58627 cycles in 5 passes
Wed Jan 28 15:51:55 2009  distribution of cycle lengths:
Wed Jan 28 15:51:55 2009     length 1 : 16387
Wed Jan 28 15:51:55 2009     length 2 : 11480
Wed Jan 28 15:51:55 2009     length 3 : 10452
Wed Jan 28 15:51:55 2009     length 4 : 7680
Wed Jan 28 15:51:55 2009     length 5 : 5251
Wed Jan 28 15:51:55 2009     length 6 : 3344
Wed Jan 28 15:51:55 2009     length 7 : 1897
Wed Jan 28 15:51:55 2009     length 9+: 2136
Wed Jan 28 15:51:55 2009  largest cycle: 20 relations
Wed Jan 28 15:51:55 2009  matrix is 58332 x 58627 (14.7 MB) with weight 3371755 (57.51/col)
Wed Jan 28 15:51:55 2009  sparse part has weight 3371755 (57.51/col)
Wed Jan 28 15:51:56 2009  filtering completed in 3 passes
Wed Jan 28 15:51:56 2009  matrix is 53667 x 53731 (13.5 MB) with weight 3121580 (58.10/col)
Wed Jan 28 15:51:56 2009  sparse part has weight 3121580 (58.10/col)
Wed Jan 28 15:51:56 2009  saving the first 48 matrix rows for later
Wed Jan 28 15:51:56 2009  matrix is 53619 x 53731 (9.6 MB) with weight 2500423 (46.54/col)
Wed Jan 28 15:51:56 2009  sparse part has weight 1968488 (36.64/col)
Wed Jan 28 15:51:56 2009  matrix includes 64 packed rows
Wed Jan 28 15:51:56 2009  using block size 21492 for processor cache size 1024 kB
Wed Jan 28 15:51:57 2009  commencing Lanczos iteration
Wed Jan 28 15:51:57 2009  memory use: 8.2 MB
Wed Jan 28 15:52:15 2009  lanczos halted after 849 iterations (dim = 53619)
Wed Jan 28 15:52:15 2009  recovered 17 nontrivial dependencies
Wed Jan 28 15:52:16 2009  prp32 factor: 33408920017609314616108752626191
Wed Jan 28 15:52:16 2009  prp57 factor: 374612401179637846452271743435694521178321815681110300299
Wed Jan 28 15:52:16 2009  elapsed time 00:39:01

(41·10¹⁹⁷-23)/9 = 4(5)₁₉₆3_<198> = 3 · 7 · 107 · 13177 · 23081 · 7187963 · C179

C179 = P34 · P146

P34 = 2099403606495907277667888894462749_<34>

P146 = 44173858540728534572528842326705003005252228743462183058663832241052976873235501629877640848318099432460716303937164016586774713227903561777753721_<146>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2823049403
Step 1 took 15948ms
********** Factor found in step 1: 2099403606495907277667888894462749
Found probable prime factor of 34 digits: 2099403606495907277667888894462749
Probable prime cofactor has 146 digits

(41·10¹⁴⁹-23)/9 = 4(5)₁₄₈3_<150> = 3⁵ · 7 · 6345629 · 325563926267_<12> · 39321173758731261670625114839_<29> · C100

C100 = P40 · P61

P40 = 2906390360860183929041325401980600571603_<40>

P61 = 1134346306261106620176688918771075343769204867780752154765463_<61>

Divisors found:
 r1=2906390360860183929041325401980600571603 (pp40)
 r2=1134346306261106620176688918771075343769204867780752154765463 (pp61)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.884).
Factorization parameters were as follows:
n: 3296853170394634386426903479758021052421717743274532650918450384213305617576039420469949938202947189
skew: 5917.96
# norm 5.93e+13
c5: 57120
c4: -320192048
c3: -593092523794
c2: -5737521223828465
c1: -90444080558235915828
c0: -4032485409702275555140
# alpha -5.83
Y1: 5964523141
Y0: -8959063309188302307
# Murphy_E 3.41e-09
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1400001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 183693 x 183941
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 4.50 hours.

(41·10¹³⁸-23)/9 = 4(5)₁₃₇3_<139> = 5783 · C135

C135 = P65 · P71

P65 = 31826703588216506921591134020605913404953501401931568298791155907_<65>

P71 = 24751213454811777993464835171415082026382268067334361474439281562727213_<71>

SNFS difficulty: 141 digits.
Divisors found:
 r1=31826703588216506921591134020605913404953501401931568298791155907 (pp65)
 r2=24751213454811777993464835171415082026382268067334361474439281562727213 (pp71)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.301).
Factorization parameters were as follows:
n: 787749534074970699560013065114223682440870751436201894441562433953926258958249274694026552923319307548946144830633850173881299594597191
m: 5000000000000000000000000000
deg: 5
c5: 328
c0: -575
skew: 1.12
type: snfs
lss: 1
rlim: 1600000
alim: 1600000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 1600000/1600000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [800000, 1800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 277212 x 277460
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,49,49,2.4,2.4,100000
total time: 10.00 hours.

Jan 29, 2009 (3rd)

By Erik Branger / Msieve, GGNFS / Jan 29, 2009

(41·10¹³⁰-23)/9 = 4(5)₁₂₉3_<131> = 313 · 36847 · 9836292279467_<13> · 86954811961293481335701497_<26> · C85

C85 = P42 · P43

P42 = 881390449722686422846375486232579191674737_<42>

P43 = 5239640491095494706973558926511971332248621_<43>

Wed Jan 28 16:28:26 2009  Msieve v. 1.38
Wed Jan 28 16:28:26 2009  random seeds: 9bceceb0 5c6c8cd8
Wed Jan 28 16:28:26 2009  factoring 4618169088831855625167377731803863520723223439399359351692257045372290483853048787677 (85 digits)
Wed Jan 28 16:28:27 2009  searching for 15-digit factors
Wed Jan 28 16:28:28 2009  commencing quadratic sieve (85-digit input)
Wed Jan 28 16:28:28 2009  using multiplier of 5
Wed Jan 28 16:28:28 2009  using 64kb Pentium 4 sieve core
Wed Jan 28 16:28:28 2009  sieve interval: 6 blocks of size 65536
Wed Jan 28 16:28:28 2009  processing polynomials in batches of 17
Wed Jan 28 16:28:28 2009  using a sieve bound of 1429849 (54706 primes)
Wed Jan 28 16:28:28 2009  using large prime bound of 115817769 (26 bits)
Wed Jan 28 16:28:29 2009  using double large prime bound of 327186471420459 (41-49 bits)
Wed Jan 28 16:28:29 2009  using trial factoring cutoff of 49 bits
Wed Jan 28 16:28:29 2009  polynomial 'A' values have 11 factors
Wed Jan 28 17:11:40 2009  54993 relations (16294 full + 38699 combined from 569218 partial), need 54802
Wed Jan 28 17:11:43 2009  begin with 585512 relations
Wed Jan 28 17:11:43 2009  reduce to 127938 relations in 10 passes
Wed Jan 28 17:11:43 2009  attempting to read 127938 relations
Wed Jan 28 17:11:48 2009  recovered 127938 relations
Wed Jan 28 17:11:48 2009  recovered 105631 polynomials
Wed Jan 28 17:11:48 2009  attempting to build 54993 cycles
Wed Jan 28 17:11:48 2009  found 54993 cycles in 5 passes
Wed Jan 28 17:11:48 2009  distribution of cycle lengths:
Wed Jan 28 17:11:48 2009     length 1 : 16294
Wed Jan 28 17:11:48 2009     length 2 : 11182
Wed Jan 28 17:11:48 2009     length 3 : 9843
Wed Jan 28 17:11:48 2009     length 4 : 7059
Wed Jan 28 17:11:48 2009     length 5 : 4643
Wed Jan 28 17:11:48 2009     length 6 : 2735
Wed Jan 28 17:11:48 2009     length 7 : 1552
Wed Jan 28 17:11:48 2009     length 9+: 1685
Wed Jan 28 17:11:48 2009  largest cycle: 17 relations
Wed Jan 28 17:11:48 2009  matrix is 54706 x 54993 (11.6 MB) with weight 2819163 (51.26/col)
Wed Jan 28 17:11:48 2009  sparse part has weight 2819163 (51.26/col)
Wed Jan 28 17:11:49 2009  filtering completed in 3 passes
Wed Jan 28 17:11:49 2009  matrix is 49283 x 49347 (10.5 MB) with weight 2553042 (51.74/col)
Wed Jan 28 17:11:49 2009  sparse part has weight 2553042 (51.74/col)
Wed Jan 28 17:11:49 2009  saving the first 48 matrix rows for later
Wed Jan 28 17:11:49 2009  matrix is 49235 x 49347 (5.8 MB) with weight 1870616 (37.91/col)
Wed Jan 28 17:11:49 2009  sparse part has weight 1212608 (24.57/col)
Wed Jan 28 17:11:49 2009  matrix includes 64 packed rows
Wed Jan 28 17:11:49 2009  using block size 19738 for processor cache size 512 kB
Wed Jan 28 17:11:50 2009  commencing Lanczos iteration
Wed Jan 28 17:11:50 2009  memory use: 6.3 MB
Wed Jan 28 17:12:10 2009  lanczos halted after 780 iterations (dim = 49234)
Wed Jan 28 17:12:10 2009  recovered 17 nontrivial dependencies
Wed Jan 28 17:12:11 2009  prp42 factor: 881390449722686422846375486232579191674737
Wed Jan 28 17:12:11 2009  prp43 factor: 5239640491095494706973558926511971332248621
Wed Jan 28 17:12:11 2009  elapsed time 00:43:45

(41·10¹⁴⁸-23)/9 = 4(5)₁₄₇3_<149> = 43 · 251 · 568693575908293016347929797_<27> · 74447260787252610730701827479_<29> · C89

C89 = P42 · P48

P42 = 148975555407778170069581589916437657429373_<42>

P48 = 669201817267739198737277759103990448518471426079_<48>

Wed Jan 28 16:28:55 2009  Msieve v. 1.39
Wed Jan 28 16:28:55 2009  random seeds: b9762c40 a5997af9
Wed Jan 28 16:28:55 2009  factoring 99694712407355923179818470270485392821917098122466030908415422358077625320009088532818467 (89 digits)
Wed Jan 28 16:28:56 2009  searching for 15-digit factors
Wed Jan 28 16:28:57 2009  commencing quadratic sieve (89-digit input)
Wed Jan 28 16:28:57 2009  using multiplier of 3
Wed Jan 28 16:28:57 2009  using 32kb Intel Core sieve core
Wed Jan 28 16:28:57 2009  sieve interval: 33 blocks of size 32768
Wed Jan 28 16:28:57 2009  processing polynomials in batches of 7
Wed Jan 28 16:28:57 2009  using a sieve bound of 1558267 (59333 primes)
Wed Jan 28 16:28:57 2009  using large prime bound of 124661360 (26 bits)
Wed Jan 28 16:28:57 2009  using double large prime bound of 373522957629360 (42-49 bits)
Wed Jan 28 16:28:57 2009  using trial factoring cutoff of 49 bits
Wed Jan 28 16:28:57 2009  polynomial 'A' values have 11 factors
Wed Jan 28 17:37:37 2009  59692 relations (16146 full + 43546 combined from 629922 partial), need 59429
Wed Jan 28 17:37:38 2009  begin with 646068 relations
Wed Jan 28 17:37:38 2009  reduce to 145663 relations in 10 passes
Wed Jan 28 17:37:38 2009  attempting to read 145663 relations
Wed Jan 28 17:37:40 2009  recovered 145663 relations
Wed Jan 28 17:37:40 2009  recovered 124755 polynomials
Wed Jan 28 17:37:40 2009  attempting to build 59692 cycles
Wed Jan 28 17:37:40 2009  found 59692 cycles in 6 passes
Wed Jan 28 17:37:40 2009  distribution of cycle lengths:
Wed Jan 28 17:37:40 2009     length 1 : 16146
Wed Jan 28 17:37:40 2009     length 2 : 11175
Wed Jan 28 17:37:40 2009     length 3 : 10326
Wed Jan 28 17:37:40 2009     length 4 : 7991
Wed Jan 28 17:37:40 2009     length 5 : 5681
Wed Jan 28 17:37:40 2009     length 6 : 3608
Wed Jan 28 17:37:40 2009     length 7 : 2154
Wed Jan 28 17:37:40 2009     length 9+: 2611
Wed Jan 28 17:37:40 2009  largest cycle: 20 relations
Wed Jan 28 17:37:40 2009  matrix is 59333 x 59692 (14.8 MB) with weight 3634461 (60.89/col)
Wed Jan 28 17:37:40 2009  sparse part has weight 3634461 (60.89/col)
Wed Jan 28 17:37:41 2009  filtering completed in 3 passes
Wed Jan 28 17:37:41 2009  matrix is 55373 x 55437 (13.8 MB) with weight 3393295 (61.21/col)
Wed Jan 28 17:37:41 2009  sparse part has weight 3393295 (61.21/col)
Wed Jan 28 17:37:41 2009  saving the first 48 matrix rows for later
Wed Jan 28 17:37:41 2009  matrix is 55325 x 55437 (10.4 MB) with weight 2859681 (51.58/col)
Wed Jan 28 17:37:41 2009  sparse part has weight 2396355 (43.23/col)
Wed Jan 28 17:37:41 2009  matrix includes 64 packed rows
Wed Jan 28 17:37:41 2009  using block size 22174 for processor cache size 2048 kB
Wed Jan 28 17:37:42 2009  commencing Lanczos iteration
Wed Jan 28 17:37:42 2009  memory use: 9.3 MB
Wed Jan 28 17:37:59 2009  lanczos halted after 876 iterations (dim = 55325)
Wed Jan 28 17:37:59 2009  recovered 18 nontrivial dependencies
Wed Jan 28 17:38:00 2009  prp42 factor: 148975555407778170069581589916437657429373
Wed Jan 28 17:38:00 2009  prp48 factor: 669201817267739198737277759103990448518471426079
Wed Jan 28 17:38:00 2009  elapsed time 01:09:05

(41·10¹¹⁹-23)/9 = 4(5)₁₁₈3_<120> = 3 · 7 · 19 · C118

C118 = P44 · P74

P44 = 13204137097414283580303342290636923082729711_<44>

P74 = 86468599847390874149233253667621779699370576402751798197713344576119700577_<74>

Number: 45553_119
N=1141743247006404901141743247006404901141743247006404901141743247006404901141743247006404901141743247006404901141743247
  ( 118 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=13204137097414283580303342290636923082729711
 r2=86468599847390874149233253667621779699370576402751798197713344576119700577
Version: 
Total time: 2.59 hours.
Scaled time: 5.48 units (timescale=2.116).
Factorization parameters were as follows:
n: 1141743247006404901141743247006404901141743247006404901141743247006404901141743247006404901141743247006404901141743247
m: 1000000000000000000000000
deg: 5
c5: 41
c0: -230
skew: 1.41
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 720001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 88538 x 88786
Total sieving time: 2.59 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 2.59 hours.
 --------- CPU info (if available) ----------

(41·10¹²¹-23)/9 = 4(5)₁₂₀3_<122> = 193 · 3535877 · 746305381 · C104

C104 = P49 · P56

P49 = 6424734750718627625220006148533474581870541453749_<49>

P56 = 13922432274087936529154302972714446189901873148104111717_<56>

Number: 45553_121
N=89447934445859334817066221992763935132167607196659414011628506260431975722429438832612506174321484477033
  ( 104 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=6424734750718627625220006148533474581870541453749
 r2=13922432274087936529154302972714446189901873148104111717
Version: 
Total time: 2.23 hours.
Scaled time: 4.46 units (timescale=2.003).
Factorization parameters were as follows:
n: 89447934445859334817066221992763935132167607196659414011628506260431975722429438832612506174321484477033
m: 1000000000000000000000000
deg: 5
c5: 410
c0: -23
skew: 0.56
type: snfs
lss: 1
rlim: 770000
alim: 770000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2Factor base limits: 770000/770000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [385000, 685001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 95980 x 96228
Total sieving time: 2.23 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,770000,770000,25,25,46,46,2.2,2.2,50000
total time: 2.23 hours.
 --------- CPU info (if available) ----------

(41·10¹¹⁸-23)/9 = 4(5)₁₁₇3_<119> = 449153 · 5529329228987_<13> · C101

C101 = P32 · P69

P32 = 21601921391699076224361216972323_<32>

P69 = 849145693764416742375873463293188330565808251248427942826893089602001_<69>

Number: 45553_118
N=18343178526798706907297331767407580668174940804953852814701597268572385811455413189451069954302418323
  ( 101 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=21601921391699076224361216972323
 r2=849145693764416742375873463293188330565808251248427942826893089602001
Version: 
Total time: 2.91 hours.
Scaled time: 2.30 units (timescale=0.790).
Factorization parameters were as follows:
n: 18343178526798706907297331767407580668174940804953852814701597268572385811455413189451069954302418323
m: 500000000000000000000000
deg: 5
c5: 328
c0: -575
skew: 1.12
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2


Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 715001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 88452 x 88688
Total sieving time: 2.91 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 2.91 hours.
 --------- CPU info (if available) ----------

(41·10¹²⁵-23)/9 = 4(5)₁₂₄3_<126> = 3 · 7 · C125

C125 = P50 · P76

P50 = 18865962222763737173683333927093976699335628416363_<50>

P76 = 1149855037181548856673552853646671174178134269707019655492195514770948005911_<76>

Number: 45553_125
N=21693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693
  ( 125 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=18865962222763737173683333927093976699335628416363
 r2=1149855037181548856673552853646671174178134269707019655492195514770948005911
Version: 
Total time: 2.71 hours.
Scaled time: 5.46 units (timescale=2.016).
Factorization parameters were as follows:
n: 21693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693
m: 10000000000000000000000000
deg: 5
c5: 41
c0: -23
skew: 0.89
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 750001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 110535 x 110774
Total sieving time: 2.71 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 2.71 hours.
 --------- CPU info (if available) ----------

Jan 29, 2009 (2nd)

By Ignacio Santos / Msieve 1.39, Yafu 1.06 / Jan 29, 2009

(41·10¹⁰⁵-23)/9 = 4(5)₁₀₄3_<106> = 953 · 9595367 · 702317546407_<12> · C84

C84 = P42 · P43

P42 = 367779635852490880335270511439720960675651_<42>

P43 = 1928704346839101571853571281460612074420179_<43>

Wed Jan 28 16:29:33 2009  
Wed Jan 28 16:29:33 2009  
Wed Jan 28 16:29:33 2009  Msieve v. 1.39
Wed Jan 28 16:29:33 2009  random seeds: 8259fdd8 6aed4e44
Wed Jan 28 16:29:33 2009  factoring 709338182347601046367561329521658935509574931985120281467871275483245561945908361529 (84 digits)
Wed Jan 28 16:29:34 2009  searching for 15-digit factors
Wed Jan 28 16:29:35 2009  commencing quadratic sieve (84-digit input)
Wed Jan 28 16:29:35 2009  using multiplier of 1
Wed Jan 28 16:29:35 2009  using 32kb Intel Core sieve core
Wed Jan 28 16:29:35 2009  sieve interval: 12 blocks of size 32768
Wed Jan 28 16:29:35 2009  processing polynomials in batches of 17
Wed Jan 28 16:29:35 2009  using a sieve bound of 1401437 (53824 primes)
Wed Jan 28 16:29:35 2009  using large prime bound of 119122145 (26 bits)
Wed Jan 28 16:29:35 2009  using trial factoring cutoff of 27 bits
Wed Jan 28 16:29:35 2009  polynomial 'A' values have 11 factors
Wed Jan 28 16:52:29 2009  54034 relations (27656 full + 26378 combined from 277915 partial), need 53920
Wed Jan 28 16:52:29 2009  begin with 305571 relations
Wed Jan 28 16:52:29 2009  reduce to 77053 relations in 2 passes
Wed Jan 28 16:52:29 2009  attempting to read 77053 relations
Wed Jan 28 16:52:30 2009  recovered 77053 relations
Wed Jan 28 16:52:30 2009  recovered 70831 polynomials
Wed Jan 28 16:52:30 2009  attempting to build 54034 cycles
Wed Jan 28 16:52:30 2009  found 54034 cycles in 1 passes
Wed Jan 28 16:52:30 2009  distribution of cycle lengths:
Wed Jan 28 16:52:30 2009     length 1 : 27656
Wed Jan 28 16:52:30 2009     length 2 : 26378
Wed Jan 28 16:52:30 2009  largest cycle: 2 relations
Wed Jan 28 16:52:30 2009  matrix is 53824 x 54034 (7.4 MB) with weight 1717018 (31.78/col)
Wed Jan 28 16:52:30 2009  sparse part has weight 1717018 (31.78/col)
Wed Jan 28 16:52:30 2009  filtering completed in 3 passes
Wed Jan 28 16:52:30 2009  matrix is 39180 x 39243 (5.9 MB) with weight 1381772 (35.21/col)
Wed Jan 28 16:52:30 2009  sparse part has weight 1381772 (35.21/col)
Wed Jan 28 16:52:30 2009  saving the first 48 matrix rows for later
Wed Jan 28 16:52:30 2009  matrix is 39132 x 39243 (3.7 MB) with weight 1032357 (26.31/col)
Wed Jan 28 16:52:30 2009  sparse part has weight 734730 (18.72/col)
Wed Jan 28 16:52:30 2009  matrix includes 64 packed rows
Wed Jan 28 16:52:30 2009  using block size 15697 for processor cache size 4096 kB
Wed Jan 28 16:52:30 2009  commencing Lanczos iteration
Wed Jan 28 16:52:30 2009  memory use: 4.3 MB
Wed Jan 28 16:52:35 2009  lanczos halted after 621 iterations (dim = 39131)
Wed Jan 28 16:52:35 2009  recovered 16 nontrivial dependencies
Wed Jan 28 16:52:35 2009  prp42 factor: 367779635852490880335270511439720960675651
Wed Jan 28 16:52:35 2009  prp43 factor: 1928704346839101571853571281460612074420179
Wed Jan 28 16:52:35 2009  elapsed time 00:23:02

(41·10¹²²-23)/9 = 4(5)₁₂₁3_<123> = 3³ · 409 · 32987 · 467868311 · 2534846137715117_<16> · C91

C91 = P39 · P52

P39 = 458015487802174727396287622703879436789_<39>

P52 = 2302268949633360740904310241142947031318315208517831_<52>

01/28/09 17:21:40 v1.06 @ IGNACIO1, starting SIQS on c91: 1054474836018124158257047066798769193462469896437805554332753148131097644739785979743884659
01/28/09 17:21:40 v1.06 @ IGNACIO1, ==== sieve params ====
01/28/09 17:21:40 v1.06 @ IGNACIO1, n = 91 digits, 304 bits
01/28/09 17:21:40 v1.06 @ IGNACIO1, factor base: 67412 primes (max prime = 1794517)
01/28/09 17:21:40 v1.06 @ IGNACIO1, single large prime cutoff: 215342040 (120 * pmax)
01/28/09 17:21:40 v1.06 @ IGNACIO1, double large prime range from 43 to 50 bits
01/28/09 17:21:40 v1.06 @ IGNACIO1, double large prime cutoff: 999152734477817
01/28/09 17:21:40 v1.06 @ IGNACIO1, using 10 large prime slices of factor base
01/28/09 17:21:40 v1.06 @ IGNACIO1, buckets hold 1024 elements
01/28/09 17:21:40 v1.06 @ IGNACIO1, sieve interval: 22 blocks of size 32768
01/28/09 17:21:40 v1.06 @ IGNACIO1, polynomial A has ~ 12 factors
01/28/09 17:21:40 v1.06 @ IGNACIO1, using multiplier of 29
01/28/09 17:21:40 v1.06 @ IGNACIO1, using small prime variation correction of 22 bits
01/28/09 17:21:40 v1.06 @ IGNACIO1, trial factoring cutoff at 97 bits
01/28/09 17:21:40 v1.06 @ IGNACIO1, ==== sieving started ====
01/28/09 18:22:30 v1.06 @ IGNACIO1, sieve time = 1199.1730, relation time = 820.1540, poly_time = 1601.3640
01/28/09 18:22:30 v1.06 @ IGNACIO1, 67481 relations found: 19365 full + 48116 from 818643 partial, using 428968 polys (209 A polys)
01/28/09 18:22:30 v1.06 @ IGNACIO1, trial division touched 28729166 sieve locations out of 618482630656
01/28/09 18:22:30 v1.06 @ IGNACIO1, ==== post processing stage (msieve-1.38) ====
01/28/09 18:22:31 v1.06 @ IGNACIO1, begin with 838008 relations
01/28/09 18:22:31 v1.06 @ IGNACIO1, reduce to 157869 relations in 10 passes
01/28/09 18:22:33 v1.06 @ IGNACIO1, recovered 157869 relations
01/28/09 18:22:33 v1.06 @ IGNACIO1, recovered 132185 polynomials
01/28/09 18:22:33 v1.06 @ IGNACIO1, attempting to build 67481 cycles
01/28/09 18:22:33 v1.06 @ IGNACIO1, found 67481 cycles in 5 passes
01/28/09 18:22:33 v1.06 @ IGNACIO1, distribution of cycle lengths:
01/28/09 18:22:33 v1.06 @ IGNACIO1,    length 1 : 19365
01/28/09 18:22:33 v1.06 @ IGNACIO1,    length 2 : 14696
01/28/09 18:22:33 v1.06 @ IGNACIO1,    length 3 : 12271
01/28/09 18:22:33 v1.06 @ IGNACIO1,    length 4 : 8498
01/28/09 18:22:33 v1.06 @ IGNACIO1,    length 5 : 5579
01/28/09 18:22:33 v1.06 @ IGNACIO1,    length 6 : 3334
01/28/09 18:22:33 v1.06 @ IGNACIO1,    length 7 : 1819
01/28/09 18:22:33 v1.06 @ IGNACIO1,    length 9+: 1919
01/28/09 18:22:33 v1.06 @ IGNACIO1, largest cycle: 18 relations
01/28/09 18:22:34 v1.06 @ IGNACIO1, matrix is 67412 x 67481 (16.1 MB) with weight 3938485 (58.36/col)
01/28/09 18:22:34 v1.06 @ IGNACIO1, sparse part has weight 3938485 (58.36/col)
01/28/09 18:22:34 v1.06 @ IGNACIO1, filtering completed in 3 passes
01/28/09 18:22:34 v1.06 @ IGNACIO1, matrix is 62217 x 62281 (15.0 MB) with weight 3685912 (59.18/col)
01/28/09 18:22:34 v1.06 @ IGNACIO1, sparse part has weight 3685912 (59.18/col)
01/28/09 18:22:34 v1.06 @ IGNACIO1, saving the first 48 matrix rows for later
01/28/09 18:22:34 v1.06 @ IGNACIO1, matrix is 62169 x 62281 (10.0 MB) with weight 2926881 (46.99/col)
01/28/09 18:22:34 v1.06 @ IGNACIO1, sparse part has weight 2258498 (36.26/col)
01/28/09 18:22:34 v1.06 @ IGNACIO1, matrix includes 64 packed rows
01/28/09 18:22:34 v1.06 @ IGNACIO1, using block size 24912 for processor cache size 4096 kB
01/28/09 18:22:35 v1.06 @ IGNACIO1, commencing Lanczos iteration
01/28/09 18:22:35 v1.06 @ IGNACIO1, memory use: 9.5 MB
01/28/09 18:22:53 v1.06 @ IGNACIO1, lanczos halted after 985 iterations (dim = 62167)
01/28/09 18:22:53 v1.06 @ IGNACIO1, recovered 18 nontrivial dependencies
01/28/09 18:22:54 v1.06 @ IGNACIO1, prp52 = 2302268949633360740904310241142947031318315208517831
01/28/09 18:22:55 v1.06 @ IGNACIO1, prp39 = 458015487802174727396287622703879436789
01/28/09 18:22:55 v1.06 @ IGNACIO1, Lanczos elapsed time = 23.3690 seconds.
01/28/09 18:22:55 v1.06 @ IGNACIO1, Sqrt elapsed time = 2.2310 seconds.
01/28/09 18:22:55 v1.06 @ IGNACIO1, Total elapsed time = 3675.7900 seconds.
01/28/09 18:22:55 v1.06 @ IGNACIO1, 
01/28/09 18:22:55 v1.06 @ IGNACIO1,

Jan 29, 2009

Factorizations of 455...553 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Jan 28, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Jan 28, 2009

(64·10²⁶⁷-1)/9 = 7(1)₂₆₇_<268> = 13 · 4391 · 23929 · 36083 · 418460458963_<12> · 41647180748521_<14> · 1015426835807649035390773_<25> · 48287267091784318382365068194688977337835393445648868307_<56> · C150

C150 = P52 · P98

P52 = 2046177675001671248721526888669069941138882384733693_<52>

P98 = 82516129198420259258519024832071643294533917541647385866698598950636164516855352871556074606688239_<98>

Number: n
N=168842661393361084737921889601152067797799178106973990993993426212219306097598366298890372513822132593172970190424243529986838118573215023486690136627
  ( 150 digits)
SNFS difficulty: 180 digits.
Divisors found:

Wed Jan 28 04:20:25 2009  prp52 factor: 2046177675001671248721526888669069941138882384733693
Wed Jan 28 04:20:25 2009  prp98 factor: 82516129198420259258519024832071643294533917541647385866698598950636164516855352871556074606688239
Wed Jan 28 04:20:25 2009  elapsed time 02:30:29 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20050930-k8
Total time: 9.30 hours.
Scaled time: 16.27 units (timescale=1.750).
Factorization parameters were as follows:
name: KA_7_1_267
n: 168842661393361084737921889601152067797799178106973990993993426212219306097598366298890372513822132593172970190424243529986838118573215023486690136627
deg: 6
c6: 4
c3: 10
c0: 25
m: 1000000000000000000000000000000
skew: 1.36
type: snfs
rlim: 7500000
alim: 7500000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 7500000/7500000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 8250001)
Primes: RFBsize:508261, AFBsize:507810, largePrimes:37433789 encountered
Relations: rels:37525126, finalFF:1242382
Max relations in full relation-set: 28
Initial matrix: 1016137 x 1242382 with sparse part having weight 155967976.
Pruned matrix : 849553 x 854697 with weight 135481370.

Msieve: found 4171754 hash collisions in 39575190 relations
Msieve: matrix is 1148262 x 1148510 (307.2 MB)

Total sieving time: 8.33 hours.
Total relation processing time: 0.97 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,180,6,0,0,0,0,0,0,0,0,7500000,7500000,29,29,58,58,2.5,2.5,100000
total time: 9.30 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.96 BogoMIPS (lpj=2830483)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457)
Total of 4 processors activated (22643.68 BogoMIPS).

Jan 28, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.1 / Jan 28, 2009

(43·10²⁰²-7)/9 = 4(7)₂₀₂_<203> = 7331 · 2224447 · 4264331689_<10> · 3282544923857_<13> · 129162515387784254409797833_<27> · C145

C145 = P33 · C112

P33 = 894140490812561508197748839283473_<33>

C112 = [1812327796811753621163200021922067097052888721647496808031500412932013350729735549051173339843739136511233703573_<112>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=209624069
Step 1 took 3916ms
Step 2 took 3799ms
********** Factor found in step 2: 894140490812561508197748839283473
Found probable prime factor of 33 digits: 894140490812561508197748839283473
Composite cofactor has 112 digits

(43·10²³⁸-7)/9 = 4(7)₂₃₈_<239> = 73 · 89 · 109 · 997 · 122701 · C225

C225 = P32 · P194

P32 = 16019823933833801017304935568263_<32>

P194 = 34425922146851837576638249702876396349794779344942534097092159794838474557251330373243197269039118582961540438685946281867896688525526005977130309937227882149560857611922657828168430494238139459_<194>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1194573843
Step 1 took 7395ms
Step 2 took 5997ms
********** Factor found in step 2: 16019823933833801017304935568263
Found probable prime factor of 32 digits: 16019823933833801017304935568263
Probable prime cofactor has 194 digits

(43·10²²⁰-7)/9 = 4(7)₂₂₀_<221> = 523 · 4057 · 656879521 · C206

C206 = P31 · P175

P31 = 3502562889301427433586357821611_<31>

P175 = 9786954860237792671607046950183269287102623628043042827218853752548798081325699178457017851643964035536282843620014130674361843688073589623733707551549094537798547254146976097_<175>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3982886919
Step 1 took 6067ms
Step 2 took 5661ms
********** Factor found in step 2: 3502562889301427433586357821611
Found probable prime factor of 31 digits: 3502562889301427433586357821611
Probable prime cofactor has 175 digits

(43·10²⁰⁴-7)/9 = 4(7)₂₀₄_<205> = 1040355723593_<13> · 92650128269537_<14> · 717267726581621_<15> · C164

C164 = P33 · P131

P33 = 707556978655308658653936630923687_<33>

P131 = 97668687460140583325533653402275318211878194887345665390224627878545528890196304695329982444456944390617538106202072842223345362611_<131>

Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=4048053174
Step 1 took 900ms
Step 2 took 592ms
********** Factor found in step 2: 707556978655308658653936630923687
Found probable prime factor of 33 digits: 707556978655308658653936630923687
Probable prime cofactor has 131 digits

(43·10²⁰⁶-7)/9 = 4(7)₂₀₆_<207> = 3 · 73 · 1197999487_<10> · 919272050133022870840781_<24> · 227091512033988664050765336907_<30> · C142

C142 = P31 · C111

P31 = 9979120019997928268416395684139_<31>

C111 = [874154093062940053723423566083923324074453222353223316638756093434022663299154755490033595932211400153439132793_<111>]

Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=748490644
Step 1 took 1189ms
Step 2 took 740ms
********** Factor found in step 2: 9979120019997928268416395684139
Found probable prime factor of 31 digits: 9979120019997928268416395684139

(43·10²³⁰-7)/9 = 4(7)₂₃₀_<231> = 3 · 73 · C229

C229 = P27 · C202

P27 = 692730088823719508465086751_<27>

C202 = [3149327167508337424894687917653959013981952149120694102773275999128510834233614653207416330576776052801668066525911784723885214992039134786270169083745020741277257567117346186246575033521599505550100733_<202>]

Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=3170109874
Step 1 took 1812ms
********** Factor found in step 1: 692730088823719508465086751
Found probable prime factor of 27 digits: 692730088823719508465086751

(43·10²⁵⁰-7)/9 = 4(7)₂₅₀_<251> = C251

C251 = P42 · C210

P42 = 382055559643912628237678729323622320324517_<42>

C210 = [125054528253189447289899294516188810544311061053758161563935547216828629946964499418093698568954568490304175173591891013243054655738225373622583204023990174911869851275001232783069648585566026456246963123490781_<210>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2259809016
Step 1 took 79929ms
Step 2 took 29982ms
********** Factor found in step 2: 382055559643912628237678729323622320324517
Found probable prime factor of 42 digits: 382055559643912628237678729323622320324517
Composite cofactor has 210 digits

(43·10²⁴⁵-7)/9 = 4(7)₂₄₅_<246> = 3² · C245

C245 = P38 · P47 · C161

P38 = 53598747618551486853933977572595599339_<38>

P47 = 27976147881343907065273464547470440058178217281_<47>

C161 = [35403066396506894069278844750214201009889285722256175087036574343440723864063382620752845855264935086210428287407910294761124301971887380413930153470653666732667_<161>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=45451499
Step 1 took 24228ms
Step 2 took 20220ms
********** Factor found in step 2: 27976147881343907065273464547470440058178217281
Found probable prime factor of 47 digits: 27976147881343907065273464547470440058178217281

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2389133407
Step 1 took 24160ms
Step 2 took 20492ms
********** Factor found in step 2: 53598747618551486853933977572595599339
Found probable prime factor of 38 digits: 53598747618551486853933977572595599339
Composite cofactor ...

(43·10²³⁴-7)/9 = 4(7)₂₃₄_<235> = 8821 · 576493 · 63521290844627070769256161_<26> · C200

C200 = P42 · C158

P42 = 192264712908627279576854165210309221783217_<42>

C158 = [76929903377789411516700093310652483045899848288680400340995715116837047878585117428117743576767502256527687059432257791095117914169589812646186467347998067857_<158>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3778725536
Step 1 took 14404ms
Step 2 took 2805ms
********** Factor found in step 2: 192264712908627279576854165210309221783217
Found probable prime factor of 42 digits: 192264712908627279576854165210309221783217
Composite cofactor has 158 digits

Jan 28, 2009

By Jo Yeong Uk / GMP-ECM / Jan 27, 2009

(8·10¹⁹¹+1)/9 = (8)₁₉₀9_<191> = 2609 · C188

C188 = P38 · P151

P38 = 19309596681702726210004771712508766867_<38>

P151 = 1764412783486459285717951078009843334141086331932434701677798688195359927405853534975872523428117711532280972811375506792046840790602551996700236286963_<151>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 34070099229164004940164388228780716323836293173203866956262510114560708658063966611302755419275158638899535794898002640432690260210382862740087730505515097312720923299689110344533878454921 (188 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3327473856
Step 1 took 19035ms
Step 2 took 8027ms
********** Factor found in step 2: 19309596681702726210004771712508766867
Found probable prime factor of 38 digits: 19309596681702726210004771712508766867
Probable prime cofactor 1764412783486459285717951078009843334141086331932434701677798688195359927405853534975872523428117711532280972811375506792046840790602551996700236286963 has 151 digits

By Jo Yeong Uk / GMP-ECM / Jan 28, 2009

(13·10¹⁶³+17)/3 = 4(3)₁₆₂9_<164> = 7 · 241 · 317 · 8795430941251_<13> · 1985156050719971_<16> · C130

C130 = P39 · P92

P39 = 385707927893908191275285558306356222409_<39>

P92 = 12031988618847673970003210390549269057789807769464350948317521072724086706486418168409870769_<92>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 4640833398618822639460743910642182851226314326510127202032591287609238917161096442916131510784187204116371553691206889178711862521 (130 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=615671262
Step 1 took 11700ms
Step 2 took 5511ms
********** Factor found in step 2: 385707927893908191275285558306356222409
Found probable prime factor of 39 digits: 385707927893908191275285558306356222409
Probable prime cofactor 12031988618847673970003210390549269057789807769464350948317521072724086706486418168409870769 has 92 digits

Jan 27, 2009 (2nd)

Factorizations of 477...77 have been extended up to n=250. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Jan 27, 2009

By Erik Branger / GGNFS, Msieve / Jan 27, 2009

(13·10¹⁶⁴+11)/3 = 4(3)₁₆₃7_<165> = 19 · 41 · 796379 · C156

C156 = P72 · P85

P72 = 598661797073473238145780382200311271428592944554907156282580452950134593_<72>

P85 = 1166764738184177016523443436582987050721413715803341695737452720587804424134807603249_<85>

Number: 43337_164
N=698497474923299913146728475612118899596341156962299667492151519836772445023403568936203868454930027765602384708635557541702678174128868592063887794294092657
  ( 156 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=598661797073473238145780382200311271428592944554907156282580452950134593
 r2=1166764738184177016523443436582987050721413715803341695737452720587804424134807603249
Version: 
Total time: 69.52 hours.
Scaled time: 54.99 units (timescale=0.791).
Factorization parameters were as follows:
n: 698497474923299913146728475612118899596341156962299667492151519836772445023403568936203868454930027765602384708635557541702678174128868592063887794294092657
m: 1000000000000000000000000000000000
deg: 5
c5: 13
c0: 110
skew: 1.53
type: snfs
lss: 1
rlim: 4100000
alim: 4100000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4

Factor base limits: 4100000/4100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2050000, 3950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 707150 x 707398
Total sieving time: 69.52 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000
total time: 69.52 hours.
 --------- CPU info (if available) ----------

(41·10¹⁷²+13)/9 = 4(5)₁₇₁7_<173> = C173

C173 = P66 · P107

P66 = 846809775727438855533422032738541504094448048857030030647203344013_<66>

P107 = 53796681216181945160186440747727142358218300032577430895455479542146640352712930288135316333731693886056889_<107>

Number: 45557_172
N=45555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557
  ( 173 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=846809775727438855533422032738541504094448048857030030647203344013
 r2=53796681216181945160186440747727142358218300032577430895455479542146640352712930288135316333731693886056889
Version: 
Total time: 153.02 hours.
Scaled time: 301.75 units (timescale=1.972).
Factorization parameters were as follows:
n: 45555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557
m: 20000000000000000000000000000000000
deg: 5
c5: 1025
c0: 104
skew: 0.63
type: snfs
lss: 1
rlim: 5700000
alim: 5700000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4Factor base limits: 5700000/5700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2850000, 7850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1140833 x 1141081
Total sieving time: 153.02 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,5700000,5700000,27,27,52,52,2.4,2.4,100000
total time: 153.02 hours.
 --------- CPU info (if available) ----------

Jan 26, 2009 (2nd)

By Wataru Sakai / Msieve / Jan 26, 2009

(38·10²⁰³+61)/9 = 4(2)₂₀₂9_<204> = 3 · C204

C204 = P40 · P164

P40 = 6856113896741631556597576234948868923421_<40>

P164 = 20527771688219442244535154146181623000054303924350561860790279591622429058862241151966970921841993193628897638361564188894699065035168720938479822972805057054160883_<164>

Number: 42229_203
N=140740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
  ( 204 digits)
SNFS difficulty: 205 digits.
Divisors found:
 r1=6856113896741631556597576234948868923421
 r2=20527771688219442244535154146181623000054303924350561860790279591622429058862241151966970921841993193628897638361564188894699065035168720938479822972805057054160883
Version: 
Total time: 1090.97 hours.
Scaled time: 2159.02 units (timescale=1.979).
Factorization parameters were as follows:
n: 140740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
m: 50000000000000000000000000000000000000000
deg: 5
c5: 304
c0: 1525
skew: 1.38
type: snfs
lss: 1
rlim: 19000000
alim: 19000000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6Factor base limits: 19000000/19000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 56/56
Sieved rational special-q in [9500000, 20100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 3217971 x 3218219
Total sieving time: 1090.97 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,205,5,0,0,0,0,0,0,0,0,19000000,19000000,29,29,56,56,2.6,2.6,100000
total time: 1090.97 hours.
 --------- CPU info (if available) ----------

Jan 26, 2009

By Serge Batalov / Msieve-1.39 / Jan 26, 2009

(43·10¹⁷⁹-7)/9 = 4(7)₁₇₉_<180> = 3 · 17² · 16363 · 37418617 · C165

C165 = P68 · P98

P68 = 14145656150669491298815154320590745375349211707577628084877873514139_<68>

P98 = 63625775577778579433341123264082604872882905945721415160648453020214286335148354296475720079558299_<98>

SNFS difficulty: 181 digits.
Divisors found:
 r1=14145656150669491298815154320590745375349211707577628084877873514139 (pp68)
 r2=63625775577778579433341123264082604872882905945721415160648453020214286335148354296475720079558299 (pp98)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.316).
Factorization parameters were as follows:
n: 900028343642920268629193882313065164523095389608686033709901992697050423470050911286995509976226984775059263572750134624657136766028945840031740266801444602051289561
m: 1000000000000000000000000000000000000
deg: 5
c5: 43
c0: -70
skew: 1.10
type: snfs
lss: 1
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [4000000, 6700001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 1586574 x 1586822
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,55,55,2.5,2.5,100000
total time: 200.00 hours.

Jan 25, 2009 (2nd)

By Ignacio Santos / GGNFS, Msieve / Jan 25, 2009

(38·10¹⁷¹+61)/9 = 4(2)₁₇₀9_<172> = 131 · C170

C170 = P56 · P115

P56 = 19656586353109644988628428880782557935174813548674463961_<56>

P115 = 1639689791881402852262937784707669473345717597586097018290930889928565528828480997000727743404647721038578540516319_<115>

Number: 42229_171
N=32230703986429177268871925360474978795589482612383375742154368108566581849024597116200169635284139100932994062765055131467345207803223070398642917726887192536047497879559
  ( 170 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=19656586353109644988628428880782557935174813548674463961 (pp56)
 r2=1639689791881402852262937784707669473345717597586097018290930889928565528828480997000727743404647721038578540516319 (pp115)
Version: Msieve-1.39
Total time: 69.27 hours.
Scaled time: 178.36 units (timescale=2.575).
Factorization parameters were as follows:
n: 32230703986429177268871925360474978795589482612383375742154368108566581849024597116200169635284139100932994062765055131467345207803223070398642917726887192536047497879559
m: 10000000000000000000000000000000000
deg: 5
c5: 380
c0: 61
skew: 0.69
type: snfs
lss: 1
rlim: 5300000
alim: 5300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5300000/5300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2650000, 5950001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 984707 x 984955
Total sieving time: 69.27 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.4,2.4,100000
total time: 69.27 hours.
 --------- CPU info (if available) ----------

Jan 25, 2009

By Jo Yeong Uk / GMP-ECM / Jan 25, 2009

(41·10¹⁶¹+13)/9 = 4(5)₁₆₀7_<162> = 19 · 313 · 224473 · 112463872818618759244091017_<27> · C127

C127 = P39 · P88

P39 = 424001769125093094621543918688662607163_<39>

P88 = 7156465706183242170212634190189296953128191851050556387767311790646055779703262249922957_<88>

GMP-ECM 6.1.3 [powered by GMP 4.2.2] [ECM]
Input number is 3034354120104753360064970435795476897443162060598250583531604564172670129454802230625243157344730258350741251453786863506340991 (127 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3609433657
Step 1 took 75297ms
Step 2 took 31281ms
********** Factor found in step 2: 424001769125093094621543918688662607163
Found probable prime factor of 39 digits: 424001769125093094621543918688662607163
Probable prime cofactor 7156465706183242170212634190189296953128191851050556387767311790646055779703262249922957 has 88 digits

Jan 24, 2009 (6th)

By Sinkiti Sibata / GGNFS / Jan 24, 2009

(41·10¹⁴¹+13)/9 = 4(5)₁₄₀7_<142> = 3² · 7 · 293 · 331 · 22391 · 24847 · 178807 · 3914509373_<10> · C112

C112 = P48 · P65

P48 = 152943647887036111477247610987697036703626392511_<48>

P65 = 12518849987703023951410464231756309915231977459305480342194679649_<65>

Number: 45557_141
N=1914678584469877649316146631311483016914465974441251203654318046447997277245008118142822154997288621883177708639
  ( 112 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=152943647887036111477247610987697036703626392511 (pp48)
 r2=12518849987703023951410464231756309915231977459305480342194679649 (pp65)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 16.53 hours.
Scaled time: 7.82 units (timescale=0.473).
Factorization parameters were as follows:
name: 45557_141
n: 1914678584469877649316146631311483016914465974441251203654318046447997277245008118142822154997288621883177708639
m: 20000000000000000000000000000
deg: 5
c5: 205
c0: 208
skew: 1.00
type: snfs
lss: 1
rlim: 1750000
alim: 1750000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1750000/1750000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [875000, 2175001)
Primes: RFBsize:131608, AFBsize:131343, largePrimes:3922682 encountered
Relations: rels:4027274, finalFF:349003
Max relations in full relation-set: 28
Initial matrix: 263018 x 349003 with sparse part having weight 34653347.
Pruned matrix : 235041 x 236420 with weight 20618698.
Total sieving time: 14.73 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 1.50 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1750000,1750000,26,26,48,48,2.3,2.3,100000
total time: 16.53 hours.
 --------- CPU info (if available) ----------

Jan 24, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.1, polysel+Msieve-1.39/gnfs! / Jan 24, 2009

(64·10²⁸⁵-1)/9 = 7(1)₂₈₅_<286> = 13 · 1009 · 1759 · 5119 · 19009 · 13785887359_<11> · 125860098473209_<15> · 133333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333_<96> · C152

C152 = P42 · P110

P42 = 177742283449499822370246322633403703464107_<42>

P110 = 77026545609119905247041531218744494750493316082997162603430569339652310526470544011921085948181440727270755427_<110>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1333131140
Step 1 took 11737ms
Step 2 took 11965ms
********** Factor found in step 2: 177742283449499822370246322633403703464107
Found probable prime factor of 42 digits: 177742283449499822370246322633403703464107
Probable prime cofactor has 110 digits

(64·10²⁷³-1)/9 = 7(1)₂₇₃_<274> = 13 · 163 · 631 · 641 · 18119 · 21757 · 114089 · 119293 · 191360089 · 2202499141477_<13> · 350952042286768401725818393576681_<33> · 13530815674137173613152643233624800312250837_<44> · C150

C150 = P35 · P116

P35 = 65255421091265276492416239359633917_<35>

P116 = 11840544870401401854493322096167872823649699908568717703660676711510644450076098392953725282422610395748825819895357_<116>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1822787502
Step 1 took 11772ms
Step 2 took 11985ms
********** Factor found in step 2: 65255421091265276492416239359633917
Found probable prime factor of 35 digits: 65255421091265276492416239359633917
Probable prime cofactor has 116 digits

(64·10²⁷⁹-1)/9 = 7(1)₂₇₉_<280> = 13 · 31 · 1733 · 128599 · 105929849 · 18488064997_<11> · 2021725114081_<13> · 7281843828283_<13> · 2014918111668095329_<19> · 79803629814813067027_<20> · 250196468209067786071679820818025320428585440233101327018900387_<63> · C125

C125 = P33 · P45 · P48

P33 = 420292438080787921643359451399119_<33>

P45 = 730419717857197262419827344582992970030619307_<45>

P48 = 222350289638073289421082995769845047699481936533_<48>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=2662482447
Step 1 took 3322ms
Step 2 took 3339ms
********** Factor found in step 2: 420292438080787921643359451399119
Found probable prime factor of 33 digits: 420292438080787921643359451399119
Composite cofactor has 93 digits

N=162409035822907584060218661916820012041441209756152258900415577554695186850665254165658442631 ( 93 digits)
Divisors found:
 r1=730419717857197262419827344582992970030619307 (pp45)
 r2=222350289638073289421082995769845047699481936533 (pp48)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.543).
Factorization parameters were as follows:
name: t
n:  162409035822907584060218661916820012041441209756152258900415577554695186850665254165658442631
Y0: -1489330692417092566815
Y1: 1
c4: 33010008
c3: -38756776794
c2: -162401737450122205
c1: 177686061167819334
c0: 55176205140900388442296
skew: 1635.250
type: gnfs
# adj. I(F,S) = 53.898
# E(F1,F2) = 7.827023e-05
# GGNFS version 0.77.1-20060722-k8 polyselect.
# Options were:
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1232767725.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1080001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 171122 x 171358
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,92,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,46,46,2.4,2.4,60000
total time: 2.20 hours.

(64·10²⁵³-1)/9 = 7(1)₂₅₃_<254> = 35911 · 4101165361_<10> · 2654271168150479_<16> · C225

C225 = P37 · P189

P37 = 1503012251188960478291218182835329853_<37>

P189 = 121030513207473234467027754682031508099466504424023458323380931963655790995763624722806664691911530138966994414975832462847883393471773674247745852259859301419652934790614763057188332045643_<189>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=358141635
Step 1 took 22129ms
Step 2 took 18756ms
********** Factor found in step 2: 1503012251188960478291218182835329853
Found probable prime factor of 37 digits: 1503012251188960478291218182835329853
Probable prime cofactor has 189 digits

Jan 24, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 24, 2009

(41·10¹⁵⁶+13)/9 = 4(5)₁₅₅7_<157> = 3 · 97 · 70406513304649986892243_<23> · C132

C132 = P56 · P77

P56 = 14434671320601927444899804781903476800304653989688760687_<56>

P77 = 15403826606643878294130122774708818300656217739989908114754788714590290120547_<77>

Number: 45557_156
N=222349174146447297456867387484271193909218826076840028739075777284927827966982782165223823799367958189327915307092989558940264535789
  ( 132 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=14434671320601927444899804781903476800304653989688760687
 r2=15403826606643878294130122774708818300656217739989908114754788714590290120547
Version: 
Total time: 14.63 hours.
Scaled time: 35.00 units (timescale=2.392).
Factorization parameters were as follows:
n: 222349174146447297456867387484271193909218826076840028739075777284927827966982782165223823799367958189327915307092989558940264535789
m: 10000000000000000000000000000000
deg: 5
c5: 410
c0: 13
skew: 0.5
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8452545
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 548700 x 548948
Total sieving time: 13.28 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 0.66 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 14.63 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 24, 2009 (3rd)

By Serge Batalov / PFGW / Jan 24, 2009

(16·10⁴⁰⁸⁸⁹-1)/3 = 5(3)₄₀₈₈₉_<40890> is PRP.

Jan 24, 2009 (2nd)

Factorizations of 711...11 have been experimentally-extended up to n=300.

Jan 24, 2009

By Serge Batalov / PFGW / Jan 23, 2009

(16·10³⁵⁷⁵³-1)/3 = 5(3)₃₅₇₅₃_<35754> is PRP.

Jan 23, 2009 (4th)

By Serge Batalov / PFGW / Jan 23, 2009

(16·10¹³⁹⁹³-1)/3 = 5(3)₁₃₉₉₃_<13994> is PRP.

Jan 23, 2009 (3rd)

By Tyler Cadigan / GGNFS, Msieve / Jan 23, 2009

(10¹⁸³+53)/9 = (1)₁₈₂7_<183> = 3³ · 13 · 67 · 479 · C175

C175 = P87 · P89

P87 = 814456279501350377438980191700008354472608345334231988740752857383691177765970748860053_<87>

P89 = 12110784655000342767971716456433469345944334541188468092672320809287673550525096267604723_<89>

Number: 11117_183
N=9863704611953624372393435913691282636397008863140279821660669682218168042352617043532681072192976831233010323639294304409923253769436910793454449564989419647929464885048830319
  ( 175 digits)
SNFS difficulty: 183 digits.
Divisors found:
 r1=814456279501350377438980191700008354472608345334231988740752857383691177765970748860053 (pp87)
 r2=12110784655000342767971716456433469345944334541188468092672320809287673550525096267604723 (pp89)
Version: Msieve-1.39
Total time: 206.87 hours.
Scaled time: 516.77 units (timescale=2.498).
Factorization parameters were as follows:
n: 9863704611953624372393435913691282636397008863140279821660669682218168042352617043532681072192976831233010323639294304409923253769436910793454449564989419647929464885048830319
m: 2000000000000000000000000000000000000
deg: 5
c5: 125
c0: 212
skew: 1.11
type: snfs
lss: 1
rlim: 8000000
alim: 8000000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 1000000Factor base limits: 8000000/8000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [4000000, 7000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1216132 x 1216380
Total sieving time: 206.87 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,183,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,53,53,2.5,2.5,100000
total time: 206.87 hours.
 --------- CPU info (if available) ----------

Jan 23, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Jan 23, 2009

(13·10¹⁴⁸+17)/3 = 4(3)₁₄₇9_<149> = 19 · 23 · 797 · 9203 · 3277258151_<10> · 176436198027869291_<18> · C113

C113 = P48 · P65

P48 = 362219108729606434290438856179997703092034416009_<48>

P65 = 64548063349944856972207822649011628277742635258341188381686224693_<65>

Number: n
N=23380541976839200282767325190671790730362187880117941372803799512694979321700372600589803038261427659300210310237
  ( 113 digits)
Divisors found:

Fri Jan 23 18:09:16 2009  prp48 factor: 362219108729606434290438856179997703092034416009
Fri Jan 23 18:09:16 2009  prp65 factor: 64548063349944856972207822649011628277742635258341188381686224693
Fri Jan 23 18:09:16 2009  elapsed time 03:32:35 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-VC8(Wed
Total time: 30.15 hours.
Scaled time: 27.13 units (timescale=0.900).
Factorization parameters were as follows:
name: KA_4_3_147_9
n: 23380541976839200282767325190671790730362187880117941372803799512694979321700372600589803038261427659300210310237
skew: 28708.99
# norm 6.29e+014
c5: 2460
c4: -633951779
c3: -20695688236272
c2: 108160939099036276
c1: 5953456783481487169340
c0: -34441072704534910994164809
# alpha -4.20
Y1: 4810509227
Y0: -6245740134592778442020
# Murphy_E 6.93e-010
# M 1477219687526669108968129462520479885433990903110149087199378865914741253162073845052820046771899641015823549705
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 2650211)
Primes: RFBsize:250150, AFBsize:249326, largePrimes:16923260 encountered
Relations: rels:14857181, finalFF:506906
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 988439 hash collisions in 15497920 relations
Msieve: matrix is 611376 x 611624 (169.8 MB)

Total sieving time: 28.28 hours.
Total relation processing time: 1.87 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,28,28,56,56,2.6,2.6,100000
total time: 30.15 hours.
 --------- CPU info (if available) ----------

Jan 23, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 22, 2009

(41·10¹⁶⁹+13)/9 = 4(5)₁₆₈7_<170> = C170

C170 = P76 · P94

P76 = 8672165459367014932964431677102992882630879566220195983511869288408607879899_<76>

P94 = 5253077304509902079900327279449122912774951534438747747863906866303207485311500450868544270143_<94>

Number: 45557_169
N=45555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557
  ( 170 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=8672165459367014932964431677102992882630879566220195983511869288408607879899
 r2=5253077304509902079900327279449122912774951534438747747863906866303207485311500450868544270143
Version: 
Total time: 46.93 hours.
Scaled time: 112.17 units (timescale=2.390).
Factorization parameters were as follows:
n: 45555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557
m: 10000000000000000000000000000000000
deg: 5
c5: 41
c0: 130
skew: 1.26
type: snfs
lss: 1
rlim: 6200000
alim: 6200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 6200000/6200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [3100000, 6600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 11408430
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1056408 x 1056656
Total sieving time: 42.17 hours.
Total relation processing time: 1.99 hours.
Matrix solve time: 2.65 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,27,27,52,52,2.4,2.4,100000
total time: 46.93 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 23, 2009

(41·10¹⁴⁸+13)/9 = 4(5)₁₄₇7_<149> = 191 · 131310209 · 14599739933_<11> · C129

C129 = P64 · P65

P64 = 1800637357783759974901763552956102654092167352953638442460850199_<64>

P65 = 69093646156740776157080773778646968153929769992325516238093404609_<65>

Number: 45557_148
N=124412600455319753291293023822905556467418502777629884221966937651002000356694604848608553625643657312604663420905456072645167191
  ( 129 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=1800637357783759974901763552956102654092167352953638442460850199
 r2=69093646156740776157080773778646968153929769992325516238093404609
Version: 
Total time: 8.40 hours.
Scaled time: 20.02 units (timescale=2.383).
Factorization parameters were as follows:
n: 124412600455319753291293023822905556467418502777629884221966937651002000356694604848608553625643657312604663420905456072645167191
m: 1000000000000000000000000000000
deg: 5
c5: 41
c0: 1300
skew: 2.00
type: snfs
lss: 1
rlim: 2000000
alim: 2000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1000000, 1800001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7444421
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 326553 x 326801
Total sieving time: 7.79 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000
total time: 8.40 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

(13·10¹⁵⁴+17)/3 = 4(3)₁₅₃9_<155> = 47 · 1289401 · 17252447681025828391281179_<26> · C122

C122 = P45 · P78

P45 = 146931176976577432525516072501443271640471689_<45>

P78 = 282079522909008801832802122354881453999237337536406519426672216146977851866127_<78>

Number: 43339_154
N=41446276302012100498146879584396609173055097640213325449671826370659005132758983843586432026920587622476154011707161578503
  ( 122 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=146931176976577432525516072501443271640471689
 r2=282079522909008801832802122354881453999237337536406519426672216146977851866127
Version: 
Total time: 9.31 hours.
Scaled time: 22.19 units (timescale=2.384).
Factorization parameters were as follows:
n: 41446276302012100498146879584396609173055097640213325449671826370659005132758983843586432026920587622476154011707161578503
m: 10000000000000000000000000000000
deg: 5
c5: 13
c0: 170
skew: 1.67
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1300000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 7954348
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 449296 x 449544
Total sieving time: 8.41 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.45 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000
total time: 9.31 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 22, 2009 (3rd)

By Sinkiti Sibata / Msieve / Jan 22, 2009

(41·10¹⁴⁷+13)/9 = 4(5)₁₄₆7_<148> = 3 · 7 · 484727 · 25526615366041_<14> · 1937528314189504345464269_<25> · C103

C103 = P41 · P63

P41 = 29355415641012754416171952787119471143967_<41>

P63 = 308244485008190237669046414380908430812930699613696887061598997_<63>

Wed Jan 21 17:08:16 2009  
Wed Jan 21 17:08:16 2009  
Wed Jan 21 17:08:16 2009  Msieve v. 1.39
Wed Jan 21 17:08:16 2009  random seeds: f2c9dc98 27ac341f
Wed Jan 21 17:08:16 2009  factoring 9048644976465349194417936214282020920405826876717322267545304616149531433795128952289790672367809801099 (103 digits)
Wed Jan 21 17:08:17 2009  searching for 15-digit factors
Wed Jan 21 17:08:19 2009  commencing quadratic sieve (103-digit input)
Wed Jan 21 17:08:19 2009  using multiplier of 1
Wed Jan 21 17:08:19 2009  using 32kb Intel Core sieve core
Wed Jan 21 17:08:19 2009  sieve interval: 36 blocks of size 32768
Wed Jan 21 17:08:19 2009  processing polynomials in batches of 6
Wed Jan 21 17:08:19 2009  using a sieve bound of 3560659 (127500 primes)
Wed Jan 21 17:08:19 2009  using large prime bound of 534098850 (28 bits)
Wed Jan 21 17:08:19 2009  using double large prime bound of 5125295884020600 (44-53 bits)
Wed Jan 21 17:08:19 2009  using trial factoring cutoff of 53 bits
Wed Jan 21 17:08:19 2009  polynomial 'A' values have 13 factors
Thu Jan 22 09:07:44 2009  127765 relations (31985 full + 95780 combined from 1881547 partial), need 127596
Thu Jan 22 09:07:46 2009  begin with 1913532 relations
Thu Jan 22 09:07:48 2009  reduce to 330770 relations in 11 passes
Thu Jan 22 09:07:48 2009  attempting to read 330770 relations
Thu Jan 22 09:07:54 2009  recovered 330770 relations
Thu Jan 22 09:07:54 2009  recovered 319137 polynomials
Thu Jan 22 09:07:55 2009  attempting to build 127765 cycles
Thu Jan 22 09:07:55 2009  found 127765 cycles in 6 passes
Thu Jan 22 09:07:55 2009  distribution of cycle lengths:
Thu Jan 22 09:07:55 2009     length 1 : 31985
Thu Jan 22 09:07:55 2009     length 2 : 22531
Thu Jan 22 09:07:55 2009     length 3 : 21549
Thu Jan 22 09:07:55 2009     length 4 : 17313
Thu Jan 22 09:07:55 2009     length 5 : 12810
Thu Jan 22 09:07:55 2009     length 6 : 8530
Thu Jan 22 09:07:55 2009     length 7 : 5448
Thu Jan 22 09:07:55 2009     length 9+: 7599
Thu Jan 22 09:07:55 2009  largest cycle: 19 relations
Thu Jan 22 09:07:56 2009  matrix is 127500 x 127765 (37.4 MB) with weight 9284987 (72.67/col)
Thu Jan 22 09:07:56 2009  sparse part has weight 9284987 (72.67/col)
Thu Jan 22 09:07:59 2009  filtering completed in 4 passes
Thu Jan 22 09:07:59 2009  matrix is 121328 x 121392 (35.7 MB) with weight 8883191 (73.18/col)
Thu Jan 22 09:07:59 2009  sparse part has weight 8883191 (73.18/col)
Thu Jan 22 09:07:59 2009  saving the first 48 matrix rows for later
Thu Jan 22 09:07:59 2009  matrix is 121280 x 121392 (26.3 MB) with weight 7483600 (61.65/col)
Thu Jan 22 09:07:59 2009  sparse part has weight 6170468 (50.83/col)
Thu Jan 22 09:07:59 2009  matrix includes 64 packed rows
Thu Jan 22 09:07:59 2009  using block size 43690 for processor cache size 1024 kB
Thu Jan 22 09:08:01 2009  commencing Lanczos iteration
Thu Jan 22 09:08:01 2009  memory use: 22.9 MB
Thu Jan 22 09:10:18 2009  lanczos halted after 1920 iterations (dim = 121278)
Thu Jan 22 09:10:18 2009  recovered 16 nontrivial dependencies
Thu Jan 22 09:10:19 2009  prp41 factor: 29355415641012754416171952787119471143967
Thu Jan 22 09:10:19 2009  prp63 factor: 308244485008190237669046414380908430812930699613696887061598997
Thu Jan 22 09:10:19 2009  elapsed time 16:02:03

Jan 22, 2009 (2nd)

By Serge Batalov / Msieve-1.39 / Jan 22, 2009

(13·10¹⁴³+17)/3 = 4(3)₁₄₂9_<144> = 595261 · 2447584577_<10> · C129

C129 = P51 · P78

P51 = 305898875245419918219285872629868213926480602328937_<51>

P78 = 972297300424393795140250280951268596451060292444954962055583775858618087659551_<78>

SNFS difficulty: 145 digits.
Divisors found:
 r1=305898875245419918219285872629868213926480602328937 (pp51)
 r2=972297300424393795140250280951268596451060292444954962055583775858618087659551 (pp78)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.733).
Factorization parameters were as follows:
n: 297424650603980208445370180543684343390316432002990258734180559806241331564648089739012138500185960159673853974878839430171727287
m: 50000000000000000000000000000
deg: 5
c5: 104
c0: 425
skew: 1.33
type: snfs
lss: 1
rlim: 1860000
alim: 1860000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 1860000/1860000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [930000, 2230001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 383995 x 384243
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1860000,1860000,26,26,49,49,2.4,2.4,100000
total time: 6.00 hours.

Jan 22, 2009

By Erik Branger / GGNFS, Msieve / Jan 22, 2009

(13·10¹³⁹+17)/3 = 4(3)₁₃₈9_<140> = 7 · 322587019395677_<15> · C125

C125 = P54 · P72

P54 = 190816151611739294445911252917288917593300029648364203_<54>

P72 = 100568514927274055488494266292260629800808063776522036000875666030563667_<72>

Number: 43339_139
N=19190096991730192555558625223758369283698411644425946513238187529045129212903903609655206267406975666951436025446928595212401
  ( 125 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=190816151611739294445911252917288917593300029648364203
 r2=100568514927274055488494266292260629800808063776522036000875666030563667
Version: 
Total time: 7.90 hours.
Scaled time: 6.19 units (timescale=0.784).
Factorization parameters were as follows:
n: 19190096991730192555558625223758369283698411644425946513238187529045129212903903609655206267406975666951436025446928595212401
m: 10000000000000000000000000000
deg: 5
c5: 13
c0: 170
skew: 1.67
type: snfs
lss: 1
rlim: 1570000
alim: 1570000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3

Factor base limits: 1570000/1570000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [785000, 1485001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 208419 x 208667
Total sieving time: 7.90 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000
total time: 7.90 hours.
 --------- CPU info (if available) ----------

(43·10¹⁶⁸-7)/9 = 4(7)₁₆₈_<169> = 530723676086574731102103897057683_<33> · C136

C136 = P55 · P82

P55 = 1308979129371218843055335143575659161498651650606112393_<55>

P82 = 6877407559410922828407190093693313130619469297610260690908537887846523454630592083_<82>

Number: 47777_168
N=9002382959448748794439199014832033133711285895903932632389666139902386003239170475300347336941766288329532183182089193481662048433984619
  ( 136 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=1308979129371218843055335143575659161498651650606112393
 r2=6877407559410922828407190093693313130619469297610260690908537887846523454630592083
Version: 
Total time: 116.36 hours.
Scaled time: 242.96 units (timescale=2.088).
Factorization parameters were as follows:
n: 9002382959448748794439199014832033133711285895903932632389666139902386003239170475300347336941766288329532183182089193481662048433984619
m: 5000000000000000000000000000000000
deg: 5
c5: 344
c0: -175
skew: 0.87
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 6300001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 998810 x 999058
Total sieving time: 116.36 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 116.36 hours.
 --------- CPU info (if available) ----------

Jan 21, 2009 (7th)

By Markus Tervooren / Msieve / Jan 21, 2009

(13·10¹⁹⁴+17)/3 = 4(3)₁₉₃9_<195> = 59 · 83 · 157 · 607 · 1361 · 6311 · 164321 · 1786969867_<10> · 19193147198594868597439948288841_<32> · 466809015184227886664481474387139_<33> · C101

C101 = P49 · P52

P49 = 6923543614221823683435637142856143697121804494349_<49>

P52 = 5935033643361588312921134997404606384549571877425379_<52>

Msieve v. 1.38
Tue Jan 20 22:17:21 2009
random seeds: 00f89e0f 4841fd03
factoring 41091464281687809280907055016363623012787750287324348861042488523828133080766450467340391897074683271 (101 digits)
searching for 15-digit factors
commencing quadratic sieve (101-digit input)
using multiplier of 1
using 32kb Intel Core sieve core
sieve interval: 36 blocks of size 32768
processing polynomials in batches of 6
using a sieve bound of 2974639 (107321 primes)
using large prime bound of 446195850 (28 bits)
using double large prime bound of 3708053052160350 (44-52 bits)
using trial factoring cutoff of 52 bits
polynomial 'A' values have 13 factors

sieving in progress (press Ctrl-C to pause)
107596 relations (26016 full + 81580 combined from 1604242 partial), need 107417
107596 relations (26016 full + 81580 combined from 1604242 partial), need 107417
sieving complete, commencing postprocessing
begin with 1630258 relations
reduce to 281849 relations in 12 passes
attempting to read 281849 relations
recovered 281849 relations
recovered 271135 polynomials
attempting to build 107596 cycles
found 107596 cycles in 6 passes
distribution of cycle lengths:
   length 1 : 26016
   length 2 : 18625
   length 3 : 18195
   length 4 : 14748
   length 5 : 11084
   length 6 : 7312
   length 7 : 4885
   length 9+: 6731
largest cycle: 21 relations
matrix is 107321 x 107596 (31.7 MB) with weight 7446349 (69.21/col)
sparse part has weight 7446349 (69.21/col)
filtering completed in 3 passes
matrix is 102535 x 102599 (30.4 MB) with weight 7138488 (69.58/col)
sparse part has weight 7138488 (69.58/col)
saving the first 48 matrix rows for later
matrix is 102487 x 102599 (19.6 MB) with weight 5683979 (55.40/col)
sparse part has weight 4114878 (40.11/col)
matrix includes 64 packed rows
using block size 41039 for processor cache size 4096 kB
commencing Lanczos iteration
memory use: 17.3 MB
linear algebra completed 101083 of 102599 dimensions (98.5%, ETA 0h 0m)
lanczos halted after 1624 iterations (dim = 102485)
recovered 17 nontrivial dependencies
prp49 factor: 6923543614221823683435637142856143697121804494349
prp52 factor: 5935033643361588312921134997404606384549571877425379
elapsed time 08:45:07

Jan 21, 2009 (6th)

By Sinkiti Sibata / Msieve / Jan 21, 2009

(41·10¹³¹+13)/9 = 4(5)₁₃₀7_<132> = 2744051 · 403261362516720769854631_<24> · C102

C102 = P35 · P67

P35 = 79005309736995305131116060227523937_<35>

P67 = 5210822446986772338468650809121467546078389156874394153991712631681_<67>

Tue Jan 20 22:13:49 2009  Msieve v. 1.39
Tue Jan 20 22:13:49 2009  random seeds: f46ffff0 52d14748
Tue Jan 20 22:13:49 2009  factoring 411682641408677746814453464337059397301767786709657824132464450814076300835690663029222620192692048097 (102 digits)
Tue Jan 20 22:13:50 2009  searching for 15-digit factors
Tue Jan 20 22:13:52 2009  commencing quadratic sieve (102-digit input)
Tue Jan 20 22:13:52 2009  using multiplier of 2
Tue Jan 20 22:13:52 2009  using 32kb Intel Core sieve core
Tue Jan 20 22:13:52 2009  sieve interval: 36 blocks of size 32768
Tue Jan 20 22:13:52 2009  processing polynomials in batches of 6
Tue Jan 20 22:13:52 2009  using a sieve bound of 3198409 (114826 primes)
Tue Jan 20 22:13:52 2009  using large prime bound of 479761350 (28 bits)
Tue Jan 20 22:13:52 2009  using double large prime bound of 4225182407156700 (44-52 bits)
Tue Jan 20 22:13:52 2009  using trial factoring cutoff of 52 bits
Tue Jan 20 22:13:52 2009  polynomial 'A' values have 13 factors
Wed Jan 21 13:03:10 2009  115071 relations (27861 full + 87210 combined from 1710804 partial), need 114922
Wed Jan 21 13:03:12 2009  begin with 1738665 relations
Wed Jan 21 13:03:14 2009  reduce to 301395 relations in 10 passes
Wed Jan 21 13:03:14 2009  attempting to read 301395 relations
Wed Jan 21 13:03:19 2009  recovered 301395 relations
Wed Jan 21 13:03:19 2009  recovered 291722 polynomials
Wed Jan 21 13:03:20 2009  attempting to build 115071 cycles
Wed Jan 21 13:03:20 2009  found 115071 cycles in 6 passes
Wed Jan 21 13:03:20 2009  distribution of cycle lengths:
Wed Jan 21 13:03:20 2009     length 1 : 27861
Wed Jan 21 13:03:20 2009     length 2 : 19785
Wed Jan 21 13:03:20 2009     length 3 : 19653
Wed Jan 21 13:03:20 2009     length 4 : 15587
Wed Jan 21 13:03:20 2009     length 5 : 11674
Wed Jan 21 13:03:20 2009     length 6 : 8109
Wed Jan 21 13:03:20 2009     length 7 : 5129
Wed Jan 21 13:03:20 2009     length 9+: 7273
Wed Jan 21 13:03:20 2009  largest cycle: 21 relations
Wed Jan 21 13:03:20 2009  matrix is 114826 x 115071 (33.4 MB) with weight 8294028 (72.08/col)
Wed Jan 21 13:03:20 2009  sparse part has weight 8294028 (72.08/col)
Wed Jan 21 13:03:23 2009  filtering completed in 3 passes
Wed Jan 21 13:03:23 2009  matrix is 109772 x 109836 (32.1 MB) with weight 7970453 (72.57/col)
Wed Jan 21 13:03:23 2009  sparse part has weight 7970453 (72.57/col)
Wed Jan 21 13:03:23 2009  saving the first 48 matrix rows for later
Wed Jan 21 13:03:23 2009  matrix is 109724 x 109836 (21.8 MB) with weight 6540242 (59.55/col)
Wed Jan 21 13:03:23 2009  sparse part has weight 5054683 (46.02/col)
Wed Jan 21 13:03:23 2009  matrix includes 64 packed rows
Wed Jan 21 13:03:23 2009  using block size 43690 for processor cache size 1024 kB
Wed Jan 21 13:03:24 2009  commencing Lanczos iteration
Wed Jan 21 13:03:24 2009  memory use: 19.8 MB
Wed Jan 21 13:04:57 2009  lanczos halted after 1737 iterations (dim = 109721)
Wed Jan 21 13:04:57 2009  recovered 16 nontrivial dependencies
Wed Jan 21 13:04:59 2009  prp35 factor: 79005309736995305131116060227523937
Wed Jan 21 13:04:59 2009  prp67 factor: 5210822446986772338468650809121467546078389156874394153991712631681
Wed Jan 21 13:04:59 2009  elapsed time 14:51:10

(13·10¹⁴⁶+17)/3 = 4(3)₁₄₅9_<147> = 12071 · 29378177 · 84570591056004857773_<20> · 792811709540546005601_<21> · C95

C95 = P41 · P55

P41 = 18207354784516050172954138782410783675017_<41>

P55 = 1000962316970499262148043364808414101538921611237419737_<55>

Wed Jan 21 13:23:17 2009  Msieve v. 1.39
Wed Jan 21 13:23:17 2009  random seeds: 932fa8c0 871e53d0
Wed Jan 21 13:23:17 2009  factoring 18224876031013090904332849103994615678017092717370950399562413140608318359411130578473429610529 (95 digits)
Wed Jan 21 13:23:18 2009  searching for 15-digit factors
Wed Jan 21 13:23:19 2009  commencing quadratic sieve (95-digit input)
Wed Jan 21 13:23:19 2009  using multiplier of 41
Wed Jan 21 13:23:19 2009  using 32kb Intel Core sieve core
Wed Jan 21 13:23:19 2009  sieve interval: 36 blocks of size 32768
Wed Jan 21 13:23:19 2009  processing polynomials in batches of 6
Wed Jan 21 13:23:19 2009  using a sieve bound of 2128183 (78718 primes)
Wed Jan 21 13:23:19 2009  using large prime bound of 310714718 (28 bits)
Wed Jan 21 13:23:19 2009  using double large prime bound of 1933086450144842 (43-51 bits)
Wed Jan 21 13:23:19 2009  using trial factoring cutoff of 51 bits
Wed Jan 21 13:23:19 2009  polynomial 'A' values have 12 factors
Wed Jan 21 16:29:21 2009  79005 relations (20068 full + 58937 combined from 1155124 partial), need 78814
Wed Jan 21 16:29:22 2009  begin with 1175192 relations
Wed Jan 21 16:29:23 2009  reduce to 203036 relations in 11 passes
Wed Jan 21 16:29:23 2009  attempting to read 203036 relations
Wed Jan 21 16:29:26 2009  recovered 203036 relations
Wed Jan 21 16:29:26 2009  recovered 184685 polynomials
Wed Jan 21 16:29:26 2009  attempting to build 79005 cycles
Wed Jan 21 16:29:26 2009  found 79005 cycles in 6 passes
Wed Jan 21 16:29:26 2009  distribution of cycle lengths:
Wed Jan 21 16:29:26 2009     length 1 : 20068
Wed Jan 21 16:29:26 2009     length 2 : 14388
Wed Jan 21 16:29:26 2009     length 3 : 13331
Wed Jan 21 16:29:26 2009     length 4 : 10426
Wed Jan 21 16:29:26 2009     length 5 : 7737
Wed Jan 21 16:29:26 2009     length 6 : 5229
Wed Jan 21 16:29:26 2009     length 7 : 3324
Wed Jan 21 16:29:26 2009     length 9+: 4502
Wed Jan 21 16:29:26 2009  largest cycle: 21 relations
Wed Jan 21 16:29:27 2009  matrix is 78718 x 79005 (21.4 MB) with weight 5297899 (67.06/col)
Wed Jan 21 16:29:27 2009  sparse part has weight 5297899 (67.06/col)
Wed Jan 21 16:29:28 2009  filtering completed in 3 passes
Wed Jan 21 16:29:28 2009  matrix is 74535 x 74599 (20.3 MB) with weight 5026664 (67.38/col)
Wed Jan 21 16:29:28 2009  sparse part has weight 5026664 (67.38/col)
Wed Jan 21 16:29:28 2009  saving the first 48 matrix rows for later
Wed Jan 21 16:29:28 2009  matrix is 74487 x 74599 (14.4 MB) with weight 4141954 (55.52/col)
Wed Jan 21 16:29:28 2009  sparse part has weight 3326541 (44.59/col)
Wed Jan 21 16:29:28 2009  matrix includes 64 packed rows
Wed Jan 21 16:29:28 2009  using block size 29839 for processor cache size 1024 kB
Wed Jan 21 16:29:29 2009  commencing Lanczos iteration
Wed Jan 21 16:29:29 2009  memory use: 12.9 MB
Wed Jan 21 16:30:08 2009  lanczos halted after 1180 iterations (dim = 74485)
Wed Jan 21 16:30:08 2009  recovered 17 nontrivial dependencies
Wed Jan 21 16:30:09 2009  prp41 factor: 18207354784516050172954138782410783675017
Wed Jan 21 16:30:09 2009  prp55 factor: 1000962316970499262148043364808414101538921611237419737
Wed Jan 21 16:30:09 2009  elapsed time 03:06:52

Jan 21, 2009 (5th)

By Erik Branger / GGNFS, Msieve / Jan 21, 2009

(13·10¹³¹+17)/3 = 4(3)₁₃₀9_<132> = 29 · 904733 · 29957120117_<11> · C114

C114 = P56 · P58

P56 = 75290545150991448414835552655069190513078881893534153027_<56>

P58 = 7322563824738082008971167079472877712083747265515945444253_<58>

Number: 43339_131
N=551319822267459194717415093064116246005032550795737682772740698942815633285096006269830717449494717586743599703831
  ( 114 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=75290545150991448414835552655069190513078881893534153027
 r2=7322563824738082008971167079472877712083747265515945444253
Version: 
Total time: 4.98 hours.
Scaled time: 3.94 units (timescale=0.792).
Factorization parameters were as follows:
n: 551319822267459194717415093064116246005032550795737682772740698942815633285096006269830717449494717586743599703831
m: 100000000000000000000000000
deg: 5
c5: 130
c0: 17
skew: 0.67
type: snfs
lss: 1
rlim: 1110000
alim: 1110000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1110000/1110000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [555000, 1055001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 167053 x 167297
Total sieving time: 4.98 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1110000,1110000,26,26,47,47,2.3,2.3,50000
total time: 4.98 hours.
 --------- CPU info (if available) ----------

(13·10¹³⁴+17)/3 = 4(3)₁₃₃9_<135> = 6673369 · C128

C128 = P46 · P83

P46 = 5170562015966718933706945307187386252346192839_<46>

P83 = 12558541543619291989344514474085687960032747195815838307724371092633277051867902229_<83>

Number: 43339_134
N=64934717881377956671260548207859228724401922527187292255730701139609293796481707115751179551637760977001771269254455033631938131
  ( 128 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=5170562015966718933706945307187386252346192839
 r2=12558541543619291989344514474085687960032747195815838307724371092633277051867902229
Version: 
Total time: 4.95 hours.
Scaled time: 3.91 units (timescale=0.790).
Factorization parameters were as follows:
n: 64934717881377956671260548207859228724401922527187292255730701139609293796481707115751179551637760977001771269254455033631938131
m: 1000000000000000000000000000
deg: 5
c5: 13
c0: 170
skew: 1.67
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3

Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [650000, 1100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 192101 x 192349
Total sieving time: 4.95 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000
total time: 4.95 hours.
 --------- CPU info (if available) ----------

Jan 21, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Jan 21, 2009

(13·10¹⁵⁶+17)/3 = 4(3)₁₅₅9_<157> = 107 · 347 · C153

C153 = P61 · P92

P61 = 7848665944310548658605692434612903025770055432499188163240129_<61>

P92 = 14870069560900029332823369079022256333783852292742853847835506034728760020780350557624843779_<92>

Number: 43339_156
N=116710208552164974368642660274538321348092685861007119322721682063436487202276746837602233653837521434278686022605869625719338881557093736252884088807491
  ( 153 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=7848665944310548658605692434612903025770055432499188163240129 (pp61)
 r2=14870069560900029332823369079022256333783852292742853847835506034728760020780350557624843779 (pp92)
Version: Msieve-1.39
Total time: 22.70 hours.
Scaled time: 58.42 units (timescale=2.574).
Factorization parameters were as follows:
n: 116710208552164974368642660274538321348092685861007119322721682063436487202276746837602233653837521434278686022605869625719338881557093736252884088807491
m: 10000000000000000000000000000000
deg: 5
c5: 130
c0: 17
skew: 0.67
type: snfs
lss: 1
rlim: 2900000
alim: 2900000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 2900000/2900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1450000, 2650001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 536829 x 537077
Total sieving time: 22.70 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000
total time: 22.70 hours.
 --------- CPU info (if available) ----------

Jan 21, 2009 (3rd)

By Serge Batalov / Msieve-1.39 / Jan 21, 2009

(41·10¹⁶⁴+13)/9 = 4(5)₁₆₃7_<165> = C165

C165 = P50 · P115

P50 = 59246473337858590252923330703876400107515991544467_<50>

P115 = 7689159031588380373504633593943740054484463334271016968033626444748578728860063210957751627326841633237210040015271_<115>

SNFS difficulty: 166 digits.
Divisors found:
 r1=59246473337858590252923330703876400107515991544467 (pp50)
 r2=7689159031588380373504633593943740054484463334271016968033626444748578728860063210957751627326841633237210040015271 (pp115)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.277).
Factorization parameters were as follows:
n: 455555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557
m: 1000000000000000000000000000000000
deg: 5
c5: 41
c0: 130
skew: 1.26
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2100000, 4500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 873659 x 873907
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,52,52,2.4,2.4,100000
total time: 52.00 hours.

(41·10¹⁶⁵+13)/9 = 4(5)₁₆₄7_<166> = 3 · 7 · 35042011 · C157

C157 = P56 · P101

P56 = 66025287958999438614254821967763657340307943048925364047_<56>

P101 = 93761107149891665630911409876334871598782580112338751013349869153898971358258464100313470301176153101_<101>

SNFS difficulty: 166 digits.
Divisors found:
 r1=66025287958999438614254821967763657340307943048925364047 (pp56)
 r2=93761107149891665630911409876334871598782580112338751013349869153898971358258464100313470301176153101 (pp101)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 6190604098926198362786063189444719117773555202959582748174219137458090838934192930058064624685244717582473540600487139029119396627414360757347265741432959747
m: 1000000000000000000000000000000000
deg: 5
c5: 41
c0: 13
skew: 0.79
type: snfs
lss: 1
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4200000/4200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2100000, 3900001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 708729 x 708977
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,52,52,2.4,2.4,200000
total time: 33.00 hours.

(13·10¹⁵²+17)/3 = 4(3)₁₅₁9_<153> = C153

C153 = P51 · P102

P51 = 670399596905264032667430020408189520755253035738719_<51>

P102 = 646380659137790069915295704552388520173975520084757105896768093685063584412243426921222988426638350981_<102>

SNFS difficulty: 154 digits.
Divisors found:
 r1=670399596905264032667430020408189520755253035738719 (pp51)
 r2=646380659137790069915295704552388520173975520084757105896768093685063584412243426921222988426638350981 (pp102)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.733).
Factorization parameters were as follows:
n: 433333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339
m: 2000000000000000000000000000000
deg: 5
c5: 325
c0: 136
skew: 0.84
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1300000, 2300001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 510307 x 510555
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,52,52,2.4,2.4,100000
total time: 13.00 hours.

Jan 21, 2009 (2nd)

By Ignacio Santos / GGNFS-Msieve / Jan 20, 2009

(13·10¹³⁰+17)/3 = 4(3)₁₂₉9_<131> = 19 · 640307 · 38351513 · 285733361 · 222209824020355909_<18> · C91

C91 = P43 · P48

P43 = 1570644324244675277406232203685467558728651_<43>

P48 = 931313054549234693627071365157441701143203771309_<48>

Tue Jan 20 13:42:23 2009  
Tue Jan 20 13:42:23 2009  
Tue Jan 20 13:42:23 2009  Msieve v. 1.39
Tue Jan 20 13:42:23 2009  random seeds: b379af00 0c33bebd
Tue Jan 20 13:42:23 2009  factoring 1462761563222727130063118075699260662700284657246345663740202539793096014122267264590074159 (91 digits)
Tue Jan 20 13:42:23 2009  searching for 15-digit factors
Tue Jan 20 13:42:25 2009  commencing quadratic sieve (91-digit input)
Tue Jan 20 13:42:25 2009  using multiplier of 5
Tue Jan 20 13:42:25 2009  using 32kb Intel Core sieve core
Tue Jan 20 13:42:25 2009  sieve interval: 36 blocks of size 32768
Tue Jan 20 13:42:25 2009  processing polynomials in batches of 6
Tue Jan 20 13:42:25 2009  using a sieve bound of 1652509 (62283 primes)
Tue Jan 20 13:42:25 2009  using large prime bound of 145420792 (27 bits)
Tue Jan 20 13:42:25 2009  using double large prime bound of 492864656290952 (42-49 bits)
Tue Jan 20 13:42:25 2009  using trial factoring cutoff of 49 bits
Tue Jan 20 13:42:25 2009  polynomial 'A' values have 12 factors
Tue Jan 20 14:50:04 2009  62440 relations (16596 full + 45844 combined from 698216 partial), need 62379
Tue Jan 20 14:50:05 2009  begin with 714812 relations
Tue Jan 20 14:50:05 2009  reduce to 153177 relations in 10 passes
Tue Jan 20 14:50:05 2009  attempting to read 153177 relations
Tue Jan 20 14:50:07 2009  recovered 153177 relations
Tue Jan 20 14:50:07 2009  recovered 132766 polynomials
Tue Jan 20 14:50:07 2009  attempting to build 62440 cycles
Tue Jan 20 14:50:07 2009  found 62440 cycles in 5 passes
Tue Jan 20 14:50:07 2009  distribution of cycle lengths:
Tue Jan 20 14:50:07 2009     length 1 : 16596
Tue Jan 20 14:50:07 2009     length 2 : 11960
Tue Jan 20 14:50:07 2009     length 3 : 10999
Tue Jan 20 14:50:07 2009     length 4 : 8205
Tue Jan 20 14:50:07 2009     length 5 : 5901
Tue Jan 20 14:50:07 2009     length 6 : 3759
Tue Jan 20 14:50:07 2009     length 7 : 2267
Tue Jan 20 14:50:07 2009     length 9+: 2753
Tue Jan 20 14:50:07 2009  largest cycle: 20 relations
Tue Jan 20 14:50:07 2009  matrix is 62283 x 62440 (15.4 MB) with weight 3790272 (60.70/col)
Tue Jan 20 14:50:07 2009  sparse part has weight 3790272 (60.70/col)
Tue Jan 20 14:50:08 2009  filtering completed in 3 passes
Tue Jan 20 14:50:08 2009  matrix is 58355 x 58418 (14.5 MB) with weight 3572990 (61.16/col)
Tue Jan 20 14:50:08 2009  sparse part has weight 3572990 (61.16/col)
Tue Jan 20 14:50:08 2009  saving the first 48 matrix rows for later
Tue Jan 20 14:50:08 2009  matrix is 58307 x 58418 (9.1 MB) with weight 2792706 (47.81/col)
Tue Jan 20 14:50:08 2009  sparse part has weight 2023535 (34.64/col)
Tue Jan 20 14:50:08 2009  matrix includes 64 packed rows
Tue Jan 20 14:50:08 2009  using block size 23367 for processor cache size 4096 kB
Tue Jan 20 14:50:08 2009  commencing Lanczos iteration
Tue Jan 20 14:50:08 2009  memory use: 8.8 MB
Tue Jan 20 14:50:22 2009  lanczos halted after 924 iterations (dim = 58307)
Tue Jan 20 14:50:23 2009  recovered 19 nontrivial dependencies
Tue Jan 20 14:50:24 2009  prp43 factor: 1570644324244675277406232203685467558728651
Tue Jan 20 14:50:24 2009  prp48 factor: 931313054549234693627071365157441701143203771309
Tue Jan 20 14:50:24 2009  elapsed time 01:08:01

By Ignacio Santos / GGNFS-Msieve / Jan 21, 2009

(13·10¹⁴⁰+17)/3 = 4(3)₁₃₉9_<141> = 53 · 863 · 929 · 140261005451431_<15> · 2990564816106821799383922547_<28> · C92

C92 = P39 · P53

P39 = 243818690817952710890544697736647626133_<39>

P53 = 99715473523447511465699370816219356662567860601605449_<53>

Tue Jan 20 22:10:54 2009  
Tue Jan 20 22:10:54 2009  
Tue Jan 20 22:10:54 2009  Msieve v. 1.39
Tue Jan 20 22:10:54 2009  random seeds: a8b04c68 749e672b
Tue Jan 20 22:10:54 2009  factoring 24312496208779198415565027300964960051932497256644440241028331720996824305447064254527598717 (92 digits)
Tue Jan 20 22:10:55 2009  searching for 15-digit factors
Tue Jan 20 22:10:56 2009  commencing quadratic sieve (92-digit input)
Tue Jan 20 22:10:56 2009  using multiplier of 53
Tue Jan 20 22:10:56 2009  using 32kb Intel Core sieve core
Tue Jan 20 22:10:56 2009  sieve interval: 36 blocks of size 32768
Tue Jan 20 22:10:56 2009  processing polynomials in batches of 6
Tue Jan 20 22:10:56 2009  using a sieve bound of 1779137 (67059 primes)
Tue Jan 20 22:10:56 2009  using large prime bound of 186809385 (27 bits)
Tue Jan 20 22:10:56 2009  using double large prime bound of 773601948505050 (42-50 bits)
Tue Jan 20 22:10:56 2009  using trial factoring cutoff of 50 bits
Tue Jan 20 22:10:56 2009  polynomial 'A' values have 12 factors
Tue Jan 20 23:37:05 2009  67588 relations (17425 full + 50163 combined from 823918 partial), need 67155
Tue Jan 20 23:37:05 2009  begin with 841343 relations
Tue Jan 20 23:37:06 2009  reduce to 168962 relations in 10 passes
Tue Jan 20 23:37:06 2009  attempting to read 168962 relations
Tue Jan 20 23:37:08 2009  recovered 168962 relations
Tue Jan 20 23:37:08 2009  recovered 149354 polynomials
Tue Jan 20 23:37:08 2009  attempting to build 67588 cycles
Tue Jan 20 23:37:08 2009  found 67588 cycles in 6 passes
Tue Jan 20 23:37:08 2009  distribution of cycle lengths:
Tue Jan 20 23:37:08 2009     length 1 : 17425
Tue Jan 20 23:37:08 2009     length 2 : 12637
Tue Jan 20 23:37:08 2009     length 3 : 11786
Tue Jan 20 23:37:08 2009     length 4 : 9225
Tue Jan 20 23:37:08 2009     length 5 : 6455
Tue Jan 20 23:37:08 2009     length 6 : 4251
Tue Jan 20 23:37:08 2009     length 7 : 2534
Tue Jan 20 23:37:08 2009     length 9+: 3275
Tue Jan 20 23:37:08 2009  largest cycle: 19 relations
Tue Jan 20 23:37:08 2009  matrix is 67059 x 67588 (16.2 MB) with weight 3965480 (58.67/col)
Tue Jan 20 23:37:08 2009  sparse part has weight 3965480 (58.67/col)
Tue Jan 20 23:37:09 2009  filtering completed in 3 passes
Tue Jan 20 23:37:09 2009  matrix is 63057 x 63121 (15.1 MB) with weight 3704002 (58.68/col)
Tue Jan 20 23:37:09 2009  sparse part has weight 3704002 (58.68/col)
Tue Jan 20 23:37:09 2009  saving the first 48 matrix rows for later
Tue Jan 20 23:37:09 2009  matrix is 63009 x 63121 (8.3 MB) with weight 2741154 (43.43/col)
Tue Jan 20 23:37:09 2009  sparse part has weight 1801245 (28.54/col)
Tue Jan 20 23:37:09 2009  matrix includes 64 packed rows
Tue Jan 20 23:37:09 2009  using block size 25248 for processor cache size 4096 kB
Tue Jan 20 23:37:09 2009  commencing Lanczos iteration
Tue Jan 20 23:37:09 2009  memory use: 8.9 MB
Tue Jan 20 23:37:25 2009  lanczos halted after 998 iterations (dim = 63007)
Tue Jan 20 23:37:25 2009  recovered 16 nontrivial dependencies
Tue Jan 20 23:37:25 2009  prp39 factor: 243818690817952710890544697736647626133
Tue Jan 20 23:37:25 2009  prp53 factor: 99715473523447511465699370816219356662567860601605449
Tue Jan 20 23:37:25 2009  elapsed time 01:26:31

Jan 21, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 20, 2009

(37·10¹⁶³+71)/9 = 4(1)₁₆₂9_<164> = 7 · 83 · 119267 · 880091 · 55050071 · C143

C143 = P68 · P76

P68 = 10612384575172811246762013681618992864158685725196076097302274309919_<68>

P76 = 1153889825563011219897015674381343240915397462487267551725993237549611584283_<76>

Number: 41119_163
N=12245522586253746099968568685920140593209283041694339776310908812238990592165703272639528019191995298183689750221363386742366663616632131403077
  ( 143 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=10612384575172811246762013681618992864158685725196076097302274309919
 r2=1153889825563011219897015674381343240915397462487267551725993237549611584283
Version: 
Total time: 28.05 hours.
Scaled time: 66.29 units (timescale=2.363).
Factorization parameters were as follows:
n: 12245522586253746099968568685920140593209283041694339776310908812238990592165703272639528019191995298183689750221363386742366663616632131403077
m: 1000000000000000000000000000000000
deg: 5
c5: 37
c0: 7100
skew: 2.86
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2400000, 4600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9817186
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 822349 x 822597
Total sieving time: 24.80 hours.
Total relation processing time: 1.08 hours.
Matrix solve time: 1.58 hours.
Time per square root: 0.60 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000
total time: 28.05 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

(13·10¹¹⁹+17)/3 = 4(3)₁₁₈9_<120> = 61 · 39409 · C114

C114 = P38 · P76

P38 = 53174504914257053921908157404715782721_<38>

P76 = 3389950781078697275386436001539122062289866786416933540275567164715600727591_<76>

Number: 43339_119
N=180258954467558726634106353060457328060342932954623136070413030115586201426624829949942088344358941613708665755111
  ( 114 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=53174504914257053921908157404715782721
 r2=3389950781078697275386436001539122062289866786416933540275567164715600727591
Version: 
Total time: 0.62 hours.
Scaled time: 1.48 units (timescale=2.373).
Factorization parameters were as follows:
n: 180258954467558726634106353060457328060342932954623136070413030115586201426624829949942088344358941613708665755111
m: 1000000000000000000000000
deg: 5
c5: 13
c0: 170
skew: 1.67
type: snfs
lss: 1
rlim: 540000
alim: 540000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 540000/540000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [270000, 480001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 1248902
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 65852 x 66093
Total sieving time: 0.57 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,540000,540000,25,25,46,46,2.2,2.2,30000
total time: 0.62 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Jan 21, 2009

(13·10¹²⁷+17)/3 = 4(3)₁₂₆9_<128> = 7² · 53 · C125

C125 = P42 · P83

P42 = 592752898039573593951004187883726962059169_<42>

P83 = 28149874435139797345546297898982553764803447148584606253445998984051523023986318623_<83>

Number: 43339_127
N=16685919650879219612373251187267359774098318572712103709408291618534206135284302400205365164933898087536901553074059812604287
  ( 125 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=592752898039573593951004187883726962059169
 r2=28149874435139797345546297898982553764803447148584606253445998984051523023986318623
Version: 
Total time: 1.46 hours.
Scaled time: 3.47 units (timescale=2.379).
Factorization parameters were as follows:
n: 16685919650879219612373251187267359774098318572712103709408291618534206135284302400205365164933898087536901553074059812604287
m: 10000000000000000000000000
deg: 5
c5: 1300
c0: 17
skew: 0.42
type: snfs
lss: 1
rlim: 1000000
alim: 1000000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved rational special-q in [500000, 900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 2874650
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 141134 x 141381
Total sieving time: 1.29 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000
total time: 1.46 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

(64·10²²⁷-1)/9 = 7(1)₂₂₇_<228> = 3² · 751 · 997 · 1987 · C218

C218 = P47 · P172

P47 = 12580688216946651173211552347847284253008814449_<47>

P172 = 4221410569361183158650323193996802358668505850306228952322782128251492447111964495002825468261701293097419367623912143526832225354450880609164265860377163061432183372371039_<172>

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM]
Input number is 53108250208856290879943190686286926212622109904300816889872200157247472868266848651592384100132642859519384361664694008385611426285586037047629303279747426443337256605822525091167881691151711478666627465243279532342511 (218 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2234649575
Step 1 took 140027ms
Step 2 took 75208ms
********** Factor found in step 2: 12580688216946651173211552347847284253008814449
Found probable prime factor of 47 digits: 12580688216946651173211552347847284253008814449
Probable prime cofactor 4221410569361183158650323193996802358668505850306228952322782128251492447111964495002825468261701293097419367623912143526832225354450880609164265860377163061432183372371039 has 172 digits

Jan 20, 2009 (10th)

By Ignacio Santos / GGNFS, Msieve / Jan 20, 2009

(41·10¹⁴⁹+13)/9 = 4(5)₁₄₈7_<150> = 2841789641_<10> · 296843519425519604081_<21> · C120

C120 = P45 · P76

P45 = 154871027594058166313738937531850792514615903_<45>

P76 = 3486997760676672775521582454506981045875820749167242223488415063348339937939_<76>

Number: 45557_149
N=540034926414176023335666056013800139388078340991658921250077831465701719953890647536283401844391126584896158401442443917
  ( 120 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=154871027594058166313738937531850792514615903 (pp45)
 r2=3486997760676672775521582454506981045875820749167242223488415063348339937939 (pp76)
Version: Msieve-1.39
Total time: 16.88 hours.
Scaled time: 43.46 units (timescale=2.575).
Factorization parameters were as follows:
n: 540034926414176023335666056013800139388078340991658921250077831465701719953890647536283401844391126584896158401442443917
m: 1000000000000000000000000000000
deg: 5
c5: 41
c0: 130
skew: 1.26
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved rational special-q in [1200000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 383145 x 383393
Total sieving time: 16.88 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000
total time: 16.88 hours.
 --------- CPU info (if available) ----------

(13·10¹¹⁷+17)/3 = 4(3)₁₁₆9_<118> = 7411 · 17471 · 6436039448261_<13> · C97

C97 = P33 · P65

P33 = 297261112967139716914723682939401_<33>

P65 = 17493258901169028703409497802873699639804029532490523703990738179_<65>

Number: 43339_117
N=5200065610383829033928010205144895632219547651445470984420115504287281256542233743045458514090779
  ( 97 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=297261112967139716914723682939401 (pp33)
 r2=17493258901169028703409497802873699639804029532490523703990738179 (pp65)
Version: Msieve-1.39
Total time: 1.46 hours.
Scaled time: 3.77 units (timescale=2.585).
Factorization parameters were as follows:
n: 5200065610383829033928010205144895632219547651445470984420115504287281256542233743045458514090779
m: 200000000000000000000000
deg: 5
c5: 325
c0: 136
skew: 0.84
type: snfs
lss: 1
rlim: 670000
alim: 670000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2
Factor base limits: 670000/670000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved rational special-q in [335000, 635001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 79175 x 79416
Total sieving time: 1.46 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,670000,670000,25,25,45,45,2.2,2.2,50000
total time: 1.46 hours.
 --------- CPU info (if available) ----------

Jan 20, 2009 (9th)

By Markus Tervooren / ggnfs, msieve / Jan 20, 2009

(11·10¹⁶⁵+1)/3 = 3(6)₁₆₄7_<166> = 19 · 61 · 887 · 10713254678080769_<17> · 12402765290298822972283_<23> · C122

C122 = P47 · P76

P47 = 26797762685568259691978304690654738199883649061_<47>

P76 = 1001672806023220538619289663280526288901729658106205228988334013295716045117_<76>

Msieve v. 1.38
Tue Jan 20 12:57:22 2009
random seeds: 42e45458 9525d86b
factoring 26842590144397512873551401406599563534311210783367865165259740185669640725921314367074253535437723207328428322873270685137 (122 digits)
searching for 15-digit factors
commencing number field sieve (122-digit input)
R0: -1000000000000000000000000000000000
R1:  1
A0:  1
A1:  0
A2:  0
A3:  0
A4:  0
A5:  11
size score = 3.209221e-11, Murphy alpha = 0.588883, combined = 2.637243e-11

commencing relation filtering
commencing duplicate removal, pass 1
found 634771 hash collisions in 10563124 relations
added 10658 free relations
commencing duplicate removal, pass 2
found 474889 duplicates and 10098893 unique relations
memory use: 50.6 MB
reading rational ideals above 7536640
reading algebraic ideals above 7536640
commencing singleton removal, pass 1
relations with 0 large ideals: 363104
relations with 1 large ideals: 1861795
relations with 2 large ideals: 3640577
relations with 3 large ideals: 2962077
relations with 4 large ideals: 896083
relations with 5 large ideals: 32823
relations with 6 large ideals: 342434
relations with 7+ large ideals: 0
10098893 relations and about 9260856 large ideals
commencing singleton removal, pass 2
found 3703655 singletons
current dataset: 6395238 relations and about 4652025 large ideals
commencing singleton removal, pass 3
found 904831 singletons
current dataset: 5490407 relations and about 3697823 large ideals
commencing singleton removal, pass 4
found 218819 singletons
current dataset: 5271588 relations and about 3475326 large ideals
commencing singleton removal, final pass
memory use: 80.9 MB
commencing in-memory singleton removal
begin with 5271588 relations and 3675324 unique ideals
reduce to 4793006 relations and 3188955 ideals in 11 passes
max relations containing the same ideal: 67
reading rational ideals above 720000
reading algebraic ideals above 720000
commencing singleton removal, final pass
keeping 3867001 ideals with weight <= 20, new excess is 405067
memory use: 128.4 MB
commencing in-memory singleton removal
begin with 4803664 relations and 3867001 unique ideals
reduce to 4780621 relations and 3791720 ideals in 9 passes
max relations containing the same ideal: 20
removing 1185259 relations and 925747 ideals in 259512 cliques
commencing in-memory singleton removal
begin with 3595362 relations and 3791720 unique ideals
reduce to 3415831 relations and 2674760 ideals in 8 passes
max relations containing the same ideal: 20
removing 914096 relations and 654584 ideals in 259512 cliques
commencing in-memory singleton removal
begin with 2501735 relations and 2674760 unique ideals
reduce to 2345224 relations and 1852304 ideals in 9 passes
max relations containing the same ideal: 19
removing 135512 relations and 112470 ideals in 23042 cliques
commencing in-memory singleton removal
begin with 2209712 relations and 1852304 unique ideals
reduce to 2204720 relations and 1734792 ideals in 5 passes
max relations containing the same ideal: 19
relations with 0 large ideals: 47447
relations with 1 large ideals: 256449
relations with 2 large ideals: 603335
relations with 3 large ideals: 695913
relations with 4 large ideals: 423179
relations with 5 large ideals: 141638
relations with 6 large ideals: 34263
relations with 7+ large ideals: 2496
commencing 2-way merge
reduce to 1440888 relation sets and 970960 unique ideals
commencing full merge
memory use: 88.6 MB
found 700024 cycles, need 637160
weight of 637160 cycles is about 44625763 (70.04/cycle)
distribution of cycle lengths:
1 relations: 71310
2 relations: 62858
3 relations: 65299
4 relations: 63476
5 relations: 60549
6 relations: 55936
7 relations: 50741
8 relations: 44766
9 relations: 39151
10+ relations: 123074
heaviest cycle: 17 relations
commencing cycle optimization
start with 3795715 relations
pruned 140533 relations
memory use: 119.7 MB
distribution of cycle lengths:
1 relations: 71310
2 relations: 64873
3 relations: 68577
4 relations: 66515
5 relations: 63668
6 relations: 58180
7 relations: 52654
8 relations: 45831
9 relations: 39129
10+ relations: 106423
heaviest cycle: 16 relations

commencing linear algebra
read 637160 cycles
cycles contain 1947546 unique relations
read 1947546 relations
using 32 quadratic characters above 134205218
building initial matrix
memory use: 241.3 MB
read 637160 cycles
matrix is 636905 x 637160 (187.8 MB) with weight 60278730 (94.61/col)
sparse part has weight 42210821 (66.25/col)
filtering completed in 3 passes
matrix is 634790 x 634990 (187.4 MB) with weight 60136200 (94.70/col)
sparse part has weight 42132219 (66.35/col)
read 634990 cycles
matrix is 634790 x 634990 (187.4 MB) with weight 60136200 (94.70/col)
sparse part has weight 42132219 (66.35/col)
saving the first 48 matrix rows for later
matrix is 634742 x 634990 (179.4 MB) with weight 46027776 (72.49/col)
sparse part has weight 40680313 (64.06/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (4 threads)
memory use: 183.7 MB
linear algebra completed 634480 of 634990 dimensions (99.9%, ETA 0h 0m)
lanczos halted after 10041 iterations (dim = 634740)
recovered 48 nontrivial dependencies

commencing square root phase
reading relations for dependency 1
read 317703 cycles
cycles contain 1209362 unique relations
read 1209362 relations
multiplying 973474 relations
multiply complete, coefficients have about 24.43 million bits
initial square root is modulo 10385591
prp47 factor: 26797762685568259691978304690654738199883649061
prp76 factor: 1001672806023220538619289663280526288901729658106205228988334013295716045117
elapsed time 00:40:42

Jan 20, 2009 (8th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39 / Jan 20, 2009

(13·10¹⁰⁸+17)/3 = 4(3)₁₀₇9_<109> = 47 · 67 · C106

C106 = P31 · P75

P31 = 7431209624337076058856861590161_<31>

P75 = 185178228284173749097301724961131305298759518123588151656392167131675512151_<75>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3907866496
Step 1 took 2766ms
Step 2 took 2914ms
********** Factor found in step 2: 7431209624337076058856861590161
Found probable prime factor of 31 digits: 7431209624337076058856861590161
Probable prime cofactor 185178228284173749097301724961131305298759518123588151656392167131675512151 has 75 digits

(41·10¹⁵⁰+13)/9 = 4(5)₁₄₉7_<151> = 3³ · C150

C150 = P73 · P77

P73 = 8088307089484207164003143469452132928076569867478172561362749573329874913_<73>

P77 = 20860271249437751623432586664881731562191259384907030463575987885758254647007_<77>

SNFS difficulty: 151 digits.
Divisors found:
 r1=8088307089484207164003143469452132928076569867478172561362749573329874913 (pp73)
 r2=20860271249437751623432586664881731562191259384907030463575987885758254647007 (pp77)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835391
m: 1000000000000000000000000000000
deg: 5
c5: 41
c0: 13
skew: 0.79
type: snfs
lss: 1
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1200000, 1800001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 378707 x 378955
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,52,52,2.5,2.5,100000
total time: 10.00 hours.

(13·10¹⁹⁴+17)/3 = 4(3)₁₉₃9_<195> = 59 · 83 · 157 · 607 · 1361 · 6311 · 164321 · 1786969867_<10> · 19193147198594868597439948288841_<32> · C134

C134 = P33 · C101

P33 = 466809015184227886664481474387139_<33>

C101 = [41091464281687809280907055016363623012787750287324348861042488523828133080766450467340391897074683271_<101>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2675547875
Step 1 took 9760ms
Step 2 took 11062ms
********** Factor found in step 2: 466809015184227886664481474387139
Found probable prime factor of 33 digits: 466809015184227886664481474387139
Composite cofactor 41091464281687809280907055016363623012787750287324348861042488523828133080766450467340391897074683271 has 101 digits

(41·10¹⁵¹+13)/9 = 4(5)₁₅₀7_<152> = 23 · 2089 · C147

C147 = P63 · P85

P63 = 412965781222919059431588990535944176008086436258231823868137137_<63>

P85 = 2295942483708757462905739091602534375427222462948952894327050495097814781823941499163_<85>

SNFS difficulty: 153 digits.
Divisors found:
 r1=412965781222919059431588990535944176008086436258231823868137137 (pp63)
 r2=2295942483708757462905739091602534375427222462948952894327050495097814781823941499163 (pp85)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.950).
Factorization parameters were as follows:
n: 948145681427676141185829615908497004090901732794046570140811196444222439601963817835776542875841479292267062575302423784118791091130675287854716331
m: 2000000000000000000000000000000
deg: 5
c5: 205
c0: 208
skew: 1.00
type: snfs
lss: 1
rlim: 2600000
alim: 2600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 2600000/2600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1300000, 2200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 484451 x 484699
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,52,52,2.5,2.5,100000
total time: 13.00 hours.

(13·10¹²⁶+17)/3 = 4(3)₁₂₅9_<127> = 23 · 823 · C123

C123 = P55 · P69

P55 = 1235037569989934703742707811318505240683506061828378703_<55>

P69 = 185359247322344949939888900134497341086497558276887388854316050833797_<69>

SNFS difficulty: 127 digits.
Divisors found:
 r1=1235037569989934703742707811318505240683506061828378703 (pp55)
 r2=185359247322344949939888900134497341086497558276887388854316050833797 (pp69)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.724).
Factorization parameters were as follows:
n: 228925634388152217937203937520911476218148519907725359677390952154542412876186451124377058129501470406959339285399827425291
m: 10000000000000000000000000
deg: 5
c5: 130
c0: 17
skew: 0.67
type: snfs
lss: 1
rlim: 920000
alim: 920000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 920000/920000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [460000, 810001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 129016 x 129264
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,920000,920000,26,26,49,49,2.3,2.3,50000
total time: 1.50 hours.

(13·10¹³²+17)/3 = 4(3)₁₃₁9_<133> = 1135151837_<10> · C124

C124 = P34 · P91

P34 = 3063094933197206012414663895563111_<34>

P91 = 1246257211466193660946936592331668212340483802847166733457467467560945277322505374209706577_<91>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1063295750
Step 1 took 12889ms
Step 2 took 13509ms
********** Factor found in step 2: 3063094933197206012414663895563111
Found probable prime factor of 34 digits: 3063094933197206012414663895563111
Probable prime cofactor has 91 digits

(13·10¹⁸³+17)/3 = 4(3)₁₈₂9_<184> = 167 · 283 · 7810225216444802043127_<22> · C158

C158 = P35 · P123

P35 = 22638610072965845146515798122211221_<35>

P123 = 518568191759354873354028254138933705605045125722879355590156955694954110429162407309398276854625923840716391560430712626397_<123>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3656209356
Step 1 took 13866ms
Step 2 took 13377ms
********** Factor found in step 2: 22638610072965845146515798122211221
Found probable prime factor of 35 digits: 22638610072965845146515798122211221
Probable prime cofactor has 123 digits

(13·10¹⁷⁸+17)/3 = 4(3)₁₇₇9_<179> = 87187 · C174

C174 = P35 · P140

P35 = 46094114770989559758421799869715111_<35>

P140 = 10782634505829926227561117112188195458713080853422097707679005993454827268815418489695411040739292454281066567653882306406788594214781617727_<140>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3477417042
Step 1 took 17027ms
Step 2 took 15009ms
********** Factor found in step 2: 46094114770989559758421799869715111
Found probable prime factor of 35 digits: 46094114770989559758421799869715111
Probable prime cofactor has 140 digits

(13·10²⁰¹+17)/3 = 4(3)₂₀₀9_<202> = 28642351 · C195

C195 = P36 · C159

P36 = 173639839240963617425889116964808219_<36>

C159 = [871292669082763675347013625435710106348585444590009214661633110386569980384531612332002172240517268624619132084082982641718821475559431420128713888427596047631_<159>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1427935662
Step 1 took 18469ms
Step 2 took 16307ms
********** Factor found in step 2: 173639839240963617425889116964808219
Found probable prime factor of 36 digits: 173639839240963617425889116964808219
Composite cofactor has 159 digits

(13·10¹⁸⁶+17)/3 = 4(3)₁₈₅9_<187> = 11747995868131_<14> · C174

C174 = P35 · P140

P35 = 12190831134079793452119572575592669_<35>

P140 = 30256939506703801770545513093878737710316949009172144340244948068423985584761342197461324879123655207269042321468266519932875399349228090301_<140>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2865496216
Step 1 took 16810ms
********** Factor found in step 1: 12190831134079793452119572575592669
Found probable prime factor of 35 digits: 12190831134079793452119572575592669
Probable prime cofactor has 140 digits

(13·10¹³³+17)/3 = 4(3)₁₃₂9_<134> = 7 · 241 · 75644713537_<11> · 29460856715745037847399_<23> · C98

C98 = P33 · P65

P33 = 698481296045572507449739791354539_<33>

P65 = 16501684500894512039853388964984732166859460649662542459577659921_<65>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1123134991
Step 1 took 8855ms
Step 2 took 8967ms
********** Factor found in step 2: 698481296045572507449739791354539
Found probable prime factor of 33 digits: 698481296045572507449739791354539
Probable prime cofactor has 65 digits

(13·10¹⁴⁷+17)/3 = 4(3)₁₄₆9_<148> = 179 · 313 · 242726741 · C135

C135 = P48 · P88

P48 = 317051071730800217076386361855545345075517377299_<48>

P88 = 1005027345848835841745604832051900561300662136688387005636253807451532975144833420805423_<88>

SNFS difficulty: 148 digits.
Divisors found:
 r1=317051071730800217076386361855545345075517377299 (pp48)
 r2=1005027345848835841745604832051900561300662136688387005636253807451532975144833420805423 (pp88)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.728).
Factorization parameters were as follows:
n: 318644997120135010242664186404623364057545817118496018099156617192090829733657448410476343054352884472704599346161173015402965156292477
m: 100000000000000000000000000000
deg: 5
c5: 1300
c0: 17
skew: 0.42
type: snfs
lss: 1
rlim: 2100000
alim: 2100000
lpbr: 26
lpba: 26
mfbr: 50
mfba: 50
rlambda: 2.3
alambda: 2.3
Factor base limits: 2100000/2100000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 50/50
Sieved rational special-q in [1050000, 2850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 373103 x 373351
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,50,50,2.3,2.3,100000
total time: 8.00 hours.

(13·10¹²⁹+17)/3 = 4(3)₁₂₈9_<130> = 11131 · 1176499763_<10> · 616446635683_<12> · C105

C105 = P37 · P69

P37 = 5084951887576689955930793519093430503_<37>

P69 = 105563489060486885995991940896116891423985958592255758808200677488687_<69>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2005348329
Step 1 took 8262ms
Step 2 took 9276ms
********** Factor found in step 2: 5084951887576689955930793519093430503
Found probable prime factor of 37 digits: 5084951887576689955930793519093430503
Probable prime cofactor has 69 digits

Jan 20, 2009 (7th)

By Sinkiti Sibata / Msieve / Jan 20, 2009

(41·10¹²¹+13)/9 = 4(5)₁₂₀7_<122> = 5399 · 644341 · 8206170209_<10> · C103

C103 = P44 · P60

P44 = 10400541347880596513151322002253490415160669_<44>

P60 = 153431943934224431017641592298558521171642330516337258884163_<60>

Mon Jan 19 20:01:43 2009  Msieve v. 1.39
Mon Jan 19 20:01:43 2009  random seeds: 5b18ff20 202f51b7
Mon Jan 19 20:01:43 2009  factoring 1595775276973598678011037831407391019992414694887644832555308608201214056077442928890564306845304585047 (103 digits)
Mon Jan 19 20:01:44 2009  searching for 15-digit factors
Mon Jan 19 20:01:46 2009  commencing quadratic sieve (103-digit input)
Mon Jan 19 20:01:46 2009  using multiplier of 2
Mon Jan 19 20:01:46 2009  using 32kb Intel Core sieve core
Mon Jan 19 20:01:46 2009  sieve interval: 36 blocks of size 32768
Mon Jan 19 20:01:46 2009  processing polynomials in batches of 6
Mon Jan 19 20:01:46 2009  using a sieve bound of 3340487 (120000 primes)
Mon Jan 19 20:01:46 2009  using large prime bound of 501073050 (28 bits)
Mon Jan 19 20:01:46 2009  using double large prime bound of 4569007548480300 (44-53 bits)
Mon Jan 19 20:01:46 2009  using trial factoring cutoff of 53 bits
Mon Jan 19 20:01:46 2009  polynomial 'A' values have 13 factors
Tue Jan 20 14:14:09 2009  120145 relations (28740 full + 91405 combined from 1795883 partial), need 120096
Tue Jan 20 14:14:11 2009  begin with 1824623 relations
Tue Jan 20 14:14:12 2009  reduce to 317252 relations in 11 passes
Tue Jan 20 14:14:12 2009  attempting to read 317252 relations
Tue Jan 20 14:14:19 2009  recovered 317252 relations
Tue Jan 20 14:14:19 2009  recovered 308230 polynomials
Tue Jan 20 14:14:19 2009  attempting to build 120145 cycles
Tue Jan 20 14:14:19 2009  found 120145 cycles in 6 passes
Tue Jan 20 14:14:19 2009  distribution of cycle lengths:
Tue Jan 20 14:14:19 2009     length 1 : 28740
Tue Jan 20 14:14:19 2009     length 2 : 20336
Tue Jan 20 14:14:19 2009     length 3 : 20009
Tue Jan 20 14:14:19 2009     length 4 : 16310
Tue Jan 20 14:14:19 2009     length 5 : 12547
Tue Jan 20 14:14:19 2009     length 6 : 8606
Tue Jan 20 14:14:19 2009     length 7 : 5637
Tue Jan 20 14:14:19 2009     length 9+: 7960
Tue Jan 20 14:14:19 2009  largest cycle: 20 relations
Tue Jan 20 14:14:20 2009  matrix is 120000 x 120145 (35.6 MB) with weight 8849223 (73.65/col)
Tue Jan 20 14:14:20 2009  sparse part has weight 8849223 (73.65/col)
Tue Jan 20 14:14:22 2009  filtering completed in 3 passes
Tue Jan 20 14:14:22 2009  matrix is 115104 x 115168 (34.3 MB) with weight 8541239 (74.16/col)
Tue Jan 20 14:14:22 2009  sparse part has weight 8541239 (74.16/col)
Tue Jan 20 14:14:22 2009  saving the first 48 matrix rows for later
Tue Jan 20 14:14:23 2009  matrix is 115056 x 115168 (24.4 MB) with weight 7127639 (61.89/col)
Tue Jan 20 14:14:23 2009  sparse part has weight 5695827 (49.46/col)
Tue Jan 20 14:14:23 2009  matrix includes 64 packed rows
Tue Jan 20 14:14:23 2009  using block size 43690 for processor cache size 1024 kB
Tue Jan 20 14:14:24 2009  commencing Lanczos iteration
Tue Jan 20 14:14:24 2009  memory use: 21.6 MB
Tue Jan 20 14:16:15 2009  lanczos halted after 1820 iterations (dim = 115054)
Tue Jan 20 14:16:16 2009  recovered 17 nontrivial dependencies
Tue Jan 20 14:16:17 2009  prp44 factor: 10400541347880596513151322002253490415160669
Tue Jan 20 14:16:17 2009  prp60 factor: 153431943934224431017641592298558521171642330516337258884163
Tue Jan 20 14:16:17 2009  elapsed time 18:14:34

(41·10¹⁷⁶+13)/9 = 4(5)₁₇₅7_<177> = 15661 · 8878663815812143_<16> · 15515053871634353_<17> · 115993927151348881399_<21> · 1966833408789686089783313_<25> · C96

C96 = P41 · P56

P41 = 19615475179920945071617458596234333359193_<41>

P56 = 47186666258012252043256895418049868713349346463656125033_<56>

Tue Jan 20 16:17:26 2009  Msieve v. 1.39
Tue Jan 20 16:17:26 2009  random seeds: ca946258 b74f2676
Tue Jan 20 16:17:26 2009  factoring 925588880807252467568771876878853373863714814721869609944208374600859523491636368735392507978369 (96 digits)
Tue Jan 20 16:17:27 2009  searching for 15-digit factors
Tue Jan 20 16:17:28 2009  commencing quadratic sieve (96-digit input)
Tue Jan 20 16:17:29 2009  using multiplier of 1
Tue Jan 20 16:17:29 2009  using 32kb Intel Core sieve core
Tue Jan 20 16:17:29 2009  sieve interval: 36 blocks of size 32768
Tue Jan 20 16:17:29 2009  processing polynomials in batches of 6
Tue Jan 20 16:17:29 2009  using a sieve bound of 2299939 (84689 primes)
Tue Jan 20 16:17:29 2009  using large prime bound of 344990850 (28 bits)
Tue Jan 20 16:17:29 2009  using double large prime bound of 2333746148351850 (43-52 bits)
Tue Jan 20 16:17:29 2009  using trial factoring cutoff of 52 bits
Tue Jan 20 16:17:29 2009  polynomial 'A' values have 12 factors
Tue Jan 20 21:50:47 2009  84787 relations (20045 full + 64742 combined from 1295802 partial), need 84785
Tue Jan 20 21:50:48 2009  begin with 1315847 relations
Tue Jan 20 21:50:49 2009  reduce to 225957 relations in 11 passes
Tue Jan 20 21:50:49 2009  attempting to read 225957 relations
Tue Jan 20 21:50:53 2009  recovered 225957 relations
Tue Jan 20 21:50:53 2009  recovered 213085 polynomials
Tue Jan 20 21:50:53 2009  attempting to build 84787 cycles
Tue Jan 20 21:50:54 2009  found 84787 cycles in 6 passes
Tue Jan 20 21:50:54 2009  distribution of cycle lengths:
Tue Jan 20 21:50:54 2009     length 1 : 20045
Tue Jan 20 21:50:54 2009     length 2 : 14023
Tue Jan 20 21:50:54 2009     length 3 : 14055
Tue Jan 20 21:50:54 2009     length 4 : 11596
Tue Jan 20 21:50:54 2009     length 5 : 8962
Tue Jan 20 21:50:54 2009     length 6 : 6115
Tue Jan 20 21:50:54 2009     length 7 : 4087
Tue Jan 20 21:50:54 2009     length 9+: 5904
Tue Jan 20 21:50:54 2009  largest cycle: 18 relations
Tue Jan 20 21:50:54 2009  matrix is 84689 x 84787 (23.6 MB) with weight 5858158 (69.09/col)
Tue Jan 20 21:50:54 2009  sparse part has weight 5858158 (69.09/col)
Tue Jan 20 21:50:55 2009  filtering completed in 3 passes
Tue Jan 20 21:50:55 2009  matrix is 81312 x 81376 (22.9 MB) with weight 5667944 (69.65/col)
Tue Jan 20 21:50:55 2009  sparse part has weight 5667944 (69.65/col)
Tue Jan 20 21:50:55 2009  saving the first 48 matrix rows for later
Tue Jan 20 21:50:56 2009  matrix is 81264 x 81376 (16.5 MB) with weight 4721586 (58.02/col)
Tue Jan 20 21:50:56 2009  sparse part has weight 3829854 (47.06/col)
Tue Jan 20 21:50:56 2009  matrix includes 64 packed rows
Tue Jan 20 21:50:56 2009  using block size 32550 for processor cache size 1024 kB
Tue Jan 20 21:50:57 2009  commencing Lanczos iteration
Tue Jan 20 21:50:57 2009  memory use: 14.7 MB
Tue Jan 20 21:51:46 2009  lanczos halted after 1286 iterations (dim = 81263)
Tue Jan 20 21:51:46 2009  recovered 16 nontrivial dependencies
Tue Jan 20 21:51:47 2009  prp41 factor: 19615475179920945071617458596234333359193
Tue Jan 20 21:51:47 2009  prp56 factor: 47186666258012252043256895418049868713349346463656125033
Tue Jan 20 21:51:47 2009  elapsed time 05:34:21

Jan 20, 2009 (6th)

By Erik Branger / GGNFS, Msieve / Jan 20, 2009

(43·10¹⁷⁰-7)/9 = 4(7)₁₇₀_<171> = 3 · 67 · 823 · 400427303 · 5932620495103062443_<19> · C139

C139 = P56 · P83

P56 = 19724348612725122674663619250491107143649597908233700859_<56>

P83 = 61639219937700802753408962418792264762496168162642674184908540680230576705040487009_<83>

Number: 47777_170
N=1215793462267647551285892538593877354317166737178594605321560408370658353862767905904353311381922334245683040902952768797380928615781640731
  ( 139 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=19724348612725122674663619250491107143649597908233700859
 r2=61639219937700802753408962418792264762496168162642674184908540680230576705040487009
Version: 
Total time: 109.07 hours.
Scaled time: 86.17 units (timescale=0.790).
Factorization parameters were as follows:
n: 1215793462267647551285892538593877354317166737178594605321560408370658353862767905904353311381922334245683040902952768797380928615781640731
m: 10000000000000000000000000000000000
deg: 5
c5: 43
c0: -7
skew: 0.70
type: snfs
lss: 1
rlim: 5100000
alim: 5100000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4

Factor base limits: 5100000/5100000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2550000, 5450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 915262 x 915510
Total sieving time: 109.07 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000
total time: 109.07 hours.
 --------- CPU info (if available) ----------

Jan 20, 2009 (5th)

By Markus Tervooren / ggnfs,msieve / Jan 20, 2009

(41·10¹⁴⁵+13)/9 = 4(5)₁₄₄7_<146> = 311 · 749129 · 967664057 · C129

C129 = P47 · P83

P47 = 10653204168755044912086128475047056724667021761_<47>

P83 = 18967910352320338815022238253260155162161188295244766291718453109239753146705462339_<83>

Msieve v. 1.38
Tue Jan 20 02:57:00 2009
random seeds: 4f200b6f 822e0064
factoring 202069021637911006139792365982193405950417196982994491279558455816628051731372278017796256873175681136201678990699486273678958979 (129 digits)
searching for 15-digit factors
commencing number field sieve (129-digit input)
R0: -100000000000000000000000000000
R1:  1
A0:  13
A1:  0
A2:  0
A3:  0
A4:  0
A5:  41
size score = 3.775105e-10, Murphy alpha = 0.741107, combined = 2.948783e-10

commencing relation filtering
commencing duplicate removal, pass 1
found 843687 hash collisions in 4404710 relations
commencing duplicate removal, pass 2
found 995671 duplicates and 3409039 unique relations
memory use: 50.6 MB
reading rational ideals above 3080192
reading algebraic ideals above 3080192
commencing singleton removal, pass 1
relations with 0 large ideals: 144617
relations with 1 large ideals: 792976
relations with 2 large ideals: 1430566
relations with 3 large ideals: 787622
relations with 4 large ideals: 99293
relations with 5 large ideals: 2793
relations with 6 large ideals: 151172
relations with 7+ large ideals: 0
3409039 relations and about 3584453 large ideals
commencing singleton removal, pass 2
found 1701329 singletons
current dataset: 1707710 relations and about 1248457 large ideals
commencing singleton removal, pass 3
found 371483 singletons
current dataset: 1336227 relations and about 845846 large ideals
commencing singleton removal, final pass
memory use: 22.6 MB
commencing in-memory singleton removal
begin with 1336227 relations and 865908 unique ideals
reduce to 1165662 relations and 690763 ideals in 12 passes
max relations containing the same ideal: 28
reading rational ideals above 720000
reading algebraic ideals above 720000
commencing singleton removal, final pass
keeping 999380 ideals with weight <= 20, new excess is 134647
memory use: 33.2 MB
commencing in-memory singleton removal
begin with 1166216 relations and 999380 unique ideals
reduce to 1132823 relations and 962999 ideals in 10 passes
max relations containing the same ideal: 20
relations with 0 large ideals: 7191
relations with 1 large ideals: 39881
relations with 2 large ideals: 156236
relations with 3 large ideals: 315706
relations with 4 large ideals: 342583
relations with 5 large ideals: 195715
relations with 6 large ideals: 66642
relations with 7+ large ideals: 8869
commencing 2-way merge
reduce to 681219 relation sets and 511407 unique ideals
ignored 12 oversize relation sets
commencing full merge
memory use: 51.5 MB
found 312399 cycles, need 285607
weight of 285607 cycles is about 20278239 (71.00/cycle)
distribution of cycle lengths:
1 relations: 29107
2 relations: 28315
3 relations: 29668
4 relations: 27878
5 relations: 26181
6 relations: 23644
7 relations: 20696
8 relations: 18433
9 relations: 15797
10+ relations: 65888
heaviest cycle: 19 relations
commencing cycle optimization
start with 1823210 relations
pruned 67262 relations
memory use: 56.6 MB
distribution of cycle lengths:
1 relations: 29107
2 relations: 29151
3 relations: 31160
4 relations: 29052
5 relations: 27443
6 relations: 24372
7 relations: 21373
8 relations: 18600
9 relations: 15958
10+ relations: 59391
heaviest cycle: 19 relations

commencing linear algebra
read 285607 cycles
cycles contain 910667 unique relations
read 910667 relations
using 32 quadratic characters above 67108748
building initial matrix
memory use: 113.4 MB
read 285607 cycles
matrix is 285292 x 285607 (84.8 MB) with weight 26928793 (94.29/col)
sparse part has weight 19096573 (66.86/col)
filtering completed in 3 passes
matrix is 283618 x 283818 (84.4 MB) with weight 26775760 (94.34/col)
sparse part has weight 18996642 (66.93/col)
read 283818 cycles
matrix is 283618 x 283818 (84.4 MB) with weight 26775760 (94.34/col)
sparse part has weight 18996642 (66.93/col)
saving the first 48 matrix rows for later
matrix is 283570 x 283818 (80.1 MB) with weight 20525132 (72.32/col)
sparse part has weight 18169096 (64.02/col)
matrix includes 64 packed rows
using block size 65536 for processor cache size 4096 kB
commencing Lanczos iteration (4 threads)
memory use: 80.8 MB
linear algebra completed 283258 of 283818 dimensions (99.8%, ETA 0h 0m)
lanczos halted after 4486 iterations (dim = 283568)
recovered 47 nontrivial dependencies

commencing square root phase
reading relations for dependency 1
read 141763 cycles
cycles contain 560270 unique relations
read 560270 relations
multiplying 453468 relations
multiply complete, coefficients have about 11.50 million bits
initial square root is modulo 4054321
prp47 factor: 10653204168755044912086128475047056724667021761
prp83 factor: 18967910352320338815022238253260155162161188295244766291718453109239753146705462339
elapsed time 00:09:19

Jan 20, 2009 (4th)

By Robert Backstrom / GGNFS / Jan 20, 2009

(41·10¹¹²+13)/9 = 4(5)₁₁₁7_<113> = 49448381 · 3789741401_<10> · C96

C96 = P43 · P54

P43 = 1756133435352425513182738620900779191051907_<43>

P54 = 138427438493586209714463563564622332183967287880120571_<54>

Number: n
N=243097053108778136984165373438571844484903522635059863349607568848040049721944322939831479478897
  ( 96 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=1756133435352425513182738620900779191051907 (pp43)
 r2=138427438493586209714463563564622332183967287880120571 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.06 hours.
Scaled time: 1.94 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_5_111_7
n: 243097053108778136984165373438571844484903522635059863349607568848040049721944322939831479478897
deg: 5
c5: 4100
c0: 13
m: 10000000000000000000000
skew: 0.32
type: snfs
rlim: 480000
alim: 480000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 5000
Factor base limits: 480000/480000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [240000, 345001)
Primes: RFBsize:40005, AFBsize:39921, largePrimes:4792058 encountered
Relations: rels:4122235, finalFF:101596
Max relations in full relation-set: 48
Initial matrix: 79993 x 101596 with sparse part having weight 13695970.
Pruned matrix : 76115 x 76578 with weight 7943284.
Total sieving time: 0.95 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,480000,480000,28,28,56,56,2.5,2.5,50000
total time: 1.06 hours.
 --------- CPU info (if available) ----------

Jan 20, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.1 / Jan 20, 2009

(41·10¹⁸⁶+13)/9 = 4(5)₁₈₅7_<187> = 3² · 182687 · 442938256226497_<15> · C166

C166 = P33 · C134

P33 = 475477038574083556369929814369943_<33>

C134 = [13155836064426885594128471441995840999104018528889838729522538451337386795995418446303058262145873857043472284395328315703288515892949_<134>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3142684540
Step 1 took 13757ms
Step 2 took 15719ms
********** Factor found in step 2: 475477038574083556369929814369943
Found probable prime factor of 33 digits: 475477038574083556369929814369943
Composite cofactor has 134 digits

(41·10¹⁸¹+13)/9 = 4(5)₁₈₀7_<182> = 12659 · 147554087 · C170

C170 = P32 · P138

P32 = 78477341455780825551529021820629_<32>

P138 = 310775248202494631264165765244128945187442184025682887089121058958659378801935873806320769270522775359779824792305932238101974779883118301_<138>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=2007374422
Step 1 took 9165ms
Step 2 took 7552ms
********** Factor found in step 2: 78477341455780825551529021820629
Found probable prime factor of 32 digits: 78477341455780825551529021820629
Probable prime cofactor has 138 digits

(41·10¹⁸⁷+13)/9 = 4(5)₁₈₆7_<188> = 17 · 21997 · C183

C183 = P32 · P151

P32 = 13310078697652045224417963250807_<32>

P151 = 9152681457356347479687513555964152495625936597914799763119468328723604835282886894235884214798391401198686408741531567478099493735823168035935778356799_<151>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=2991966525
Step 1 took 10725ms
Step 2 took 8230ms
********** Factor found in step 2: 13310078697652045224417963250807
Found probable prime factor of 32 digits: 13310078697652045224417963250807
Probable prime cofactor has 151 digits

(41·10¹⁹⁹+13)/9 = 4(5)₁₉₈7_<200> = 83 · 1237 · 3527 · 983947660636931_<15> · C177

C177 = P35 · C142

P35 = 58353764412673836663918994118972963_<35>

C142 = [2191024432013634960794090277665614347010855183558630212912013314951732600038683331878702811507365885655845895638870854178571130009885108643157_<142>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2107319941
Step 1 took 16034ms
Step 2 took 17177ms
********** Factor found in step 2: 58353764412673836663918994118972963
Found probable prime factor of 35 digits: 58353764412673836663918994118972963
Composite cofactor has 142 digits

Jan 20, 2009 (2nd)

Factorizations of 433...339 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Jan 20, 2009

By Robert Backstrom / GGNFS, Msieve / Jan 19, 2009

(41·10¹⁰⁸+13)/9 = 4(5)₁₀₇7_<109> = 3 · 31 · 59 · C105

C105 = P37 · P69

P37 = 6977028609160864473596822556661339871_<37>

P69 = 118996964553052701797392385505489843383257279117694713186886257581941_<69>

Number: n
N=830245226089949982787598971305914990988801814389567259988255067533361683170321770649818763542109632869611
  ( 105 digits)
SNFS difficulty: 111 digits.
Divisors found:

Tue Jan 20 00:07:32 2009  prp37 factor: 6977028609160864473596822556661339871
Tue Jan 20 00:07:32 2009  prp69 factor: 118996964553052701797392385505489843383257279117694713186886257581941
Tue Jan 20 00:07:32 2009  elapsed time 00:06:34 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.69 hours.
Scaled time: 1.27 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_5_107_7
n: 830245226089949982787598971305914990988801814389567259988255067533361683170321770649818763542109632869611
deg: 5
c5: 41
c0: 1300
m: 10000000000000000000000
skew: 1.99
type: snfs
rlim: 450000
alim: 450000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 5000
Factor base limits: 450000/450000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 290141)
Primes: RFBsize:37706, AFBsize:37795, largePrimes:4122943 encountered
Relations: rels:3438265, finalFF:80821
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 112338 hash collisions in 3530633 relations
Msieve: matrix is 89236 x 89484 (23.8 MB)

Total sieving time: 0.65 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,450000,450000,28,28,56,56,2.5,2.5,50000
total time: 0.69 hours.
 --------- CPU info (if available) ----------

By Robert Backstrom / GGNFS, Msieve / Jan 20, 2009

(41·10¹⁰⁹+13)/9 = 4(5)₁₀₈7_<110> = 89 · C108

C108 = P43 · P66

P43 = 2390184965030426407296407175875310828352169_<43>

P66 = 214150863749160623946326406200826672877838975845177529655688925477_<66>

Number: n
N=511860174781523096129837702871410736579275905118601747815230961298377028714107365792759051186017478152309613
  ( 108 digits)
SNFS difficulty: 111 digits.
Divisors found:

Tue Jan 20 02:34:57 2009  prp43 factor: 2390184965030426407296407175875310828352169
Tue Jan 20 02:34:57 2009  prp66 factor: 214150863749160623946326406200826672877838975845177529655688925477
Tue Jan 20 02:34:57 2009  elapsed time 00:05:39 (Msieve 1.39 - dependency 2)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.77 hours.
Scaled time: 1.41 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_5_108_7
n: 511860174781523096129837702871410736579275905118601747815230961298377028714107365792759051186017478152309613
deg: 5
c5: 41
c0: 130
m: 10000000000000000000000
skew: 1.99
type: snfs
rlim: 450000
alim: 450000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 5000
Factor base limits: 450000/450000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 300191)
Primes: RFBsize:37706, AFBsize:37735, largePrimes:4200323 encountered
Relations: rels:3518037, finalFF:79232
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 132689 hash collisions in 3630178 relations
Msieve: matrix is 94444 x 94692 (24.7 MB)

Total sieving time: 0.72 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,450000,450000,28,28,56,56,2.5,2.5,50000
total time: 0.77 hours.
 --------- CPU info (if available) ----------

Jan 19, 2009 (12th)

By Wataru Sakai / Msieve / Jan 19, 2009

(19·10¹⁹⁶+71)/9 = 2(1)₁₉₅9_<197> = 7 · C196

C196 = P88 · P108

P88 = 4024550742728356898279108029508093226251113429243623259829018016784236730049498559965681_<88>

P108 = 749368863424609268346748573675398417191779704699583690103757751394161833140023105513882632166295016315653257_<108>

Number: 21119_196
N=3015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873017
  ( 196 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=4024550742728356898279108029508093226251113429243623259829018016784236730049498559965681
 r2=749368863424609268346748573675398417191779704699583690103757751394161833140023105513882632166295016315653257
Version: 
Total time: 966.43 hours.
Scaled time: 1823.66 units (timescale=1.887).
Factorization parameters were as follows:
n: 3015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873017
m: 1000000000000000000000000000000000000000
deg: 5
c5: 190
c0: 71
skew: 0.82
type: snfs
lss: 1
rlim: 13600000
alim: 13600000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 13600000/13600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6800000, 17400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2466460 x 2466708
Total sieving time: 966.43 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,13600000,13600000,28,28,55,55,2.5,2.5,100000
total time: 966.43 hours.
 --------- CPU info (if available) ----------

Jan 19, 2009 (11th)

By Markus Tervooren / ggnfs-lasieve4I12e, msieve / Jan 19, 2009

(41·10¹²⁵+13)/9 = 4(5)₁₂₄7_<126> = 19 · 30809 · C120

C120 = P59 · P62

P59 = 20243241615867601351382161917901417424745360191571433538399_<59>

P62 = 38444134271346041617717354848500875864662068641723260690270433_<62>

Number: 125
N=778233898767714074587834989358125967216612294690983249179675036097715048329274179205248561263806296443717839721399856767
  ( 120 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=20243241615867601351382161917901417424745360191571433538399
 r2=38444134271346041617717354848500875864662068641723260690270433
Version:
Total time: 1.52 hours.
Scaled time: 3.09 units (timescale=2.031).
Factorization parameters were as follows:
n: 778233898767714074587834989358125967216612294690983249179675036097715048329274179205248561263806296443717839721399856767
m: 10000000000000000000000000
deg: 5
c5: 41
c0: 13
skew: 0.79
type: snfs
lss: 1
rlim: 900000
alim: 900000
lpbr: 26
lpba: 26
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3

Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 46/46
Sieved rational special-q in [450000, 700001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 109798 x 110038
Total sieving time: 1.52 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000
total time: 1.52 hours.

Jan 19, 2009 (10th)

By Sinkiti Sibata / Msieve / Jan 19, 2009

(41·10¹²⁰+13)/9 = 4(5)₁₁₉7_<121> = 3 · C121

C121 = P35 · P86

P35 = 41942095426732369193715236502410893_<35>

P86 = 36205118105536280255069438315208949195889419727129346127774643983566290888742102900883_<86>

Number: 45557_120
N=1518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519
  ( 121 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=41942095426732369193715236502410893
 r2=36205118105536280255069438315208949195889419727129346127774643983566290888742102900883
Version: 
Total time: 1.59 hours.
Scaled time: 3.17 units (timescale=1.991).
Factorization parameters were as follows:
name: 45557_120
n: 1518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519
m: 1000000000000000000000000
deg: 5
c5: 41
c0: 13
skew: 0.79
type: snfs
lss: 1
rlim: 740000
alim: 740000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2
Factor base limits: 740000/740000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [370000, 570001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 84577 x 84825
Total sieving time: 1.59 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000
total time: 1.59 hours.
 --------- CPU info (if available) ----------

(41·10¹⁵⁹+13)/9 = 4(5)₁₅₈7_<160> = 3² · 7 · 23071 · 591164084701_<12> · 964350536796688660109_<21> · 301356908876733753686272429_<27> · C95

C95 = P46 · P50

P46 = 1323084657260748762081931294088186861983105043_<46>

P50 = 13788677845491133788833382578002306992383451342683_<50>

Mon Jan 19 16:58:58 2009  Msieve v. 1.39
Mon Jan 19 16:58:58 2009  random seeds: b244ea38 8f6c6e48
Mon Jan 19 16:58:58 2009  factoring 18243588101280516424498091055426832910648896917003601129649960924737111973905782692799778450369 (95 digits)
Mon Jan 19 16:58:59 2009  searching for 15-digit factors
Mon Jan 19 16:59:01 2009  commencing quadratic sieve (95-digit input)
Mon Jan 19 16:59:01 2009  using multiplier of 1
Mon Jan 19 16:59:01 2009  using 32kb Intel Core sieve core
Mon Jan 19 16:59:01 2009  sieve interval: 36 blocks of size 32768
Mon Jan 19 16:59:01 2009  processing polynomials in batches of 6
Mon Jan 19 16:59:01 2009  using a sieve bound of 2128183 (78513 primes)
Mon Jan 19 16:59:01 2009  using large prime bound of 310714718 (28 bits)
Mon Jan 19 16:59:01 2009  using double large prime bound of 1933086450144842 (43-51 bits)
Mon Jan 19 16:59:01 2009  using trial factoring cutoff of 51 bits
Mon Jan 19 16:59:01 2009  polynomial 'A' values have 12 factors
Mon Jan 19 19:52:38 2009  78710 relations (19906 full + 58804 combined from 1154571 partial), need 78609
Mon Jan 19 19:52:39 2009  begin with 1174477 relations
Mon Jan 19 19:52:41 2009  reduce to 201809 relations in 11 passes
Mon Jan 19 19:52:41 2009  attempting to read 201809 relations
Mon Jan 19 19:52:44 2009  recovered 201809 relations
Mon Jan 19 19:52:44 2009  recovered 181459 polynomials
Mon Jan 19 19:52:44 2009  attempting to build 78710 cycles
Mon Jan 19 19:52:44 2009  found 78710 cycles in 6 passes
Mon Jan 19 19:52:44 2009  distribution of cycle lengths:
Mon Jan 19 19:52:44 2009     length 1 : 19906
Mon Jan 19 19:52:44 2009     length 2 : 14145
Mon Jan 19 19:52:44 2009     length 3 : 13515
Mon Jan 19 19:52:44 2009     length 4 : 10573
Mon Jan 19 19:52:44 2009     length 5 : 7714
Mon Jan 19 19:52:44 2009     length 6 : 5210
Mon Jan 19 19:52:44 2009     length 7 : 3266
Mon Jan 19 19:52:44 2009     length 9+: 4381
Mon Jan 19 19:52:44 2009  largest cycle: 20 relations
Mon Jan 19 19:52:45 2009  matrix is 78513 x 78710 (19.9 MB) with weight 4897447 (62.22/col)
Mon Jan 19 19:52:45 2009  sparse part has weight 4897447 (62.22/col)
Mon Jan 19 19:52:46 2009  filtering completed in 3 passes
Mon Jan 19 19:52:46 2009  matrix is 74338 x 74402 (18.9 MB) with weight 4664277 (62.69/col)
Mon Jan 19 19:52:46 2009  sparse part has weight 4664277 (62.69/col)
Mon Jan 19 19:52:46 2009  saving the first 48 matrix rows for later
Mon Jan 19 19:52:46 2009  matrix is 74290 x 74402 (11.7 MB) with weight 3587319 (48.22/col)
Mon Jan 19 19:52:46 2009  sparse part has weight 2609601 (35.07/col)
Mon Jan 19 19:52:46 2009  matrix includes 64 packed rows
Mon Jan 19 19:52:46 2009  using block size 29760 for processor cache size 1024 kB
Mon Jan 19 19:52:47 2009  commencing Lanczos iteration
Mon Jan 19 19:52:47 2009  memory use: 11.5 MB
Mon Jan 19 19:53:24 2009  lanczos halted after 1176 iterations (dim = 74290)
Mon Jan 19 19:53:24 2009  recovered 17 nontrivial dependencies
Mon Jan 19 19:53:25 2009  prp46 factor: 1323084657260748762081931294088186861983105043
Mon Jan 19 19:53:25 2009  prp50 factor: 13788677845491133788833382578002306992383451342683
Mon Jan 19 19:53:25 2009  elapsed time 02:54:27

Jan 19, 2009 (9th)

By Robert Backstrom / GGNFS, GMP-ECM / Jan 19, 2009

(41·10¹⁰¹+13)/9 = 4(5)₁₀₀7_<102> = 1349637629_<10> · C93

C93 = P45 · P49

P45 = 191496859003974475105682158910488587574696781_<45>

P49 = 1762635505817914536013970629736936246987392363693_<49>

Number: n
N=337539162933012410515382537215517688826646930689241738350758117129791107473305010789348372233
  ( 93 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=191496859003974475105682158910488587574696781 (pp45)
 r2=1762635505817914536013970629736936246987392363693 (pp49)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.53 hours.
Scaled time: 0.97 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_4_5_100_7
n: 337539162933012410515382537215517688826646930689241738350758117129791107473305010789348372233
deg: 5
c5: 410
c0: 13
m: 100000000000000000000
skew: 0.50
type: snfs
rlim: 320000
alim: 320000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 5000
Factor base limits: 320000/320000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved algebraic special-q in [160000, 205001)
Primes: RFBsize:27608, AFBsize:27356, largePrimes:3421418 encountered
Relations: rels:2947643, finalFF:110338
Max relations in full relation-set: 48
Initial matrix: 55031 x 110338 with sparse part having weight 13990398.
Pruned matrix : 47933 x 48272 with weight 3369240.
Total sieving time: 0.47 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,320000,320000,28,28,56,56,2.5,2.5,20000
total time: 0.53 hours.
 --------- CPU info (if available) ----------

(41·10¹⁰⁷+13)/9 = 4(5)₁₀₆7_<108> = 17 · 19 · 23 · 29 · 1039 · 824837579 · C91

C91 = P33 · P58

P33 = 541569653892075251734476295882633_<33>

P58 = 4555905249401482963380109946391715265753948941966190484649_<58>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 2467340029083449908401427777071389719828177794433844854548394187576771140822696501492200817 (91 digits)
Using B1=998000, B2=1045563762, polynomial Dickson(6), sigma=3539449428
Step 1 took 6203ms
Step 2 took 3703ms
********** Factor found in step 2: 541569653892075251734476295882633
Found probable prime factor of 33 digits: 541569653892075251734476295882633
Probable prime cofactor 4555905249401482963380109946391715265753948941966190484649 has 58 digits

Jan 19, 2009 (8th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 19, 2009

(37·10¹⁶³+17)/9 = 4(1)₁₆₂3_<164> = 68483 · 6032309821_<10> · 52051080620258933_<17> · C133

C133 = P39 · P45 · P50

P39 = 201971245076419635985427244193183158857_<39>

P45 = 766865902905323843944912313206274717756086063_<45>

P50 = 12343947829085375388272773864904907879747898874597_<50>

Number: 41113_163
N=1911890646370876376235553188966780688265478666291531097174081860068199318204711570672140611944772184016625969886744063563671797998627
  ( 133 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=201971245076419635985427244193183158857
 r2=766865902905323843944912313206274717756086063
 r3=12343947829085375388272773864904907879747898874597
Version: 
Total time: 31.70 hours.
Scaled time: 75.68 units (timescale=2.387).
Factorization parameters were as follows:
n: 1911890646370876376235553188966780688265478666291531097174081860068199318204711570672140611944772184016625969886744063563671797998627
m: 1000000000000000000000000000000000
deg: 5
c5: 37
c0: 1700
skew: 2.15
type: snfs
lss: 1
rlim: 4800000
alim: 4800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2400000, 4900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9945719
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 872346 x 872593
Total sieving time: 28.46 hours.
Total relation processing time: 1.22 hours.
Matrix solve time: 1.80 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000
total time: 31.70 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 19, 2009 (7th)

By Serge Batalov / GMP-ECM 6.2.1 / Jan 19, 2009

(41·10¹¹⁴+13)/9 = 4(5)₁₁₃7_<115> = 3² · 1463386738819003634121253_<25> · C90

C90 = P34 · P56

P34 = 3930355513162091606821126039498691_<34>

P56 = 88005109415345588123073252123601333380510933225681922451_<56>

Factor found in step 2: 3930355513162091606821126039498691

(41·10¹³⁹+13)/9 = 4(5)₁₃₈7_<140> = 17 · 47 · 607 · 1741 · 2374277 · 429292313655220207781_<21> · C104

C104 = P29 · P76

P29 = 21801657963205126583049668893_<29>

P76 = 2427912805886171394548275652570474227869473125503474032897907815700875098229_<76>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3728230061
Step 1 took 7005ms
********** Factor found in step 1: 21801657963205126583049668893
Found probable prime factor of 29 digits: 21801657963205126583049668893
Probable prime cofactor has 76 digits

(41·10¹³⁴+13)/9 = 4(5)₁₃₃7_<135> = 177797 · 290827 · C124

C124 = P31 · P94

P31 = 1137775100406018011521513383173_<31>

P94 = 7743294372051181915320432604097700365171873233887895228198421676496704674483207801736789446311_<94>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=207593391
Step 1 took 2720ms
Step 2 took 2063ms
********** Factor found in step 2: 1137775100406018011521513383173
Found probable prime factor of 31 digits: 1137775100406018011521513383173
Probable prime cofactor has 94 digits

(41·10¹³⁰+13)/9 = 4(5)₁₂₉7_<131> = 547 · 1567 · C125

C125 = P29 · P97

P29 = 30674541940541323556463883511_<29>

P97 = 1732634422343984716886855445721622722403019886436256791707786647044682028108458886668414627731263_<97>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=855165405
Step 1 took 2745ms
Step 2 took 2061ms
********** Factor found in step 2: 30674541940541323556463883511
Found probable prime factor of 29 digits: 30674541940541323556463883511
Probable prime cofactor has 97 digits

(41·10¹²⁴+13)/9 = 4(5)₁₂₃7_<125> = 109 · 2459 · C120

C120 = P32 · P88

P32 = 27552660149342947824495408694073_<32>

P88 = 6168687718140127868368841956002554606415386279442679587977932353995948714156451167473139_<88>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4175459408
Step 1 took 9950ms
Step 2 took 12236ms
********** Factor found in step 2: 27552660149342947824495408694073
Found probable prime factor of 32 digits: 27552660149342947824495408694073
Probable prime cofactor has 88 digits

(41·10¹⁸⁵+13)/9 = 4(5)₁₈₄7_<186> = 47 · 1051 · 25204917910717160308267_<23> · C159

C159 = P32 · P128

P32 = 28892316820112975460853426075387_<32>

P128 = 12664064608002915777788152889905085475736571681017867784965528678359881731741429305462714381414364105333224200043928341290790089_<128>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1958335583
Step 1 took 11805ms
Step 2 took 12660ms
********** Factor found in step 2: 28892316820112975460853426075387
Found probable prime factor of 32 digits: 28892316820112975460853426075387
Probable prime cofactor has 128 digits

Jan 19, 2009 (6th)

Factorizations of 455...557 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

433...339 and 455...553 will be extended later.

Jan 19, 2009 (5th)

By Serge Batalov / GMP-ECM 6.2.1 / Jan 19, 2009

(38·10¹⁷²+43)/9 = 4(2)₁₇₁7_<173> = 78904708409084059771_<20> · 203557052143526710221580765970953_<33> · C121

C121 = P36 · P85

P36 = 420734513010606963946049354023057901_<36>

P85 = 6248041078509551353101256469453718149726177872481573643816712145739964244757462590629_<85>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3144912507
Step 1 took 9919ms
Step 2 took 12237ms
********** Factor found in step 2: 420734513010606963946049354023057901
Found probable prime factor of 36 digits: 420734513010606963946049354023057901
Probable prime cofactor has 85 digits

(31·10¹⁷³+23)/9 = 3(4)₁₇₂7_<174> = 9492103471_<10> · 27069297163_<11> · 92908475405229428506788810564397_<32> · C122

C122 = P37 · P86

P37 = 1271867235151492354244516276979799369_<37>

P86 = 11344428648092218894095486717270656404383494382905349632292223973872748424954682767623_<86>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2246719298
Step 1 took 9904ms
Step 2 took 11833ms
********** Factor found in step 2: 1271867235151492354244516276979799369
Found probable prime factor of 37 digits: 1271867235151492354244516276979799369
Probable prime cofactor has 86 digits

(35·10¹⁷⁸+1)/9 = 3(8)₁₇₇9_<179> = 3 · 723328843723621_<15> · 1604042672514887393_<19> · 113924427578431510728409_<24> · C122

C122 = P38 · P85

P38 = 52353651649346759585876888758979954129_<38>

P85 = 1873219822685721131438109990191872553706066300586969533989207471921093745994540622111_<85>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4024858816
Step 1 took 10025ms
Step 2 took 12274ms
********** Factor found in step 2: 52353651649346759585876888758979954129
Found probable prime factor of 38 digits: 52353651649346759585876888758979954129
Probable prime cofactor has 85 digits

Jan 19, 2009 (4th)

By Erik Branger / GGNFS, Msieve / Jan 19, 2009

(43·10¹⁷²-7)/9 = 4(7)₁₇₂_<173> = 19 · 223 · 273842461 · C161

C161 = P70 · P91

P70 = 6941291317736286782073303602411662044216942598401706881620737753047439_<70>

P91 = 5932345295064880058048049218132535850826803648773363051774178987910528595746827458377686199_<91>

Number: 47777_172
N=41178136890447562326026403306646311339851781446200174720208011694883423225884632443497443169775352122387018738833041769196401751763481244442735023304349902594361
  ( 161 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=6941291317736286782073303602411662044216942598401706881620737753047439
 r2=5932345295064880058048049218132535850826803648773363051774178987910528595746827458377686199
Version: 
Total time: 126.49 hours.
Scaled time: 254.24 units (timescale=2.010).
Factorization parameters were as follows:
n: 41178136890447562326026403306646311339851781446200174720208011694883423225884632443497443169775352122387018738833041769196401751763481244442735023304349902594361
m: 50000000000000000000000000000000000
deg: 5
c5: 172
c0: -875
skew: 1.38
type: snfs
lss: 1
rlim: 5900000
alim: 5900000
lpbr: 28
lpba: 28
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5

Factor base limits: 5900000/5900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 52/52
Sieved rational special-q in [2950000, 6850001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1176953 x 1177201
Total sieving time: 126.49 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,5900000,5900000,28,28,52,52,2.5,2.5,100000
total time: 126.49 hours.
 --------- CPU info (if available) ----------

Jan 19, 2009 (3rd)

By Markus Tervooren / PRIMO / Jan 15, 2009

(13·10²⁷⁴³+11)/3 = 4(3)₂₇₄₂7_<2744> is prime.

Jan 19, 2009 (2nd)

List of near-repdigit-related prime numbers is available.

Jan 19, 2009

By Tyler Cadigan / GGNFS msieve / Jan 19, 2009

(43·10¹⁸¹-7)/9 = 4(7)₁₈₁_<182> = 941 · 394782412033130453791_<21> · C159

C159 = P50 · P110

P50 = 11762494900496736764278874195216335838416155314149_<50>

P110 = 10934000222758789623278936927899822714858830939221261071656118922521895869107432990306817336243775060012500783_<110>

Number: 47777_181
N=128611121862230446765269107714484784834155430912953973027917455389262678968963120276135652426748429840669621417121389597978273948148186906111154745216473478667
  ( 159 digits)
SNFS difficulty: 183 digits.
Divisors found:
 r1=11762494900496736764278874195216335838416155314149 (pp50)
 r2=10934000222758789623278936927899822714858830939221261071656118922521895869107432990306817336243775060012500783 (pp110)
Version: Msieve-1.39
Total time: 208.06 hours.
Scaled time: 469.38 units (timescale=2.256).
Factorization parameters were as follows:
n: 128611121862230446765269107714484784834155430912953973027917455389262678968963120276135652426748429840669621417121389597978273948148186906111154745216473478667
m: 2000000000000000000000000000000000000
deg: 5
c5: 215
c0: -112
skew: 0.88
type: snfs
lss: 1
rlim: 8100000
alim: 8100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
qintsize: 1000000Factor base limits: 8100000/8100000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [4050000, 7050001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1150786 x 1151034
Total sieving time: 208.06 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,183,5,0,0,0,0,0,0,0,0,8100000,8100000,28,28,53,53,2.5,2.5,100000
total time: 208.06 hours.
 --------- CPU info (if available) ----------

Jan 18, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 18, 2009

(13·10¹⁷⁶+11)/3 = 4(3)₁₇₅7_<177> = 1627 · 3244693 · 9839424687175087_<16> · 7214678530365912514392376942580747_<34> · C118

C118 = P55 · P63

P55 = 2647921762108576264092059984134504698004998754236125413_<55>

P63 = 436685823521850048650697860974923802737776010762066685670397031_<63>

Number: 43337_176
N=1156309895307811941622908693198246922243653991539782167408598606417694458851169627709353999330698718727763054818848803
  ( 118 digits)
Divisors found:
 r1=2647921762108576264092059984134504698004998754236125413
 r2=436685823521850048650697860974923802737776010762066685670397031
Version: 
Total time: 20.45 hours.
Scaled time: 48.82 units (timescale=2.387).
Factorization parameters were as follows:
name: 43337_176
n: 1156309895307811941622908693198246922243653991539782167408598606417694458851169627709353999330698718727763054818848803
skew: 86938.81
# norm 1.35e+16
c5: 6300
c4: 4926644502
c3: -246507659994353
c2: -32087229166127883695
c1: 545959753297972335924309
c0: 16408727250791251967319716217
# alpha -6.33
Y1: 6224387125139
Y0: -44950790497788532043480
# Murphy_E 4.23e-10
# M 491803742154308281868070421448617208199764438528474791943785419864700658290962699773504730358650003601248810959189583
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2000000, 3500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9094056
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 641503 x 641751
Polynomial selection time: 2.00 hours.
Total sieving time: 16.72 hours.
Total relation processing time: 0.64 hours.
Matrix solve time: 0.95 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,52,52,2.4,2.4,100000
total time: 20.45 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 18, 2009 (2nd)

By Serge Batalov / Msieve-1.39 / Jan 18, 2009

(13·10¹⁶⁹+11)/3 = 4(3)₁₆₈7_<170> = 17 · 41 · 8599 · C163

C163 = P44 · P120

P44 = 22087011810801629543251722041130620916073931_<44>

P120 = 327344016680742970688278759292115174513035620073606621698749651782305565580130278811022668813825639938252180855560809909_<120>

SNFS difficulty: 171 digits.
Divisors found:
 r1=22087011810801629543251722041130620916073931 (pp44)
 r2=327344016680742970688278759292115174513035620073606621698749651782305565580130278811022668813825639938252180855560809909 (pp120)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.288).
Factorization parameters were as follows:
n: 7230051162622815627744464853581175037925789531319719591920339963679559905673415585732306020925214074862952989818030179234636794764820061545532442935847922881382279
m: 10000000000000000000000000000000000
deg: 5
c5: 13
c0: 110
skew: 1.53
type: snfs
lss: 1
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2500000, 5200001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 901506 x 901754
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000
total time: 60.00 hours.

Jan 18, 2009

By Serge Batalov / PFGW / Jan 18, 2009

(7·10¹⁸⁵³⁶+11)/9 = (7)₁₈₅₃₅9_<18536> is PRP.

(25·10⁴³⁷⁵³-1)/3 = 8(3)₄₃₇₅₃_<43754> is PRP.

Jan 17, 2009 (3rd)

By Serge Batalov / PFGW / Jan 17, 2009

(25·10¹⁹⁵⁷³-1)/3 = 8(3)₁₉₅₇₃_<19574> is PRP.

Jan 17, 2009 (2nd)

By Sinkiti Sibata / Msieve / Jan 17, 2009

(13·10¹⁶²+11)/3 = 4(3)₁₆₁7_<163> = C163

C163 = P32 · P132

P32 = 34524487186108164589266926227963_<32>

P132 = 125514777669947954110061487216222423812216625154435593299309682944607690319606094120290179827989603346109673239467770114779667655099_<132>

Number: 43337_162
N=4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337
  ( 163 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=34524487186108164589266926227963
 r2=125514777669947954110061487216222423812216625154435593299309682944607690319606094120290179827989603346109673239467770114779667655099
Version: 
Total time: 60.01 hours.
Scaled time: 118.05 units (timescale=1.967).
Factorization parameters were as follows:
name: 43337_162
n: 4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337
m: 200000000000000000000000000000000
deg: 5
c5: 325
c0: 88
skew: 0.77
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 4000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 721900 x 722148
Total sieving time: 60.01 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 60.01 hours.
 --------- CPU info (if available) ----------

Jan 17, 2009

By Serge Batalov / Msieve-1.39 / Jan 17, 2009

(13·10¹⁶⁷+11)/3 = 4(3)₁₆₆7_<168> = 53 · 59 · 463 · 2873041 · C156

C156 = P51 · P105

P51 = 194455719932452560733660170761976392451739776790187_<51>

P105 = 535735812999399153606191070676975358670063586820885715143607054168922311995203320428355887483546091708211_<105>

SNFS difficulty: 169 digits.
Divisors found:
 r1=194455719932452560733660170761976392451739776790187 (pp51)
 r2=535735812999399153606191070676975358670063586820885715143607054168922311995203320428355887483546091708211 (pp105)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.951).
Factorization parameters were as follows:
n: 104176893210395939690502374790242590846413000580702197124951516286550964995388752088010593638802767954770278632816407445627521800813303371615530069372125457
m: 2000000000000000000000000000000000
deg: 5
c5: 325
c0: 88
skew: 0.77
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2300000, 5100001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 964562 x 964810
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.5,2.5,200000
total time: 48.00 hours.

Jan 16, 2009 (2nd)

By Sinkiti Sibata / Msieve / Jan 16, 2009

(13·10¹⁶⁸+11)/3 = 4(3)₁₆₇7_<169> = C169

C169 = P31 · P38 · P100

P31 = 5846472133582342637694713367859_<31>

P38 = 74900637750264860219951078932462865953_<38>

P100 = 9895612898452368895553154031861840324724793753937589708723250272302747379331205428168055115630613731_<100>

Number: 43337_168
N=4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337
  ( 169 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=5846472133582342637694713367859
 r2=74900637750264860219951078932462865953
 r3=9895612898452368895553154031861840324724793753937589708723250272302747379331205428168055115630613731
Version: 
Total time: 66.86 hours.
Scaled time: 172.16 units (timescale=2.575).
Factorization parameters were as follows:
name: 43337_168
n: 4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337
m: 5000000000000000000000000000000000
deg: 5
c5: 104
c0: 275
skew: 1.21
type: snfs
lss: 1
rlim: 4900000
alim: 4900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 4900000/4900000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [2450000, 5250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 912020 x 912268
Total sieving time: 66.86 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000
total time: 66.86 hours.
 --------- CPU info (if available) ----------

Jan 16, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 16, 2009

(13·10¹⁶¹+11)/3 = 4(3)₁₆₀7_<162> = 109496623 · 14378378550629_<14> · C141

C141 = P49 · P92

P49 = 5715212407053093801499963783289143078633450460831_<49>

P92 = 48159179955016448416285230370078531173553150252889640143095600012242736469510165425171816181_<92>

Number: 43337_161
N=275239942792412661818761527536279723042021475242063102757272718266105632150916056789799483048330444045627931665600434601838675125207672506411
  ( 141 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=5715212407053093801499963783289143078633450460831
 r2=48159179955016448416285230370078531173553150252889640143095600012242736469510165425171816181
Version: 
Total time: 18.32 hours.
Scaled time: 43.67 units (timescale=2.384).
Factorization parameters were as follows:
n: 275239942792412661818761527536279723042021475242063102757272718266105632150916056789799483048330444045627931665600434601838675125207672506411
m: 100000000000000000000000000000000
deg: 5
c5: 130
c0: 11
skew: 0.61
type: snfs
lss: 1
rlim: 3800000
alim: 3800000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3800000/3800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1900000, 3400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9505448
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 669558 x 669806
Total sieving time: 16.36 hours.
Total relation processing time: 0.70 hours.
Matrix solve time: 1.01 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000
total time: 18.32 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 15, 2009 (2nd)

By Jo Yeong Uk / GGNFS / Msieve v1.39 / Jan 15, 2009

(13·10¹⁶⁰+11)/3 = 4(3)₁₅₉7_<161> = 7 · 179 · 3764899 · 1327389905836927_<16> · C136

C136 = P62 · P75

P62 = 23089315162879420588279523578469903211678270597405443440485281_<62>

P75 = 299714762079039746128520371602155646310929719488958029620447471553499575433_<75>

Number: 43337_160
N=6920208600610370385069482795491829542945590344404204683796070425699101258300635541173618459414190728743093248609380824846048836985701673
  ( 136 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=23089315162879420588279523578469903211678270597405443440485281
 r2=299714762079039746128520371602155646310929719488958029620447471553499575433
Version: 
Total time: 14.39 hours.
Scaled time: 34.33 units (timescale=2.386).
Factorization parameters were as follows:
n: 6920208600610370385069482795491829542945590344404204683796070425699101258300635541173618459414190728743093248609380824846048836985701673
m: 100000000000000000000000000000000
deg: 5
c5: 13
c0: 11
skew: 0.97
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 2900001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9337232
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 582785 x 583033
Total sieving time: 13.00 hours.
Total relation processing time: 0.56 hours.
Matrix solve time: 0.77 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 14.39 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 15, 2009

By Serge Batalov / Msieve-1.39 gnfs, GMP-ECM 6.2.1 / Jan 15, 2009

(13·10¹⁵⁷+11)/3 = 4(3)₁₅₆7_<158> = 102880669 · 369766790874394873_<18> · 139134154642600968853_<21> · C112

C112 = P45 · P68

P45 = 216208054409157593062352088920460849768841063_<45>

P68 = 37866467412705690316757476796901761998436087074646294065413033980759_<68>

#borderline gnfs/snfs; found good polynomial => gnfs was faster
#
N=8187035246648864842469428858836938255001110448154352590335554145448569846238531738387635346650027384212871106817
  ( 112 digits)
Divisors found:
 r1=216208054409157593062352088920460849768841063 (pp45)
 r2=37866467412705690316757476796901761998436087074646294065413033980759 (pp68)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.710).
Factorization parameters were as follows:
name: 43337_157
n: 8187035246648864842469428858836938255001110448154352590335554145448569846238531738387635346650027384212871106817
skew: 61167.96
# norm 4.07e+15
c5: 6660
c4: 1079689452
c3: 25319299532829
c2: 863041214119956334
c1: -120283268263238551988060
c0: -871283991612239151823826625
# alpha -6.23
Y1: 31108648087
Y0: -4148875289325198945706
# Murphy_E 7.77e-10
# M 3263885175971627639211022329669223352106913257185713554496169784071687074017242523197383252707752474719357954621
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1750000, 3450001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 518623 x 518869
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,52,52,2.4,2.4,100000
total time: 13.00 hours.

(64·10²²¹+53)/9 = 7(1)₂₂₀7_<222> = 3² · 11 · 128239 · 503398933 · 1004825417137_<13> · 27740572834433626007911111_<26> · 38068287072532520234581880952761336179_<38> · C132

C132 = P42 · P90

P42 = 363210988727484372496492328545443062110799_<42>

P90 = 288696490555827973898065260140780868120540968915440564796920084345573963153343559060691847_<90>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=3349363715
Step 1 took 141507ms
Step 2 took 59822ms
********** Factor found in step 2: 363210988727484372496492328545443062110799
Found probable prime factor of 42 digits: 363210988727484372496492328545443062110799
Probable prime cofactor has 90 digits

Jan 14, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 14, 2009

(13·10¹⁵⁶+11)/3 = 4(3)₁₅₅7_<157> = 23 · 461 · 142142397253024033_<18> · 315050806155779087190431_<24> · C112

C112 = P50 · P62

P50 = 94337234232523356167988582191740606707889003037461_<50>

P62 = 96739973889631009267195768717081156635720572453826531736908193_<62>

Number: 43337_156
N=9126181576474314099316202688733744758158416274557063351600048441236717182538166050024590943065552750697896817973
  ( 112 digits)
Divisors found:
 r1=94337234232523356167988582191740606707889003037461
 r2=96739973889631009267195768717081156635720572453826531736908193
Version: 
Total time: 12.22 hours.
Scaled time: 29.16 units (timescale=2.386).
Factorization parameters were as follows:
name: 43337_156
n: 9126181576474314099316202688733744758158416274557063351600048441236717182538166050024590943065552750697896817973
skew: 18641.35
# norm 1.12e+16
c5: 51300
c4: 9553100985
c3: -245158431981470
c2: -9997132154517714014
c1: -29187811733112763484300
c0: 864894561673356993925839
# alpha -6.16
Y1: 252042445787
Y0: -2818596457005864723910
# Murphy_E 7.05e-10
# M 3166073086433628145140272011787914321793077868154941162459374115294849123320903337401078096742166896587091018999
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved algebraic special-q in [1200000, 2100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8304063
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 434330 x 434578
Polynomial selection time: 0.87 hours.
Total sieving time: 10.15 hours.
Total relation processing time: 0.61 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000
total time: 12.22 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 14, 2009 (3rd)

By Sinkiti Sibata / Msieve / Jan 14, 2009

(13·10¹³³+11)/3 = 4(3)₁₃₂7_<134> = 2179 · 10910803 · 921578036018367563267_<21> · C103

C103 = P50 · P53

P50 = 38536635444786366417186177412639724374473793960999_<50>

P53 = 51321842865559002570186158967759114685637664711207997_<53>

Tue Jan 13 14:36:39 2009  Msieve v. 1.39
Tue Jan 13 14:36:39 2009  random seeds: 56a1c8f0 8269d6a3
Tue Jan 13 14:36:39 2009  factoring 1977771148864657359017104644824987705954905186916919276490415161915497019205156970524246398328794909003 (103 digits)
Tue Jan 13 14:36:40 2009  searching for 15-digit factors
Tue Jan 13 14:36:42 2009  commencing quadratic sieve (103-digit input)
Tue Jan 13 14:36:42 2009  using multiplier of 43
Tue Jan 13 14:36:42 2009  using 32kb Intel Core sieve core
Tue Jan 13 14:36:42 2009  sieve interval: 36 blocks of size 32768
Tue Jan 13 14:36:42 2009  processing polynomials in batches of 6
Tue Jan 13 14:36:42 2009  using a sieve bound of 3327859 (120000 primes)
Tue Jan 13 14:36:42 2009  using large prime bound of 499178850 (28 bits)
Tue Jan 13 14:36:42 2009  using double large prime bound of 4537964541132150 (44-53 bits)
Tue Jan 13 14:36:42 2009  using trial factoring cutoff of 53 bits
Tue Jan 13 14:36:42 2009  polynomial 'A' values have 14 factors
Wed Jan 14 07:35:42 2009  120314 relations (29962 full + 90352 combined from 1763406 partial), need 120096
Wed Jan 14 07:35:46 2009  begin with 1793368 relations
Wed Jan 14 07:35:47 2009  reduce to 310748 relations in 11 passes
Wed Jan 14 07:35:47 2009  attempting to read 310748 relations
Wed Jan 14 07:35:54 2009  recovered 310748 relations
Wed Jan 14 07:35:54 2009  recovered 301487 polynomials
Wed Jan 14 07:35:54 2009  attempting to build 120314 cycles
Wed Jan 14 07:35:54 2009  found 120314 cycles in 5 passes
Wed Jan 14 07:35:54 2009  distribution of cycle lengths:
Wed Jan 14 07:35:54 2009     length 1 : 29962
Wed Jan 14 07:35:54 2009     length 2 : 21154
Wed Jan 14 07:35:54 2009     length 3 : 20471
Wed Jan 14 07:35:54 2009     length 4 : 16386
Wed Jan 14 07:35:54 2009     length 5 : 12141
Wed Jan 14 07:35:54 2009     length 6 : 8168
Wed Jan 14 07:35:54 2009     length 7 : 5007
Wed Jan 14 07:35:54 2009     length 9+: 7025
Wed Jan 14 07:35:54 2009  largest cycle: 18 relations
Wed Jan 14 07:35:55 2009  matrix is 120000 x 120314 (34.0 MB) with weight 8436990 (70.12/col)
Wed Jan 14 07:35:55 2009  sparse part has weight 8436990 (70.12/col)
Wed Jan 14 07:35:57 2009  filtering completed in 3 passes
Wed Jan 14 07:35:57 2009  matrix is 114543 x 114607 (32.6 MB) with weight 8076914 (70.47/col)
Wed Jan 14 07:35:57 2009  sparse part has weight 8076914 (70.47/col)
Wed Jan 14 07:35:57 2009  saving the first 48 matrix rows for later
Wed Jan 14 07:35:58 2009  matrix is 114495 x 114607 (20.7 MB) with weight 6465094 (56.41/col)
Wed Jan 14 07:35:58 2009  sparse part has weight 4740334 (41.36/col)
Wed Jan 14 07:35:58 2009  matrix includes 64 packed rows
Wed Jan 14 07:35:58 2009  using block size 43690 for processor cache size 1024 kB
Wed Jan 14 07:35:59 2009  commencing Lanczos iteration
Wed Jan 14 07:35:59 2009  memory use: 19.6 MB
Wed Jan 14 07:37:31 2009  lanczos halted after 1812 iterations (dim = 114493)
Wed Jan 14 07:37:32 2009  recovered 16 nontrivial dependencies
Wed Jan 14 07:37:33 2009  prp50 factor: 38536635444786366417186177412639724374473793960999
Wed Jan 14 07:37:33 2009  prp53 factor: 51321842865559002570186158967759114685637664711207997
Wed Jan 14 07:37:33 2009  elapsed time 17:00:54

Jan 14, 2009 (2nd)

By Erik Branger / Msieve, GGNFS / Jan 14, 2009

(13·10¹⁵²+11)/3 = 4(3)₁₅₁7_<153> = 686270785677248325068309143_<27> · 2641783753842599494853063694281_<31> · C96

C96 = P48 · P49

P48 = 120905449768733457519894583951105281814559946607_<48>

P49 = 1976894276472640254386872707511473139863658297177_<49>

Tue Jan 13 16:04:46 2009  Msieve v. 1.38
Tue Jan 13 16:04:46 2009  random seeds: 5ea5d600 8195fe1a
Tue Jan 13 16:04:46 2009  factoring 239017291642159478476222200461765008396478220370329255792346259720554607262768237545189658828439 (96 digits)
Tue Jan 13 16:04:47 2009  searching for 15-digit factors
Tue Jan 13 16:04:49 2009  commencing quadratic sieve (96-digit input)
Tue Jan 13 16:04:49 2009  using multiplier of 1
Tue Jan 13 16:04:49 2009  using 64kb Pentium 4 sieve core
Tue Jan 13 16:04:49 2009  sieve interval: 18 blocks of size 65536
Tue Jan 13 16:04:49 2009  processing polynomials in batches of 6
Tue Jan 13 16:04:49 2009  using a sieve bound of 2229089 (82353 primes)
Tue Jan 13 16:04:49 2009  using large prime bound of 334363350 (28 bits)
Tue Jan 13 16:04:49 2009  using double large prime bound of 2205939464917200 (43-51 bits)
Tue Jan 13 16:04:49 2009  using trial factoring cutoff of 51 bits
Tue Jan 13 16:04:49 2009  polynomial 'A' values have 12 factors
Tue Jan 13 22:46:03 2009  82620 relations (19831 full + 62789 combined from 1238445 partial), need 82449
Tue Jan 13 22:46:09 2009  begin with 1258276 relations
Tue Jan 13 22:46:10 2009  reduce to 216862 relations in 11 passes
Tue Jan 13 22:46:10 2009  attempting to read 216862 relations
Tue Jan 13 22:46:19 2009  recovered 216862 relations
Tue Jan 13 22:46:19 2009  recovered 202259 polynomials
Tue Jan 13 22:46:20 2009  attempting to build 82620 cycles
Tue Jan 13 22:46:20 2009  found 82620 cycles in 5 passes
Tue Jan 13 22:46:20 2009  distribution of cycle lengths:
Tue Jan 13 22:46:20 2009     length 1 : 19831
Tue Jan 13 22:46:20 2009     length 2 : 14384
Tue Jan 13 22:46:20 2009     length 3 : 13780
Tue Jan 13 22:46:20 2009     length 4 : 11180
Tue Jan 13 22:46:20 2009     length 5 : 8539
Tue Jan 13 22:46:20 2009     length 6 : 5941
Tue Jan 13 22:46:20 2009     length 7 : 3722
Tue Jan 13 22:46:20 2009     length 9+: 5243
Tue Jan 13 22:46:20 2009  largest cycle: 21 relations
Tue Jan 13 22:46:20 2009  matrix is 82353 x 82620 (22.5 MB) with weight 5571702 (67.44/col)
Tue Jan 13 22:46:20 2009  sparse part has weight 5571702 (67.44/col)
Tue Jan 13 22:46:22 2009  filtering completed in 3 passes
Tue Jan 13 22:46:22 2009  matrix is 78709 x 78773 (21.6 MB) with weight 5338672 (67.77/col)
Tue Jan 13 22:46:22 2009  sparse part has weight 5338672 (67.77/col)
Tue Jan 13 22:46:23 2009  saving the first 48 matrix rows for later
Tue Jan 13 22:46:23 2009  matrix is 78661 x 78773 (14.5 MB) with weight 4301329 (54.60/col)
Tue Jan 13 22:46:23 2009  sparse part has weight 3319361 (42.14/col)
Tue Jan 13 22:46:23 2009  matrix includes 64 packed rows
Tue Jan 13 22:46:23 2009  using block size 21845 for processor cache size 512 kB
Tue Jan 13 22:46:24 2009  commencing Lanczos iteration
Tue Jan 13 22:46:24 2009  memory use: 13.4 MB
Tue Jan 13 22:47:36 2009  lanczos halted after 1245 iterations (dim = 78659)
Tue Jan 13 22:47:36 2009  recovered 17 nontrivial dependencies
Tue Jan 13 22:47:37 2009  prp48 factor: 120905449768733457519894583951105281814559946607
Tue Jan 13 22:47:37 2009  prp49 factor: 1976894276472640254386872707511473139863658297177
Tue Jan 13 22:47:37 2009  elapsed time 06:42:51

(13·10¹⁵³+11)/3 = 4(3)₁₅₂7_<154> = 17 · 847373 · 12196369 · C140

C140 = P62 · P78

P62 = 65584580921735305097374227398029523494342491423519119650530487_<62>

P78 = 376067887997921142110137083688739434973552935635838676784563793032808788990219_<78>

Number: 43337_153
N=24664254832465748459502657707992646079096609823530663662827043415488430096613894185804502758072751671330661198306629868323758976748404306653
  ( 140 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=65584580921735305097374227398029523494342491423519119650530487
 r2=376067887997921142110137083688739434973552935635838676784563793032808788990219
Version: 
Total time: 26.20 hours.
Scaled time: 55.80 units (timescale=2.130).
Factorization parameters were as follows:
n: 24664254832465748459502657707992646079096609823530663662827043415488430096613894185804502758072751671330661198306629868323758976748404306653
m: 5000000000000000000000000000000
deg: 5
c5: 104
c0: 275
skew: 1.21
type: snfs
lss: 1
rlim: 2700000
alim: 2700000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4

Factor base limits: 2700000/2700000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1350000, 2250001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 489813 x 490061
Total sieving time: 26.20 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,50,50,2.4,2.4,100000
total time: 26.20 hours.
 --------- CPU info (if available) ----------

Jan 14, 2009

By Serge Batalov / Msieve-1.39 / Jan 14, 2009

(13·10¹⁴⁹+11)/3 = 4(3)₁₄₈7_<150> = 41 · C149

C149 = P37 · P49 · P63

P37 = 5774320557453509533551655639465224157_<37>

P49 = 5039432299373936049812725523191262751395620895863_<49>

P63 = 363208276154368335977320655706641846126561844130682961655421827_<63>

SNFS difficulty: 151 digits.
Divisors found:
 r1=5774320557453509533551655639465224157 (pp37)
 r2=5039432299373936049812725523191262751395620895863 (pp49)
 r3=363208276154368335977320655706641846126561844130682961655421827 (pp63)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.558).
Factorization parameters were as follows:
n: 10569105691056910569105691056910569105691056910569105691056910569105691056910569105691056910569105691056910569105691056910569105691056910569105691057
m: 1000000000000000000000000000000
deg: 5
c5: 13
c0: 110
skew: 1.53
type: snfs
lss: 1
rlim: 2300000
alim: 2300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved rational special-q in [1150000, 1750001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 440738 x 440986
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,52,52,2.4,2.4,100000
total time: 8.50 hours.

Jan 13, 2009 (5th)

By Sinkiti Sibata / Msieve / Jan 13, 2009

(13·10¹¹⁹+11)/3 = 4(3)₁₁₈7_<120> = 29 · 41 · 4236371 · 1843458323135467_<16> · C95

C95 = P34 · P62

P34 = 1878925753271548350891453683398909_<34>

P62 = 24837238859994793450933098574132030571190107627519248166255641_<62>

ue Jan 13 08:53:45 2009  Msieve v. 1.39
Tue Jan 13 08:53:45 2009  random seeds: 4b861124 0f720d93
Tue Jan 13 08:53:45 2009  factoring 46667327734201090114002656028416818839645552235174196745415465210051218566528013255728674495669 (95 digits)
Tue Jan 13 08:53:46 2009  searching for 15-digit factors
Tue Jan 13 08:53:48 2009  commencing quadratic sieve (95-digit input)
Tue Jan 13 08:53:48 2009  using multiplier of 1
Tue Jan 13 08:53:48 2009  using 32kb Intel Core sieve core
Tue Jan 13 08:53:48 2009  sieve interval: 36 blocks of size 32768
Tue Jan 13 08:53:48 2009  processing polynomials in batches of 6
Tue Jan 13 08:53:48 2009  using a sieve bound of 2154241 (80000 primes)
Tue Jan 13 08:53:48 2009  using large prime bound of 323136150 (28 bits)
Tue Jan 13 08:53:48 2009  using double large prime bound of 2074406767356900 (43-51 bits)
Tue Jan 13 08:53:48 2009  using trial factoring cutoff of 51 bits
Tue Jan 13 08:53:48 2009  polynomial 'A' values have 12 factors
Tue Jan 13 12:43:20 2009  80203 relations (19438 full + 60765 combined from 1206755 partial), need 80096
Tue Jan 13 12:43:22 2009  begin with 1226193 relations
Tue Jan 13 12:43:23 2009  reduce to 210402 relations in 12 passes
Tue Jan 13 12:43:23 2009  attempting to read 210402 relations
Tue Jan 13 12:43:26 2009  recovered 210402 relations
Tue Jan 13 12:43:26 2009  recovered 194756 polynomials
Tue Jan 13 12:43:26 2009  attempting to build 80203 cycles
Tue Jan 13 12:43:26 2009  found 80203 cycles in 6 passes
Tue Jan 13 12:43:26 2009  distribution of cycle lengths:
Tue Jan 13 12:43:26 2009     length 1 : 19438
Tue Jan 13 12:43:26 2009     length 2 : 13891
Tue Jan 13 12:43:26 2009     length 3 : 13446
Tue Jan 13 12:43:26 2009     length 4 : 11032
Tue Jan 13 12:43:26 2009     length 5 : 8138
Tue Jan 13 12:43:26 2009     length 6 : 5435
Tue Jan 13 12:43:26 2009     length 7 : 3618
Tue Jan 13 12:43:26 2009     length 9+: 5205
Tue Jan 13 12:43:26 2009  largest cycle: 19 relations
Tue Jan 13 12:43:27 2009  matrix is 80000 x 80203 (21.4 MB) with weight 5300120 (66.08/col)
Tue Jan 13 12:43:27 2009  sparse part has weight 5300120 (66.08/col)
Tue Jan 13 12:43:28 2009  filtering completed in 3 passes
Tue Jan 13 12:43:28 2009  matrix is 76294 x 76358 (20.5 MB) with weight 5073539 (66.44/col)
Tue Jan 13 12:43:28 2009  sparse part has weight 5073539 (66.44/col)
Tue Jan 13 12:43:28 2009  saving the first 48 matrix rows for later
Tue Jan 13 12:43:28 2009  matrix is 76246 x 76358 (13.6 MB) with weight 4108305 (53.80/col)
Tue Jan 13 12:43:28 2009  sparse part has weight 3104632 (40.66/col)
Tue Jan 13 12:43:28 2009  matrix includes 64 packed rows
Tue Jan 13 12:43:28 2009  using block size 30543 for processor cache size 1024 kB
Tue Jan 13 12:43:29 2009  commencing Lanczos iteration
Tue Jan 13 12:43:29 2009  memory use: 12.7 MB
Tue Jan 13 12:44:08 2009  lanczos halted after 1206 iterations (dim = 76244)
Tue Jan 13 12:44:08 2009  recovered 16 nontrivial dependencies
Tue Jan 13 12:44:09 2009  prp34 factor: 1878925753271548350891453683398909
Tue Jan 13 12:44:09 2009  prp62 factor: 24837238859994793450933098574132030571190107627519248166255641
Tue Jan 13 12:44:09 2009  elapsed time 03:50:24

Jan 13, 2009 (4th)

By Tyler Cadigan / GGNFS, msieve / Jan 13, 2009

(43·10¹⁸²-7)/9 = 4(7)₁₈₂_<183> = 3² · 73 · 1181 · 433373007451_<12> · C166

C166 = P52 · P114

P52 = 9186931074291987184692831511277158395546328415501621_<52>

P114 = 154660127199746895179494726776156683293322589732934675735755785599291749630480175689205742714029631751147398445811_<114>

Number: 47777_182
N=1420851928525306131384810224137335708768862208498603709062388536173963432978334067142466657738746292096501148717730968627053157488992019955679761766260696175351159631
  ( 166 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=9186931074291987184692831511277158395546328415501621
 r2=154660127199746895179494726776156683293322589732934675735755785599291749630480175689205742714029631751147398445811
Version: 
Total time: 273.73 hours.
Scaled time: 702.12 units (timescale=2.565).
Factorization parameters were as follows:
n: 1420851928525306131384810224137335708768862208498603709062388536173963432978334067142466657738746292096501148717730968627053157488992019955679761766260696175351159631
m: 5000000000000000000000000000000000000
deg: 5
c5: 172
c0: -875
skew: 1.38
type: snfs
lss: 1
rlim: 8700000
alim: 8700000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 1000000Factor base limits: 8700000/8700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4350000, 8350001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1267000 x 1267248
Total sieving time: 273.73 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,8700000,8700000,28,28,54,54,2.5,2.5,100000
total time: 273.73 hours.
 --------- CPU info (if available) ----------

Jan 13, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 13, 2009

(13·10¹⁵⁵+11)/3 = 4(3)₁₅₄7_<156> = 15047321 · 49563511001_<11> · 3135915200879_<13> · 202634515218602715532928720597_<30> · C96

C96 = P42 · P55

P42 = 441057055858236537663291454087634300850011_<42>

P55 = 2073138620268022456807154469119127942872134591485365329_<55>

Number: 43337_155
N=914372416241420607028108988210983881684880008198519659068075381745308228072890313094251568668619
  ( 96 digits)
Divisors found:
 r1=441057055858236537663291454087634300850011
 r2=2073138620268022456807154469119127942872134591485365329
Version: 
Total time: 1.74 hours.
Scaled time: 4.08 units (timescale=2.344).
Factorization parameters were as follows:
name: 43337_155
n: 914372416241420607028108988210983881684880008198519659068075381745308228072890313094251568668619
skew: 850.27
# norm 1.28e+13
c5: 1722240
c4: 2528621504
c3: -3201503230244
c2: -1551922914281701
c1: -56054921225939732
c0: 163929427857595464981
# alpha -5.18
Y1: 6580789747
Y0: -881058887475319886
# Murphy_E 5.08e-09
# M 757439245795757934347877784253836113424870900628781300281117679238811095220990558846603867178560
type: gnfs
rlim: 800000
alim: 800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 40000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [400000, 760001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 3487001
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 164098 x 164346
Polynomial selection time: 0.10 hours.
Total sieving time: 1.41 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,95,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,800000,800000,26,26,48,48,2.5,2.5,40000
total time: 1.74 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

(35·10¹⁶²-17)/9 = 3(8)₁₆₁7_<163> = 2589231713141_<13> · 12349029638342801933_<20> · C132

C132 = P59 · P74

P59 = 11781950893253965807469256867841699660786517244589420402301_<59>

P74 = 10322967879635049910907388130429762547909825198231377987413088190570273779_<74>

Number: 38887_162
N=121624700630498173684945589913751429441110900948082268499060929326699912364448415246381069923413339739090111816543268001429891565479
  ( 132 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=11781950893253965807469256867841699660786517244589420402301
 r2=10322967879635049910907388130429762547909825198231377987413088190570273779
Version: 
Total time: 23.59 hours.
Scaled time: 56.16 units (timescale=2.381).
Factorization parameters were as follows:
n: 121624700630498173684945589913751429441110900948082268499060929326699912364448415246381069923413339739090111816543268001429891565479
m: 500000000000000000000000000000000
deg: 5
c5: 28
c0: -425
skew: 1.72
type: snfs
lss: 1
rlim: 4400000
alim: 4400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4400000/4400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2200000, 4100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9656646
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 787435 x 787683
Total sieving time: 21.02 hours.
Total relation processing time: 0.90 hours.
Matrix solve time: 1.42 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000
total time: 23.59 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 13, 2009 (2nd)

By Erik Branger / Msieve, GGNFS, GMP-ECM / Jan 13, 2009

(13·10¹⁰⁹+11)/3 = 4(3)₁₀₈7_<110> = 41 · 59 · 9733 · 1865681 · 676804619 · C88

C88 = P39 · P49

P39 = 256520167070456431216017369001734033877_<39>

P49 = 5682210117085333630347759668811604515091349537777_<49>

Mon Jan 12 21:26:42 2009  
Mon Jan 12 21:26:42 2009  
Mon Jan 12 21:26:42 2009  Msieve v. 1.38
Mon Jan 12 21:26:42 2009  random seeds: 69bc3878 fadd585e
Mon Jan 12 21:26:42 2009  factoring 1457601488564167582376904387965802781013594372918615550739594838256848206561153609271429 (88 digits)
Mon Jan 12 21:26:43 2009  searching for 15-digit factors
Mon Jan 12 21:26:45 2009  commencing quadratic sieve (88-digit input)
Mon Jan 12 21:26:45 2009  using multiplier of 5
Mon Jan 12 21:26:45 2009  using 64kb Pentium 4 sieve core
Mon Jan 12 21:26:45 2009  sieve interval: 12 blocks of size 65536
Mon Jan 12 21:26:45 2009  processing polynomials in batches of 9
Mon Jan 12 21:26:45 2009  using a sieve bound of 1508323 (57218 primes)
Mon Jan 12 21:26:45 2009  using large prime bound of 120665840 (26 bits)
Mon Jan 12 21:26:45 2009  using double large prime bound of 352250616108160 (42-49 bits)
Mon Jan 12 21:26:45 2009  using trial factoring cutoff of 49 bits
Mon Jan 12 21:26:45 2009  polynomial 'A' values have 11 factors
Mon Jan 12 22:23:31 2009  57690 relations (16809 full + 40881 combined from 591692 partial), need 57314
Mon Jan 12 22:23:33 2009  begin with 608501 relations
Mon Jan 12 22:23:34 2009  reduce to 134916 relations in 10 passes
Mon Jan 12 22:23:34 2009  attempting to read 134916 relations
Mon Jan 12 22:23:36 2009  recovered 134916 relations
Mon Jan 12 22:23:36 2009  recovered 105504 polynomials
Mon Jan 12 22:23:36 2009  attempting to build 57690 cycles
Mon Jan 12 22:23:36 2009  found 57690 cycles in 7 passes
Mon Jan 12 22:23:36 2009  distribution of cycle lengths:
Mon Jan 12 22:23:36 2009     length 1 : 16809
Mon Jan 12 22:23:36 2009     length 2 : 11829
Mon Jan 12 22:23:36 2009     length 3 : 10374
Mon Jan 12 22:23:36 2009     length 4 : 7297
Mon Jan 12 22:23:36 2009     length 5 : 4893
Mon Jan 12 22:23:36 2009     length 6 : 2942
Mon Jan 12 22:23:36 2009     length 7 : 1710
Mon Jan 12 22:23:36 2009     length 9+: 1836
Mon Jan 12 22:23:36 2009  largest cycle: 19 relations
Mon Jan 12 22:23:36 2009  matrix is 57218 x 57690 (13.2 MB) with weight 3227221 (55.94/col)
Mon Jan 12 22:23:36 2009  sparse part has weight 3227221 (55.94/col)
Mon Jan 12 22:23:37 2009  filtering completed in 3 passes
Mon Jan 12 22:23:37 2009  matrix is 51828 x 51892 (11.9 MB) with weight 2919739 (56.27/col)
Mon Jan 12 22:23:37 2009  sparse part has weight 2919739 (56.27/col)
Mon Jan 12 22:23:38 2009  saving the first 48 matrix rows for later
Mon Jan 12 22:23:38 2009  matrix is 51780 x 51892 (7.8 MB) with weight 2281073 (43.96/col)
Mon Jan 12 22:23:38 2009  sparse part has weight 1732802 (33.39/col)
Mon Jan 12 22:23:38 2009  matrix includes 64 packed rows
Mon Jan 12 22:23:38 2009  using block size 20756 for processor cache size 512 kB
Mon Jan 12 22:23:38 2009  commencing Lanczos iteration
Mon Jan 12 22:23:38 2009  memory use: 7.6 MB
Mon Jan 12 22:24:04 2009  lanczos halted after 821 iterations (dim = 51779)
Mon Jan 12 22:24:05 2009  recovered 17 nontrivial dependencies
Mon Jan 12 22:24:05 2009  prp39 factor: 256520167070456431216017369001734033877
Mon Jan 12 22:24:05 2009  prp49 factor: 5682210117085333630347759668811604515091349537777
Mon Jan 12 22:24:05 2009  elapsed time 00:57:23

(13·10¹¹⁸+11)/3 = 4(3)₁₁₇7_<119> = 7 · 3907 · 46993697 · 260909002660049647_<18> · C90

C90 = P45 · P45

P45 = 168029835493934377112414378163671931047062153_<45>

P45 = 769069462436099182225717832905662638971957219_<45>

Total time: 1h10min

Mon Jan 12 21:24:41 2009  
Mon Jan 12 21:24:41 2009  Msieve v. 1.39
Mon Jan 12 21:24:41 2009  random seeds: f2f3bb18 d32cd53b
Mon Jan 12 21:24:41 2009  factoring 129226615256546289517576317486989013308626224249216040685175451358625604564801902350032507 (90 digits)
Mon Jan 12 21:24:43 2009  searching for 15-digit factors
Mon Jan 12 21:24:45 2009  commencing quadratic sieve (90-digit input)
Mon Jan 12 21:24:45 2009  using multiplier of 3
Mon Jan 12 21:24:45 2009  using 32kb Intel Core sieve core
Mon Jan 12 21:24:45 2009  sieve interval: 35 blocks of size 32768
Mon Jan 12 21:24:45 2009  processing polynomials in batches of 6
Mon Jan 12 21:24:45 2009  using a sieve bound of 1575269 (59667 primes)
Mon Jan 12 21:24:45 2009  using large prime bound of 126021520 (26 bits)
Mon Jan 12 21:24:45 2009  using double large prime bound of 380890718607520 (42-49 bits)
Mon Jan 12 21:24:45 2009  using trial factoring cutoff of 49 bits
Mon Jan 12 21:24:45 2009  polynomial 'A' values have 11 factors
Mon Jan 12 22:26:09 2009  59944 relations (16389 full + 43555 combined from 627938 partial), need 59763

Mon Jan 12 22:32:22 2009  
Mon Jan 12 22:32:22 2009  Msieve v. 1.39
Mon Jan 12 22:32:22 2009  random seeds: 22ab1b00 118d0d91
Mon Jan 12 22:32:22 2009  factoring 129226615256546289517576317486989013308626224249216040685175451358625604564801902350032507 (90 digits)
Mon Jan 12 22:32:23 2009  searching for 15-digit factors
Mon Jan 12 22:32:24 2009  commencing quadratic sieve (90-digit input)
Mon Jan 12 22:32:25 2009  using multiplier of 3
Mon Jan 12 22:32:25 2009  using 32kb Intel Core sieve core
Mon Jan 12 22:32:25 2009  sieve interval: 35 blocks of size 32768
Mon Jan 12 22:32:25 2009  processing polynomials in batches of 6
Mon Jan 12 22:32:25 2009  using a sieve bound of 1575269 (59667 primes)
Mon Jan 12 22:32:25 2009  using large prime bound of 126021520 (26 bits)
Mon Jan 12 22:32:25 2009  using double large prime bound of 380890718607520 (42-49 bits)
Mon Jan 12 22:32:25 2009  using trial factoring cutoff of 49 bits
Mon Jan 12 22:32:25 2009  polynomial 'A' values have 11 factors
Mon Jan 12 22:32:25 2009  restarting with 17385 full and 660657 partial relations
Mon Jan 12 22:32:25 2009  67663 relations (17385 full + 50278 combined from 660657 partial), need 59763
Mon Jan 12 22:32:26 2009  begin with 678042 relations
Mon Jan 12 22:32:26 2009  reduce to 163919 relations in 11 passes
Mon Jan 12 22:32:26 2009  attempting to read 163919 relations

Mon Jan 12 22:32:33 2009  recovered 162520 relations
Mon Jan 12 22:32:33 2009  recovered 132645 polynomials
Mon Jan 12 22:32:33 2009  attempting to build 66275 cycles
Mon Jan 12 22:32:33 2009  found 66275 cycles in 5 passes
Mon Jan 12 22:32:33 2009  distribution of cycle lengths:
Mon Jan 12 22:32:33 2009     length 1 : 17235
Mon Jan 12 22:32:33 2009     length 2 : 12652
Mon Jan 12 22:32:33 2009     length 3 : 11758
Mon Jan 12 22:32:33 2009     length 4 : 9057
Mon Jan 12 22:32:33 2009     length 5 : 6448
Mon Jan 12 22:32:33 2009     length 6 : 4039
Mon Jan 12 22:32:33 2009     length 7 : 2302
Mon Jan 12 22:32:33 2009     length 9+: 2784
Mon Jan 12 22:32:33 2009  largest cycle: 19 relations
Mon Jan 12 22:32:34 2009  matrix is 59667 x 66275 (16.6 MB) with weight 4087103 (61.67/col)
Mon Jan 12 22:32:34 2009  sparse part has weight 4087103 (61.67/col)
Mon Jan 12 22:32:34 2009  filtering completed in 4 passes
Mon Jan 12 22:32:34 2009  matrix is 54146 x 54210 (12.4 MB) with weight 3023133 (55.77/col)
Mon Jan 12 22:32:34 2009  sparse part has weight 3023133 (55.77/col)
Mon Jan 12 22:32:34 2009  saving the first 48 matrix rows for later
Mon Jan 12 22:32:34 2009  matrix is 54098 x 54210 (9.3 MB) with weight 2525714 (46.59/col)
Mon Jan 12 22:32:34 2009  sparse part has weight 2115653 (39.03/col)
Mon Jan 12 22:32:34 2009  matrix includes 64 packed rows
Mon Jan 12 22:32:35 2009  using block size 21684 for processor cache size 2048 kB
Mon Jan 12 22:32:35 2009  commencing Lanczos iteration
Mon Jan 12 22:32:35 2009  memory use: 8.5 MB
Mon Jan 12 22:32:51 2009  lanczos halted after 857 iterations (dim = 54096)
Mon Jan 12 22:32:51 2009  recovered 17 nontrivial dependencies
Mon Jan 12 22:32:52 2009  prp45 factor: 168029835493934377112414378163671931047062153
Mon Jan 12 22:32:52 2009  prp45 factor: 769069462436099182225717832905662638971957219
Mon Jan 12 22:32:52 2009  elapsed time 00:00:30

(13·10¹²⁰+11)/3 = 4(3)₁₁₉7_<121> = 409 · 324949958126413_<15> · C104

C104 = P48 · P57

P48 = 227050036432175964827663796653111153454106407169_<48>

P57 = 143602079285817911224220194059875432673371152120802566469_<57>

Number: 43337_120
N=32604857333581178199511028593996626669495904955556867346769957950556347799824542384755536881031900616261
  ( 104 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=227050036432175964827663796653111153454106407169
 r2=143602079285817911224220194059875432673371152120802566469
Version: 
Total time: 2.10 hours.
Scaled time: 4.40 units (timescale=2.095).
Factorization parameters were as follows:
n: 32604857333581178199511028593996626669495904955556867346769957950556347799824542384755536881031900616261
m: 1000000000000000000000000
deg: 5
c5: 13
c0: 11
skew: 0.97
type: snfs
lss: 1
rlim: 730000
alim: 730000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.2
alambda: 2.2 

Factor base limits: 730000/730000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [365000, 615001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 73952 x 74184
Total sieving time: 2.10 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000
total time: 2.10 hours.
 --------- CPU info (if available) ----------

(13·10¹⁴⁴+11)/3 = 4(3)₁₄₃7_<145> = 41 · 647 · 1109 · 7561082407_<10> · C128

C128 = P38 · P42 · P49

P38 = 24353796243374302911046568308905788143_<38>

P42 = 451509433028751312085588314867466560521161_<42>

P49 = 1771678628451735717484316845181719869224421486619_<49>

Number: 43337_144
N=19481322805051481457546269534110260714900539419098714595161198172145325771983636749495559156356002297169680525224476574968078237
  ( 128 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=24353796243374302911046568308905788143
 r2=451509433028751312085588314867466560521161
 r3=1771678628451735717484316845181719869224421486619
Version: 
Total time: 10.80 hours.
Scaled time: 23.40 units (timescale=2.166).
Factorization parameters were as follows:
n: 19481322805051481457546269534110260714900539419098714595161198172145325771983636749495559156356002297169680525224476574968078237
m: 100000000000000000000000000000
deg: 5
c5: 13
c0: 110
skew: 1.53
type: snfs
lss: 1
rlim: 1910000
alim: 1910000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3

Factor base limits: 1910000/1910000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [955000, 2055001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 304445 x 304693
Total sieving time: 10.80 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000
total time: 10.80 hours.
 --------- CPU info (if available) ----------

(13·10¹³⁸+11)/3 = 4(3)₁₃₇7_<139> = 1023833 · 42538632981937_<14> · C119

C119 = P36 · P84

P36 = 447180441827714627908526856724608823_<36>

P84 = 222498272794804930710956102860230693645267326212839296532940428281757809275112947639_<84>

Number: 43337_138
N=99496875934284246500941660778777866839855336465972506147730272280918518895060912149506031717411859566251369164756418897
  ( 119 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=447180441827714627908526856724608823
 r2=222498272794804930710956102860230693645267326212839296532940428281757809275112947639
Version: 
Total time: 8.45 hours.
Scaled time: 6.65 units (timescale=0.788).
Factorization parameters were as follows:
n: 99496875934284246500941660778777866839855336465972506147730272280918518895060912149506031717411859566251369164756418897
m: 5000000000000000000000000000
deg: 5
c5: 104
c0: 275
skew: 1.21
type: snfs
lss: 1
rlim: 1540000
alim: 1540000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
Factor base limits: 1540000/1540000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved rational special-q in [770000, 1570001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 237133 x 237381
Total sieving time: 8.45 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1540000,1540000,26,26,48,48,2.3,2.3,100000
total time: 8.45 hours.
 --------- CPU info (if available) ----------

(13·10¹⁴⁶+11)/3 = 4(3)₁₄₅7_<147> = 19 · 83 · 2061038947620030393512130854959_<31> · C114

C114 = P36 · P78

P36 = 163493563027500334028675025536906033_<36>

P78 = 815461660049604937978163799568239320621530827894288671469726321744430193811023_<78>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 133322732313830136091385992077768305157424353549583445582707356592375648731047454889267483803451585005072510601759 (114 digits)
Using B1=3000000, B2=3000000-5706890290, polynomial Dickson(6), sigma=303601485
Step 1 took 31122ms
Step 2 took 11638ms
********** Factor found in step 2: 163493563027500334028675025536906033
Found probable prime factor of 36 digits: 163493563027500334028675025536906033
Probable prime cofactor 815461660049604937978163799568239320621530827894288671469726321744430193811023 has 78 digits

Jan 13, 2009

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39

(13·10¹³⁵+11)/3 = 4(3)₁₃₄7_<136> = 383 · 6895616658353_<13> · C121

C121 = P31 · P91

P31 = 1179740285286225325598394472151_<31>

P91 = 1390797187214783276169378207767343950303330104479721308431542522056108887221238741129373313_<91>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=362790999
Step 1 took 3304ms
Step 2 took 2472ms
********** Factor found in step 2: 1179740285286225325598394472151
Found probable prime factor of 31 digits: 1179740285286225325598394472151
Probable prime cofactor has 91 digits

(13·10¹⁴¹+11)/3 = 4(3)₁₄₀7_<142> = 53 · 486667 · 402091448583563_<15> · C120

C120 = P33 · P87

P33 = 734205875738359990609171143110293_<33>

P87 = 569077790659862392446982150080883761511884714960641444153678930769424205644134611144393_<87>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3488388741
Step 1 took 3303ms
********** Factor found in step 1: 734205875738359990609171143110293
Found probable prime factor of 33 digits: 734205875738359990609171143110293
Probable prime cofactor has 87 digits

(13·10¹⁰¹+11)/3 = 4(3)₁₀₀7_<102> = 1871 · C99

C99 = P39 · P60

P39 = 287901958827662472078564273285171611759_<39>

P60 = 804458584277280715235351680045826648501228131747829929796633_<60>

SNFS difficulty: 103 digits.
Divisors found:
 r1=287901958827662472078564273285171611759 (pp39)
 r2=804458584277280715235351680045826648501228131747829929796633 (pp60)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.298).
Factorization parameters were as follows:
n: 231605202209157313379654373775164796009264208088366292535186174951006591840370568323534651701407447
m: 20000000000000000000000000
deg: 4
c4: 65
c0: 88
skew: 1.08
type: snfs
lss: 1
rlim: 360000
alim: 360000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved rational special-q in [180000, 220001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 35265 x 35500
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,103,4,0,0,0,0,0,0,0,0,360000,360000,25,25,46,46,2.3,2.3,20000
total time: 0.50 hours.

(13·10¹¹⁶+11)/3 = 4(3)₁₁₅7_<117> = 2243 · C114

C114 = P56 · P58

P56 = 24723085706747411858193701032591750746561027082019126789_<56>

P58 = 7814301247122253025846086919338828487274309830393265849431_<58>

SNFS difficulty: 117 digits.
Divisors found:
 r1=24723085706747411858193701032591750746561027082019126789 (pp56)
 r2=7814301247122253025846086919338828487274309830393265849431 (pp58)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.297).
Factorization parameters were as follows:
n: 193193639470946648833407638579283697429038490117402288601575271214147718828949323822261851686729083073264972507059
m: 100000000000000000000000
deg: 5
c5: 130
c0: 11
skew: 0.61
type: snfs
lss: 1
rlim: 630000
alim: 630000
lpbr: 25
lpba: 25
mfbr: 48
mfba: 48
rlambda: 2.2
alambda: 2.2
Factor base limits: 630000/630000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 48/48
Sieved rational special-q in [315000, 515001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 65631 x 65861
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,630000,630000,25,25,48,48,2.2,2.2,50000
total time: 0.90 hours.

(13·10¹⁹⁸+11)/3 = 4(3)₁₉₇7_<199> = 228521 · C194

C194 = P28 · C166

P28 = 7398690232181262061837908593_<28>

C166 = [2562955921056643657369718794314123503026583369057025549235277178026716563560559650778997176320033555655178458140715495725060185839224317583375229287594620326583476929_<166>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=643488791
Step 1 took 6296ms
Step 2 took 3919ms
********** Factor found in step 2: 7398690232181262061837908593
Found probable prime factor of 28 digits: 7398690232181262061837908593
Composite cofactor has 166 digits

(13·10¹⁷¹+11)/3 = 4(3)₁₇₀7_<172> = 197 · 493457 · 218656623667_<12> · 9240619543413967_<16> · 181007105164409904932089_<24> · C114

C114 = P35 · P79

P35 = 42437908770327161353502748258707797_<35>

P79 = 2872058172684506346630550954044468196069561799481335826483411687432830745426269_<79>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1644727183
Step 1 took 8191ms
Step 2 took 9318ms
********** Factor found in step 2: 42437908770327161353502748258707797
Found probable prime factor of 35 digits: 42437908770327161353502748258707797
Probable prime cofactor has 79 digits

(13·10¹⁴⁵+11)/3 = 4(3)₁₄₄7_<146> = 1259 · 1072826963357_<13> · 2036616450721_<13> · C119

C119 = P33 · P34 · P53

P33 = 478862024668223181910294165350637_<33>

P34 = 2090097750097179593328371828976553_<34>

P53 = 15739119933263023002620364116075849632754645511358379_<53>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2413085966
Step 1 took 9950ms
Step 2 took 2478ms
********** Factor found in step 2: 2090097750097179593328371828976553
Found probable prime factor of 34 digits: 2090097750097179593328371828976553
Composite cofactor has 85 digits

Mon Jan 12 14:39:25 2009  Msieve v. 1.39
Mon Jan 12 14:39:25 2009  random seeds: bad1e317 a2e5f3cc
Mon Jan 12 14:39:25 2009  factoring 7536866837738320921666098847731440383268647485457604604108798019696763265724702937423 (85 digits)
Mon Jan 12 14:39:26 2009  searching for 15-digit factors
Mon Jan 12 14:39:26 2009  commencing quadratic sieve (85-digit input)
Mon Jan 12 14:39:26 2009  using multiplier of 5
Mon Jan 12 14:39:26 2009  using 64kb Opteron sieve core
Mon Jan 12 14:39:26 2009  sieve interval: 6 blocks of size 65536
Mon Jan 12 14:39:26 2009  processing polynomials in batches of 17
Mon Jan 12 14:39:26 2009  using a sieve bound of 1426393 (54706 primes)
Mon Jan 12 14:39:26 2009  using large prime bound of 115537833 (26 bits)
Mon Jan 12 14:39:26 2009  using double large prime bound of 325764350421651 (41-49 bits)
Mon Jan 12 14:39:26 2009  using trial factoring cutoff of 49 bits
Mon Jan 12 14:39:26 2009  polynomial 'A' values have 11 factors
Mon Jan 12 14:39:26 2009  restarting with 2034 full and 73370 partial relations
Mon Jan 12 15:10:08 2009  54908 relations (15814 full + 39094 combined from 574147 partial), need 54802
Mon Jan 12 15:10:08 2009  begin with 589961 relations
Mon Jan 12 15:10:09 2009  reduce to 129977 relations in 9 passes
Mon Jan 12 15:10:09 2009  attempting to read 129977 relations
Mon Jan 12 15:10:10 2009  recovered 129977 relations
Mon Jan 12 15:10:10 2009  recovered 112279 polynomials
Mon Jan 12 15:10:10 2009  attempting to build 54908 cycles
Mon Jan 12 15:10:10 2009  found 54908 cycles in 5 passes
Mon Jan 12 15:10:10 2009  distribution of cycle lengths:
Mon Jan 12 15:10:10 2009     length 1 : 15814
Mon Jan 12 15:10:10 2009     length 2 : 10905
Mon Jan 12 15:10:10 2009     length 3 : 9701
Mon Jan 12 15:10:10 2009     length 4 : 7053
Mon Jan 12 15:10:10 2009     length 5 : 4821
Mon Jan 12 15:10:10 2009     length 6 : 2985
Mon Jan 12 15:10:10 2009     length 7 : 1681
Mon Jan 12 15:10:10 2009     length 9+: 1948
Mon Jan 12 15:10:10 2009  largest cycle: 19 relations
Mon Jan 12 15:10:10 2009  matrix is 54706 x 54908 (13.0 MB) with weight 2967305 (54.04/col)
Mon Jan 12 15:10:10 2009  sparse part has weight 2967305 (54.04/col)
Mon Jan 12 15:10:11 2009  filtering completed in 3 passes
Mon Jan 12 15:10:11 2009  matrix is 50009 x 50073 (12.0 MB) with weight 2733224 (54.58/col)
Mon Jan 12 15:10:11 2009  sparse part has weight 2733224 (54.58/col)
Mon Jan 12 15:10:11 2009  saving the first 48 matrix rows for later
Mon Jan 12 15:10:11 2009  matrix is 49961 x 50073 (7.3 MB) with weight 2067954 (41.30/col)
Mon Jan 12 15:10:11 2009  sparse part has weight 1414146 (28.24/col)
Mon Jan 12 15:10:11 2009  matrix includes 64 packed rows
Mon Jan 12 15:10:11 2009  using block size 20029 for processor cache size 1024 kB
Mon Jan 12 15:10:11 2009  commencing Lanczos iteration
Mon Jan 12 15:10:11 2009  memory use: 6.8 MB
Mon Jan 12 15:10:23 2009  lanczos halted after 791 iterations (dim = 49957)
Mon Jan 12 15:10:24 2009  recovered 16 nontrivial dependencies
Mon Jan 12 15:10:24 2009  prp33 factor: 478862024668223181910294165350637
Mon Jan 12 15:10:24 2009  prp53 factor: 15739119933263023002620364116075849632754645511358379
Mon Jan 12 15:10:24 2009  elapsed time 00:30:59

(13·10¹⁷⁷+11)/3 = 4(3)₁₇₆7_<178> = 139 · 79801 · 379612468397_<12> · 466858693163647_<15> · C145

C145 = P33 · P112

P33 = 517032018136409059571353874400367_<33>

P112 = 4263395347163435754605167105549384651423460652755404927762370848388609390026405509148863593252815692516229219711_<112>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=593251309
Step 1 took 11725ms
Step 2 took 11716ms
********** Factor found in step 2: 517032018136409059571353874400367
Found probable prime factor of 33 digits: 517032018136409059571353874400367
Probable prime cofactor has 112 digits

(13·10¹⁵²+11)/3 = 4(3)₁₅₁7_<153> = 686270785677248325068309143_<27> · C126

C126 = P31 · C96

P31 = 2641783753842599494853063694281_<31>

C96 = [239017291642159478476222200461765008396478220370329255792346259720554607262768237545189658828439_<96>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1460152651
Step 1 took 9733ms
Step 2 took 10264ms
********** Factor found in step 2: 2641783753842599494853063694281
Found probable prime factor of 31 digits: 2641783753842599494853063694281
Composite cofactor has 96 digits

(13·10¹⁷⁶+11)/3 = 4(3)₁₇₅7_<177> = 1627 · 3244693 · 9839424687175087_<16> · C151

C151 = P34 · C118

P34 = 7214678530365912514392376942580747_<34>

C118 = [1156309895307811941622908693198246922243653991539782167408598606417694458851169627709353999330698718727763054818848803_<118>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1504423703
Step 1 took 11712ms
Step 2 took 12076ms
********** Factor found in step 2: 7214678530365912514392376942580747
Found probable prime factor of 34 digits: 7214678530365912514392376942580747
Composite cofactor has 118 digits

(13·10¹⁷⁰+11)/3 = 4(3)₁₆₉7_<171> = 1499 · 567902254172162219_<18> · C150

C150 = P28 · C123

P28 = 1373651784966490440402937717_<28>

C123 = [370569965767644980357356235399428856137811078710645235253822530344840763763076823444886948979877902193136601912075023451181_<123>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2409739674
Step 1 took 11736ms
********** Factor found in step 1: 1373651784966490440402937717
Found probable prime factor of 28 digits: 1373651784966490440402937717
Composite cofactor has 123 digits

(13·10¹⁹⁴+11)/3 = 4(3)₁₉₃7_<195> = 41 · 135721 · 1536617 · 2790600979_<10> · 1239946990790578721657_<22> · C152

C152 = P31 · P121

P31 = 6080092611502949989510099120823_<31>

P121 = 2408876310650925262480767490286417447634363404060717087626403216670946806218350381194813011157655867258367905899750623429_<121>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3066536428
Step 1 took 11722ms
Step 2 took 12009ms
********** Factor found in step 2: 6080092611502949989510099120823
Found probable prime factor of 31 digits: 6080092611502949989510099120823
Probable prime cofactor has 121 digits

(13·10¹⁸⁸+11)/3 = 4(3)₁₈₇7_<189> = 1543 · 142860607 · 255207723123768259319_<21> · C157

C157 = P33 · C125

P33 = 106516169444251311571441538317907_<33>

C125 = [72315988608969549766354716564088708863361398791668800127495140769387943021448338653197888223981621630401019958904218407786589_<125>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2305462360
Step 1 took 13810ms
Step 2 took 13184ms
********** Factor found in step 2: 106516169444251311571441538317907
Found probable prime factor of 33 digits: 106516169444251311571441538317907
Composite cofactor has 125 digits

(13·10¹⁹³+11)/3 = 4(3)₁₉₂7_<194> = 53 · 401393 · 411072007 · 274601721738892619_<18> · C161

C161 = P30 · P131

P30 = 528939695216908001586855390299_<30>

P131 = 34115293629840614800212793487061778880381322301987682674528561980984797481451268135182069095737192125952710750608718824379108161659_<131>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2053943442
Step 1 took 14717ms
Step 2 took 13078ms
********** Factor found in step 2: 528939695216908001586855390299
Found probable prime factor of 30 digits: 528939695216908001586855390299
Probable prime cofactor has 131 digits

(13·10¹³⁷+11)/3 = 4(3)₁₃₆7_<138> = 17 · C137

C137 = P66 · P71

P66 = 807637985960916768831740876387492333779169190633031900872576802793_<66>

P71 = 31561413060708730150872571599062549070601558958879766962070075808593377_<71>

SNFS difficulty: 139 digits.
Divisors found:
 r1=807637985960916768831740876387492333779169190633031900872576802793 (pp66)
 r2=31561413060708730150872571599062549070601558958879766962070075808593377 (pp71)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.294).
Factorization parameters were as follows:
n: 25490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901961
m: 2000000000000000000000000000
deg: 5
c5: 325
c0: 88
skew: 0.77
type: snfs
lss: 1
rlim: 1450000
alim: 1450000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1450000/1450000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [725000, 1550001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 246638 x 246886
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,49,49,2.3,2.3,75000
total time: 5.00 hours.

(13·10¹²⁹+11)/3 = 4(3)₁₂₈7_<130> = 41 · 2389 · 1249529719_<10> · C116

C116 = P31 · P85

P31 = 9281663010039532950468760843457_<31>

P85 = 3814606151552466573303099303750536701596970698329405314826953837863735073362736633211_<85>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4061892878
Step 1 took 9167ms
Step 2 took 8799ms
********** Factor found in step 2: 9281663010039532950468760843457
Found probable prime factor of 31 digits: 9281663010039532950468760843457
Probable prime cofactor has 85 digits

(13·10¹³⁴+11)/3 = 4(3)₁₃₃7_<135> = 23 · 41 · 2545227932836422739_<19> · C114

C114 = P41 · P74

P41 = 11958553032490865212908609128910029714171_<41>

P74 = 15097501805726385936048310070893266742178719854170264340828668499522481111_<74>

SNFS difficulty: 136 digits.
Divisors found:
 r1=11958553032490865212908609128910029714171 (pp41)
 r2=15097501805726385936048310070893266742178719854170264340828668499522481111 (pp74)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.304).
Factorization parameters were as follows:
n: 180544276001905585936188669707667634298162509150541346315109038714131653485746682884521027430565136143432076523981
m: 1000000000000000000000000000
deg: 5
c5: 13
c0: 110
skew: 1.53
type: snfs
lss: 1
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.3
alambda: 2.3
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved rational special-q in [650000, 1175001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 184954 x 185202
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,49,49,2.3,2.3,75000
total time: 4.00 hours.

(13·10¹⁶³+11)/3 = 4(3)₁₆₂7_<164> = 6481 · 8345621 · 5396446101430979761_<19> · 1657874515633727895602144651126113_<34> · C101

C101 = P48 · P54

P48 = 125111068703916647393850098641471129981479630019_<48>

P54 = 715757956709940897574201232426194262350826823645064711_<54>

Number: 43337_163
N=89549242897312413145121015477987605938666360001715878782232515183403517627085365493127792527593159509
  ( 101 digits)
Divisors found:
 r1=125111068703916647393850098641471129981479630019 (pp48)
 r2=715757956709940897574201232426194262350826823645064711 (pp54)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.530).
Factorization parameters were as follows:
name: 43337_163
n: 89549242897312413145121015477987605938666360001715878782232515183403517627085365493127792527593159509
skew: 14219.20
# norm 4.72e+13
c5: 6720
c4: 1607219
c3: -3781792674674
c2: -20391760325156031
c1: 389716915741807259611
c0: -741615802863451244838340
# alpha -5.31
Y1: 21711660839
Y0: -26603483783377273221
# Murphy_E 2.92e-09
# M 18256076264919045554073716051401304772283243952469251928239199987692922377652841597411127307286087277
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 203363 x 203611
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 4.00 hours.

(13·10¹⁷²+11)/3 = 4(3)₁₇₁7_<173> = 7 · 124683707642868001_<18> · 19261998159045934249641919_<26> · 1025177561752975972475736113_<28> · C103

C103 = P46 · P57

P46 = 7484592628038052621285087704880092637265857489_<46>

P57 = 335927650726956320807691331130396826552727400188028875777_<57>

Number: 43337_172
N=2514281618185119047267551628988833847305791628965405631217338056079108891052479407838212838722566143953
  ( 103 digits)
Divisors found:
 r1=7484592628038052621285087704880092637265857489 (pp46)
 r2=335927650726956320807691331130396826552727400188028875777 (pp57)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.724).
Factorization parameters were as follows:
name: 43337_172
n: 2514281618185119047267551628988833847305791628965405631217338056079108891052479407838212838722566143953
skew: 15171.04
# norm 3.51e+14
c5: 22680
c4: -124055346
c3: -30204415768669
c2: 1652155236686905
c1: 1833485328963513386013
c0: -2986641083616374487288735
# alpha -6.05
Y1: 8174481641
Y0: -40640053367376438856
# Murphy_E 2.35e-09
# M 984034130476818682388074087529638493249314732894513911123846271023921439173263023879179576856922289270
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 289389 x 289636
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 5.00 hours.

(13·10¹⁴⁷+11)/3 = 4(3)₁₄₆7_<148> = 29 · 34632467242938281_<17> · 666707790664577506063621777_<27> · C103

C103 = P46 · P58

P46 = 1632689107448837283748587003497437630804378717_<46>

P58 = 3963707899643478820787903054646032550519819003208303853657_<58>

Number: 43337_147
N=6471502712856816941534410396616323458062704121632605765152696107776979645565714978126919250460773418069
  ( 103 digits)
Divisors found:
 r1=1632689107448837283748587003497437630804378717 (pp46)
 r2=3963707899643478820787903054646032550519819003208303853657 (pp58)
Version: Msieve-1.39
Total time: 0.00 hours.
Scaled time: 0.00 units (timescale=2.728).
Factorization parameters were as follows:
name: 43337_147
n: 6471502712856816941534410396616323458062704121632605765152696107776979645565714978126919250460773418069
skew: 12803.66
# norm 1.56e+14
c5: 25200
c4: 6526908
c3: -16208983640194
c2: 36664277029938906
c1: 1517588518650563580273
c0: 4101674119551640223937604
# alpha -5.86
Y1: 12176988151
Y0: -48075179412327603905
# Murphy_E 2.43e-09
# M 765771848902745999549250401080960786347242002138049323590434441771344197826450219537382559039935974
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1850001)
Primes: rational ideals reading, algebraic ideals reading,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 219161 x 219409
Total sieving time: 0.00 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 5.00 hours.

Jan 12, 2009 (3rd)

Factorizations of 433...337 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Jan 12, 2009 (2nd)

By Jo Yeong Uk / Msieve / Jan 12, 2009

(37·10¹⁶²+53)/9 = 4(1)₁₆₁7_<163> = 43 · 769 · 6888289 · 49682126487359_<14> · C138

C138 = P50 · P88

P50 = 42028157780136442442379542414682359487864735723991_<50>

P88 = 8643955636962190706372478541886100514006131870100713909201584397138993894515028748366511_<88>

Number: 41117_162
N=363289531354746753320799714164560359754424340577689448833156203649841655419145956572610748257666769704275970426653960602488750448203665401
  ( 138 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=42028157780136442442379542414682359487864735723991
 r2=8643955636962190706372478541886100514006131870100713909201584397138993894515028748366511
Version: 
Total time: 25.85 hours.
Scaled time: 61.62 units (timescale=2.384).
Factorization parameters were as follows:
n: 363289531354746753320799714164560359754424340577689448833156203649841655419145956572610748257666769704275970426653960602488750448203665401
m: 100000000000000000000000000000000
deg: 5
c5: 3700
c0: 53
skew: 0.43
type: snfs
lss: 1
rlim: 4600000
alim: 4600000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 4600000/4600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [2300000, 4400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9823817
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 794867 x 795114
Total sieving time: 23.16 hours.
Total relation processing time: 1.02 hours.
Matrix solve time: 1.41 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,51,51,2.4,2.4,100000
total time: 25.85 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 12, 2009

By Sinkiti Sibata / Msieve / Jan 12, 2009

(38·10¹⁸⁶+61)/9 = 4(2)₁₈₅9_<187> = 11 · C186

C186 = P83 · P104

P83 = 13933545557012191347373389258569209249638126493880758322318981598763635852951224089_<83>

P104 = 27547789775963625085903934524733271215585771546540325688065243371806745946230760472112031271164240237751_<104>

Number: 42229_186
N=383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383839
  ( 186 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=13933545557012191347373389258569209249638126493880758322318981598763635852951224089
 r2=27547789775963625085903934524733271215585771546540325688065243371806745946230760472112031271164240237751
Version: 
Total time: 289.16 hours.
Scaled time: 729.85 units (timescale=2.524).
Factorization parameters were as follows:
name: 42229_186
n: 383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383839
m: 10000000000000000000000000000000000000
deg: 5
c5: 380
c0: 61
skew: 0.69
type: snfs
lss: 1
rlim: 9400000
alim: 9400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 9400000/9400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4700000, 8500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1786141 x 1786389
Total sieving time: 289.16 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,9400000,9400000,28,28,54,54,2.5,2.5,100000
total time: 289.16 hours.
 --------- CPU info (if available) ----------

Jan 11, 2009

By Jo Yeong Uk / GGNFS,Msieve v1.39 / Jan 11, 2009

(38·10¹⁸⁷+61)/9 = 4(2)₁₈₆9_<188> = 7 · 23 · 4133 · 339381782281_<12> · 14075029066853_<14> · 144197773736360629_<18> · 45994881214842165755089_<23> · C118

C118 = P41 · P77

P41 = 50967802797581625985097478423989003403541_<41>

P77 = 39295969740735967852621112679477369452786973644518223666651441987423587742861_<77>

Number: 42229_187
N=2002829236485565584268140691732974433612639511098407138412154547996959651462215442914520265753338661383557778924870801
  ( 118 digits)
Divisors found:
 r1=50967802797581625985097478423989003403541
 r2=39295969740735967852621112679477369452786973644518223666651441987423587742861
Version: 
Total time: 20.95 hours.
Scaled time: 50.10 units (timescale=2.392).
Factorization parameters were as follows:
name: 42229_187
n: 2002829236485565584268140691732974433612639511098407138412154547996959651462215442914520265753338661383557778924870801
skew: 50181.87
# norm 2.28e+16
c5: 50940
c4: 19532943756
c3: -146582757507473
c2: -47355629610985993948
c1: 532654329772897813291676
c0: -41567750101170860235893120
# alpha -6.32
Y1: 7973840395103
Y0: -33030029096995216166631
# Murphy_E 3.85e-10
# M 316121329102452193654767749257544142231626197662659818279564247885496932610354662673936415656052558511673138286534187
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [2000000, 3500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9431831
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 581575 x 581823
Polynomial selection time: 1.99 hours.
Total sieving time: 17.45 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 0.69 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,52,52,2.4,2.4,100000
total time: 20.95 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 10, 2009 (4th)

The maintenance system is currently running with the new machine. The latest factor table of repunit numbers is available.

Jan 10, 2009 (3rd)

By Jo Yeong Uk / GGNFS / Msieve v1.39 / Jan 10, 2009

(38·10¹⁷⁶+43)/9 = 4(2)₁₇₅7_<177> = 7 · 953 · 18013 · 276447312401475563_<18> · 178756426448137413914826142437964919_<36> · C116

C116 = P56 · P61

P56 = 30482242843051625212413261317342328142108260988731555571_<56>

P61 = 2332615422504949792148260086568871957753601757513041367550327_<61>

Number: 42227_176
N=71103349768243348700450905945142994417179643820598258646824953982535526988209326934630523825762360058327976339721717
  ( 116 digits)
Divisors found:
 r1=30482242843051625212413261317342328142108260988731555571
 r2=2332615422504949792148260086568871957753601757513041367550327
Version: 
Total time: 17.83 hours.
Scaled time: 42.64 units (timescale=2.392).
Factorization parameters were as follows:
name: 42227_176
n: 71103349768243348700450905945142994417179643820598258646824953982535526988209326934630523825762360058327976339721717
skew: 26032.75
# norm 4.33e+15
c5: 108180
c4: 4459312752
c3: -46190052771889
c2: -6904408880014373882
c1: -13229336043547270296464
c0: 539733616727763783241807616
# alpha -5.62
Y1: 929245002037
Y0: -14572980660116137675005
# Murphy_E 4.64e-10
# M 57258185201645401085393804515614427325718700776340221333725020184573222142112606157960434857721364147424672513767023
type: gnfs
rlim: 3300000
alim: 3300000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3300000/3300000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1650000, 3000001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 8772174
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 554186 x 554434
Polynomial selection time: 1.51 hours.
Total sieving time: 14.83 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 0.64 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3300000,3300000,27,27,52,52,2.4,2.4,75000
total time: 17.83 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 10, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.1 / Jan 10, 2009

(4·10²⁴⁵-1)/3 = 1(3)₂₄₅_<246> = 293 · 4428013 · 436570924477_<12> · 197820650760877883_<18> · 1940832977077439598289_<22> · 245134337177055685486188936209_<30> · 1675203063576126721567576664071_<31> · C127

C127 = P43 · P84

P43 = 6790775658469834479820078727143989820043129_<43>

P84 = 219865273571187201579781503790690827059370707506151263702320080862487340541571697173_<84>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2724191139
Step 1 took 36312ms
Step 2 took 25686ms
********** Factor found in step 2: 6790775658469834479820078727143989820043129
Found probable prime factor of 43 digits: 6790775658469834479820078727143989820043129
Probable prime cofactor has 84 digits

Jan 10, 2009

By Sinkiti Sibata / Msieve / Jan 10, 2009

10²¹³-9 = (9)₂₁₂1_<213> = 2671 · 832477 · 3405841 · 5328359 · 5607750409_<10> · 24831611120690827_<17> · 489257181515888972676839_<24> · 2732757469571315596232602778709665753077_<40> · C102

C102 = P42 · P60

P42 = 582858443410441071978771347365210311353479_<42>

P60 = 228371053847304148819820096048179809718818515793823952998837_<60>

Fri Jan 09 16:34:18 2009  Msieve v. 1.39
Fri Jan 09 16:34:18 2009  random seeds: 70bd276c 631bbe8b
Fri Jan 09 16:34:18 2009  factoring 133107996965441716078569858100441760864844458768441551457233330059494248457182487821678740490382903923 (102 digits)
Fri Jan 09 16:34:19 2009  searching for 15-digit factors
Fri Jan 09 16:34:21 2009  commencing quadratic sieve (102-digit input)
Fri Jan 09 16:34:21 2009  using multiplier of 43
Fri Jan 09 16:34:21 2009  using 32kb Intel Core sieve core
Fri Jan 09 16:34:21 2009  sieve interval: 36 blocks of size 32768
Fri Jan 09 16:34:21 2009  processing polynomials in batches of 6
Fri Jan 09 16:34:21 2009  using a sieve bound of 3041849 (110000 primes)
Fri Jan 09 16:34:21 2009  using large prime bound of 456277350 (28 bits)
Fri Jan 09 16:34:21 2009  using double large prime bound of 3860219537782800 (44-52 bits)
Fri Jan 09 16:34:21 2009  using trial factoring cutoff of 52 bits
Fri Jan 09 16:34:21 2009  polynomial 'A' values have 13 factors
Sat Jan 10 09:09:01 2009  110123 relations (26170 full + 83953 combined from 1641709 partial), need 110096
Sat Jan 10 09:09:03 2009  begin with 1667879 relations
Sat Jan 10 09:09:04 2009  reduce to 289724 relations in 11 passes
Sat Jan 10 09:09:04 2009  attempting to read 289724 relations
Sat Jan 10 09:09:10 2009  recovered 289724 relations
Sat Jan 10 09:09:10 2009  recovered 281939 polynomials
Sat Jan 10 09:09:10 2009  attempting to build 110123 cycles
Sat Jan 10 09:09:11 2009  found 110123 cycles in 6 passes
Sat Jan 10 09:09:11 2009  distribution of cycle lengths:
Sat Jan 10 09:09:11 2009     length 1 : 26170
Sat Jan 10 09:09:11 2009     length 2 : 18921
Sat Jan 10 09:09:11 2009     length 3 : 18607
Sat Jan 10 09:09:11 2009     length 4 : 14860
Sat Jan 10 09:09:11 2009     length 5 : 11537
Sat Jan 10 09:09:11 2009     length 6 : 7928
Sat Jan 10 09:09:11 2009     length 7 : 5001
Sat Jan 10 09:09:11 2009     length 9+: 7099
Sat Jan 10 09:09:11 2009  largest cycle: 20 relations
Sat Jan 10 09:09:11 2009  matrix is 110000 x 110123 (32.4 MB) with weight 8061711 (73.21/col)
Sat Jan 10 09:09:11 2009  sparse part has weight 8061711 (73.21/col)
Sat Jan 10 09:09:13 2009  filtering completed in 3 passes
Sat Jan 10 09:09:13 2009  matrix is 105828 x 105892 (31.4 MB) with weight 7802831 (73.69/col)
Sat Jan 10 09:09:13 2009  sparse part has weight 7802831 (73.69/col)
Sat Jan 10 09:09:13 2009  saving the first 48 matrix rows for later
Sat Jan 10 09:09:13 2009  matrix is 105780 x 105892 (22.7 MB) with weight 6525771 (61.63/col)
Sat Jan 10 09:09:13 2009  sparse part has weight 5323421 (50.27/col)
Sat Jan 10 09:09:13 2009  matrix includes 64 packed rows
Sat Jan 10 09:09:13 2009  using block size 42356 for processor cache size 1024 kB
Sat Jan 10 09:09:15 2009  commencing Lanczos iteration
Sat Jan 10 09:09:15 2009  memory use: 20.0 MB
Sat Jan 10 09:10:45 2009  lanczos halted after 1674 iterations (dim = 105780)
Sat Jan 10 09:10:45 2009  recovered 18 nontrivial dependencies
Sat Jan 10 09:10:46 2009  prp42 factor: 582858443410441071978771347365210311353479
Sat Jan 10 09:10:46 2009  prp60 factor: 228371053847304148819820096048179809718818515793823952998837
Sat Jan 10 09:10:46 2009  elapsed time 16:36:28

Jan 9, 2009 (3rd)

By Jo Yeong Uk / GGNFS / Msieve v1.39 / Jan 9, 2009

(38·10¹⁷⁴+61)/9 = 4(2)₁₇₃9_<175> = 11 · 557 · 23333 · 59218732301_<11> · 262088313569048659823633945899080702035203_<42> · C115

C115 = P33 · P40 · P43

P33 = 225417303760371613051787015751701_<33>

P40 = 3509660100567937909308937499352854860151_<40>

P43 = 2405268446283875882037061284565419763257923_<43>

Number: 42229_174
N=1902899549437374369035951375932780225773552267114939321874434723505133347794160411662937567103887497100312817310473
  ( 115 digits)
Divisors found:
 r1=225417303760371613051787015751701
 r2=3509660100567937909308937499352854860151
 r3=2405268446283875882037061284565419763257923
Version: 
Total time: 15.58 hours.
Scaled time: 37.20 units (timescale=2.388).
Factorization parameters were as follows:
name: 42229_174
n: 1902899549437374369035951375932780225773552267114939321874434723505133347794160411662937567103887497100312817310473
skew: 13305.32
# norm 1.25e+15
c5: 34380
c4: -7761979098
c3: -40170364027258
c2: 1216859679370801634
c1: 2137936139042537055913
c0: -37443904713974567970199586
# alpha -5.26
Y1: 2839122733007
Y0: -8884403306900197748349
# Murphy_E 6.23e-10
# M 1013688461298236633418369179942359190638312815538318044515649165909945628291609200031522087797218085581150778639140
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 52/52
Sieved algebraic special-q in [1400000, 2450001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 9217367
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 514466 x 514714
Polynomial selection time: 1.35 hours.
Total sieving time: 12.39 hours.
Total relation processing time: 0.66 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.61 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000
total time: 15.58 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805)
Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421)
Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207)
Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)

Jan 9, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.1 / Jan 9, 2009

10²¹³-9 = (9)₂₁₂1_<213> = 2671 · 832477 · 3405841 · 5328359 · 5607750409_<10> · 24831611120690827_<17> · 489257181515888972676839_<24> · C141

C141 = P40 · C102

P40 = 2732757469571315596232602778709665753077_<40>

C102 = [133107996965441716078569858100441760864844458768441551457233330059494248457182487821678740490382903923_<102>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1234666248
Step 1 took 43505ms
Step 2 took 20647ms
********** Factor found in step 2: 2732757469571315596232602778709665753077
Found probable prime factor of 40 digits: 2732757469571315596232602778709665753077
Composite cofactor 133107996965441716078569858100441760864844458768441551457233330059494248457182487821678740490382903923 has 102 digits

Jan 9, 2009

By Wataru Sakai / Msieve / Jan 9, 2009

(10¹⁸⁹+53)/9 = (1)₁₈₈7_<189> = 3 · 13 · 281 · 15696287951_<11> · C174

C174 = P43 · P132

P43 = 2966053554214492112333066088061367989981783_<43>

P132 = 217776301578075309920820042799517030257727277508499057170455912299319301245210201540772768640946562600901533506129647135786653246811_<132>

Number: 11117_189
N=645936173319337380411863953498993104769684528176623414613699613686861428843235993970593716471912306280514580984750785536925480164420937113239219942611158442079139517692844013
  ( 174 digits)
SNFS difficulty: 189 digits.
Divisors found:
 r1=2966053554214492112333066088061367989981783
 r2=217776301578075309920820042799517030257727277508499057170455912299319301245210201540772768640946562600901533506129647135786653246811
Version: 
Total time: 388.16 hours.
Scaled time: 780.19 units (timescale=2.010).
Factorization parameters were as follows:
n: 645936173319337380411863953498993104769684528176623414613699613686861428843235993970593716471912306280514580984750785536925480164420937113239219942611158442079139517692844013
m: 50000000000000000000000000000000000000
deg: 5
c5: 16
c0: 265
skew: 1.75
type: snfs
lss: 1
rlim: 10200000
alim: 10200000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 10200000/10200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5100000, 8700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1819800 x 1820048
Total sieving time: 388.16 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,189,5,0,0,0,0,0,0,0,0,10200000,10200000,28,28,54,54,2.5,2.5,100000
total time: 388.16 hours.
 --------- CPU info (if available) ----------

Jan 8, 2009 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve v1.39 / Jan 8, 2009

(38·10¹⁹³+43)/9 = 4(2)₁₉₂7_<194> = C194

C194 = P90 · P105

P90 = 152784569578034018071739097799518165623885883503374346108642124458545616770104505255344901_<90>

P105 = 276351351048296902131663932803456124639908210818778760937627498047154906872033486981422679102588102399927_<105>

Number: 42227_193
N=42222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
  ( 194 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=152784569578034018071739097799518165623885883503374346108642124458545616770104505255344901
 r2=276351351048296902131663932803456124639908210818778760937627498047154906872033486981422679102588102399927
Version: 
Total time: 392.71 hours.
Scaled time: 938.57 units (timescale=2.390).
Factorization parameters were as follows:
n: 42222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
m: 1000000000000000000000000000000000000000
deg: 5
c5: 19
c0: 2150
skew: 2.57
type: snfs
lss: 1
rlim: 16000000
alim: 16000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 16000000/16000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [8000000, 17100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 24324690
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2685234 x 2685482
Total sieving time: 359.53 hours.
Total relation processing time: 12.20 hours.
Matrix solve time: 20.58 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,16000000,16000000,28,28,55,55,2.5,2.5,100000
total time: 392.71 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047064k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804)
Calibrating delay using timer specific routine.. 5344.80 BogoMIPS (lpj=2672401)
Calibrating delay using timer specific routine.. 5344.34 BogoMIPS (lpj=2672172)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Jan 8, 2009

By Robert Backstrom / GGNFS, Msieve / Jan 8, 2009

(29·10¹⁸⁶+43)/9 = 3(2)₁₈₅7_<187> = 4703 · C183

C183 = P69 · P115

P69 = 555923217597268132599534094433976495047551289000224776872217296769257_<69>

P115 = 1232439750546506891785593310267887304617348141319633071530047011017494600720295029123922027255808926803985878794437_<115>

Number: n
N=685141871618588607744465707468046400642615824414676211401705767004512486119970704278592860349186098707680676636662177806128475913719375339617738086800387459541191201833345146124223309
  ( 183 digits)
SNFS difficulty: 187 digits.
Divisors found:

Thu Jan 08 04:20:59 2009  prp69 factor: 555923217597268132599534094433976495047551289000224776872217296769257
Thu Jan 08 04:20:59 2009  prp115 factor: 1232439750546506891785593310267887304617348141319633071530047011017494600720295029123922027255808926803985878794437
Thu Jan 08 04:20:59 2009  elapsed time 06:18:34 (Msieve 1.39 - dependency 3)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.95 hours.
Scaled time: 61.25 units (timescale=2.045).
Factorization parameters were as follows:
name: KA_3_2_185_7
n: 685141871618588607744465707468046400642615824414676211401705767004512486119970704278592860349186098707680676636662177806128475913719375339617738086800387459541191201833345146124223309
deg: 5
c5: 290
c0: 43
m: 10000000000000000000000000000000000000
skew: 0.68
type: snfs
rlim: 8500000
alim: 8500000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 8500000/8500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 56/56
Sieved  special-q in [100000, 10294351)
Primes: RFBsize:571119, AFBsize:569357, largePrimes:21303335 encountered
Relations: rels:21658760, finalFF:1003877
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 2773120 hash collisions in 23837692 relations
Msieve: matrix is 1553711 x 1553959 (416.7 MB)

Total sieving time: 28.98 hours.
Total relation processing time: 0.97 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,8500000,8500000,28,28,56,56,2.5,2.5,100000
total time: 29.95 hours.
 --------- CPU info (if available) ----------

Jan 6, 2009 (5th)

By Wataru Sakai / Msieve / Jan 6, 2009

(38·10¹⁹⁵+61)/9 = 4(2)₁₉₄9_<196> = C196

C196 = P63 · P134

P63 = 115667220018910122248194085154980724584857915458079192026711121_<63>

P134 = 36503187519609639479341262940543033550745399336765316360179329732149272103637012814543123192279806906800310222096607380858092086521349_<134>

Number: 42229_195
N=4222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
  ( 196 digits)
SNFS difficulty: 196 digits.
Divisors found:
 r1=115667220018910122248194085154980724584857915458079192026711121
 r2=36503187519609639479341262940543033550745399336765316360179329732149272103637012814543123192279806906800310222096607380858092086521349
Version: 
Total time: 671.52 hours.
Scaled time: 1286.64 units (timescale=1.916).
Factorization parameters were as follows:
n: 4222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229
m: 1000000000000000000000000000000000000000
deg: 5
c5: 38
c0: 61
skew: 1.10
type: snfs
lss: 1
rlim: 13200000
alim: 13200000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 13200000/13200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6600000, 13100001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2267319 x 2267567
Total sieving time: 671.52 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,196,5,0,0,0,0,0,0,0,0,13200000,13200000,28,28,55,55,2.5,2.5,100000
total time: 671.52 hours.
 --------- CPU info (if available) ----------

10¹⁸⁹+3 = 1(0)₁₈₈3_<190> = 149 · 2579 · 7541 · 18804384407_<11> · 89411784830227_<14> · C156

C156 = P69 · P87

P69 = 302326156316901099415054234018340088084227443035320038122354865868161_<69>

P87 = 678896924250950617425559235848387983568344761375171256368612766118378019400194027494837_<87>

Number: 10003_189
N=205248297644156261196720985253614172077029245438613226830452987675960883098054087210769404046438306485121986264348749244919350699056988552234916435950184757
  ( 156 digits)
SNFS difficulty: 189 digits.
Divisors found:
 r1=302326156316901099415054234018340088084227443035320038122354865868161
 r2=678896924250950617425559235848387983568344761375171256368612766118378019400194027494837
Version: 
Total time: 342.40 hours.
Scaled time: 599.54 units (timescale=1.751).
Factorization parameters were as follows:
n: 205248297644156261196720985253614172077029245438613226830452987675960883098054087210769404046438306485121986264348749244919350699056988552234916435950184757
m: 50000000000000000000000000000000000000
deg: 5
c5: 16
c0: 15
skew: 0.99
type: snfs
lss: 1
rlim: 10200000
alim: 10200000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5Factor base limits: 10200000/10200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [5100000, 8700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1273208 x 1273456
Total sieving time: 342.40 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,189,5,0,0,0,0,0,0,0,0,10200000,10200000,28,28,54,54,2.5,2.5,100000
total time: 342.40 hours.
 --------- CPU info (if available) ----------

Jan 6, 2009 (4th)

By Serge Batalov / PFGW / Jan 6, 2009

(5·10³⁸⁶⁹⁰+31)/9 = (5)₃₈₆₈₉9_<38690> is PRP.

(5·10³⁹⁴⁶⁴+31)/9 = (5)₃₉₄₆₃9_<39464> is PRP.

Jan 6, 2009 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Jan 6, 2009

4·10²⁰⁷+1 = 4(0)₂₀₆1_<208> = C208

C208 = P43 · P46 · P55 · P66

P43 = 2137537151086140780378598137246884887064851_<43>

P46 = 2812726946992196303955780250469663669810710081_<46>

P55 = 4510386964277796118081223118223701478503227449062032837_<55>

P66 = 147504388817832250629782059406052001349839987803889705588283463583_<66>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM]
Input number is 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 (208 digits)
Using B1=3628000, B2=8561127130, polynomial Dickson(6), sigma=3845259699
Step 1 took 70828ms
Step 2 took 27344ms
********** Factor found in step 2: 2137537151086140780378598137246884887064851
Found probable prime factor of 43 digits: 2137537151086140780378598137246884887064851
Composite cofactor 1871312504658686833048859441299535119697043458364557065452864462272856482238047511640262600039514668896561348370461632396040769157857079230807910497093290327153082651 has 166 digits

Number: n
N=1871312504658686833048859441299535119697043458364557065452864462272856482238047511640262600039514668896561348370461632396040769157857079230807910497093290327153082651
  ( 166 digits)
SNFS difficulty: 207 digits.
Divisors found:

Tue Jan  6 12:17:23 2009  prp46 factor: 2812726946992196303955780250469663669810710081
Tue Jan  6 12:17:23 2009  prp55 factor: 4510386964277796118081223118223701478503227449062032837
Tue Jan  6 12:17:23 2009  prp66 factor: 147504388817832250629782059406052001349839987803889705588283463583
Tue Jan  6 12:17:23 2009  elapsed time 17:15:12 (Msieve 1.39 - dependency 4)

Version: GGNFS-0.77.1-20050930-k8
Total time: 101.97 hours.
Scaled time: 204.97 units (timescale=2.010).
Factorization parameters were as follows:
name: KA_4_0_206_1
n: 1871312504658686833048859441299535119697043458364557065452864462272856482238047511640262600039514668896561348370461632396040769157857079230807910497093290327153082651

# n: 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001

deg: 5
c5: 25
c0: 2
m: 200000000000000000000000000000000000000000
skew: 0.60
type: snfs
rlim: 10000000
alim: 10000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved  special-q in [100000, 30599990)
Primes: RFBsize:664579, AFBsize:664295, largePrimes:36509320 encountered
Relations: rels:31588687, finalFF:75919
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 

Msieve: found 7840833 hash collisions in 43268992 relations
Msieve: matrix is 3150865 x 3151113 (859.6 MB)

Total sieving time: 100.96 hours.
Total relation processing time: 1.01 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,207,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000
total time: 101.97 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU1: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU2: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
CPU3: Intel(R) Core(TM)2 Quad  CPU   Q9550  @ 2.83GHz stepping 07
Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem)
Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.96 BogoMIPS (lpj=2830481)
Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459)
Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456)
Total of 4 processors activated (22643.69 BogoMIPS).

Jan 6, 2009 (2nd)

By Justin Card / ggnfs,msieve / Jan 6, 2009

(29·10¹¹²+43)/9 = 3(2)₁₁₁7_<113> = 13 · 37 · 103 · 43239121 · C101

C101 = P29 · P72

P29 = 45090396972221616172354904437_<29>

P72 = 333589422784143321541957121594048625347148135316145689550420073192386257_<72>

Sun Dec  7 00:36:59 2008  Msieve v. 1.39
Sun Dec  7 00:36:59 2008  random seeds: 760852d7 bc69bd5e
Sun Dec  7 00:36:59 2008  factoring 15041679499071292646284989557979980982308780587943355373610269065634432656659938885011590841227122309 (101 digits)
Sun Dec  7 00:37:00 2008  searching for 15-digit factors
Sun Dec  7 00:37:00 2008  commencing number field sieve (101-digit input)
Sun Dec  7 00:37:00 2008  R0: -20000000000000000000000
Sun Dec  7 00:37:00 2008  R1:  1
Sun Dec  7 00:37:00 2008  A0:  344
Sun Dec  7 00:37:00 2008  A1:  0
Sun Dec  7 00:37:00 2008  A2:  0
Sun Dec  7 00:37:00 2008  A3:  0
Sun Dec  7 00:37:00 2008  A4:  0
Sun Dec  7 00:37:00 2008  A5:  725
Sun Dec  7 00:37:00 2008  skew 1.00, size 2.348152e-08, alpha 0.523263, combined = 1.972314e-08
Sun Dec  7 00:37:00 2008
Sun Dec  7 00:37:00 2008  commencing relation filtering
Sun Dec  7 00:37:00 2008  commencing duplicate removal, pass 1
Sun Dec  7 00:37:00 2008  error -9 reading relation 57
Sun Dec  7 00:37:00 2008  error -9 reading relation 600
Sun Dec  7 00:37:01 2008  error -9 reading relation 6662
Sun Dec  7 00:37:16 2008  found 62189 hash collisions in 1229541 relations
Sun Dec  7 00:37:20 2008  added 7524 free relations
Sun Dec  7 00:37:20 2008  commencing duplicate removal, pass 2
Sun Dec  7 00:37:21 2008  found 62231 duplicates and 1174834 unique relations
Sun Dec  7 00:37:21 2008  memory use: 36.9 MB
Sun Dec  7 00:37:21 2008  reading rational ideals above 458752
Sun Dec  7 00:37:21 2008  reading algebraic ideals above 458752
Sun Dec  7 00:37:21 2008  commencing singleton removal, pass 1
Sun Dec  7 00:37:37 2008  relations with 0 large ideals: 17359
Sun Dec  7 00:37:37 2008  relations with 1 large ideals: 170040
Sun Dec  7 00:37:37 2008  relations with 2 large ideals: 503738
Sun Dec  7 00:37:37 2008  relations with 3 large ideals: 322915
Sun Dec  7 00:37:37 2008  relations with 4 large ideals: 78947
Sun Dec  7 00:37:37 2008  relations with 5 large ideals: 9452
Sun Dec  7 00:37:37 2008  relations with 6 large ideals: 72368
Sun Dec  7 00:37:37 2008  relations with 7+ large ideals: 15
Sun Dec  7 00:37:37 2008  1174834 relations and about 1430364 large ideals
Sun Dec  7 00:37:37 2008  commencing singleton removal, pass 2
Sun Dec  7 00:37:53 2008  found 678514 singletons
Sun Dec  7 00:37:53 2008  current dataset: 496320 relations and about 407268 large ideals
Sun Dec  7 00:37:53 2008  commencing singleton removal, pass 3
Sun Dec  7 00:37:59 2008  found 143234 singletons
Sun Dec  7 00:37:59 2008  current dataset: 353086 relations and about 251585 large ideals
Sun Dec  7 00:37:59 2008  commencing singleton removal, final pass
Sun Dec  7 00:38:03 2008  memory use: 11.7 MB
Sun Dec  7 00:38:03 2008  commencing in-memory singleton removal
Sun Dec  7 00:38:03 2008  begin with 353086 relations and 253896 unique ideals
Sun Dec  7 00:38:04 2008  reduce to 310065 relations and 209765 ideals in 10 passes
Sun Dec  7 00:38:04 2008  max relations containing the same ideal: 38
Sun Dec  7 00:38:04 2008  reading rational ideals above 229376
Sun Dec  7 00:38:04 2008  reading algebraic ideals above 229376
Sun Dec  7 00:38:04 2008  commencing singleton removal, final pass
Sun Dec  7 00:38:08 2008  keeping 280459 ideals with weight <= 20, new excess is 51103
Sun Dec  7 00:38:09 2008  memory use: 11.7 MB
Sun Dec  7 00:38:09 2008  commencing in-memory singleton removal
Sun Dec  7 00:38:09 2008  begin with 317593 relations and 280459 unique ideals
Sun Dec  7 00:38:09 2008  reduce to 309989 relations and 235373 ideals in 4 passes
Sun Dec  7 00:38:09 2008  max relations containing the same ideal: 20
Sun Dec  7 00:38:09 2008  relations with 0 large ideals: 5366
Sun Dec  7 00:38:09 2008  relations with 1 large ideals: 31032
Sun Dec  7 00:38:09 2008  relations with 2 large ideals: 79805
Sun Dec  7 00:38:09 2008  relations with 3 large ideals: 98556
Sun Dec  7 00:38:09 2008  relations with 4 large ideals: 62857
Sun Dec  7 00:38:09 2008  relations with 5 large ideals: 23612
Sun Dec  7 00:38:09 2008  relations with 6 large ideals: 8091
Sun Dec  7 00:38:09 2008  relations with 7+ large ideals: 670
Sun Dec  7 00:38:09 2008  commencing 2-way merge
Sun Dec  7 00:38:09 2008  reduce to 194123 relation sets and 119507 unique ideals
Sun Dec  7 00:38:09 2008  commencing full merge
Sun Dec  7 00:38:12 2008  memory use: 9.9 MB
Sun Dec  7 00:38:12 2008  found 80647 cycles, need 65707
Sun Dec  7 00:38:12 2008  weight of 65707 cycles is about 5097139 (77.57/cycle)
Sun Dec  7 00:38:12 2008  distribution of cycle lengths:
Sun Dec  7 00:38:12 2008  1 relations: 6358
Sun Dec  7 00:38:12 2008  2 relations: 5050
Sun Dec  7 00:38:12 2008  3 relations: 5181
Sun Dec  7 00:38:12 2008  4 relations: 5044
Sun Dec  7 00:38:12 2008  5 relations: 4944
Sun Dec  7 00:38:12 2008  6 relations: 4810
Sun Dec  7 00:38:12 2008  7 relations: 4483
Sun Dec  7 00:38:12 2008  8 relations: 4259
Sun Dec  7 00:38:12 2008  9 relations: 3928
Sun Dec  7 00:38:12 2008  10+ relations: 21650
Sun Dec  7 00:38:12 2008  heaviest cycle: 20 relations
Sun Dec  7 00:38:12 2008  commencing cycle optimization
Sun Dec  7 00:38:13 2008  start with 486593 relations
Sun Dec  7 00:38:14 2008  pruned 33805 relations
Sun Dec  7 00:38:14 2008  memory use: 13.5 MB
Sun Dec  7 00:38:14 2008  distribution of cycle lengths:
Sun Dec  7 00:38:14 2008  1 relations: 6358
Sun Dec  7 00:38:14 2008  2 relations: 5301
Sun Dec  7 00:38:14 2008  3 relations: 5583
Sun Dec  7 00:38:14 2008  4 relations: 5487
Sun Dec  7 00:38:14 2008  5 relations: 5416
Sun Dec  7 00:38:14 2008  6 relations: 5327
Sun Dec  7 00:38:14 2008  7 relations: 4957
Sun Dec  7 00:38:14 2008  8 relations: 4627
Sun Dec  7 00:38:14 2008  9 relations: 4289
Sun Dec  7 00:38:14 2008  10+ relations: 18362
Sun Dec  7 00:38:14 2008  heaviest cycle: 19 relations
Sun Dec  7 00:38:14 2008  elapsed time 00:01:15
Sun Dec  7 00:38:14 2008
Sun Dec  7 00:38:14 2008
Sun Dec  7 00:38:14 2008  Msieve v. 1.39
Sun Dec  7 00:38:14 2008  random seeds: 1b990db7 ba65cf40
Sun Dec  7 00:38:14 2008  factoring 15041679499071292646284989557979980982308780587943355373610269065634432656659938885011590841227122309 (101 digits)
Sun Dec  7 00:38:15 2008  searching for 15-digit factors
Sun Dec  7 00:38:16 2008  commencing number field sieve (101-digit input)
Sun Dec  7 00:38:16 2008  R0: -20000000000000000000000
Sun Dec  7 00:38:16 2008  R1:  1
Sun Dec  7 00:38:16 2008  A0:  344
Sun Dec  7 00:38:16 2008  A1:  0
Sun Dec  7 00:38:16 2008  A2:  0Sun Dec  7 00:38:16 2008  A3:  0
Sun Dec  7 00:38:16 2008  A4:  0
Sun Dec  7 00:38:16 2008  A5:  725
Sun Dec  7 00:38:16 2008  skew 1.00, size 2.348152e-08, alpha 0.523263, combined = 1.972314e-08
Sun Dec  7 00:38:16 2008
Sun Dec  7 00:38:16 2008  commencing linear algebra
Sun Dec  7 00:38:16 2008  read 65707 cycles
Sun Dec  7 00:38:16 2008  cycles contain 206245 unique relations
Sun Dec  7 00:38:18 2008  read 206245 relations
Sun Dec  7 00:38:19 2008  using 20 quadratic characters above 33552150
Sun Dec  7 00:38:21 2008  building initial matrix
Sun Dec  7 00:38:23 2008  memory use: 32.0 MB
Sun Dec  7 00:38:23 2008  read 65707 cycles
Sun Dec  7 00:38:24 2008  matrix is 65498 x 65707 (20.1 MB) with weight 6006938 (91.42/col)
Sun Dec  7 00:38:24 2008  sparse part has weight 4541869 (69.12/col)
Sun Dec  7 00:38:25 2008  filtering completed in 2 passes
Sun Dec  7 00:38:25 2008  matrix is 65276 x 65476 (20.0 MB) with weight 5989908 (91.48/col)
Sun Dec  7 00:38:25 2008  sparse part has weight 4530167 (69.19/col)
Sun Dec  7 00:38:25 2008  read 65476 cyclesSun Dec  7 00:38:25 2008  matrix is 65276 x 65476 (20.0 MB) with weight 5989908 (91.48/col)
Sun Dec  7 00:38:25 2008  sparse part has weight 4530167 (69.19/col)
Sun Dec  7 00:38:25 2008  saving the first 48 matrix rows for later
Sun Dec  7 00:38:25 2008  matrix is 65228 x 65476 (18.6 MB) with weight 4719058 (72.07/col)
Sun Dec  7 00:38:25 2008  sparse part has weight 4224151 (64.51/col)
Sun Dec  7 00:38:25 2008  matrix includes 64 packed rows
Sun Dec  7 00:38:25 2008  using block size 10922 for processor cache size 256 kB
Sun Dec  7 00:38:26 2008  commencing Lanczos iteration
Sun Dec  7 00:38:26 2008  memory use: 16.7 MB
Sun Dec  7 00:39:09 2008  lanczos halted after 1033 iterations (dim = 65228)
Sun Dec  7 00:39:09 2008  recovered 39 nontrivial dependencies
Sun Dec  7 00:39:09 2008  elapsed time 00:00:55
Sun Dec  7 00:39:09 2008
Sun Dec  7 00:39:09 2008
Sun Dec  7 00:39:09 2008  Msieve v. 1.39
Sun Dec  7 00:39:09 2008  random seeds: 226198c7 36d1bb1e
Sun Dec  7 00:39:09 2008  factoring 15041679499071292646284989557979980982308780587943355373610269065634432656659938885011590841227122309 (101 digits)
Sun Dec  7 00:39:10 2008  searching for 15-digit factors
Sun Dec  7 00:39:11 2008  commencing number field sieve (101-digit input)
Sun Dec  7 00:39:11 2008  R0: -20000000000000000000000
Sun Dec  7 00:39:11 2008  R1:  1
Sun Dec  7 00:39:11 2008  A0:  344
Sun Dec  7 00:39:11 2008  A1:  0
Sun Dec  7 00:39:11 2008  A2:  0
Sun Dec  7 00:39:11 2008  A3:  0
Sun Dec  7 00:39:11 2008  A4:  0
Sun Dec  7 00:39:11 2008  A5:  725
Sun Dec  7 00:39:11 2008  skew 1.00, size 2.348152e-08, alpha 0.523263, combined = 1.972314e-08
Sun Dec  7 00:39:11 2008
Sun Dec  7 00:39:11 2008  commencing square root phase
Sun Dec  7 00:39:11 2008  reading relations for dependency 1
Sun Dec  7 00:39:11 2008  read 32712 cycles
Sun Dec  7 00:39:11 2008  cycles contain 128877 unique relations
Sun Dec  7 00:39:13 2008  read 128877 relations
Sun Dec  7 00:39:13 2008  multiplying 102694 relations
Sun Dec  7 00:39:22 2008  multiply complete, coefficients have about 2.89 million bits
Sun Dec  7 00:39:22 2008  initial square root is modulo 4567151
Sun Dec  7 00:39:38 2008  prp29 factor: 45090396972221616172354904437
Sun Dec  7 00:39:38 2008  prp72 factor: 333589422784143321541957121594048625347148135316145689550420073192386257
Sun Dec  7 00:39:38 2008  elapsed time 00:00:29

Jan 6, 2009

By Tyler Cadigan / ggnfs, msieve / Jan 6, 2009

(43·10¹⁸⁴-7)/9 = 4(7)₁₈₄_<185> = 53 · 26287823 · 4895902625197_<13> · C163

C163 = P81 · P83

P81 = 100986265192381720719980286210366635840357108525083480574351389325029919037606947_<81>

P83 = 69358608608073139344127843528616553111361386937716623546623185659992381518608784037_<83>

Number: 47777_184
N=7004266842269483659952767910075690687168034383305029594855242179827887829067467896729417906148100412760492466019505809155804252673388696948980973408703058013905039
  ( 163 digits)
SNFS difficulty: 186 digits.
Divisors found:
 r1=100986265192381720719980286210366635840357108525083480574351389325029919037606947
 r2=69358608608073139344127843528616553111361386937716623546623185659992381518608784037
Version: 
Total time: 347.18 hours.
Scaled time: 889.14 units (timescale=2.561).
Factorization parameters were as follows:
n: 7004266842269483659952767910075690687168034383305029594855242179827887829067467896729417906148100412760492466019505809155804252673388696948980973408703058013905039
m: 10000000000000000000000000000000000000
deg: 5
c5: 43
c0: -70
skew: 1.10
type: snfs
lss: 1
rlim: 9000000
alim: 9000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
qintsize: 1000000Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4500000, 9500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1331819 x 1332067
Total sieving time: 347.18 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000
total time: 347.18 hours.
 --------- CPU info (if available) ----------

Jan 5, 2009 (8th)

By Luigi Morelli / GGNFS 0.77.1, msieve / Jan 4, 2009

(38·10¹⁷⁴-11)/9 = 4(2)₁₇₃1_<175> = 3³ · 7629737812981_<13> · 31668315658185358241_<20> · 64583320974668012969282589628685014327_<38> · C104

C104 = P44 · P60

P44 = 13572177173944141379230865642040566250314827_<44>

P60 = 738367971619864478723854016085408967268073560203846001125847_<60>

Sat Jan  3 17:34:21 2009  Msieve v. 1.39
Sat Jan  3 17:34:21 2009  random seeds: 811586e7 042c0979
Sat Jan  3 17:34:21 2009  factoring 10021260930390560266594511156264428707661578748567959642375971936717369835041789453030241615860197033469 (104 digits)
Sat Jan  3 17:34:24 2009  searching for 15-digit factors
Sat Jan  3 17:34:26 2009  commencing number field sieve (104-digit input)
Sat Jan  3 17:34:26 2009  R0: -41755367312430798657
Sat Jan  3 17:34:26 2009  R1:  129924582887
Sat Jan  3 17:34:26 2009  A0: -12813572907496742341700
Sat Jan  3 17:34:26 2009  A1:  688027892716311984598
Sat Jan  3 17:34:26 2009  A2:  343348771692294918
Sat Jan  3 17:34:26 2009  A3: -3426111865027
Sat Jan  3 17:34:26 2009  A4: -2705875132
Sat Jan  3 17:34:26 2009  A5:  78960
Sat Jan  3 17:34:26 2009  skew 1.00, size 1.020312e-10, alpha -6.266562, combined = 8.239688e-10
Sat Jan  3 17:34:26 2009  
Sat Jan  3 17:34:26 2009  commencing relation filtering
Sat Jan  3 17:34:26 2009  commencing duplicate removal, pass 1
Sat Jan  3 17:36:04 2009  found 333597 hash collisions in 4633238 relations
Sat Jan  3 17:36:40 2009  added 31398 free relations
Sat Jan  3 17:36:40 2009  commencing duplicate removal, pass 2
Sat Jan  3 17:36:47 2009  found 311101 duplicates and 4353535 unique relations
Sat Jan  3 17:36:47 2009  memory use: 43.3 MB
Sat Jan  3 17:36:47 2009  reading rational ideals above 1900544
Sat Jan  3 17:36:47 2009  reading algebraic ideals above 1900544
Sat Jan  3 17:36:47 2009  commencing singleton removal, pass 1
Sat Jan  3 17:38:25 2009  relations with 0 large ideals: 66751
Sat Jan  3 17:38:25 2009  relations with 1 large ideals: 508305
Sat Jan  3 17:38:25 2009  relations with 2 large ideals: 1420633
Sat Jan  3 17:38:25 2009  relations with 3 large ideals: 1653235
Sat Jan  3 17:38:25 2009  relations with 4 large ideals: 658720
Sat Jan  3 17:38:25 2009  relations with 5 large ideals: 15644
Sat Jan  3 17:38:25 2009  relations with 6 large ideals: 30247
Sat Jan  3 17:38:25 2009  relations with 7+ large ideals: 0
Sat Jan  3 17:38:25 2009  4353535 relations and about 4377821 large ideals
Sat Jan  3 17:38:25 2009  commencing singleton removal, pass 2
Sat Jan  3 17:40:01 2009  found 1971537 singletons
Sat Jan  3 17:40:01 2009  current dataset: 2381998 relations and about 1995952 large ideals
Sat Jan  3 17:40:01 2009  commencing singleton removal, pass 3
Sat Jan  3 17:40:56 2009  found 459886 singletons
Sat Jan  3 17:40:56 2009  current dataset: 1922112 relations and about 1500649 large ideals
Sat Jan  3 17:40:56 2009  commencing singleton removal, final pass
Sat Jan  3 17:41:44 2009  memory use: 37.3 MB
Sat Jan  3 17:41:44 2009  commencing in-memory singleton removal
Sat Jan  3 17:41:45 2009  begin with 1922112 relations and 1542283 unique ideals
Sat Jan  3 17:41:51 2009  reduce to 1596578 relations and 1207151 ideals in 15 passes
Sat Jan  3 17:41:51 2009  max relations containing the same ideal: 18
Sat Jan  3 17:41:53 2009  reading rational ideals above 720000
Sat Jan  3 17:41:53 2009  reading algebraic ideals above 720000
Sat Jan  3 17:41:53 2009  commencing singleton removal, final pass
Sat Jan  3 17:42:38 2009  keeping 1386175 ideals with weight <= 20, new excess is 174884
Sat Jan  3 17:42:39 2009  memory use: 46.5 MB
Sat Jan  3 17:42:40 2009  commencing in-memory singleton removal
Sat Jan  3 17:42:40 2009  begin with 1608672 relations and 1386175 unique ideals
Sat Jan  3 17:42:45 2009  reduce to 1594481 relations and 1314144 ideals in 12 passes
Sat Jan  3 17:42:45 2009  max relations containing the same ideal: 20
Sat Jan  3 17:42:48 2009  removing 283569 relations and 244833 ideals in 38736 cliques
Sat Jan  3 17:42:48 2009  commencing in-memory singleton removal
Sat Jan  3 17:42:49 2009  begin with 1310912 relations and 1314144 unique ideals
Sat Jan  3 17:42:52 2009  reduce to 1278048 relations and 1035423 ideals in 10 passes
Sat Jan  3 17:42:52 2009  max relations containing the same ideal: 20
Sat Jan  3 17:42:54 2009  removing 211724 relations and 172988 ideals in 38736 cliques
Sat Jan  3 17:42:54 2009  commencing in-memory singleton removal
Sat Jan  3 17:42:55 2009  begin with 1066324 relations and 1035423 unique ideals
Sat Jan  3 17:42:57 2009  reduce to 1040992 relations and 836386 ideals in 8 passes
Sat Jan  3 17:42:57 2009  max relations containing the same ideal: 20
Sat Jan  3 17:42:59 2009  relations with 0 large ideals: 23367
Sat Jan  3 17:42:59 2009  relations with 1 large ideals: 137128
Sat Jan  3 17:42:59 2009  relations with 2 large ideals: 316252
Sat Jan  3 17:42:59 2009  relations with 3 large ideals: 342472
Sat Jan  3 17:42:59 2009  relations with 4 large ideals: 175722
Sat Jan  3 17:42:59 2009  relations with 5 large ideals: 40480
Sat Jan  3 17:42:59 2009  relations with 6 large ideals: 5342
Sat Jan  3 17:42:59 2009  relations with 7+ large ideals: 229
Sat Jan  3 17:42:59 2009  commencing 2-way merge
Sat Jan  3 17:43:01 2009  reduce to 620654 relation sets and 416048 unique ideals
Sat Jan  3 17:43:01 2009  commencing full merge
Sat Jan  3 17:43:15 2009  memory use: 35.2 MB
Sat Jan  3 17:43:15 2009  found 281974 cycles, need 256248
Sat Jan  3 17:43:15 2009  weight of 256248 cycles is about 18213555 (71.08/cycle)
Sat Jan  3 17:43:15 2009  distribution of cycle lengths:
Sat Jan  3 17:43:15 2009  1 relations: 31071
Sat Jan  3 17:43:15 2009  2 relations: 24040
Sat Jan  3 17:43:15 2009  3 relations: 23564
Sat Jan  3 17:43:15 2009  4 relations: 22461
Sat Jan  3 17:43:15 2009  5 relations: 21110
Sat Jan  3 17:43:15 2009  6 relations: 19272
Sat Jan  3 17:43:15 2009  7 relations: 17944
Sat Jan  3 17:43:15 2009  8 relations: 16146
Sat Jan  3 17:43:15 2009  9 relations: 14902
Sat Jan  3 17:43:15 2009  10+ relations: 65738
Sat Jan  3 17:43:15 2009  heaviest cycle: 18 relations
Sat Jan  3 17:43:15 2009  commencing cycle optimization
Sat Jan  3 17:43:17 2009  start with 1677773 relations
Sat Jan  3 17:43:25 2009  pruned 57629 relations
Sat Jan  3 17:43:25 2009  memory use: 53.4 MB
Sat Jan  3 17:43:25 2009  distribution of cycle lengths:
Sat Jan  3 17:43:25 2009  1 relations: 31071
Sat Jan  3 17:43:25 2009  2 relations: 24750
Sat Jan  3 17:43:25 2009  3 relations: 24618
Sat Jan  3 17:43:25 2009  4 relations: 23440
Sat Jan  3 17:43:25 2009  5 relations: 21963
Sat Jan  3 17:43:25 2009  6 relations: 19954
Sat Jan  3 17:43:25 2009  7 relations: 18480
Sat Jan  3 17:43:25 2009  8 relations: 16597
Sat Jan  3 17:43:25 2009  9 relations: 15206
Sat Jan  3 17:43:25 2009  10+ relations: 60169
Sat Jan  3 17:43:25 2009  heaviest cycle: 18 relations
Sat Jan  3 17:43:27 2009  
Sat Jan  3 17:43:27 2009  commencing linear algebra
Sat Jan  3 17:43:27 2009  read 256248 cycles
Sat Jan  3 17:43:28 2009  cycles contain 881602 unique relations
Sat Jan  3 17:43:49 2009  read 881602 relations
Sat Jan  3 17:43:52 2009  using 20 quadratic characters above 67108004
Sat Jan  3 17:44:06 2009  building initial matrix
Sat Jan  3 17:44:32 2009  memory use: 113.5 MB
Sat Jan  3 17:44:32 2009  read 256248 cycles
Sat Jan  3 17:44:33 2009  matrix is 255986 x 256248 (76.0 MB) with weight 24294011 (94.81/col)
Sat Jan  3 17:44:33 2009  sparse part has weight 17112766 (66.78/col)
Sat Jan  3 17:44:47 2009  filtering completed in 3 passes
Sat Jan  3 17:44:47 2009  matrix is 254372 x 254572 (75.7 MB) with weight 24167826 (94.94/col)
Sat Jan  3 17:44:47 2009  sparse part has weight 17038763 (66.93/col)
Sat Jan  3 17:44:49 2009  read 254572 cycles
Sat Jan  3 17:44:50 2009  matrix is 254372 x 254572 (75.7 MB) with weight 24167826 (94.94/col)
Sat Jan  3 17:44:50 2009  sparse part has weight 17038763 (66.93/col)
Sat Jan  3 17:44:50 2009  saving the first 48 matrix rows for later
Sat Jan  3 17:44:50 2009  matrix is 254324 x 254572 (73.0 MB) with weight 19149842 (75.22/col)
Sat Jan  3 17:44:50 2009  sparse part has weight 16585514 (65.15/col)
Sat Jan  3 17:44:50 2009  matrix includes 64 packed rows
Sat Jan  3 17:44:50 2009  using block size 65536 for processor cache size 2048 kB
Sat Jan  3 17:44:57 2009  commencing Lanczos iteration
Sat Jan  3 17:44:57 2009  memory use: 66.9 MB
Sat Jan  3 18:15:46 2009  lanczos halted after 4023 iterations (dim = 254323)
Sat Jan  3 18:15:48 2009  recovered 28 nontrivial dependencies
Sat Jan  3 18:15:48 2009  
Sat Jan  3 18:15:48 2009  commencing square root phase
Sat Jan  3 18:15:48 2009  reading relations for dependency 1
Sat Jan  3 18:15:48 2009  read 127522 cycles
Sat Jan  3 18:15:49 2009  cycles contain 543861 unique relations
Sat Jan  3 18:16:02 2009  read 543861 relations
Sat Jan  3 18:16:09 2009  multiplying 439974 relations
Sat Jan  3 18:18:40 2009  multiply complete, coefficients have about 19.10 million bits
Sat Jan  3 18:18:42 2009  initial square root is modulo 306049
Sat Jan  3 18:23:57 2009  prp44 factor: 13572177173944141379230865642040566250314827
Sat Jan  3 18:23:57 2009  prp60 factor: 738367971619864478723854016085408967268073560203846001125847
Sat Jan  3 18:23:57 2009  elapsed time 00:49:36

Jan 5, 2009 (7th)

By matsui / GMP-ECM / Jan 3, 2009

(38·10¹⁷⁷+7)/9 = 4(2)₁₇₆3_<178> = 16831 · C174

C174 = P33 · P141

P33 = 808020975537356813887688012648849_<33>

P141 = 310462058233838072707345486814826980908540325495516767238876034746810469799572718449241791002063641759970155278075383181344441444526372947617_<141>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]

250859855161441519946659272902514539969236659867044276764435994428270585361667293816304570270466533314848922953016589758316334277358577756652737343130070834901207428092342833
=
808020975537356813887688012648849* 310462058233838072707345486814826980908540325495516767238876034746810469799572718449241791002063641759970155278075383181344441444526372947617

Jan 5, 2009 (6th)

By Wataru Sakai / Msieve / Dec 28, 2008

(37·10¹⁹⁶+53)/9 = 4(1)₁₉₅7_<197> = C197

C197 = P57 · P66 · P74

P57 = 787928319933580324079324593875726511993688471405608499053_<57>

P66 = 706012788310465914244833920240020167224475218813102557627242440651_<66>

P74 = 73902637246869378978147840235120773789941657681890367360187082285806641539_<74>

Number: 41117_196
N=41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
  ( 197 digits)
SNFS difficulty: 197 digits.
Divisors found:
 r1=787928319933580324079324593875726511993688471405608499053
 r2=706012788310465914244833920240020167224475218813102557627242440651
 r3=73902637246869378978147840235120773789941657681890367360187082285806641539
Version: 
Total time: 1131.63 hours.
Scaled time: 2058.43 units (timescale=1.819).
Factorization parameters were as follows:
n: 41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117
m: 1000000000000000000000000000000000000000
deg: 5
c5: 370
c0: 53
skew: 0.68
type: snfs
lss: 1
rlim: 13700000
alim: 13700000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 13700000/13700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6850000, 19550001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2616836 x 2617084
Total sieving time: 1131.63 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,197,5,0,0,0,0,0,0,0,0,13700000,13700000,28,28,55,55,2.5,2.5,100000
total time: 1131.63 hours.
 --------- CPU info (if available) ----------

By Wataru Sakai / Msieve / Dec 28, 2008

10¹⁹⁵+3 = 1(0)₁₉₄3_<196> = 17 · 547 · 14549 · 3486070789921_<13> · 5665894963755404087_<19> · C156

C156 = P71 · P86

P71 = 20272161969880531371430224661237837143004245314829323956717291302611671_<71>

P86 = 18459750205074881191572660444812378965121433733944512974732242794281011685914941573309_<86>

Number: 10003_195
N=374219046080813346453326646441267156034345085487650370040062476729896969884729327545583720587165323414765099952683896438559950257399288091712019285405489339
  ( 156 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=20272161969880531371430224661237837143004245314829323956717291302611671
 r2=18459750205074881191572660444812378965121433733944512974732242794281011685914941573309
Version: 
Total time: 436.80 hours.
Scaled time: 880.16 units (timescale=2.015).
Factorization parameters were as follows:
n: 374219046080813346453326646441267156034345085487650370040062476729896969884729327545583720587165323414765099952683896438559950257399288091712019285405489339
m: 1000000000000000000000000000000000000000
deg: 5
c5: 1
c0: 3
skew: 1.25
type: snfs
lss: 1
rlim: 12400000
alim: 12400000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5Factor base limits: 12400000/12400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [6200000, 10500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2156382 x 2156628
Total sieving time: 436.80 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,12400000,12400000,28,28,55,55,2.5,2.5,100000
total time: 436.80 hours.
 --------- CPU info (if available) ----------

By Wataru Sakai / Msieve / Dec 28, 2008

(28·10¹⁹⁸+53)/9 = 3(1)₁₉₇7_<199> = 3² · C198

C198 = P40 · P158

P40 = 3649332252990078880852899480628274961427_<40>

P158 = 94723907932046213585023172949738787991480229480739179737363021751442282548661569399706013860101034321205826303279398761288808502140485924795670612716211919719_<158>

Number: 31117_198
N=345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679013
  ( 198 digits)
SNFS difficulty: 199 digits.
Divisors found:
 r1=3649332252990078880852899480628274961427
 r2=94723907932046213585023172949738787991480229480739179737363021751442282548661569399706013860101034321205826303279398761288808502140485924795670612716211919719
Version: 
Total time: 1064.77 hours.
Scaled time: 2123.15 units (timescale=1.994).
Factorization parameters were as follows:
n: 345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679013
m: 2000000000000000000000000000000000000000
deg: 5
c5: 875
c0: 53
skew: 0.57
type: snfs
lss: 1
rlim: 14800000
alim: 14800000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5
Factor base limits: 14800000/14800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 55/55
Sieved rational special-q in [7400000, 19400001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 2649513 x 2649761
Total sieving time: 1064.77 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,199,5,0,0,0,0,0,0,0,0,14800000,14800000,28,28,55,55,2.5,2.5,100000
total time: 1064.77 hours.
 --------- CPU info (if available) ----------

By Wataru Sakai / Msieve / Jan 4, 2009

(10¹⁸⁴+53)/9 = (1)₁₈₃7_<184> = 25931 · C179

C179 = P66 · P113

P66 = 792056942417260752013943287577332059199532709715550910871166602123_<66>

P113 = 54098076096087152994248770015733377320347175047305220233121079901747953425719984522642163758267738475346218307509_<113>

Number: 11117_184
N=42848756743323092480471679114230500602025032243689449350627091554938533458451703023836763376310636346886395091246427484906525437164440673753851032012306162936682392160391466241607
  ( 179 digits)
SNFS difficulty: 184 digits.
Divisors found:
 r1=792056942417260752013943287577332059199532709715550910871166602123
 r2=54098076096087152994248770015733377320347175047305220233121079901747953425719984522642163758267738475346218307509
Version: 
Total time: 323.64 hours.
Scaled time: 626.89 units (timescale=1.937).
Factorization parameters were as follows:
n: 42848756743323092480471679114230500602025032243689449350627091554938533458451703023836763376310636346886395091246427484906525437164440673753851032012306162936682392160391466241607
m: 5000000000000000000000000000000000000
deg: 5
c5: 16
c0: 265
skew: 1.75
type: snfs
lss: 1
rlim: 8400000
alim: 8400000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5
Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 54/54
Sieved rational special-q in [4200000, 7500001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1177876 x 1178124
Total sieving time: 323.64 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,184,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,54,54,2.5,2.5,100000
total time: 323.64 hours.
 --------- CPU info (if available) ----------

Jan 5, 2009 (5th)

By Jo Yeong Uk / GGNFS / Msieve v1.39 / Dec 27, 2008

(13·10¹⁸⁰-7)/3 = 4(3)₁₇₉1_<181> = C181

C181 = P45 · P137

P45 = 133183810233677421714973688754211562543765317_<45>

P137 = 32536487173105281333067272791516917637471199207130413085188359827144021898760251672172023912689675343132715372285707394906776189397129143_<137>

Number: 43331_180
N=4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
  ( 181 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=133183810233677421714973688754211562543765317
 r2=32536487173105281333067272791516917637471199207130413085188359827144021898760251672172023912689675343132715372285707394906776189397129143
Version: 
Total time: 91.31 hours.
Scaled time: 218.15 units (timescale=2.389).
Factorization parameters were as follows:
n: 4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
m: 1000000000000000000000000000000000000
deg: 5
c5: 13
c0: -7
skew: 0.88
type: snfs
lss: 1
rlim: 6400000
alim: 6400000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5
Factor base limits: 6400000/6400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 53/53
Sieved rational special-q in [3200000, 5700001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: 18375208
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 1307433 x 1307681
Total sieving time: 84.50 hours.
Total relation processing time: 2.37 hours.
Matrix solve time: 4.11 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,6400000,6400000,28,28,53,53,2.5,2.5,100000
total time: 91.31 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Intel(R) Core(TM)2 Quad CPU    Q6700  @ 2.66GHz stepping 0b
Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init)
Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803)
Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384)
Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880)
Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

By Jo Yeong Uk / GMP-ECM / Jan 3, 2008

(64·10²³³-1)/9 = 7(1)₂₃₃_<234> = 3 · 99315959 · 8290079151717433488691043_<25> · C201

C201 = P39 · C163

P39 = 244999355897374262095731654588996987803_<39>

C163 = [1175096545584055105250951509988618729791632937145951352860247520445895686478618432283375088249068144836193263705482510866613839205023692202682641801126636599436267_<163>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 287897896785322994555674978735968899193228526507440203019621524304219703606465390376414637835676262450237955603657481790170414110522262553993340237389283920579700454909980877098926836312194350874851401 (201 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3210162980
Step 1 took 22449ms
Step 2 took 8672ms
********** Factor found in step 2: 244999355897374262095731654588996987803
Found probable prime factor of 39 digits: 244999355897374262095731654588996987803
Composite cofactor 1175096545584055105250951509988618729791632937145951352860247520445895686478618432283375088249068144836193263705482510866613839205023692202682641801126636599436267 has 163 digits

By Jo Yeong Uk / GMP-ECM / Jan 3, 2008

(64·10²⁰⁵-1)/9 = 7(1)₂₀₅_<206> = 431 · 37940267 · 45453581976434362961_<20> · C176

C176 = P40 · C137

P40 = 3413498540067034957579963393050135213037_<40>

C137 = [28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999_<137>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM]
Input number is 95673507938569544419059184259217858706183654907488877608498088047569608854258353672123533863115165791173052496922107368259780351867183146813879315893305406356587115353521925963 (176 digits)
Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=27677106
Step 1 took 18946ms
Step 2 took 7711ms
********** Factor found in step 2: 3413498540067034957579963393050135213037
Found probable prime factor of 40 digits: 3413498540067034957579963393050135213037
Composite cofactor 28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999 has 137 digits

Jan 5, 2009 (4th)

By Sinkiti Sibata / GGNFS, Msieve / Dec 26, 2008

(13·10¹⁵⁶-7)/3 = 4(3)₁₅₅1_<157> = 41 · 373 · 2143 · 11719 · 9094703 · 185189431516811_<15> · C124

C124 = P57 · P68

P57 = 324398260686691813162866343117371269663267936287799013143_<57>

P68 = 20650636734644430907618223992790982393292044921765406119716528349629_<68>

Number: 43331_156
N=6699030638791358287402250465874032297664402985450649877562708199444280779852023252445956714120090595355942969673208670173947
  ( 124 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=324398260686691813162866343117371269663267936287799013143
 r2=20650636734644430907618223992790982393292044921765406119716528349629
Version: 
Total time: 30.15 hours.
Scaled time: 76.99 units (timescale=2.554).
Factorization parameters were as follows:
name: 43331_156
n: 6699030638791358287402250465874032297664402985450649877562708199444280779852023252445956714120090595355942969673208670173947
m: 20000000000000000000000000000000
deg: 5
c5: 65
c0: -112
skew: 1.11
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 510325 x 510573
Total sieving time: 30.15 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 30.15 hours.
 --------- CPU info (if available) ----------

By Sinkiti Sibata / GGNFS, Msieve / Dec 26, 2008

(38·10¹⁵⁶+61)/9 = 4(2)₁₅₅9_<157> = 11 · 139277740661_<12> · 30738460965305809_<17> · C128

C128 = P57 · P72

P57 = 260143260050233689064483536734775966389994188398184680541_<57>

P72 = 344645007197955662990211669087773268820445474115533760904170023354945071_<72>

Number: 42229_156
N=89657075732512441634943806879080168667130713554798202567148299186828703838676016744071926873134410604543640813584660148737563411
  ( 128 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=260143260050233689064483536734775966389994188398184680541
 r2=344645007197955662990211669087773268820445474115533760904170023354945071
Version: 
Total time: 30.26 hours.
Scaled time: 64.45 units (timescale=2.130).
Factorization parameters were as follows:
name: 42229_156
n: 89657075732512441634943806879080168667130713554798202567148299186828703838676016744071926873134410604543640813584660148737563411
m: 10000000000000000000000000000000
deg: 5
c5: 380
c0: 61
skew: 0.69
type: snfs
lss: 1
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved rational special-q in [1500000, 2600001)
Primes: rational ideals reading, algebraic ideals reading, 
Relations: relations 
Max relations in full relation-set: 
Initial matrix: 
Pruned matrix : 502089 x 502337
Total sieving time: 30.26 hours.
Total relation processing time: 0.00 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000
total time: 30.26 hours.
 --------- CPU info (if available) ----------

By Sinkiti Sibata / GGNFS, Msieve / Dec 26, 2008

(38·10¹⁵⁸+43)/9 = 4(2)₁₅₇7_<159> = 7 · 23914675839563_<14> · 27158072252539381_<17> · C128

C128 = P46 · P83

P46 = 2144079130668631481647808214278063607290278667_<46>

P83 = 43315047967083261756515628744608261986207073370289699235452899200702857612505217961_<83>

Number: 42227_158
N=92870890390133953204349065543637257872814042586690164133184967513777941557759002933246154398397579798202131837405662527263537987
  ( 128 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=2144079130668631481647808214278063607290278667 (pp46)
 r2=43315047967083261756515628744608261986207073370289699235452899200702857612505217961 (pp83)
Version: GGNFS-0.77.1-20060513-k8
Total time: 68.70 hours.
Scaled time: 135.14 units (timescale=1.967).
Factorization parameters were as follows:
name: 42227_158
n: 92870890390133953204349065543637257872814042586690164133184967513777941557759002933246154398397579798202131837405662527263537987
m: 50000000000000000000000000000000
deg: 5
c5: 304
c0: 1075
skew: 1.29
type: snfs
lss: 1
rlim: 3400000
alim: 3400000
lpbr: 27
lpba: 27
mfbr: 51
mfba: 51
rlambda: 2.4
alambda: 2.4
Factor base limits: 3400000/3400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 51/51
Sieved rational special-q in [1700000, 3800001)
Primes: RFBsize:243539, AFBsize:244049, largePrimes:9512566 encountered
Relations: rels:10279905, finalFF:737657
Max relations in full relation-set: 28
Initial matrix: 487655 x 737657 with sparse part having weight 92990337.
Pruned matrix : 406380 x 408882 with weight 56550234.
Total sieving time: 64.49 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 3.58 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000
total time: 68.70 hours.
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